Thermodynamic Investigations of Pure and Blended Cement Mixtures

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Doctoral Dissertations Student Theses and Dissertations

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Thermodynamic investigations of pure and blended cement mixtures

Jonathan Lapeyre

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This thesis is brought to you by Scholars' Mine, a service of the Missouri S&T Library and Learning Resources. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. THERMODYNAMIC INVESTIGATIONS OF PURE AND BLENDED CEMENT

MIXTURES

JONATHAN LEE LAPEYRE

A DISSERTATION

Presented to the Graduate Faculty of the

MISSOURI UNIVERSITY OF SCIENCE AND TECHNOLOGY

In Partial Fulfillment of the Requirements for the Degree

DOCTOR OF PHILOSOPHY

MATERIALS SCIENCE & ENGINEERING

2020

Approved by:

Jonathan Lee Lapeyre

PUBLICATION DISSERTATION OPTION

This dissertation consists of the following six manuscripts published or submitted

for publication, formatted in the style used by Missouri University of Science and

Technology.

Paper I, (found on pages 13-58) “Influence of Pozzolanic Additives on Hydration

Mechanisms of Tricalcium Silicate” was published in the Journal of the American

Ceramic Society.

Paper II, (found on pages 59-100) “Elucidating the Effect of Water-To-Cement

Ratio on the Hydration Mechanisms of Cement” was in the ACS Omega Journal.

Paper III, (found on pages 101-136) “Effect of Particle Size Distribution of

Metakaolin on Hydration Kinetics of Tricalcium Silicate” the Journal of the American

Ceramic Society.

Paper IV, (found on pages 137-184) “Prediction of Compressive Strength of

Concrete: Critical Comparison of Performance of a Hybrid Machine Learning Model

with Standalone Models” was published the Journal of Materials in Civil Engineering.

Paper V, (found on pages 185-236) “Influence of Water Activity on Hydration of

Tricalcium Aluminate Calcium Sulfate Systems” was published in the Journal of the

American Ceramic Society.

Paper VI, (found on pages 237-268) “Hydration of High-Alumina Calcium

Aluminate Cements with Carbonate and Sulfate Additives” was submitted the Journal of

Thermal Analysis and Calorimetry. v

ABSTRACT

This research is made up of several studies. The first study focused on

understanding the reaction kinetics of CasSiOs and metakaolin (MK) mixtures compared

to CasSiOs and silica fume (SF) mixtures. It was shown that MK was a more effective

additive than SF at small replacement levels (i.e. >10% by mass) while higher

replacement levels of MK became a detriment due to excess (Al(OH)4 ) ions preventing

the nucleation and growth of C-S-H. In a follow-up study where the MK particle size

distribution (PSD) was modified, similar effects were observed but unlike typical mineral

additives (e.g. limestone), it was the coarse PSD that was optimal. A different study

examined the contradiction between experimental data and classical phase boundary

nucleation and growth (pBNG) models as the water to cement content (w/c) increases.

When the reaction rates were measured via isothermal calorimetry, they were insensitive

to changes in w/c whereas increasing w/c affected simulated reaction rates. Utilizing a

modified pBNG model, these contradictions were rectified by accounting for physical

phenomena. It was demonstrated that hybrid random forest firefly algorithm (RF-FFA) is

highly effective at predicting compressive strength of concrete with the mix design as an

input. The subsequent study, [Ca3AhO6 + CaSO4] mixtures were hydrated in solutions of varying water activity (aH), the solubility product of Ca3AhO6 and the critical aH to arrest

hydration were determined as 10-20 65 and 0.45 for the first time. In the final study, high a-

AhO3 calcium aluminate cements mixtures were hydrated with limestone or calcium

sulfate. While the binary mixtures exhibited an increase in the heat released, this did not translate to greater the compressive strengths. vi

ACKNOWLEDGMENTS

First, I want to express my deepest gratitude to Dr. Aditya Kumar. As my advisor, he has given me many opportunities to excel and to learn as an academic professional.

His guidance and patience have made me a better researcher and individual. The National

Science Foundation has been instrumental in supporting me and my research through grants CMMI: 1661609 and 1932690. Likewise, I want to thank my committee for their time and input in my work. Especially Dr. Jeffrey Smith, who suggested and subsequently encouraged me to continue my education with graduate school with Dr.

Kumar. I want to thank Dr. Eric Bohannan, Todd Sanders, and Dr. Jeremy Watts for their time and experience teaching me learn equipment for my experiments and successful research. Likewise, the help of Teneke Hill, Denise Eddings, and Jennifer Pratt at McNutt

Hall and Patty Smith, Sissy Cox, and Kerry Borthacyre at Straumanis-James Hall; all of them have been instrumental in helping me with orders, answering my questions, and offering numerous candies and snacks all of which I have appreciated.

Next, my past and current group members: Rachel Cook, Ajay Banala, Taihao

Han, and Sai Akshay Ponduru for their help and discussions inside and outside the office.

Particular appreciation is noted for Rachel who started the same day as me and has become a leader and researcher. Similarly, Ajay has become one of my great friends outside of school and is an inspiration for his kindness and resolve in his work. Finally, my family, who may not be entirely sure of what my research entails, has been supportive and proud of my work. This includes my fiance, Brenda, who has made many sacrifices along with my family to help me succeed for which I am forever grateful. vii

TABLE OF CONTENTS

Page

PUBLICATION DISSERTATION OPTION...... iv

ABSTRACT...... v

ACKNOWLEDGMENTS...... vi

LIST OF ILLUSTRATIONS...... xii

LIST OF TABLES...... xix

1. INTRODUCTION...... 1

2. LITERATURE REVIEW...... 6

2.1. REVIEW OF THE HYDRATION KINETICS OF THE CONSTITUENT PHASES OF ORDINARY PORTLAND CEMENT (OPC)...... 6

2.2. INFLUENCE OF NON-CEMENTITIOUS ADDITIVES ON HYDRATION KINETICS OF CEMENTITIOUS SYSTEMS...... 11

PAPER

I. INFLUENCE OF POZZOLANIC ADDITIVES ON HYDRATION MECHANISMS OF TRICALCIUM SILICATE...... 13

ABSTRACT...... 13

1. INTRODUCTION...... 14

2. MATERIALS AND EXPERIMENTAL METHODS...... 19

3. PHASE BOUNDARY NUCLEATION AND GROWTH (pBNG) MODEL...... 24

4. EFFECTS OF SF AND MK ON HYDRATION KINETICS OF C3 S ...... 29

5. ASSESSMENT OF FILLER AND POZZOLANIC EFFECTS OF SF AND MK...... 34 viii

6. NUMERICAL SIMULATIONS OF HYDRATION KINETICS OF C3 S PASTES...... 42

7. SUMMARY AND CONCLUSIONS...... 49

ACKNOWLEDGEMENTS...... 50

REFERENCES...... 51

II. ELUCIDATING THE EFFECT OF WATER-TO-CEMENT RATIO ON THE HYDRATION MECHANISMS OF CEMENT...... 59

ABSTRACT ...... 59

1. INTRODUCTION...... 60

2. MATERIALS AND METHODS...... 64

3. pBNG MODEL...... 68

4. RESULTS AND DISCUSSION ...... 74

5. SUMMARY AND CONCLUSIONS...... 93

ACKNOWLEDGEMENTS...... 94

REFERENCES...... 95

III. EFFECT OF PARTICLE SIZE DISTRIBUTION OF METAKAOLIN ON HYDRATION KINETICS OF TRICALCIUM SILICATE...... 101

ABSTRACT...... 101

1. INTRODUCTION...... 102

2. MATERIALS AND METHODS...... 106

3. PHASE BOUNDARY NUCLEATION AND GROWTH MODEL...... 111

4. RESULTS AND DISCUSSION...... 114

4.1. EFFECT OF PSD OF METAKAOLIN ON HYDRATION OF C3 S 114 ix

4.2. EFFECT OF PSD ON DISSOLUTION DYNAMICS OF MK...... 122

4.3. NUMERICAL SIMULATIONS OF HYDRATION KINETICS OF [C3 S + MK] PASTES...... 124

5. CONCLUSIONS...... 128

ACKNOWLEDGEMENTS...... 130

REFERENCES...... 130

IV. PREDICTION OF COMPRESSIVE STRENGTH OF CONCRETE: CRITICAL COMPARISON OF PERFORMANCE OF A HYBRID MACHINE LEARNING MODEL WITH STANDALONE MODELS...... 137

ABSTRACT...... 137

1. INTRODUCTION...... 138

2. MACHINE LEARNING MODELS...... 144

2.1. MULTILAYER PERCEPTRON ARTIFICIAL NEURAL NETWORK...... 144

2.2. SUPPORT VECTOR MACHINE...... 147

2.3. M5PRIME MODEL TREE ALGORITHM...... 149

2.4. RANDOM FORESTS...... 151

2.5. HYBRID RANDOM FORESTS: FIREFLY ALGORITHM MODEL...... 153

2.6. HYBRID MODEL...... 156

2.7. DATA COLLECTION AND PERFORMANCE EVALUATION OF MACHINE LEARNING MODELS...... 157

3. RESULTS AND DISCUSSION...... 161

3.1. HIGHLY NONLINEAR AND PERIODIC TRIGNOMETRIC FUNCTIONS...... 161

3.2. COMPRESSIVE STRENGTH OF CONCRETE: DATASET 1 167 x

3.3. COMPRESSIVE STRENGTH OF CONCRETE: DATASET 2 ...... 173

4. SUMMARY AND CONCLUSIONS...... 175

ACKNOWLEDGMENTS...... 177

REFERENCES...... 178

V. INFLUENCE OF WATER ACTIVITY ON HYDRATION OF TRICALCIUM ALUMINATE-CALCIUM SULFATE SYSTEMS...... 185

ABSTRACT...... 185

1. INTRODUCTION...... 186

2. REVIEW OF HYDRATION OF C3A IN [C3A + C$ + H] PASTES...... 191

2.1. STAGE 1...... 191

2.2. STAGE I I ...... 193

2.3. STAGE III...... 194

3. CALCULATION OF WATER ACTIVITY IN [C3A + C$ + H] SYSTEMS 196

4. ESTIMATION OF CRITICAL WATER ACTIVITY AND SOLUBILITY CONSTANT BASED ON THERMODYNAMIC CONSIDERATIONS...... 197

5. MATERIALS AND METHODS...... 204

6. EXPERIMENTAL RESULTS AND DISCUSSION...... 207

7. SUMMARY AND CONCLUSIONS...... 228

ACKNOWLEDGEMENTS...... 230

REFERENCES...... 230

VI. HYDRATION OF HIGH ALUMINA-CALCIUM ALUMIANTE CEMENTS WITH CARBONATE AND SULFATE ADDITIVES...... 237

ABSTRACT 237 xi

1. INTRODUCTION...... 238

2. MATERIALS AND METHODS...... 243

3. RESULTS...... 247

3.1. HYDRATION KINETICS OF LS + CAC AND C$ + CAC PASTES...... 247

4. CONCLUSIONS...... 261

ACKNOWLEDGMENTS...... 263

REFERENCES...... 264

SECTION

3. CONCLUSIONS AND RECOMMENDATIONS...... 269

3.1. CONCLUSIONS...... 269

3.2. FUTURE WORK...... 274

APPENDICES

A. METHODOLOGY AND POWDER PARTICLE SIZE DISTRIBUTIONS FOR MACHINE LEARNING STUDY...... 276

B. SUPPLEMENTAL INFORMATION ELUCIDATING THE EFFECT OF WATER-TO-CEMENT RATIO ON THE HYDRATION MECHANISMS OF CEMENT...... 289

C. SUPPLEMENTAL INFORMATION TO INFLUENCE OF WATER ACTIVITY OF TRICALCIUM ALUMINATE-CALCIUM SULFATE SYSTEMS...... 301

BIBLIOGRAPHY...... 309

VITA 317 xii

LIST OF ILLUSTRATIONS

SECTION Page

Figure 1.1. (A) World cement production from notable countries around the world as reported by the USGS Mineral Commodities reports (3). (B) World production of cement compared to the estimated CO2 production by the CICERO report (11)...... 2

Figure 1.2. The heat flow rate calorimetry of synthetic cements mixed with metakaolin and limestone (A) the low C3A/C$H2 cement would represent a “sulfated” cement (B) an “undersulfated” system (C) an “oversulfated” cement (D) a paste comprised of pure C3 S containing no aluminate or sulfate...... 5

Figure 2.1. Typical calorimetry heat flow rate profiles of OPC...... 8

PAPER I

Figure 1. Particle size distribution (PSD) of C3 S, SF, and MK used in this study...... 21

Figure 2. Measured heat evolution profiles of pastes prepared with C3 S replaced by SF at different replacement levels...... 30

Figure 3. Measured heat evolution profiles of pastes prepared with C3 S replaced by MK at different replacement levels...... 32

Figure 4. The calorimetric parameters...... 33

Figure 6. (A), Isothermal microcalorimetry based determinations of time-dependent degree of reaction (a: solid lines, primary y-axis) and cumulative heat release (dashed lines, secondary y-axis) of C3 S in plain paste, and SF in saturated lime solution. The methodology used to convert the heat release from SF's dissolution in saturated lime solution to a of SF is described briefly in Section 2, and in detail in a prior study (5) (B), DTG traces showing differential mass loss traces of a SF + CH (1:1 molar ratio) paste at 24 hours after mixing. (C), shows the CH contents (as %mass of the binder, i.e., dry paste) in [C3 S + SF] pastes after 24 hours of hydration, as determined from DTG analyses...... 36

Figure 7. (A), Isothermal microcalorimetry based determinations of time-dependent degree of reaction (a: solid lines, primary y-axis) and cumulative heat release (dashed lines, secondary y-axis) of C3 S in plain paste, and MK in saturated lime solution. The methodology used to convert the heat release from MK's dissolution in saturated lime solution to a of MK is described briefly in Section 2, and in detail in a prior study (5) (B), DTG traces showing differential mass loss traces of a MK + CH (1:1 molar ratio) paste at 24 hours after mixing. (C), The mass contents of CH (as %mass of the binder, i.e., dry paste) in [C3 S + MK] pastes after 24 hours of hydration, as determined from DTG analyses...... 39

Figure 9. Parameters derived from the simulations...... 44

Figure 10. The outward growth rate of the product (Gout), as obtained from pBNG simulations, as a function of the time, for: (A), [C3 S + SF] pastes, and (B), [C3 S + MK] pastes...... 47

Figure 11. The outward growth rate of the product (Gout), as obtained from pBNG simulations, (A), at the main hydration peak, and (B), at t = 24 hours in plain and blended pastes...... 48

PAPER II

Figure 1. PSDs of the “as-received” (coarse) and ground (fine) cements measured using SLS methods...... 66 xiv

Figure 2. Isothermal microcalorimetry-based determinations of (A) heat flow rates, and (B) cumulative heat release of pastes prepared using the coarse cement at different w/c. (C) repeatability of heat flow rate determinations for a representative system...... 75

Figure 3. Isothermal microcalorimetry-based determinations of (A) heat flow rates and (B) cumulative heat release of pastes prepared using the fine cement at different w/c ratios. (C) Comparison of heat flow rates of pastes prepared at equivalent w/c using cements of different fineness...... 76

Figure 5. (A) Correlation between capillary porosity and degree of hydration (a) in pastes prepared at different w/c. In these calculations, a is provided as an input, and the corresponding capillary porosity is calculated based on the phase assemblages predicted by the Powers model.(54,55) The solid vertical line indicates the average value of a of all pastes, prepared using the coarse cement at the main hydration peak. 3D virtual microstructures of cement pastes prepared using the coarse cement at (B) w/c = 0.45 and (C) w/c = 10 when a = 0.13 (i.e., at the main hydration peak). The anhydrous cement particles (red) are packed as randomly dispersed spheres within the cubic representative elementary volume (size = 100 pm3)...... 79

Figure 6. Representative set of simulated and measured hydration rates (da/dt) of cement in pastes prepared at different w/c...... 80

Figure 7. Parameters derived from the simulations...... 82

Figure 8. 3D virtual microstructures showing the packing of particles at the time of mixing (i.e., without sedimentation of particles) in pastes prepared at (A) w/c = 0.45 and (B) w/c = 10. (C) effects of sedimentation of particles in a paste prepared at w/c = 10...... 85

Figure 9. Outward growth rate of the product (Gout) as a function of the (A) time and (B) degree of hydration of the coarse cement...... 86

Figure 10. Outward growth rate of the product (Gout) as a function of w/c when (A) a = 0.10, (B) a = 0.20, and (C) a = 0.30. Results for both coarse and fine cements are shown...... 87 xv

Figure 11. Estimated temporal evolution of the supersaturation of C-S-H (^csh) in pastes prepared using (A) the coarse cement at different w/c, (B) the coarse and fine cements at w/c = 3, and (C) the coarse and fine cements at w/c = 10...... 89

Figure 12. (A) Electrical conductivity and (B) pH of the pore solution of pastes prepared using the coarse cement at different w/c. Because of the large difference in the magnitudes of the solution’s electrical conductivity, rescaled subplots for the two curves are included within (A). (C) Heat flow rates of pastes, prepared using the coarse cement at w/c = 10, measured without (static) and with in situ stirring...... 90

PAPER III

Figure 1. The PSDs of C3S and MK used in this study...... 109

Figure 2. Measured calorimetry profiles of [C3 S + MK] pastes, wherein 8%mass of C3 S is replaced by MK...... 116

Figure 3. Measured calorimetry profiles of [C3 S + MK] pastes, wherein 30%mass of C3 S is replaced by MK...... 117

Figure 4. The temporal evolution of CH content (expressed as dry mass fraction) in [C3 S + MK] pastes, prepared at: (A) 8% replacement; and (B) 30% replacement level of C3 S with MK. The upper bound of the gray area represents the CH content formed in the control paste, and the lower bound represents the dilution line (i.e., proportional reduction in CH content in relation to the reduction in C3 S content). (C) DTG traces showing differential mass loss, as function of temperature, in a [MK + CH (1:1 molar ratio)] paste (l/s = 0.45) at 72 h after mixing...... 119

Figure 5. Calorimetric parameters extracted from heat evolution profiles of pastes...... 120

Figure 7. Parameters derived from pBNG simulations of [C3S + MK] pastes...... 126

Figure 8. Outward growth rate of the product (Gout) as a function of the (A) time and (B) degree of hydration of the coarse cement...... 127 xvi

PAPER IV

Figure 1. Predictions made by ML models: (A) MLP-ANN; (B) SVM; (C) M5P; (D) RF; and (E) RF-FFA compared against actual values of the trigonometric function, F1(x) [Equation (17)]...... 165

Figure 2. Predictions made by ML models: (A) MLP-ANN; (B) SVM; (C) M5P; (D) RF; and (E) RF-FFA compared against actual values of the trigonometric function, F2(x) [Equation (18)]...... 166

Figure 3. Predictions made by ML models: (A) MLP-ANN; (B) SVM; (C) M5P; (D) RF; and (E) RF-FFA compared against actual compressive strength of concretes (drawn from Dataset 1)...... 170

Figure 4. Predictions made by ML models: (A) MLP-ANN; (B) SVM; (C) M5P; (D) RF; and (E) RF-FFA compared against actual compressive strength of concretes (drawn from Dataset 2)...... 175

PAPER V

Figure 1. Activities (a) of water (H) and isopropyl alcohol (IPA) in [water + IPA] mixtures, as calculated from the van Laar equations (Equations 5-6)...... 198

Figure 2. Plots of the solubility constant of C3A (Kc3a) as function of water activity (aH), as derived from the equilibrium of C3A ^ AFt and C3A ^ AFm reactions...... 203

Figure 3. Particle size distributions (PSDs) of C3A and C$ powders used in this study...... 205

Figure 4. Isothermal microcalorimetry based determinations of heat evolution profiles of [C3A + 15% C$ + H] pastes, prepared at different levels of replacement of water with IPA...... 208

Figure 5. Isothermal microcalorimetry based determinations of heat evolution profiles of [C3A + 30% C$ + H] pastes, prepared at different levels of replacement of water with IPA...... 210

Figure 6. Relationship between initial water activity (aH0) and the corresponding calorimetric parameters pertaining to the stage II peak...... 212

Figure 7. Cumulative heat released after 72 h of hydration of C3A in [C3A + C$ + H] pastes plotted against aH0 (primary x-axis) and IPA replacement level (secondary x-axis)...... 214 xvii

Figure 8. Cumulative heat release profiles of [C3A + C$ + H] pastes, prepared at: (A) high IPA replacement levels (>87%); and (B) low IPA replacement levels (<60%)...... 215

Figure 9. Cumulative heat release profiles of: (A) [C3A + H] and [C$ + H] pastes; and (B) [C3A + H], [C3A + 15% C$ + H], and [C3A + 30% C$ + H] pastes...... 218

Figure 10. Degree of hydration of C3A (ao3A), after 72 h of hydration, in: (A) [C3A + 15% C$ + H]; and (B) [C3A + 30% C$ + H] pastes, plotted against am ...... 221

Figure 11. XRD patterns of (A) [C3A + 15% C$ + H]; and (B) [C3A + 30% C$ + H] pastes, prepared at different IPA replacement levels, after 72 h of hydration...... 223

Figure 12. Differential TGA traces (differential mass loss) of [C3A + 30% C$ + H] pastes prepared at different IPA replacement levels, after 72 h of hydration...... 225

Figure 13. XRD patterns of (A) [C3A + 15% C$ + H]; and (B) [C3A + 30% C$ + H] suspensions, prepared at 20% and 95% IPA replacement levels, after 72 h of hydration...... 227

PAPER VI

Figure 1. Particle size distribution of the calcium aluminate cement (CAC), calcium sulfate (C$), and limestone (LS)...... 244

Figure 2. The calorimetry profiles of [CAC + LS] pastes with increasing percent of CAC replaced with LS...... 248

Figure 3. The calorimetry profiles of [CAC + C$] pastes with increasing percent of CAC replaced with C$...... 249

Figure 4. The peak heat flow rate and inverse time to the peak extracted from the calorimetry curves for CAC, [CAC + C$], and [CAC + LS] pastes...... 251

Figure 5. The calorimetry profiles of CAC pastes hydrated with increasing water to cement (w/c) ratio (A) heat flow rate up to 72 hours and linear x-axis (B) heat flow rate with logarithmic x -axis (C) the cumulative heat release...... 253 xviii

Figure 6. A series of GEMs simulations for the (A) pure CAC paste, (B) - (D) 17%, 25% and 50% LS replacement levels as well as (E) - (G) 17%, 25%, and 50% C$ replacement with excess water (1:1 total solid to liquid mass ratio) ...... 255

Figure 7. XRD patterns of (A) [CAC + LS] and (B) [CAC + C$] paste after 72 hours of hydration...... 257

Figure 8. DTGA scans of (A) [CAC + LS] pastes and (B) [CAC + C$] pastes from 0°C - 1000°C for 0%, 17%, 25%, and 50% replacement level respectively...... 259

Figure 9. The strength of the 6mm side length cubic samples with the standard deviation shown as error bars...... 260 xix

LIST OF TABLES

PAPER I Page

Table 1. Bulk oxide composition of pozzolans, as determined from XRF...... 20

PAPER III

Table 1. Composition of metakaolin, in terms of oxides, as determined from x-ray fluorescence (XRF)...... 107

PAPER IV

Table 1. Summary of statistical parameters pertaining to each of the 9 attributes (8 input and 1 output) of Dataset 1...... 158

Table 2. Summary of statistical parameters pertaining to each of the 6 attributes (5 input and 1 output) of Dataset 2 ...... 159

Table 3. Prediction performance of ML models, measured on the basis of the test set developed using Equation (17)...... 162

Table 4. Prediction performance of ML models, measured on the basis of the test set developed using Equation (18)...... 164

Table 5. Prediction performance of ML models, measured on the basis of the test set of Dataset 1...... 169

Table 6. Prediction performance of ML models, measured on the basis of the test set of Dataset 2 ...... 173

PAPER V

Table 1. Densities (p) and molar volumes (V) at standard conditions for the cementitious phases utilized in equilibrium calculations...... 200

Table 2. The solubility constant of C3A, calculated via GEMS, in relation to varying l/s...... 204 xx

Table 3. Limiting values of cumulative heat (Q) released from reactions corresponding to Equations 2, 3, and 4, and limiting values of ao3A at the ends of stage I, II, and III...... 220

PAPER VI

Table 1. Chemical composition by mass percent (%mass) of CA-25-C determined via XRF...... 243

Table 2. The degree of hydration (a) of the binary pastes for the different [CAC + LS] and [CAC + C$] pastes after hydrating for 72 hours...... 254 1. INTRODUCTION

Since the invention of ordinary portland cement (OPC) almost 200 years ago by

Joseph Aspin (1), cement and by extension concrete has become a principal part of

modern infrastructure throughout the world. While the mineral composition for cement

has remained the same since the beginning of the 20th century (2), the demand for cement

has only increased starting in the 21st century. Notable countries such as China, India, and

Brazil have increased their production of cement whereas in industrialized/post-

industrialized countries (e.g., United States, Japan, Germany, United Kingdom) the total

production has decreased or has remain steady as shown in Figure 1.1A (3). However, the threat of climate change due to anthropogenic CO2 has and continues to be a prevailing

socio-economic issue due to the steady increase in CO2 emissions throughout the world

(see Figure 1.1B).

This has prompted governments and international organizations to propose laws

and to provide research funds to investigate strategies and methodologies to reduce

emissions as well as reduce the environmental impact of cement production. During the

production of cement, there are two processes that emit CO2 : burning of fossil fuels

required for the calcination and drying stages of production, and the liberation of CO2

from the calcination of limestone, clay, and other minerals (e.g., dolomite, chalk, and

marlstone) (4,5). For context, these raw materials are fired at 1450°C to synthesize the

cement clinker and have been estimated to release -0.87 kg of CO2 per kg of portland

cement (6,7). Cement production contributes a significant amount CO2 into the

atmosphere and is estimated to contribute 5% to 8% of the world’s CO2 emissions (8,9). 2

Similarly, the production of cement is very energy intensive due to the pre- and post processing energy costs such as preheating, grinding, and final transport. Madlool et al.

(10) estimated that the production and manufacturing of cement consumes 12% - 15% of a country’s total energy consumption which is in part due to the high usage of fossil fuels such as coal, natural gas, and petro-coke.

10000-:- 5000- World Production ooooooooooooo + C02 ■)00000 o Cement ★ ~ 4 0 0 0 - o°oooa 1000 - oo y o XXXXXXXXX)f £ 3000 -| o o o 0c o 2™Rp,[iEiBEiWFRRR 1 o o | 2000 - o Production Region ■ o O. o c World J o « Brazil + + + + + + + E 10^ © * China O 5 1000 - ++ + + x India + + + • Japan - + + + ^ Russia a United States —i ------1------1------1------1------1------1------1------1------1------1— 2000 2003 2006 2009 2012 2015 2018 2000 2003 2006 2009 2012 2015 2018 Year Year (A) (B) Figure 1.1. (A) World cement production from notable countries around the world as reported by the USGS Mineral Commodities reports (3). (B) World production of cement compared to the estimated CO2 production by the CICERO report (11).

In conjunction with energy and thermal efficiency improvements during the clinkering process (12,13), researchers have focused on reduction of cement with supplementary cementitious materials (SCMs) or utilizing alternative cementitious binders as a solution to carbon emissions and energy costs. Beginning with the former,

SCMs are defined by ASTM C125 as “an inorganic material that contributes to the properties of a cementitious mixture through hydraulic or pozzolanic activity, or both”

(14). Therefore, SCMs can be thought of as materials that intrinsically react with water 3

similar to cement or react via the pozzolanic effect. Pozzolans cannot undergo a

cementing reaction solely in the presence of water; rather, these materials react in the

presence of calcium hydroxide and water to form the cementing phase (6,15-18). SCMs

can originate from sedimentary or igneous rock veins as well as industrial sources such as blast furnace slag, silica fume, or fly ash (6,19,20). Consequentially, the characteristics of

SCMs can vary depending on the source location. For example, the particle morphology,

chemical composition, mineral phases, and amorphous content for many SCMs. Due to this variability, fly ash variants are given designations of type C and F depending on these factors. As a quick aside, although limestone (CaCO3) is ubiquitous in its usage in

cement mix designs, it is not by this definition a SCM because limestone does not exhibit

either reaction mechanism but is sometimes referred to as a SCM due to convenience.

This does not mean that limestone is an ineffective additive; however, the benefits due to

limestone originate from different mechanisms. Likewise, the pozzolanic reaction should

not be confused with alkali-activated or geopolymer reactions. While both often utilize

similar material precursors (e.g., metakaolin and fly ash), the latter are an alternative binder that require alkali hydroxides and/or alkali silicates as an “activator” to create a binder. Along with alkali-activated and geopolymer binders there is renewed interest

alternative binders such as calcium aluminate, calcium sulfoaluminate or belite-

sulfoaluminate cements with a variety of trade-offs, advantages, and disadvantages

compared to OPC (2,21-28). However, there is not enough these alternative binders in

reserve or production to significantly replace the 4000 Mt of cement at least at recent

levels (see Figure 1.1). Therefore, rather than replacing OPC with niche binders, there

has been significant interest and international investment into developing novel mix 4

designs of multi-component blended cements with a diluted OPC content known as

limestone calcined clay cements (LC3) (29-32).

The advantage of LC3 compared to OPC in addition to environmental benefits is

that both calcined clay and limestone is prevalent in natural reserves not just

industrialized countries but throughout the world, facilitating countries that do not have

the industrial resources for synthetic SCMs (2,6,19,33). However, the challenge with LC3

is characterizing and understanding prevalent issues present in traditional OPC. Notably

the effects of aluminate and sulfate content present within the clinker (34-36). This last

point can be demonstrated in calorimetry profiles present in Figure 1.2. The cements

present in Figure 1.2 A - D vary in aluminate (C3A) and sulfate (C$H2) content designed to emulate the various commercially available cement types for particular properties or

applications (e.g., early set, enhanced durability, or oil well applications) (4,5). As it can be seen, the effects replacing these cements with varying metakaolin and limestone

replacement levels have significant effects on the calorimetry profiles like in Figure 1.2B.

While this is only a sample of a dataset containing over 230 calorimetry measurements as

a part of a larger database and study, it shows that there is a complex combination of

chemical reactions and physical phenomena occurring during the hydration reaction.

Appendix A contains details regarding these measurements (e.g., mix design and the

general methodology). This dissertation includes papers examining specific effects in

simplified systems (e.g., addition of metakaolin with pure cement phase in Paper I) as well as a macro approach utilizing machine-learning methodologies and algorithms to

identify patterns in composition to physical properties see Paper IV. To understand these

systems, a combination of these strategies is required due to the complexity and difficulty 5 of isolating simple systems to study. The remainder of this section focuses on a literature review for both cementitious materials and SCMs followed by the manuscripts (in order of submission and/or publication).

1.5 = C$H2/CsA 4% C ,A MK + Coarse-LS — 0% ------10%- 10% --15%-15% ------20 %- 20 % - 25%-25% — 30%-30% ------20 %- 10 % 40%-20%

i 1 n 1 1 i 1 1 i 6 9 12 15 Time (Hour) Time (Hour) (A) (B) ■ i ■■ i i i i i i i i i i

1.5 C$H2/C3A 12% C,A MK + Coarse-LS — 0% ------10%-10% ----- 15%-15% ------20%-20% 25%-25% — 30%-30% ------20%-10% 40%-20%

1 l 1 1 l 1 1 l 1 1 l 1 1 l 9 12 15 18 21 Time (Hour) Time (Hour) (C) (D) Figure 1.2. The heat flow rate calorimetry of synthetic cements mixed with metakaolin and limestone (A) the low C3A/C$H2 cement would represent a “sulfated” cement (B) an “undersulfated” system (C) an “oversulfated” cement (D) a paste comprised of pure C3 S containing no aluminate or sulfate. In Appendix A, these would correspond to Cements #1, 3, 5, and 7 respectively 6

2. LITERATURE REVIEW

2.1. REVIEW OF THE HYDRATION KINETICS OF THE CONSTITUENT PHASES OF ORDINARY PORTLAND CEMENT (OPC)

OPC is a synthetic rock comprised of four cementitious phases: Ca3SiO5,

Ca2 SiO4, Ca3AkO6, and Ca4(Al,Fe)2O10 as well as minor amounts of gypsum

(CaSO4*2H2O) which is added to cement clinker after it is fired (4,5). The mineral names: alite, belite, aluminate, and ferrite are often used to denote the impure phase found in cement (5,7,37). These impure phases form because the crystalline phases readily intake impurities in the melt which can prompt changes in the crystalline structure and/or consequentially change the hydraulic reactivity (e.g., the reactivity of monoclinic

P - C2 S is greater than orthorhombic y - C2 S) among others (38-40). However, for the sake of simplicity, this manuscript will utilize conventional cement chemistry notation shorthand when referring to these cementitious phases regardless if it is a system containing only a pure phase or as a constituent within OPC. The shorthand utilizes capital letters and/or symbols are used to denoted simple oxides and combines them for cementitious or hydrate compounds or phases. For example, oxides present in OPC systems are simplified as such C = CaO, S = SiO2, A = AhO3, F = Fe2O3, and $ = CaSO4 .

For compounds, tricalcium silicate would simplify from Ca3SiO5 to C3S and ettringite, crystalline calcium sulfoaluminate hydrate, would simplify from

Ca6Ah(SO4)3(OH)12*26H2O to C6A$3H32. Finally, calcium silicate hydrate is a non stoichiometric hydrate with a varying chemical composition (often designated via the ratio of calcium to silica or C/S) is written as C-S-H unless a specific composition is investigated (41,42) see Paper II. 7

The hydration reaction is complicated due in part to the numerous factors notably

the varying dissolution rates between the different anhydrous phases, the nucleation and

growth of numerous metastable and/or stable hydration products, as well as other

interactions between the ionic species occurring simultaneously (42). Therefore, as a way

to simplify the hydration kinetics, the hydration kinetics of singular C3 S and [C3A +

C$H2] are investigated to reduce the complexity of normal OPC mixtures. For this

review, the hydration reaction kinetics of the [C3S + H] and [C3A + C$H2 + H] systems will be the focus of this review because these reactions are imperative to the early

properties such as strength and rheology subsequently followed by the effects of SCMs

(4,5,42). Since the majority of the papers in this document focus on OPC system, an

additional review focusing on calcium aluminate cements (the topic of Paper VI) is not

included rather a review is present within that manuscript. Isothermal calorimetry is a

powerful tool for monitoring the highly exothermic hydration reaction in [OPC + H]

pastes as shown in the heat flow rate profile in Figure 2.1. The annotations refer to

calorimetric parameters corresponding to silicate and aluminate reactions (time to peak,

heat flow rate at a peak, and the slope of the acceleration period). There are several stages

(denoted herein as 0 - IV) that occur as hydration occurs and although the number of

stages varies in the literature, other investigations had divided them in a similar manner

(42-45). Stage 0 represents the moment when the OPC powder is introduced with water.

This initiates the dissolution process of the reactive species specifically C3 S, C3A, and

C$H2 as shown in Equation (1)-(3) and consequently a substantial amount of heat is

released very quickly. 8

Figure 2.1. Typical calorimetry heat flow rate profiles of OPC. The number 0 and the Roman numerals I - IV refer the distinct stages of hydration: induction period, acceleration period, deceleration period, and low reactivity period. The calorimetric parameters: the time to the peak heat flow rate (tPeak) and the heat flow rate at the peak heat flow rate (HFRPeak) for the respective phases as well as the slope of the acceleration period utilized for quantifying hydration kinetics

Soon after this initial stage, both C3S and [C3A + C$H2] systems undergo a period

of low heat release although for distinct reasons. For C3 S, this is referred to as the

“induction” period where the heat flow rate is reduced for a duration of time as shown in

stage I. For the [C3A + C$H2 + H] reaction, the aluminate and sulfate species react

quickly forming ettringite (C3A$3H32) see Equation (4).

C3S + 3H2O ^ 3Ca2+ + H2SiO4- + 4OH- (1)

C3A + 6H2O ^ 3Ca2+ + 2Al(OH)- + 4OH- (2)

C$H2 ^ Ca2+ + SO2- + 2H2O (3)

Without the proper amount of C$H2, the C3A would have quickly dissolved into

Ca2+ and Al(OH)4 at the onset of being wetted, prompting a sharp increase in the heat

flow rate (see Figure 1.2B with higher replacement levels). This causes a “flash” set which is a premature hardening of the paste. The precipitation of ettringite prompts low 9

heat release that occur in tandem with the induction period of the C3 S hydration. The

origin for the initiation and termination of this period for [C3S + H] has long been

debated between several mechanisms previously as summarized in (42,44-46) but

evidence has pointed towards a solution controlled dissolution hypothesis similar to

observations in the geochemical literature for mineral weathering (46-50). According to

this hypothesis, the rate of dissolution of C3S varies as the degree of undersaturation of the solvent changes. The initially high undersaturation facilitates the rapid dissolution of

energetic surfaces (e.g. crystalline or surface defects) prompting the ingress of ions (for

C3 S this is Ca2+ and H2SiO42" or H3 SiO4 ; see Equation (1) into solution (46) . The

concentration of the ionic species increases until the Ca2+ approaches the saturation point

-23 mmol L"1 of portlandite (i.e., Ca(OH)2; CH) prompting its precipitation (43,46,47).

The precipitation of CH consequentially consumes ions in solution and consequentially

increasing the degree of undersaturation driving rapid dissolution and nucleation and

growth of C-S-H and CH (46) (see Equation (5). While the hydration of C3 S is

simultaneously occurring, the precipitation of ettringite continues during the induction

period until C$H2 is exhausted from the system. Once, C$H2 completely dissolves, the

remaining C3A (if any) reacts with the ettringite to form monosulfoaluminate hydrate as

shown in Equation 6.

C3A + 3C$H2 + 26H2O ^ C3A$3H32 (4)

C3S + (2x + 4)H ^ CxSH3x+1 + (3 - x)CH (5)

C3A + 0.5C6A$3H32 + 2H ^ 1.5C4A$H12 (6)

The term x denotes the C/S molar ratio of the calcium silicate hydrate since C-S-H

can exhibit a varying composition from C/S -0.67 up to -2.00 (e.g. C0.67SH3.01 to C2SH7) 10

but non-blended OPC systems an average ratio of 1.75 has been reported (51-56).

Characterization of C-S-H by traditional methodologies is difficult since it requires

extensive sample preparation (57-59) and special care is required to prevent dehydration

and/or carbonation of samples. While C-S-H is an amorphous/disordered material making

it difficult to be characterized, the accompanying CH and ettringite remains crystalline

(53,55,60). Following the induction period, the acceleration period (stage II) occurs as

shown with renewed dissolution corresponding to a rapid growth of C-S-H and CH

product (61,62).

Similar to the induction period of C3 S (stage II), the mechanisms responsible for the transition to the deceleration period and later periods (stage III and V) have been

heavily debated. A myriad of models have been proposed to predict hydration kinetics as well as early properties such as set time by utilizing physical and chemical phenomena

[C-S-H temporal growth rate, densification rates, critical C-S-H length, etc... .(63-67)].

But these models often utilize parameters that are not easily measured and/or replicated

experimentally or have irreconcilable differences between experimental observations

(63,68). Therefore instead of using a these traditional models, a machine learning model with a dataset of calorimetry data can be utilized to predict hydration kinetics without

having to reconcile these complex and often simultaneous physical and/or chemical

mechanisms occurring during the hydration of OPC. Machine learning (ML) has been

proposed and utilized in several different materials fields for the design of new materials, the optimization of physical properties, or the calculation of computational parameters with a great deal of success (2,69-73). 11

2.2. INFLUENCE OF NON-CEMENTITIOUS ADDITIVES ON HYDRATION KINETICS OF CEMENTITIOUS SYSTEMS

Both supplementary cementitious materials (SCMs) and other natural minerals are

utilized as a solution to offset emissions by reducing clinker content (i.e. the amount of

C3 S, C3A, C2 S, etc. within a cement + SCM mixture...) within the mix design while

retaining similar bulk properties. SCMs is a broad classification of post-industrial waste

streams or natural minerals that exhibit reactivity in cementitious conditions (6,19,21,74

76) although they are not as reactive as OPC or the constituting cementitious phases.

There are a myriad of SCMs and minerals being researched and implemented in cement, but for this review will focus on the SCMs: silica fume and metakaolin as well as

limestone followed by the reaction mechanisms that these additives can exhibit: the pozzolanic and filler effects.

Silica fume (SF) is an industrial byproduct formed from the condensation of SiO vapor in ferrosilicon alloy production (77). The rapid condensation of SiO vapor in air

forms glassy silica spheres and/or clusters with diameters below 1pm (78). On the other

hand, metakaolin (MK, AhSi2O?) is an anhydrous mineral formed by firing the clay

mineral kaolinite (AhSi2O5(OH)4) within a temperature range of 500 °C - 800°C (79

81). Higher temperatures facilitate the transformation process but temperatures above

800°C energetically favor the non-reversible transformation of MK into mullite and/or y-

Al2O3 nullifying all reactivity (82,83).

The reaction of these species is complex, and the degree of reactivity varies on

several parameters such as chemical composition, fineness, and amorphous content are

all notable examples of parameters that are used to qualitatively describe the reactivity of

silica fume or metakaolin (or SCMs in general). The reactivity of SCMs manifests in 12 either in cementing properties (i.e. similar behavior as cementitious clinker) or through the pozzolanic effect. The pozzolanic effect describes the chemical reaction between silicates and/or aluminosilicates with CH to form C-S-H or alumina substituted C-S-H

(i.e., C-A-S-H) (84-86), see Equation 7a and 7b for SF and MK respectively.

SiO2 + Ca(OH)2 ^ C - S - H (7a)

Al2Si2O7 + Ca(OH)2 ^C-A-S-H (7b)

The formation of pozzolanic C-S-H and/or C-(A)-S-H benefits the bulk properties by decreasing the internal porosity present in the paste microstructure. This consequentially enhances the physical strength as well as preventing the ingress of corrosive species (87-89). Furthermore, fine additives enhance the hydration reaction via the filler effect. Rather than a chemical reaction, these fine additives act as an energetically favorable substrate for the heterogeneous nucleation and growth of C-S-H

(analogous to nucleating agents utilized in glass-ceramic systems (90)). For both metakaolin and silica fume, the enhancements to the later age properties of cementitious systems have been attributed to filler and pozzolanic effects (due to both materials having small particle sizes and being highly reactive in alkaline conditions) have been documented in the literature (81,91-93). It should be noted that materials that do not react in the highly alkaline environments can benefit the cement hydration reaction. For example, limestone does not exhibit any intrinsic cementitious or pozzolanic reactivity, but numerous countries have implemented several standard cement mixtures that incorporate fine limestone due to it benefiting the hydration reaction with the filler effect

(29,94-97). 13

PAPER

I. INFLUENCE OF POZZOLANIC ADDITIVES ON HYDRATION MECHANISMS OF TRICALCIUM SILICATE

Jonathan Lapeyre and Aditya Kumar

Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409

ABSTRACT

Pozzolanic mineral additives, such as silica fume (SF) and metakaolin (MK), are used to partially replace cement in concrete. This study employs extensive experimentation and simulations to elucidate and contrast the influence of SF and MK on the early age hydration rates of tricalcium silicate (triclinic C3 S), the major phase in cement. Results show that at low replacement levels (i.e., <10%), both SF and MK accelerate C3 S hydration rates via the filler effect, that is, enhanced heterogeneous nucleation of the main hydration product (C-S-H: calcium-silicate-hydrate) on the extra surfaces provided by the additive. The filler effect of SF is inferior to that of MK because of agglomeration of the fine particles of SF, which causes significant reduction (i.e., up to

97%) in its surface area. At higher replacement levels (i.e., >20%), while SF continues to serve as a filler, the propensity of MK to allow nucleation of C-S-H on its surface is substantially suppressed. This reversal in the filler effect of MK is attributed to the abundance of aluminate [Al(OH)4-1] ions in the solution—released from the dissolution of MK—which inhibit topographical sites for C-S-H nucleation and impede its 14 subsequent growth. Results also show that in the first 24 hours of hydration, MK is a superior pozzolan compared to SF. However, the pozzolanic activities of both SF and

MK are limited and, thus, do not produce significant alterations in the early age hydration kinetics of C3 S. Overall, the outcomes of this study provide novel insights into the mechanistic origins of the filler and pozzolanic effects of SF and MK, and their impact on cementitious reaction rates.

Keywords: C3 S, filler effect, hydration kinetics, metakaolin, pozzolanic effect silica fume

1. INTRODUCTION

Ordinary Portland cement (subsequently referred to as cement) and concrete are indispensable to the infrastructure of the modern world. As global demand for concrete increases continually, the construction community faces the crucial challenge of finding ways to reduce the carbon footprint and embodied energy associated with cement production (1-4). In response to this challenge, increasing attention is being given to reduce the cement content of concrete by partially replacing cement with pozzolanic mineral additives (subsequently referred to as pozzolans), such as silica fume (SF) and metakaolin (MK). At very early ages (i.e. within a few hours of hydration), the enhanced heterogeneous nucleation of calcium-silicate-hydrate (C-S-H*) gel - the main hydration

* As per the standard cement-based notation C = CaO, A = A F O 3, F = Fe2O 3, S = SiO 2, T = T iO 2, and H = H 2O. 15

product in cementitious systems—on the extra surfaces provided by the pozzolan (5,6)

results in acceleration of the overall hydration kinetics. This acceleratory effect is

typically termed as the filler effect, (7-10) wherein the term filler connotes chemical

inertness of the material. At later ages, however, the pozzolan does react chemically with

calcium hydroxide (i.e., CH: a hydration product present in cementitious systems) to

form space-filling pozzolanic C-S-H gel (11-16). Such formation of pozzolanic C-S-H

improves the solid-to-solid phase connectivity within the paste’s microstructure, which,

in turn, manifest as improvement in properties, including higher strength and enhanced

durability (17-19). Although both SF and MK are expected to alter cement hydration

rates though similar mechanisms, the early age hydration (i.e., time <24 hours) behavior

of a blended paste prepared by partial replacement of cement with SF is significantly

different from its MK counterpart. These disparities between the influence of SF and MK

on early age hydration rates of cement are not well understood and are the main focus of

this study.

Silica fume, composed of amorphous silicon dioxide (SiO2), is typically used to bolster the performance and durability of high-performance concrete (20). Several past

studies have reported that SF produces enhancement in cement hydration rates (21-23 at

early ages by offering additional preferential sites for product nucleation, via the filler

effect. In another study, however, Tomas et al. (9) hypothesized that the seeding effect— which is different from the filler effect—is responsible for the acceleratory effect of SF.

According to the authors, within the first few hours of hydration, SF dissolves and reacts with CH—formed as a result of cement hydration—to form pozzolanic C-S-H (11-13)

The pozzolanic C-S-H then acts as an energetically favored template (i.e., a seed) for 16 enhanced nucleation and growth of C-S-H that precipitates subsequently. As C-S-H continues to form and grow in an autocatalytic manner away from the cement particles

(i.e., atop the pozzolanic C-S-H layer formed on SF particles), the hydration of cement is enhanced. Numerous prior studies, however, have shown that the pozzolanic activity of

SF is kinetically slow and restricted at early ages (5,12,21), on account of its slow dissolution (24,25) and sparse availability of CH in the system. Limited pozzolanic activity of SF would result in formation of negligible amount of pozzolanic C-S-H, which would entail that at early ages SF acts predominantly as a filler—such as limestone and quartz (7,10,26,27) -rather than a “seed” for C-S-H nucleation. To reconcile these contradicting theories proposed in prior studies, a more systematic study, focused on mechanistic description of the role of SF on early age hydration of cement is warranted.

Metakaolin, composed of a glassy aluminosilicate with a stoichiometry of

Al2 Si2O7, is a widely available pozzolan (17,28-33) and reported to impart improvements in the performance and durability of concrete. MK is formed by the calcination of the crystalline clay mineral kaolinite [AhSi2O5(OH)4], within the temperature range of

500°C-800°C. The firing process breaks the Al—OH bonds, and results in the transformation of the 6-cordinated Al sites to lower 5- and 4-coordinated sites, thus transforming the crystalline lattice into a highly disordered structure and enhancing the material’s reactivity (15,17,30,34,35). Although the role of MK in enhancement of later age properties of cementitious systems has been widely studied (15,17,30,36-40), literature on the influence of MK on early age hydration of cement is scarce. In the limited studies (28,37,41,42), that do report on the topic, contradictory conclusions have been drawn. Some studies (28,41) have reported negligible influence of MK on cement 17 hydration rates in the first 24 hours, thus suggesting that at early ages, MK has limited pozzolanic reactivity and is also unable to offer its surface for the nucleation of C-S-H as a filler would. These characteristics of limited early age filler effect and pozzolanic activity of MK are shared by some low-calcium (i.e., class F) fly ashes (42-45) -which are compositionally analogous to MK, in terms of being rich in glassy aluminosilicate content. In other studies (46-48), however, MK and low-calcium fly ashes have been shown to accelerate the early age hydration kinetics of cement. The exact reasons for such retardation are not explicitly described in literature; however, in a recent study conducted by Pustovgar et al., (49) it has been shown that in cementitious systems provisioned with high concentrations of aqueous aluminate [Al(OH)4 ] species—which could be released from the dissolution of the fly ash or MK—the aluminate ions act to passivate the surfaces of anhydrous cement particles, which, in turn, causes retardation of cement hydration rates. In contrast to these studies, which report either negligible or decelerated effect of MK (and other aluminosilicates) on cement hydration rates, other studies (37,42) have shown that MK does indeed act as a filler and, hence, is able to exert catalytic effects on cement hydration at early ages. As would be expected of a filler, the catalytic effect scale proportionally with the fineness of MK particulates (37). The main reason, that would explain the opposing findings, is that these studies have examined the role of MK in complex multicomponent cement systems, in which it is difficult to isolate and quantify the different effects MK may exert. For example, in such multicomponent cement systems, the aluminate [Al(OH)4 ] ions released from the dissolution of MK can react with paste components (i.e. ionic species in solution or solid hydration products) resulting in precipitation of secondary hydrates (e.g., AFm phases, such as C3AH6 : 18 ettringite, and C4A$3Hi2: monosulfoaluminate) (17,30). These effects, in turn, may influence overall hydration rates in a way that is difficult to separate from the filler and pozzolanic effects of MK. Furthermore, these past studies do not shed light on the actual mechanisms describing the influence of MK on the dissolution of cementitious phases and the overall kinetics of hydration in cement systems. Due to such gaps in knowledge, the disparities between the influences of MK vis-a-vis other pozzolans (e.g., SF) on cement hydration rates are not well understood. Thus, it is important to evaluate such behaviors in single-compound systems that still feature the filler and pozzolanic effects but are simpler to analyze than cement. This study takes a foundational step in that direction by closely examining and contrasting the influences of MK and SF in C3 S

(triclinic Ti-Ca3SiO5) pastes. C3 S is the major phase present in cement, mimics the overall hydration behavior of cement, and, therefore, is deemed to be the ideal single compound alternative for cement (16).

A confluence of experimental methods and computer simulations is employed to elucidate the effects of Sf and MK additions on the early age (i.e., up to 24 hours) hydration kinetics of C3 S pastes. The hydration rates are measured, using isothermal microcalorimetry methods, across a wide range of replacement levels of C3 S with the pozzolans. A modified phase boundary nucleation and growth (pBNG) model, with time- dependent anisotropic growth rate of hydration products, is employed to describe the progress of hydration in such systems. Focus is given to consolidate the results obtained from experiments and simulations to elucidate the mechanistic origins of the filler and pozzolanic effects of SF and MK, and their influences on C3 S hydration rates. 19

2. MATERIALS AND EXPERIMENTAL METHODS

Triclinic C3 S (Ti-CasSiOs) was synthesized by solid-state reaction using

analytical react (AR)-grade precursors. Calcium oxide (CaO), prepared by the thermal

decomposition of calcium carbonate (CaCO3), was mixed in stoichiometric quantities

(CaO: SiO2 = 3:1) with fine silica (SiO2 a-quartz) and pelleted at a compaction pressure

of 100 MPa. The compacted pellets were fired in a muffle furnace in air at 1500°C for 12

hours in platinum crucibles, and subsequently quenched in air (50,51). The sintered

pellets were subsequently crushed with mortar and pestle, followed by ball milling for 24

hours. The final product obtained was almost phase pure C3 S, containing approximately

0.80% ± 0.25% residual CaO by mass based on Rietveld analysis of its X-ray Diffraction

(XRD) patterns.

The SF and MK powder used in this study are commercially available products.

SF is composed of amorphous SiO2 at nominal purity (i.e., 96.50%mass). And, the MK

powder (amorphous AhO2O7) is composed of 51.30% SiO2 and 47.80% AhO3, with

minor amounts (i.e., ~1.04%mass) of other oxide impurities (e.g., TiO2). Detailed

composition of the materials as obtained from X-ray fluorescence (XRF) method, is

shown in Table 1. It is pointed out that both SF and MK contain minor amounts of alkali

oxides. Dissolution of such alkali oxides upon contact with water could potentially

increase the pH of the contiguous solution, and, thus, influence C3 S hydration rate (52).

Notwithstanding, in the context of the pastes described in this study, based on their

mixture proportions and considering the low alkali content of the pozzolans, it is 20

expected that the effect of alkalis, present in the pozzolans, on C3 S hydration rates is

negligible.

The particle size distribution (PSD) of the solids were measured using a Beckman

Coulter static light scattering (SLS) analyzer (Microtrac S3500 and Malvern Zetasizer

Nano) using a 750 nm laser source that is incident on a dilute suspension of ultra-

sonicated powder particles in isopropyl alcohol (Figure 1). The median particle sizes (d.50,

pm) of C3 S, SF, and MK were determined as 7.78, 0.23, and 5.40 pm, respectively. By

factoring the bulk density (i.e., 3150, 2200, and 2550 kg/m3 for C3 S, SF, and MK,

respectively), the total specific surface area (SSA) of C3 S, SF, and MK were calculated

from the PSDs as 562, 18200, and 530 m2/kg, respectively. The SSA calculations are based on the assumption that the particles are spherical, while discounting the effects of the particulates’ topographical roughness and internal porosity (53-57).

Table 1. Bulk oxide composition of pozzolans, as cetermined from XRF Oxides # Silica Fume (SF) %mass Metakaolin (MK) %mass SiO2 96.50 51.30 AEO3 0.70 47.80 Fe2O3 0.50 0.44 CaO 0.40 0.04 MgO 0.50 0.09 SO3 - <0.01 TiO2 - 0.90 Na2O Equivalent 0.40 0.21 Loss of Ignition 1.00 0.52

Therefore, the SSAs calculated from SLS method are expected to be smaller than

those determined from Brunauer-Emmett-Teller (BET) method by a factor of ~1.6-to-2.2

(58,59). All pastes were prepared by mixing the solids with Di-water at a constant liquid- 21 to-solid ratio (l/s) of 0.45, by mass. To describe the influence of SF and MK on the reaction response of the paste, C3 S was partially replaced by the pozzolans at 0%, 5%,

10%, 20%, 30%, 40%, and 50% by mass. In accordance with these increasing replacement levels, the water-to-C3 S ratios (w/c: mass basis) are 0.450, 0.474, 0.500,

0.563, 0.643, 0.750, and 0.900, respectively. All pastes were mixed following identical protocols (e.g. equivalent speed and time of mixing). Special care was taken to ensure homogeneity of the paste (i.e. complete wetting of the solids with DI-water).

Figure 1. Particle size distribution (PSD) of C3 S, SF, and MK used in this study. The largest relative uncertainty in the median diameter (d50, pm) of the powders, based on 6 replicate measurements, was on the order of ±6%. SF, silica fume

The kinetics of hydration of C3 S in the pastes were monitored up to 24 hours after mixing using a TAM IV isothermal conduction microcalorimeter, programmed to maintain the sample at a constant temperature of 20 ± 0.1°C. Compared to conventional methods of reactivity assessment (e.g., isothermal calorimetry), microcalorimetry methods are deemed more accurate as they allow quantification of heat flow rate of the 22

reaction at very high resolution (10-7 J/s). The cumulative and differential heat release

obtained from calorimetry experiments were normalized by the enthalpy of C3 S (16,51),

484 J gC3S-1, to determine the degree of hydration (a, expressed as the fraction of C3 S

reacted) and the rate of hydration (da/dt, units of h-1) of C3 S, respectively, as function of time. This method of derivation of a and da/dt is based on the assumption that the

measured heat released is solely on account of C3 S hydration, that is, discounting heat

release due to dissolution and pozzolanic reaction of the pozzolan (i.e., SF or MK) with

CH. This assumption is reasonable because various previous studies have shown that the

dissolution and pozzolanic reaction of SF and MK release very small amounts of heat

(5,9,16), and occur at very slow rates within the first 24 hours (13,21). To corroborate this, additional experiments were conducted to monitor the heat release from the

dissolution of SF and MK in saturated lime solution (as in C3 S pastes, the composition

and pH of the pore solution are similar to saturated lime solution (16,60-62)) using the

isothermal microcalorimetry method. In the heat evolution profiles (shown later in

Section 4), it was found that the cumulative release at 24 hours in such systems is less than 5 J per gram of the pozzolan—which is significantly lower than the cumulative heat

evolved due to the hydration of C3 S at equivalent time. Therefore, it can be said in the

[C3 S = pozzolan] pastes, the evolution of heat is predominantly due to the hydration of

C3 S with water. The heat evolution profiles of [pozzolan + saturated lime solution] pastes were also used to quantify the time-dependent extent of reaction (a) of the pozzolan, by

following the same procedure as described above for C3 S pastes (i.e., by combining heat

release with the enthalpy of reaction). To determine the enthalpy of reaction (Hpoz in units

of J gPoz-1) of each pozzolan (i.e., SF and MK) in saturated lime solution, a two-step 23

method, detailed in a prior publication (5), was implemented. In the first step, the heat of

[pozzolan + saturated lime solution] pastes, prepared at different l/s (i.e., 0.45, 1.0, 3.0,

and 10.0), were monitored (at T = 20°C, using isothermal microcalorimetry) over the

course of 28 days. And, in the next step, Hpoz was calculated by dividing the cumulative

heat release (J) of the paste at 28 days by the amount of pozzolan consumed (i.e.,

difference between initial and residual amount of the pozzolan in the units of grams) in the same period; here, the final value of Hpoz (i.e. for SF, or for MK) corresponds to the

average of the individual Hpoz values (which within ±6% of each other) obtained for the

different l/s. A SDT600 thermogravimetric analyzer (TGA) was used to identify and

measure the quantities of phases present at different hydration times. The temperature

and mass sensitivity of the analyzer are 0.25°C and 0.1 pg, respectively. Hydration was

arrested at a given age by crushing the hydrated pastes into grains smaller than 5 mm, and

submerging them in isopropyl alcohol for 24 hours (63). The samples were then dried in the oven (T = 85°C), after which they were finely powdered using an agate mortar and

pestle. The powder samples were heated under N2 purged at a flow rate of 100 mL/min

and a heating rate of 10°C/min in pure aluminum oxide crucibles over a temperature

range of 30°C to 1000°C. The mass (TG) and the differential mass loss (DTG) patterns were used to quantify the amount of CH and of calcite (if any may have formed due to

carbonation of C-S-H and CH) present in the system. For these phase quantifications well-established methods detailed in prior studies (63,64) were used. 24

3. PHASE BOUNDARY NUCLEATION AND GROWTH (pBNG) MODEL

A modified pBNG model is applied to describe the effects of SF and MK addition

on C3 S hydration rates. In classical pBNG models applied to cementitious pastes (7,9,65

68), including the model used herein, a single product of constant density is assumed to

form at a given nucleation event, and its subsequent growth on solid-phase substrate

boundaries (i.e., C3 S and filler/pozzolan surfaces) is treated as the rate-controlling

mechanism that drives the kinetics during the early ages of C3 S hydration. This

assumption of site saturation implies that the growth of product phase begins from a

fixed number of nuclei that the growth of the product phase begins from a fixed number

of nuclei that form at very early ages (i.e., at time = t h), and no further nuclei are

permitted to form after this very initial nucleation burst (61,69) [i.e., nucleation rate (/rate)

= 0 pm-2 h-1]. Based on these criteria, at any time t (h), the volume fraction of the product

within the system [X(t), unitless] is given by Equation (1) (5,51,66,70)

FD[K ( t-T ) T X(t) = 1 — exp -2kG • (t — t) • (1 (1) ks(t — t)

where,

Fd(x) = exp(—x2) I exp(y 2) dy (2) Jr1

In Equation 1, F d is the f-Dawson function, expressed as an integral (Equation 2).

The variable ks (h-1) is related to the inverse of time required by the product nuclei to

provide complete coverage of the anhydrous C3 S particles (65,66) The value of ks

depends on the nucleation density of the product (/density, pm-2), that is, the number of total supercritical nuclei produced per unit surface area of C3 S, as well as the geometry 25

and rate of their growth (Equation 3). In the model presented in this study, the growth of

the product is assumed to occur in an anisotropic fashion, while varying with respect to

time. Gout (t) (pm h-1) is the growth rate in lateral direction, that is, along the two

dimensional (2D) plane parallel to the boundary of the substrate. Along this 2D plane, the

growth rate is assumed to be isotropic. The introduction of a time dependency on the

product growth rate is a digression from the classical form of pBNG, in which the growth

rate is assumed to remain constant though the entire duration of hydration. This is based

on an implementation originally formulated by Bullard et al. (70) and subsequently

adopted by Oey et al. (51), and Meng et al. (5) to capture the temporal variation in the

growth rate of C-S-H as its supersaturation in the solution varies non-linearly with time.

As both the outward (Gout) and the parallel (Gpar) growth rates vary with time, a constant

2:1 ratio for GoutGpar is assumed, such that the anisotropic factor, that is g (unitless) in

Equation 4, is 0.25 throughout the hydration process. This relationship between Gout and

Gpar represents anisotropic growth of needlelike domains of the product (65,66), and

agrees with recent experimental data of the geometry of C-S-H growth at early ages

(71,72). i — G0ut(t')(nglciensity)'2 (3) 2 Gparfa') g = (4) Gout(t)

^G — rG^out(f)aS7 (5)

In Equation 1, the variable Ug (h-1) is related to the reciprocal of time required for the product to fill the capillary pore space. The value of kG depends on the products’

outward growth rate (Gout), as well as the constant m (unitless), which represents the ratio 26 of the growth rate into and out of the substrate in the normal direction (Equation 5). In their, Scherer et al. (65,66) noted that at early ages of hydration, hydrates do not penetrate the cement (or C3 S) particles, and, therefore, m ~ 0.50. This is because at early ages, the ionic species, that is H3 SiO4 /H2 SiO42"", CaOH+/Ca2+, and OH , responsible for the precipitation of C-S-H, transport predominantly from the substrate’s surface towards the contiguous solution, while showing little movement though the product in the reverse direction (65). Therefore, in all simulations presented in this study, the value of m was assumed to be constant at 0.50. Another important parameter that dictates the value of &g, and thus the kinetics of C3 S hydration, is the boundary area of the substrate per unit volume of the paste («bv, gm"1) (Equation 6). The paste’s volume is simply the cumulative volume of the paste’s components (i.e., C3 S, pozzolan, and water) and the substrate’s area is the sum of the initial surface area of C3 S and pozzolan particles that is available for the nucleation of the product. In the model, the substrate’s area (SSATotal) is calculated using Equation 7, where w/c (unitless) is the ratio of the mass of water to the mass of C3 S, p is the density (water = 1000 kg m"3, C3 S = 3150 kg m"3, SF = 2200 kg m"3, and MK = 2550 kg m"3), and z (unitless) is the %mass of C3S replaced by the pozzolan. In

Equation 7, the parameter apoz (unitless) acts as a free variable used in the simulations to represent the reaction area fraction of the pozzolan, that is, fraction of area that remains unaffected by agglomerations and/or other ion specific effects (e.g., inhibition of the topographical nucleation sites due to the adsorption of ions) and, thus, is able to provide sites for C-S-H nucleation. The introduction of this variable to account for the loss the surface area of pozzolan particles—due to agglomeration and/or ion"specific effects—is adopted from prior studies (5,73"75). By Combining SSAsolid and /density, the total number 27

of supercritical product nuclei (Nnuc, unit of gc3S-1) produced per gram of C3 S can be

calculated (7,8,76) (Equation 8).

SSAsolid aBV = w (6) ______c . + J ^ + ( 1 ) 1 Pwater Pc3S V100 z) Ppc

Z (7) SSAsolid — SSAC.S + aPozSSAPc 100 - Z

^nuc — SSAsolid ^density (8)

The volume fraction of the reactants transformed to products [X(t)], as calculated

from Equation 1, and the degree of hydration (a, unitless) of C3 S are related by a constant

B (unitless) (5,51,70) described in Equation 9. Where, ^product is the bulk density of

combined hydration products (assumed to be 2070 kg/m3) (77,78), and the parameter c =

-7.04 x 10"5 m3 kg-1 represents the chemical shrinkage per kilogram of C3 S that is

consumed over the course of its hydration (79).

a(t) — BX(t) (9a)

1 1 Pc3s \ C + ■ Pproducts Pc3S Pwater B — (9b) W 1 1 c Pc3s + 1 \P:product Pwater \Pwater

With these assumed relationships to simulate the measured reaction rates, the

variables that must be determined are: Gout (t), /density, and apoz. Of the three variables,

/density and apoz are constants (with respect to time), whereas Gout (t) varies with respect to time. Therefore, to obtain the optimum values of /density and apoz and the optimum

function form of Gout for a given system, a Nelder-Mead-based simplex algorithm 28

(51,80,81), that uses derivation-free and nonlinear optimization principles, is employed in

two steps. In the first step, the value of Gout is kept constant at 0.075 pm h-1—a value

derived from scanning transmission electron microscopy (STEM) analyses of early age

hydration of C3 S (71). The algorithm iteratively varies the values of /density and apoz within

predefined bounds until the magnitude of the difference between the simulated and

measured rates of reaction (da/dt) is minimized. It is pointed out that up to this point, the

model represents classical pBNG formulation (68), wherein the anisotropic growth of the

products, which nucleate at a virtual time t (h), is kept constant throughout the hydration

process. To account for the time-dependent variation in product growth rate, a second

simulation step is employed. Here, at any given time t, the optimum values of /desnity and apoz yielded from the first step are used as constants, whereas Gout is allowed to vary

iteratively within the bounds of 10-4 to 102 pm h-1 to minimize the deviation between the

simulated and measured reaction rates. When the simplex algorithm converges, the value

of Gout is taken to be the optimum value at that time. The optimum values of Gout for the

entire duration of C3 S hydration are thus determined by implementing such an

optimization process over the first 24 hours of hydration using a time stop of 0.01 hour.

The time-dependent Gout, obtained as such, mimics the non-monotonic and nonlinear rate

of growth of the product in relation to the evolution of its supersaturation in the solution.

In prior publications (5,51,70), a similar simulation scheme was employed, and it was

shown that the simulated evolution of the product growth rate reproduced the intrinsic

changes in the initial, as well as the time-dependent evolution of the chemistry of the

solution, as determined from experiments. Therefore, while this scheme of deriving the

product growth is indirect (i.e. obtained from experimental measurements of reaction 29 rate), the simulations are still representative of the physical processes occurring in the system, and able to capture the progressive decline in the product growth rate as its supersaturation in the solution declines; this cannot be effectively captured by classical pBNG models (51,70).

4. EFFECTS OF SF AND MK ON HYDRATION KINETICS OF C3 S

Figure 2 shows representative heat evolution profiles of plain and binary C3 S pastes prepared by replacing C3 S with SF at different replacement levels. As can be seen,

SF produces significant enhancements in C3 S hydration rates, as marked by the leftward shift of the heat evolution curves, higher heat flow rates at the main hydration peak, and shortening of the induction period (i.e., the period corresponding to ~1-3 hours, between the initial dissolution and onset of acceleration, as highlighted in Figure 2B). The acceleration induced by SF increases with increasing replacement levels, which suggests that there is a good correlation between is indicative of enhanced heterogeneous nucleation of the main hydration product, that is, C-S-H, either on the extra surfaces provided by the fine SF particles, or on the pozzolanic C-S-H layer formed atop the SF particles due to their reaction with CH (5,7,9,10). It is worth pointing out that although

SF results in faster approach to the peak (i.e., greater slope of the acceleration regime), the postpeak deceleration is still broadly the same as the control system (i.e., [C3 S + 0%

SF]); this better shown in Figure 2A. As such, the enhancements in hydration rates of

[C3 S + SF] systems, which occur very early, are carried over to later stages resulting in 30

higher cumulate heat release and, thus, greater degree of C3 S hydration at 24 hours (see

Figure 2C).

Figure 2. Measured heat evolution profiles of pastes prepared with C3 S replaced by SF at different replacement levels. (A), Heat flow rates up to 24 hours of hydration, (B), Heat flow rates up to 9 hours of hydration, and (C), cumulative heat release up to 24 hours of hydration. The l/s for all pastes is 0.45. For a given system, the uncertainty in the measured heat flow rate at the main hydration peak is ±2%. SF, silica fume

Figure 3 shows representative heat evolution profiles of C3 S pastes prepared by

partial replacement of C3 S with MK. As can be seen, the profiles qualitatively show that the changes (i.e., acceleration or deceleration) in C3 S hydration rates do not exhibit

monotonic trends as in the case of [C3 S + SF] pastes. To better reveal these non

monotonic relations, and to gain quantitative information of the hydration kinetics,

characteristic calorimetric parameters, that is, slope of the acceleration regime (mW gC3S-1

h-1), heat flow rate at the main hydration peak (mW gC3S-1), and inverse of the time

corresponding to the main peak (h-1) indicative of acceleration or retardation in hydration

kinetics (5,7,26,82)—were extracted and plotted against the replacement level of C3 S by

the pozzolan (Figure 4). As can be seen, with increasing replacement levels of MK, the

length of the induction period increases (Figure 3B), and this results in increasing delay 31

in the occurrence of the main hydration peak (Figure 4A). This indicates that interactions

between MK and the paste components act to delay the massive precipitation of

hydration products, that is, C-S-H and CH and, thus, result in prolongation of the

induction period (5,60,62,83). In contrast to the trends in time of the main hydration peak

(or the length of the induction), the other two calorimetric parameters—slope of the

acceleration regime and heat flow rate at the peak—exhibited non-monotonic trends with

respect to MK replacement level (Figure 4B and C). These results suggest that at

relatively low replacement levels (i.e., <10%), the role of MK is broadly similar to that of

SF wherein acceleration is proportional to the extra surface area provided by the

pozzolan. These reactivity enhancements, which occur very early, are carried over to later

stages resulting in higher cumulate heat release at 24 hours (Figure 3). However, at

higher replacement levels (i.e., >20%) of MK, these acceleratory effects are progressively

diminished (Figure 4B and C). This is in contrast to [C3 S + SF] pastes, wherein SF

contents > 20% lead to further enhancements in C3 S hydration rates. These results, therefore, suggest that beyond a threshold level of replacement of C3 S, the effect of MK

and SF on C3 S hydration rates are dissimilar. Figure 4 contrasts the influence of MK and

SF on C3 S hydration rates at equivalent replacement levels. It could be argued that the

changes in C3 S hydration rates, as induced by the pozzolans, are disparate due to the

differences between the pozzolans’ SSA. Therefore, to better differentiate the effect of SF

and MK, the heat evolution profiles of area-matched (i.e., equivalent initial surface area

of the solids per unit mass of C3 S) [C3S + pozzolan] systems were obtained (Figure 5).

As can be seen, the hydration kinetics of C3 S are very different between the two pastes in

spite of the equivalency in initial solid surface area. In the case of [C3 S + SF] paste, it is 32

noted that the enhancements in hydration rates occur early, are carried over to later ages,

and remain disproportionately smaller with respect to the augmentation in the solid

surface area as provided by SF. While the first 2 points are symptomatic of the filler

effect(5,7,9,10), the last point, that is, disproportionate relation between area increments

and hydration enhancement, is hypothesized to be on account of agglomeration of SF

particles which reduces their exposed surface area, thus rendering a fraction of it

unavailable for heterogeneous nucleation of C-S-H (5,7,10).

(A) (B) (C) Figure 3. Measured heat evolution profiles of pastes prepared with C3 S replaced by MK at different replacement levels. (A), Heat flow rates up to 24 hours of hydration, (B), Heat flow rates up to 9 hours of hydration, and (C), cumulative heat release up to 24 hours of hydration. The l/s for all pastes is 0.45. For a given system, the uncertainty in the measured heat evolution profile is ±2%. MK, metakaolin

Further details corroborating this hypothesis pertaining to the propensity of SF

particles to agglomerate are described using the pBNG model in Section 6 . In the case of the [C3 S + MK] paste, the prolongation of the induction period is clearly noted (Figure

5B); this is in alignment with trends shown in Figures 3B and 4A. Once the induction

period ends, the acceleration in hydration rates in larger compared to the control system 33

(and the [C3 S + SF] pastes), resulting in a higher heat flow rate at the peak as well as higher cumulative heat release at 24 hours (Figure 5C). This suggest that although MK additions result in suppressed hydration kinetics of C3 S for the first few hours, the acceleratory effects of MK are recouped once the induction period terminates.

Figure 4. The calorimetric parameters. (A), inverse of the time to the main hydration peak, (B), heat flow rate at the main hydration peak, and (C), slope of the acceleration regime extracted from the calorimetry profiles. The l/s for all pastes is 0.45. For a given system, the uncertainty in each calorimetric parameter is ±2%

Interestingly, these effects of MK of C3 S hydration rates, that is, deceleration at early ages and accelerating at later ages, are similar to those induced by delayed accelerators (84). It could be argued that the differences between hydration kinetics of area-matched [C3 S + MK] and [C3 S + SF] pastes could arise due to differences between evolutions of pH of the pore solution (e.g., due to hydroxylation of silicate surfaces) of such pastes. However, upon monitoring the pH of control C3 S pastes, [C3 S + 20% MK] paste, and [C3 S + 20% SF] paste (prepared at l/s = 1.00) at discrete time-steps up to 24 hours, it was found that pH evolutions of the pore solutions of blended pastes are broadly similar to that of pure C3 S paste (results not shown). Specifically, it was observed that, in 34 all pastes, the pH rises until the end of the induction period, and beyond that stabilizes to a value close to calcium hydroxide saturation (pH -12.68)—as would be expected in

C3 S-based systems (85,86). Therefore, it can be said that mechanisms other than differences in pH evolution are responsible for the differences between hydration kinetics of [C3S + MK] and [C3S + SF] pastes. These mechanisms are described below, in

Sections 5 and 6.

Figure 5. Measured heat evolution profiles of pastes prepared with C3 S replaced by MK (replacement level = 35%) and SF (replacement level = 1.54%), such that the overall initial solid surface area per unit mass of C3 S is the same (i.e., SSAsolid = 847 m2 kgC3S-1). (A), Heat flow rates up to 24 hours of hydration, (B), Heat flow rates up to 6 hours of hydration, and (C), cumulative heat release up to 24 hours of hydration. The l/s for all pastes is 0.45. MK, metakaolin; SF, silica fume

5. ASSESSMENT OF FILLER AND POZZOLANIC EFFECTS OF SF AND MK

Heat evolution profiles (Figure 2) and calorimetric parameters (Figure 4) show that the enhancement in C3 S hydration rates in [C3 S + SF] pastes increases with SF content in the paste. This suggests enhanced heterogeneous nucleation of C-S-H, either on the extra surfaces provided by the fine SF particles, or on the pozzolanic C-S-H 35 formed on SF particles’ surfaces due to the reaction of SF with CH. Thomas et al. (9) hypothesized that in [C3S + SF] pastes, the seeding effect is responsible for the acceleration, wherein the nucleating agent is the pozzolanic C-S-H layer formed on SF particles’ rather than the SF surface itself. The authors (9) argue that enhanced nucleation of C-S-H on the pozzolanic C-S-H layer only becomes significant at the end of the induction period, when massive precipitation of CH crystals occurs (60,62). As such, the length of the induction period and the time required to reach the main hydration peak would remain almost unchanged between the plain and [C3 S + SF] pastes. However, as shown in Figures 2B and 4A, the length of the induction period and the time of the main hydration peak decrease significantly—and broadly in a linear manner—with SF replacement level. This suggest that in [C3 S + SF] pastes, the additional heterogeneous nucleation of C-S-H occurs primarily on the SF surfaces via the filler effect (7), as has been reported in various previous studies (5,21-23). Nucleation of C-S-H on the pozzolanic C-S-H, though possible, is expected to be a secondary effect at early ages mainly due to the slow dissolution of SF in the paste’s alkaline environment (24,25), and scant availability of CH in the system. To corroborate this hypothesis, the temporal reactivity of SF in saturated lime solution (which mimics the pore solution of C3 S pastes

(16,60-62) was monitored using the isothermal microcalorimetry method (Figure 6A). As can be seen, due to its low solubility in alkaline environments and its intrinsically low dissolution rate, the degree of reaction of SF after 24 hours is minuscule (i.e., a ~ 1.3%) as compared to that of C3 S (i.e., a ~ 43%) reacting in Di-water. The agglomeration of the fine SF particles—which results in reduction of the particles’ overall surface area and limits their access to the contiguous solution—is expected to be a significant factor 36 contributing to its slow dissolution kinetics. These results showing low reactivity of SF in cementitious environments are in good agreement with those reported in prior studies

(5,87).

Next, to quantify the pozzolanic activity of SF, CH and SF were mixed proportionally, (i.e., 1:1 molar ratio) with water (i.e., l/s = 0.45), and the progress of the pozzolanic reaction, as the 2 compounds react with each other, was quantified using TGA at 24 hours (Figure 6B). Upon processing the DTG traces, it was confirmed that the decrease in CH content on account of the pozzolanic reaction with SF is less than 1.5%

(i.e. within the error of TG analyses); this is associated with the formulation of trace amounts of pozzolanic C-S-H (see Figure 6B). This negligible pozzolanic activity of SF 37

is expected because of its intrinsically slow kinetics of dissolution—further aggravated

by the effects of particle agglomeration—and low degree of reaction in saturated lime

solution (Figure 5A). The filler effect, as well as the negligible pozzolanic activity, of SF

are further confirmed in the results shown in Figure 5C. As can be seen, in [C3 S + SF]

pastes, the CH contents are consistently higher than the dilution line—which represents the proportional decrease in CH content with respect to decreasing C3 S content in the blended [C3 S + SF] paste. This suggests enhanced hydration of C3 S due to the filler effect

of SF and negligible consumption of CH due to the pozzolanic reaction with SF. These

results, obtained from calorimetry and TG methods, therefore, confirm that in [C3 S + SF]

pastes, the role of SF within the first 24 hours is characteristically that of a filler, that is,

devoid of pozzolanic interaction with CH.

To better assess the filler and pozzolanic effects of MK, the temporal reactivity of

MK in saturation lime solution was monitored using the isothermal microcalorimetry

method (Figure 7A). As can be seen, MK dissolves rapidly within a few minutes of

contact with the contiguous solution, beyond which the dissolution rate slows down

considerably leading to a degree of reaction of -8.5% at 24 hours. The early rapid

dissolution of MK leads to the release of aluminate [Al(OH)4 ] and silicate [H2SiO42-

/H3 SiO4 ] ionic species into the solution. Of these ionic species, the aluminate ions are

hypothesized to be at the origin on suppression in C3 S hydration rates until the end of the

induction period (i.e., prolongation of the induction period, as shown in Figure 3B). Some

paste studies (88,89) have reported that the aluminate ions combined with other aqueous

ionic species to form C-A-S-H and AFm phases (e.g., stratlingite, hydrogarnet) on C3 S

surfaces, which, in turn, poison C3S dissolution sites (and/or C-S-H nucleation sites). 38

Notwithstanding, due to the relatively low concentration of aqueous aluminate ions in the

paste (due to limited amount of Al in MK and limited dissolution of MK in the first few

hours), the amounts of such C-A-S-H and AFm phases are expected to be negligible

(more details discussed later), and, therefore, inadequate to consume substantial amounts

of aqueous calcium (Ca2+) ions or to suppress C3 S dissolution (49). Furthermore, even if

C-A-S-H and AFm phases were to form, direct evidence correlating the formation of such

phases with early age retardation of C3 S hydration rate is missing in literature. It is

hypothesized that the aqueous aluminate ions absorb of aluminate ions results in

inhibition of C3 S dissolution sites (e.g., kink sites found on etch pits (49,91)), which, in turn, decelerates the dissolution rate of C3 S and prolongs the induction period (Figure

3B). This hypothesis gains support from results reported in a recent paper by Pustovgar et

al. (49), as well as those published previously in references (88,90,92). Expectedly, these

effects of adsorption of aluminate ions leading to suppressed dissolution of C3 S become

more pronounced in pastes with higher MK contents (Figures 3B and 4A). As C3 S

continues to dissolve (albeit at a slower rate compared to the [C3 S + 0% MK] system), the pH of the solution continues to increase. At a critical pH—when the concentration of

Ca2+ and OH ions close to C3 S surfaces becomes sufficiently large and close to CH

saturation level (i.e., when the solution pH ~ 12.68; (10,49,62,90))—the aluminosilicate

complexes formed on C3 S surfaces become thermodynamically unstable and, as a result, the aluminate ions desorb from C3 S surfaces (49,90). As C3 S continues to dissolve (albeit

at a slower rate compared to the [C3 S + 0% MK] system), the pH of the solution

continues to increase. At a critical pH—when the concentration of Ca2+ and OH ions

close to C3 S surfaces becomes sufficiently large and close to CH saturation level (i.e., 39 when the solution pH ~ 12.68; (10,49,62,90))—the aluminosilicate complexes formed on

C3 S surfaces become thermodynamically unstable and, as a result, the aluminate ions desorb from C3 S surfaces (49,90).

This desorption of aluminate ions from C3 S surfaces triggers a sequence of concomitant events, including renewed dissolution of C3 S, termination of the induction period, massive nucleation of CH crystals and C-S-H, and onset of the acceleration regime. Although the length of the induction period increases monotonically with MK content (Figure 3B), the postinduction period hydration of C3 S is highly non-monotonic in relation to MK replacement levels (Figure 4B and C). These non-monotonic relations 40 are also hypothesized to be directly linked to the release of aluminate ions from the dissolution of MK. At low MK replacement levels (i.e., <10%), the limited concentration of aluminate ions in the solution adsorb onto the substrate (i.e., C3 S and MK particles’ surfaces), and inhibit a fraction of C3 S dissolution sites. Once the pH of the solution reaches a critical value (i.e., at the end of the induction period), these adsorbed ions desorb completely from the substrates’ surfaces (49). As such, at the end of the induction period, the nucleation of C-S-H occurs not just on C3 S surfaces, but also on the bare MK surfaces. This enhanced nucleation of C-S-H on C3 S and MK surfaces manifests as accelerated hydration kinetics, as observed in Figure 4B and C. However, at high MK replacement levels (i.e., >20%), the concentration of aluminate ions in the solution is high, the concentration of aluminate ions in the solution is high, and this leads to adsorption of larger concentration of aluminate ions on both C3S and MK surfaces. At the end of the induction period—when the pH is high—aluminate ions desorb from C3 S and

MK surfaces, but not exhaustively. It is hypothesized that the residual aluminate ions

(i.e., ions that remain absorbed on substrates’ surfaces) continue to inhibit C-S-H nucleation sites on C3 S and MK surfaces. As a result, the ability of MK to allow C-S-H nucleation on its particles’ surfaces is progressively diminished at higher replacement levels (Figure 4B and C). This hypothesis is revisited in Section 6, and further corroboration is provided by means of results obtained from simulations.

Another important implication of the rapid early dissolution of MK (Figure 7A) is its ability to partake in pozzolanic reactions with CH. As can be seen in Figure 7B, in a paste prepared with MK and CH (at 1:1 molar ratio, and mixed with water at l/s = 0.45), the decrease in CH content after 24 hours of reaction is -8.3%, which is significantly 41

higher than that of SF. These results, showing superior pozzolanic activity of MK

compared to that of SF, are in good agreement with prior studies (41,93,94). The

consumption of CH leads to the formation of proportional (albeit, small) amount of

pozzolanic C-S-H. Such low amounts of pozzolanic C-S-H formed in [MK+CH] pastes

at 24 hours imply that the amount of pozzolanic C-S-H formed in [C3 S + MK] pastes

within the first few hours of hydration (i.e., around the time of termination of the

induction period, when the degree of reaction of MK is low and the amount of CH in the

paste is limited) is minuscule.^ Hence, on the basis of these results, it can be said that in

[C3 S + MK] pastes and within the first 24 hours of hydration, MK—unlike SF—does

exhibit pozzolanic activity; however, the pozzolanic activity is limited and, as such, the

ability of MK to accelerate C3 S hydration rates via the seeding effect is deemed to be

negligible, by the process of elimination, the acceleratory effect of MK (shown in Figure

4B and C) is attributed to can also be inferred from the results shown in Figure 7C, which

shows that the CH contents in [C3S + MK] pastes are consistently higher than the dilution

line. This trend in CH content suggests enhanced hydration of C3 S due to the filler effect

(larger enhancements at <10% replacement, and progressively diminishing enhancements

at >20% replacement), couple with minor consumption of CH due to its (limited)

Tn a [C3S + 40% M K ] paste, prepared at l / s o f 0.45, i f 8.3% o f M K is assumed to react pozzolanically with CH, the amount o f pozzolanic C -S -H (C 1.7SH4) [or C-(A )-S -H [ formed is <0.003

moles (i.e., < 4.031% o f the paste’ s volume). Around the time o f termination o f the induction period, the

degree o f reaction o f M K is expected to be << 8.3%, and the amount o CH is also expected to be small; therefore, the amount o f pozzolanic C -S -H [or C-(A)-S-H ] is expected to be far less than the

aforementioned value. 42

pozzolanic reaction with MK (particularly, at higher MK replacement levels). Overall,

these results show that in [C3 S MK] pastes, at low replacement levels and within the first

24 hours, the role of MK is characteristically that of a filler, with limited pozzolanic

activity. At high replacement levels, while the pozzolanic activity of MK is retained (and

still limited), its filler effect is significantly diminished due to the inhibition of C-S-H

nucleation sites on its particles’ surfaces.

6. NUMERICAL SIMULATIONS OF HYDRATION KINETICS OF C3 S PASTES

To better understand and contrast the roles of MK and SF on hydration rates of

C3 S, and to validate the hypotheses made in the preceding sections, the pBNG model

(described in Section 3) was applied to simulate the temporal reaction rates of plain and

blended pastes. As stated previously, within the pBNG framework, simulations are

employed in two steps. In the first step, optimum values of product nucleation density

(/density) and the reactive area fraction of the pozzolan (aPoz) are determined. In the second

step, the optimum function form of the outward growth rate of the product [Gout (t)] is

determined. Figure 8 shows the measure reaction rates of pastes compared again those

simulated using the pBNG model. As can be seen, by optimizing the values of Gout(t),

/density, and aPoz, the model is able to reproduce the experimental results. The variation in

these simulation parameters are analyzed below to describe the alterations in the

nucleation and growth process in relation to the type of content of the pozzolan. The

parameter optimizations show that both pozzolans have profound effects on the product

nucleation process, occurring at early ages (i.e., around the time the induction period 43 terminates). The model predicts that a significant fraction (i.e., up to 97%) of the surface area of SF does not participate in the nucleation and growth process (Figure 9A).

Figure 8. Representative set of simulated and measured hydration rates (da/dt) of C3 S in pastes prepared at: (A), 0% replacement of C3 S, (B), 20% replacement of C3 S by SF, and (C), 20% replacement of C3 S by MK. The blue solid line represents model output at its intermediate step, wherein the outward product growth rate (Gout) is assumed to remain constant throughout the hydration process. The red dashed line represents the final output from the simulations, wherein Gout is allowed to vary with time. MK, metakaolin; SF, silica fume

This is attributed to the enhanced agglomeration of the fine SF particles, which reduces their surface area and access to the contiguous solution, thus making a fraction of the particles’ surface area unavailable for C-S-H nucleation. These effects of agglomeration become progressively more pronounced as the SF content in the system increases, as also reported in previous studies (5,73-75,95). In the case of MK, up to replacement level of 10%, majority of the surface area of MK particles participates in the nucleation and growth of C-S-H (Figure 9A). However, all replacement levels >20%, there is a substantial, and progressive, decline in the reactive surface area of MK. It is 44 hypothesized that this decline occurs—not due to the adsorption of aluminate ions on the topographical sties of MK particles, as discussed previously in Section 5.

(A) (B) Figure 9. Parameters derived from the simulations: (A), reactive area fraction of the pozzolan (aPoz), and (B), total number of supercritical product nuclei formed per gram of C3 S (AWc) as functions of the pozzolan replacement level

More specifically, at low replacement levels of MK, majority of the aluminate ions adsorbed on MK surfaces (i.e., during the induction period) are expected to desorb at the termination of the induction period; this frees up MK surfaces to partake in nucleation and growth of C-S-H. However, at high MK replacement levels, the abundance of aluminate ions in the solution ensures that large concentrations of those ions remain adsorbed on MK surfaces even beyond the induction period; this, consequently, blocks a large fraction of MK particles’ surfaces and disallows them from offering sites for C-S-

H nucleation.

In addition to the aPoz parameter, /density was also found to vary with the pozzolan replacement level. These variations in /density are better revealed in Figure 9B, which 45

shows the total number of supercritical product nuclei per unit mass of C3 S (Nnuc:

calculated using Equation 8). The trends observed in Figure 9B are in very good

agreement with the hypotheses presented above. Across all replacement levels, the role of

SF is that of a filler—which enhances product formation (i.e., higher values of Nnuc)

monotonically with its content in the paste. In the case of MK, similar enhancements in

Nnuc are observed, but only for replacement levels <10%. It is worth pointing out that t

such low replacement levels, the values of Nnuc in [C3 S + MK] pastes are higher

compared to their SF counterparts (Figure 9B). Larger number of product nuclei in MK

pastes can also be can also be inferred from experimental results (Figure 4B and C), which clearly show that at replacement levels <10%. MK produces superior acceleration

(i.e., higher slope of the acceleration regime, and higher heat flow rate at the peak)

compared to SF. Based on these results, obtained from both experiments and simulations,

it can thus be said that at low replacement levels MK acts a filler, wherein its filler effect

is superior compared to that of SF. The inferiority of SF’s filler effect is attributed to the

agglomeration of its fine particles (Figure 9A). As MK particles are relative larger (d50 of

5.40 pm, as opposed to SF’s d50 of 0.23 pm), they are not as susceptible to

agglomeration, and, therefore, are able to offer larger proportions of their surfaces for the

nucleation and growth of C-S-H.

Going back to Figure 9B, it can be seen that at higher MK replacement levels

(i.e., >20%), the values of Nnuc in [C3 S + MK] pastes decline, and remain consistently

lower than [C3 S + SF] pastes. This reversal in the role of MK on C3 S’s hydration behavior—between low and high replacement levels—can also be observed in the

experimental results shown in Figure 4B and C. The decline in Nnuc at higher MK 46 replacement levels is simply a manifestation of the diminishment of reactive surface area of MK particles (Figure 9A). As stated previously, in pastes with higher MK content

(and, consequently, larger concentrations of aluminate ions in the solution), the excess aluminate ions, that remained adsorbed on MK surfaces beyond the induction period, inhibit the topographical sites for C-S-H nucleation, and thus results in reduced number of product nuclei. It is worth pointing out that while the reactive surface area (aP oz ) of both SF and MK are reduced at high replacement levels—due to agglomeration in the case of SF, and due to aluminate ion adsorption in the case of MK—the overall filler effect of SF is superior (Figures 9B and 4B-C). Although the reasons for this are not fully clear, it is speculated that the effects of aluminate ion adsorption are comparatively more severe (than the effects of agglomerations), resulting in near complete inhibition of nucleation sites of MK surfaces (see Figure 9A).

Lastly, the variations in the outward growth rate of the product [Gout (f)], as obtained from the pBNG simulations, are shown in Figure 10. As shown, the product grows at rates that decrease nonlinearly by about 2 orders of magnitude over the course of C3S hydration within the first 24 hours. This functional form of the growth rate has been reported5 (51,70), to mimic the evolving supersaturation of C-S-H in the solution.

At early ages, when C-S-H supersaturation is high, the driving force for C-S-H’s growth is large, thus resulting in higher growth rates. At later ages, when C-S-H supersaturation is low, its growth occurs at a slower rate. It is noted that at any given age, in [C3S + SF] pastes, Gout increases with increasing SF replacement levels (Figure 10A).

However, in [C3S + MK] pastes, the trends in Gout observed at early ages are not retained at later ages (Figure 10B). To better understand these trends, the values of Gout were 47 extracted at different times, that is, at the main hydration peak (at an early age) and at t =

24 hours (at a later age), and plotted against the replacement level of the pozzolan (Figure

11). As can be seen in Figure 11A, at early ages, Gout in [C3S + MK] pastes in consistently lower than in [C3S + SF] pastes.

Figure 10. The outward growth rate of the product (Gout), as obtained from pBNG simulations, as a function of the time, for: (A), [C3S + SF] pastes, and (B), [C3S + MK] pastes. MK, metakaolin; SF, silica fume

While the exact mechanisms for this are not understood, it is hypothesized that the excess aluminate ions, released from the dissolution of MK and present in the solution

(i.e., not adsorbed onto substrates’ surfaces during the induction period), adsorb onto C-

S-H and, subsequently cut off their access to the contiguous solution, thus resulting in inhibition of its growth rate (88,89). As SF does not contain any aluminum, it does not exert such inhibiting effects. Instead, the release of H2SiO42"/H3SiO4 ions from the dissolution of SF is expected to bolster the local supersaturation, and, thus, the growth of

C-S-H in proximity to the SF; this manifests as small increments in the product growth 48 rates with increasing SF replacement levels (Figure 11A). At later ages when the supersaturation of C-S-H in the solution is low, it is expected that these effects of ion- release from the pozzolans’ dissolution, on the growth rate becomes less pronounced. As such, Gout converges to similar values regardless of the type or content of the pozzolan

(Figure 11B). Overall, the results from the simulations, in conjunction with those obtained from experiments, show that in cementitious environments—and within the first

24 hours of hydration—the role of SF is that of a filler with negligible pozzolanic activity. MK, which has limited pozzolanic activity in the first 24 hours of hydration, also acts a filler with superior filler effect compared to SF, but only when present at low replacement levels (i.e. <1 0 %).

Mass Replacement ( (A) Figure 11. The outward growth rate of the product (Gout), as obtained from pBNG simulations, (A), at the main hydration peak, and (B), at t = 24 hours in plain and blended pastes. MK, metakaolin; SF, silica fume

At high MK replacement levels, the aluminate ions, released from the dissolution of MK into the solution act to diminish the filler effect of MK; this is because of 49 inhibition of C-S-H nucleation sites on MK surfaces as well as the suppression of the

(post nucleation) growth of C-S-H. On the bases of the results it can be said that at low replacement levels, MK is a better replacement agent for cement than SF due to its superior filler and pozzolanic effects. At high replacement levels, although the pozzolanic activity of MK is still superior, SF would serve as the better replacement agent.

7. SUMMARY AND CONCLUSIONS

A series of experiments and pBNG simulations were applied to elucidate the role of 2 widely used pozzolanic mineral additives, i.e., silica fume (SF) and metakaolin

(MK), on early age hydration kinetics of tricalcium silicate (C3S). Focus was given to describe and contrast the filler and pozzolanic effects of SF and MK over the course of 24 hours of hydration. Results show that SF enhances hydration of C3S in relation to its content in the paste. These reactivity improvements are linked to the provision of product nucleation sites on the extra surface area provided by SF. However, due to the agglomeration of SF particles, which becomes progressively dominant with increasing SF contents, up to 97% of its surface is unavailable for reaction. The effects of particle agglomeration—along with the slow intrinsic dissolution kinetics of SF—act to diminish the pozzolanic activity of SF and render it negligible within the first 24 hours of hydration. As such, the pozzolanic activity of SF imparts negligible contribution on the nucleation and growth process, as well as hydration kinetics of C3S at early ages.

The combination of experimental results and simulations show that, like SF, MK is also able to enhance C3S hydration rates as a filler, but only when present at low 50 replacement levels (i.e., <10%). At such low replacements, as MK particles are not as susceptible to agglomeration as SF particles, the filler effect of MK is superior than that of SF, leading to enhanced formation of the product. However, at high replacement levels, the aluminate [Al(OH)4 ] ions—released from the dissolution of MK into the solution—inhibit C-S-H nucleation sites on MK surfaces and suppress the subsequent growth of C-S-H, thus diminishing the filler effect of MK. This results in lower rate/amount of C-S-H precipitation in [C3S + MK] pastes as compared to their SF counterparts. Furthermore, the results show that across all replacement levels MK is superior pozzolan as compared to SF. However, within the first 24 hours, the pozzolanic activity of MK is limited, and, thus, does not affect C3S hydration behavior in a significant way.

Overall, the outcomes of the work provide mechanistic insights into the origins of filler and pozzolanic effects of SF and MK. The discussion provides a better understanding on the changes (or lack thereof) in the filler effect of these materials in relation to their content in the system, and highlight aspects that need further investigation. Such knowledge is expected to aid in the design of sustainable cementitious binders, prepared by partially replacing cement with pozzolanic materials.

ACKNOWLEDGEMENTS

This research was conducted in the Materials Research Center (MRC) at Missouri

S&T. The authors gratefully acknowledge the financial support that has made these laboratories and their operations possible. Funding for this research was provided by the 51

National Science Foundation (NSF, CMMI: 1661609), Materials Research Center (MRC)

at Missouri S&T (MRC Young Investigator Seed Funding), and University of Missouri

Research Board (UMRB).

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II. ELUCIDATING THE EFFECT OF WATER-TO-CEMENT RATIO ON THE HYDRATION MECHANISMS OF CEMENT

Aida Margarita Ley-Hernandez*, Jonathan Lapeyre§, Rachel Cook§, Aditya Kumar§, and Dimitri Feys*

^Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409

*Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO 65409

ABSTRACT

The hydration of cement is often modeled as a phase boundary nucleation and growth (pBNG) process. Classical pBNG models, based on the use of isotropic and constant growth rate of the main hydrate, that is, calcium - silicate - hydrate (C-S-H), are unable to explain the lack of any significant effect of the water-to-cement (w/c) ratio on the hydration kinetics of cement. This paper presents a modified form of the pBNG model, in which the anisotropic growth of C-S-H is allowed to vary in relation to the nonlinear evolution of its supersaturation in solution. Results show that once the supercritical C-S-H nuclei form, their growth remains confined within a region in proximity to the cement particles. This is hypothesized to be a manifestation of the sedimentation of cement particles, which imposes a space constraint for C-S-H growth.

In paste wherein the sedimentation of cement particles is disrupted, the hydration kinetics are no longer unresponsive to changes in w/c. Unlike C-S-H, the ions in solution are not confined, and hence the supersaturation-dependent growth rate of C-S-H diminishes monotonically with increasing w/c. Overall, the outcomes of this work highlight 60 important aspects that need to be considered in employing pBNG models for simulating hydration of cement-based systems.

1. INTRODUCTION

The reaction between cement and water, that is, hydration, involves dissolution of the anhydrous phases concomitant with precipitation of the hydration products

(subsequently referred to as hydrates). Extensive research has been devoted to study the kinetic of cement hydration, as it principally dictates the development of the microstructure and the consequent evolution of both fresh (e.g., workability and time of set) and hardened properties (e.g., the rate/extent of strength development) of concrete (1

3). It is widely accepted (1,2,4-6) that the early stage of cement hydration is driven by the nucleation and growth (7-10) of the main hydration product, that is, calcium - silicate - hydrate (1,5,11-13) (C-S-H, as per cement chemistry notation: C = CaO, S = SiO2, H =

H2O, A = Al2O3, and F = Fe2O3); although, it is worth mentioning that in some studies,

(14,15) it has been argued that kinetics of cement hydration is controlled by dissolution of the phases present in cement. In a typical plain cement paste (i.e., cement + water), C-

S-H nucleates heterogeneously on the solid-phase boundaries, that is, surfaces of cement particles, and therefore, the mechanism of its formation is usually termed as phase boundary nucleation and growth (pBNG). As hydration progresses, the percolation of the overlapping layers of C-S-H binds the paste cohesively and leads to setting and subsequent development of mechanical properties (5,11,16,17). Akin to pBNG processes occurring in metallic systems (e.g., solidification of metal) (18,19), the temporal 61 evolution of cement hydration rate as monitored using isothermal calorimetry techniques, comprises a comprises a characteristic reaction rate peak (i.e., the main hydration peak) up to which the rate of reaction accelerates and beyond which it declines (1,13).

Several numerical models based on the pBNG mechanism have been developed to reproduce the experimental measurements of cement hydration rates (5,6,11,12,16,20,21.

In these models, a single product of constant density is assumed to form heterogeneously on solid phase boundaries at a given nucleation event, and its subsequent growth into the contiguous capillary pore space is treated as the rate-controlling mechanism. As the product fills up the capillary pore space, impingements between product nuclei, growing on the same or adjacent anhydrous particles, becoming increasingly dominant and ultimately cause a deceleration in the overall hydration rate. Numerical models, based on this premise and some additional assumptions (e.g., spherical or needlelike geometry of the product, diffusion-limited kinetics at later ages, and time-dependent growth of C-S-

H) have successfully been used to fit the hydration rates of cementitious systems

(5,6,12,16,20-24). These fits are typically obtained by iteratively varying relevant pBNG parameters (e.g., nucleation site frequency and product growth rate) to minimize the deviation between numerical and experimental hydration rates. However, as pointed out

(6,22,25), the parameters derived from such a fitting can be misleading as some underlying assumptions of the classical pBNG mechanism do not necessarily represent the physics of C-S-H nucleation and growth accurately. More specifically, the assumptions of (i) isotropic (i.e., spherical) growth of the product does not represent the experimentally observed needlelike geometry of C-S-H growth at early ages (26-28), (ii) the constant rate of product growth does not comply with the time-dependent variation of 62 its supersaturation in the solution (13,22,27,29,30), and (iii) unconstrained formation of the product throughout the capillary pore space fails to explain the lack of any significant effect of the water-to-cement ratio ( w/c mass basis) on the hydration kinetics of cement

(16,31,32). The last point is the main focus of this study and is described in further detail below. Past studies (12,16,31) have shown that the early age (i.e., up to 24 h) hydration kinetics of cement are broadly unaffected by the w/c of the system. However, in pBNG models, (6,16,25,32) an increase in w/c implies a decrease in the area of the substrate per unit volume of the paste, which in turn affects the rate of formation of C-S-H and thus the overall hydration kinetics. Specifically, with increasing w/c, whereas impingements between C-S-H nuclei growing on the same particle remain broadly unaffected (i.e., assuming the same nucleation density of C-S-H_, impingements between C-S-H layers growing on adjacent cement particles are fewer because of larger spacing between them.

As a result, pBNG models predict a dependency of the hydration rate on w/c, unlike what is observed in experiments (12,16,31). These contradictions between experimentally observed hydration rates and predictions of the pBNG model, including ones that involve the implementation of the nucleation and densifying growth theory (i.e., time-dependent densification of C-S-H) (5,16,33), are highlighted in the work of Kirby and Biernacki

(31). In a recent study, Masoero et al. (34) purposed a reaction zone hypothesis to reconcile the aforementioned contradictions. The authors proposed that during the early hydration period, C-S-H grows exclusively within regions close to surfaces of the reactant particles; these regions collectively were designated as the reaction zone. Within the reaction zone, as the amount of C-S-H increases with hydration, growing impingements between C-S-H nuclei causes deceleration of the hydration rate, all while 63

abundant capillary pore space remains unoccupied outside of the reaction zone. The

hypothesis provides novel and significant insights and, more importantly, explains the

mechanisms driving the deceleration of the hydration rate beyond the main hydration

peak in high w/c systems. However, the assumption of the growth rate of C-S-H being

constant throughout the process of hydration, as used in the study (34), is inconsistent

with recent studies that clearly show a temporal decline of C-S-H supersaturation (i.e.,

driving force of the growth of C-S-H) in solution (22,27,29,30). In addition, Masoero et

al. (34) assumed the growth of C-S-H to occur at equivalent rates in all directions. This

assumption has implications not just on the geometry of C-S-H nuclei but also on the

overall rate of hydration. Scherer et al. (6,28) noted that at early stages of cement

hydration, the growth of C-S-H occurs in a highly anisotropic manner. Specifically, the

growth rate of C-S-H in the direction normal to and away from the substrate is higher

than its growth rate in the direction parallel to the substrate. This theory of anisotropic

growth of C-S-H gains support from recent microscopic observation of the geometry of

C-S-H growth (26-28). Assuming isotropic growth of C-S-H also results in greater

impingements of its nuclei and, thus, a faster approach to the main hydration peak (6,25).

As a result of these discrepancies between experiments and assumptions made within the

model presented in ref 43, the pBNG parameters derived from the simulations are

difficult to interpret. As examples, the predictions of (i) significantly higher nucleation

density of C-S-H in C3S (i.e., tricalcium silicate, the major phase in cement constituting

50-70% of its mass (3)) suspensions (i.e., w/c = 50) as compared to that in pastes (i.e., w/c = 0.40) (34) are difficult to reconcile considering that the critical supersaturation at which nucleation of C-S-H occurs should be independent of the w/c, (5,22,35) and (ii) 64

the smaller size of the reaction zone in suspensions as compared to that in pastes (43) is

counterintuitive, considering that the capillary pore space increases with increasing w/c,

thus allowing C-S-H to grow more freely. To resolve these inconsistencies and to better

explain the role of w/c on the mechanisms of cement hydration, further refinement of the

pBNG model is needed. Such refinements need to be based on observations from

experiments reported in various recent studies (26,27).

This study employs a combination of experiments and computer simulation to

elucidate the effect of w/c on the early age hydration kinetics of cement. Isothermal

microcalorimetry is used to measure the hydration rates of cementitious systems across a

wide range of w/c, including both pastes and suspensions. A pBNG model, incorporating

a modification of the reaction zone hypothesis and allowing anisotropic and time-

dependent growth rate of the hydrate, is developed, and tested against experiments.

Results obtained are used to describe the mechanisms that drive the progress of

nucleation and growth of the C-S-H in such systems. The outcomes provide new understanding and quantification of rate controls of cement hydration and highlight

important aspects pertaining to pBNG processes that need to be considered in the

development of numerical pBNG models.

2. MATERIALS AND METHODS

A commercially available type I ordinary Portland cement with an estimated

crystalline phase composition of 61% C3S, 8% C2S, 6% C3A, 9% C4AF and 3.4% of

gypsum (CaSO4*2H2O) was used in this study. Further details pertaining to the chemical 65 composition of the cement—as obtained using a combination of X-ray fluorescence and quantitative X-ray diffraction (XRD) methods—are provided in the Appendix B. The cement, as received from the supplier was ground using a ring grinder to generate two different PSDs. In the subsequent discussions, the “as-received” and ground cements are referred to as coarse and fine cements, respectively. The PSDs of the cements, shown in

Figure 1, were measured using a Beckman Coulter static light scattering (SLS) analyzer

(LS13-320) using a 750 nm laser source that is incident on a dilute suspension of powder particles in isopropyl alcohol, dispersed by ultrasonication. The median particle sizes

(d50, pm) of the PSDs of the coarse and fine cements were determined as 15.55 and 9.23 pm, respectively. By factoring the bulk density (i.e., 31350 kg m-3, as measured sing a pycnometer), the total SSA (m2 kg-1) of the coarse and fine cements were calculated from the PSDs as 196 and 441 m2 kg-1, respectively. XRD patterns were obtained for the coarse and fine cements, and based on the results, it was confirmed that there was no change in the cement’s composition as a result of grinding. To study the effects of the water content, cement + water mixtures were prepared at different w/c (mass basis) ranging from 0.45 to 10. Low and high w/c cementitious mixtures are typically described as paste and suspension, respectively. However, as the limiting w/c beyond which mixtures ceases to be a paste (or becomes a suspension) is not well-known in this paper, all mixtures are referred to as pastes. It should be noted that all pastes included in this study are water-rich as their w/c exceeds the critical value of 0.45 (i.e., minimum w/c needed for complete hydration of cement (54,55)). 66

Figure 1. PSDs of the “as-received” (coarse) and ground (fine) cements measured using SLS methods. The largest uncertainty in the median diameter (d5o, gm) of the powders based on six replicate measurements was ±6 %.

The rate and extent of hydration were monitored up to 24 h after mixing using a

TAM IV isothermal conduction microcalorimeter programmed to maintain the sample at a constant temperature of 20°C ± 0.1°C. Compared to conventional methods of reactivity assessment (e.g., isothermal calorimetry), microcalorimetry methods are considered more accurate as they allow quantification of the heat flow rate of the reaction at a very high resolution (10-7 J s-1), which enables monitoring the dissolution of compounds even at high dilutions (13,73,74). The titration cell (maximum diameter = 1.25 cm) of the microcalorimeter is fitted with an electrically driven agitator, which allows in situ mixing of hydrating pastes prepared at high w/c. However, with the exception of selected experiments (which are identified in the text), heat evolution profiles of all pastes discussed in this paper were obtained without the use of the agitator. In situ mixing was purposely avoided for two reasons: (i) to mimic practical concrete mixing protocols, which are also devoid of in situ mixing and (ii) to maintain consistent protocols across 67 experiments, as in situ mixing cannot be applied to low w/c pastes. The cumulative and differential heat release obtained from calorimetry experiments were normalized by the enthalpy of cement hydration (as calculated from mass fractions and enthalpy of individual phases (5)), 472 J gCement-1, to determine the extent of hydration (13,16) (i.e., degree of hydration, a , expressed as the fraction of cement reacted) and the rate of hydration (i.e., da/dt, h-1) of cement respectively, as function of time. This method of derivation of a and da/dt is based on the assumption that the measured heat release is solely on account of cement hydration. In addition to monitoring the evolution of heat linked to hydration, the evolutions of the electrical conductivity and pH of the pore solution of the pastes were measured at discrete time steps between mixing and 48 h of hydration. These measurements were carried out using a HI5522 electric conductivity and pH meter with the HI76312 and HI1131 probes, respectively. Samples used for these measurements were prepared using the same protocols as those for calorimetry experiments.

A Netzsch STA 409 PC thermogravimetric analyzer was used to identify and measure the quantities of phases present at different hydration times. Toward this, the mass loss (thermogravimetry) and the differential mass loss (DTG) traces were processed to quantify the degree of hydration and phase contents, that is, loss on ignition, evaporable and nonevaporable water, portlandite, and calcite (if any may have formed because of carbonation of calcium-rich phases). For these quantifications (i.e., a and phase contents), well-established methods detailed in prior studies (51,75) were used. 68

3. pBNG MODEL

A modified pBNG formulation is applied to describe the effects of w/c on the hydration kinetics of cement. The cement used in our study is composed of four phases

(C3S, C2S, C3A, and C4AF), all of which react with water simultaneously, though at different rates (1). C2S and C4AF have low intrinsic dissolution rates and, hence, do not release substantial amounts of heat at early ages (1,6,14). In contrast to these phases, the reaction of C3A with water and aqueous SO42- ions (i.e., resulting from the dissolution of gypsum) is rapid; this causes nucleation of ettringite crystals within the first few minutes of mixing (36,37). Nonetheless, after the initial nucleation burst, ettringite subsequently grows at a very slow (and near constant) rate for the next few hours, thus releasing little heat (36,38) As such, in pBNG models applied to cement pastes (6,11,12,16,25,39) including the model used herein, early age kinetics of cement hydration is assumed to be dominated by the hydration of C3S phase. The same assumption implies that during the early stages of cement hydration, the major products in the cement paste are C-S-H and

CH, both of which form in stoichiometric amounts in relation to the amount of hydrated

C3S. On the basis of these assumptions, in pBNG models, a single product of constant density (i.e., combining the bulk density of CH and C-S-H phases) is assumed to form at a given nucleation event, and its subsequent growth on solid-phase substrate boundaries

(i.e., cement surfaces) is treated as the rate-controlling mechanism that drives the kinetics during the early ages of cement hydration. This assumption is referred to as the site saturation condition, implying that the growth of the product phase begins from a fixed number of nuclei that form at very early ages (i.e., at time = t h), and no further nuclei are 69 permitted to form after this very initial nucleation burst (40,41) (i.e., nucleation rate = 0 pm -2 h-1). On the basis of these criteria, at any given time t (h), the volume fraction of the reactants (i.e., C3S and water) transformed to product (X(t), unitless: volume of product divided by the total initial volume of the paste) is given by Equation 1 (13,22,25,35,42)

FD[K (t-T )T X(t) = 1 — exp -2kG • (t — t) • ( 1 (1) ks(t — t) where,

Fd(x) = exp(—x2) exp(y 2) dy (2 ) l 1

In Equation 1, F d is the f-Dawson function, expressed as an integral (Equation 2).

The variable ks (h-1) is related to the reciprocal of time required by the product nuclei to provide complete coverage of anhydrous cement particles (6,25). The value of ks depends on the product’s nucleation density (/desnity, units of pm-2), that is, the number of total supercritical nuclei produced per unit surface area of cement as well as on the geometry and rate of their growth (Equation 3). In the model presented in this study, the growth of the product is assumed to occur in an anisotropic fashion while varying with respect to time. Gout(t) (pm h-1) is the growth rate in a lateral direction that is, along the two dimensional (2D) plane parallel to the boundary of the substrate. Along this 2D plane, the growth rate is assumed to be isotropic. The introduction of a time dependency on the product growth rate is a digression from the classical form of pBNG, which assumes the growth rate to remain constant throughout the hydration process. This is based on an implementation originally formulated by Bullard et al. (22) and subsequently adopted by

Oey et al. (35), Meng et al. (13), and Lapeyre and Kumar (42) to capture the temporal variation in the growth rate of C-S-H, as its supersaturation in the solution varies 70

nonlinearly with time. As both the outward (Gout) and parallel (Gpar) growth rates vary

with time, a constant 2 :1 ratio for Gout/Gpar is assumed, such that the anisotropy factor, that is, g (unitless) in Equation 4, is 0.25 throughout the hydration process. This

relationship between Gout and Gpar represents the anisotropic growth of needlelike

domains of the product (6,25) and is in good agreement with recent experimental data of the geometry of C-S-H growth at early ages (26-28, 30).

i (3) k-s = ^out(0(^5^density)2

2 ^par( 0 (4) 9 = ^out(0 /

In Equation 1, the variable ko (h-1) is related to the reciprocal of time required for the product to fill the capillary pore space. The value of kG depends on the product’s

outward growth rate (Gout) as well as on the constant m (unitless), which represents the

ratio for the growth rate into and out of the substrate in the normal direction (Equation 5).

In their study, Scherer et al. (6,25) noted that at early ages of hydration, hydrates do not

penetrate the cement particles, and therefore, m ~ 0.50. This is because at early ages, the

ionic species, that is, H3SiO4 /H2SiO42-, C-S-H transport predominantly from the

substrate’s surface toward the contiguous solution while showing l8 ittle movement

through the product in the reverse direction (6 ). Therefore, in all simulations presented in

this study, the value of m was assumed to be constant at 0.50. Another important

parameter that dictates the value of kG, and thus the kinetics of hydration, is the boundary

area of the substrate per unit volume of the reaction vessel («bv, pm-1) (Equations 5 and

6 ). Here, the area of the substrate is simply the initial total surface area of the cement 71

particles. The definition of the reaction vessel, however, differs among different studies.

Thomas (12) defined the reaction vessel as the space required by hydrates when the

hydration of cement is complete (i.e., a = 1), thus rendering the volume of the reaction vessel, and consequently aBV, independent of the w/c ratio. As per this definition, the

reaction vessel’s volume is set at its minimum value, just enough to accommodate the

hydrates. In several subsequent studies (5,6,13,25,32,35), however, the reaction vessel’s volume was set as its maximum allowable value, that is, equal to the volume of the paste.

On the basis of this definition, aBV changes in response to changes in w/c, and the

implication is that the hydrates are allowed to grow throughout the capillary pore space until either it is fully occupied or the hydration of cement is complete. As different

definition of aBV exist in the literature, in this study, a modified definition has been used that allows the volume of the reaction vessel to vary between the minimum and

maximum allowable values (Equation 6 ). In Equation 6 , p is the density (water = 1000 kg

m-3 and cement = 3150 kg m-3) and SSAcem (m2 kg-1) is the specific surface area of

cement particles. The parameter pf (unitless) acts as a free variable used in the

simulations to represent the reactive paste fraction, that is, the fraction of the paste’s

volume within which the formation of hydrates occurs. When pf (unitless) acts as a free

variable used in the simulation to represent the reactive paste fraction, that is, the fraction

of the paste’s volume within which the formation of hydrates occurs. When pf = 1, the

entire volume of the paste acts as the reaction vessel, whereas for fractional values of pf,

the volume of the reaction vessel is smaller than that of the paste. In such cases (i.e., pf <

1), the amount of water contained within the reaction vessel is smaller than that of the

paste. In such cases (i.e., pf < 1), the amount of water contained within the reaction vessel 72

is smaller than the amount of water added to the paste, though all of the solid phases (i.e.,

anhydrous cement particles and hydrates) are assumed to be bounded within the reaction

vessel. By accounting for the excess water (i.e., water outside of the reaction vessel), the w/c ratio of the reaction vessel (w/crv, by mass) can be calculated from Equation 7.

(5) k-G = rG^out(f)aBV

SSAr aBV w (6) 1 c + ■ Pw ater Pcement Pf

w w Pwater , (7) — =Pf~------( 1 - Pf) c RV c '-Pcement

The volume fraction of the product X(t), as calculated from Equation 1, and the

degree of hydration (a, unitless) of cement are related by a constant B (unitless) (13,22,35

described in Equation 8 a. Where, ^products is the bulk density of combined hydration

products (assumed to be 2070 kg m-3) (43,44), and the parameter c = -7.04 x 10"5 m3 kg-1

represents the chemical shrinkage per kilogram of cement that is consumed over the

course of its hydration (45).

a(t) = B X(t) (8 a)

-1 ( Pcement \ 1 1 C + Pproducts (8 b) B = Pcement Pwater | W_ 1______I Pcement ------+ 1 \ Pproducts Pwater / Pwater

On the basis of the scheme described above, measured hydration rates can be

simulated using the pBNG model by varying three parameters: Gout (t), /density, andpt. Of 73

the three parameters, /density and pt are constants with respect to time, whereas Gout(t) varies with respect to time. Therefore, to obtain the optimum values (i.e., of /density and pf)

or functional forms (i.e., of Gout(t)) of these parameters for a given system, a Nelder-

Mead-based simplex algorithm (35,46,47) that uses derivative-free and nonlinear

optimization principles is employed in two steps. In the first step, the value of Gout is kept

constant throughout the 24 h of cement hydration and fixed at 0.075 pm h'1 for all

systems. Similar values of Gout have been reported in a prior study (26) based on

scanning transmission electron microscopy (STEM) analyses of early age hydration of

impure C3S. The simplex algorithm then iteratively varies /density and pf, within predefined bounds (i.e., 0.1 pm'2 < /density < 1000 pm"2, and 0.0 < pf < 1.0), until the magnitude of the

difference between the simulated and measured rates of product formation-expressed as

dX/dt, or the derivative of Equation 1-for each paste is minimized. It is pointed out that within the first step, the model represents the classical pBNG formulation (12), wherein the anisotropic growth of the product nucleating at virtual time t (h) is kept constant throughout the hydration process. Past studies (12,22,35,42), however, have shown that

such classical pBNG models are unable to capture the decline in the growth rate of the

product as its supersaturation in the solution decline with time. Therefore, to account for the time-dependent variation in the growth rate, a second simulation step is employed.

Here, at any given time t, the optimum values of /density and pf yielded from the first step

are used as constants, whereas Gout is allowed to vary iteratively within the bounds of 10"

4-to-102 pm h"1 to minimize the deviation between the simulated and measured hydration

rates (expressed as da/dt or derivative of Equation 8a) for each paste. When the simplex

algorithm converges, the value of Gout, obtained as such, mimics the growth of the 74 product in relation to its supersaturation in the solution (13,22,35,42) as described in the

Section 4.

4. RESULTS AND DISCUSSION

To study the effect of w/c on the hydration mechanisms of cement, the kinetics of hydration of two different particle size distributions (PSDs: see Figure 1) of the same cement (i.e., of the same composition) were determined. Figure 2 shows representative heat evolution profiles of pastes prepared using the coarse cement at different w/c ratios.

As can be seen despite significant differences in water contents (i.e., 58.64 and 96.93%vol of water in pastes prepared at w/c of 0.45 and 10, respectively), the kinetics and degree of cement hydration within the first 24 h are broadly similar across all pastes. The lack of any significant effect of w/c was also observed for pastes prepared with the fine cement

(Figure 3). These results are in good agreement with those reported in prior studies

(12,16,31). Upon comparing the heat evolution profiles of pastes prepared with fine and coarse cements, faster hydration kinetics was noted for the former (Figure 3C). This enhancement in hydration of the fine cement is highlighted as the leftward shift of the heat evolution profile and a higher heat flow rate at the main hydration peak and can be attributed to the higher SSA of its particles (5,48-50), which enhances the number density of topological dissolution sites as well as sites for heterogeneous nucleation of hydrates. It should be pointed out that these enhancements in hydration rates of the fine cement are smaller in relation to the augmentation in the SSA of its particles with respect to those of the coarse cement (e.g., 72% increment in the heat flow rate at the peak vis-a 75

vis 125% increment in SSA). This suggest a nonlinear relationship between reactivity

enhancements and surface area increments.

On the basis of these results as well as those reported in prior studies (13,16, 50),

it is hypothesized that improvements in reactivity are realizable only up to a threshold

level of particulate fineness. Beyond this threshold, reactivity enhancements decline due

to agglomeration of the finer particles, which renders a fraction of their surface area

unavailable for reaction (13,16,50). It is clarified however, that the aforementioned loss

in the surface area is not responsible for the apparent insensitivity to w/c. Figures 2 and 3

qualitatively show the influence of w/c and cement fineness on the hydration kinetics of

cement. To obtain quantitative information, portlandite contents of the pastes and the

degree of hydration of cement after 24 h of hydration were determined using differential thermogravimetry (DTG) (51) and calorimetry methods (Figure 4). 76

As can be seen, across all w/c, portlandite contents are broadly similar, provided that the fineness of the cement does not change. Paste prepared with the finer cement have higher portlandite contents compared to their coarser cement counterparts. This is attributed to the higher degree of hydration of the finer cement (Figure 4B). Past studies, based on microstructural investigation (34,52,53) have shown that the precipitation of portlandite occurs homogenously in the capillary pore space. However, the equivalency in portlandite contents across pastes prepared at different w/c ratios suggests that the rate controlling factor for the precipitation of portlandite is not the volume of capillary pores, but rather the rate of cement hydration, which, in turn, is driven by the nucleation and growth of C-S-H. The heat evolution profiles (Figure 2 and 3) and the results obtained from DTG analyses (Figure 4) show that the rates of cement hydration and C-S-H precipitation are independent of the w/c and, therefore, the availability of space in the microstructural volume (i.e., capillary pore space). 77

Figure 4. (A) Portlandite mass contents (as mass percent of the binder) and (B) degree of hydration of cement (a) after 24 h of hydration in pastes prepared at different w/c, as determined from DTG analyses. (C) Comparison between a calculated from microcalorimetry and DTG methods. The dashed lines represent ±2.5% bounds. The highest uncertainty in phase quantifications or determination of a by DTG methods is ±2.5%.

To quantify the evolution of the unoccupied space in the microstructure (i.e.,

capillary porosity) as a function of the degree of hydration of cement, the Powers model

(54,55) was used. The results obtained from the Powers model (Figure 5A) clearly show

that at the degree of hydration corresponding to the time of occurrence of the main

hydration peak (i.e., a = 0.13, obtained by averaging values of a determined from

calorimetry profiles of pastes prepared using the coarse cement at different w/c ratios), there is plenty of space available in the microstructural volume, even in pastes prepared

at low w/c. For example, in pastes prepared at w/c of 0.45 and 10, capillary pores

comprise of 52.1% and 96.3% of the paste’s volume, when a = 0.13. The decline in the

hydration in the hydration rate, after the main hydration peak, in spite of the abundance in

space cannot be explained solely on account of impingements between C-S-H nuclei

growing on cement particle surfaces. To illustrate this point, virtual microstructures of

pastes generated by a three-dimensional (3D) microstructural model (5,16,33,42,56-59) 78

are shown (Figure 5B, 5C). In these simulations, C-S-H and other hydrates (e.g.,

portlandite), precipitating as a result of cement hydration, are allowed to grow

heterogeneously on cement particles surfaces and homogeneously in the pore space,

respectively. Further details pertaining to the generation of virtual microstructures can be

found in the Appendix B. As can be seen in Figure 5B and 5C, at the main hydration

peak, although C-S-H nuclei provide partial coverage of the cement particles,

impingements between C-S-H layers growing on neighboring particles are insignificant,

especially in high w/c pastes. Therefore, mechanisms other than the impingements

between C-S-H nuclei are responsible for deceleration of the hydration rate of cement in

pastes.To further investigate the role of w/c on cement hydration, measured hydration

rates of pastes were simulated using the pBNG model. As can be seen in Figure 6 ,

through the evaluation of optimum values of the outward growth rate of the product

(Gout(O), the product nucleation density (/density), and the reactive fraction of the paste (pf),

the model is able to reproduce the experimental results. The variations in these simulation

parameters are analyzed below to describe the alterations in the nucleation and growth

process in relation to the initial process parameters, that is, w/c and cement fineness. As

stated previously, within the pBNG framework, simulations are employed in two steps. In the first step, optimum values of /density and pf are determined, and in the second step, the

optimum function forms of Gout (t) is determined. On the basis of the optimizations, it was found that /density is 3.50 ± 0.08 pm"2 for all pastes, regardless of the w/c ratio and the

SSA of cement. This value of /density is within the same order of magnitude of values

reported in previous studies involving pBNG simulations of cement"based systems 79

(6,13,16,34,35) as well as those determined from STEM analyses of early age hydration

of impure C3 S (26).

Degree of Hydration, a (Fraction) (A) (B) (C) Figure 5. (A) Correlation between capillary porosity and degree of hydration (a) in pastes prepared at different w/c. In these calculations, a is provided as an input, and the corresponding capillary porosity is calculated based on the phase assemblages predicted by the Powers model.(54,55) The solid vertical line indicates the average value of a of all pastes, prepared using the coarse cement at the main hydration peak. 3D virtual microstructures of cement pastes prepared using the coarse cement at (B) w/c = 0.45 and (C) w/c = 10 when a = 0.13 (i.e., at the main hydration peak). The anhydrous cement particles (red) are packed as randomly dispersed spheres within the cubic representative elementary volume (size = 100 gm3). As cement reacts with water, C-S-H (blue) and other hydrates (green) are allowed to grow heterogeneously on cement surfaces and homogeneously in the pore space, respectively. See the Supporting Information (section B) for further details pertaining to the simulations.

Minor differences in value of /density between this study and those derived from

other pBNG models (6,16,16,34,35) can be attributed to multiple factors including

differences in the cement composition and assumptions involving the nature of growth of

the product (6 ) (e.g., anisotropy factor). As examples, in the simulations presented in this

study, (i) changing the value of m from 0.5 (i.e., penetration of hydrate into the substrate

grain is not permitted) to 1 .0 (i.e., penetration of hydrate into the substrate is permitted) would necessitate a decrease in /density (6,25) from ~ 3.50 to ~ 1.62 gm-2 and (ii) 80

increasing the anisotropy factor (g) from 0.25 to 1.0 would enhance the probability of

lateral impingements between C-S-H nuclei (6 ), and, thus, require a reduction in /density

from ~ 3.50 to ~ 0.87 pm-2.

Figure 6 . Representative set of simulated and measured hydration rates (da/dt) of cement in pastes prepared at different w/c. The red dashed line represents the final output from the simulations, wherein Gout is allowed to vary with time

However, regardless of the choice of these parameters, measured hydration rates

of all pastes presented in this study could be fitted using a unique value of /density. This

equivalency in the value of /density across all pastes is expected because when water is

abundant, as it is during the first 24 h of hydration, the critical supersaturation at which

nucleation of C-S-H occurs should be about the same and, thus, independent of the

amount of water present in the system or the SSA of the cement particles (35). It should

be noted that at a high w/c, the larger dilution is expected to cause a slight delay in

reaching C-S-H supersaturation. However, because of the intrinsically high dissolution

rate of cement (60) and the very low solubility (i.e., Ksp) of C-S-H (29.44) it is expected that the solution rapidly supersaturates with respect to C-S-H in all pastes regardless of 81 the w/c, and, thus, does not cause significant alterations (e.g., lengthening of the induction period) in the early age hydration behavior (26,39,61-66).

While the product nucleation density was found to be independent of the w/c, significantly changes in the reactive paste fraction (pf) were noted across different pastes

(Figure 7a). As can be seen, pf is unaffected by the cement’s SSA, but decreases broadly in a linear manner with increasing w/c. This implies that as the water content of the paste increases, the formation of C-S-H is confined within smaller volume fractions of the paste. This implies that as the water content of the paste increases, the formation of C-S-

H is confined within smaller volume fraction of the paste. It is pointed out that if simulations are implemented by imposing a constant value of pf (i.e., pf = 1 )—essentially assuming that the entire reaction vessel participates in the nucleation and growth process—the hydration rates of high w/c pastes, as estimated from the pBNG simulations are significantly different (i.e., broader) compared to those obtained from experiments.

This is because at larger values of pf, the enlargement of the reaction vessel ensures larger spacing between the cement particles, which results in fewer impingements between product nuclei growing on neighboring particles; this manifests as a slower approach to the main hydration peak and, more importantly, a slower decline in the hydration rate after the peak. Further details pertaining to the sensitivity of the pBNG simulations with respect to variations in pf and the justification for varying pf are included in the Appendix

B (specifically Figure B3 in Appendix B). In the model used by Masoero et al. (34), it is assumed that the cement particles remain suspended, and the growth of C-S-H occurs in a confined region (i.e., in the semipore space) in proximity to the cement particles. 82

Figure 7. Parameters derived from the simulations: (A) reactive paste fraction (pf) and (B) w/c ratio within the reaction vessel (w/crv) as functions of w/c. (C) Comparison between the average spacing between cement particle surfaces within the reaction vessel (y-axis) vis-a-vis the average spacing between them when they are assumed to remain suspended (x-axis). The dashed lines represent the lines of ideality.

First, in practice, because of the large density difference between cement (i.e.,

3150 kg m-3) and water (i.e., 1000 kg m-3), the sedimentation of cement particles always occurs in pastes (in the absence of viscosity-modifying admixtures or when in situ mixing is not employed), as was also observed in current experiments. Second, the assumption of particles being suspended combined with the confinement of C-S-H, assumed in the model developed by Masoero et al. (34), significantly marginalizes the likelihood of impingement between C-S-H layers growing on different particles, especially at early ages when the degree of hydration is low. This is difficult to reconcile as the setting of the paste (67), which occurs at a low degree of hydration of cement, necessitates such early age impingements between C-S-H layers growing on adjacent cement grains. In contrast to the model presented in reference 34, the pBNG model used in this study does not incorporate any assumption regarding the occurrence, or lack thereof, of sedimentation of cement particles. However, based on the simulation results, which indicate that in higher w/c pastes, the reaction vessel is consistently smaller than the 83 paste’s volume (Figure 7), it is inferred that the sedimentation of cement particles does occur. This inference gains support from experiments, in which the solids (i.e., cement particles and hydrates) were consistently found to be settled at the bottom of the reaction container after 24 h of hydration. This assemblage of cement particles within a fraction of the paste’s volume causes the particles to pack more closely as compared to an equivalent system in which particles remain suspended. To better illustrate the effects of sedimentation of cement particles on particle packing, the 3D microstructural model, described above in references (5, 15, 33, 56-59) was used to generate virtual microstructures for two cases: one in which cement particles remain suspended and the other in which sedimentation occurs. In the former and latter cases, the water contents resemble the original w /c and the w / cr v (determined form pBNG simulations), respectively. Once the sought packing is achieved, the average initial spacing between cement particles surfaces (i.e., interparticle distance) is calculated using algorithms described in reference (8 ). The virtual microstructures generated from the simulations are shown in Figure 8 , and the calculated interparticle distances are shown in Figure 7C. As can be seen, because of the sedimentation of cement particles in high w /c pastes, the interparticle distance within the reaction vessel is reduced to a fraction of the interparticle distance at the time of mixing (i.e., when sedimentation has not occurred). It is also noteworthy that across pastes prepared using the same PSD of cement but at different w /c ratios, the interparticle distances within the reaction vessel remain broadly the same. This is due to the equivalency in the values of w / cr v (Figure 7b) suggests that as cement particles settle, their assemblage and access to water needed for hydration remain broadly the same regardless of the original w /c . In pastes prepared with the fine cement, the 84

interparticle distance within the reaction vessel are smaller (i.e., - 1 .0 pm) as compared to those prepared with the coarse cement (i.e., - 2 .1 pm), although the volumes of the

reaction vessel are equivalent across all pastes. This is attributed to the larger number of

particles (per unit mass) in the fine cement. These interparticle distances, presented in

Figure 7C, are analogous to the size of the reaction zone reported by Masoero et al. (34),

as in both studies, these sizes represent the linearized space within which the growth of

C-S-H occurs and remains confined. In this study, the interparticle distances range between 1.0 and 2.1 pm, whereas in reference 34, the sizes of the reaction zone were

estimated between -0.38 and -1.1 pm. It is reasonable to say that these differences are

small and can be attributed to differences in the schemes (e.g., anisotropy in the growth

of C-S-H) employed in the pBNG simulations as well as the differences in the properties

(i.e., PSD and composition) of the cementing material. The assumption of particles

remaining suspended, as implemented in reference 34, is also expected to alter the

likelihood of impingement between C-S-H nuclei and, thus, contribute to the

aforementioned differences. On the basis of these results, it is hypothesized that the

confinement of C-S-H is a manifestation of the space constraint induced by the close

packing of the settled cement particles within the reaction vessel. Because of the smaller

spacing between cement particles within the reaction vessel, C-S-H layers growing on

adjacent cement particles are able to percolate and cause the paste to set, even when the w/c is relatively high (e.g., w/c = 0.75). In addition to these impingements, the temporal variation in the growth rate of C-S-H (described below), as driven by its supersaturation,

is expected to affect the hydration rates. Figure 9A describes the influence of w/c on the

product growth rate (Gout(0). 85

(A) (B) (C) Figure 8 . 3D virtual microstructures showing the packing of particles at the time of mixing (i.e., without sedimentation of particles) in pastes prepared at (A) w/c = 0.45 and (B) w/c = 10. (C) effects of sedimentation of particles in a paste prepared at w/c = 10. The smaller cubic volume schematically represents the reaction vessel, which includes all of the cement particles but only a fraction of the water. The volumetric content of water in the reaction vessel is derived from w/crv, as calculated from pBNG simulations.

As shown, the product growth grows at rates that decrease nonlinearly by about two orders of magnitude over the course of cement hydration in the first 24 h. This function form of the growth rate has been reported (13, 22, 35)) to mimic the evolving supersaturation of C-S-H in solution, wherein high and low supersaturations imply larger and smaller driving forces for C-S-H growth, respectively. It is noted that at any given time (Figure 9A) or degree of hydration of cement (Figure 9B), Gout decreases with increasing w/c. This is better shown in Figure 10, which plots the growth rates of pastes, extracted at a = 10, 20, and 30% against the w/c. The diminishment of the product growth rate with increasing w/c suggests abatement in the driving force for C-S-H growth in diluted systems.It is hypothesized that in high C-S-H systems, though C-S-H is confined within a smaller fraction of the paste volume (i.e., the reaction vessel), the ions

(29) (i.e., H3 SiO4 / H2 SiO42", CaOH+/Ca2+ and OH ) responsible for the precipitation of

C-S-H are able to transport across the entire paste’s volume. 86

(A) (B) Figure 9. Outward growth rate of the product (Gout) as a function of the (A) time and (B) degree of hydration of the coarse cement.

As such, the supersaturation of C-S-H in the solution and, hence, the driving

force for its growth are sensitive to the paste’s water content and decrease with increasing w/c; this point is described in more detail through experimental results further in the text.

This decrease in C-S-H supersaturation manifests as a systematic diminishment of its

growth rate with increasing w/c (Figures 9 and 10). It is pointed out that, in spite of the

ions being able to move throughout the paste’s volume, it is expected that their

abundance is relatively higher in regions in proximity to their source, that is, cement

particles. While the current simulations do not consider gradients in ion concentrations,

results shown in Figure 10 do support the theory. As can be seen, at equivalent w/c,

growth rates at early ages (i.e., when a = 0 .1 0 ) are higher in pastes prepared with the fine

cement as compared to those prepared with the coarse cement. This is hypothesized to be

on account of smaller spacing between particles (Figure 7C) in pastes prepared with the

fine cement, such that the overlapping (or closely packed) ion-abundant regions around the closely packed particles bolster the driving force for the growth of C-S-H. At later 87 ages, when the supersaturation of C-S-H in the solution is low (22), the effect of interparticle spacing on the growth rate diminishes. This is reflected in Figure 10B, and

10C which show that at higher degrees of cement hydration, growth rates are independent of the spacing between particles (or fineness of the cement). The growth rates shown in

Figure 9 qualitatively allude to the temporal evolution of the supersaturation of C-S-H in the solution. For quantitative determinations of the supersaturation, a generic relationship between the growth rate and supersaturation of C-S-H must be known. In a recent study,

Scherer et al. (27) showed that the growth rate of C-S-H exhibits a cubic dependence on its supersaturation, as shown in Equation 9.

Figure 1 0 . Outward growth rate of the product (Gout) as a function of w/c when (A) a = 0.10, (B) a = 0.20, and (C) a = 0.30. Results for both coarse and fine cements are shown.

Where, Gout-c (pm h-1) is a constant and ^ csh(0 (unitless) is the time-dependent supersaturation of C-S-H in the solution. As the exacted value of Gout-c is not known and is expected to change depending on the concentration of calcium (i.e., Ca2+) in the solution (27), a value of Gout-c = 0.075 pm h-1 is assumed in this study. This value, as 88

described previously, is used in the first step of the pBNG simulations and is within the

same order of magnitude as experimental values (26,27,64). By plugging in the estimated

value of Gout-c, the values of ^ csh are expected to be a rough, rather than an accurate

estimate.

G0ut(t) = G0Ut-c[Pc sh(0 — l ] 3 (9)

However, these estimated values are expected to capture the effects of variations

in the process parameters, that is, w/c and SSA of cement, as they are all derived using

the same value of Gout-c. The temporal evolutions of ^ csh, shown in Figure 11, are

qualitatively similar to those reported in the literature and derived from kinetic cellular

automata simulations (22,27,29,30,61,69) and reflect the trends in the abundance of

aqueous ionic species—the silicate species (i.e., H2 SiO42- and H3 SiO4 ) in particular—in

solution (61,69-72). At very early ages (i.e., around the time of mixing), when C-S-H is

present in small amounts and cement continues to dissolve rapidly releasing ions at a fast

rate into the solution, ^ csh is expectedly high. With time, the dissolution rate of cement

declines, and more ions, including aqueous silicate species, are consumed as the rate of

precipitation of C-S-H increases; this manifests as a steep decline in ^ csh. It should be

noted, however, that this decline in ^ csh is non-monotonic, particularly in the case of low w/c systems. Specifically, around the main hydration peak, ^ csh increases—albeit

slightly—and then continues to decrease. These minor fluctuations in the evolution of

^ csh are expected to mimic the increase in the silicate concentration that occurs around the main hydration peak when there is a sharp decrease in the Ca2+ concentration (22,35).

At later ages (i.e., in the subsequent hours following the main hydration peak), ion

concentrations in the solution stabilize (22,39,61,70), and thus ^ csh also stabilizes. 89

At any given time, pastes prepared at a lower w/c have higher ficsH as compared

to those prepared at a higher w/c. This, as stated previously, is expected to be due to the

larger dilution in the higher w/c pastes and is corroborated by the evolutions of the

solution electrical conductivity and pH. As can be seen in Figure 12A, and 12B, whereas

the overall profiles of electrical conductivity and pH evolution are similar across different w/c— which is expected due to similar hydration kinetics (Figure 2)—the magnitudes of

both parameters at equivalent times are lower in high w/c pastes on account of higher

dilution (i.e., larger volume of solution per mole of a given ion). Lower concentration of

ions in the pore solutions of high w/c pastes causes Pcsh to be lower compared to those

prepared at low w/c. It is also interesting to note that Pcsh is broadly insensitive to the

PSD of cement (Figure 11B, and 11C). This suggests that the differences in the hydration

kinetics induced by the SSA of cement (as shown in Figure 3) are unable to cast a

significant impact on the composition of the solution and, therefore, the supersaturation

of C-S-H. 90

Figure 12. (A) Electrical conductivity and (B) pH of the pore solution of pastes prepared using the coarse cement at different w/c. Because of the large difference in the magnitudes of the solution’s electrical conductivity, rescaled subplots for the two curves are included within (A). (C) Heat flow rates of pastes, prepared using the coarse cement at w/c = 1 0 , measured without (static) and with in situ stirring.

Overall, the results described thus far suggest that the hydration kinetics of

cement is not affected by the w/c on account of the sedimentation of cement particles. As

cement particles settle, they are packed more closely, which in turn creates a space

constraint for the growth of C-S-H and results in its confinement. On the basis of this

theory, it could be hypothesized that if the sedimentation of cement particles is

prevented—or even disrupted—C-S-H would not remain confined, thus causing the

hydration kinetics to change. To test this hypothesis, hydration kinetics was monitored

for a paste prepared at w/c = 1 0 , wherein the paste was continuously stirred at a low

speed (i.e., 80 rpm) using an electrically-driven agitator throughout the 24 h of hydration.

It is clarified that the low rotational speed of the agitator minimizes the heat released due to mixing action (i.e., <0.15 J of cumulative heat over a 24 hour period, see Appendix B) but is unable to completely prevent the sedimentation of cement particles. As shown in

Figure 12c, in the stirred paste, the hydration rates are indeed different—broader, with 91

delayed occurrence of the main hydration peak and slower postpeak decline of the

hydrate rate—compared to the static paste (i.e., without in situ mixing).

These differences can be reconciled by considering the effect of stirring on the

spacing between cement particles. Specifically, in the stirred pastes, sedimentation of

cement particles is partially prevented, which results in larger spacing between them and,

consequently, fewer impingements between C-S-H layers growing on neighboring

cement particles. Because of such lack in confinement of C-S-H in the stirred pastes, the

main hydration peak is delayed and the decline in the postpeak hydration rate is slower.

By contrast, in the static paste, the closely packed cement particles ensure more

impingements between the C-S-H layers and thus a faster approach to and departure

from the main hydration peak. The results shown in Figure 12 are in good agreement with

the results shown in Figure 3B of the Appendix B, wherein it is shown that if the reaction

vessel’s volume is larger (i.e.,pf -1.00), the pBNG-simulated hydration rates of high w/c

pastes have a delayed occurrence of the main hydration peak and a slower postpeak

decline of the hydration rate. The results shown in Figure 12 are also in good agreement with a prior study (31), which shows that in pastes provisioned with dispersants, the

enhanced dispersion of cement particles causes cement hydration rates to change (i.e., to

get progressively broader) in relation to increasing w/c.

On the basis of these results, it is hypothesized that sedimentation of cement

particles is at the origin of C-S-H confinement and insensitivity of cement hydration

rates to changes in w/c. It is clarified that, although this hypothesis has been construed

from the hydration behavior of water-rich systems (i.e., w/c > 0.42), past studies (12,31)

and additional data in Appendix B show that early age hydration rates of low w/c pastes 92

(i.e., w/c < 0.42) are also insensitive to w/c. Results obtained from pBNG simulations

(not shown) indicate that even in low w/c pastes, the reaction vessel’s volume is

equivalent to the volume occupied by hydrates at a = 1. Thus, it is proposed that in pBNG

models, to account for C-S-H confinement, the determination of the boundary area per unit volume of the substrate (otbv: Equation 6 ) for plain pastes should be calculated based

on the volume of hydrates that would form when all of the cement has reacted, rather than the total volume of the paste (including excess water) which depends on the w/c. As

per this definition, in blended systems wherein cement is partially replaced by a filler, aBV would be equal to the ratio of the total solid surface area at a = 0 (i.e., combined

surface areas of cement and filler) to the total volume of solids at a = 1 (i.e., combined volumes of hydrates and filler). As pointed out by Scherer and Bellmann (27), pBNG

models should account for the highly nonlinear supersaturation-dependent variation in the

growth rate of C - S-H. In this study, although the evolution of growth rate and

supersaturation of C-S-H were derived indirectly from heat evolution profiles, it is

possible to incorporate a supersaturation-dependent growth rate directly into pBNG

models through experimental measurements of the evolving solution composition (27).

Last, it is recognized that further investigation of cement hydration kinetics in pastes, wherein sedimentation of particles is progressively mitigated (e.g., using viscosity

modifying admixtures), is required for validation and further refinement of the

hypotheses presented in this study. A study focused on the description of hydration

kinetics of C3 S suspensions, with and without the disruption of particle sedimentation, is

currently underway at Missouri S&T; outcomes of this study will be presented in a future

publication. 93

5. SUMMARY AND CONCLUSIONS

A series of experiments and pBNG simulations were applied to elucidate the role of w/c ratio on the hydration kinetics of cement in plain pastes. The experiments, conducted using isothermal microcalorimetry methods, show that cement hydration rates are insensitive to changes in w/c. As classical pBNG models are unable to explain such effects, a modified pBNG model is presented, in which the growth of the main hydrate, that is, C-S-H, is assumed to be anisotropic and allowed to vary in relation to the nonlinear evolution of its supersaturation in the solution. Results obtained from the pBNG simulations show that the nucleation density of C-S-H, forming heterogeneously on cement surfaces, is unaffected by the w/c of the paste as well as the SSA of cement particulates. However, as the w/c increases, the fraction of the paste’s volume that participates in the nucleation and growth process reduces. This reactive (i.e., participatory) fraction of the paste, termed as the reaction vessel in this study, was found to be equivalent (i.e., equivalent size/volume and water content) across pastes prepared at different w/c ratios and cements of different SSAs. On the basis of these results, it is hypothesized that at early ages, the nucleation and growth of C-S-H remains confined within the reaction vessel, such that its formation is limited to ion-abundant regions in proximity to cement particles. This confinement of C-S-H is hypothesized to be a manifestation of the sedimentation of cement particles. As cement particles settle, they are packed more closely, which in turn creates a space constraint for the growth of

C-S-H and results in its confinement. Indeed, in pastes, wherein the sedimentation of cement particles is disrupted using in situ stirring, the hydration kinetics is no longer 94

insensitive to changes in the w/c. Results from this study also suggest that, unlike

C-S-H, the ions in solution are not confined within the reaction vessel. The transport of

ions throughout the volume of the paste causes the supersaturation of C-S-H, that is, the

driving force for its growth, to decline with increasing w/c. This results in a systematic

diminishment of C-S-H growth rate with increasing w/c. Overall, the outcomes of this work provide novel insights into the mechanisms that cause cement hydration rates to

remain insensitive to changes in the paste’s water content. Whereas a simplified view is presented, the discussion highlights important aspects that need to be incorporated in

pBNG models to account for C-S-H confinement as well as the sedimentation of cement

particles. Investigation of the cement hydration kinetics in systems, wherein

sedimentation of particles is progressively mitigated (e.g., using viscosity modifying

admixtures), is expected to aid in validation and in further refinement of the hypotheses

presented in this study.

ACKNOWLEDGEMENTS

This research was conducted in the Materials Research Center (MRC) at Missouri

S&T. The authors gratefully acknowledge the financial support that has made these

laboratories and their operations possible. Funding for this research was provided by the

National Science Foundation [NSF, CMMI: 1661609], MRC at Missouri S&T [MRC

Young Investigator Seed Funding] and the University of Missouri Research Board

[UMRB]. 95

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III. EFFECT OF PARTICLE SIZE DISTRIBUTION OF METAKAOLIN ON HYDRATION KINETICS OF TRICALCIUM SILICATE

Jonathan Lapeyre§, Hongyan Ma*, and Aditya Kumar§

^Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409

*Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO 65409

ABSTRACT

The focus of this study is to elucidate the role of particle size distribution (PSD)

of metakaolin (MK) on hydration kinetics of tricalcium silicate (C3 S-T 1 ) pastes.

Investigations were carried out utilizing both physical experiments and phase boundary

nucleation and growth (pBNG) simulations. [C3 S + MK] pastes, prepared using 8 %mass or

30%mass MK, were investigated. Three different PSDs of MK were used: fine MK, with

particulate sizes <20 pm; intermediate MK, with particulate sizes between 20 and 32 pm;

and coarse MK, with particulate sizes >32 pm. Results show that the correlation between

specific surface area (SSA) of MK's particulates and the consequent alteration in

hydration behavior of C3 S in first 72 hours is nonlinear and non-monotonic. At low

replacement of C3 S (i.e., at 8 % mass), fine MK, and, to some extent, coarse MK act as

fillers, and facilitate additional nucleation and growth of calcium silicate hydrate (C-S-

H). When C3 S replacement increases to 30% mass, the filler effects of both fine and

coarse MK are reversed, leading to suppression of C-S-H nucleation and growth. Such

reversal of filler effect is also observed in the case of intermediate MK; but unlike the 102 other PSDs, the intermediate MK shows reversal at both low and high replacement levels.

This is due to the ability of intermediate MK to dissolve rapidly—with faster kinetics compared to both coarse and fine MK—which results in faster release of aluminate

[Al(OH)4-] ions in the solution. The aluminate ions adsorb onto C3 S and MK particulates and suppress C3 S hydration by blocking C3 S dissolution sites and C-S-H nucleation sites on the substrates’ surfaces and suppressing the post-nucleation growth of C-S-H.

Overall, the results suggest that grinding-based enhancement in SSA of MK particulates does not necessarily enhance early-age hydration of C3 S.

Keywords: tricalcium silicate (C3 S); metakaolin; filler effect; hydration kinetics; particle size

1. INTRODUCTION

The benefits of partially replacing ordinary portland cement (subsequently referred to as cement) with widely available and abundant aluminosilicate materials (e.g., waste glass, calcined clays, blast furnace slag, and fly ash) have been widely investigated as part of a broad strategy to offset the environmental effects (i.e., CO2 emissions and energy consumption) of cement production (1-6). When cement or tricalcium silicate

(C3 S: the major phase in cement) is partially replaced with an aluminosilicate material

(i.e., [cement/C3 S + aluminosilicate] pastes), hydration kinetics of the former are altered on account of two effects exerted by the additive, that is, filler effect and pozzolanic 103

effect (7-9). Both effects enhance formation of calcium silicate hydrate (C-S-H: the

major hydration product in cement and C3 S systems), albeit through two different

processes. The filler effect is a physical mechanism, wherein fine particles of the additive

act as energetically favorable substrates for heterogeneous nucleation and subsequent

growth of C-S-H nuclei (8-12). The additional C-S-H formed as a result of the filler

effect results in improved solid-to-solid phase connectivity within the microstructure,

thus leading to improved properties (e.g., compressive strength) of the bulk material

(8,10,13). Although fillers are typically assumed to be inert, aluminosilicate, as well as

silica based (e.g., silica fume), material additives are also able to undergo pozzolanic

reaction in cementitious environments (9,14-18). The pozzolanic reaction pertains to

chemical reaction of the aluminosilicate/silicate additive with portlandite (CH or calcium

hydroxide) to produce C-S-H (19-23). The additional (pozzolanic) C-S-H formed as a

result of the pozzolanic reaction is a space-filling hydrate (especially when compared to

its precursor, CH) and contributes toward enhancement of the bulk material's physical

properties, such as lowering water permeability and improving strength (24-28).

The focus of this study is metakaolin (AhSi2O7 : subsequently abbreviated as

MK), an anhydrous aluminosilicate material derived from calcination of kaolinite

(Al2 Si2O5(OH)4) clay at temperatures between 500°C and 800°C (29-32). Calcination of

kaolin above 900°C transforms MK into crystalline mullite and/or y-AhO3, significantly

attenuating its pozzolanic reactivity (31-33). Calcination breaks covalent bonds between

1 Portions o f the manuscript w ill implement standard cement chemistry notation: C = CaO, S =

SiO 2 , A = A l 2 O s , H = H 2O, $ = SO3 104

hydroxyl groups and aluminum octahedral groups transforming the triclinic crystal

structure of kaolinite into an amorphous network (34,35). The amorphous structure is

energetically less stable than the crystalline structure, thus leading to faster dissolution

dynamics and enhanced overall reactivity of MK, as compared to kaolin, in alkaline

conditions of cement and C3 S pastes (21,36-38). There have been several investigations

identifying and assessing the benefits of MK, as well as other calcined clay minerals,

when used to replace cement in pastes, concretes, and mortars (21-23,39-41). While

majority of these studies have focused on quantifying the aforementioned benefits in

terms of improvement in properties of the bulk material, (31,42) there are only a few

studies that have examined, and attempted to decouple, the filler and pozzolanic

contributions of MK. Notable among these is a recent study conducted by Lapeyre and

Kumar (9), in which hydration behavior of C3 S in [C3 S + MK] pastes were examined.

The study concluded that the pozzolanic activity of MK is negligible at early ages (i.e.,

up to 24 hours after mixing), and, therefore, does not cause significant alteration in

hydration behavior of C3 S. MK, however, does serve as a filler, and facilitates nucleation

and growth of C-S-H on its particulates’ surface. At low replacements (i.e., up to 10%

mass) of C3 S, the filler effect of MK is substantial, and even superior in comparison to that of silica fume, the fine particulates of which are highly susceptible to effects of

particle agglomeration. At higher replacement levels (i.e., >20%), however, the filler

effect of MK is either substantially diminished or reversed (i.e., suppression, rather than

enhancement, of C-S-H nucleation and growth). Such diminishment or reversal of MK's

filler effect is attributed to the abundance of aluminate anions [Al(OH)4-] in the solution,

released from the dissolution of MK. More specifically, the study (9) reported that the 105

aluminate anions adsorb onto C3S and MK particulates’ surfaces, and inhibit topographical sites for C-S-H nucleation; furthermore, the same anions adsorb onto C-

S-H and impede its post-nucleation growth. Such inhibition of C3 S hydration has also been reported in other aluminate-rich systems, for example, when AhO3-doped C3 S

(instead of pure C3 S) is used or when C3 S/cement pastes are provisioned with AhO3

nanoparticles and highly soluble aluminate salts (e.g., NaAlO2 and AlCb) (43-47).

Based on the above discussion, it is apparent that dissolution dynamics of MK

play a significant role in altering the hydration behavior of cementitious systems. It could

be argued that any factor that affects MK's dissolution would also affect overall hydration

of the host cementitious material. One such factor is the particle size distribution (PSD)

of MK. This is based on a vast number of prior studies that have shown that in aqueous

environments, finer particulates dissolve faster compared to coarser ones (48-52). Prior

literature, however, provides little information on the effect of PSD of MK on hydration

kinetics of C3 S or cement systems. In two separate studies, conducted by Justice and

Kurtis as well as Lagier and Kurtis (53,54) it was shown that fine MK particulates (90%

of particulates finer than 2 pm) accelerated—albeit only slightly—the hydration of

cement. However, in pastes prepared with MK comprised of particulates coarser than the

aforementioned one, the filler effect was negligible; furthermore, the onset of

acceleration period (i.e., when massive precipitation of C-S-H and CH occur) in such

pastes was significantly delayed. While insights provided by the aforementioned pair of

studies (53,54) are significant, the utilization of cement—which is a multicomponent

material, consisting of other phases (e.g., C3A) in addition to C3 S—makes it difficult to

conclude that the effects of MK scale monotonically with fineness (i.e., SSA: specific 106

surface area) of its particulates. This is because in cement paste, the aluminate ions

released from dissolution of MK can undergo reactions with paste components other than

C3 S, resulting in precipitation of secondary hydrates (e.g., stratlingite and hydrogarnet)

and alterations in stability of sulfate-bearing phases (e.g., ettringite) (1,21). Such

reactions, and their net effect on cement's hydration behavior, make it difficult to

sequester the filler and pozzolanic effects of MK from its overall effect. Thus, it is

important to evaluate such behaviors in single-compound systems (e.g., C3 S) that still

feature the filler and pozzolanic effects, but present fewer complexities compared to

cement. This study investigates the influence of PSD of MK on its pozzolanic and filler

effects in [C3S + MK] pastes. Pastes featuring three different PSDs of MK and two

different C3 S mass replacement levels (i.e., 8%mass and 30%mass) have been used. Toward the examination of hydration behavior of C3 S in such pastes, a combination of

experimental methods (e.g., isothermal microcalorimetry and TGA: thermogravimetric

analysis) and phase boundary nucleation and growth (pBNG) simulations have been

implemented. Emphasis has been given to consolidate results obtained from experiments

and simulations to elucidate, from a mechanistic standpoint, the correlation between SSA

of MK particulates and the resultant effect on C3 S hydration behavior in [C3 S + MK]

pastes.

2. MATERIALS AND METHODS

Triclinic C3 S (Ca3SiO5-T1) was produced via solid-state thermal processing of

reagent grade quartz and calcite precursors. Details regarding synthesis are presented 107 elsewhere (9). After synthesis, the final powder was evaluated—using X-ray diffraction and Rietveld analyses—to be nearly phase pure C3 S, containing only 0.80% ± 0.25% of residual free lime (i.e., CaO). The composition of MK (Imerys-Kaolin Metastar HP501), in terms of mass percentages of oxides as determined from x-ray florescence, is shown in

Table 1. As shown in the table, the MK powder is composed of 51.30%mass SiO2 and

47.80%mass AhO3, with minor titanium and iron oxide contaminants.

Table 1. Composition of metakaolin, in terms of oxides, as determined from x-ray ______fluorescence (XRF)______Components MK # %mass SiO2 51.30 AhO3 47.80 Fe2O3 0.44 CaO 0.04 MgO 0.09 SO3 <0 .0 1 TiO2 0.90 Na2O Equivalent 0 .2 1 Loss of Ignition (LOI) 0.52

Three different particle sizes distributions (PSDs) of MK were generated from the bulk powder, utilizing a modified wet-sieving process based on the ASTM C325-

07(2014) (55) method. It is clarified that both dry- and wet-sieving methods were attempted in this study; however, the latter was chosen as it resulted in superior particulate yields (i.e., greater amounts) and better size classification of particulates into three unique PSDs as compared to the former method. With respect to the aforementioned ASTM standard, minor modifications in the wet-sieving method were made to ensure consistency between different batches of each PSD of MK. Notably, the 108 amount of distilled water (used for mixing with MK to produce a wet mix) was set at

-200 mL, and the mixture was shaken by hand to ensure homogeneity after the 2-hour shaking process. Although MK is the dehydrated form of kaolin, prior studies and results obtained from XRD (not shown), have shown that under standard temperature and pressure (STP) conditions, MK does not significantly rehydrate (during the wet-sieving process), and, therefore, does not revert back to kaolin (56). As the final part of the wet- sieving process, the “as-received” PSD of MK was sifted through 20 pm and 32 pm sieves to yield three unique PSDs: (a) fine—with particulate sizes (i.e., diameters) <20 pm; (b) intermediate—with particulate sizes ranging between 20 and 32 pm; and (c) coarse—with particulate sizes >32 pm. In the subsequent sections, the three PSDs of MK with increasing fineness are referred to as fine MK, intermediate MK, and coarse MK, respectively. All PSDs of MK, as well as of C3S, were measured using a static light scattering (SLS) analyzer (Microtrac S3500). Toward this, the powders were suspended in isopropyl alcohol, and agitated with ultrasonic impulse for 30 seconds to prevent agglomeration. Results obtained from PSD determinations are shown in Figure 1. The median particle size (d.50) for fine, intermediate, and coarse MK are 4.6200, 28.530, and

148.00 pm, respectively. By factoring the bulk density of MK (i.e., 2550 kg m-3), the

SSAs of fine, intermediate, and coarse MK were estimated to be 672, 80, and 29 m2 kg-1, respectively. For the C3 S powder, the d50 and SSA were 7.78 pm and 562 m2 kg, respectively; the density of C3 S was assumed to be 3150 kg m-3. It is clarified that estimations of SSA from PSD are premised on the assumptions that all particulates are spherical, and that the effects of topographical roughness and internal porosity (57-61) on the overall SSA are negligible (62,63). Because of these assumptions, the SSAs 109

reported above are expected to be smaller than those derived from the Brunauer-Emmett-

Teller method (62,63).

Figure 1. The PSDs of C3S and MK used in this study. The largest relative uncertainty in median diameter (J50, gm) of the powders is on the order of ± 6 %

[C3 S + MK] pastes were prepared by mixing the powders with deionized water at

a fixed liquid-to-solid mass ratio (l/s) of 0.45. The mixing protocols (i.e., rate and time of

mixing) were kept consistent for all pastes. In binary (i.e., [C3 S + MK]) pastes, C3 S was

partially replaced by MK (for each of the three PSDs) at two different mass replacement

levels: low (i.e., 8 %mass) and high (i.e., 30%mass). In such pastes, the mass-based water-to-

C3 S ratios (w/c) are 0.450, 0.489, and 0.643 for 0%mass (control system), 8 %mass, and

30%mass replacements by MK, respectively. It is clarified that in preparation of the pastes, the utilization of dispersants (e.g., high-range water reducing chemical admixtures such

as polycarboxylate ether polymer) was avoided. This is because the provision of

dispersant could result in complex alterations in C3 S dissolution behavior and nucleation 110

and growth of the hydrates (16) that would be difficult to sequester (and subsequently

analyze) from the effect of particulate dispersion (or suppressed agglomeration of

particulates) brought about by the dispersant. Hydration kinetics of C3 S in the pastes were

monitored for 72 hours after mixing using a TAM IV (TA Instruments) isothermal

conduction microcalorimeter, programed to maintain a constant temperature of 20°C ±

0.1°C. Heat evolution profiles collected from the microcalorimetry experiments were

processed—using a method employed in several prior studies (9,48,50,64)—to determine the degree of reaction (a, fraction of C3 S that has undergone hydration) and the rate of

reaction (da/dt, units of h-1 ) of C3S; the enthalpy of hydration (48,64-66) of C3 S used for

such analyses was 484 J gC3S-1. To monitor the dissolution dynamics of MK in C3 S paste

environments, separate microcalorimetry experiments were conducted on pastes prepared by mixing MK (for all three PSDs) with saturated lime solution at l/s of 0.45. Heat

evolution profiles collected from such experiments were processed in two steps, as

described in prior studies (9,16) to firstly determine the enthalpy of dissolution of MK,

and to subsequently estimate the degree of reaction (a) for MK by plugging in the

enthalpy of dissolution.

For identification and quantification of hydrates (i.e., C-S-H and CH) and calcite

(if any) in pastes, an SDT-Q600 thermogravimetric analyzer (TGA) was used. For

arresting hydration of C3 S in such pastes, hydrated samples (after undergoing hydration

for 72 hours) were firstly crushed, and then submerged in isopropyl alcohol for 24 hours.

In some cases, the samples were kept in isopropyl alcohol for longer periods; in such

cases, “fresh” isopropyl alcohol was used to replenish the old one periodically (i.e., after

every 24 hours). Prior to conducting the TGA experiments, the bulk isopropyl alcohol 111

was drained, and the samples were oven-dried at 85°C for an hour. During the TGA

experiments, the samples were placed in an AI2O3 crucible and heated from room temperature to 1000°C, at a temperature ramp rate of 10°C min-1. N2 gas, passing at a

constant flow rate of 100 mL min-1, was used to maintain an inert atmosphere within the

TGA apparatus. The mass loss (TG) and the differential mass loss (DTG) patterns,

derived from the experiments, were used to quantify the amount of CH and calcite (if

any) in the samples. For such phase quantifications, methods delineated in prior studies

(67,68) were adopted.

3. PHASE BOUNDARY NUCLEATION AND GROWTH MODEL

A modified phase boundary nucleation and growth (pBNG) model was used to

simulate hydration kinetics of C3 S and [C3 S + MK] pastes. The pBNG model has been used in prior studies (9,16,50,64,66). Therefore, to avoid replication of information, in this section, the underlying assumptions and principles of the pBNG model, and their

mathematical formulations, are presented in brief; for further details, readers are

requested to refer to references (9,50). The pBNG model simulates C3 S hydration as a

process driven by heterogeneous nucleation and growth of a single hydration product

(i.e., C-S-H) of a fixed density (69,70). Product nucleation is assumed to occur under

site saturation conditions—wherein all product nuclei form at a given nucleation event,

and the product nucleation rate is zero at all times after such event. Once nucleated, the

product subsequently grows heterogeneously on solid substrate boundaries (in this case,

on C3 S and MK particulates’ surfaces). Growth of the product is permitted in all 112 directions except into the substrate (69,70). The degree of hydration of C3 S as a function of time, a(t), is calculated from Equation 1. Here, B (unitless) envelops the paste's characteristics (i.e., density of components, chemical shrinkage, and w/c), and the function X(t) describes the temporal evolution of volume fraction of reactant transformed into hydrate (Equation 2) (16, 6 6 , 69-71).

a(t) = B X(t) (1a)

- 1 ( Pcement \ 1 1 Pproducts Pcement Pwater B = ( 1b) W 1 1 7 T Pcement £------+ 1 Pproducts Pwater Pwater /

Pp[fc5(f - ^ )]N X(t) = 1 — exp - 2 fcc • (t — t) • ( 1 — (2 ) fcs(t —r) ,

In Equation 2, F d is the f-Dawson function. The variables ks (h-1) and ko (h-1) are functions of the nucleation density (/density, pm-2) and the outward growth rate [Gout(t), pm h-1] of the product (see references (9,50) for more details). It should be noted that in the pBNG model, the growth of the product is assumed to occur in an anisotropic fashion, while varying with respect to time. In the lateral direction (i.e., parallel to the substrate’s surface), the growth rate is isotropic; however, in the longitudinal direction (i.e., perpendicular to the substrate’s surface), the outward growth rate (Gout) is double the rate in the lateral direction. Such anisotropy in product’s growth has been implemented to mimic the actual geometry of C-S-H’s early-age growth, as observed in experiments

(72,73). The temporal variation in growth rate is based on an implementation originally formulated by Bullard et al. (70), and subsequently adopted in several studies 113

(9,50,64,66,69), to capture the correlation between C-S-H’s growth rate and its

supersaturation in the solution.

It should be noted that in the pBNG model, the growth of the product is assumed

to occur in an anisotropic fashion, while varying with respect to time. In the lateral

direction (i.e., parallel to the substrate's surface), the growth rate is isotropic; however, in

the longitudinal direction (i.e., perpendicular to the substrate's surface), the outward

growth rate (Gout) is double the rate in the lateral direction. Such anisotropy in product's

growth has been implemented to mimic the actual geometry of C-S-H's early-age

growth, as observed in experiments (72,73). The temporal variation in growth rate is

based on an implementation originally formulated by Bullard et al, (71) and subsequently

adopted in several studies (9,16,50,64,66), to capture changes in C-S-H's growth rate in

relation to its supersaturation in the solution. By coupling the product nucleation density

with the substrate's (i.e., of C3 S and MK particulates) overall specific surface area

(SSAsolid, m2 kgC3S- 1 , as shown in Equations 3 and 4), the number of supercritical product

nuclei per unit mass of C3 S in the paste (Nnuc, kgC3S-1 ) can be estimated (9,16,74). Here, amk (unitless) acts a free simulation variable (9) that represents the reactive area fraction

of MK, that is, the area fraction not affected by particulate agglomeration and/or other

ion-specific effects (e.g., inhibition due to aluminate-ion adsorption). The other

parameter, z (%mass), represents the replacement level of C3 S by MK in the paste.

By coupling the product nucleation density with the substrate’s specific surface

area (SSAsolid, m2 kgC3S-1) - as shown in Equations 3 and 4 - the number of supercritical

product nuclei per unit mass of C3 S in the paste (Nnuc, kgC3S-1) can be estimated. Here,

amk (unitless) acts a free simulation variable (9) that represents the reactive area fraction 114

of MK, that is, the area fraction not affected by particulate agglomeration and/or other

ion-specific effects (e.g., inhibition due to ion adsorption). The other parameter, z (%mass),

represents the replacement level of C3 S by MK in the paste.

^Nuc — SSAsolid/density (3) Z SSAsolid — SSAC3S + aMKSSAMK ^qq _ ^ (4)

Within the pBNG framework, as described above and in references (9,50), the

variables that need to be ascertained for reproduction of the measured reaction rates are:

Gout(0, -/density, and amk. A Nelder-Mead-based simplex algorithm (75) is used to

determine optimum values of these variables in two steps. In the first step, Gout is fixed at

0.075 pm h-1 (a value derived from scanning transmission electron microscopy (72,73,76) whereas /density and omk are allowed to vary. The first step yields optimum values of /density

and amk, which are subsequently used in the second step to estimate the optimal

functional form of Gout(t). It is clarified that during the aforementioned optimizations,

convergence is assumed to have reached when: (a) the deviation between measured and

simulated reaction rates are within 1 %; and (b) the simulation output does not change by

more than ± 1 0 - 6 units in three successive simulation steps.

4. RESULTS AND DISCUSSION

4.1. EFFECT OF PSD OF METAKAOLIN ON HYDRATION OF C3 S

Figure 2 shows heat evolution profiles of [C3 S + MK] pastes, prepared by

replacing 8 %mass of C3 S with MK. As can be seen in Figure 2A, at low replacement level, both fine and coarse MK produce greater peak heat flow rates (i.e., heat flow rates at the 115

main hydration peaks) compared to the control (i.e., pure C3 S) paste. This is indicative of the “filler effect,” wherein provision of additional solid surface area by the additive's (i.e.,

MK's) particulates results in creation of supplementary sites for heterogeneous nucleation

and subsequent growth of C-S-H (9,10,15,49). Unlike the fine and coarse MK, the

intermediate MK suppresses nucleation and growth of C-S-H, as evidenced by lower

peak flow rate compared to the control paste. While the peak heat flow rates (and, therefore, alterations in C3 S hydration kinetics) do not exhibit monotonic relationship with fineness of MK particulates, all three [C3 S + MK] pastes reliably show prolongation

of the induction period as compared to the control paste (Figure 2B). The intermediate

MK prompts the largest extension in the induction period, followed by the fine and

coarse MK, respectively. Such prolongation of the induction period results in lower early-

age (e.g., at 12 hours) cumulative heat release in all [C3 S + MK] pastes compared to that

of the control paste (Figure 2C). As cumulative heat release is a direct indicator of degree

of reaction of C3 S, it can be said that provision of MK in the paste results in lower degree

of C3 S hydration at early ages. Notwithstanding, at the age of 72 hours, the cumulative

heat release of each of three [C3 S + MK] pastes surpasses that of the control paste. This is because in [C3 S + MK] pastes, the post-peak deceleration is slower (see Figure 2B), and, therefore, C3 S hydration kinetics beyond the peak are faster (i.e., heat flow rates are

higher) compared to that of the control paste. In summary, at low replacement level of

MK and at later ages (i.e., age ~72 hours), the degree of C3 S hydration in binary pastes is

superior compared to the control paste. At high replacement level (i.e., 30%mass) of C3 S

with MK, hydration of the host material is suppressed (see Figure 3A), regardless of the

PSD of MK, throughout the 72 hours after mixing. This is better shown in Figure 3B, 116 which focuses on the first 24 hours of hydration. As can be seen, all three PSDs of M K cause substantial prolongation of induction period, delayed occurrence of the main hydration peak, slower acceleration to the peak, and lower peak heat flow rate as compared to the control paste.

(A) (B) (C) Figure 2. M easured calorimetry profiles of [C 3 S + MK] pastes, wherein 8% mass o f C 3 S is replaced by MK. Three different PSDs of MK have been used. (A) Heat flow rates up to 72 h of hydration; (B) heat flow rates up to 24 h of hydration; and (C) cumulative heat release up to 72 h of hydration. The l/s of all pastes is 0.45. For a given system, the uncertainty in the measured heat flow rate at the main hydration peak is ±2%

Akin to results of [C 3 S + 8 % mass MK] pastes shown in Figure 2, the intermediate

M K has the most prominent effect on C 3 S hydration among all [C 3 S + 3 0 % mass MK] pastes, as evidenced by the protracted induction period, lowest slope of acceleration to the peak, and the greatest delay in occurrence of the main hydration peak (Figure 3B). Also, due to the lower slope of post-peak deceleration (i.e., slower departure from the main hydration peak), the degrees of C 3 S hydration in all [C 3 S + MK] pastes surpass that of the control paste at 72 hours (Figure 3C). Therefore, based on the results shown in Figure 3, it can be said that at high replacement level of MK, regardless of the PSD (or SSA) of the additive's 117 particulates, hydration of C 3 S is suppressed at early ages. Such suppression of C 3 S hydration, however, progressively diminishes with age, and ultimately reverses producing greater degrees of C 3 S hydration in binary pastes compared to the control paste. The results were found to be in very good agreement with inferences made from the heat evolution profiles. As can be seen, at both low and high replacement levels, the intermediate MK suppresses early-age (i.e., up to ~24 hours) hydration of C 3S the most. This is evidenced by CH contents that are consistently lowest among all pastes, and even below the dilution line (which represents the proportional decrease in CH content with respect to decreasing

C 3 S content in binary paste).

is replaced by MK. Three different PSDs of MK have been used. (A) Heat flow rates up to 72 h of hydration; (B) heat flow rates up to 24 h of hydration; and (C) cumulative heat release up to 72 h of hydration. The l/s of all pastes is 0.45. For a given system, the uncertainty in the measured heat flow rate at the main hydration peak is ±2%

At the age of 72 hours, however, the CH contents in binary pastes— regardless of the PSD of M K— are above the dilution line. This corroborates the argument made earlier in this section that the M K-induced suppression of C 3 S hydration, observed at early ages, 118 is reversed at later ages. M ore importantly, as CH contents of binary pastes invariably stay above the dilution line (at 72 hours, see Figure 4A and B), it can be said that the pozzolanic reaction between M K (regardless of its PSD) and CH within the first 72 hours of hydration is not significant. This is in very good agreement with findings of prior studies, (42, 77-79) and strongly suggests that within the first 72 hours after mixing, the impact of pozzolanic activity of M K on hydration behavior of C 3 S in [C 3 S + MK] pastes is insignificant. It is worth clarifying that the poor pozzolanic activity of M K in [C 3 S +

MK] pastes is not exclusively due to the slower dissolution dynamics of M K (this is further described in Section 4.2). Rather, the limiting factor is expected to be the low content of CH in such binary pastes. To corroborate this, additional TGA experiments were conducted to examine the reduction in CH content and the resultant formation of pozzolanic C -S-H in [MK + CH, at 1:1 molar ratio] pastes, prepared by mixing M K and

CH with water at l/s of 0.45. As can be seen in Figure 4C, when adequate amount of CH is present, the pozzolanic reaction of M K with CH is substantial (i.e., up to 20% mass reduction in CH content, and formation of pozzolanic C -S-H in equivalent amount). This suggests that in a mature [C 3 S + MK] paste (i.e., after age» 72 hours), when substantial amount of CH is present, the pozzolanic activity of M K is expected to upsurge.

Heat flow rate profiles, shown in Figures 2 and 3, qualitatively contrast C 3 S hydration kinetics in [C 3S + MK] pastes in relation to PSD and replacement level of MK.

To gain proper, quantitative understanding, additional data (i.e., calorimetric parameters

(9,10,16,64): inverse of time to the peak (h -1 ), maximum heat flow rate (mW g C3S-1 ), and slope of the acceleration regime (mW g C3S-1 h -1 )) were extracted from the heat evolution profiles, consolidated, and plotted (Figure 5). As can be seen (Figure 5A), the main 119 hydration peak is delayed in all binary pastes; the delay magnifies as the M K content in the paste increases. In a prior study (9), it was reported that such prolongation of the induction period is directly related to the release of aluminate (i.e., [Al(OH)4-]) ions from the dissolution of MK. M ore specifically, the adsorption of aluminate ions onto C 3S particulates’ surfaces blocks dissolution sites (e.g., kinks on etch pits of C 3 S surfaces

(4 3 ,8 0 )).

Figure 4. The temporal evolution of CH content (expressed as dry mass fraction) in [C 3 S + MK] pastes, prepared at: (A) 8% replacement; and (B) 30% replacement level of C 3 S with MK. The upper bound of the gray area represents the CH content formed in the control paste, and the lower bound represents the dilution line (i.e., proportional reduction in CH content in relation to the reduction in C 3S content). (C) DTG traces showing differential mass loss, as function of temperature, in a [MK + CH (1:1 molar ratio)] paste (l/s = 0.45) at 72 h after mixing. The highest uncertainty in phase quantifications by DTG is ± 2.5%

This, in turn, slows C 3 S dissolution dynamics and prolongs the induction period.

Expectedly, these effects of aluminate-ion adsorption (which leads to inhibited dissolution of C 3 S) become progressively more pronounced as the content of MK in the paste increases (Figure 5A). 120

(A) (B) (C) Figure 5. Calorimetric parameters extracted from heat evolution profiles of pastes: (A) inverse of time to the main hydration peak; (B) heat flow rate at the main hydration peak; and (C) slope of the acceleration period. The uncertainty in each calorimetric parameter is the same as the uncertainty in calorimetry profiles, that is, ±2 %

Using molecular dynamics simulations, Pustovgar et al. (43) showed that the absorption of aluminate anions onto C3S particulates’ surfaces is energetically favorable due to formation of aluminosilicate complexes, comprising of ionic and hydrogen bonds between the aluminate ions and Ca2+ and OH ions (that remain in the vicinity to C3 S particulate surfaces forming an electric double-layer). As C3 S continues to dissolve

(though at a slower rate), the pH of the contacting solution continues to increase. At a critical pH, when the concentrations of Ca2+ and OH ions in the solution are elevated to

CH saturation level (i.e., pH ~ 12.68 (43,44,48,66)), the aforementioned aluminosilicate complexes on C3S surfaces become thermodynamically unstable; as a result, the aluminate ions desorb from C3S surfaces (43, 44). This event is marked by termination of the induction period and onset of the acceleration regime. In Figure 5A, it is interesting that although the intermediate MK does not have the largest SSA, its ability to passivate

C3 S surface (and, therefore, it's potential to prolong the induction period and delay the main hydration peak) is superior compared to the fine (with largest SSA) and coarse 121

(with lowest SSA) MK. Since the ability to passivate C3 S surface is directly linked with the release of aluminate ions, it is hypothesized that the intermediate MK has the fastest

dissolution rate in C3S paste environments. This hypothesis will be corroborated later in

Section 4.2.

Going back to Figure 5, it can be seen that at low replacement level, fine and

coarse MK produce higher peak heat flow rates (Figure 5B) and slopes of acceleration

regimes (Figure 5C) compared to the control paste. In contrast, at high replacement level,

both calorimetric parameters are lower than those of the control paste. These results,

therefore, suggest that at low replacement level, both the fine and coarse MK act as

fillers, and enhance nucleation and growth of C-S-H through provision of additional

nucleation sites on their surfaces. At high replacement level, however, the ability of MK

to serve as a filler is not just diminished but reversed. As reported in a prior study (9), this

reversal in MK's filler effect is attributed to the higher concentration of aluminate ions

(resulting from dissolution of MK) in the solution of such pastes. The large abundance of

aluminate ions causes passivation of MK particulates’ surfaces in addition to those of C3 S

particulates. Such passivation blocks C-S-H nucleation sites on MK surfaces, thus

diminishing and ultimately reversing (akin to “poisoning” of) its filler effect. Figure 5B

and C clearly show that, among the three PSDs of MK, the intermediate MK suppresses

C-S-H nucleation and growth the most. This suggests that the intermediate MK is most

proficient (compared to the other PSDs of MK) at releasing aluminate ions in the

solution, which essentially lies at the origin of suppression of C3 S dissolution (Figure 5A)

and C-S-H nucleation and growth (Figure 5B and C). 122

4.2. EFFECT OF PSD ON DISSOLUTION DYNAMICS OF MK

The hypotheses derived from the results presented in Section 4.1 are premised on

one central concept that of all PSDs of MK (i.e., fine, intermediate, and coarse), the

intermediate one has the fastest dissolution dynamics, and, consequently, prompts the

fastest release of aluminate ions into the contacting solution. It has been argued that

greater abundance of aluminate ions in pore solution of [C3S + intermediate MK] paste is the principal reason for C3 S hydration suppression. To test the veracity of the concept,

additional calorimetry experiments were conducted to monitor the dissolution dynamics

of MK in saturated lime solution. The solvent was chosen to be DI-water saturated with

calcium hydroxide [i.e., Ca(OH)2], because several past studies (48,65,66,71,84,85) have

shown that in C3 S pastes, following a few hours after mixing, the pore-solution

[consisting of Ca2+, OH- ions at millimolar (mmol L-1) levels, and H2 SiO42-/HaSiO4- ions

at micromolar (pmol L-1) level] composition remains in vicinity of Ca(OH)2 saturation

level for protracted periods.

As can be seen in Figure 6 , the intermediate MK, indeed, dissolves faster, and to

greater extents, than the fine and coarse MK throughout the 168 hours after mixing.

Based on the SSAs of the PSDs of MK (reported in Section 2.0), it would be expected

that dissolution dynamics would be fastest for the fine, followed by the intermediate and

then by the coarse MK. The results shown in Figure 6 are, therefore, counterintuitive as the dissolution kinetics do not appear to follow a monotonic relationship with SSA of

MK particulates. Although the exact reasons for this anomaly are not known, it is

expected that slower dissolution kinetics of the fine MK is due to the following reasons:

(a) agglomeration of its fine particulates, which, in turn, results in significant reduction of 123 overall surface area, thus causing deceleration of dissolution kinetics; and (b) passivation of MK particulates’ surfaces, caused by aluminate ions released from the initial (and rapid) burst of dissolution of the fine particulates. The intermediate MK, which comprises of particulates between 20 and 32 pm, has lower SSA compared to the fine MK, but is not expected to be susceptible to agglomeration. As such, it is possible that the “reactive surface area” (i.e., surface area that is unaffected by particle agglomeration or aluminate- ion adsorption, and, therefore, able to partake in dissolution) of intermediate MK is larger than that of fine MK (and coarse MK), resulting in the fastest dissolution kinetics.

Validation of this hypothesis is provided in Section 4.3 with the aid of simulations conducted using the pBNG model.

Figure 6 . Isothermal microcalorimetry-based determinations of time-dependent degree of reaction (primary y-axis) and cumulative heat release (secondary y-axis) of MK dissolving in saturated lime solution. For such low heat evolving systems, the uncertainty in the measured heat flow rate at any given point in time is within ±5% 124

4.3. NUMERICAL SIMULATIONS OF HYDRATION KINETICS OF [C3 S + MK] PASTES

To gain further insights into the role of PSD of MK on C3 S hydration kinetics, the pBNG model (described in Section 3.0) was employed. Experimentally derived reaction rates (i.e., da/dt, calculated from calorimetry profiles) of pastes were used as inputs. The simplex algorithm, embedded within the pBNG model, was invoked to reproduce the input profiles by optimizing the following simulation variables: product nucleation density (/density), reactive area fraction of MK participating in product nucleation (amk), and the time-dependent outward growth rate of product [Gout (t)]. Through such optimizations, the pBNG model was able to reproduce the experimental results (figure not shown). Optimum values of the aforementioned simulation parameters, for the different pastes, were subsequently consolidated, and plotted (Figure 7).

Figure 7A and B show variations in amk and /density, respectively, in relation to the

MK replacement level. The plots show that at low replacement level (i.e., 8 %mass), majority of surface area of MK particulates—regardless of the PSD of MK—is available for C-S-H nucleation. In accordance with this, both the fine and coarse MK serve as fillers and enhance heterogeneous nucleation of C-S-H on their particulates’ surfaces

(see Figure 7B). Due to its higher SSA, expectedly, the fine MK enhances /density more than the coarse MK. The intermediate MK, however, causes a decline in /density—a clear reversal of the filler effect. This reversal is attributed to its faster dissolution kinetics (see

Figure 6 ), which causes rapid release of aluminate ions into the contacting solution. The aluminate ions, in due time, adsorb onto C3 S and MK particulates’ surfaces, thus blocking potential C-S-H nucleation sites. At high replacement level (i.e., 30%mass), a large fraction of surface area of fine MK (with the largest SSA) is unable to partake in the 125 nucleation and growth process (Figure 7A); furthermore, /density is significantly lower compared to the control paste (Figure 7B). These results are in good agreement with the discussion in Section 4.2, wherein it was hypothesized that in fine MK, effects of particle agglomeration and (aluminate ion induced) passivation of particulates’ surfaces result in significant diminishment of reactive surface area and blockage of potential sites for C-S-

H nucleation. Notably in the [C3 S + intermediate MK] paste, at 30% mass replacement level of MK, -70% of the surface area is rendered unreactive (Figure 7A) and /density is reduced by -1 order of magnitude with respect to the control paste (Figure 7B). Such large reductions in amk and /density are attributed exclusively to the passivation caused by rapid release (Figure 6 ) and subsequent adsorption of aluminate ions onto the MK particulates’ surfaces; particulate agglomeration is expected to be negligible in the intermediate MK. The reduction in /density of [C3 S + coarse MK] paste—albeit small—is also attributed solely to the surface passivation induced by aluminate ions.

The two simulation parameters, amk and /density, were combined [as described in

Section 3.0 (Equation 3)] to estimate the total number of supercritical product nuclei formed at the nucleation event (Nnuc: Figure 7C). As can be seen, the trends in Nnuc with respect to MK replacement level are remarkably similar to those exhibited by calorimetric parameters (shown in Figure 4) extracted directly from experiments. It is posited that such similarity between experiments and simulations validates the pBNG model and its implementation. Figure 7C shows that at low replacement level, the fine and coarse MK are able to exert filler effect and enhance the number of C-S-H nuclei in the paste. At high replacement level, owing to the reduction in reactive surface area of

MK particulates (Figure 7A) and concurrent reduction in /density (Figure 7B), the values of 126

Nnuc of all [C3S + MK] pastes remain consistently below the control paste. The

intermediate MK, in particular, significantly reduces Nnuc, almost by an order of

magnitude with respect to the control paste. This corroborates the hypothesis that faster

dissolution kinetics of intermediate MK (as shown previously in Figure 6 ) results in

faster release of aluminate ions, which then passivate the substrates’ surfaces thus blocking potential C-S-H nucleation sites. The other simulation parameter optimized

from pBNG simulations is the outward product growth rate [Gout (t)] (Figure 8 ). This

functional form of Gout has been reported (9,50,64,71) to emulate evolution of C-S-H

supersaturation in the solution. It is noted that, at early ages (i.e., up to ~12 hours), Gout of

[C3 S + 8 %mass MK] and [C3 S + 30%mass MK] pastes are lower than those of the control

paste.

' ’ iw p iro m w n p*» Mass Replacement (%) (A) (B) (C) Figure 7. Parameters derived from pBNG simulations of [C3S + MK] pastes: (A) reactive area fraction of MK (amk); (B) product nucleation density (/density); and (C) total number of product nuclei per gram of C3 S (Nnuc). All parameters are plotted against the MK replacement level (%mass) in the pastes. Simulations are deterministic, and, therefore, there is no uncertainty associated with them 127

This suggests that MK not only suppresses nucleation of C-S-H, but also its post- nucleation growth. Although the exact mechanisms for this are not understood, it is speculated, as has also been suggested in a prior study (9), that the residual aluminate ions present in the solution (i.e., ions that are not adsorbed onto substrates’ surfaces during the first few hours of hydration) adsorb onto C-S-H and, subsequently cut off its access to the contiguous solution, thus subduing its growth. When the paste is mature

(i.e., age ~72 hours), that is, when the supersaturation of C-S-H is relegated to low values, (50, 71, 85) such effects of aluminate ions on product growth rate become less discernible. As such, Gout converges to similar (and low) values regardless of the PSD or replacement level of MK.

(A) (B) Figure 8 . Outward growth rate of the product (Gout) as a function of the (A) time and (B) degree of hydration of the coarse cement.

Overall, the results reported and discussed in Sections 4.1-4.3 show that within the first 72 hours of hydration of [C3S + MK] pastes, the pozzolanic activity of MK is insignificant (see Figure 4), and, therefore, unable to affect C3 S hydration behavior in a 128 consequential way. MK, however, has the potential to serve as a filler, but magnitude of its filler effect is strongly dependent on its PSD and content in the paste. Importantly, this study shows that a mere increase in SSA of MK particulates (e.g., achieved using grinding methods) does not lead to proportional or monotonic enhancement of the filler effect as it does for other inert fillers (e.g., limestone and quartz (8,10,49)).

5. CONCLUSIONS

This study attempts to elucidate the effect of particle size distribution (PSD) of metakaolin (MK) on hydration kinetics of tricalcium silicate (C3 S) during the first 72 hours after mixing. Three unique PSDs—fine, with particulate sizes <20 pm; intermediate, with particulate sizes between 20 and 32 pm; and coarse, with particulate sizes >32 pm—of MK were used. The additive was used to partially replace C3 S in pastes (prepared as constant liquid-to-solid mass ratio of 0.45); two different replacements [i.e., low (8 %mass) and high (30%mass)] were used. Isothermal microcalorimetry, in conjunction with TGA, was used to monitor kinetics of C3 S hydration in the pastes. A phase boundary nucleation and growth model was applied to reproduce the experimentally derived hydration kinetics profiles, and assess variations in key nucleation and growth parameters in relation to the PSD and content of MK in the pastes.

The results show that—unlike other fillers such as limestone and quartz—the correlation between SSA of MK's particulates and the consequent alteration in hydration behavior of C3 S is nonlinear and non-monotonic. MK is able to exert filler effect, albeit 129

the magnitude of the filler effect depends strongly on the PSD and content of MK. Very

fine (high SSA) or coarse (low SSA) particulates of MK are able to exert filler effect at

low replacement level. The filler effect manifests as enhanced nucleation density of C-S-

H, resulting in faster kinetics of C3 S hydration in neighborhood of the main hydration

peak. At high replacement level, however, the filler effect of MK is reversed. This is due to effects of particulate agglomeration (especially, in the case of fine MK) and aluminate

[Al(OH)4-] ion induced surface passivation (in both coarse and fine MK). The surface

passivation effect is caused by adsorption of aluminate ions (released from the dissolution

of MK into the solution) onto C3S and MK particulates, which inhibit C-S-H nucleation

sites on the substrates’ surfaces and suppress the post-nucleation growth of C-S-H.

In the case of intermediate MK, the SSA of which intermediates between those of

the coarse and fine MK, the filler effect is observed neither at low nor at high

replacement levels. In fact, the filler effect is reversed even at low replacement level, and

the nucleation density of C-S-H is diminished progressively (with respect to the control

paste) as the content of MK in the paste increases. This is due to faster dissolution

kinetics of intermediate MK, which results in faster release of aluminate ions in the

solution, and, therefore, more pronounced inhibition of C3 S dissolution and C-S-H

nucleation sites.

Overall, outcomes of this work provide new insights into the role of particle size

of MK on hydration mechanisms of C3 S. For the first time, it is shown that grinding- based improvements in specific surface area (or fineness) of MK particulates does not

necessarily result in enhanced early-age hydration of C3 S. The results, which are rather

counterintuitive, strongly suggest that low replacement level of MK, wherein particulates 130 of MK are predominantly coarse (i.e., low SSA), are optimal for enhancement of hydration of C3 S (i.e., up to 72 hours). This is because coarse MK particulates are least susceptible to effects of particulate agglomeration and aluminate ions-induced surface passivation.

ACKNOWLEDGEMENTS

This study was conducted in the Materials Research Center (MRC) of Missouri

University of Science and Technology (Missouri S&T). The authors acknowledge the financial support provided by the National Science Foundation (NSF, CMMI: 1661609 and CMMI: 1761697). The authors declare no conflict of interest.

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IV. PREDICTION OF COMPRESSIVE STRENGTH OF CONCRETE: CRITICAL COMPARISON OF PERFORMANCE OF A HYBRID MACHINE LEARNING MODEL WITH STANDALONE MODELS

Rachel Cook§, Jonathan Lapeyre§, Hongyan Ma* and Aditya Kumar§

^Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409

*Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO 65409

ABSTRACT

The use of machine learning (ML) techniques to model quantitative composition- property relationships in concrete has received substantial attention in the past few years.

This paper presents a novel hybrid ML model (RF-FFA) for prediction of compressive strength of concrete by combining the random forests (RF) model with the firefly algorithm (FFA). The firefly algorithm is utilized to determine optimum values of two hyper-parameters (i.e., number of trees and number of leaves per tree in the forest) of the

RF model in relation to the nature and volume of the dataset. The RF-FFA model was trained to develop correlations between input variables and output of two different categories of datasets; such correlations were subsequently leveraged by the model to make predictions in previously untrained data domains. The first category included two separate datasets featuring highly nonlinear and periodic relationship between input variables and output, as given by trigonometric functions. The second category included two real-world datasets, composed of mixture design variables of concretes as inputs and their age-dependent compressive strengths as outputs. The prediction performance of the 138 hybrid RF-FFA model was benchmarked against commonly used standalone ML models—support vector machine (SVM), multilayer perceptron artificial neural network

(MLP-ANN), M5Prime model tree algorithm (M5P), and RF. The metrics used for evaluation of prediction accuracy included five different statistical parameters as well as a composite performance index (CPI). Results show that the hybrid RF-FFA model consistently outperforms the standalone ML models in terms of prediction accuracy— regardless of the nature and volume of datasets.

Keywords: Machine learning, concrete, compressive strength, random forest, firefly algorithm

1. INTRODUCTION

The idea of using data-driven methods—such as supervised machine learning

(ML)—for prediction and optimization of materials’ performance forms the premise of the United States Materials Genome Initiative (1). In pursuit of the idea, researchers from various scientific domains have compiled extensive datasets of materials and subsequently employed ML models to better understand the underlying quantitative composition-performance correlations (2-5). Knowledge of such correlations, for any given material, can be leveraged to mitigate the cost and time involved in an Edisonian approach—involving rigorous and iterative synthesis-testing/analyses cycles (6)—to predict a material’s properties or to design a new material that meets a desired set of performance criteria. 139

Concrete— the most produced and used material in the world— has garnered the interest of several researchers working the area of ML. The focus of various research articles (7-20) has been to employ M L models to predict concretes’ properties (e.g., compressive strength and rheological parameters) using their mixture design variables

[e.g., contents of cement, water, mineral additive(s), and admixture(s)] and age as inputs.

Among concrete’s properties, compressive strength is deemed relatively more important for quality control, and it is widely used as the primary specification criterion for construction of structures. Furthermore, compressive strength of concrete is very well correlated with other mechanical properties (e.g., elastic modulus, flexural strength) and, therefore, can be used to qualitatively estimate the overall mechanical stability and survivability of the structure (21,22). Because of these reasons, most of the aforementioned studies have focused on predicting the compressive strength of concrete.

The utilization of ML models— as opposed to Edisonian approaches, or simple linear regression models— is to overcome complexities pertaining to (i) the staggeringly large compositional degrees of freedom in concrete (i.e., mixture design variables, permutations and combinations of which can vary within wide ranges and exert significant influence on properties) and (ii) the inherent nonlinear relationships between mixture design variables and properties of concrete. To be more specific on the latter point, the properties of concrete are complex— highly nonlinear, and, often, non monotonous— functions of mixture design variables. For example, within the cement paste component of concrete, compressive strength decreases with increasing water-to- cement ratio (w /c , mass basis); however, this relationship exhibits nondifferentiability at the critical w /c of 0.42, below which the paste becomes water-deficient (23,24). This 140

relationship between the w/c and compressive strength is further convoluted when a

fraction of the cement is replaced with a reactive mineral additive (e.g., fly ash and blast

furnace slag) (25,26). Therefore, sophisticated approaches, such as ML, are required to

reveal the hidden, and complex, semiempirical rules that govern the correlation between

mixture design and properties of concrete.

The majority of past studies, focused on prediction of compressive strength of

concrete, have used nonlinear regression based ML models [i.e., artificial neural network

(ANN) (27) or support vector machine (SVM) (28)]—presumably because of nonlinear

correlations between mixture design variables and properties of concrete. Many studies

(7,9,10,14,16,17,19,29-31) have shown that both ANN and SVM models, when trained

using a sufficiently large dataset, can predict compressive strength of concrete with

reasonable accuracy (i.e., coefficient of determination, R2 > 0.90). However, it has been

reported that ANN and SVM models are unreliable in making predictions in data

domains that feature a highly nonlinear, periodic functional relationship between one or

more input variables and the output (32-34). This is because both ANN and SVN models

employ local search or optimization algorithms (e.g., back-propagation algorithm used in

ANN), which are faced with an inherent drawback of getting trapped in local minima—

especially when the functional relationship between input variables and output is

composed of multiple local minima (e.g., periodic trigonometric functions)—rather than

converging to the global minima. Because of this drawback, with every rerun of ANN or

SVM during the training period (i.e., when different subsets of the same dataset are used to train the models) the convergence could occur at different local minima, thus resulting

in disparate prediction performances (i.e., the ability to reliably predict outputs using 141 previously unseen input variables) during the testing (32-34). This deficiency can be amended by using algorithms based on genetic programing (15,29). Alternatively, bootstrap aggregation of outputs of several models developed from various subsets of the training dataset—for example, by using bagging, voting, or stacking approaches

(31,35)—can also be used. However, such techniques could slow down the rate of convergence or, in the worst case, result in overfitting (36). This issue of ANN and SVM models, pertaining to their inferior performance on datasets featuring periodic input- output relationship, is further examined in the “Results and Discussion” section.

ANN and SVM models have another drawback—the objective functions produced by them are difficult to interpret and, therefore, difficult (albeit not impossible) to employ for optimization purposes. This is because the functional relationship between input variables and output is not yielded as a transparent mathematical formula. To overcome this limitation, in some recent studies (8,14,15,19,31) decision trees-based ML models have been employed. Decision trees are essentially rules-based models, wherein the training dataset is classified into multiple independent subsets and subsequently processed using a collection of linear or nonlinear regression methods to develop multiple

(transparent) functional relationships between input variables and output. Notable among these are application of the M5Prime (M5P) (8,14,37-39) and random forests (RF)

(8,19,30,37,40) showed that prediction accuracy of the M5P model was superior compared to the ANN model. Similarly, as per the R2 values reported by Young et al.

(19), predictions of concrete compressive strength using the RF model were more accurate (albeit not comprehensively) compared to those using ANN and SVM models. 142

To the best of the authors’ knowledge, the prediction performances of M 5P and

RF models (i.e., in terms of predicting the compressive strength of concrete) have not been compared. Notwithstanding, the RF model is hypothesized to be superior compared to the M5P model; this hypothesis will be corroborated in the “Results and Discussion” section. The premise of this hypothesis is that the M 5P model assumes a multivariate linear relationship between input variables and output in each subset of the training data

(38,39). M ore specifically, the training dataset is split into multiple subsets until in each subset a simple, linear input-output correlation can be established. Because of this limitation— like in the ANN and SVM models— predictions made by the M5P model in domains that feature highly nonlinear and/or periodic relationships between input variables and output are expected to be inaccurate. The RF model, on the other hand, does not suffer from this limitation because of its ability to handle continuous and discrete variables over both monotonous and non-monotonous domains (40).

Notwithstanding, in the RF model, it is important to fine-tune two hyper-parameters— that is, the number of trees in the forest and the number of leaves per tree— to ensure that input- output correlations are identified and captured, and predictions are accurate. In the absence of an optimization algorithm, the two hyper-parameters need to be adjusted through trial and error [e.g., by using multifold cross-validation (41)], which can be tim e consuming and difficult. In a recent study (42), it was shown that the firefly algorithm

(FFA)— a metaheuristic optimization algorithm (43)— can be used to determine optimum values of the two aforementioned hyper-parameters in relation to the volume and nature of the training dataset. The authors showed that by combining RF with FFA predictions

(of global solar radiation) were rendered more accurate compared to those made by 143 various standalone and ensemble M L models. In another study (44), FFA was used in conjunction with SVM to predict concretes’ compressive strength. Although the combined [SVM + FFA] model had better prediction performance than the standalone

SVM model, it is expected that inherent limitations of SVM— as described previously— could have compromised the prediction performance of the combined model. To the best of the authors’ knowledge, the combination of RF and FFA has never been used to process concrete datasets. Given the superior prediction performance of RF [compared to

SVM as well as other ML models (19)], it is deemed important to examine whether combining RF with FFA would result in further improvements in accuracy of predictions of concretes’ compressive strength.

This study presents the first application of the hybrid RF-FFA model— developed by combining the RF model with FFA— to predict compressive strength of concretes in relation to their mixture design and age. The performance of the hybrid model is benchmarked against commonly used standalone M L models (i.e., SVM, multilayer perceptron ANN, M5P, and RF). Six different statistical parameters are used for comprehensive evaluation of the m odels’ prediction performance. Firstly, highly nonlinear, non-monotonous, and periodic trigonometric functions are used to evaluate the performance of the M L models. Focus is given to determine if the hybrid model is able to reveal the complex relationship between input variables and output of the trigonometric functions and, more importantly, reliably predict the function outputs in blank (i.e., previously untrained) data domains. Secondly, the prediction performance of the ML models is tested using two real-world concrete datasets, composed of concretes’ mixture designs and their corresponding age-dependent compressive strengths. Based on 144 comparisons of prediction performances— of the hybrid RF-FFA model vis-a-vis the standalone M L models— it is shown that the hybrid M L model consistently outperforms the standalone M L models.

The paper is organized as follows. “M achine Learning M odels” describes the five

M L models implemented in this study. “Data Collection and Performance Evaluation of

M achine Learning M odels” describes the datasets used for training and testing of the ML models. A brief description of statistical parameters used for evaluation of prediction performance of the models is also included. “Results and Discussion” reports the results and comparison of prediction performances of various M L models. “Conclusions” presents a summary of the main findings of the study.

2. MACHINE LEARNING MODELS

This section provides a brief overview of the machine learning (ML) models implemented in this study. In each of the following subsections, one or more original references are provided that describe the formulation and implementation of the ML model in more detail.

2.1. MULTILAYER PERCEPTRON ARTIFICIAL NEURAL NETWORK

An artificial neural network (ANN) consists of several computational elements

(termed as neurons) arranged in layers, resembling the network of neurons in the human brain responsible for processing information in a hierarchical fashion (27). The multilayer perceptron artificial neural network (MLP-ANN) is a subclass of ANN with strong self 145

learning capabilities (45). The hierarchical structure of MLP-ANN is composed of (i) one

input layer, which contains a set of neurons representing the input variables (e.g.,

concrete mixture design variables); (ii) one or more hierarchical hidden layers, which

contain computational neurons to process the information received from the previous

layer so that it can be refined and passed on to the next layer; and (iii) one output layer,

which contains a computation node to produce the final prediction (e.g., compressive

strength of concrete). Each neuron in any given hidden layer is functionally related—as

shown in Equation (1)—to all neurons in the previous layer

(1) WjiOi

1 (2) Vi = f (Nj) 1 + ewJiNJ

here, Nj = activation of the jth neuron; i = set of all neurons present in the previous layer;

Wji = weight of connection between neurons j and i; and Oi = output of the neuron. Each

neuron uses activation functions (while using all neurons from the previous layer) to

calculate intermediate-output values, which are subsequently passed on as input values to

the next neuron layer. This process proceeds throughout the network until reaching the

final neuron layer that produces the final output. In the MLP-ANN model, activation

functions are represented as sigmoidal or logistic-transfer functions (45)—as shown in

Equation (2), wherein yj = f(Nj) is the activation function of the jth neuron. During

training of the MLP-ANN model, a back-propagation algorithm (46,47) is used to

minimize deviation [i.e., root-mean squared error (RMSE) or mean absolute error

(MAE)] between actual and predicted values (of the activation functions). This is

accomplished by iteratively adjusting and finally determining the optimal connection 146

weights (i.e., wji) —pertaining to each activation function—by using the gradient descent

approach or the Levenberg-Marquardt algorithm (45,48).

In the MLP-ANN model used in this study, the neural network architecture is

composed of five hidden layers, wherein each layer is composed of (2m + 1 ) neurons

(49); m is the number of input variables of the training dataset. The choice of five hidden

layers was made based on comparison of prediction performances of the model—whilst varying the number of hidden layers between unity and higher values—against

experimental datasets (i.e., datasets pertaining to concrete and those generated using trigonometric functions) described in the “Data Collection” section. For fine-tuning of the

parameters (i.e., connection weights of each of the activation functions), the Levenberg-

Marquart algorithm, as described in More (48), was chosen because it resulted in superior

prediction performance compared to the gradient descent approach. It is clarified that for

determination of optimal parametric values (i.e., number of hidden layers) and for

selection of the Levenberg-Marquart algorithm, a 10-fold cross-validation (CV) method

(31,36,41) was used as the primary performance-assessment method. The same method

has also been used to optimize parameters and functions of other ML models described

subsequently in this section. In general, ap-fold CV method (wherep is the number of

folds, for example, 1 0 as used in this study) involves the randomized stratification of the

original dataset into p folds such that each fold contains 1 0 0 p/N% of the total number

(i.e., N) of data-records of the original dataset. It is also important to ensure each of thep

folds encompasses an approximately similar proportion of predictor labels as in the

original dataset. Next, the model is trained using data-records inp - 1 folds out of thep

folds and test against the last fold. This process is repeatedp - 1 times, in an iterative 147 manner, such that each of the p folds encompasses an approximately similar proportion of predictor labels as in the original dataset. It is also important to ensure each of the p fo ld s encompasses an approximately similar proportion of predictor labels as in the original dataset. Next, the model is trained using data-records in p - 1 folds out of the p folds and tested against the last fold. This process is repeated p - 1 times, in an iterative manner, such that each of the p folds are used once for testing and p - 1 times for training the model. W ith each training-followed-by-testing iteration, the CV error (usually expressed in the form of root-mean squared error) is estimated, and on such basis the optimum functions (e.g., for determination of functional forms of neuron activation) are chosen and the parameters of the M L model (e.g., number of hidden layers in M LP-ANN model) are progressively fine-tuned. Ultimately, the optimum function(s) and values of parameters of the M L model correspond to those that result in the smallest overall value of CV error when accumulated over all experimental datasets.

2.2. SUPPORT VECTOR MACHINE

Support vector machine (SVM) is an M L methodology for approximating the nonlinear relationship between input variables and output of a dataset by using an optimization approach— rather than a regression approach— to minimize a cost (i.e., e- insensitive loss) function (50,51). During training, the SVM, firstly, maps the input dataset from a lower-dimensional to a higher-dimensional feature space by using a mapping procedure. Toward this, a nonlinear kernel function [e.g., polynomial function, sigmoidal function, Gaussian radial basis kernel function, or hyperbolic tangent function

(52,53)] is used to fit the input data into a higher-dimensional feature space, wherein the 148

data is distributed in a more sparse form compared to the original one. Next, the SVM

attempts to determine a linear objective functionfsvM (x, m) [see Equation (3)] —such

that its output has a maximum deviation of e with respect to the actual (measured) value

in the training dataset n fsvM(x,v) = ^ + b (3) i=i

In Equation (3), Ki = set of n nonlinear kernel (i.e., mapping) functions used for transforming the original input data (x) into higher-dimensional feature space; b = a bias term; and m represents the weight vector consisting of n choice coefficients. In order to

derive the optimum objective function fsvM(x,m)]—and the associated parameters (i.e., b

and m)—the task of regression is approached as an optimization problem [Equation (4)], within the constraints shown in Equation (5). The objective of the optimization effect is to determine the global minimum of Equation (4) such that for each input value (x), the

output offsvM (x, m) is within ta Euclidian distance of e from the actual value (54). In

Equation (4), the constant C is called the regularization term and represents the degree of

penalty of the sample with error exceeding e (i.e., when the prediction is farther than s

from the actual value). The parameters, & and &*, shown in Equation (5) are positive

slack variables that represent the Euclidian distance of the predicted value from the

corresponding boundary value of the e -tube (i.e., a tube representing the actual training

dataset, wherein each data record is bounded by the maximum allowable error of e).

Therefore, based on the formulation described here, to derive the optimum objective

function, fsvM (x, m) (and optimum values of the bias, b, and choice coefficients, m)—that

reliably links input variables with the output—the parameters that need to be optimized 149 are e, C, and any parameter associated with the kernel function (e.g., the parameter y, which is associated with the Gaussian radial basis kernel function, as shown in Equation

(6) (52,53). n (4) t=i

(5)

K(x,y) = e-^ * -^ (6)

In the SVM model used in this study, three different kernel functions (i.e.,

Gaussian radial basis kernel function, 3rd-to-5th order polynomial functions, and sigmoidal function) were used. Based on comparisons of prediction performances of the model— ascertained using the 10-fold CV method (41,55)— on experimental datasets

(described in the “Data Collection” section), the Gaussian radial basis kernel function was chosen. W ithin the kernel function [see Equation (6)], the optimum value of y w a s determined (as per the CV method) as 0.10. The optimum values of e (representing the radius of the e-tube) and C (the regularization term) were determined as 1.5 M Pa and 5.0, respectively.

2.3. M5PRIME MODEL TREE ALGORITHM

The M 5Prime model tree algorithm— often abbreviated as the M5P model— is a modification (39) of the M 5Rules algorithm introduced by Quinlan (38). The M 5P model is, essentially, a decision tree model that performs logical splits in the training dataset so that the input variables can be linked with the output using multivariate linear functions. 150

During training of the M 5P model, the input space is split in several subspaces, while ensuring that data in each subspace share at least one common attribute (e.g., similar range of one or more input variables). M ore specifically, the splitting of data is performed in a manner that data that are alike— in terms of one or more of their attributes— are clustered and contained within the same subspace. By repeating this procedure iteratively, several subspaces, each consisting of harmonious data, are obtained. Standard deviation is typically used as the criterion for determining the specific attribute or attributes on the bases of which optimal splitting of the dataset can be achieved. Such reduction in standard deviation allows determination, and subsequent creation, of several nodes (i.e., data clusters) on the bases of attributes. By creating such nodes, the model enables the building of an upside-down tree-like structure, wherein the root is at the top and the leaves are at the bottom. Once the tree is built, a new data-record propagates hierarchically from the root and down through the nodes until it reaches a leaf. Each node consists of a mathematical logic, which compares the new data-record with that of the split value and helps the data-record propagate down through the nodes until it reaches the appropriate leaf. In the M 5P model, a linear regression model is used as the aforementioned mathematical logic. The regression model is developed in each of the subspaces, linking input variables and output of the data-records contained within it. To ensure that the tree-structure is optimal, a pruning technique is used to overcome the issue of overtraining— that is, when the chosen attribute, for any given subspace, is not the optimal one with the maximum expectation to reduce error (i.e., standard deviation, in this study). Use of the pruning technique, however, can result in discontinuities between adjacent linear models. To mitigate this issue, a smoothing operation is employed in the 151

final step. Such iterative pruning and smoothening operations ultimately unify all linear

regression models—across all the nodes between the root and leaf of the tree—into a

singular, continuous model.

The M5P model used in this study was implemented using the Waikato

Environment for Knowledge Analysis (WEKA) workbench toolbox (56,57). The only

variable parameter in the M5P model is the minimum number of splits in the dataset. This value was varied widely from unity to higher values, and the prediction performance was

measured—using the 10-fold CV method—using experimental datasets (described in the

“Data Collection” section) for both training and testing. Based on such evaluations, the

optimum value of minimum number of splits was selected as 4.

2.4. RANDOM FORESTS

First, “nt” bootstrap samples are drawn randomly from the original training

dataset. At this point, the number of bootstrap samples (i.e., nt) is equal to the number of trees. Based on prior studies (42,58,60), the optimum value of nt is ~ 6 6 .6 6 % of the

overall training dataset. The remaining ~ 33.33% of the dataset are labelled as out-of-bag

(OOB) data. For each of the nt bootstrap datasets, a tree is grown. Unlike conventional

decision tree models (e.g., the M5P and CART models), each tree in the RF model is an unpruned regression tree, wherein at each node, rather than choosing all variables of the training dataset, a random sample of mtry variables is chosen. As the tree is grown, the

number of leaves per tree (nLV) is held constant across the entire ensemble. Based on

previous studies (42,58), the optimum value of nLV is between 3 and 10. In this study, the

optimum value—assessed by performing predictions on different experimental datasets 152

(described in the “Data Collection” section)—was determined as 5. Next, each of the nt trees is utilized to predict a data point outside of the selected bootstrap space. Output of the prediction is designated as out of bag (OOB) prediction (59). These OOB predictions, for a given input vector (x), are designated as/rf(x) for each of the nt decision trees; all

OOB predictions are subsequently aggregated and averaged to produce the overall OOB prediction fpp(x) and OOB error rate [see Equation (7)]. Simply put, fpp(x) is the arithmetic mean of the predicted values collated from all of the nt trees. The OOB predictions—especially the OOB error rate—provide a good measure of influence of each variable on the output, which can be quantitatively estimated as variable importance

(VI), thus eliminating the need for a test set or cross-validation (Schaffer 1993). The VI of a given variable is, essentially, a measure of increment in OOB error rate when OOB prediction for a given variable is permuted while all others are left unchanged (60). Once the OBB predictions, OOB error rate, and VI are calculated, outliers in the training dataset are detected using cluster analysis (e.g., K - means cluster analysis, density model, and mean-shift clustering) (61). In this study, the V-means cluster analysis (62) was used to determine data-records that do and do not belong in clusters. The data- records that do not belong in clusters are removed and subsequently replaced in an iterative manner through the training process. Lastly, in the testing phase, a new input dataset—which is not part of the training dataset—is used to perform predictions. For each input data-record, the predicted value corresponds to the average of predictions from all of the nt trees. The RF model has a number of unique advantages. In the RF model, a large number of trees are grown (as opposed to other decision tree models)—on a one- 153

node-at-a-time basis; as such, errors resulting from generalization are minimized and,

therefore, the likelihood of overfitting the training data is negligible (63). nt

C (x) = -1 Y fRFi(x} (7) t ;=i

Minimization of generalization, enabled by the large number of trees, entails that

the RF model is able to proficiently deal with complex interactions and correlations

among variables of the training dataset. By allowing each of nt trees to grow to its

maximum size (i.e., by allowing deep trees), without any pruning, and selecting only the best splits among a random subset at each node, the RF model is able to concurrently

maintain diversity among trees and prediction performance. The two-stage

randomization—as described previously—diminishes correlation among unpruned trees,

keeps the bias low, and reduces variance. Lastly, the RF model is easy to implement because the number of trees (nt) and the number of leave per tree (niv) are the only two

hyper-parameters that need to be optimized by the user. Both of these hyper-parameters were optimized by the 10-fold CV method (41,55), whilst training and testing the model using experimental datasets described in the Data Collection section. Through such

assessments, the optimum values of nt and niv for the standalone RF model were

determined as 450 and 5, respectively.

2.5. HYBRID RANDOM FORESTS: FIREFLY ALGORITHM MODEL

The FFA—originally conceived by Yang (2009)—is an optimization algorithm

(64,65) based on idealized behavior of the flashing characteristics of fireflies. The rules

of idealized flashing characteristics are (i) each firefly is attracted to all other fireflies; (ii) 154

the magnitude of attractiveness between any two fireflies is proportional to the difference

in brightness between them; (iii) the movement of a firefly is always toward a firefly with

greater brightness; and (iv) the brightness of the firefly is determined by the landscape

[i.e., the objective function, fx), that is to be optimized]. The brightness, I, of a firefly at

a particular location, x, can be chosen as I(x), which is directly proportional to the

objective function,fx). The attractiveness, ft, between a pair of fireflies is a function of

the distance, r j, between firefly I and firefly j. Likewise, the brightness, Ii, of firefly i varies with the distance ri from the source in a monotonic and exponential manner

Equation 8 a.

It = V -™ (8 a)

where,

Y o Y (8 b) r,max

Here, Io = brightness at the source (typically set at 1.0); and y = light absorption

coefficient (representing the potential of fireflies to absorb light from the source). The

value of y can range from 0 to 10 (43). In this study, however, y was calculated using

Equation (8 b), wherein yo = 1.0, and rmax is the maximum of distances between all pairs

of fireflies (64) in the landscape. The mathematical formulation of the magnitude of

attractiveness (ftij) between two fireflies (I and j) in relation to the distance between them

(rj) is given by Equation (9)

Pij=Poe-rrV (9)

where fto = maximum attractiveness between a pair of fireflies (i.e., at r = 0 ); and m = a

positive coefficient (ranging between 2 and 4). The values of ft can range from 0 to 1, 155

wherein the upper bound represents cooperative local search with the brightness firefly

dictating position of most fireflies in the swarm. As the value of fa0 digresses from 1,

dominance of the brightest firefly decreases, thus rendering the local search progressively

more noncooperative. In this study, a value of 0.80 used for fa and m was set at 2.0. The

movement of a firefly i, as it is attracted to a brighter firefly j, is determined by Equation

(10). Here, x;,old and Xj are locations of the fireflies i and j, respectively, and the last term

is randomized with the vector of random variables (e) drawn from a Gaussian

distribution; X;,new is the new position of firefly I as its moves because of its attraction

toward firefly j

xi,new xi,old + fi0& ^ (10)

Based on the previously mentioned criteria and definitions, the FFA can be used

to minimize a continuous, constrained cost functionfx). Firstly, it is assumed that there

exists a swarm of m fireflies—distributed randomly over the landscape. The fireflies are tasked to find x*, wherein the value of the cost function fx*)—or, in other words, the

overall brightness of the landscape—is minimum. Next, the FFA is implemented in the

following steps: (i) all fireflies of the swarm are allowed to move, in a sequential manner,

such that each firefly moves toward another in the neighborhood on the basis of its

attractiveness toward the other firefly (which is a function of difference in brightness and the distance between the two fireflies); (ii) once all fireflies have been allowed to move to their new locations, based on the new configuration of fireflies, the overall brightness of the landscape is updated, and assessed if it is lower than the original one; and (iii) Steps 1

and 2 are repeated iteratively until convergence is reached, wherein the overall brightness 156 of the landscape reaches the global minimum (i.e., the value does not change by more than 1 0 -6 units between three successive iterations).

2.6. HYBRID MODEL

In the RF model—as described in the previous subsection [i.e., Random Forests

(RF)]—it is important to fine-tune the two hyper-parameters—that is, the number of trees in the forest (n) and the number of leaves per tree (niv)—to ensure that predictions are accurate. Typically, the two parameters are adjusted through trial and error or by cross validation, which can be time-consuming and difficult. In a recent study (42), it was shown that the firefly algorithm (FFA)—described in the section on the firefly algorithm

(FFA)—can be used to determine optimum values of the two aforementioned hyper parameters in relation to the nature and volume of the dataset. The authors showed that by combining RF with FFA, predictions were rendered more accurate compared to those made by various standalone and hybrid ML models—including the RF model.

In this study, the structure of the hybrid model has been drawn from the work of

Ibrahim and Khatib (42). In Stage 1, the RF model is implemented, wherein the values of nt and niv are set at 450 and 5, respectively. In Stage 2, the FFA is implemented in the following steps:

• An objective function, fx), is defined, which corresponds to the total root-

mean squared error (RMSE: described in the “Evaluation of Prediction

Performance of Machine Learning Models” section) of predictions of the

RF model with respect to actual values of the training dataset used in

Stage 1. 157

• The FFA is implemented— by following the steps detailed in the firefly

algorithm (FFA) section— to optimize the values of nt a n d n i v such that

the objective function [i.e., f x ) = RM SE of the RF model] continually

decreases. Toward this, at the end of every iteration of the FFA, the RF

model is implemented to update predictions based on new values of the

two hyper-parameters; based on the predictions, the RM SE is also updated

to be used in the next iteration.

• The values of nt a n d n iv , at which the objective function reaches a global

minimum (changes by less than 10-6 units between three successive

iterations), are selected as the final, optimum values.

Lastly, in Stage 3, the RF model is implemented to make predictions against the test dataset using the FFA-determined optimum values of the hyper-parameters.

2.7. DATA COLLECTION AND PERFORMANCE EVALUATION OF MACHINE LEARNING MODELS

Experimental datasets, consolidated from published studies (16,17,66), were used to train the M L models (described in the “M achine Learning M odels” section) and to assess their prediction performance in previously untrained data domains. The first dataset— subsequently referred to as Dataset 1— was first published by (16,17), and subsequently used by several researchers (7-15,18-20,31,44) for training, testing, and validation of statistical and M L models. Dataset 1 consists of 1,030 data-records, featuring 278 unique concrete mixture designs and their age-dependent compressive strengths. In the context of ML, in each data record, there are eight input variables

[contents of cement (kg m-3), blast furnace slag (kg m-3), fly ash (kg m-3), superplasticizer 158

(kg m-3), water (kg m-3), fine aggregate (kg m-3), and coarse aggregate (kg m-3), and age

(days)] and one output—compressive strength (MPa). Statistical parameter pertaining to

Dataset 1 are summarized in Table 1 .

Table 1. Summary of statistical parameters pertaining to each of the 9 attributes (8 input and 1 output) of Dataset 1. The dataset consists of 1,030 unique data-records

S ta n d a rd A ttrib u te U n it M in im u m M a x im u m M ean D ev ia tio n

Cement kg m-3 1 0 2 . 0 0 540.00 281.27 104.51

Blast furnace kg m-3 0 . 0 0 0 0 359.40 73.896 86.279 slag

Fly ash kg m-3 0 . 0 0 0 0 2 0 0 . 1 0 54.188 63.997

Superplasticizer kg m-3 121.80 247.00 181.57 21.354

Coarse kg m-3 0 . 0 0 0 0 32.200 6.2050 5.9740 aggregate

Fine aggregate kg m-3 801.00 1,145.0 972.92 77.754

Age Days 594.00 992.60 773.58 80.176

Compressive MPa 1 . 0 0 0 0 365.00 45.662 63.170 strength

The second dataset—subsequently referred to as Dataset 2—was first published by Chopra et al. (6 6 ) and utilized in several later studies (29,30,67). Dataset 2 consists of

76 data-records, featuring different concrete mixture designs and their compressive strengths at 28 days. In the context of ML, in each data record, there are five input 159

variables [contents of cement (kg m-3), fly ash (kg m-3), water (kg m-3), fine aggregate (kg

m-3) and coarse aggregate (kg m-3)] and one—compressive strength (MPa) at 28 days.

Statistical parameters pertaining to Dataset 2 are summarized in Table 2 . For training,

and assessment of the prediction performance of ML models, the dataset (i.e., Dataset 1

or Dataset 2, as described in the Data Collection section) was randomly partitioned into two sets: a training set and a testing set.

Table 2. Summary of statistical parameters pertaining to each of the 6 attributes (5 input and 1 output) of Dataset 2. The dataset consists of 76 unique data-records

Attribute Unit M inim um M axim um M ean Standard

Deviation

Cement kg m-3 350.00 475.00 433.88 34.810

Fly ash kg m-3 0 . 0 0 0 0 71.250 24.030 32.641

W ater kg m-3 178.50 229.50 202.81 12.821

Coarse aggregate kg m-3 798.00 1,253.8 1,050.9 134.52

Fine A ggregate kg m-3 175.95 641.75 524.31 69.378

28-day compressive MPa 31.660 54.490 44.374 5.2120

strength

Among the data-records, 75% of the parent dataset were used for training of the

ML models (i.e., for fine-tuning and, ultimately, finalizing the optimum model

parameters), and the remaining 25% were used for testing (i.e., for determination of

cumulative error between predicted and actual values). Such a split of 75%-25% between

the training and test sets—or a ratio close to that—has been used in various past studies 160

(9,19,31). Although the splitting was done randomly, special care was taken to guarantee that the training dataset was representative of the parent dataset. Toward this, it was ensured that the training dataset was composed of input attributes (i.e., concrete mixture design variables) with widespread values encompassing the entire range between the two extrema. For quantitative measure of prediction performance of the ML models (against the test set), five different statistical parameters were used. The parameters, essentially, estimate the cumulative error in predictions—of compressive strength of concretes in the test dataset—with respect to the actual measurements.

n^yy' - (Z y)(Z y') R = (11) Vn(Zy2) - (Zy ) 2 Jn(Zy'2) - (Z y ' ) 2

2 n lyy' - (Z y)(Z y') R2 = (1 2 )

Vn (S y 2 ) - (Zy)2 Jn(Zy'2) - (Zy')2

i=n , 1 0 0 % y |y - y | mape = (13) n L. j y i=i l=n i y \y-y \ MAE (1 4 ) nZ_i y i=i

i=n 1 RMSE = (1 5 ) n Y ly-y'l t=i

j=N 1 \ ’ Pj Pminj CPI (1 6 ) JVM / .p 1 max,] . - 1p min,] . .

The statistical parameters are the Pearson correlation coefficient (R), coefficient of determination (R2), mean absolute percentage error (MAPE), mean absolute error 161

(MAE), and root-mean squared error (RMSE). The mathematical formulations to

estimate those errors are shown in Equations (11) - (15); here, y ’ and y are predicted and

actual values, and n is the total number of data-records in the test dataset. To obtain a

comprehensive measure of prediction performance of the ML models—and to compare them—the five statistical parameters described in Equation (11) - (15) were unified into

a composite performance index [CPI, see Equation (16)] (31,68). In Equation (16), N is the total number of performance measures (= 5 because five statistical parameters were used in this study), Pj is the value of the jth statistical parameter, and Pj,min and Pj,max are the minimum (i.e., worst) and maximum (i.e., best) values of the jth statistical parameter

across the five values generated by the same number of ML models. Based on the

formulation in Equation (16), the values of CPI would range from 0 to 1, wherein 0 (or the lowest value) would represent the best ML model and 1 (or the maximum value) would represent the worst ML model in terms of overall prediction performance. In this

study, the different ML models were ranked—from worst to best in terms of prediction

performance—based on their CPI values.

3. RESULTS AND DISCUSSION

3.1. HIGHLY NONLINEAR AND PERIODIC TRIGNOMETRIC FUNCTIONS

In conventional regression-based machine learning (ML), the quality of an ML

model is measured by its capability to learn from a training set and apply the knowledge

to forecast in previously unseen data domains from the same distribution. Simply put, the

prediction performance of an ML model boils down to its ability to identify trends in the 162 dataset and subsequently use such trends for interpolation. When trained properly (e.g., by training with an adequately large dataset and by avoiding overfitting), nonlinear ML models are often able to perform interpolations with sufficient accuracy. However, it has been reported that the interpolation accuracy of many ML models (e.g., ANN and SVM) becomes unreliable in data domains that feature complex, highly nonlinear, and periodic functional relationships between one or more input variables and the output (32-34,69).

Table 3. Prediction performance of ML models, measured on the basis of the test set developed using Equation (17). Five statistical parameters (i.e., R,R2,MAE, MAPE, and RMSE) and the composite performance index (CPI) are shown.

M L model R R2 MAE MAPE RMSE CPI

MLP-ANN 0.8425 0.7098 2.4633 102.87 2.8552 1.0000

SVM 0.8707 0.7581 1.2353 51.588 1.5245 0.6334

M 5P 0.9718 0.9443 0.6113 25.530 0.7891 0.2212

RF 0.9995 0.9990 0.0753 3.1436 0.0977 0.0106

RF-FFA 0.9999 0.9998 0.0354 1.4790 0.0563 0.0000

In the context of concrete, the ability to interpolate in such highly nonlinear domains could be the difference between reliable and unreliable predictions; this is because the relationships between mixture design variables and properties of concrete are also expected to be highly nonlinear and non-monotonous. To test the ability of ML models—described in the “Machine Learning Models” section—to interpolate in highly nonlinear and periodic data domains, datasets generated from trigonometric functions shown in Equations (17) and (18) was used. Similar functions were originally suggested by Martius and Lampert (69) to test the ability of various ML models to interpolate (and 163

extrapolate) within periodic data domains. In Equation (17), x is an input vector

consisting of X1, X2, X3, and X4 variables, and yi = Fi(x) is the output. For this function, xi

= X2 = X3 = 2x4. In Equation (18), x in an input vector consisting of the same xi, X2, X3, and

X4 variables, and y2 = F 2(x) in the output. Here, xi = x2 = x3 = -5x4. Two separate datasets were generated by varying x1 (and, on account of the aforementioned equality, x2, x3, and x4 as well) between -4.0 and 4.0, and calculating F 1(x) and F2(x) as functions of all four variables. The increment in x1 was set at 0.01; as such, each of the two datasets consisted

of 800 data-records with four input variables and a single output. Next, each dataset was

split randomly into a training set (75%, or 600 data-records) and a test set (25%, or 200

data-records), using the procedure described in the Data Collection section. All five ML

models implemented in this study (i.e., MLP-ANN, SVM, M5P, RF, and RF-FFA) were then trained using the training dataset; subsequently, their prediction performances were

assessed using the corresponding test dataset.

yi = Fi(x) = ^sin(^Xi)] + [x2 cos ( 2 ^X1 + ^)] + [X3] - [x|] (1 7 )

y2 = F2(x) = - [ ( 1 + X2 )(sin(^X!))] + [X2 X3 X4 ] (1 8 )

Figures 1 and 2 show predictions made by the five ML models plotted against the

actual values, calculated using Equation (17) [i.e., for F 1(x)] and Equation (18) [i.e., for

F(x)], respectively. Tables 3 and 4 summarize the statistical parameters (i.e., cumulative

errors) pertaining to predictions made by the ML models, and the composite performance

index [CPI, Equation (16)] calculated using the five statistical parameters. As can be seen

in Figures. 1 and 2, the MLP-ANN and SVM models are unable to capture the periodic

nature of the dataset. As stated previously in the Introduction, this is because both models 164 employ local search or optimization algorithms, which are faced with an inherent drawback of getting trapped in local minima—especially when the functional relationship between the input variables and output is composed of multiple local minima [e.g., datasets generated using Equations (17) and (18)]—rather than converging to the global minima.

Table 4. Prediction performance of ML models, measured on the basis of the test set developed using Equation (18). Five statistical parameters (i.e., R,R2,MAE, MAPE, and RMSE) and the composite performance index (CPI) are shown.

M L model R R 2 MAE MAPE RMSE CPI

MLP-ANN 0.8598 0.7392 1.0794 91.133 1.2602 0.9633

SVM 0.8450 0.7140 0.7201 60.797 0.9570 0.8175

M 5 P 0.9963 0.9926 0.1272 10.737 0.1648 0.0797

RF 0.9998 0.9996 0.0239 2.0158 0.0312 0.0104

RF-FFA 1.0000 1.0000 0.0063 0.5359 0.0107 0.0000

The poor prediction performance of MLP-ANN and SVM models is also reflected in the values of statistical parameters listed in Tables 1 and 2 [e.g., RMSE of 2.8552 and

1.5245 for MLP-ANN and SVM models, respectively, when used for prediction of F\(x) and RMSE of 1.2602 and 0.9570 for MLP-ANN and SVM models, respectively, when used for prediction of F 2(x)]. It is indeed possible to improve prediction performance of the models by incorporating algorithms based on genetic programing (15,29), or by using ensemble techniques [e.g., bagging, voting, or stacking approaches (31,35)]. However, as stated previously in the Introduction, such techniques could result in slower convergence and/or overfitting. The M5P model—which attempts to split data logically and then apply 165 linear regression models in each data-split—performed better at predictions compared to

MLP-ANN and SVM models [i.e., CPI of 0.2212 of M5P vis-a-vis 1.0000 and 0.6334 of

MLP-ANN and SVM models, respectively, when used for prediction of Ai(x)]. Although the M5P model captures the periodic nature of the dataset because of the application of linear models and limited size of the decision tree, the actual intensities of the local minima and maxima are not well captured (Figure 1).

(D) (E) Figure 1. Predictions made by ML models: (A) MLP-ANN; (B) SVM; (C) M5P; (D) RF; and (E) RF-FFA compared against actual values of the trigonometric function, F1(x) [Equation (17)]. Both the actual values and predictions are plotted against X1, an input variable ranging from -4 to 4. Here, X1 = X2 = X3 = 2 x4 166

As such, the RMSE of the model’s prediction are still high, that is, 0.7891 for

Fi(x) and 0.1648 for Fiix). The RF model outperformed all the aforementioned models

(i.e., MLP-ANN, SVM, and M5P) in terms of prediction accuracy. This is expected

because, in the RF model, a large number of trees are grown [i.e., 450 trees, with 5 leaves

per tree, as described in the Random Forests (RF) section] without pruning or

smoothening (as opposed to the M5P model, wherein the number of trees is restricted and

pruning and smoothening are required).

Figure 2. Predictions made by ML models: (A) MLP-ANN; (B) SVM; (C) M5P; (D) RF; and (E) RF-FFA compared against actual values of the trigonometric function, F 2(x) [Equation (18)]. Both the actual values and predictions are plotted against X1, an input variable ranging from -4 to 4. Here, X1 = X2 = X3 = -5 x4 167

On account of having a large number of the trees, splits in data are more logical,

and, therefore, errors resulting from generalization are minimized and overfitting of the

training data is mitigated (59,63). Furthermore, because of the two-stage randomization

employed in the RF model—as described earlier and in Biau et al. (63)—correlation

among unpruned trees is minimized (diversity among trees is high), the bias is kept low,

and variance is significantly reduced. The prediction of the RF model further improved

when it was combined with the firefly algorithm (FFA). As shown in Figures. 1 and 2,

and Tables 3 and 4, the hybrid RF-FFA model was not only able to capture the periodic

nature of the dataset but also able to reliably interpolate the local minima and maxima

(and the intermediate values) across the entire -4.0 to 4.0 range of the input variable X1.

This enhancement in prediction performance of the hybrid model, with respect to the

standalone RF model, can be attributed to the FFA, which is able to optimize the two

hyper-parameters (i.e., number of trees and number of leaves per tree) of the RF model based on the nature and volume of the dataset. Based on overall prediction

performance—as estimated using the CPI, which takes in account all of the statistical

parameters [see Equation (16)]—the ranking of the ML models is as follows: RF-FFA >

RF > M5P > SVM > MLP - ANN.

3.2. COMPRESSIVE STRENGTH OF CONCRETE: DATASET 1

Based on results shown in the previous subsection, it was established that the

hybrid RF-FFA model outperformed the standalone MLP-ANN, SVM, M5P, and RF

models in terms of prediction accuracy. The standalone RF model came as a close

second. Notwithstanding, these results pertain to user-created trigonometric functions, 168 wherein the relationship between input variables and output could be far more complex than real-world datasets. Therefore, to get a better understanding of prediction performance of the ML models, a real-world dataset of concrete—that is, Dataset 1, described in the Data Collection section—was used. Each data-record in the dataset consists of eight input variables—representing contents of cementitious materials and admixture, and age—and one output (i.e., compressive strength). Predictions of compressive strength of concretes from the test set of Dataset 1, as produced by the ML models, are shown in Figure 3; statistical errors pertaining to predictions are summarized in Table 5. As shown in Figure 3 and Table 5, all ML models presented in this study were able to predict the age-dependent compressive strength of concrete with reasonable accuracy. This is evidenced by the relatively low and high values of RMSE (ranging between 4.0098 and 6.3300 MPa) and R2 (ranging between 0.8664 and 0.9448), respectively, of predictions made by the ML models. It must be pointed out that the differences in statistical parameters among the different ML models are not as significant as in the case of Highly Nonlinear and Periodic Trigonometric Functions, wherein datasets developed from periodic trigonometric functions [Equations. (17) and (18)] were used. This is hypothesized to be on account of the relatively simpler input-output relationship in the concrete dataset compared to the ones dictated by trigonometric functions. Several other studies—that have used the same dataset (i.e., published originally in (16,17) and applied different ML models for predictions—have reported

RMSE and/or R2 values similar to those shown in Table 5. Selected examples of prediction performance of various ML models (on Dataset 1) reported in literature are provided in the following; a comprehensive review, with additional examples, can be 169 found in another study (14). In the study conducted by Young et al. (19), linear regression, ANN, RF, boosted tree, and SVM models were used, and the RMSE of predictions made by the models ranged between 4.4 and 5.0 MPa.

In another study conducted by Veloso de Melo and Banzhaf (15), kaizen programming with simulated annealing was used, and the RMSE was ~ 6 . 8 MPa. In the study by Chou et al. (31), several standalone and ensemble ML models were implemented to forecast compressive strengths of concretes listed in Dataset 1.

Table 5. Prediction performance of ML models, measured on the basis of the test set of Dataset 1. Five statistical parameters (i.e., R,R2,MAE, MAPE, and RMSE) and the composite performance index (CPI) are shown

M L model R R 2 MAE MAPE RMSE CPI

MLP-ANN 0.9308 0.8664 5.0421 36.143 6.3300 1.0000

SVM 0.9525 0.9073 3.5756 25.624 5.2234 0.4385

M 5 P 0.9502 0.9029 4.2369 30.367 5.3518 0.5884

RF 0.9654 0.9320 3.2674 23.443 4.5103 0.1999

RF-FFA 0.9720 0.9448 2.7301 19.571 4.0098 0.0000

Among the standalone models, the RMSE was between 5.59 and 10.11 MPa; and, among the ensemble models, the RMSE was between 5.51 and 38.41 MPa. In the study by Behnood et al. (8 ), the M5P model was used, and the RMSE of predictions was reported as 6.178 MPa—a value close to the one obtained by the M5P model used in this study (Table 5). Lastly, in a study conducted by Chou and Pham (44), the SVM algorithm was combined with FFA, and applied to predict compressive strength of concretes from

Dataset 1. Based on the reported results, the hybrid [SVM + FFA] model outperformed 170 other standalone (e.g., SVM) and ensemble models (e.g., ANN + SVM), and yielded predictions with RM SE of 5.631 MPa. Going back to Table 5, it is clear from all five statistical parameters that the RF and the hybrid RF-FFA models have superior prediction performance compared to MLP, SVM, and M5P models. Based on the values of CPI— the unified measure of prediction performance— the M L models can be ranked as RF-

FFA > RF > SVM > M5P > MLP - ANN.

(A) (B) (C)

Figure 3. Predictions made by ML models: (A) MLP-ANN; (B) SVM; (C) M5P; (D) RF; and (E) RF-FFA compared against actual compressive strength of concretes (drawn from Dataset 1). The dashed line represents the line of ideality and the solid lines represent a ±10% bound. 171

This order is similar to the one that emerged in the section on Highly Nonlinear and Periodic Trigonometric Functions, wherein periodic trigonometric functions were used to generate datasets. Here again, the superiority of the RF model— compared to

MLP-ANN, SVM, and M5P models— is attributed to the large number of unpruned trees that are grown [i.e., 450 trees, with 5 leaves per tree, as described in the Random Forests

(RF) section]. Such depth in the m odel’s structure allows more logical splits in the data, which, in turn, results in development of logical input-output correlations and mitigates overfitting and generalization errors. Even further enhancement in prediction performance was achieved when the RF model was combined with FFA. This enhancement is attributed to the FFA’s ability to optimize the number of trees and leaves per tree of the RF model— based on intrinsic characteristics of the dataset, and all without any user intervention. On a closing note for this subsection, it is pointed out that the

RM SE of predictions produced by the RF-FFA model are lower (i.e., RM SE = 4.0098

M Pa) than the values reported in all other studies found in the authors’ literature review

(7-20,31,44). Admittedly, the RM SE value alone cannot be used to assert that the RF-

FFA model is superior compared to others. This is mainly because such comparison of prediction performance of ML models, developed and implemented by different users (in spite of utilization of the same database), is complex on account of differences in (i) description of cumulative statistical error (e.g., in some papers, R 2 -rather than RMSE— was used to assess accuracy); (ii) splitting of parent dataset into training and test sets

(e.g., in some papers, the parent dataset was split as per 80% and 20% or 66.66% and

33.33% between the training and test sets— as opposed to 75% and 25%, as used in this study); (iii) total number of data-records used for training and testing of the M L models 172

(e.g., in some papers, all 1,030 data-records of Dataset 1 were used, whereas in some only a fraction of them were used); and (iv) methodology used for optimization of model parameters (e.g., some papers used the cross-validation method to optimize model parameters using the training dataset, whereas, in this study, the FFA was used to optimize hyper-parameters of the RF model). Notwithstanding, the low RM SE (i.e.,

4.0098 MPa)— combined with low values of MAE and M APE and high values of R an d

R 2 (Table 5)— produced by the hybrid RF-FFA model certainly suggest that the model is a promising tool for prompt, reliable, and accurate predictions of age-dependent compressive strength of concretes using their mixture design variables as inputs. It is worth mentioning that incorporation of FFA within the RF model does not increase computational complexity and, therefore, does not increase computational time compared to the standalone RF model in a significant manner. In fact, compared to parameter optimization conducted using the traditional multifold CV method, the FFA is more efficient because it is more convenient (e.g., it eliminates the need for trail-and-error or

CV method based optimization of parameters), requires less time for computations, and produces more accurate predictions. Lastly, it should be pointed out that Dataset 1 provides a singular, albeit important, corroboration of superiority of RF-FFA over the standalone RF model as well as other M L models. It is conceivable that utilization of a higher-quality training database— for example, one with a large number of data-records, or one wherein significant physical (e.g., particle size distribution) and chemical (e.g., composition) characteristics of concrete components (e.g., cement and fly ash) and experimental process parameters (e.g., temperature and relative humidity of curing) are also described— will lead to even better prediction performance of the RF-FFA model. 173

3.3. COMPRESSIVE STRENGTH OF CONCRETE: DATASET 2

In the previous subsection, it was shown that the proposed hybrid RF-FFA model produced predictions of concrete compressive strength with RMSE of 4.0098 MPa— suggesting a reasonably high degree of accuracy, especially in comparison to predictions produced by ML models reported in the literature as well as other ML models presented in this study (i.e., MLP-ANN, SVM, M5P, and RF). The dataset used in the section

Compressive Strength of Concrete: Dataset 1 is composed of 1,030 data-records, providing the RF-FFA model an adequate number of data-records (i.e., 0.75 x 1,030 =

772) for developing logical input-output correlations and, thus, making accurate predictions. It is, however, important to examine if the RF-FFA model is able to retain its superior prediction performance when a much smaller dataset is used for training (and testing). Such examination is deemed necessary because generating large datasets of concrete performance is very time-consuming; thus, it is important to evaluate whether or not the proposed RF-FFA model is applicable to smaller concrete datasets that are more abundant and easily found in literature.

Table 6 . Prediction performance of ML models, measured on the basis of the test set of Dataset 2. Five statistical parameters (i.e., R,R2,MAE, MAPE, and RMSE) and the composite performance index (CPI) are shown

M L model R R 2 MAE MAPE RMSE CPI

MLP-ANN 0.9201 0.8464 0.9163 27.352 1.8783 0.2857

SVM 0.9565 0.9149 1.0635 31.744 1.3841 0.1876

M 5 P 0.8003 0.6400 2.1480 64.127 2.6754 1.0000

RF 0.9778 0.9561 0.7718 23.041 0.92313 0.0000

RF-FFA 0.9778 0.9561 0.7718 23.041 0.92313 0.0000 174

Toward this, the prediction performance of the RF-FFA model was evaluated using Dataset 2 (described in the “Data Collection” section) and benchmarked against the performance of other M L models. Readers are reminded that Dataset 2 consists of 76 data-records, featuring different concrete mixture designs and their compressive strengths at 28 days. The mixture design variables were used as inputs; the 28-day compressive strength was used as an output. Predictions of compressive strength of concretes from the test set of Dataset 2, as produced by the M L models, are shown in Figure 4; statistical errors pertaining to the predictions are summarized in Table 6. Akin to the results shown in the section “Compressive Strength of Concrete: Dataset 1,” all five M L models were able to predict the age-dependent compressive strength of concretes from Dataset 2 with reasonable accuracy. The poor prediction performance of the M5P model indicates— as was also suggested in a prior study (30)— that, when the dataset volume is small, decision tree models with limited number of trees (i) cannot ensure homogeneity in data clustered in each node, (ii) cannot maintain diversity among the different nodes, and, therefore, (iii) are unable to make predictions in an accurate manner. Secondly, it is also interesting to note in Table 6 that both the RF and RF-FFA models have similar prediction performances. The implication of this equivalency is that when the dataset is small, the application of FFA— for optimization of the two hyper-parameters (i.e., number of trees and number of leaves per tree in the forest) of the RF model— is redundant and does not necessarily elicit any substantial improvement in prediction performance. However, when the dataset is large— for example, Dataset 1— the application of FFA is beneficial in that it produces substantial improvement in prediction performance of the RF model by 175 optimizing its two hyper-parameters in relation to the nature and volume of the dataset

(T a b le 5).

(A) (B) (C)

(D ) (E ) Figure 4. Predictions made by ML models: (A) MLP-ANN; (B) SVM; (C) M5P; (D) RF; and (E) RF-FFA compared against actual compressive strength of concretes (drawn from Dataset 2). The dashed line represents the line of ideality and the solid lines represent a ±10% bound.

4. SUMMARY AND CONCLUSIONS

This study developed and presented a novel hybrid machine learning (ML) model

(RF-FFA) for prediction of compressive strength of concrete, in relation to its mixture design and age, by combining the random forests (RF) model with the firefly algorithm 176

(FFA). The firefly algorithm—a metaheuristic optimization technique—was used to

optimize the two hyper-parameters of the RF model (i.e., the number of trees and the

number of leaves per tree in the forest) in relation to the volume and nature of the dataset,

and without any user intervention.

The RF-FFA model was trained to develop correlations between input variables

and output of two different categories of datasets; such correlations were subsequently

leveraged by the model to make predictions. The first category included two separate

datasets featuring highly nonlinear and periodic relationships between input variables and

output as given by trigonometric functions. The second category included two real-world

datasets, composed of mixture design variables and age of concretes as inputs and their

compressive strengths as outputs. The performance of the hybrid RF-FFA model was

benchmarked against commonly used standalone ML models—support vector machine

(SVM), multilayer perceptron artificial neural network (MLP-ANN), M5Prime model

tree algorithm (M5P), and RF. The metrics used for evaluation of prediction accuracy of

the ML models included five different statistical measures (i.e., R, R2, MAE, RMSE, and

MAPE) as well as a composite performance index (CPI).

The prediction performances of MLP-ANN and SVM models were reasonable for

concrete datasets; however, their inability to identify and converge to global minima

rendered their prediction performances poor when datasets generated from trigonometric

functions were used. The prediction performance of the M5P model, in general, was

commensurable to, or slightly superior compared to, those of MLP-ANN and SVM

models. However, on account of limited size (or depth) of the decision tree and utilization

of multivariate linear regression models, prediction performance of the M5P model was 177 consistently inferior compared to those of RF and RF-FFA models. The superiority of the

RF model was attributed to the large number of unpruned trees, which, in turn, results in development of logical input-output correlations and mitigates overfitting and generalization errors. Even further enhancement in prediction performance was achieved when the RF model was combined with FFA (i.e., the RF-FFA model). This enhancement in prediction performance was attributed to the FFA’s ability to optimize the number of trees and leaves per tree of the RF model based on the volume and nature of the dataset.

The high degree of prediction accuracy (i.e., RMSE of -4.0 and -0.92 MPa for the large and small datasets, respectively) produced by the hybrid RF-FFA model suggests that the model is a promising tool for prompt and reliable prediction of composition-dependent properties of concrete, provided that the training is accomplished using adequate number of data-records. It is expected that utilization of a higher-quality database— wherein the dataset volume is large, and/or wherein influential physical (e.g., particle size distribution) and chemical (e.g., composition) attributes of concrete components (e.g., cement and fly ash) and curing conditions (e.g., temperature and relative humidity of curing) are also described— will further bolster the prediction performance of the RF-FFA model.

ACKNOWLEDGMENTS

Funding for this research was provided by the National Science Foundation [NSF,

CMMI: 1661609]. Computational tasks were conducted in the M aterials Research Center 178 and Department of M aterials Science and Engineering at Missouri S&T. The authors gratefully acknowledge the financial support that has made these laboratories and their operations possible.

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V. INFLUENCE OF WATER ACTIVITY ON HYDRATION OF TRICALCIUM ALUMINATE-CALCIUM SULFATE SYSTEMS

Jonathan Lapeyre§, Hongyan Ma*, Monday Okoronkwo*, Gaurav Sant*, and Aditya Kumar§

^Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409

*Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO 65409

^Department of Chemical and Biochemical Engineering, Missouri University of Science and Technology, Rolla, MO 65409

^Department of Civil and Environmental Engineering; Department of Materials Science and Engineering; California NanoSystems Institute; and Institute for Carbon Management; University of California Los Angeles, Los Angeles, CA

ABSTRACT

The hydration of tricalcium silicate (C3 S) - the major phase in cement - is

effectively arrested when the activity of water (aH) decreases below the critical value of

0.70. While it is implicitly understood that reduction in aH suppresses the hydration of tricalcium aluminate (C3A: the most reactive phase in cement), the dependence of

kinetics of C3A hydration on aH and the critical aH at which hydration of C3A is arrested

is not known. This study employs isothermal microcalorimetry and complementary

material characterization techniques to elucidate the influence of aH on the hydration of

C3A in [C3A + calcium sulfate (C$) + water] pastes. Reductions in water activity are

achieved by partially replacing the water in the pastes with isopropyl alcohol. The results

show that with decreasing aH, the kinetics of all reactions associated with C3A (e.g., with 186

C$, resulting in ettringite formation; and with ettringite, resulting in monosulfoaluminate

formation) are proportionately suppressed. When aH < 0.45, the hydration of C3A and the

precipitation of all resultant hydrates are arrested, even in liquid saturated systems. In

addition to - and separate from - the experiments, a thermodynamic analysis also

indicates that the hydration of C3A does not commence or advance when aH < 0.45. On the basis of this critical aH, the solubility product of C3A (Kc3a) was estimated as 10-2065.

The outcomes of this work articulate the dependency of C3A hydration and its kinetics on water activity, and establish - for the first time - significant thermodynamic parameters

(i.e., critical aH and Kc3a) that are prerequisites for numerical modeling of C3A hydration.

Keywords: tricalcium aluminate; hydration; water activity; thermodynamics;

calorimetry

1. INTRODUCTION

Conventional concrete is a mixture of ordinary portland cement (OPC;

subsequently referred to as cement), water, sand, and large aggregates. Herein, the

reaction between cement and water (i.e., hydration) results in precipitation of hydration

products, evolution of the microstructure, and development of properties (e.g., strength).

Reduction in internal relative humidity (RH) of concrete - for example, via drying-

induced removal of liquid water - suppresses the kinetics of cement hydration, and,

consequentially, slows down all processes linked with cement hydration (e.g.,

development of properties). Powers (1) and, later, Spears (2) suggested that below a

critical RH of 80%, the hydration of cement is arrested. Flatt et al. (3) showed that the 187

aforesaid critical value of RH (i.e., 80%) was applicable to tricalcium silicate (Ca3 SiOs; written as C3 S in cement chemistry notation), the major phase in cement (4). Flatt et al.

(3) estimated that when the internal RH of C3 S paste [i.e., C3S + water (H)] decreases below 80%, the chemical potential of water is significantly reduced. This is due to the

development of immense negative capillary stress (i.e., ~ -30 MPa, as calculated from the

Laplace-Young equation) within the pore-network of the microstructure, and emptying

of all pores with diameters larger than ~5.4 nm. Interestingly, even at such low RH, a thin

layer (thickness of approximately 0.6 nm) of liquid water remains adsorbed on the pores’ walls. However, as the chemical potential of the liquid layer is equivalent to that of C3 S, the hydration of C3 S - in spite of being in contact with liquid water - is infeasible, thereby enforcing equilibrium of C3 S with respect to the contiguous liquid water layer as well as the hydration products (i.e., CH: portlandite; and C-S-H: calcium-silicate-

hydrate).

In the work of Flatt et al. (3) - which was broadly analytical, rather than

experimental - chemical potential of water was manipulated via vapor pressure (i.e.,

ambient/internal RH) reductions; that is, a vapor-phase route. Nonetheless, changes in water’s chemical potential can also be induced via the liquid-phase route. For example,

Oey et al. (5) altered the chemical potential of water - specifically, the activity of water

(aH) - by partially or fully replacing it with isopropyl alcohol (IPA). The authors reported that - much like RH - with decreasing aH, C3 S hydration is suppressed, and,

consequently, the rates of growth of the hydrates (i.e., C-S-H and CH) decline

progressively. As aH regresses to a value of 0.70 - which is achieved when 63%mass of

water is replaced with IPA - equilibrium is achieved between C3 S, water, and the 188

hydration products. Even in water-abundant suspensions (i.e., [C3 S + H] mixtures

prepared at high liquid-to-solid mass ratios), below the critical aH of 0.70, the hydration

of C3 S, despite its unhindered access to liquid water, is effectually arrested.

Several other studies (6-9) have reported that below the critical RH of 80%,

hydration of cement or of C3 S neither initiates nor advances. Conversely, for the other

anhydrous phases present in cement, the dependency of their hydration kinetics on RH (or aH) and the critical RH (or aH) at which their hydrations are arrested are not well

established. Among these phases, perhaps the most important is tricalcium aluminate

(Ca3AhO6; or C3A, as per cement chemistry notation), the most reactive phase in cement

(4,10,11). In typical cements (i.e., OPC), a highly-soluble sulfate compound - for

example, calcium sulfate (CaSO4; or C$, as per cement chemistry notation) or gypsum

(CaSO4 . 2 H2O; or C$H2) - is added to avert flash-setting (4,12-15). In a classic study,

Patel et al. (6 ) showed that, in cement pastes, the ultimate degree of hydration of C3A

(ac3A'; Unitless) decreases from -100% (i.e., near-complete hydration, wherein aC3A -

1.0) for samples cured in saturated conditions (i.e., RH-100%) to -60% (i.e., aC3A -0.60) when the curing is conducted at RH of 49% or below. Although the authors did not

quantify a critical RH for C3A hydration, their results clearly showed that as RH

decreases - and, presumably, water is gradually removed from the paste’s microstructure, thus resulting in decline of aH - the hydration of C3A is progressively suppressed. These

inferences of Patel et al. (6 ), were corroborated by Jensen (7), who showed that, in [C3A

+ C$H2 + H] pastes, the hydration of C3A did not progress to a significant degree (i.e.,

«C3A < 0.02) when it was exposed to moisture maintained at RH of < 43% for an entire year. However, as the RH was increased to 6 6 % and 75%, aC3A increased to 0.08 and 189

0.28, respectively, after a year. On the bases of these results, Jensen (7) estimated that RH of 60% was the limiting value for cessation of C3A hydration. In another study conducted by Dubina et al. (16), the critical RH for C3A hydration was estimated as 55% - which is in good agreement with the value reported by Jensen (7).

Although the studies cited in the preceding paragraph do show that the hydration of C3A is limited, or entirely arrested, at RH ^ 60% (6,7), none of them describe the influence of RH - or aH, which, like RH, is linked to the chemical potential of water - on the temporal rate of C3A hydration (in the presence of a soluble sulfate compound).

Importantly, prior studies do not shed any light on the influence of aH on hydration of

C3A in water-abundant systems, wherein C3A particulates have unremitting access to water and capillary stress development is effectively avoided. Such knowledge, of dependency of C3A hydration on aH, is a prerequisite for: quantification of rate controls on C3A (and, therefore, cement) hydration; determination of thermodynamic parameters relevant to C3A hydration (e.g., solubility constant of C3A, which is needed to develop and/or validate cement hydration models (17-22)); and accurate estimation of critical aH at which hydration of C3A is arrested. The last point is expressly significant, because, in practice, to arrest the hydration of cement (for example, to characterize the microstructure at a given degree of hydration), cementitious specimens are typically immersed in [water

+ IPA] mixtures for prolonged periods (23,24). Proper knowledge of critical aH for C3A hydration would enable the estimation of appropriate amount of IPA that would ensure that hydration of C3A is no longer feasible. Knowledge of critical aH for C3A hydration would also enable the selection of appropriate curing conditions (e.g., ambient RH, that is high enough to ensure that aH is above the critical value at all times) of cementitious 190

systems - including calcium sulfoaluminate systems (25,26) - that would warrant faster

(or slower) kinetics of reactions, and, therefore, swift (or gradual) development of

physical properties. Lastly, such knowledge is also expected to aid in development of

strategies to mitigate delayed ettringite formation (27), a degradation phenomenon that

negatively affects the durability and service life of concrete infrastructure.

To address the abovementioned knowledge-gaps, this study employs a

combination of experimental techniques (e.g., isothermal microcalorimetry; X-ray

diffraction; and thermogravimetric analyses) and thermodynamic calculations to elucidate

the effect of water activity on the hydration of C3A in [C3A + C$ + H] pastes. All pastes were prepared at high liquid-to-solid mass ratios (l/s > 2 .0 ) such that majority of the pores within the pastes remain saturated with liquid at all times; this is important because

partial desaturation of the pores could result in development of large capillary stresses.

To regulate the activity of water in the mixing solution, IPA was used to replace 0-to-

1 0 0 %mass of the water, hence encompassing a wide range of water activities ( 1 .0 > initial aH (aH0) > 0.0). IPA - as opposed to other organic alcohols such as ethanol or methanol - was chosen to achieve desired water activities because of its: miscibility with water;

inertness (i.e., inability to react with C3A or C$ or any of the hydration products in the

paste); and small molecular size, which permits its access to large as well as very small

pores within the microstructure (5,23,28-32). Overall, outcomes of this work clearly

express the dependency of the C3A hydration kinetics on water activity, and establish, for

the first time, significant thermodynamic parameters relevant to hydration of C3A - that

is, solubility constant of C3A and critical water activity below which hydration of C3A is

arrested. 191

2. REVIEW OF HYDRATION OF C3A IN [C3A + C$ + H] PASTES

The section presents a brief overview of the three distinct stages of C3A hydration

in [C3A + C$ + H] pastes. The reactions pertaining to each stage, and mechanisms

associated with the reactions, are described for pastes in which the mixing solution is

pure water (i.e., aH at the time of mixing is 1.00). The influence of aH on the various

reactions are discussed towards the end of this section.

2.1. STAGE I

After initial contact with water and wetting of the surface, C3A begins to dissolve; the consequent release of ions is described by Equation 1.

Ca3 Al2 O6 + 6 H2O ^ 3Ca2+ + 2Al(OH)- + 4OH- (1)

Akin to C3A, dissolution of C$ commences shortly after contact with water,

resulting in the release Ca2+ and SO42' into the contacting solution. Within a few minutes

of dissolution, crystals of ettringite [C6A$3H32; an alumina-ferric oxide-trisulfate (AFt)

phase] precipitate in a nucleation burst; the crystals subsequently grow into the capillary

pore space (12,14,15). The chemical reaction for ettringite precipitation is shown in

Equation 2. While the change in enthalpy (AH) of this reaction, as reported in literature,

has varied from -452 kJ per mole C3A to -600 kJ per mole C3A, the value used in this

study is -522.04 kJ per mole of C3A; this value was drawn from Cemdata18 database

(4,33-35).

C3A + 3C$ + 32H ^ C6A$3H32 (2) 192

The rate of ettringite precipitation (and, thus, the kinetics of C 3A hydration and rate of heat evolution during stage I) is rapid for a short period (following the initial nucleation burst), and thenceforth very slow, proceeding at a near-constant rate for several hours until C$ is the system is exhausted (12,34,36). As such, the duration over which ettringite continues to form, increases as C$ content in the paste increases. The underlying mechanisms that explain the highly nonlinear and non-monotonic variations in the hydration kinetics during the precipitation of ettringite (Equation. 2) have long been debated by researchers. Some studies have postulated that the kinetics of ettringite precipitation is dictated exclusively by morphology and size of C 3A particulates, whereas others have suggested that the low, near-constant rate of C 3A hydration (after nucleation of ettringite crystals) is due to the formation of a barrier-layer that prevents C 3A fro m dissolving rapidly (12,34). The aforesaid barrier-layer hypothesis, however, appears implausible in light of recent findings. Notably, X-ray synchrotron analysis (37) and other examinations of C 3A particulates’ surfaces (38,39) have shown that a metastable calcium aluminate hydrate phase does form on C 3A surface; however, this phase does not appear to inhibit dissolution of C 3A or the transport of ions from C 3A surface to the contiguous solution. In other studies (13,34,37-40), a surface passivation mechanism has been theorized to be at the origin of retardation of C 3A hydration during the period when ettringite crystals grow at a slow rate. Though, there is still no consensus on which chemical species or surface complex is responsible for passivation of the C 3A surface.

Some studies have argued that the passivation layer comprises of SO 42" ions (12,34); although, results contradicting this argument have been presented in a study conducted by 193

Collepardi et al. (41). Other studies (37-39), have reported that Ca-Al-SO3 complexes

that preferentially adsorb onto the Al-rich C3A surface are responsible for passivating it.

2.2. STAGE II

After complete depletion of C$ in the paste, hydration of C3A (if still left) is

invigorated. In an isothermal calorimetry profile (i.e., heat evolution profile), this is

observed as rapid increase in heat flow rate up to an intense exothermic peak, followed by a sharp decline, and then an exponentially decaying shoulder that lasts for several

hours (12,34,36,42). Depending on the C3A and C$ particulate sizes, and their contents,

characteristics of this peak (i.e., approach to, departure from, and intensity of the peak)

are subject to change (12,33,43). During this stage (i.e., stage II), ettringite reacts with

C3A and water to form monosulfoaluminate [C4A$H12; an alumina-ferric oxide-

monosulfate (AFm) hydrate phase as described in Equation. 3]; AH of the reaction is -

237.64 kJ per mole C3A (4,33-35).

C3A + 0.5C6 A$3 H32 + 2H ^ 1.5C4 A$H12 (3)

The kinetics of C3A hydration during stage II - albeit, not fully understood - is

assumed to be dictated by the nucleation-and-growth of monosulfoaluminate

(12,34,36,44). As with other nucleation-and-growth processes (e.g., precipitation of ice

from liquid water), the rate of C3A hydration varies in a nonlinear and non-monotonic

manner with respect to time. 194

2.3. STAGE III

After ettringite in the paste is exhausted, the anhydrous C3A (if still left) reacts

directly with water to form a solid-solution (45-47) of metastable calcium aluminate

hydrate phases (e.g., C2AH8 and C4AH13) and poorly-crystalline aluminum hydroxide

(AH3) (48). Over time, these metastable hydrates transform into a singular stable phase -

hydrogarnet (C3AH6) (49). As the formation of hydrogarnet is predicated upon the

exhaustion of ettringite (unless C3A is exhausted before complete depletion of ettringite),

in sulfate-rich [C3A + C$ + H] pastes, the formation of hydrogarnet is wholly negated.

Contrastingly, in sulfate-deficient [C3A + C$ + H] pastes, hydrogarnet does form; its

formation, however, begins tens-to-hundreds of hours after mixing (12,34). Such delayed

formation of hydrogarnet is attributed to two reasons: (i) the slow, exponential decay of the rate of monosulfoaluminate precipitation (and ettringite consumption) during stage II;

and (ii) slow kinetics of transformation of metastable calcium aluminate hydrates to

hydrogarnet. For the sake of simplicity, in this study, the formation of metastable

hydrates and their subsequent transformation to hydrogarnet during stage III have been

combined into a single reaction with C3AH6 as the singular hydration product (Equation

4); AH of this reaction is -261.02 kJ per mole C3A (4,33-35).

C3 A + 6 H ^ C3A H (4)

Readers are reminded that reactions described in Equations 1-4 pertain to [C3A +

C$ + H] pastes, in which the initial aH = 1.00. In a prior study conducted on [C3A + H]

suspensions, Brand and Bullard (50) demonstrated that the dissolution rate of C3A

decreases as the aH in the contacting solution decreases (N. B., aH was controlled by

partially replacing water with ethanol). Therefore, in [C3A + C$ + H] paste, reduction in 195 aH is expected to decelerate C 3A dissolution kinetics (Equation 1), and, consequentially, retard the release of Ca 2+, OH , and Al(OH) 4 ions into the contacting solution. Slower release of ionic species is expected to suppress the kinetics of all succeeding reactions: the precipitation of ettringite (Equation 2), monosulfoaluminate (Equation 3), and hydrogarnet (Equation 4). Although the influence of aH on the kinetics of these reactions has not been established yet, the effect of RH reductions on the stability of ettringite and monosulfoaluminate has been extensively studied (45,51-56). Ettringite (C 6A $ 3H 32) lo se s a maximum of two moles of water (resulting in stabilization of C 6A $ 3H 30) as RH is reduced from 100% to 10%; this loss of loosely-bound water does not induce any perceptible distortion of ettringite’s crystalline structure. Below 10% RH, h o w e v e r, ettringite begins to destabilize, and decompose into calcium sulfates and calcium aluminate hydrates (51-53). Owing to its stability across a wide range of R H s , in th is study, the stoichiometry of ettringite is assumed to remain constant at C 6A $ 3H 32, irrespective of the mixture design of the paste or the aH at the time of mixing. Unlike ettringite, the stability of monosulfoaluminate (C 4A $ H 12) is strongly dependent on RH.

A s RH reduces from 100% to lower values, the moles of water per mole of the hydrate change drastically (i.e., 16, 14, 12, 10.5, or 9 in relation to decreasing RH), thus inducing substantial changes in its crystalline structure (55,56). In all [C 3A + C$ + H] systems described in this study, C 4A $ H 12 is assumed to be predominant AFm phase that forms during stage II, since it is the most stable one (among other forms of monosulfoaluminate) at R H s between 97-and-23% (at room temperature) (55,56). 196

3. CALCULATION OF WATER ACTIVITY IN [C3A + C$ + H] SYSTEMS

To study the effect of water activity (aH) on hydration of C3A, this study

emphasizes achieving reductions in aH via the liquid-phase route - that is, by partially

replacing water, in the mixing solution, with IPA. aH represents the net differential in the

chemical potential of liquid water as it transitions from a pure state (i.e., when solute

concentration in the water is zero) to that of a solution (i.e., when a finite amount of

solute is dissolved in the water). The mathematical formalisms used to calculate aH in

[water + IPA] mixtures are identical to those implemented in the study of Oey et al. (5).

Therefore, to avoid replication of information, descriptions of the principal equations used for estimation of aH are kept succinct in this section; for further details, readers are

requested to consult references (3,5) and Appendix C. In this study, the van Laar

equations (Equations 5-6) were used to calculate aH and aIpA as the IPA replacement

increases in the mixing solutions (5,57,58).

B aH = XH exp (5)

A aIPA = ^IPA exp (6)

The variables utilized the van Laar equations are the mole fraction of water and of

IPA (Xh and Xipa respectively; both unitless) in the mixing solution as well as the unitless

coefficients A and B. These were previously determined to be 1.000 and 0.483 through

regression analysis of liquid-vapor equilibrium data, at standard temperature and 197

pressure conditions, by Wilson and Simmons (57). As can be seen in Figure 1, aH

monotonically reduces with increasing IPA replacements; sharp reductions in aH occur

when the IPA content in the mixture exceeds 35%.

4. ESTIMATION OF CRITICAL WATER ACTIVITY AND SOLUBILITY CONSTANT BASED ON THERMODYNAMIC CONSIDERATIONS

In the works of Flatt et al. (3) and Oey et al. (5), a common thermodynamic

approach was used to estimate important thermodynamic constants associated with C3 S

hydration: solubility constant of C-S-H; and equilibrium constant of C3 S hydration (i.e.,

C3 S-C-S-H reaction). In both studies, the critical chemical potential of water - estimated

on the bases of critical RH (3) or critical aH (5), below which hydration of C3 S is arrested

- was used as the primary input. In this study, a modification of the aforementioned thermodynamic approach is used to estimate two significant thermodynamic parameters

associated with the hydration of C3A in [C3A + C$ + H] systems: critical aH below which

hydration of C3A is arrested, and solubility constant of C3A (Kc3a).

In [C3A + C$ + H] pastes, the hydration of C3A advances sequentially through

stages I, II, and III, as delineated by reactions shown in Equations 2, 3, and 4,

respectively. Hydration of C3A in such pastes terminates if one or both of the following

conditions are met: (i) C3A is exhausted; or (ii) equilibrium between water and all solidus

phases (i.e., C3A, C$, and whichever hydration products that are present in the paste at

the point in time) is reached. When equilibrium is indeed reached, the implication is that

the Gibbs free energy of reactions (AGrxn), associated with ettringite precipitation (i.e.,

C3A-AFt; Equation 2), monosulfoaluminate precipitation (i.e., C3A-AFm; Equation 3), 198 and hydrogarnet precipitation (i.e., C3A-C3AH6; Equation 4), are all 0 at the same time.

In this study, for calculation of thermodynamic parameters (i.e., critical aH and Kc3a), the thermodynamic approach only considers the equilibrium of C3A-AFt and C3A-AFm reactions; the C3A-C3AH6 reaction is disregarded. This is for two reasons: (i) for calculation of thermodynamic parameters, two reactions (i.e., Equations 2-3) involving

C3A are sufficient, hence, making the inclusion of the third reaction (i.e., Equation 4) redundant; and (ii) assessing the conditions of equilibrium of C3A-C3AH6 reaction is difficult, because the precipitation of C3AH6 does not occur directly, but rather indirectly through two separate stages - precipitation of metastable hydrates (e.g., C2AH8 and

C4AH13) followed by transformation of the metastable hydrates to C3AH6 (45-47).

Figure 1. Activities (a) of water (H) and isopropyl alcohol (IPA) in [water + IPA] mixtures, as calculated from the van Laar equations (Equations 5-6). Dashed lines represent ideal behavior, as described by Raoult's Law (i.e., aH = Xh and aIPA = Xipa). All calculations are deterministic; as such, there is no uncertainty associated with them 199

Using the same approach as that described in Ref. (3,5), the equilibrium constants

(Krxn; Unitless) for both C3A-AFt and C3A-AFm reactions, at pressure (p) = 1 bar and temperature (T) = 25°C, can be estimated by solving Equation 7. In Equation 7: RHk is the ambient relative humidity that would correspond to chemical equilibrium of water in the vapor phase with pure liquid water in a partially saturated pore; VH (cm3 molc3A-1) is the chemical shrinkage associated with the reaction; «H (mole) is the number of moles of

water per mole of C3A required for completion of the chemical reaction; and VH (cm3

molwater-1) is the molar volume of water. It should be noted that Equation 7 can be

concurrently applied to both C3A-AFt and C3A-AFm reactions, as long as both reactions

have reached equilibrium, RH k < 1 0 0 %, and 0 . 0 < an < 1 .0 .

V„ f nJVn \ ln (RHK) = ^ \n(Krxn) + ln(0H ) (7)

It is also worth pointing out that Equation 7 considers the combined effects of

liquid-vapor meniscus curvature and the suppression of aH (due to the dissolution of

solute, for example IPA, in water) on the state of equilibrium of the two reactions.

Therefore, Equation 7 can be applied - as is - to [C3A + C$ + H] pastes, wherein pure water is used as the mixing solution, or even in cases wherein water is partially replaced with IPA. Using the molar masses and densities (p) of relevant phases - as reported in the

prior work of Balonis and Glasser (59) -the phases’ molar volumes were estimated (see

Table 1). On the bases of these molar volumes and stoichiometries of the chemical

reactions shown in Equations 2-3, the chemical shrinkage (AF) associated with C3A-AFt

and C3A-AFm reactions were estimated as -97.824 cm3 molC3A-1 and -14.744 cm3

molC3A-1 respectively. 200

Table 1. Densities (p) and molar volumes (V) at standard conditions for the cementitious phases utilized in equilibrium calculations. The densities reported herein originated from reference (59)

Cementitious Phases Density (g cm-3) Molar Volume (cm3 mol-1) C3A 3.030 89.17 C$ 2.958 46.02 H 1 . 0 0 0 18.02 C6A$3H32 1.778 705.9 C4A$Hl2 2.015 308.9

In Equation 7, the Krxn term is a shorthand for equilibrium constant for each of the

two reactions: C3A-AFt (Kc3A-AFt) and C3A-AFm reactions (Kc3A-AFm), represented by

Equations 2 and 3, respectively. In a [C3A + C$ + H] paste, if C3A stops hydrating during

stage I - thereby, reaching equilibrium with C$, water, and ettringite - the equilibrium

constant of C3A-AFt reaction (Kc3A-AFt) can be estimated as function of solubility

constants of the reactants (i.e., C3A and C$) and the hydration product (i.e., the AFt

phase: ettringite). This is shown in Equation 8 . Likewise, if hydration of C3A is terminated during stage II, and it reaches a state of equilibrium with water and the

hydration products (i.e., AFt; and AFm phase: monosulfoaluminate), the equilibrium

constant of C3A-AFm reaction (Kc3A-AFm) can be estimated using Equation 9.

By solving Equations 7-9 simultaneously, the equilibrium constants for the

aforementioned pair of reactions (i.e., Kc3A-AFt and Kc3A-AFm), the solubility constant of

C3A (Kc3a), and the critical an at which hydration of C3A is arrested can be estimated.

Firstly, the equilibrium constant of the C3A-AFt reaction (Kc3A-AFt) as a function of aH

(0.0 < aH < 1.0) can be calculated from Equation 7, while assuming near-liquid saturation conditions (i.e., RHk ~ 100%). Secondly, and once again assuming near-liquid saturation conditions, the equilibrium constant of the C3A-AFm reaction (Kc3A-AFm) as a 201

function of aH can be calculated from Equation 7. Thirdly, by using Equation 8 in

conjunction with the functional relationship between Kc3A-AFt and aH, as derived from the

first step, the solubility constant of C3A (Kc3a) can be plotted as a function of aH. And,

lastly, by using Equation 9 in tandem with the Kc3A-AFm vs. aH relationship, as derived

from the second step, the solubility constant of C3A (Kc3a) can once again be plotted as a

function of aH. For the penultimate and last steps, the solubility constants of relevant

phases must be known. Towards this, K c$, K afx, and K AFm can be assumed as 1 0 -4357, 1 0

4 4 9 , and 10-29 23, respectively; these values correspond top = 1 bar and T = 25°C, and were drawn from the Cemdata18 database (35).

3 KC3 aK

V jx0.5 AC3AAAFt ^CqA-AFm — zxi.5 (9) AAFm

By following the steps described above, Kc3a was obtained as a function of aH

(Figure 2). As can be seen, two different curves are obtained: one that is derived from the

equilibrium of the C3A-AFt reaction and other derived from the C3A-AFm reaction. The

two curves intersect at a unique value of aH, that is, at aH = 0.45. This intersection point is

significant because it represents the exclusive value of aH at which both C3A-AFt and

C3A-AFt reactions reach equilibrium. In other words, at the critical aH of 0.45, C3A

reaches a state of equilibrium with all other constituents of the system - that is, water,

C$, ettringite, and monosulfoaluminate. On account of establishment of equilibrium

between all solidus phases and water, it can, thus, be said that hydration of C3A is

effectually arrested when aH reaches the critical value of 0.45. It should be noted that in a

[water + IPA] mixture, aH of 0.45 corresponds to IPA replacement level of 87.1% (see 202

Figures 1 and 2), thereby implying that the same or higher percentage of water ought to be replaced in a [C3A + C$ + H] paste to ensure that the hydration of C3A is ceased.

Importantly, at the critical an (= 0.45), the solubility constant of C3A (Kc3a) - as derived from equilibrium of either of two reactions (i.e., C3A-AFt and C3A-AFm) - is 1 0 -2065.

By inserting this value of Kc3a into Equations 8-9, equilibrium constants of the C3A-AFt reaction (Kc3A-AFt) and the C3A-AFm reaction (Kc3A-AFm) were estimated as 1 0 11180 and

1 0 0742, respectively.

Given the sheer number of equations, parameters, and their interrelations that have been described thus far in this section, is worth reiterating the two significant thermodynamic parameters that were estimated on the basis of thermodynamic considerations of C3A hydration in near-liquid saturation conditions: critical aH at which hydration of C3A is arrested = 0.45; and the solubility constant of C3A (Kc3a) = 10-2065.

These are the first estimates of either parameter; hence, their corroboration from literature is not feasible. Notwithstanding, in Section 6 , results obtained from a series of experiments are analyzed to verify the critical aH of C3A hydration in [C3A + C$ + H] pastes. And, to corroborate the aforesaid value of Kc3a, additional simulations in GEMS, the thermodynamic modeling software package (35,60,61), were implemented.

Specifically, in these simulations, a single gram of C3A was allowed to dissolved in water, under extremely dilute conditions (i.e., water-to-C3A mass ratio (l/s) = 1000-to-

3000) and exposed to an inert (nitrogen) atmosphere maintained at 1 bar of pressure and temperature of 25 °C. In these suspensions, the formation of hydrates was forbidden, thereby allowing C3A to dissolve until it reached a state of equilibrium with the ionic species released from its dissolution (i.e., Ca2+, Al(OH)4 , and OH ). At equilibrium, the 203

activities of the ionic species (denoted as a) were calculated using the extended Debye-

Huckel equations (62) (embedded within GEMS), and then inserted in Equation 10 to

calculate Kc3a (see Table 2).

Figure 2. Plots of the solubility constant of C3A (Kc3a) as function of water activity (aH), as derived from the equilibrium of C3A ^ AFt and C3A ^ AFm reactions. The unique point of intersection between the two curves is highlighted by means of the dashed lines. The point of intersection corresponds to aH = 0.45, that is, when IPA content in the [water + IPA] mixture is 87.1%mass. At aH = 0.45, Kc3a = 10-20.65. All calculations are deterministic; as such, there is no uncertainty associated with them

As can be seen in Table 2, the values of Kc3a determined from the GEMS

simulations are within two orders of magnitude of 1 0 -2065, the value estimated from thermodynamic considerations described earlier in this section. It is acknowledged that, within the GEMS software, assumptions have been made to simplify the simulations

(e.g., precipitation of hydrates is disallowed); therefore, it is possible that the dissolution

reaction of C3A may not have reached equilibrium, especially at higher l/s.

2 Kc3A = (aCa2+ ) 3(aOH-)4(aAl(OH)-) (10) 204

This is likely the reason why the GEMS-derived values of Kc3a are altered with

increasing l/s (as opposed to remaining unchanged), and different (albeit, by less than 2

orders of magnitude) from the value derived from the above-described thermodynamic

approach.

Table 2. The solubility constant of C3A, calculated via GEMS, in relation to varying l/s

Simulated l/s Kc3A log (Kc3a) 1 0 0 0 9.04 x 10-20 -19.043 2 0 0 0 4.71 x 10-22 -21.327 3000 1.95 x 10-23 -22.709

In prior studies (3,63), the dissolution rate of C3 S, at very low undersaturation, was measured and subsequently processed to estimate its solubility constant. It is

expected that similar experimental protocols could be applied to obtain more accurate

estimates of the solubility constant of C3A.

5. MATERIALS AND METHODS

Both the C3A (cubic polymorph) and C$ powders were sourced from commercial

suppliers. Quantitative X-ray diffraction (QXRD) revealed that the C3A (sourced from

Kunshan Chinese Technology New Materials Co., Ltd) is > 98% pure, with < 2% of free

lime (CaO). Likewise, the AR-grade anhydrous C$ (sourced from Alfa Aesar) was found to be > 99% pure, with trace amounts of impurities. The particle size distributions (PSDs)

of C3A and C$ powders, as obtained from static light scattering (Microtrac S3500 particle

size analyzer), are presented in Figure 3. Prior to PSD measurements, each powder 205

specimen was suspended in IPA, and subsequently agitated at ultrasonic frequencies for 4

minutes to alleviate the effects of particulate agglomeration that may have occurred

during storage of the materials. The median particle sizes (d5o, pm) of the PSDs of C3A

and C$ powders are 6.51 pm and 9.99 pm, respectively; their specific surface areas (SSA,

cm2 g-1) were estimated to be 3554.21 cm2 g-1 and 5130.81 cm2 g-1, respectively.

Figure 3. Particle size distributions (PSDs) of C3A and C$ powders used in this study. Uncertainty in the median particle diameter (d5o) of each PSD is within ±6 %

To monitor the rate and extent of C3A hydration, [C3A + C$ + H] pastes were

prepared by mixing the two anhydrous powders (i.e., C3A and C$) at two distinct mass

proportions: [85% C3A + 15% C$] and [70% C3A + 30% C$]. The mixing solutions were

comprised of mixtures of water and reagent-grade (99.9% pure) isopropyl alcohol (IPA;

sourced from Fisher Chemical). IPA was used to replace 0-to-100%mass of water in the

mixture, to encompass a wide range of water activities (0.0 < aH < 1.0). These solutions were added to the powder mixtures at a fixed l/s of 2. A fairly high value of l/s was 206

chosen for this study to ensure that complete hydration of C3A could be achieved in

majority of the pastes (with the exception of the few prepared at IPA replacement levels

of > 80%; see Appendix C). Although IPA and water are completely miscible, the [water

+ IPA] mixtures were shaken to ensure homogeneity before introducing them to the

anhydrous powder mixtures, followed by hand-mixing of the paste for 1 minute.

Hydration kinetics of C3A in each paste was monitored for 72 h using a TAM IV (TA

Instruments) isothermal conduction microcalorimeter, programmed to maintain a

constant sample temperature of 20 °C (± 0.1 °C). In each calorimetry experiment, the

logging of calorimetric data (i.e., heat flow rate and heat release) was delayed by 15

minutes to ensure that the signal was stable. Calorimetry profiles of the pastes, as

obtained from isothermal microcalorimetry, were processed - using enthalpies of -522.04

kJ moleC3A-1 for stage I; -237.64 kJ moleC3A-1 for stage II; and -261.02 kJ moleC3A-1 for

stage III of C3A hydration (see the Review of C3A Hydration in Section 2) - to estimate time-dependent evolutions of degree of reaction (ao3A) and the rate of reaction (da/dt; units of h-1) of C3A.

X-ray diffraction (XRD) and thermogravimetric analysis (TGA) experiments were

carried out to identify anhydrous phases and hydration products in [C3A + C$ + H] pastes

after 72 h of hydration. For such investigations, hydration of C3A in the paste was

arrested by submerging the crushed (or powdered) paste in “fresh” IPA for 12 h or longer

(in which case, IPA was periodically replenished). Prior to testing, the samples were

oven-dried at 65 °C for 4 h. XRD was conducted in continuous scan mode using a

Phillips Panalytical X'pert MPD diffractometer; the diffractometer uses CuKa radiation (1

= 1.5418 A) with fixed divergence and anti-scatter slit-sizes of 0.5° and 0.25°, 207 respectively. The X-ray tube was operated at a voltage of 45 kV and current of 40 mA.

The powdered sample was placed within the sample holder, and X-ray diffractograms were obtained for the scanning range of 4.995°20 -to-89.989°20, with a step size of

0.026°26t For the TGA experiments, the dried powders were heated at 10 °C. min-1 from room temperature to 1000 °C in AhO3 crucible, with inert gas flowing over the specimen at a flow rate of 100 mL min-1.

6. EXPERIMENTAL RESULTS AND DISCUSSION

Figure 4 presents heat evolution profiles of [C3A + 15% C$ + H] pastes, prepared by replacing 0-to-85% of water with IPA. Readers are reminded that in pastes prepared with 0% and 85% of water replaced with IPA, the initial water activities («H0) are 1.00 and 0.50, respectively (see Section 3). To better understand the influence of water activity reductions on hydration kinetics of C3A in such pastes, it is important to describe the various stages of C3A hydration that are revealed in the heat flow rate profile of the control paste (IPA replacement level = 0%). As described earlier in Section 2, during stage I, crystals of ettringite precipitate during a nucleation burst, which occurs shortly after mixing; the crystals then grow slowly, at a near-constant rate, until C$ in the system is depleted (12,34,42). As such, in the control paste, the heat flow rate rapidly increases during stage I and then declines swiftly to stable low value (Figure 4A-B). The onset of stage II is marked by rapid increase in the heat flow rate up to an intense exothermic peak, followed by a sharp decline, and then an exponentially decaying shoulder that lasts for several hours. During this period, C3A reacts with water and ettringite to form 208 monosulfoaluminate. Stage II ends - and stage III begins - once ettringite is the system is depleted. This transition from stage II to stage III, however, cannot be inferred directly from visual observation of the heat flow rate profile of the control paste. During stage III,

C 3 A reacts with water to form metastable hydration products, all of which ultimately

transform to hydrogarnet (C 3 AH 6); see Section 2 for more details.

Figure 4. Isothermal microcalorimetry based determinations of heat evolution profiles of [C 3A + 15% C$ + H] pastes, prepared at different levels of replacement of water with IPA. (A) shows the heat flow rates in linear scale; (B) shows the heat flow rates in semi log scale; and (C) shows the cumulative heat releases in linear scale. l/s = 2 in all pastes. For a given system, uncertainty in the peak heat flow rate (i.e., the intensity of the stage II peak)— as determined from 3 repetitions— is within ±2%

Going back to Figure 4, it can be seen that in [C 3A + 15% C$ + H] pastes, as the

IPA content increases (and consequentially, a m decreases), the stage II peak - corresponding to monosulfoaluminate precipitation - is increasingly delayed and broadened. Delay in occurrence of the stage II peak entails slower kinetics of ettringite precipitation, therefore, inhibits the hydration kinetics of C 3A and slows the consumption of C$ during stage I. Broadening of the stage II peak - including a decline in its peak intensity - entails deceleration of kinetics of monosulfoaluminate precipitation. At high 209

IPA replacement levels (i.e., > 85%), the delay in occurrence of the stage II peak is substantial, so much so that it does not even appear within the 72 h of hydration. All things considered, these results suggest that reductions in a m result in proportionate suppression of C 3A hydration, and retardation of all processes (i.e., precipitation of hydration products and consumption of C$) that are derived from hydration of C 3A through the different stages. In a prior study, Oey et al. (5) reported that in [C 3 S + H ] pastes, reductions in a H0 (achieved via IPA addition) result in sustained inhibition of growth of the main hydrate (i.e., C -S-H ) as soon as it nucleates. Likewise, it is hypothesized that in [C 3A + 15% C$ + H] pastes, IPA-induced reductions in a H0 re su lt in suppression of post-nucleation growth of ettringite, monosulfoaluminate, and hydrogarnet

(and/or metastable hydrates) during stages I, II, and III of C 3A hydration, respectively.

This hypothesis will be revisited later in this section, where its veracity will be further examined. IPA-induced suppression of C 3A hydration, as observed in heat flow rate profiles (Figure 4A-B), are expectedly reflected in the cumulative heat release profiles as well (Figure 4C). In general, with decreasing values of a H0, the cumulative heat released from the pastes at 72 h decreases. As an example, at 72 h, the cumulative heat released from hydration of the control paste (aH0 = 1.00) amounted to - 810 J per gram of C 3A ; whereas, in the paste prepared with 85% IPA (aH0 = 0.50), the cumulative heat release was relegated to -175 J per gram of C 3A. The effects of a H0 reductions - resulting from partial replacement of mixing water with IPA - on hydration kinetics of C 3A in [C 3A +

30% C$ + H] pastes (Figure 5) are analogous to those in pastes prepared with 15% C$. In the heat flow rate profile of [C 3A + 30% C$ + H] paste prepared with 0% IPA, the first two stages of C 3A hydration are clearly noticeable. Owing to its higher C$ content, stage 210

I of the control paste is longer - leading to precipitation of larger amount of ettringite - compared to control [C 3A + 15% C$ + H] paste (12,33,34,36). Akin to the trends shown in Figure 4, IPA-induced reductions in a m result in proportionate suppression of C 3A hydration across all stages in [C 3A + 30% C$ + H] pastes (Figure 5A-B).

Figure 5. Isothermal microcalorimetry based determinations of heat evolution profiles o f [C 3A + 30% C$ + H] pastes, prepared at different levels of replacement of water with IPA. (A) shows the heat flow rates in linear scale; (B) shows the heat flow rates in semi log scale; and (C) shows the cumulative heat releases in linear scale. l/s = 2 in all pastes. For a given system, uncertainty in the peak heat flow rate (i.e., the intensity of the stage II peak)— as determined from 3 repetitions— is within ±2%

W ith increasing IPA replacement levels, the stage II peak is progressively delayed, and becomes less intense and broader. Owing to these alterations in heat flow rates, [C 3A + 30% C$ + H] pastes prepared with higher IPA contents feature lower cumulative heat release, at any given age, compared to pastes prepared with lower IPA contents. The inferences made thus far, regarding the influence of a H0 on hydration kinetics of C 3A, have been based on visual observations of the pastes’ heat evolution profiles, and, thus, are qualitative in nature. For more quantitative description of the C 3A hydration dynamics, the calorimetry profiles of all [C 3A + C$ + H] pastes were processed 211 to extract four distinct calorimetric parameters: inverse of time to the stage II peak (h -1); heat flow rate (mW g C3A-1) at the stage II peak; and slopes of acceleration (i.e., approach to the peak) and deceleration (i.e., departure from the peak) regimes of the stage II peak

[m W (h • g C3A)-1] (18,64-66) . Upon extraction, the calorimetric parameters of all [C 3A +

C$ + H] pastes were plotted against the corresponding a m (primary x-axis) and IPA replacement level (secondary x-axis).

As can be seen in Figure 6, with increasing IPA replacement levels, as a H0 reduces, all four calorimetric parameters are progressively reduced in monotonic manner.

Firstly, the delay in occurrence of the stage II peak with respect to decreasing values of a H0 (Figure 6A) signifies prolongation of stage I. This decelerates the ettringite precipitation kinetics, thereby delaying the nucleation of monosulfoaluminate. Secondly, the progressive decrease in intensity of the stage II peak (Figure 6B) with respect to decreasing values of a H0 entails deceleration of kinetics of monosulfoaluminate precipitation. Lastly, the reductions in slopes of acceleration and deceleration regimes of the stage II peaks (Figure 6C) with decreasing values of a H0 - once again - suggest that the kinetics of monosulfoaluminate precipitation are retarded in pastes with higher IPA contents. In Figure 6, it should be noted that any given value of a H0 (including when a H0

= 1), all four calorimetric parameters of [C 3A + 30% C$ + H] pastes are consistently lower than those of [C 3A + 15% C$ + H] pastes.

This - as stated in Section 3 - is because in the [C 3A + 30% C$ + H] pastes, as th e C $ /C 3A molar ratio is higher compared to that in [C 3A + 15% C$ + H] paste, stage I of the hydration process (i.e., Equation 2: ettringite precipitation reaction) is lengthier.

Consequently, in all [C 3A + 30% C$ + H] pastes: (i) the ‘nucleation event’, when crystals 212 of monosulfoaluminate precipitate for the first time is delayed; and (ii) following the nucleation event, the kinetics of monosulfoaluminate precipitation is suppressed due to the lack of free-space in the microstructure (which, compared to equivalent pastes prepared with 15% C$, contain more ettringite). Regarding the latter point, prior studies

(12,33,34,36,44) have shown that in [C 3 A + C $ /C $ H 2 + H] pastes, the rate of growth of monosulfoaluminate crystals decreases proportionately with respect to decreasing volume of free-space in the microstructure at the time of the crystals’ nucleation.

calorimetric parameters pertaining to the stage II peak: (A) inverse of time to the stage II peak; (B) heat flow rate at the stage II peak; and (C) slopes of acceleration and deceleration regimes of the stage II peak. The corresponding IPA replacement levels are shown in the secondary x-axis. Results pertaining to all [C3A + C$ + H] pastes evaluated in this study are included. l/s = 2 in all pastes. Uncertainty in each

calorimetric parameter is within ± 2 %

On account of suppressed kinetics of monosulfoaluminate precipitation in [C 3A +

30 % C$ + H] pastes, as compared to their counterparts prepared using 15% C$, the

effects of a m on the former set of pastes are more severe. As can be seen in Figure 6 , in

[C 3A + 30 % C$ + H] pastes, that were prepared at IPA replacement levels of 30% or 213 above (i.e., a H0 < 0.90), the stage II peak does not even occur within the 72 h of hydration. In contrast, calorimetry profiles of all [C 3A + 15 % C$ + H] pastes prepared at

IPA replacement levels of 70% or below (i.e., a m > 0.70) do feature the stage II peak within the same period of hydration. Calorimetric parameters featured in Figure 6 pertain primarily to kinetics of C 3A hydration during stage II. To better understand the overarching influence of a H0 on hydration of C 3A - across all three stages - the cumulative heat released from the pastes at 72 h of hydration were extracted, and plotted against the corresponding a H0 (primary x-axis) and IPA replacement level (secondary x- axis). As can be seen in Figure 7, in both sets of pastes (i.e., [C 3A + 15 % C$ + H] and

[C 3A + 30 % C$ + H] pastes), the cumulative heat (at 72 h) declines monotonically, and broadly in an exponential manner, with respect to decreasing values of a H0 . Importantly, as cumulative heat is an explicit indicator of degree of C 3A hydration (a o3A) in the pastes, it can be said that reductions in a H0 suppress the hydration of C 3A throughout stages I and

II (as shown in Figure 6) and even stage III (if it occurs), thus resulting in lower values of

« C3A at later ages. It must be pointed out that the exponential relationship between cumulative heat and a H0 in [C 3A + C$ + H] pastes is strikingly similar to that observed in

[C 3 S + H] pastes (see Figure 7). In their study, Oey et al. (5) reported that lower cumulative heats (and, thus, lower degree of C 3 S hydration) in [C 3 S + H] pastes prepared at lo w e r a H0 were due to the suppression of growth rate of C -S-H nuclei. Likewise, in

[C 3A + C$ + H] pastes, it is hypothesized that reductions in ano result in suppression of post-nucleation growths of ettringite, monosulfoaluminate, and hydrogarnet (and/or metastable hydration products) during stages I, II, and III of the C 3A hydration process, respectively. This hypothesis gains support from another study (36), wherein it was 214

shown in [C 3 A + C $ H 2 + H] pastes, the disparities in kinetics of ettringite and

monosulfoaluminate precipitation with respect to differences in C$H 2/C 3 A molar ratio (at the time of mixing) are predominantly due to differences in post-nucleation growth rates

of the crystals. In Figure 7, it is also interesting to note that while hydration of C 3 S is

arrested at critical a n of 0.70 (cumulative heat at 72 h is 0), the hydration of C 3 A - albeit

suppressed - is not entirely ceased at the same aH. In fact, even at aH 0 of 0.50, which

corresponds to IPA replacement level of 85%, hydration of C 3 A is not arrested. This

suggests that the intrinsically higher reactivity of C 3 A - compared to that of C 3 S - enables the commencement and/or advancement of its hydration even at very low water activities (0.50 < aH < 0.70).

Figure 7. Cumulative heat released after 72 h of hydration of C 3 A in [C 3 A + C$ + H]

pastes plotted against aH 0 (primary x-axis) and IPA replacement level (secondary x-

axis). Data pertaining to [C 3 S + H] pastes have been adapted from Ref. (5). The

dashed lines are exponential fits to the datasets. l/s = 2 in all [C 3 A + C$ + H] pastes. Uncertainty in each heat release value is within ±2% 215

In the above discussions, emphasis has been given to describe the kinetics of C 3A hydration in pastes prepared at IPA replacement levels of 85% or below (i.e., a m > 0 .5 0 ).

However, it is important to examine C 3A hydration in pastes prepared at higher IPA replacement levels, especially considering that in Section 4, it was concluded that the h y d ra tio n o f C 3A would be arrested at the critical a H of 0.45, which corresponds to IPA replacement level of 87.1%.

(A ) (B ) Figure 8. Cumulative heat release profiles of [C 3A + C$ + H] pastes, prepared at: (A) high IPA replacement levels (>87%); and (B) low IPA replacement levels (<60%). The solid lines correspond to [C 3A + 15% C$ + H] pastes, whereas the dashed lines represent [C 3A + 30% C$ + H] pastes. l/s = 2 in all pastes. Uncertainty in the cumulative heat release, at any given time, is within ± 2%

Therefore, additional calorimetry experiments were conducted to examine the h y d ra tio n o f C 3A in [C 3A + C$ + H] pastes prepared with IPA contents > 87% (i.e., a H0 <

0.45). Results obtained from such experiments are shown in Figure 8A. As can be seen in

Figure 8A, even at high IPA replacement levels, the cumulative heat released from all 216 pastes are positive (i.e., always > 0, after mixing), and monotonically increasing with time. This suggests that even at very low initial water activities (i.e., a m < 0.45), one or more exothermic processes - for example, the dissolution of C 3A and C$ - are able to commence and advance. Notwithstanding, it is important to note that the heat release profiles shown in Figure 8A are different from those of pastes prepared at IPA replacement levels of < 85% (shown in Figure 8B). As can be seen in pastes prepared at

IPA replacement levels of < 85% (i.e., aH0 > 0.50), the temporal release of heat is significantly altered in relation to the initial C$ content (or C$/C 3A molar ratio). This is expected because depending on the C$ content, the lengths of stage I (ettringite precipitation) and stage II (monosulfoaluminate precipitation) of C 3A hydration are different. Conversely, in pastes prepared at IPA replacement levels of > 87% (i.e., aH0 <

0.45), the influence of C$ content on the heat release profiles is imperceptible. As can be seen in Figure 8A, at any given IPA replacement level, heat release profile of [C 3A +

15% C$ + H] paste overlaps with that of its counterpart prepared using 30% C$. This result is significant because it indicates that in pastes prepared at aH0 < 0.45, the presence of C$ is redundant in that it is unable to exert any perceptible influence on the exothermic reactions. This implies that when the pastes are prepared with a mixing solution with a H0

< 0.45, the reaction of C$ with C 3A and water to form ettringite (i.e., stage I of C 3A hydration) does not take place - at any rate, not to an appreciable degree. As stage I of

C 3A hydration is broadly annulled, it can be deduced that the lack of ettringite in the system also prevents the commencement of subsequent stages of C 3A hydration (i.e., stage II: monosulfoaluminate precipitation; and stage III: precipitation of metastable calcium aluminate hydrates and, ultimately, C 3AH 6). Simply put, results shown in Figure 217

8A indicate that in pastes prepared at am < 0.45 (IPA replacement level > 87%), the

precipitation of all hydration products - including ettringite (during stage I) - is

precluded, and the hydration of C3A (i.e., reaction of C3A with C$ and water) is

effectually arrested. Validation of this assertion is provided later in this section by means

of results obtained from additional calorimetry experiments and material characterization techniques (i.e., XRD and TGA). If we accept the premise that in pastes prepared at aH0 <

0.45, the precipitation of hydration products is disallowed (as discussed above), there still

needs to be an explanation for the heat released in such pastes (see Figure 8A). It is

hypothesized that in the pastes, the heat release is exclusively due to the (exothermic)

dissolution of C3A and C$ - which initiate and advance even at very low values of aH0, thereby releasing heat that monotonically increases with time. As aH0 in the paste

decreases, the kinetics of C3A and C$ dissolution are retarded (50); consequently, the

cumulative heat release, at any given point in time, also reduces (Figure 8A). To verify

this hypothesis, additional calorimetry experiments were conducted to monitor the heat

release in single-phase systems: [C3A + H] paste and [C$ + H] paste. In either paste, as

there is no chemical interaction between C3A and C$, the precipitation of ettringite or

monosulfoaluminate is infeasible. Both pastes were prepared at l/s of 2.0, and, in each

paste, 92%mass of the water was replaced with IPA (i.e., aH0 = 0.33). As can be seen in

Figure 9A, even at such low value of aH0, both C3A and C$ are able to dissolve, and,

thus, release heat. After 72 h, the cumulative heats released from C3A’s and C$’s

dissolution are ~85 J gC3A-1 and ~1 J gC$-1, respectively; this difference in heat release is

expected to arise due to differences in enthalpies and kinetics (e.g., differences in SSA of

the particulates) of dissolution of the two phases. Next, the cumulative heat release 218 profiles of [C 3A + H] and [C$ + H] pastes were compared against those of [C 3A + 15%

C$ + H] and [C 3A + 30% C$ + H] pastes (Figure 9B); all pastes were prepared at the sam e l/s of 2 and IPA replacement level of 92%. As can be seen, the cumulative heat release profile obtained by adding the heats released from C 3A ’s and C$’s dissolution in

[C 3A + H] and [C$ + H] pastes, respectively, is very similar to the cumulative heat release profiles of [C 3A + 15% C$ + H] and [C 3A + 30% C$ + H] pastes.

Figure 9. Cumulative heat release profiles of: (A) [C 3A + H] and [C$ + H] pastes; and (B ) [C 3A + H ], [C 3A + 15% C$ + H], and [C 3A + 30% C$ + H] pastes. All pastes were prepared at l/s of 2, and IPA replacement level of 92% mass (i.e., a m = 0.33). In (B), the symbols represent the sum of cumulative heats released from the dissolution of C 3A and C$ in single-phase [C 3A + H] and [C$ + H] pastes, respectively. Uncertainty in the cumulative heat release, at any given time, is within ±2%

This equivalency in the cumulative heat release profiles is significant because it suggests that in [C 3A + C$ + H] pastes, prepared at low initial water activities, the release of heat is exclusively due to the dissolution of C 3A and C$; between the two phases, C 3A is the major contributor of heat release. W hen combined, the results shown in Figures 8-9 219

corroborate the hypothesis presented above - that in [C 3 A + C$ + H] pastes, prepared at

low initial water activities (i.e., ana < 0.45), while the dissolutions of C 3 A and C$ do commence and advance, the precipitation of hydration products (i.e., ettringite and

monosulfoaluminate, resulting from C 3 A-C$ interactions), and, therefore, the hydration

o f C 3 A is arrested. It could still be argued that in [C 3 A + C$ + H] and single-phase [C 3 A

+ H] pastes, prepared at aH 0 < 0 .4 5 , C 3 A could react directly with water to form

metastable calcium aluminate hydrates (e.g., C 2 AH 8 a n d C 4AH 13 ) (48), which would

subsequently transform to hydrogarnet (C 3 AH 6). Nevertheless, results obtained from

XRD and TGA - that are described next - clearly show that the formation of such

hydration products is also disallowed at aH 0 < 0.45. Based on results obtained from thermodynamic calculations (Section 4) and analyses of experimental results (described

thus far in Section 6), it has been posited that the hydration of C 3 A in [C 3 A + C$ + H]

pastes is arrested at aH 0 < 0.45 (i.e., when 87% or more of mixing water is replaced with

IPA). This entails that precipitation of all hydration products (e.g., ettringite,

monosulfoaluminate, and hydrogarnet) - that are derived from C 3 A ’s hydration - is

disallowed in pastes prepared at aH 0 < 0.45. To corroborate this hypothesis, additional numerical analyses of calorimetry results and experimental characterizations of the pastes were conducted.

For the numerical analyses, emphasis was given to utilize the cumulative heat

release profiles of [C 3 A + C$ + H] pastes (shown in Figures 4-5) to estimate the hydration products that are expected to be present at 72 h. Towards this, enthalpies of reactions corresponding to ettringite precipitation (stage I; Equation 2), monosulfoaluminate precipitation (stage II; Equation 3), and hydrogarnet precipitation 220

(stage III; Equation 4), as described in Section 2 were used. On the bases of these

enthalpies, for both sets of pastes (i.e., [C3A + 15% C$ + H] and [C3A + 30 % C$ + H]

pastes), the limiting values (i.e., when am = 1) of cumulative heat release (Q; units of J

gc3A-1) and the corresponding values of oc3a at the ends of stages I, II, and III were

estimated. Lastly, by using each paste’s cumulative heat release at 72 h (drawn from

Figures 4C and 5C), in conjunction with the ultimate heat of C3A hydration (see last row

of Table 3) in the paste, the degree of hydration of C3A (ac3A) and the corresponding

combination of hydration products that are expected to be present in the paste at 72 h

were estimated. Results obtained from the analyses are shown in Figure 10.

Table 3. Limiting values of cumulative heat (Q) released from reactions corresponding to Equations 2, 3, and 4, and limiting values of ac3A at the ends of stage I, II, and III. Results for both [C3A + 15% C$ + H] and [C3A + 30% C$ + H] pastes are shown

Q (J gC3A-1) ac 3A (Unitless) Reaction 15% C$ 30% C$ 15% C$ 30% C$ C3A + C$ + 32H ^ AFt 225.03 547.89 0.117 0.284 C3A + 0.5AFt + 2H ^ 0.5AFm 307.83 498.82 0.350 0.854 C3A+ 6H ^ C3AH6 627.93 144.22 1.000 1.000 Ultimate value of Q 1160.8 1190.9

As can be seen in Figure 10, in both sets of pastes (i.e., [C3A + 15% C$ + H] and

[C3A + 30 % C$ + H] pastes), the values of ac3A (at 72 h) decay in exponential manner with respect to decreasing a . Nevertheless, these trends are expected considering the

exponential relationship between the 72-h cumulative heat release and aH0 of the pastes

(shown in Figure 9). Importantly, Figure 10 shows that in [C3A + C$ + H] pastes, ac3A

and the corresponding solid phase assemblage at 72 h are dictated by aH0 . Starting with 221

[C 3A + 15% C$ + H] pastes (Figure 10A), when 1.0 > aH0 > 0.85 (i.e., 44% > IPA replacement level > 0%), the hydration of C 3A is expected to have advanced to stage III; as such, the pastes are expected to comprise of C 3A, monosulfoaluminate, and C 3AH 6

(and/or metastable calcium aluminate hydrates). W hen 0.85 > aH0 > 0.50 (i.e., 85% >

IPA replacement level > 44%), the pastes are expected to comprise of C 3A, ettringite, and monosulfoaluminate; as such, the hydration of C 3A is expected to remain in stage II.

Figure 10. Degree of hydration of C 3A (aC3A), after 72 h of hydration, in: (A) [C 3A + 15% C$ + H]; and (B) [C 3A + 30% C$ + H] pastes, plotted against a m . Phases, listed in the shaded areas, are expected to be present in the paste, depending on the values of «C3A a n d aH0 . F o r aH0 <0.45, hydration of C 3A is assumed to be arrested; as such, only C 3A and C$ are assumed to be present

And lastly, when aH0 ^ 0.50 (i.e., IPA replacement level > 85%), the hydration of

C 3A does not progress beyond stage I; as such, the pastes are expected to comprise of

C 3A, C$, and ettringite (which is not expected to precipitate when aH0 < 0.45). In [C 3A + 222

30% C$ + H] pastes (Figure 10B), even at aH0 = 1, the hydration of C 3A at 72 h does not advance to stage III. W hen 1.0 > aH0 > 0.80 (i.e., 55% > IPA replacement level > 0%), th e h y d ra tio n o f C 3A advances to stage II; whereas, when 0.45 < aH0 ^ 0.80 (i.e., 87% >

IPA replacement level > 55%), the hydration of C 3A is constrained to stage I. W hen aH0

< 0.45 (i.e., IPA replacement level > 87%), it is assumed that hydration of C 3A does not commence and no hydration products are precipitated (although C 3A and C$ are expected to dissolve and release heat; see Figures 8-9). Therefore, at 72 h, the solid phase assemblage is expected to comprise of only C 3A and C$. Results shown in Figure 10 provide rough estimate of solid phase assemblages in [C 3A + C$ + H] pastes after 72 h of hydration. To substantiate these findings, XRD was employed; the objective was to identify the phases present in the pastes at 72 h. As can be seen in Figure 11, for the [C 3A

+ 15% C$ + H] pastes, there is good agreement between phases predicted from the numerical analyses (Figure 10) and those identified from XRD patterns.

In the paste prepared using pure water as the mixing solution (i.e., a m = 1.00), metastable calcium aluminate hydrates (C 2AH 8 a n d C 4AH 19) and monosulfoaluminate were found confirming that the hydration of C 3A had entered into stage III. Presence of metastable hydrates is expected since the transformation of these hydrates to hydrogarnet

(C 3AH 6) is kinetically limited. W hen the IPA replacement level was increased to 20%

(i.e., aH0 = 0.94), monosulfoaluminate was the only sulfate containing hydrate in the paste; this, also, is representative of C 3A hydration being in stage III. W hen the IPA content was increased to 50% (i.e., aH0 = 0.83), the peaks corresponding to ettringite (67) emerged with greater intensity than those of monosulfoaluminate. The presence of both ettringite and monosulfoaluminate indicates that the hydration of C 3A is in stage II; this is 223 in agreement with predictions made in Figure 10. In all [C 3A + 15% C$ + H] pastes, containing > 87% IPA in the mixing solution (i.e., a m < 0.45), no hydration products

(not even metastable calcium aluminate hydrates or C 3AH 6) were detected (68-72). This confirms that the hydration of C 3A in [C 3A + 15% C$ + H] pastes does not initiate when the initial water activity is 0.45 or below.

(A) 85% C,A+ 15% C$

♦

IPA in Solution % Mass Initial W ater Activity (aHD) l/s = 2 ------0% ( 1.00) ------2 0 % (0 .9 4 ------5 0 % (0 .8 3 ) 8 5 % (0 .5 0 ) 8 7 % (0 .4 5 ) ------9 0 % (0 .3 8 ) Diffraction Angle, 28 (Degrees) ------9 5 % (0 .2 3

(B) 70% C,A + 30% C$ Mineral Species

C a S 0 4 E ttr in g ite Monosulfoaluminate Hemicarboaluminate Monocarboaluminate

Diffraction Angle, 28 (Degrees) Figure 11. XRD patterns of (A) [C 3A + 15% C$ + H]; and (B) [C 3A + 30% C$ + H] pastes, prepared at different IPA replacement levels, after 72 h of hydration. For each IPA replacement level, the corresponding a H0 are indicated within parentheses. l/s = 2 in all pastes 224

Going back to Figure 11, for the [C3A + 30% C$ + H] pastes as well, good agreement was found between the phases predicted from the numerical analyses (Figure

10) and those identified from XRD patterns. In the paste prepared using pure water as the mixing solution (i.e., aH0 = 1.00), ettringite and monosulfoaluminate were detected - thus confirming that, at 72 h (after mixing), the hydration of C3A had transitioned to stage II.

As the IPA replacement level was increased from 0% to 50% (i.e., aH0 = 0.83), the intensities of peaks corresponding to ettringite and monosulfoaluminate progressively increased and decreased, respectively. This is indicative of C3A hydration being in stage

II, and confirms - as was stated earlier in this section - that the kinetics of ettringite-to- monosulfoaluminate transformation during stage II is progressively suppressed with decreasing aH0 . Lastly, akin to pastes prepared with 15% C$, in all [C3A + 30% C$ + H] pastes, no hydration products were detected at IPA replacement levels of > 87% (i.e., aH0

< 0.45); this confirms that the hydration of C3A in the pastes did not commence.

Cessation of C3A hydration in [C3A + 30% C$ + H] pastes prepared at IPA replacement levels of > 87% was also confirmed by TGA data. As can be seen in Figure 12, the characteristic differential TGA (DTGA) peaks of ettringite and monosulfoaluminate (73)

- that are clearly seen in the control paste (aH0 = 1.00) - are absent in pastes prepared at

IPA replacement levels of 90% (aH0 = 0.38) and 95% (aH0 = 0.23).

In Figure 11, it is worth noting that in selected pastes, traces of CO3-AFm phases

(i.e., hemi- and mono-carboaluminate) were also found. While the exact reason for the presence of these phases in the pastes is not clear, it is hypothesized that the CO3-AFm phases precipitated due to one or both of the following: (i) reaction of aqueous

Ca2+, Al(OH)-, and OH- ions, released from the dissolution of C3A (see Equation 2), 225 with atmospheric CO 2 (4,35); and/or (ii) reaction of CaO impurity in C 3A with IPA, water (if present), and atmospheric CO 2 (likely during storage of the paste specimens).

The latter hypothesis is supported by a prior study (5), wherein it was shown that in pastes prepared by mixing C 3 S with pure IPA (no water), the CaO impurity in C 3S reacted with IPA and atmospheric CO 2 to form CaCO 3 that subsequently forms CO 3-

AFm phase. It is worth noting that the CaO impurity in C 3A is detectable in the DTGA traces shown in Figure 12. In the DTGA traces, the mass losses in the pastes (including the pristine system, i.e. the anhydrate solid mixture of 70% C 3A and 30% C$) between temperatures of 350-and-420°C are thought be linked the formation an unknown carbonate phase resulting from the carbonation of the CaO impurity present in C 3A.

0 100 200 300 400 500 600 700 800 Temperature (°C) Figure 12. Differential TGA traces (differential mass loss) of [C 3A + 30% C$ + H] pastes prepared at different IPA replacement levels, after 72 h of hydration. The “pristine” system represents a solid, powder mixture of 70% C 3A and 30% C$. For each IPA replacement level, the corresponding a H0 are indicated within parentheses. l/s = 2 in all pastes 226

Overall, the results shown in Figures 11-12 clearly show that in [C 3A + C$ + H] pastes, regardless of the C$ content, the hydration of C 3A - and, therefore, the precipitation of hydration products (i.e., ettringite, monosulfoaluminate, metastable calcium aluminate hydrates, and C 3AH 6) - did not commence or advance when the initial water activity (a H0) is < 0.45 (i.e., IPA replacement level = 87%). This confirms the results obtained from thermodynamic considerations (Section 4) and inferences drawn from calorimetry experiments (Figures 4-10) - that the critical water activity below which hydration of C 3A is arrested is 0.45. Notwithstanding, it should be noted that even at ano < 0.45, both C 3A and C$ are still able to dissolve (see Figures 8-9); however, at such low water activities, the ions released from dissolution of the anhydrous phases are unable to combine and precipitate as reaction products.

W hile the results described thus far overwhelmingly indicate that the critical water activity below which C 3A stops hydrating is 0.45, there is a small - yet finite - chance that the cessation of C 3A hydration in the pastes (which were all prepared at a reasonably high l/s of 2) was caused due to the scarcity of water, thereby leading to the development of capillary stresses within the pore network of the pastes. Thus, it is deemed important to determine whether or not the hydration of C 3A would be arrested in

[C 3A + C$ + H] suspensions, in which liquid saturation - even after hundreds of hours of hydration - would be guaranteed (thereby ensuring that capillary stresses in the pores remain insignificant). Towards this, [C 3A + C$ + H] suspensions were prepared at l/s o f

100 and allowed to hydrate for 72 h (at 20 °C), following which they were examined using XRD. As can be seen in Figure 13, when IPA replacement level is 20% (i.e., ano =

0.94), the hydration of C 3A commences and advances to stage II in both suspensions; 227 monosulfoaluminate is detected in the [C 3A + 15% C$ + H] suspension, and ettringite and monosulfoaluminate are detected in the [C 3A + 30% C$ + H] suspension. However, when the IPA replacement level is increased to 95% (i.e., a m = 0.23), no hydration products (including metastable calcium aluminate hydrates and C 3AH 6) are detected in either suspension. This confirms that the hydration of C 3A is arrested in both suspensions, in spite of C 3A particulates having unrestricted access to liquid water.

Hence, in light of the above discussions and results shown in Figure 13, it can generically be said that in [C 3A + C$ + H] systems prepared at a H0 < 0.45, the hydration of C 3A (and, thus, the precipitation of all hydration products) is arrested, regardless of the water and

C$ contents in the system.

(A) 85% C,A + 15% C$

IPA in Solution % Mass Initial W ater Activity (aH0) l/s = 100 ----- 2 0 % (0 .9 4 ) ----- 9 5 % (0 .2 3 )

Diffraction Angle. 20 (Degrees)

70% C.A + 30% C$ Mineral Species

C a S 0 4 E ttrin g ite (B) Monosulfoaluminate

Diffraction Angle. 20 (Degrees) Figure 13. XRD patterns of (A) [C 3A + 15% C$ + H]; and (B) [C 3A + 30% C$ + H] suspensions, prepared at 20% and 95% IPA replacement levels, after 72 h of hydration. For each IPA replacement level, the corresponding a H0 are indicated within parentheses. l/s = 100 in all suspensions 228

By the same logic, it can be said that even if hydration of C 3A were to initiate (for example, in a [C 3A + C$ + H] or cement paste prepared at a m >> 0.45), it is expected to be arrested as soon as the water activity declines below the critical value of 0.45. If drying - as opposed to replacement of mixing water with IPA - is used to stop C 3A hydration in cementitious systems, then the internal RH would have to be reduced to ~

45% or below (N.B., once equilibrium is reached, internal RH = a H in the solution =

0.45); this value of critical RH fo r C 3A hydration is in good agreement with those reported in prior literature (6, 7, 16).

7. SUMMARY AND CONCLUSIONS

This study examined the influence of water activity (a H) on the hydration of tricalcium aluminate (C 3A ) in [C 3A + calcium sulfate (C$) + water (H)] systems.

Reductions in water activity were achieved by partially replacing water - meant to be used as the mixing liquid for formulation of the pastes - with isopropyl alcohol (IPA).

IPA - as opposed to other organic alcohols (e.g., ethanol) - was chosen because of its excellent miscibility with water, inertness, and small molecular size, which permits its access to large as well as very small pores within the microstructure. Isothermal microcalorimetry, along with other experimental techniques, was employed to monitor th e h y d ra tio n o f C 3A in [C 3A + 15 % C$ + H] and [C 3A + 30 % C$ + H] pastes, encompassing a wide range of initial water activities (0.00 < a H0 < 1.00).

Results obtained from the experiments clearly showed that with decreasing initial water activity, the kinetics of all reactions associated with C 3A (e.g., with C$, resulting in 229 ettringite formation; and with ettringite, resulting in monosulfoaluminate formation) are proportionately suppressed. As the initial water activity declines below the critical value of 0.45, the hydration of C 3A, and the resultant precipitation of hydration products (i.e., ettringite, monosulfoaluminate, metastable calcium aluminate hydrates, and C 3AH 6) are essentially arrested. In a [water + IPA] mixture, an initial water activity of 0.45 corresponds to replacement of 87.1% mass of the water with IPA. However, even at initial water activities that are less than the critical value of 0.45, both C 3A and C$ are still able to dissolve and release ions into the contiguous solution; however, at such low water activities, the ions are unable to combine and precipitate as reaction products.

W hile majority of the [C 3A + C$ + H] pastes examined in this study were prepared at liquid-to-solid mass ratio (l/s ) of 2, it was shown that even in [C 3A + C$ + H] suspensions - that were prepared at l/s of 100, to ensure that all pores remain near saturated with the liquid phase - the hydration of C 3A was arrested below the critical water activity of 0.45. Alongside, and independent of, the experiments, a thermodynamic approach was devised and employed to estimate two significant thermodynamic parameters associated with the hydration of C 3A in [C 3A + C$ + H] systems: critical water activity below which hydration of C 3A is arrested, and solubility constant of C 3A

(K c 3a). In excellent agreement with experiments, the thermodynamic calculations also indicated that the critical water activity for C 3A hydration is 0.451. On the basis of the c ritic a l aH, the solubility product of C 3A (K c3a) was estimated as 10'2065. To the best of the authors’ knowledge, this is the very first estimation of K c3a; determination of this value is expected to aid in the development and validation of sophisticated cement hydration models (17,18, 20-22,65,74-76). 230

Overall, this work presents cogent arguments - derived from, and supported by, rigorous experimentation and thorough numerical analyses - that unequivocally show that the hydration of C 3A is significantly affected by the activity of water, and thus by reductions in relative humidity. In [C 3A + C$ + H] pastes, or even in cement pastes, regardless of the l/s or the amount of C$ (or C$H 2), the hydration of C 3A is terminated once the water activity decreases below the critical value of 0.45. On the basis of conclusions drawn from this study, it can be said that for cement-based systems, especially for those prepared at low l/s , it is important to maintain saturated curing conditions to ensure that water activity is retained well above the values of 0.45 and 0.70 to ensure the continuation of C 3A a n d C 3 S hydration, respectively. Failure to do so would result in suppression of reaction rates of anhydrous phases (i.e., C 3 S a n d C 3A ), and, ultimately manifest as impoverished mechanical properties.

ACKNOWLEDGEMENTS

Funding for this study was provided by the National Science Foundation (CMMI:

1661609 and CMMI: 1932690). All experiments and simulations were conducted at the

M aterials Research Center, Missouri S&T.

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VI. HYDRATION OF HIGH ALUMINA-CALCIUM ALUMIANTE CEMENTS WITH CARBONATE AND SULFATE ADDITIVES

Jonathan Lapeyre§, Sai Akshay Ponduru§, Monday Okoronkwo^, Hongyan Ma*, and Aditya Kumar

^Department of Materials Science and Engineering, Missouri University of Science and Technology, Rolla, MO 65409

^Department of Chemical and Biochemical Engineering, Missouri University of Science and Technology, Rolla, MO 65409

*Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO 65409

ABSTRACT

This study investigated the influence of limestone (LS) and calcium sulfate (C$) mineral additives on the hydration kinetics of high a-AhO3 calcium aluminate cement

(CAC) utilizing experimental techniques and thermodynamic simulations. Increasing the replacement level of limestone or calcium sulfate increased the cumulative heat of the hydration reaction. The limestone exhibited limited acceleratory effects to the CAC hydration kinetics due to the coarseness of the powder. The coarse particle size distribution limited any heterogeneous nucleation that would have occurred with a finer particle size as well as the intrinsic insolubility kinetically limits the formation of monocarboaluminate phases. Conversely, the cumulative heat release increased as the limestone content increased; however, this was not due to any enhance reactivity provided by the limestone. Instead, this increase in the cumulative heat is due to a combination of the LS and the increase in the amount of water available to react with 238

CAC via the dilution effect. In comparison, the increase in the C$ replacement level accelerated the heat flow rate of CAC with the C$ particles acting as a favorable surface for heterogenous nucleation of the hydrates during the initial stages of the hydration reaction. Increasing the C$ replacement level does not form more ettringite and does not translate in an increase in the compressive strength. After the 72-hour hydration period,

C$ remains in the microstructure showing that the complete dissolution of C$ is not responsible for the monotonic increase in heat flow rate. It is expected that the amount of hydrates or residual unreacted particles cannot compensate for the decrease in strength caused by the reduction of a-AhO3 present in the CAC.

Keywords: Calcium aluminate cement, hydration kinetics, filler effect, thermodynamics

1. INTRODUCTION

Calcium aluminate cement (CAC) is a hydraulic binder that provides many advantages like enhanced abrasion resistance, resistance to biogenic corrosion, low permeability and rapid hardening compared to hardened ordinary portland cement (OPC).

Even though CACs exhibit these superior properties, the usage of CACs outside of niche applications such as refractory castables, wastewater or sewers linings, dental applications, among others is limited due to the higher price of CAC compared to OPC

(1-3). Monocalcium aluminate (CaAhO 4 , CA) is the main phase present in CACs and is the most reactive phase compared to the other prominent calcium aluminate phases such

as C A 2 , C 1 2 A 7 , a n d /o r C 4AF present in CAC. For convenience, cement chemistry 239 shorthand for the cementitious compounds and constituent oxides is utilized (e.g.,

C a A l2 O 4 = CA and CaO = C, AhO 3 = A , C a S O 4 = $ respectively). These reactants form different hydrate phases depending on the duration of the hydration reaction or the temperature conditions during the hydration reaction. The temporal evolution of these hydration products is called the “conversion” process. The conversion process is the time-dependent transformation of metastable calcium aluminate hydrate phases: calcium

aluminate decahydrate (CaAhO4*10H2O, CAH 10) and hydroxyl-AFm [C 2 AHx where x is

m o le s o f H 2 O which is reported to vary from 7, or 8 moles, for this manuscript 8 moles is assumed to be present (4,5)] eventually these phases transforms into the

thermodynamically stable phase: hydrogarnet (Ca3Ah(OH)i2, C 3 AH 6). Additionally,

amorphous aluminum hydroxide gel (Al(OH) 3 , A H 3 ) forms during the hydration of CAC

phases. The result of the conversion process is the metastable CAH 10 a n d C 2 AH 8 p h a ses

release free-water (i.e., non-chemically bound water) as C 3 AH 6 forms increasing the

density of the hydrate (the density of the stable C 3 AH 6 is 2.52 g cm-3 compared to 1.72 g

cm-3 and 1.95 g cm-3 for CAH 10 a n d C 2 AH 8 respectively) (6). This transformation reduces the volume of hydrates and reduces the connectivity of the hydrates in the microstructure causing a significant increase in the porosity, decreasing the strength of the bulk material.

Separate from the conversion process, there are several temperature regimes in which certain reactions are thermodynamically favored and therefore certain calcium aluminate

hydrates are predominant. Between 0°C - 20°C CAH 10 forms, 20°C - 35°C C 2 AH 8

forms, and above 35°C C 3 AH 6 forms (7). For simplicity, the hydration of CA for different reactions as well as the conversion process for those temperatures is shown in

Equations (1) - (3). The other clinker phases undergo similar reaction but require longer 240 timeframes due to the other phases being intrinsically less reactive (8,9). When CA reacts in lower temperature regimes (shown in Equations 1a and 2a), metastable CAH10 initially forms but given enough time, CAH10 decomposes into C2AH8, AH3 and free water.

Subsequently the C2AH8 hydrate can transform into C3AH6 as seen in Equation 2b.

Similarly, for temperate temperatures, the CA hydrates form C2AH8 from the onset of the hydration reaction in addition to AH3 but later, the C2AH8 converts in the C3AH6, AH3 and free water. Equation 3 is the higher temperature case where C3AH6 forms outright instead of the metastable hydrates. The experiments herein where conducted near room temperature (i.e., 20°C - 25°C) therefore the CAH10 and hydroxyl-AFm phases are expected to form.

T < 20°C

CA+10H^CAH10 (1a)

2CAH10 ^ C2AH8 + AH3 + 9H (2a)

20°C < T < 35°C

2CA + 11H ^ C2AH8 + AH3 (1b)

3C2AH8 ^ 2C3AH6 + AH3 + 9H (2b)

T > 35°C

3CA + 12H ^ C3AH6 + 2AH3 (3)

To avoid the conversion process, many researchers have replaced CAC with additives such as limestone, silica fume, and blast furnace slag that to react with hydroxyl-AFm (aluminate-ferrite-mono) to form other AFm phases or suppress the formation of the CAH10. The general formula for AFm phases (or layered double hydroxides in other scientific fields (14,15)) can be described as [Ca2Al(OH)6]+*A- 241

•nHO where A is an anionic species such as OH and n represents the number of moles

of water (16,17). To obtain charge balance, several anions species can coordinate with the

positive calcium aluminate complex forming the AFm hydrate; some examples of the

anionic species and the respective of AFm phases that form in cement are aluminosilicate

[AlSi(OH)8]- forming stratlingite, sulfate (SO2 ) forming monosulfoaluminate,

hydroxyl-carbonate [(OH)(CO3)0.5 ]- forming hemicarboalumiante, and carbonate

(CO3 ) forming monocarboaluminate respectively (4,5,18,19). In this study, two binary

mix designs will be investigated: calcium aluminate cement mixed with limestone [CAC

+ LS] and calcium aluminate cement and anhydrous calcium sulfate [CAC + C$]. The

corresponding AFm phases associated with these additives are monosulfoaluminate and the hemicarboaluminate and monocarboaluminate phases, respectively. The reaction between limestone and CAC follows the following Equations 4 and 5. The difference between hemicarboaluminate and monocarboaluminate is dependent on the initial

carbonate content of the mixture. As the initial carbonate chemical concentration

increases [quantified via the ratio of CO3/(CO3 + 2OH ) in (4)], the prominent hydration

products changes from the hydroxyl-AFm phase to hemicarboaluminate and then

monocarboaluminate (4,20).

3CA + 0.5CaCO3 + 18H ^ C4A(CO3)0.5H12 + 2AH3 (4)

3CA + CaCO3 + 17H ^ C4A(CO3)H11 + 2AH3 (5)

The reaction [CAC+C$] initially forms ettringite with amorphous aluminum

hydroxide as shown in Equation 6. If the calcium sulfate is depleted and excess CA is

available, the ettringite is consumed to form monosulfoaluminate see Equation 7. The

thermodynamic stability of these AFm phases varies with temperature or the particular 242

anionic species but it is understood that the carbonate AFm phases are more

thermodynamically stable than the monosulfoaluminate phase followed by the metastable

hydroxyl-AFm (4).

3CA + 3C$ + 38H ^ C6 A$3 H32 + 2AH3 (6 )

6 CA + C6 A$3 H32 + 16H ^ 3C4 A$H12 + 4AH3 (7)

In addition to reducing the amount of metastable CAH10 or hydroxyl-AFm phases, the replacement of CAC with fine additives can prompt beneficial effects to the hydration

kinetics. In OPC systems, it is well-understood that fine additives can enhance the

reaction rates during the initial stages of the hydration reaction by prompting the

heterogeneous nucleation of the hydrates known as the filler effect (21-25). CAC

systems experience similar benefits as observed in the works of Puerta-Falla et al. and

Klaus et al. (10,26) in which increasing the total specific surface area of the paste

decreased the low heat rate period and increase the cumulative heat release of the system.

In contrast to OPC systems where limestone appears to be a more effective filler than

quartz (22,27,28), both carbonate and quartz fillers exhibit similar benefits to the

hydration kinetics of CAC (10). Likewise, the fineness of additives such as C$ in [C3A +

C$] systems can influence the rate of which the ettringite and monosulfoaluminate

reactions [Equations (6 ) and (7)] occur (29-31). The objective for this study is to

investigate the effects of replacing a commercial high a-AhO3 calcium aluminate cement with limestone or calcium sulfate and observe the change in the hydration kinetics due to these additives (or combination of any beneficial effects introduced with these mineral

additives) as well as utilizing both characterization methods and thermodynamic 243 simulations to gain insight on how these additives can affect the hydration kinetics, phase composition, and strength of the bulk material.

2. MATERIALS AND METHODS

Commercially available high alumina calcium aluminate cement CA-25 C

(Almatis, Rotterdam Netherlands) was used for this study. The cement composition was measured by X-ray fluorescence (XRF) with the result shown in Table 1. X-ray diffraction (XRD) was utilized and confirmed that the cementitious phases present were

C A , C A 2 , a n d C 1 2 A 7 along with corundum (i.e., a - AhO 3 ), a non-cementitious phase added for elevated temperature properties. Similarly, the limestone (CaCO3, LS) powders

and anhydrous calcium sulfate (CaSO 4 , C$) powders are commercially available from

Mississippi Lime Company (St. Louis, MO USA) and Alfa Asear (Tewksbury, M A

USA), respectively. The powders were used as received and no additional powder processing or grinding processes were utilized.

Table 1. Chemical composition by mass percent (%mass) of CA-25-C determined via XRF

O x id e A h O 3 C aO SiO2 M g O N a2O Fe2O3 %mass 8 1 .0 0 18.00 0 .1 7 6 0 .2 3 5 0.471 0 .1 1 8

The particle size distribution (PSD) of each of the solid particles were measured using a M icrotrac (York, PA USA) S3500 particle size analyzer. The volumetric distribution of each powder is shown in Figure 1. These powders were immersed in 244 isopropyl alcohol and subsequently ultra-sonically agitated to enhance dispersion of the mixture before measuring. The median particle sizes (d50, pm) of the CAC, C$, and LS were determined as 15.17 pm, 42.15 pm, and 9.99 pm, respectively. Using both the respective densities ( 3.29 g cm-3, 2.97 g cm-3, and 2.71 g cm-3 for CAC, C$, and LS, respectively) and PSDs of the powders, the specific surface area (SSA) for the powders were calculated as 3690 kg m-3, 4091 kg m-3 and 2370 kg m-3 for CAC, C$, and LS, respectively. These calculations assume the individual particles are smooth and solid (i.e., no exterior roughness nor internal porosity) (23,24). The SSA is slightly underestimated by a factor of *1.6 to *2.2 compared to Brunauer-Emmett-Teller (BET) method (32,33).

Figure 1. Particle size distribution of the calcium aluminate cement (CAC), calcium sulfate (C$), and limestone (LS). The d50 for those powders are 15.17pm, 9.99 pm, and 42.15 pm respectively

All the pastes were prepared by mixing the total solids with deionized-water (18.3

MQ) at a constant liquid-to-solid ratio (l/s) of 0.45. It should be noted that in the l/s ratio, 245 the “solid” is the summation of CAC plus additive (if the latter is present in that mix design). The replacement level was as follows by mass basis 0%, 9%, 17%, 20%, 25%,

33%, and 50%. The hydration kinetics of the CAC and binary CAC pastes were monitored for a 72-hour hydration period after mixing in an I-Cal 8000 (Calmetrix,

USA). The calorimeter is programmed to maintain a constant temperature at 25°C within the testing period. Finally, a series of strength measurements were conducted with an

Instron-5881 (Norwood, M A USA) with a 0.5 mm. mm-1 rate. Cubic samples 6 x 6 x 6 mm3 were cast in customized silicone molds and placed in a humid chamber at room temperature for three days. For the strength results, both the average strength and standard deviation for the pure CAC paste as well as 17%, 25%, and 50% for both [CAC

+ LS] and [CAC + C$] are reported herein.

The characterization of the pastes was conducted through differential thermogravimetric analysis (DTGA) and X-ray Diffraction (XRD) on pastes hydrated for

72 hours. Isopropyl alcohol (IPA) was used to arrest the hydration process via the solvent exchange method (34,35). For the DTGA, a Q600 SDT (TA Instruments, New Castle,

DE) instrument was used with temperature and mass sensitivity of 0.25°C and 0.1pg, respectively. The crushed CAC or binary CAC pastes were immersed in IPA for 24 hours before drying in an electric drying oven at 60°C for an hour. The DTGA apparatus was

heated starting at 25°C with a heating rate of 10°C per minute in A hO 3 crucibles up to a maximum temperature of 1000°C. The XRD for the binary CAC systems were prepared using sliced sections method as described (36), likewise a Panalytical X ’Pert PRO in continuous scan mode with fixed divergence slit size of 0.125° was utilized. A scan step size of 0.03°20 between the scanning range of 5.025°20 to 89.985 ° 2 6 was utilized with a 246

Kai wavelength = 1.54056 A. The X-ray tube was operated at a voltage of 45 kV and a current of 40 mA. The pure CAC paste was measured via Panalytical X ’PERT Pro M ulti

Purpose Diffractometer using the following measurement parameters: fixed divergence slit size of 0.38°, scan step 0.0262° and K ai wavelength = 1.540598A with the same voltage, tube current, and scanning range. Due to these differences, quantitative comparisons of the intensities will not be made between the pure CAC pastes and the binary CAC pastes.

Coupled with these experimental methods, a series of thermodynamic calculations were made to predict the composition of the paste microstructure. This was carried out utilizing the GEM-Selektor (Gibbs Energy M inimization Software for Geochemical

Modeling, version 3.4) in conjunction with Cemdata18 thermodynamic database (37-39).

The simulated CAC was represented in the form of simple oxides for the CAC precursor

(e.g., CaO, AEO 3 ) as determined through the XRF dataset utilized in Table 1. These simulated solids in addition to water were utilized as the input to calculate the product phases as the hydration reaction occurs. For the sake of simplicity, these simulations are conducted with a 1:1 water to total solid ratio so that the simulations can run until the

CAC has completely hydrated. This prevents inconsistencies where there is not enough water for the CAC or binary CAC pastes to completely react. 247

3. RESULTS

3.1. HYDRATION KINETICS OF LS + CAC AND C$ + CAC PASTES

Figure 2 shows the heat evolution calorimetry of the CAC as well as the binary

[LS + CAC] paste. The effect of the limestone additions does not appear to accelerate the heat flow rate at either the first or second hydration peak. These results are similar to the

study by Cook et al. (25) in which C 3 S was partially replaced with LS with a similar

reported PSD (J 50 reported was 43.35 pm). The benefits of coarse LS were not as high compared to the other finer filler additives within that same paper or other investigations

(10,22,24,25). Examining the first hydration peak via Figure 2B, any early acceleratory effects that could be attributed to heterogeneous nucleation before 10 hours is limited.

Likewise, the addition of LS does not appear to accelerate the formation of the second peak present at 10 hours, but some broadening is observed. W hile the heat flow rates between the different LS replacement levels are similar, the cumulative heat release increases as the replacement level increases. This will be examined more in-depth and compared to the [CAC + C$] calorimetry curves in the discussion of Figures 4 and 5. The effect of the heat flow rate with the varying C$ replacement level is shown in Figure 3.

Compared to the [CAC + LS] mixtures, the first peak exhibits a monotonic increase in the heat flow rate as well as a leftward shift as the C$ replacement level increases. This is

contrary in [C 3 A + C$] systems, where the [CAC + C$] pastes do not have a positive correlation between the C$ replacement level and the time to the ettringite peak (29

31,40). Although the exact mechanism in the [C 3A + C$] systems is hypothesized as some surface passivation mechanism (29,41-43), the effect does not appear to correlate 248 with the increasing C$ replacement levels herein with [CAC + C$]. There appears to be a rightward (i.e., delayed) shift in the second peak with the highest and lowest replacement level (50% and 9% respectively) but the remaining binary pastes experience a slight leftward shift at the second peak. At later times approaching ~ 20 hours, a third heat flow rate peak appears for some of the [CAC + C$] pastes (e.g., 17%, 20%, 25% and 33% replacement levels).

Figure 2. The calorimetry profiles of [CAC + LS] pastes with increasing percent of CAC replaced with LS. (A) Heat flow rate up to 72 hours with linear axis, (B) heat flow rate with logarithmic x-axis and (C) cumulative heat release of the [CAC + LS] p a ste s

A complimentary heat flow rate peak is not seen in the [CAC + LS] pastes. This calorimetry peak is likely associated with the formation of monosulfoaluminate as observed previously in the literature and the XRD results presented later in Figure 7 (29

31). The cumulative heats released for the [CAC + C$] pastes increase as the C$ content increases; however, it does not appear to simply be shifted upwards like the [CAC + LS] paste. Comparing the calorimetry curves of the binary pastes could elucidate the origins of these effects in the binary LS and CS systems. To quantitatively compare the CAC 249 pastes with the LS and C$ binary systems, certain calorimetric parameters were extracted from the calorimetry profiles and were plotted with respect to the additive replacement level. These parameters were the heat flow rate of both first and second heat flow rate peaks as well as the inverse time to those corresponding peaks. As shown in Figure 4A and Figure 4B focusing on the first peak, the addition of LS does not prompt an increase nor a decrease (except at 9% replacement) for the heat flow rate or the inverse time to peak.

Figure 3. The calorimetry profiles of [CAC + C$] pastes with increasing percent of CAC replaced with C$. (A) heat flow rate up to 72 hours with linear axis, (B) heat flow rate with logarithmic x-axis focus on the first peak and inset for peaks after 10 hours (C) cumulative heat release of the [CAC + C$] pastes

It is expected that the coarse LS powders limit any benefit via the filler effect; this is compounded with the intrinsic low solubility limiting any chemical reactivity

(9,10,44). On the other hand, the increase in C$ replacement level increases the heat flow rate and accelerates (i.e. prompts a leftward shift) the first heat flow rate curve reaching the first peak within first three hours. The fineness of the C$ particles as well as dissolution of C$ could be factors in the early enhancements of the calorimetry curve. 250

Both the high specific surface area and intrinsic solubility of C$ both favor the heterogenous nucleation and growth of ettringite which is known to occur very rapidly during the initial stages of hydration (29,30,45); however, calorimetry by itself cannot elucidate the degree of which one or the other is occurring. For the second peak, there is no positive or negative correlation as the replacement level increases. Although the 9% and 50% C$ replacement level do delay the second hydration peak it is not consistent as the replacement level increases. After the initial hydration peak, the beneficial effects provided by the C$ powder is limited. This can be attributed to the complete dissolution of the C$ or, in addition to dissolution, any removal of any reactive surface area previously available for dissolution and/or heterogenous nucleation by a passivation mechanism (e.g. protective barrier layer, heterogenous nucleation of hydrates onto

surface sites, or ionic complexes as seen in [C 3 A + C$] systems (29-31, 41).

In both binary systems, there was an increase in the cumulative heat release as the replacement levels increases. Although the effectiveness of the coarse limestone to accelerate CAC appears minimal in these systems, there is a monotonic increase in the cumulative heat release (i.e., the reactivity per gram of CAC) with the 50% LS replacement level releasing 334.6 J gCAC-1 whereas the [CAC + C$] paste released 373.2 J gCAC-1 after the 72 hour period. W hile hemicarboaluminate or monocarboaluminate hydrate species can form in the presence of LS in these conditions, LS dissolution in cementitious conditions can be described as kinetically limited with dissolution rates on the order of 10 nm hour-1 while in a 12 pH solution (44). Likewise, the work of Puerta-

Fall et al. (9) showed via thermal analysis that the residual amount of unreacted LS in a 251

CAC mixture with a 10% LS replacement level was -70% for 3 days and -60% for 7 days while about 50% LS remains after hydrating for 90 days.

Additive Replacement Level/%, Unitless Additive Replacement Level/%, Unitless (A) (B)

Additive Replacement Level/%, Unitless Additive Replacement Level/%, Unitless (C ) (D ) Figure 4. The peak heat flow rate and inverse time to the peak extracted from the calorimetry curves for CAC, [CAC + C$], and [CAC + LS] pastes. (A) and (B) are the peak heat flow rate and inverse time to peak for the first hydration peak whereas (C) and (D) are the same parameters but for the second hydration peak

Therefore, this increase in the cumulative heat release could not be wholly attributed to increased effectiveness in LS to heterogeneously nucleate hydrates nor LS readily participating in the hydration reaction. But as the LS content increases, a greater fraction of LS will replace CAC allowing a greater amount of water available to react with the residual anhydrous CAC powder and subsequently incorporate into the 252 hydroxyl-AFm phases as well as some carbonate-based AFm hydrates. W hile increasing th e l/s in OPC systems has little effect on the hydration kinetics during the early stages of hydration (46,47), there is evidence that increasing the l/s ratio in pure CAC systems as

w e ll as [C 3 A + C $ H 2 ] systems increases heat flow rate (30,31,48). Figure 5 presents the calorimetry curves of pure CAC pastes with increasing water content and comparable results as seen in the literature are obtained where the calorimetry profile is slightly enhanced with increasing l/s.This manifests in a slight leftward shift in both hydration peaks as well as an increase in the cumulative heat release as the l/s increases in the pure

CAC paste. Therefore, increasing the LS or C$ replacement level in the binary paste consequently increases the effective water to cement (w/c*) ratio (i.e., the amount of

CAC cement decreases as replacement level increases even though the amount of water remains the same resulting in the phenomena described as the dilution effect (49,50)). It can be surmised that the enhancements seen in the [CAC + LS] pastes and [CAC + C$] pastes calorimetry can be attributed to a combination of chemical and physical factors of the additives as well as the dilution effect. To gain an understanding of degree of hydration of the pastes, calorimetry was conducted on pure CAC paste with a 0.45 l/s fo r a duration of 10 days. After the 10 days, the cumulative heat release was 242.481 J g-1CAC which was used to quantify the degree of hydration (a, the fraction of CAC reacted). For the pure CAC pastes with varying l/s , the values of a increase from 0.861, 0.998, 0.996, and 1.000 for 0.45, 0.60, 0.75, and 0.90, respectively. 253

This process was used previously for mixtures of C 3 S and pozzolanic additives for a 24-hour hydration period (23,24). However, the longer time periods as well as the addition of LS and C$ prompts a much greater cumulative heat release than the pure

CAC paste observed previously. Therefore, instead of using the cumulative heat release of the pure CAC paste, the cumulative heats released of the binary pastes were extrapolated to 10 days to determine a. The calculated values of a for the C$ and LS binary pastes are presented in Table 2 below. Compared to the pure CAC paste, the value of a changes depending on the additive in the binary system. The addition of coarse limestone slightly lowers a compared to the neat CAC paste. Conversely, after three days the [CAC + C$] pastes exhibit almost near completion indicating acceleration in the hydration kinetics compared to the neat CAC. Coupling these calculated values of a and the GEMS simulations, the phase composition present in microstructure at three days can be estimate as a function of a as presented in Figure 6 For the sake of simplicity and for direct comparison to the later experiments, the pure CAC paste as well as the 17%, the

25%, and, the 50% replacement levels for both the [CAC + LS] and [CAC + C$] systems 254 are shown. The formation of hydrotalcite forms due to the small amount of magnesia

present in the CAC whereas the other constituent oxides (e.g., Fe 2 O 3 o r S iO 2 ) are assumed to substitute in the AFm phases or hydrogarnet phases.

Table 2. The degree of hydration (a) of the binary pastes for the different [CAC + LS] and [CAC + C$] pastes after hydrating for 72 hours Replacement Level of Degree of Reaction (a) Additive (%) [CAC + LS] Pastes [CAC + C$] Pastes 9% 0.825 0 .9 9 0 17% 0 .7 9 9 0 .9 5 5 2 0 % 0 .7 9 7 0 .9 2 6 2 5 % 0.813 0.983 3 3 % 0.823 0 .9 5 6 50 % 0 .8 3 2 0 .9 5 2

This can be attributed to how the software calculates the steps before the reaction is completed. Each step of the hydration reaction in GEMS is based on a series of

equilibrium steps before reaching an a = 1.0. W hile C 3 A H does not form outright from

CA at 20°C, the C 2 A H an d C A H 10 will eventually convert into C 3 A H obtaining equilibrium. For the binary pastes, the difference in a between the [CAC + LS] and [CAC

+ C$] pastes become apparent due to the difference in dissolution rates of LS and C$. As shown in FigureB - 6D, LS is calculated to remain in the microstructure throughout the duration of the CAC hydration whereas for the [CAC + C$] pastes, the C$ is calculated to completely dissolve except at the 50% replacement level. Examining the [CAC + LS]

pastes, the GEMS simulations predict a reduction of AH 3 due to the reduction in CAC.

The simulation does not predict any of the hydroxyl-AFm or CAH 10 coexisting with the monocarboaluminate phase which is contradicting experimental observations herein in 255

Figure 7 or from the literature (9,10). This can be attributed to the limited solubility of the

LS and how this insolubility kinetically limits the amount of monocarboaluminate present in the microstructure (9).

Degree of Hydration of CACla, Unitless (A)

50% CAC + 50% LS - 3-Day a = 0.832 ->• 120- Pore Solution

80-

Hydrotalclte

CAC Degree of Hydration/a, Unitless CAC Degree of Hydration/a, Unitless CAC Degree of Hydration/a Unitless (B) (C) (D)

Degree of Hydration of CAC/o, Unitless Degree of Hydration of CAC la , Unitless Degree of Hydration of CAC la , Unitless (E) (F) (G) Figure 6. A series of GEMs simulations for the (A) pure CAC paste, (B) - (D) 17%, 25% and 50% LS replacement levels as well as (E) - (G) 17%, 25%, and 50% C$ replacement with excess water (1:1 total solid to liquid mass ratio) 256

Although these calcium aluminate hydrates are permitted to form in the simulation, the addition of LS prevents the formation of these phases due in part to the formation of monocarboaluminate hydrate would reduce Gibb’s free energy of the system more so than the metastable phases and therefore prevent the latter from forming. The microstructure of the [CAC + C$] paste is expected to be comparable to expansive calcium sulfoaluminate cements in which ettringite and aluminum hydroxide are considered the main hydration products (51). These results are replicated in the thermodynamic simulations showing these hydrates being the most prominent in the

GEMS simulations as well as monosulfoaluminate phase being present in the 17% and

25% C$ replacement level. The presence of monosulfoaluminate for the 17% and 25% replacement levels collaborates the third peak seen in the inset of Figure 3B. Similarly, within that inset of 3B, the magnitude of the third peak is greater for the 17% than the

25% which indicates increased growth of monosulfoaluminate in the microstructure.

The XRD patterns show that the phase composition of the paste is not as consolidated as the GEMS simulations calculated previously in for both singular and binary pastes. The only calcium aluminate hydrate phase detected in the pure CAC pastes

w a s C A H 10 in addition to residual CA and CA 2 that remained unreacted. The slight carbonation of the sample lead to the formation of hemicarboaluminate (C4A(CO3)0.5H12)

and monosulfoaluminate perhaps transforming any C 2 AH 8 that would have formed due to the greater thermodynamic stability of the carbonate phases. M oreover, there are some

weak diffraction peaks corresponding to AH 3 (particularly at lower diffraction angles

18.28° and 20.30°) but this could be due to the amorphous nature of the phase. As the limestone content increases (as shown with the increase in intensity and sharpening of the 257 diffraction peak at 29.408°) the hemicarboaluminate diffraction peak disappears while the monocarboaluminate peak intensity increases albeit the number of counts does not increase by large degree. The hydration products present in the [CAC + C$] pastes are like the GEM S simulations and between three different C$ replacement levels with

ettringite (C 6A $ 3H 3 2 ) and monosulfoaluminate (C4A$H12) and AH 3 phases. For the

monosulfoaluminate, the 11 molar H 2 O species was detected in all three replacement levels albeit with a low intensity count.

[C A C + L S ]

CAC + Additive 72 Hours of Hydration — 0% (A) 17% — 25% 50%

[C A C + C $] Mineral Species • CA > CA2 + a-AI20 3 + CAH10 - * C2AH8 (B) — a h 3 + c$ * C6A$3H32 ♦ c 4a $h 12 • LS a C.AfCOJH,, ▼ C4A(CO3)05H12

Figure 7. XRD patterns of (A) [CAC + LS] and (B) [CAC + C$] paste after 72 hours of hydration. The diffraction patterns are ordered so that the bottom is the pure CAC paste while the higher diffractograms are of higher replacement level 258

The 14 molar H 2 O monosulfoaluminate hydrate (PDF# 00-042-0062) was not detected in the diffractograms of the [CAC + C$] paste. However, all three replacement levels for [CAC + C$] pastes contain XRD peaks corresponding to C$. This indicates that the complete dissolution of C$ does not occur and therefore, a different mechanism instead of the depletion of C$ is responsible for the C$ not affecting the second hydration peak. M oreover, none of the diffraction peaks associated with the calcium aluminate hydrates are detected in the [CAC + C$] pastes which can be attributed to the presence of

SO 42- ions facilitating the formation of ettringite and/or monosulfoaluminate rather than

the metastable CAH 10 o r C 2 AH 8 phases. This is similar to previous observations by Son et al. where they replaced CAC with 8% C$ (for a CAC mortar) limited the formation of

CAH 10 (13). For additional examination, the XRD results are be cross-examined with the

DTGA results in Figure 8. Starting with the DTGA scan corresponding to the pure CAC paste, the paste exhibits mass losses near 120 °C and later near ~280°C. These are

characteristic temperatures of the dehydroxylation of CAH 10 a n d A H 3 according to

Scrivener et al. (52) which collaborates the XRD results presented previously in Figure 7.

Conversely, the [CAC + LS] pastes prompt a peak before 200°C as well as a second peak between 200°C - 320°C. The 17% LS replacement exhibits a slightly increase in mass loss rate at ~ 280°C compared to the other LS replacement levels. The dehydroxylation of monocarboaluminate occurs via two steps. First, the chemically bound water within the interlayer becomes liberated at temperatures before 200°C. Afterwards, the remaining chemically bound water is released between 200°C - 300°C. Since the mass loss rate of the first interlayer water from the monocarboaluminate species appears similar, the remaining mass loss rate at the second stage would be attributed to the 259

monocarboaluminate and the AH 3 present. As expected, the decomposition rate of LS increased between 600°C - 800°C as the LS replacement level increases, showing that a significant amount of LS remains after three days hydrating. Conversely, the [CAC + C$] pastes exhibit a sharp mass loss rate at ~ 100°C with similar mass loss rates at 200°C -

300°C as the neat CAC paste. The first mass loss peak is the dehydroxylation of the water molecules from the ettringite structure and since ettringite can contain 26 moles of

chemically bounded H 2 O per molecule, this contributes to a high mass loss rate (52).

0 200 400 600 800 1000 0 200 400 600 800 1000 Temperature/°C Temperature/°C (A ) (B ) Figure 8. DTGA scans of (A) [CAC + LS] pastes and (B) [CAC + C$] pastes from 0°C - 1000°C for 0%, 17%, 25%, and 50% replacement level respectively

After the dehydroxylation of ettringite, the remaining water bounded to the aluminum hydroxide is removed between 200°C - 300°C which reflects similar DTGA signal as the pure CAC pastes. The 25% C$ paste exhibited the highest mass loss rate during the first stage but for the second decomposition stage, it was the 17% replacement level which exhibited the lowest dehydroxylation rate at ~ 100°C but conversely higher 260

DTGA signal associated with AH 3 . However, all three of the [CAC + C$] pastes exhibited a lower DTGA signal than the pure CAC paste. W hile the XRD results showed that monosulfoaluminate is present in the microstructure of the [CAC + C$] pastes, the amount appears to be overshadowed by the mass loss rates corresponding to the other hydrates. W hile the higher C$ replacement levels prompt acceleration for the first hydration peak (see Figure 4), it does not lead to an increase in the amount of ettringite at

72 h o u rs.

Additive Replacement Level/%, Unitless Figure 9. The strength of the 6mm side length cubic samples with the standard deviation shown as error bars

Rather, there is residual C$ remaining in the microstructure after 72 hours as seen in the XRD results which could provide energetically favorable nucleation sites for ettringite accelerating the hydration kinetics initially, but later for the second hydration peak is minimized. The compression strength results for the CAC pastes is presented in

Figure 9 The [CAC + LS] pastes exhibit a decrease in strength compared to the pure CAC 261 paste with an average strength ranging from 12 M Pa to 15 M Pa compared to the 27.45

M Pa ± 3.001 M Pa of the pure CAC paste. In contrast, the strength of the [CAC + C$] pastes exhibit higher strengths than the [CAC + LS] counterparts. Although the 25% C$ and 50% C$ replacement levels prompt a greater amount of ettringite as depicted in

DTGA, it does not appear that increasing the amount of ettringite correlates with strength gain. In fact, the paste containing 17% C$ replacement level exhibits the greatest compressive strength with 37.00 M Pa ± 6.725 M Pa (while having less ettringite than

25% C$ and 50% C$ replacement levels) is the only paste to exhibit strength increase compared to the pure CAC paste. It should be noted that CA-25 C is a high a-AhO3 cement for high-temperature applications and is has compressive strengths x10 higher than conventional concrete as catalogued in Appendix C of Ashby (53). Therefore, the reduction in the amount of a-AhO3 by replacing the CAC with LS or C$ (both of which exhibit much lower Mohs hardness levels than a-AhO3; 3 and 3.5 compared to 9 respectively) will reduce the strength of the bulk material.

4. CONCLUSIONS

Replacing high a-A hO 3 calcium aluminate cement (CAC) with limestone or calcium sulfate greatly changed the hydration kinetics of the CAC paste. The limestone exhibited limited benefits to the hydration kinetics of the CAC system in part to coarseness of the powder. For the two hydration peaks, there was no positive nor negative correlation in the peak heat flow rate or the time to that peak as the limestone replacement level increased. The coarse particle size distribution prevented enhanced 262 heterogenous nucleation and growth (i.e. filler effect) due to the limited reactive surface area as well as the intrinsic insolubility kinetically limits the formation of monocarboaluminate phases. Conversely, the cumulative heat release increased as the limestone content increased; however this was not due to any enhance reactivity provided by the limestone rather the increase in the amount of water available to reactive with

CAC via the dilution effect. The GEMS simulations overestimated the effect that LS had on the phase composition predicting monocarboaluminate would destabilize the

formation of metastable CAH 10 o r C 2 AH 8 whereas the phase composition was shown via

XRD and DTGA to contain a mixture of metastable calcium aluminate hydrate hydrates and the monocarboaluminate hydrate.

In comparison, the increase in the C$ replacement levels accelerated the early hydration CAC kinetics (i.e. the first hydration peak). There are several compounding effects provided by C$ that could accelerate the hydration kinetics of CAC such as the heat generated by dissolution of C$ or the heterogenous nucleation of ettringite on the C$ surface. But the results herein provide evidence that C$ acts as an effective material for the heterogenous nucleation of ettringite and appears to be the dominating mechanism for the first hydration peak. If the acceleration was due to the dissolution of C$, then it would be expected that more ettringite would form due to increase in sulfate ions present in the microstructure. This is not the case however, because the 25% C$ replacement level formed more ettringite than the [CAC + C$] paste with 50% C$ replacement level.

Additionally, the 17%, 25% and 50% replacement level exhibited evidence that C$ remained in the microstructure after the 72-hour hydration period in contrast to the thermodynamic simulations. The replacement level of C$ does not strongly influence the 263 peak heat flow rate or the time to the second hydration peak although C$ is present in the microstructure. W hile the exact mechanism for C$ not affecting the second hydration peak is not clear and additional investigations can elucidate this, the presence of C$ after the 72 hour hydration period indicates that any acceleratory benefits provided by C$ earlier in the hydration reaction is reduced and/or removed. Both sets of binary pastes exhibited higher cumulative heat released, but this did not result in benefits in the strength of the bulk material. Only the 17% C$ replacement level exhibited a positive effect on the compressive strength whereas the remaining binary pastes exhibited compressive strengths less than the pure CAC pastes. W hile ettringite exhibits cementing properties, as seen in calcium sulfoaluminate systems, the increase in ettringite did not translate in an increase in compressive strength of the sample. It is expected that the amount of hydrates nor residual unreacted LS or C$ cannot compensate for the decrease in strength by reducing the a-AhO3 content present in the CAC.

ACKNOWLEDGMENTS

Funding for this study was provided by the National Science Foundation (CMMI:

1661609 and CMMI: 1932690). Experiments were conducted at the M aterials Research

Center and the Center for Infrastructure Engineering Studies at M issouri S&T. 264

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SECTION

3. CONCLUSIONS AND RECOMMENDATIONS

3.1. CONCLUSIONS

There are several conclusions that can be drawn from the work presented in the manuscript.

First, the first paper shows that both silica fume and metakaolin are effective mineral additives for tricalcium silicate (C3 S) and enhance the hydration reaction within the first 24 hours. The hydration kinetics of C3 S are enhanced (i.e., higher cumulative heats which corresponds to greater reactivity) as the proportion of silica fume increases in the [C3 S + SF] binary paste. Silica fume due to its small particle size (dso = 0.23 pm) increases the total surface area available for C-S-H to heterogeneously nucleate and grow. However, the boon provided by the small particle size favors agglomeration. At higher replacement levels, up to 97% of the silica fume surface area is unavailable limiting dissolution as well as heterogeneous nucleation. Although this results in a greater cumulative heat, these enhancements are not efficient. Likewise, the pozzolanic activity of silica fume is negligible within the first 24 hours of hydration. While metakaolin exhibits a larger particle size than silica fume, metakaolin is a more effective filler (i.e., nucleating agent of C-S-H) at lower replacement levels (i.e., <10% by mass) by utilizing a greater fraction of the surface area than silica fume as well as increasing the amount of product nuclei (Anuc; no. C-S-H nuclei per gram of C3 S) compared to silica fume. When the metakaolin content increases above this threshold, the effectiveness of metakaolin 270 decreases not due agglomeration but because of the ingress of Al(OH)4 ions into solution from metakaolin. The Al(OH)4 ions inhibit the nucleation and growth of C -S -

H by absorbing onto the nucleating surfaces. Additionally, M K exhibits superior pozzolan activity than SF but it remains limited within the first 24 hours. In the follow-up study (denoted as Paper III), it was shown that in contrast to other mineral additives (e.g.,

quartz and limestone), metakaolin does not benefit the hydration kinetics of C 3 S in a linear and monotonic manner. In other words, just because the particle size distribution of metakaolin decreases (or conversely the specific surface area increases) does not correlate with benefits to the hydration kinetics as observed in typical additives. As the replacement level increased the delay effect due to aluminate species became more apparent. It was the intermediate particle size distribution that exhibited the most severe delay followed by the fine particle size distribution with the coarse powders being the least affected. Rather in a counterintuitive manner, the coarse metakaolin was optimal for

C 3 S hydration because the coarse powders limit dissolution sites available for the

A l(O H )4 ions to ingress into solution and/or nucleation surfaces but consequently has less specific surface area available to nucleate C -S-H . Conversely, the fine particle size facilitated nucleation and growth but also ingress of Al(OH)4 ions and the intermediate particle size having the worst of both situations with limiting nucleation and growth but high dissolution facilitating Al(OH)4 ions suppressing the hydration reaction.

In the second paper, the focus was elucidating the role of the water to cement ratio

(w /c ) during the hydration of cement and the contradiction between experimental data

(i.e., isothermal microcalorimetry) and traditional phase boundary nucleation and growth

(pBNG) model. In isothermal microcalorimetry, as long as there is sufficient amount of 271 w a te r (w /c > 0 .4 2 ), the hydration kinetics are insensitive to changes in the w /c . This is not replicated in traditional pBNG models because the model assumes the particles remain static and consequentially the greater amount of water is assumed to increase the interparticle distance between cementitious particles. Therefore, the classical model predicts that more time is required for the reaction to complete as the product phase impinges its nearest neighbor. A new modified pBNG model was proposed that made some new assumptions to rectify these aforementioned issues in present within the classical pBNG model. The innovation proposed was to define a varying reaction vessel and assuming the cementitious particle experience sedimentation. The reaction vessel can be thought of as the fraction of the paste (i.e., water + cement) that is participating in the hydration reaction. At early stages of the hydration reaction, for low and high w /c systems, the hydration reaction is highly localized near the cementitious particles. But as the cementitious particles begin to sink, the interparticle distance between cementitious particles begin to reach equivalent value regardless of w /c . Because of this the volume available for hydrates to nucleate and grow becomes limited resulting in impingement of nearby hydrates. W hile the hydrates are physically confined, the ions present in the solution can equilibrate throughout the pore solution. For a system with a large w /c th e ions will ingress throughout the supernatant reducing the supersaturation of C -S-H to decrease (less ions are locally available) limiting growth.

W ith the fourth paper, a novel combination of random forest (RF) and firefly algorithm (FFA) models (i.e., RF-FFA) is investigated utilizing two real-world datasets

(one containing over 1000 data entries and the other contains 76) composed of several notable input variables such as varying amounts of supplemental cementitious material, 272

different proportions of superplasticizer, and hydration age, with the output variable

being the compressive strength. When compared to other machine learning models:

multilayer perceptron artificial neural network (MLP-ANN), support vector machine

(SVM), M5 Prime model tree algorithm (M5P) and traditional random, the hybrid RF-

FFA model exhibited high degree of prediction accuracy in both datasets. The prediction

performance was evaluated utilizing statistical parameters: R, R2, MAE (MPa), MAPE,

RMSE (MPa), and CPI showing promise for prompt and dependable prediction of

composition-dependent properties of concrete. These models can be further expanded and

enhanced with additional influential input variables such as particle size distribution,

cement composition, or age can benefit the prediction performance. Utilizing these

prediction models, contractors and engineers create tailored mix-designs based on locally

available aggregates, materials, and SCMs to predict compressive strengths or other

physical parameters.

The fifth paper shows that hydrating [C3A + C$] with solutions comprised of

isopropyl alcohol (IPA) and water can reduce the water activity of the solution.

Decreasing the water activity of the liquid solution suppresses the highly energetic

reaction until a critical water activity (aH) is reach, completely arresting and preventing

any hydrates (in this case, ettringite, monosulfoaluminate, or calcium aluminate hydrates)

from precipitating. This value calculated via thermodynamic framework as of 0.45

(corresponding to a water-IPA solution comprised of 87.1 %mass IPA) and later

investigated with experimental methods such as isothermal microcalorimetry, differential thermogravimetric analysis, and X-ray diffraction. For X-ray diffraction, this threshold was replicated in two different suspensions: a liquid to solid ratio of 2 and of 100. Even 273 in the extremely diluted suspension, no hydrates precipitated even though the suspension with a liquid to solid ratio of 100 had excess water available. Additionally, the solubility product of C 3A (K c3a) was calculated to be 10-2065 utilizing the same thermodynamic approach to determine the critical an . This appears to be the first published estimate of

K c3a and is invaluable in the development and validation of hydration models and cementitious systems. Although C 3A can continue to hydrate at a lower water activity th a n C 3 S (for reference the critical a H fo r C 3 S is 0.70), it is important for high- performance concretes that have w /c less than 0.42 are properly cured to ensure that the hydration reaction continues throughout the prescribed period of time at normal reaction rates ensuring adequate strength and other physical properties.

Finally, the last manuscript investigates the hydration kinetics of high a-A hO 3 calcium aluminate cements replaced with limestone or calcium sulfate. The limestone exhibited limited benefits to the hydration kinetics of the CAC system in part to the coarseness of the powder. The addition of limestone does not correlate with an increase or decrease in the heat flow rate or the time to either hydration peak. Thermodynamic simulations overestimated the effect of LS had on the phase composition compared to the

X-ray diffraction and differential thermogravimetric analysis. In the experimental results, a mixture of calcium aluminate hydrates and monocarboaluminate hydrates were observed instead of the presence of monocarboaluminate in the thermodynamic simulations. In comparison, the increase in the C$ replacement levels accelerated the early hydration as the replacement level increased due to being an effective material for the heterogenous nucleation of ettringite. W hile this could be attributed to increase dissolution as shown in the thermodynamic simulations, the X-ray diffraction and 274 thermogravimetric analysis showed that C$ remained in the microstructure after the 72 hours as well as similar amounts of ettringite between the different pastes. Only the 17%

C$ replacement level exhibited a positive effect on the compressive strength whereas the remaining binary pastes exhibited compressive strengths less than the pure CAC pastes.

W hile ettringite exhibits cementing properties, as seen in calcium sulfoaluminate systems, the increase in ettringite did not translate in an increase in compressive strength of the sample. Overall, there are demonstrable advances in knowledge in the field of cement hydration and the thermodynamics of the hydration reaction.

3.2. FUTURE WORK

There are several intriguing pathways to further the diverse research present in this dissertation. The calorimetry database establishes a foundation for future machine learning applications and additional input/output data. The rationale for the current mix design is a “bottom-up” approach taking controlled mixtures of pure phases and additives. The mix designs currently present in the database do not incorporate any chemical admixtures such as water-reducers, retarders, accelerators, superplasticizers or air-entrainment agents. All these admixtures are prevalent in the current state of practice; therefore, building database that accurately emulates commercial cements systems while accurately controlling mineral and/or chemical compositions would be invaluable. It is understood that there are some interactions between chemical admixtures and chemical

species, notably C 3A, ettringite, and sulfate species which can limit the effectiveness of the (often expensive) admixtures. Likewise, the database can be expanded into different 275 supplemental cementitious materials or pozzolans such as fly ash, blast furnace slag, impure clays, etc.

Conversely, there are opportunities to expand studies separate from the machine learning database. There are exciting opportunities with the M aterials Research Center here at M issouri S&T since the center is in the process of acquiring new equipment notably an environmental scanning electron microscope (ESEM) and X-ray tomography instruments. The ESEM facilitates the observation of different hydrate phases in less harsh vacuum conditions than the typical SEM counterparts. In the [C3A + C$] water activity study presented in Paper V, critical water activity was determined via thermodynamic calculations to be 0.45. W ith the advent of ESEM in combination with

the knowledge of the calculated water activity limit for [C3A + C$] as well as for C 3 S

(98,99), different characteristics or traits (e.g., growth rate, nucleation density, morphology, critical nuclei size) can be measured with varying water activity.

Likewise, X-ray tomography is a powerful tool that allows for the in-situ observation of cement hydration and the temporal evolution of certain features of the cementitious paste. For example, the 3D pore size distribution and degree of hydration of cementitious phases can be observed in real time. Combining these results with other continuous measurements such as isothermal calorimetry or X-ray diffraction can provide insight on early hydration behavior of pure pastes and mixtures and consequentially these results can be implemented into an already established machine learning database. APPENDIX A.

METHODOLOGY AND POWDER PARTICLE SIZE DISTRIBUTIONS FOR

MACHINE LEARNING STUDY 277

1. SYNTHETIC CEMENT COMPOSITION, POWDER CHARACTERIZATION AND MIXING PROCEDURE

M ost of the powders utilized in this study were obtained from commercial

suppliers except for the C 3 S which was synthesized at Missouri S&T. The details regarding the synthesis is located in Paper I (1). To obtain two different particle size distribution of limestone, the as-received powder (denoted as coarse limestone or C-LS here) ground utilizing wet ball milled method with half inch cylindrical alumina milling media for about 48 hours. The particle size distribution (PSD) of the constituent powders were measured utilizing a static light scattering particle size analyzer (M icrotrac S3500).

A sample of the powders were immersed in isopropyl alcohol and the suspension was subsequently ultrasonically agitated to prevent agglomeration during measurement. The cumulative particle size distribution for each powder is presented in Figure 1A.

Figure A1. Cumulative particle size distribution for the materials that constitute the

cementitious phases (C 3 S, C 3A , a n d C $ H 2) and the mineral additives (MK, C-LS, and F-LS) 278

The summary of the particle size and the specific surface area is included in Table

A1. The specific surface areas (SSA) were calculated from the PSDS based on the assumption that the particles have a spherical morphology while having limited surface roughness and internal porosity. This SSAs calculated via this method area expected to be smaller than values experimentally measured from the Brunauer-Emmett-Teller (BET) method by ~ 1.6-to-2.2. (2-3)

Table A1. Particle size and surface area characteristics for the clinker powders and a d d itiv e s P o w d er 10th Percentile, Median Particle 90th Percentile, Specific Surface S p ecies (d ^) size, (d5tf) (d w) Area (m2 kg-1) C 3 S 1.315 5.850 72.47 5760

C 3A 2.961 6.534 17.20 3550

C $ H 2 5.680 21.91 53.46 1360 MK 2.175 4.520 9.270 5940 Coarse - LS 3.488 34.03 113.0 2380 Fine - L S 0.466 1.476 4.330 20800

All the pastes were prepared by mixing the solids with DI-W ater (MQ 18.3) with a constant liquid-to-solid ratio (l/s ) of 0.45 by mass basis for all the synthetic cements.

The influence of clinker compositions (e.g., C 3 S, C 3A , a n d C $ H 2) to form seven different synthetic cements for the testing dataset. These cements were formulated with varying

C 3A to C $ H 2 ratios to emulate different sulfate levels that could occur in an OPC system.

The mix design for these cements and the C 3A / C 3 S a n d C 3A / C $ H 2 ratios are included in T a b le A 2. In addition, the influence partially replacing these synthetic cements with proportions of fine metakaolin as well as coarse limestone and fine limestone was investigated. The replacement levels varied 10%, 20%, 30%, 40%, 50%, and 60% for binary systems (e.g., Cement 1 + 20% MK). For ternary mixtures, the cement was 279 replaced by a 1:1 ratio mixture of LS and M K or a 1:2 ratio mixture of LS and M K up to

60% for both LS particle size distributions. An example of the mix design used for the

Cement #1 replaced with metakaolin and Cement #1 replaced with a mixture of metakaolin and coarse limestone see Table A3.

Table A2. The mix design of the eight synthetic cements used herein as well as the C 3A

/ C 3 S a n d C 3A / C $ H 2 ratios. Cements 1 - 7 are utilized for training dataset whereas ______c e m e n t 8 is a sa m p le fo r te stin g ______

C e m e n t C 3 S C 3A C $ H 2 C 3A / C $ H 2 N o . (% M a s s ) (% M a s s ) (% M a s s ) (U nitless by m ass) 1 90 4 6 1.50 2 92 4 4 1.00 3 88 8 4 0 .5 0 4 80 8 12 1.50 5 70 12 18 1.50 6 82 12 6 0 .5 0 7 100 0 0 1.50

The liquid-to-solid ratio by mass basis (l/s ) for the pastes was kept constant at

0.45. The corresponding water-to-cement ratio by mass basis (w /c ) for these replacement levels are 0.450, 0.500, 0.563, 0.643, 0.750, 0.900, 1.125 for 0% to 60% replacement levels, respectively. Each mix design was given a number designation corresponding to the mix design (i.e., cement number, replacement additive, and replacement level).

The heat flow rate and cumulative heat release of the synthetic cements were utilizing a TAM IV (TA Instruments, New Castle DE) isothermal conduction microcalorimeter for a 24-hour hydration period. The microcalorimeter was programmed to maintain the sample chamber at a constant temperature of 20 ± 0.1°C. For each calorimetry run, five mix designs were selected randomly according to the experimental 280 number. Likewise, each specimen was randomly assigned to one of the five calorimetry channels and consequently the starting order of inserting the specimen was randomized as well. All the pastes were mixed outside the calorimeter inside the 4 mL glass ampoule before placing the sample into the channel. Due to the nature of the device, there is a 15- minute waiting period for the channel to acclimate to the heat generated by introducing the specimen into the calorimetry chamber.

Table A3. Example mix design of binary and ternary mixtures for Cement #1. The ternary mix design uses a 1:1 ratio between the MK:C-LS as well as a 2:1 MK:C-LS ra tio T o t a l T o t a l C 3 S C 3A C $ H 2 MK C-LS C e m e n t # 1 A d d i t i v e (% M a s s ) (% M a s s ) (% M a s s ) (% M a s s ) (% M a s s ) (% M a s s ) (% M a s s ) 8 1 3 .6 5 .4 9 0 1 0 0 1 0 7 2 3 .2 4 .8 8 0 2 0 0 2 0 6 3 2 .8 4 .2 7 0 3 0 0 3 0 5 4 2 .4 3 .6 6 0 4 0 0 4 0 4 5 2 3 .0 5 0 5 0 0 5 0 3 6 1 .6 2 .4 4 0 6 0 0 6 0

7 2 3 .2 4 .8 8 0 1 0 1 0 2 0 6 3 2 .8 4 .2 7 0 15 15 3 0 5 4 2 .4 3 .6 6 0 2 0 2 0 4 0 4 5 2 .0 3 .0 5 0 2 5 2 5 5 0 3 6 1 .6 2 .4 4 0 3 0 3 0 6 0 6 3 2 .8 4 .2 7 0 2 0 1 0 3 0 3 6 1 .6 2 .4 4 0 4 0 2 0 6 0 281

2. PRELIMINARY CALORIMETRY OF METAKAOLIN - LIMESTONE CEMENTS

The calorimetry profiles of the synthetic cements mixed with metakaolin fine or coarse limestone. For the sake of brevity, the binary calorimetry profiles are omitted.

Cement #1 MK + C-LS 0% — 10%- 10% — 15%-15% — 20%- 20% 25%-25% 30%-30% ----- 20%- 10% 40%-20%

I 1 1 I 1 1 I 1 1 I 1 1 I 1 1 I 1 1 I 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Time (Hour) Time (Hour) (A) (B) ...... Cement #1 MK + F-LS — 0% — 10%-10% — 15%- 15% — 20%- 20% 25%-25% 30%-30% ----- 20%- 10% 40%-20%

I 1 1 I 1 1 I 1 1 I 1 1 I 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Time (Hour) Time (Hour) (C ) (D ) Figure A2. (A) Heat flow rate (B) Cumulative heat release of Cement #1 mixed with coarse limestone and metakaolin and (C) Heat flow rate (D) Cumulative heat release of Cement #1 mixed with fine limestone and metakaolin s lmesone and akaoln and C)Heatfow ae ( Cumul i heatr eas of o se a le re t a e h e tiv la u m u C ) (D rate w flo t a e H ) (C d n a lin o a k ta e m d n a e n sto e lim rse a o c F ig u re A 3. (A ) H e a t flo w ra te (B ) C u m u la tiv e h e a t re le a se o f C e m e n t t n e m e C f o se a le re t a e h e tiv la u m u C ) (B te ra w flo t a e H ) (A 3. A re u ig F Heat Flow Rate (mW. gCem'1) Heat Flow Rate (mW. gCam'1) i ■ ■ i Cement #2 mixed with fine limestone and metakaolin and limestone fine with mixed #2 Cement Time (Hour) Time (Hour) Time 1 1 1 2 24 21 18 15 12 9 A) (A C) D) (D ) (C — 20%-i 20%-i 0%: — — 20%-20%: 15%-15%: — 10%-10%C — Cement #2 Cement MK + C-LS + MK 40%-20%: 30%-30%: 25%-25%: 0 %

3 9 2 5 8 1 24 21 18 15 12 9 6 3 0 3 9 2 5 8 1 24 21 18 15 12 9 6 3 0 Time (Hour) Time Time (Hour) Time B) (B 2 # xed t ith w d e ix m 282 s lmesone and akaoln and C)Heatfow ae ( Cumul i heatr eas of o se a le re t a e h e tiv la u m u C ) (D rate w flo t a e H ) (C d n a lin o a k ta e m d n a e n sto e lim rse a o c F ig u re A 4. (A ) H e a t flo w ra te (B ) C u m u la tiv e h e a t re le a se o f C e m e n t t n e m e C f o se a le re t a e h e tiv la u m u C ) (B te ra w flo t a e H ) (A 4. A re u ig F Heat Flow Rate (mW. gCem'1) Heat Flow Rate (mW. gCem'1) Cement #3 mixed with fine limestone and metakaolin and limestone fine with mixed #3 Cement Time (Hour) Time (Hour) Time 1 1 1 2 24 21 18 15 12 9 A) (A C) (C 3 9 2 5 8 1 24 21 18 15 12 9 6 3 0 3 9 2 5 8 1 24 21 18 15 12 9 6 3 0 Time (Hour) Time Time (Hour) Time B) (B D) (D 3 # xed t ith w d e ix m 283 coarse limestone and metakaolin and (C) Heat flow rate (D) Cumulative heat release of release heat Cumulative (D) rate flow Heat (C) and metakaolin and limestone coarse Figure A5. (A) Heat flow rate (B) Cumulative heat release of Cement Cement of release heat Cumulative (B) rate flow Heat (A) A5. Figure Heat Flow Rate (mW. gCem'1) Heat Flow Rate (mW. gCem'1) Cement #4 mixed with fine limestone and metakaolin and limestone fine with mixed #4 Cement Time (Hour) Time A) (A C) (C o S. | 300 - 3. 1S 100- 3 E a> (0 a (0 (A o 200 400 ------Cement #4 Cement MK + C-LS + MK 20 20 15%-15% 10%-10% 40%-20 30%-30% 25%-25% 0 % - % - % 20 %

Time (Hour) Time

1 1 1 21 18 15 12 9 Time (Hour) Time B) (B I 1 11 1 11 1 1 I ...... D) (D #4 mixed with mixed 284 s lmesone and akaoln and C)Heatfow ae ( Cumul i heatr eas of o se a le re t a e h e tiv la u m u C ) (D rate w flo t a e H ) (C d n a lin o a k ta e m d n a e n sto e lim rse a o c F ig u re A 6. (A ) H e a t flo w ra te (B ) C u m u la tiv e h e a t re le a se o f C e m e n t t n e m e C f o se a le re t a e h e tiv la u m u C ) (B te ra w flo t a e H ) (A 6. A re u ig F Heat Flow Rate (mW. gCem'1) Heat Flow Rate (mW. gCam'1) 10 12 14 10 12 14 2 4 6 8 2 4 6 8 0 0

3 9 2 5 8 1 24 21 18 15 12 9 6 3 0 Cement #5 mixed with fine limestone and metakaolin and limestone fine with mixed #5 Cement Time (Hour) Time (Hour) Time A) (A C) D) (D ) (C 3 9 2 5 8 1 24 21 18 15 12 9 6 3 0 3 9 2 5 8 1 24 21 18 15 12 9 6 3 0 Time (Hour) Time Time (Hour) Time B) (B 5 # xed t ith w d e ix m 285 coarse limestone and metakaolin and (C) Heat flow rate (D) Cumulative heat release of release heat Cumulative (D) rate flow Heat (C) and metakaolin and limestone coarse Figure A7. (A) Heat flow rate (B) Cumulative heat release of Cement Cement of release heat Cumulative (B) rate flow Heat (A) A7. Figure Heat Flow Rate (mW. gCem'1) Heat Flow Rate (mW. gCem'1) 9 2 5 8 1 24 21 18 15 12 9 6 l Cement #6 mixed with fine limestone and metakaolin and limestone fine with mixed #6 Cement 1

1 l Time (Hour) Time (Hour) Time t 1 1 1 2 24 21 18 15 12 9 1

A) (A C) (C 1 l 1

1 l 1

1 1 1 l

B) (B D) (D #6 mixed with mixed 286 coarse limestone and metakaolin and (C) Heat flow rate (D) Cumulative heat release of release heat Cumulative (D) rate flow Heat (C) and metakaolin and limestone coarse Figure A8. (A) Heat flow rate (B) Cumulative heat release of Cement Cement of release heat Cumulative (B) rate flow Heat (A) A8. Figure Heat Flow Rate (mW. gCem'1) Heat Flow Rate (mW. gCem'1) Cement #1 mixed with fine limestone and metakaolin and limestone fine with mixed #1 Cement Time (Hour) Time 1 1 1 2 24 21 18 15 12 9 A) (A C) (C 300- 0 0 3 3 o S 00- 0 1S 10 4-< DC 3 E a> a o> o> ra 400 200 - — ------Cement #7 Cement MK + F-LS + MK 20 20 15%-15% 40%-20% 30%-30% 25%-25% 0 10 % - % - % - % 20 10 10 Time (Hour) Time 1 1 1 2 24 21 18 15 12 9 % % %

Time (Hour) Time B) (B D) (D 2 5 8 1 24 21 18 15 12 #1 mixed with mixed 287 288

REFERENCES

1. Lapeyre J, Kumar A. Influence of pozzolanic additives on hydration mechanisms of tricalcium silicate. J Am Ceram Soc. 2018 Aug;101(8):3557-74.

2. Bullard JW, Garboczi EJ. A model investigation of the influence of particle shape on portland cement hydration. Cem Concr Res. 2006 Jun;36(6):1007-15.

3. Garboczi EJ, Bullard JW. Shape analysis of a reference cement. Cem Concr Res. 2004 Oct;34(10):1933-7. APPENDIX B.

SUPPLEMENTAL INFORMATION ELUCIDATING THE EFFECT OF WATER-

TO-CEMENT RATIO ON THE HYDRATION MECHANISMS OF CEMENT 290

1. CEMENT COMPOSITION AND MIXING PROCEDURE

A type I ordinary Portland cement (OPC) is used in this study. Their composition, as determined from a combination of X-ray fluorescence (XRF) and quantitative X-ray diffraction methods (QXRD methods, are listed in Table B1. All pastes were prepared at room temperature (23°C ± 2°C). The mixing procedure involved the gradual addition of water to the cementitious material (i.e., cement) followed by hand-mixing (i.e., ~ 100 rpm) for 90 sec.

Table B1. Chemical composition of cementitious materials P h a s e s T y p e I c e m e n t Oxide composition determined via XRF method # M a ss%

S iO 2 19.8 A h O 3 4.5

F e 2O 3 3.2 C aO 6 4 .2 M g O 2 .7 SO3 3.4 N a 2 O Equivalent 2 . 2

Loss of Ignition (LOI) 2 . 6 Crystalline phase contents determined from QXRD method A lite (C 3 S) 61

B e lite (C 2 S 8

Aluminate (C 3A) 6

F e rrite (C 4AF) 9

Gypsum (C$H 2) 3.4 291

2. 3D MICROSTRUCTURAL MODEL

To generate 3D microstructures of cementitious systems, a 3D microstructural model, which has bene used previously to study the effects of various process parameters on the evolution of the microstructure of various plain and blended cement-based systems

(1-8), was used. The model implements a vector approach (9) in conjunction with particle packing and microstructural development algorithms, to reproduce the evolution of the microstructure as driven by chemical reactions between the solid precursors (e.g., cement) and water. The model uses the measured (or calculated) PSDs and volumetric fractions of the components of the system (i.e., cement and water) as inputs. A particle packing algorithm is then employed to generate a 3D cubic representative elementary volume (REV: the size of which is defined by the user), wherein the solid phases, represented as spheres corresponding their original PSD, are randomly dispersed and packed following periodic boundary conditions within the REV. The volume of the REV not occupied by the solid spheres is left empty to represent water. Next, to simulate the evolution of the microstructure as the reaction progresses, the degree of hydration of cement (DOH) is used as an input, and based on the amount of cement reacted, the corresponding amount of hydrates formed is represented as a combination of layered- hydrates (i.e., nuclei formed on the receding anhydrous particles) and discrete-hydrates

(i.e., new spherical grains formed in the empty pore space). The scheme of distribution of the overall volume of the hydrates into layered- and discrete-hydrates is implemented to mimic both heterogeneous (e.g., nucleation of C-S-H on cement particles’ surfaces) and homogeneous (e.g., nucleation of CH in the pore space) forms of nucleation of hydrates, 292 as observed in microstructures of cement pastes (1,7,10). The distribution of the hydrate volume into layered- and discrete-hydrates is fixed throughout the simulations.

Specifically, for every unit volume (expressed as cm3) of hydrates formed, 60% and 40%

of the overall hydrate volume is based on the hydration reaction of C 3 S with water, which results in the formation of C -S-H and CH, wherein C -S-H occupies ~ 60% of the

overall volume of hydrates and grows heterogeneously on the surfaces of C 3 S particles, whereas CH amounts to ~ 40% of the overall hydrate volume and grows in the capillary pore space* (1,11-14). As reaction progresses, both layered- and discrete-hydrates are allowed to grow, in relation to their volumetric increase (based on amount of cement reacted ).

(A) (B) (C) Figure B1. Virtual 3D microstructures of cement paste prepared at l/s = 10 at DOH (a) of: (A) 0.00, (B) 0.20, and (C) 0.60. The anhydrous cement particles are represented in red, and packed within the cubic REV (size = 100 pm3) as randomly dispersed spheres with sizes drawn directly from the input PSD. As cement reacts with water and hydrates are formed, the hydrates are allowed to grow as layered hydrates (blue) and as discrete-hydrates (green).

* The volume o f C -S -H and CH formed per unit volume o f C 3 S reacted depend on the assumptions o f the molar mass (or composition) and the density o f C-S-H . Here, the molar mass and density o f of - were assumed as 227.2 g mol-1 and 1.97 g cm-3, respectively. 293

Therefore, at any given degree of hydration (DOH), a virtual microstructure is generated, which consists of anhydrous (i.e., unreacted precursor materials) particles, layered- and discrete-hydrates, and pores. An example of this is shown in Figure B1. In

Figure B1, as well as the simulations presented in the manuscript, the cement is assumed to be a standard type I Portland cement, with an estimated Bogue phase composition as listed in Table B1. The overall quantity of hydrates formed as a result of the hydration of cement, and the corresponding capillary porosity (i.e., unoccupied space in the microstructure), are described as per the formulation used in the Powers M odel (15,16). 294

3. ISOTHERMAL MICROCALORIMETRY

A TA Instruments TAM IV M icrocalorimeter was used to determine the time- dependent reactivity of cement. Compared to conventional methods of reactivity assessment (e.g., isothermal calorimetry), microcalorimetry methods offer a number of unique advantages that enable rapid, direct, and precise measurement of time-dependent reactivity of materials. Some key advantages include. (a) quantification of heat flow- rate/release of reaction at very high resolution (10-7 J s-1), which enables monitoring dissolution of very slow (e.g., silicates) and very fast (e.g., cement) dissolving compounds even at high dilutions (e.g., l/s = 10000), and (b) a built-in injection kit and a magnetically-driven stirrer for “in-situ” studies of solute-solvent interactions, all while the system is continuously stirred (8.17-19).

(A ) (B ) Figure B2. (A) A schematic of the titration cell of the microcalorimeter. The cell is fitted with an electrically-driven agitator which allows in-situ mixing of hydrating pastes. (B) Heat release and heat flow rate associated with the mixing of DI-water in the titration cell. The rotational speed of the agitator was fixed at 80 rpm. 295

To quantify the time dependent reactivity of cement (i.e., degree of hydration: a ) using isothermal microcalorimetry, the experimental protocols, as well as the methods of analyses, are identical to those used in conventional isothermal calorimetry methods (3,

13). Specifically, the cumulative and differential heat release (resulting from the exothermic heat release of cement-water interactions) are normalized by the enthalpy of cement hydration, 472 J gcement-1, to derive the extent of reaction (a) and the rate of reaction (da/dt), respectively, as a function of time (1,13,19). For plain cement pastes prepared at l/s = 0.45, the values of a determined from isothermal calorimetry and isothermal microcalorimetry were compared, and found to be within ±1% of each other.

Selected experiments presented in Paper II were carried out using the titration cell

(Figure B2A). As can be seen, the cell is fitted with an electrically driven agitator that allows in in-situ mixing of the hydrating pastes that are prepared at high w /c . The turbine shaped blades of the agitator are gold-plated, and, therefore, do not partake in chemical interactions with any of the paste components. However, on account of mixing action

(i.e., shear force between the blades of the agitator and paste components), a finite, albeit small, amount of heat is released. To isolate and quantify the heat associated exclusively with the mixing action, experiments were carried out using DI-water (and no cement), while rotating the agitator at a constant speed of 80 rpm over the course of 24 h. As shown in Figure B2B, ~ 0.15 J of heat is released due to the mixing action between the agitator’s blades and water, which is considerably smaller than the heat release associated with the highly exothermic interactions between cement and water. 296

4. SENSITIVITY OF pBNG PARAMETERS

Figure B3 shows the sensitivity of the pBNG simulations with respect to variations in the reactive paste fraction parameter (pf). In Figure B3, simulations were employed in two steps, using SSAcem = 196 m 2 kg-1, /density = 3.50 pm"2, g = 0.25, m =

0.50, and keeping the product growth rate (Gout) constant at 0.075 pm h"1 throughout the simulations (i.e., akin to classical pBNG models).

Figure B3. Simulations demonstrating the sensitivity of the pBNG simulations conducted using constant Gout of 0.075 pm h"1, /density = 3.50 pm"2, g = 0.25, m = 0.50, SSAcem = 196 m 2 kg"1. Variations in (A) dX/dt (i.e., rate of product formation, or the derivative of Equation (1)) and (B) d a /d t (i.e., rate of reaction or the derivative of Equation 8A) with respect to w /c while keepingpf constant at 1.00 (C) shows variation in dX/dt with respect to pf while keeping w /c constant at 3.00

In Figure 3A and 3B, the values of w /c were varied over a wide range while keeping the values of other parameters fixed. In Figure B3C, simulations were employed in a similar manner, except that the w /c was kept constant at 3.00 and the parameters pf was allowed to vary over a wide range. As can be seen in Figures B3A and B3B, at larger 297 values of w/c (andpt = 1.00), the enlargement of reaction vessel and reduction of aBv

(Equation 6 in Paper II) ensure larger spacing between the cement particles and fewer impingements between product nuclei; this results in slower approach to the main hydration peak and, more importantly slower decline in the hydration rate after the peak.

These results qualitatively show that at higher w/c, if the entire reaction vessel is assumed to participate in the nucleation and growth process, the hydration rates estimated from the pBNG simulations (shown in Figure B3B) are significantly different compared to those obtained from experiments (Figures 2-3). However, by restricting the size of the reaction vessel (i.e., by usingp f < 1, as shown in Figure B3C), aBV increases and the effective w/c

(i.e., w /crv) reduces; on account of these changes, the impingements between product nuclei amplify, and as such simulate rate of product formation (expressed as dX/df) of higher w/c pastes exhibit trends similar to those of lower w/c pastes (see the grey curves in Figures B3A and B3C). It is important to note that optimization of p f only provides good fits between the rates of product formation (i.e., dX /df) of the simulated and measured hydration profiles. Optimization of the [Gout(f)] - which is employed in the final step of the simulations using the Nelder-mead simplex approach - is needed in the next (and final) step to match the net reaction rates (expressed as da /df) of the simulations with the experiments. 298

5. HEAT EVOLUTION PROFILES OF WATER-DEFICIENT PASTES

Figure B4 shows the heat flow rates and cumulative heat release of pastes prepared at w /c < 0.42. For comparison, heat evolution profiles of a water-rich paste, i.e., w /c = 10, is shown. As can be seen, even in water-deficient pastes, the hydration kinetics are broadly insensitive to changes in the w /c , akin to pastes prepared with excess water

(i.e., w /c > 0.42).

(A ) (B ) Figure B4. Isothermal microcalorimetry based determinations of (A) heat flow rates, and (B) cumulative heat release of water-deficient pastes prepared using the coarse cement. For comparison, heat evolution profiles of a water-rich paste prepared at w /c is a lso sh o w n 299

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SUPPLEMENTAL INFORMATION TO INFLUENCE OF WATER ACTIVITY

OF TRICALCIUM ALUMINATE-CALCIUM SULFATE SYSTEMS 302

1. CALCULATION OF W ATER ACTIVITY IN [C 3A + C$ + H] SYSTEM S

In a real (i.e., non-ideal) binary solution, the activity of each component is equal

to the product of its activity coefficient and its mole fraction. Therefore, in a [water +

IPA] mixture, aH (Unitless) is equivalent to yH XH, where yH (Unitless) and XH (Unitless)

represent the activity coefficient and mole fraction of water, respectively. Likewise, the

activity of IPA (opa) is equal to the product of IPA’s activity coefficient (yIPA; Unitless)

and IPA’s mole fraction (Ajpa; Unitless). In this study, the van Laar equations [Equations

(1) - (2)] were used to calculate aH and aIpA (1-3).

B aH=XHYH = XH exp (1) h 2 1 + BX \ AXi p a ) -

aiPA =Xipa7ipa=Xipa exp 2 (2)

The terms A and B are unitless coefficients, previously determined to be 1.000

and 0.483 through regression analysis of liquid-vapor equilibrium data, at standard temperature and pressure conditions, by Wilson and Simmons (2). Figure 1A shows the

activity coefficients of water and IPA in binary [water + IPA] mixtures, wherein IPA is used to replace 0-to-100%mass of the water. As can be seen, across all IPA replacement

levels (i.e., decreasing water content), activity coefficients of both water and IPA are

consistently greater than 1. This suggests that [water + IPA] mixtures exhibit positive

deviation from Raoultian behavior, and that cohesive (i.e., water-IPA) interactions in the

mixture are stronger than adhesive (i.e., water-water, and IPA-IPA) ones. Strong cohesive 303 forces between water and IPA molecules also signifies excellent miscibility between the two liquids. Based on the activity coefficients, the activities of water and IPA were calculated; these activities, along with the activities calculated on the basis of Raoult’s law (i.e., ideal behavior), are shown in Figure C1. As can be seen, aH monotonically reduces with increasing IPA replacements; sharp reductions in aH occur when the IPA content in the mixture exceeds 35%.

(A) (B)

Figure C1. (A) Activity coefficients (7); and (B) activities (a) of water (H) and isopropyl alcohol (IPA) in [water + IPA] mixtures, as calculated from the van Laar equations: Equations (1)-(2). Dashed lines represent ideal behavior, as described by Raoult’s Law (i.e., 7 = 1, and, therefore, aH = Xh and aIPA = Xipa). All calculations are deterministic; as such, there is no uncertainty associated with them

While the van Laar equations do accurately describe the IPA-induced reduction in aH, they do not account for reduction in aH due to the presence of ionic species (i.e., Ca2+, 304

A l(O H ) 4", O H ", a n d S O 42", released from the dissolution of C 3A and C$) in the solution.

Notwithstanding, in [C 3A + C$ + H] pastes, the reduction in aH due to such ions is expected to be minuscule compared to that induced by IPA. To verify this, pore solution compositions of typical [C 3A + C $ H 2 + H] pastes were extracted from works of Minard et al. (4) and M eyers et al. (5). Next, using the thermodynamic modeling tool, PHREEQC

(software version 3.5.0) (6), the ionic strength and aH of such pore solutions were estimated. The ionic strengths of the pore solutions were found to range between 95 m m o l L "1 (during stage I, that is, before the exhaustion of C$H 2) and 73.5 mmol L "1

(during stage II, that is, after the exhaustion of C$H 2). On the basis of these ionic strengths, the corresponding decrease in aH was estimated to range from 0.002-to-0.001 - which is not just minuscule, but also substantially smaller than the decrease in a^ corresponding to replacement of 4% mass of water with IPA (N. B., aH = 0.9879, for [96% water + 4% IPA]).

In [C 3A + C$ + H] pastes, wherein water is partially replaced with IPA, there is another factor that causes reductions in aH. As hydration of C 3A progresses, water present in the paste is progressively consumed, whereas the amount of IPA - which is assumed to be inert throughout the hydration process - remains constant. This causes the effective mole fraction of IPA (A ipa) in the solution to steadily increase with increasing degree of

C 3A hydration (o c3a), thus resulting in reduction of a H. Such reductions in a H, in relation to the degree of hydration of C 3A in [C 3A + C$ + H] pastes, are shown in Figure C2. For these calculations, [C 3A + C$ + H] pastes, prepared at a fixed l/s of 2 and comprised of

15% mass a n d 3 0 % mass replacement of C 3A with C$, were used. The water content in the 305 mixing solution was reduced from 100-to-3%mass, and replaced with IPA. Next, hydration reactions shown in Equations (3)-(5) were used to estimate the reduction in the amount

of water in relation to aC 3A.

C3A + 3C$ + 32H ^ C6 A $ 3 H 3 2 (3)

C3A + 0 .5 C 6A $ 3 H 32 + 2H ^ 1.5C 4 A $ H 1 2 (4)

C3 A + 6 H ^ C3 AH 6 (5)

It should be noted that Equation (3)-(5) were used in a sequential manner to

mimic the progression of C 3A hydration - through stages I, II, and III, respectively - as would be expected to occur in practice. Lastly, at each value of a c 3A, the van Laar equations were employed to estimate aH on the bases of the effective mole fractions of

IPA and water at that point. As can be seen in Figure C2, as hydration of C 3A progresses and water is continually consumed, a decreases in a monotonic manner due to progressive increase in the IPA-to-water molar ratio. As the pastes were prepared at l/s o f

2 - which is fairly high - reductions in a n (compared to their values at the time of

mixing, that is, when aC 3A = 0 ) are minor, and complete hydration (ultimate value of aC 3A

= 1) o f C 3A is achieved in all pastes except for those prepared at IPA replacement levels of 80% or above. As would be expected, at such high IPA replacements, the ultimate

value of aC 3A is < 1 . 0 because the amount of water is less than what would be needed for

all o f C 3A to hydrate. In general, reductions in a n (with respect to aC 3A) are m o re sev ere

fo r [C 3A + 30% C$ + H] pastes compared to those prepared using 15% C$. For example,

at IPA replacement level of 80%, the ultimate values of aC 3A fo r [C 3A + 15% C$ + H]

a n d [C 3A + 30% C$ + H] pastes are 0.82 and 0.27, respectively. This is because in the

[C 3A + 30% C$ + H] paste, as the C$/C 3A molar ratio is higher compared to that in [C 3A 306

+ 15% C$ + H] paste, stage I of the hydration process (i.e., ettringite precipitation reaction, shown in Equation 3), during which 32 moles of water are consumed for every

m o le o f C 3A, is longer.

85% C,A + 15% C$

IPA in Solution A (A) Initial Water Activity (aH„)

0. 0% ( 1.00) -----2.5% (=1.00) -----5.0% (0.98) -----10% (0.97) 20% 0.94) C,A Degree of Hydration, n, ,, (Unitless ---- 30% (0.91) 70% C,A + 30% C$ ---- 40% (0.87) 50% (0.83) — 60% 0.77 — 70% (0.70) — 80% (0.58) — 85% (0.50) D . 6 - (B) — 90% (0.38) C„A + A Ft + AFm c 3a + AFm • — 95% 0.23 0 .4 - c 3a + C AH % c$ + 97 0.14 vAFt 0.2-

CjA Degree of Hydration, ac A (Unitless) Figure C2. The decline in water activity (aH) in relation to increasing degree of

hydration of C 3A (aC 3A) in: (A ) [C 3A + 15% C$ + H]; and (B) [C 3A + 30% C$ + H] pastes prepared at a fixed l/s of 2 and different levels of replacement of water with IPA. The solid vertical lines indicate threshold values of a c 3A at which the hydration reactions switch from one stage to the next; that is, from stage I (Equation 3: ettringite (AFt) precipitation), to stage II (Equation 4: monosulfoaluminate (AFm) precipitation),

and, ultimately, to stage III (Equation 5: hydrogarnet (C 3AH 6) precipitation). All calculations are deterministic; as such, there is no uncertainty associated with them

Consequently, at IPA replacement of 80%, all of the water in [C 3A + 30% C$ +

H] paste is consumed - and hydration of C 3A is suitably terminated - before stage II even

begins. Once the IPA replacement level exceeds 90%, the water-to-C 3A molar ratio in all 307

pastes reduces to values << 32. As such, the reductions in aH with respect to ac 3A are

drastic for all pastes, regardless of their initial C$ contents, and hydration of C 3A in n o n e of the pastes advance beyond stage I. (Figure C2). 308

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VITA

Jonathan Lee Lapeyre was born in Houston, Texas. From 2012 - 2016, Jon attended M issouri University of Science & Technology initially undecided but decided to pursue in a Bachelor of Science for Ceramic Engineering. W hile he was working on his undergraduate degree, Jon participated in student groups inside as well as outside the

Department of M aterials Science and Engineering, primarily Keramos and Gaffer’s

Guild. In 2015, Jon participated in a Research Experience for Undergraduates (REU) workshop focusing on advance manufacturing and 3D printing of materials. Jon finished and received the Bachelor of Science in Ceramic Engineering in August of 2016, while working a processing engineering internship with Daltile, Group Inc. in Oklahoma.

Afterwards, Jon started his PhD research in Fall 2016 under the guidance of Dr.

Aditya Kumar. Jon’s PhD research investigated the effects of calcined clays on the hydration kinetics of pure tricalcium silicate pastes. Additionally, Jon researched tricalcium aluminate and calcium sulfate pastes, and the kinetics of high aluminum calcium aluminate cements, as well as implementing machine learning on synthetic cement mixtures. He presented work nationally at conferences and has wrote/co-wrote several manuscripts published in peer-reviewed journals. In December 2020, he received his Doctor of Philosophy in M aterials Science and Engineering from Missouri S&T. Over the years, he developed a passion for popular and avant-garde music. This has prompted several interviews with musicians and resulted in thousand of views online.