Improving Thermodynamic Consistency Among Vapor Pressure, Heat of Vaporization, and Liquid and Ideal Gas Heat Capacities Joseph Wallace Hogge Brigham Young University

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This Dissertation is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in All Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Improving Thermodynamic Consistency Among Vapor Pressure, Heat of Vaporization, and Liquid and Ideal Gas Heat Capacities

Joseph Wallace Hogge

A dissertation submitted to the faculty of Brigham Young University In partial fulfillment of the requirements for the degree of

Doctor of Philosophy

W. Vincent Wilding, Chair Thomas A. Knotts Dean Wheeler Thomas H. Fletcher John D. Hedengren

Department of Chemical Engineering Brigham Young University

ABSTRACT

Improving Thermodynamic Consistency Among Vapor Pressure, Heat of Vaporization, and Liquid and Ideal Gas Heat Capacity

Joseph Wallace Hogge Department of Chemical Engineering, BYU Doctor of Philosophy

Vapor pressure ( ), heat of vaporization ( ), liquid heat capacity ( ), and ideal gas heat capacity ( ) are important properties for process design and optimization.𝑙𝑙 This work 𝑃𝑃vap Δ𝐻𝐻vap 𝐶𝐶𝑝𝑝 focuses on improving𝑖𝑖𝑖𝑖 the thermodynamic consistency and accuracy of the aforementioned 𝑝𝑝 properties since these𝐶𝐶 can drastically affect the reliability, safety, and profitability of chemical processes. They can be measured for pure organic compounds from the triple point, through the normal boiling point, and up to the critical point. Additionally, is proportional to the derivative of vapor pressure with respect to temperature through the Clapeyron equation, and the vap difference between and is proportional to the derivative Δof𝐻𝐻 heat of vaporization with respect to temperature.𝑙𝑙 𝑖𝑖𝑖𝑖 𝑝𝑝 𝑝𝑝 𝐶𝐶 𝐶𝐶 In order to improve temperature-dependent correlations, all the properties were analyzed simultaneously. First, a temperature-dependent error model was developed using several versions of the Riedel and Wagner correlations. The ability of each correlation to match data was determined for 5 well-known compounds. The Riedel equation performed better than the𝑙𝑙 Wagner vap 𝑝𝑝 equation when the best form𝑃𝑃 was used. Second, the Riedel equation form was further𝐶𝐶 modified, and the best correlation form was found for about 50 compounds over 7 families. This led to the development of a new vapor pressure prediction method using different Riedel equation forms to fit , , and data simultaneously. Seventy compounds were tested, and the error compared to liquid heat𝑙𝑙 capacity data dropped from 10% with previous methods to 3% with this vap vap 𝑝𝑝 new𝑃𝑃 predictionΔ𝐻𝐻 method.𝐶𝐶

Additionally a differential scanning calorimeter (DSC) was purchased, and melting points ( ), enthalpies of fusion ( ), and liquid heat capacities ( ) were measured for over twenty compounds. For many of these compounds, the vapor pressure data𝑙𝑙 and critical constants were 𝑚𝑚 fus 𝑝𝑝 re𝑇𝑇-evaluated, and new vaporΔ 𝐻𝐻pressure correlations were recommended𝐶𝐶 that were thermodynamically consistent with measured liquid heat capacity data.

The Design Institute for Physical Properties (DIPPR) recommends best constants and temperature-dependent values for pure compounds. These improvements were added to DIPPR procedures, and over 200 compounds were re-analyzed so that the temperature-dependent correlations for , , , and became more internally consistent. Recommendations were made for the calculation procedures𝑖𝑖𝑖𝑖 𝑙𝑙 of these properties for the DIPPR database. vap vap 𝑝𝑝 𝑝𝑝 𝑃𝑃 Δ𝐻𝐻 𝐶𝐶 𝐶𝐶

Keywords: multi-property optimization, vapor pressure, heat capacity, heat of vaporization

ACKNOWLEDGEMENTS

I would like to thank all of the people who helped me in this project and made it possible.

I thank my wife, Julie, and our 2 kids, Louisa and Adelaide, for all of their unwavering support and motivation. My gratitude goes out to my advisor, Dr. Wilding, along with Dr. Knotts, Dr.

Giles, and other members of my committee that helped bring this project to fruition. I would also like to thank my father, Jeff, who talked me through my freshman writing class. Without his encouragement, I would never have thought it possible to write this document. I thank my mother,

Kim, for instilling in me a desire to learn about the world around us.

TABLE OF CONTENTS

LIST OF TABLES ...... viii LIST OF FIGURES ...... xvi 1 Introduction ...... 1 2 Thermodynamic Relationships ...... 4 3 Literature Review of Thermophysical Properties ...... 7 3.1 Vapor Pressure ...... 7 3.1.1 Vapor Pressure Correlation Equations ...... 7 3.1.2 Vapor Pressure Data Availability ...... 9 3.2 Heat of Vaporization ...... 9 3.2.1 Heat of Vaporization Correlation Equations ...... 10 3.2.2 Heat of Vaporization Data Availability ...... 10 3.3 Ideal Gas Heat Capacity ...... 12 3.3.1 Ideal Gas Heat Capacity Correlation Equations ...... 12 3.3.2 Ideal Gas Heat Capacity Data Availability ...... 13 3.4 Liquid Heat Capacity ...... 17 3.4.1 Liquid Heat Capacity Temperature Behavior ...... 18 3.4.2 Liquid Heat Capacity Data Availability ...... 20 3.5 Analysis of Experimental Data and Correlations ...... 20 4 Multi-Property Optimization – Temperature Dependent Errors ...... 23 4.1 Weight Model ...... 23 4.2 Results/Discussion ...... 25 4.3 Conclusions ...... 29 5 Multi-Property Optimization – The Riedel Equation ...... 31 5.1 Methods ...... 31 5.2 Results ...... 34 5.3 Conclusions ...... 44 6 New Thermodynamically Consistent Vapor Pressure Prediction ...... 46 6.1 Introduction ...... 47

6.2 Overview of Vapor Pressure Prediction and Correlation Methods ...... 48 6.3 Theory ...... 51 6.3.1 Thermodynamic Relationships ...... 51 6.3.1 New Predictive Vapor Pressure Method ...... 51 6.4 Methods ...... 53

6.4.1 Regression of K and Xc as a Function of E ...... 53 6.4.2 E Training Method ...... 56 6.5 Results ...... 57 6.5.1 Optimized E by Family ...... 57 6.5.2 Comparison to Other Predictive Methods...... 60 6.5.3 Testing the Methods with Compounds Not Used in the Training Set ...... 63 6.6 Conclusions ...... 64 7 Experimental Work...... 67 7.1 Compounds...... 67 7.2 Calibrations/Verifications ...... 70 7.3 Uncertainties ...... 76 7.4 Property Selection for Thermodynamic Analysis ...... 77 7.5 Results ...... 77 7.5.1 Toluene Derivatives ...... 81 7.5.2 Phenyl Propanols ...... 86 7.5.3 Furans ...... 88 7.5.4 Phenyl Acetates ...... 90 7.5.5 n-Hexylcyclohexane ...... 92 7.5.6 6-Undecanone ...... 95 7.5.7 1H-Perfluorooctane ...... 96 7.5.8 2,6-Dimethoxyphenol ...... 97 7.5.9 trans-Isoeugenol ...... 99 7.5.10 1-Propoxy-2-Propanol...... 102 7.6 Conclusions ...... 103 8 Best Practices, Recommendations, and Incorporations into the Database ...... 105 8.1 Introduction ...... 105

8.2 Ideal Gas Heat Capacity Database Fixes ...... 105 8.3 Derivative vs. Integral Methods ...... 108 8.4 Compounds without Liquid Heat Capacity Data ...... 113 8.5 Recommendation Summary ...... 115 8.6 DIPPR Database Improvements ...... 117 8.7 Association ...... 118 8.7.1 Saturated Monomer Mole Fraction ...... 120 8.7.2 Heat of Vaporization ...... 122 8.7.3 Future Work ...... 123 9 Conclusions ...... 124 9.1 Future Work ...... 126 9.1.1 Continue Liquid Heat Capacity Measurements ...... 127 9.1.2 Measure Vapor Pressure ...... 127 9.1.3 Improve the Multi-Property Optimization ...... 128 9.1.4 Measure the Solid Phase Properties ...... 129 9.1.5 Measure Ideal Gas Heat Capacity ...... 129 9.1.6 Improve Methods for Associating Compounds ...... 129 9.1.7 Reduce Heat of Vaporization Uncertainty ...... 130 References ...... 131 Appendix A. Thermodynamic Derivations ...... 204 A.1 Clapeyron Equation Derivation ...... 204 A.2 Derivative Method Derivation ...... 204 A.2.1 Saturation and Isobaric Heat Capacities ...... 205 A.2.2 Vapor and Ideal Gas Heat Capacities ...... 206 A.2.2 The Derivative Method ...... 207 A.3 Ideal Gas Heat Capacity Derivation using Statistical Mechanics ...... 208 Appendix B. Data Used ...... 211 B.1 Vapor Pressure Data ...... 211 B.1.1 Vapor Pressure Data for Riedel Equation Analysis ...... 211 B.1.2 Vapor Pressure Data for New Predictive Riedel Equation ...... 215 B.2 Heat of Vaporization Data...... 223

B.3 Liquid Heat Capacity Data ...... 230 B.3.1 Liquid Heat Capacity Data for Riedel Equation Analysis ...... 230 B.3.2 Liquid Heat Capacity Data for New Predictive Riedel Equation ...... 234 B.4 Compounds measured ...... 241 Appendix C. Sample Calculation for Predictive Method ...... 245

vii

LIST OF TABLES

Table 2-1: Calculation methods for properties in the Derivative method for finding ...... 6

Table 4-1: Summary of the sum squared errors used ...... 𝑪𝑪𝑪𝑪𝑪𝑪 ... 24

Table 4-2: Optimized vapor pressure correlations with triple point pressures ...... 29

Table 5-1: A list of hydrocarbons investigated in this study, grouped by chemical family ...... 32

Table 5-2: A list of non-hydrocarbons investigated in this study, ...... 32

Table 5-3: Absolute average deviation of Equation 5-1 fit to vapor pressure data ...... 34

Table 5-4: Summary of triple point pressures (in Pa) from literature ...... 42

Table 5-5: Summary of triple point pressures (in Pa) from literature ...... 42

Table 5-6: Summary of triple point pressures (in Pa) from literature ...... 42

Table 5-7: Summary of triple point pressures (in Pa) from literature ...... 43

Table 5-8: Summary of triple point pressures (in Pa) from literature ...... 43

Table 5-9: Summary of triple point pressures (in Pa) from literature ...... 43

Table 5-10: Summary of triple point pressure (in Pa) from literature ...... 44

Table 6-1: Compounds originally investigated by Riedel, ...... 49

Table 6-2: Training set of compounds for the new ...... 55

Table 6-3: Summary of prediction constants for the original ...... 55

l Table 6-4: Average Pvap, ΔHvap, and Cp absolute average deviations (AAD) for the

compounds in each chemical family using the best value for each compound ...... 58

Table 6-5: Recommended E values for each of the ...... 𝑬𝑬 ...... 60

Table 7-1: Purities of compounds measured in this study ...... 71

Table 7-2: Purities of verification compounds used in this study ...... 71

Table 7-3: Temperature and heat verification of melting point (Tm/K) ...... 73

viii

Table 7-4 Summary of vapor pressure fitting techniques ...... 77

Table 7-5: Summary of liquid heat capacity measurements with uncertainties ...... 78

Table 7-6: Summary of experimental melting point measurements a ...... 80

Table 7-7 Summary of experimental enthalpy of fusion measurements a ...... 81

Table 7-8: Summary of experimental melting points for the toluene derivatives ...... 82

Table 7-10: Summary of enthalpy of fusion experimental results for the toluene derivatives ...... 83

Table 7-11: Summary of best critical constants and vapor pressure coefficients ...... 85

Table 7-12: Summary of experimental glass transition temperatures ...... 86

Table 7-13: Summary of experimental melting points for the phenyl propanols ...... 87

Table 7-14: Summary of enthalpy of fusion experimental results for the phenyl propanols ...... 87

Table 7-15: Summary of experimental melting points for the furans ...... 89

Table 7-16: Summary of enthalpy of fusion experimental results for the furans ...... 89

Table 7-17: Summary of best critical constants and vapor pressure ...... 90

Table 7-18: Summary of experimental melting points for the phenyl acetates ...... 91

Table 7-19: Summary of enthalpy of fusion experimental results for the phenyl acetates ...... 92

Table 7-20: Summary of best critical constants and vapor pressure ...... 92

Table 7-21: Summary of experimental melting points for the alkylcyclohexanes ...... 93

Table 7-22: Summary of enthalpy of fusion experimental results for the alkylcyclohexanes ...... 93

Table 7-23: Summary of best critical constants and vapor pressure ...... 94

Table 7-24: Summary of experimental melting points for the di-n-alkyl ketones ...... 95

Table 7-25: Summary of enthalpy of fusion experimental results for the di-n-alkyl ketones ...... 95

Table 7-26: Summary of best critical constants and vapor pressure ...... 95

Table 7-27: Summary of experimental melting points for ...... 96

Table 7-28: Summary of enthalpy of fusion experimental results for ...... 97

Table 7-29: Summary of experimental melting points for ...... 98

Table 7-30: Summary of enthalpy of fusion experimental results for ...... 98

Table 7-31: Summary of best critical constants and vapor pressure ...... 99

Table 7-32: Summary of experimental melting points for trans-isoeugenol ...... 101

Table 7-33: Summary of experimental enthalpy of fusion for trans-isoeugenol ...... 101

Table 7-34: Summary of best critical constants and vapor pressure ...... 102

Table 8-1: Summary of best recommendations for achieving thermodynamic consistency ...... 116

Table B-1: Summary of vapor pressure data used in this work for the n-alkanes ...... 212

Table B-2: Summary of vapor pressure data used in this work for the 2-methylalkanes ...... 212

Table B-3: Summary of vapor pressure data used in this work for the 1-alkenes ...... 212

Table B-4: Summary of vapor pressure data used in this work for the n-aldehydes ...... 212

Table B-5: Summary of vapor pressure data used in this work for aromatic compounds ...... 213

Table B-6: Summary of vapor pressure data used in this work for the ethers ...... 213

Table B-7: Summary of vapor pressure data used in this work for the ketones ...... 213

Table B-8: Summary of vapor pressure data used in this work for alkanes and alkenes ...... 216

Table B-9: Summary of vapor pressure data used in this work for aromatic compounds ...... 216

Table B-10: Summary of vapor pressure data used in this work for the esters and ethers ...... 216

Table B-11: Summary of vapor pressure data used in this work for the gases ...... 217

Table B-12: Summary of vapor pressure data used in this work for the halogenated compounds ...... 217

Table B-13: Summary of vapor pressure data used in this work for the ketones ...... 217

Table B-14: Summary of vapor pressure data used in this work for alkanes ...... 217

Table B-15: Summary of vapor pressure data used in this work for multifunctional compounds ...... 218

Table B-16: Summary of vapor pressure data used in this work for the 1-alkenes ...... 218

Table B-16: Summary of vapor pressure data used in this work for the 1-alkenes ...... 219

Table B-17: Summary of vapor pressure data used in this work for the n-aldehydes ...... 219

Table B-18: Summary of vapor pressure data used in this work for aromatic compounds ...... 219

Table B-19: Summary of vapor pressure data used in this work for the ethers ...... 220

Table B-20: Summary of vapor pressure data used in this work for the ketones ...... 220

Table B-21: Summary of vapor pressure data used in this work for the amines ...... 220

Table B-22: Summary of vapor pressure data used in this work for the ringed alkanes ...... 221

Table B-23: Summary of vapor pressure data used in this work for the halogenated compounds ...... 221

Table B-24: Summary of vapor pressure data used in this work for the esters ...... 221

Table B-25: Summary of vapor pressure data used in this work for the sulfides ...... 221

Table B-26: Summary of vapor pressure data used in this work for the alkynes and silanes ...... 222

Table B-80: Summary of heat of vaporization data used in this work for alkanes and alkenes...... 224

Table B-81: Summary of heat of vaporization data used in this work for the aromatic compounds ...... 224

Table B-82: Summary of heat of vaporization data used in this work for the esters and ethers ...... 224

Table B-83: Summary of heat of vaporization data used in this work for the gases ...... 225

Table B-84: Summary of heat of vaporization data used in this work for the halogenated compounds ...... 225

Table B-85: Summary of heat of vaporization data used in this work for the ketones ...... 225

Table B-86: Summary of heat of vaporization data used in this work for alkanes ...... 225

Table B-87: Summary of heat of vaporization used in this work for the 1-alkenes ...... 226

Table B-88: Summary of heat of vaporization data used in this work for the n-aldehydes ...... 226

Table B-89: Summary of heat of vaporization data used in this work for the aromatic compounds ...... 227

Table B-90: Summary of heat of vaporization data used in this work for the ethers ...... 227

Table B-91: Summary of heat of vaporization data used in this work for the ketones ...... 227

Table B-92: Summary of heat of vaporization data used in this work for the amines ...... 227

Table B-93: Summary of heat of vaporization data used in this work for the ringed alkanes...... 228

Table B-94: Summary of heat of vaporization data used in this work for the halogenated compounds ...... 228

Table B-95: Summary of heat of vaporization data used in this work for the esters ...... 228

Table B-96: Summary of heat of vaporization data used in this work for the sulfides ...... 229

xii

Table B-97: Summary of heat of vaporization data used in this work for the alkynes and silanes ...... 229

Table B-98: Summary of heat of vaporization data used in this work for multifunctional

compounds ...... 229

Table B-46: Summary of liquid heat capacity data used in this work for the n-alkanes ...... 231

Table B-47: Summary of liquid heat capacity data used in this work for the 2-

methylalkanes ...... 231

Table B-48: Summary of liquid heat capacity data used in this work for the 1-alkenes ...... 231

Table B-49: Summary of liquid heat capacity data used in this work for the n-aldehydes ...... 231

Table B-50: Summary of liquid heat capacity data used in this work for the aromatic

compounds ...... 232

Table B-51: Summary of liquid heat capacity data used in this work for the ethers ...... 232

Table B-52: Summary of liquid heat capacity data used in this work for the ketones ...... 232

Table B-53: Summary of liquid heat capacity data used in this work for alkanes and

alkenes...... 235

Table B-54: Summary of liquid heat capacity data used in this work for the aromatic

compounds ...... 235

Table B-55: Summary of liquid heat capacity data used in this work for the esters and

ethers ...... 235

Table B-56: Summary of liquid heat capacity data used in this work for the gases ...... 236

Table B-57: Summary of liquid heat capacity data used in this work for the halogenated

compounds ...... 236

Table B-58: Summary of liquid heat capacity data used in this work for the ketones ...... 236

xiii

Table B-59: Summary of liquid heat capacity data used in this work for alkanes ...... 236

Table B-60: Summary of liquid heat capacity data used in this work for the 1-alkenes ...... 237

Table B-61: Summary of liquid heat capacity data used in this work for the n-aldehydes ...... 237

Table B-62: Summary of liquid heat capacity data used in this work for the aromatic compounds ...... 237

Table B-63: Summary of liquid heat capacity data used in this work for the ethers ...... 238

Table B-64: Summary of liquid heat capacity data used in this work for the ketones ...... 238

Table B-65: Summary of liquid heat capacity data used in this work for the amines ...... 238

Table B-66: Summary of liquid heat capacity data used in this work for the ringed alkanes...... 239

Table B-67: Summary of liquid heat capacity data used in this work for the halogenated compounds ...... 239

Table B-68: Summary of liquid heat capacity data used in this work for the esters ...... 239

Table B-69: Summary of liquid heat capacity data used in this work for the sulfides ...... 239

Table B-70: Summary of liquid heat capacity data used in this work for the alkynes and silanes ...... 240

Table B-71: Summary of liquid heat capacity data used in this work for multifunctional compounds ...... 240

Table B-72: Summary of melting point and melting enthalpy literature data ...... 241

Table B-73: Summary of vapor pressure literature data ...... 242

Table B-74: Summary of heat of vaporization literature data ...... 244

Table B-75: Summary of liquid heat capacity literature data ...... 244

Table C-1: Summary of compound constants for 2,2-dimethylpentane ...... 245

xiv

Table C-2: Summary of reduced properties for 2,2-dimethylpentane ...... 245

LIST OF FIGURES

Figure 3-1: Pie chart of ΔHvap data labeled as “Experimental” in the DIPPR database ...... 11

Figure 3-2: ΔHvap calorimetric and derived data with the DIPPR correlation for propylene ...... 11

ig Figure 3-3: Pie chart of Cp data labeled as “Experimental” in the DIPPR database ...... 14

ig Figure 3-4: Pie chart of measurement techniques used for actual experimental Cp data in the DIPPR database ...... 15

ig Figure 3-5: Quantum mechanical calculation error versus temperature for Cp compared

to true experimental data in the literature ...... 16

Figure 3-6: Error distribution for quantum mechanical values compared to experimental

ig Cp data ...... 17

l Figure 3-7: Cp data and DIPPR correlations for butane, 1-butene, 1-propanol, and

ethylene glycol ...... 19

l Figure 3-8: Cp Data and DIPPR correlation for propylene, along with the Derivative

method prediction from the start of this project ...... 19

Figure 3-9: A qualitative look at the relative frequency of experimental data for vapor

pressure, heat of vaporization, and liquid heat capacity around the normal boiling point ...... 21

Figure 4-1: Temperature dependent weight model used in the multi-property optimization for vapor pressure, heat of vaporization, and liquid heat capacity around the normal boiling point ...... 25

Figure 4-2: Average absolute deviation (AAD) for propylene across vapor pressure, heat

of vaporization, and liquid heat capacity data with the starting fit, the R1 fit, the R2 fit,

the R6 fit, the W2 fit, and the W3 fit with temperature dependent weights ...... 27

xvi

Figure 4-3: Experimental data for propylene with the starting and optimized Riedel 2 fits

for (a) vapor pressure, (b) natural log of vapor pressure, (c) heat of vaporization, and (d)

liquid isobaric heat capacity ...... 28

l Figure 4-4: The average AAD from Pvap, ΔHvap, and Cp using the starting fit to Pvap data

only and the optimized R1, R2, R6, W2, and W3 fits for the five compounds studied...... 29

Figure 5-1: Heat of vaporization experimental data and Clapeyron equations using the

Riedel equation with E = 1 through with the temperature range of vapor pressure data

shown ...... 𝟔𝟔 ...... 36

Figure 5-2: Liquid heat capacity data and Derivative method predictions from the Riedel

equation with E = 1 through 6 with the temperature range of vapor pressure data shown ...... 37

Figure 5-3: Absolute average deviation of a) vapor pressure data and b) liquid heat

capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the

n-alkanes ethane ( ), propane ( ), butane ( ), pentane𝑬𝑬 ( ), hexane ( ), heptane ( ), and octane ( ) ...... 38

Figure 5-4: Absolute average deviation of a) vapor pressure data and b) liquid heat

capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the

2-methylalkanes isopropane ( ), 2-methylbutane ( ), 2𝑬𝑬-methylpentane ( ), 2-

methylhexane ( ), and 2-methylheptane ( ) ...... 39

Figure 5-5: Absolute average deviation of a) vapor pressure data and b) liquid heat

capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the

1-alkenes propylene ( ), 1-butene ( ), 1-pentene ( ),𝑬𝑬 1-hexene ( ), and 1-

heptene ( ) ...... 39

xvii

Figure 5-6: Absolute average deviation of a) vapor pressure data and b) liquid heat capacity data of fits with the use of the Riedel equation with = 0.5 through E=6 for the

n-aldehydes butanal ( ), pentanal ( ), hexanal ( ), and𝑬𝑬 heptanal ( ) ...... 40

Figure 5-7: Absolute average deviation of a) vapor pressure data and b) liquid heat

capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the

aromatic compounds benzene ( ), toluene ( ), m-xylene𝑬𝑬 ( ), o-xylene ( ), p-

xylene ( ), ethylbenzene ( ), propylbenzene ( ), and butylbenzene ( ) ...... 40

Figure 5-8: Absolute average deviation of a) vapor pressure data and b) liquid heat

capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the

ethers dimethyl ether ( ), diethyl ether ( ), ethyl propyl𝑬𝑬 ether ( ), di-n-propyl

ether ( ), and methyl tert-butyl ether ( ) ...... 41

Figure 5-9: Absolute average deviation of a) vapor pressure data and b) liquid heat

capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the

ketones methyl ethyl ketone ( ), methyl isopropyl ketone𝑬𝑬 ( ), methyl isobutyl

ketone ( ), 2-pentanone ( ), 2-hexanone ( ), 3-hexanone ( ), 2-heptanone (

), and 2-octanone ( ) ...... 41

Figure 5-10: Triple point pressures versus carbon number for n-alkanes comparing

DIPPR values [44], REFPROP values [54], and values from this work ...... 44

Figure 6-1: Fitting parameters K and Xc as functions of E ...... 55

Figure 6-2: Distribution of best E values using the new predictive Riedel Pvap method on

the test compounds ...... 59

xviii

Figure 6-3: The distribution of Pvap AAD for 106 test compounds using Pvap prediction

methods: Riedel’s original method, Lee-Kesler, Vetere’s Wagner method, Vetere’s

Riedel method, and this work ...... 61

Figure 6-4: The distribution of ΔHvap for 106 test compounds using Pvap prediction

methods: Riedel’s original method, Lee-Kesler, Vetere’s Wagner method, Vetere’s

Riedel method, and this work ...... 62

l Figure 6-5: The distribution of Cp AAD for the test compounds using Pvap prediction methods within the Derivative method: Riedel’s original method, Lee-Kesler, Vetere’s

Wagner method, Vetere’s Riedel method, and this work ...... 63

l Figure 6-6: Average Pvap, ΔHvap, and Cp AAD for five sets of 40 compounds using

different Pvap prediction methods ...... 64

Figure 7-1: Verification results for a) temperature and b) heat calibrations, with the

average difference for each compound from the DIPPR value [44] ( ) and 95%

confidence intervals on the measurements, and the uncertainties from this study ( ) ...... 74

Figure 7-2: Verification results for heat capacity of n-heptane with 95% confidence intervals compared to the DIPPR correlation, DIPPR uncertainty, and literature data ...... 75

Figure 7-3: Verification results for heat capacity of sapphire with 95% confidence

intervals compared to the DIPPR correlation, DIPPR uncertainty, and literature data ...... 76

Figure 7-4 The toluene derivatives measured in this study ...... 82

Figure 7-5 Melting points for xylenes ( ), tolualdehydes ( ), tolualcohols ( ), and toluic

acids ( ) with uncertainties contained within the size of the markers, open symbols

represent new data from this study ...... 83

xix

Figure 7-6 Enthalpies of fusion for xylenes ( ), tolualdehydes ( ), tolualcohols ( ), and

toluic acids ( ) with uncertainties from DIPPR and this study, open symbols represent

new data from this study ...... 84

Figure 7-7 Liquid heat capacity measurements for m-tolualdehyde ( ), o-tolualdehyde (

), p-tolualdehyde ( ), m-tolualcohol ( ), and p-toluic acid ( ) with experimental

uncertainty from this study ...... 85

Figure 7-8: The phenyl propanols measured in this study ...... 86

Figure 7-9 Liquid heat capacity measurements for 1-phenyl-1-propanol ( ), 1-phenyl-2- propanol ( ), 2-phenyl-1-propanol ( ), and 2-isopropylphenol ( ) with experimental uncertainty...... 88

Figure 7-10: The furans measured in this study ...... 88

Figure 7-11: Comparison compounds for the furans ...... 88

Figure 7-12: The phenyl acetates measured in this study ...... 91

Figure 7-13: Comparison compounds for the phenyl acetates ...... 91

Figure 7-14: n-hexylcyclohexane ...... 93

Figure 7-15: Liquid heat capacity data for n-ethyl- ( ) and n-butyl- ( ) with DIPPR

uncertainty, and n-hexyl- ( ) cyclohexane and experimental uncertainty ...... 94

Figure 7-16: 6-undecanone ...... 95

Figure 7-17: 1H-perfluorooctane ...... 96

Figure 7-18: 2,6-dimethoxyphenol ...... 97

Figure 7-19: Compounds compared to 2,6-dimethoxyphenol ...... 98

Figure 7-20: trans-isoeugenol ...... 100

Figure 7-21: Comparison compounds for trans-isoeugenol ...... 100

Figure 7-22: 1-propoxyl-2-propanol ...... 102

Figure 8-1: The ideal gas heat capacity for methyl ethyl ketone with data and DIPPR

uncertainty and different basis sets, levels of theory, and scaling factors ...... 107

Figure 8-2: Liquid heat capacity data for propylene with the derivative and integral

methods from the start of this project (2013) ...... 110

Figure 8-3: Liquid heat capacity data for propylene with the derivative and integral

methods with a better ideal gas heat capacity correlation (2014) ...... 110

Figure 8-4: Liquid heat capacity data for propylene with the Derivative and Integral

methods with the Derivative method extended above normal boiling point (2015) ...... 112

Figure 8-5 The equation used to calculate coefficients for the integral method (2014) ...... 112

Figure 8-6: Liquid heat capacity data for propylene with the derivative and integral

methods now (2017) compared to the start of this project (2013) ...... 113

Figure 8-7: Liquid heat capacity for trans-1-chloro-3,3,3-trifluoro-1-propene with several prediction methods ...... 114

Figure 8-8: The average absolute deviations for the vapor pressure and Derivative method

heat capacity fits before and after analysis ...... 118

Figure 8-9: The monomer mole fractions for n-alkanoic acids along the saturation curve ...... 121

Figure 8-10: Heat of vaporization experimental data and curves derived using the

Clapeyron equation for n-carboxylic acids with association ...... 123

Figure 9-1: The experimental setup recommended by ASTM E1782-14 to measure Pvap

via DSC ...... 128

xxi

1 INTRODUCTION

The U.S. chemical process industry converts raw materials into more than 70,000 products worth about $760 billion dollars annually [1]. These products contribute to nearly every object used by a modern society, which has come to rely on their consistent production.

Chemical processing plant design and operation require accurate values of thermophysical properties. Some of the most important material properties include:

• Vapor pressure ( ) – the pressure exerted by a saturated liquid

vap • Heat of vaporization𝑃𝑃 ( ) – the heat required to convert a liquid to a gas

vap • Isobaric heat capacities𝛥𝛥 𝐻𝐻– the heat required to change a material’s temperature ( for liquids and 𝑙𝑙 𝐶𝐶𝑝𝑝 for ideal gases) 𝑖𝑖𝑖𝑖 𝑝𝑝 𝐶𝐶Vapor pressure is used to determine the size and pressure rating of materials needed for process equipment, such as distillation columns. Heat capacities and heat of vaporization are used to determine heat exchanger duties and other energy-dependent quantities. These properties are functions of temperature and experimental data are often fit to correlations to facilitate design calculations.

, , , and are related thermodynamically. Using these thermodynamic 𝑙𝑙 𝑖𝑖𝑖𝑖 𝑝𝑝 𝑝𝑝 vap vap relations,𝐶𝐶 one𝐶𝐶 ofΔ the𝐻𝐻 properties𝑃𝑃 can be exactly predicted if the other three are known. However, using temperature-dependent correlations causes inaccuracies such that thermodynamic predictions do not match experimental data. In temperature regions where measurements can be

1 easily and accurately made, the thermodynamic relationships can predict properties reasonably well with well-known procedures. Hence, for compounds and regions without accurate experimental data, the use of predictive thermodynamics in calculating these properties is less reliable.

One of the reasons for this uncertainty is that the traditional process for data reduction is to fit the data for each property independent of the others, without regard for the effect of the regression on the other properties. Consider the following example. Data for vapor pressure and liquid heat capacity are available for a compound. The former are usually found at temperatures above the normal boiling point while the latter are taken below the normal boiling point.

Regression of the vapor pressure data is done solely to reduce the error between the higher- temperature data and the correlation. This means the low-temperature behavior is not based on experimental data. Likewise, the liquid heat capacity, low-temperature data are fit to the correlating equation such that the high-temperature behavior is extrapolation. These two properties are related by rigorous thermodynamic relationships, but because each was regressed independently the expected relationship is not seen.

This project fixed this situation by improving agreement between experimental data and thermodynamically predicted data for , , and by developing a regression scheme 𝑙𝑙 vap vap 𝑝𝑝 that simultaneously optimizes the fit for𝑃𝑃 eachΔ 𝐻𝐻of the properties𝐶𝐶 using the interproperty relationships. This was be done by:

1. Gathering and evaluating data in the literature

2. Developing a correct understanding of the temperature dependent shapes of data correlations and

of interrelationships among these properties

3. Finding and recommending best practices

4. Experimentally measuring some properties to improve understanding and fill gaps in data

5. Implementing updated procedures into the Design Institute for Physical Properties (DIPPR)

compound review protocol

The remainder of this document is organized as follows. First, the thermodynamic relationships between these properties are shown. Following this background, correlations and

general literature reviews are written for each property. Then, improvements made by this

project in the multi-property optimization scheme are given in Chapters 5 and 6. A new prediction method for vapor pressure is described in Chapter 6. Experimental measurements are supplied and analyzed in Chapter 7. After that, other database fixes and recommendations are detailed in Chapter 8. Finally, conclusions formed in the course of this project are detailed, and a list of recommendations for future work is given.

2 THERMODYNAMIC RELATIONSHIPS

and both describe phase equilibrium between liquid and vapor. The

vap vap relationship𝑃𝑃 betweenΔ𝐻𝐻 these two properties can by found by equating the changes in Gibbs energy

across phases as shown in the Appendix. This results in the famous Clapeyron equation which

relates the two properties. Specifically, assuming limited vapor association [2], the Clapeyron

equation is:

= (2-1) ( ) 𝑑𝑑𝑃𝑃vap Δ𝐻𝐻vap � � vap liq where is vapor pressure, is the temperature,𝑑𝑑 𝑇𝑇 𝑇𝑇 𝑉𝑉 − 𝑉𝑉is the heat of vaporization, is the

vap vap vap vapor molar𝑃𝑃 volume, is the𝑇𝑇 liquid molar volumeΔ.𝐻𝐻 This equation may also be written𝑉𝑉 in terms

liq of the compressibility𝑉𝑉 of each phase according to:

ln( ) = 1/ ( ) (2-2) 𝑑𝑑 𝑃𝑃vap Δ𝐻𝐻vap � � vap liq where is the vapor compressibility𝑑𝑑 factor𝑇𝑇 and 𝑍𝑍 is− the𝑍𝑍 liquid compressibility factor. This

vap liq project𝑍𝑍 focused on using the first form, though the second𝑍𝑍 form is often seen in literature.

Due to the equilibrium condition between pure vapor and liquid, another relationship may

be written that relates the heat of vaporization to the heat capacities of each phase, specifically:

= (2-3)

𝑑𝑑Δ𝐻𝐻vap vap liq � � 𝐶𝐶𝜎𝜎 − 𝐶𝐶𝜎𝜎 𝑑𝑑 𝑇𝑇

where is temperature and and refer to heat capacities along the saturation curve for vap liq 𝜎𝜎 𝜎𝜎 vapor and𝑇𝑇 liquid, respectively.𝐶𝐶 and𝐶𝐶 differ from and (the values of most interest vap liq 𝑖𝑖𝑖𝑖 𝑙𝑙 𝜎𝜎 𝜎𝜎 𝑝𝑝 𝑝𝑝 to industry and most commonly𝐶𝐶 encountered)𝐶𝐶 in two ways:𝐶𝐶 1) they𝐶𝐶 reflect the change in enthalpy

along the saturation pressure curve, and 2) vapor heat capacity differs from ideal gas heat

capacity due to molecular interactions present in the real gas that are neglected in the ideal gas

model. Correcting for these differences gives [2, 3]:

= 𝑉𝑉𝑉𝑉 + 2 (2-4) vap 𝑖𝑖𝑖𝑖 𝜕𝜕 𝑉𝑉vap 𝜕𝜕𝑉𝑉vap 𝑑𝑑𝑃𝑃vap 𝐶𝐶𝜎𝜎 𝐶𝐶𝑝𝑝 − 𝑇𝑇 � � 2 � 𝑑𝑑𝑑𝑑 �𝑉𝑉vap − 𝑇𝑇 � � � 0 𝜕𝜕𝑇𝑇 𝜕𝜕𝜕𝜕 𝑃𝑃 𝑑𝑑𝑑𝑑

= + (2-5) liq 𝑙𝑙 𝜕𝜕𝑉𝑉liq 𝑑𝑑𝑃𝑃vap 𝐶𝐶𝜎𝜎 𝐶𝐶𝑝𝑝 �𝑉𝑉liq − 𝑇𝑇 � � � 𝑃𝑃 Derivations of these two equations are given in the Appendix.𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑

Substituting these relationships into Equation 2-3 allows us to relate derivatives of vapor

pressure and heat of vaporization to the heat capacities. Specifically, the thermodynamically-

rigorous expression that relates to ideal gas heat capacity, heat of vaporization, and vapor 𝑙𝑙 𝑝𝑝 pressure is: 𝐶𝐶

= 𝑃𝑃vap + (2-6) 2 𝑙𝑙 𝑖𝑖𝑖𝑖 𝜕𝜕 𝑉𝑉vap 𝑑𝑑𝑑𝑑𝐻𝐻vap 𝜕𝜕Δ𝑉𝑉 𝑑𝑑𝑃𝑃vap 𝑝𝑝 𝑝𝑝 2 𝐶𝐶 𝐶𝐶 − 𝑇𝑇 � � � 𝑑𝑑𝑑𝑑 − �Δ𝑉𝑉 − 𝑇𝑇 � �𝑃𝑃� 0 𝜕𝜕𝑇𝑇 𝑑𝑑𝑑𝑑 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑 where is the difference between vapor and liquid molar volumes. This is the key equation

used inΔ this𝑉𝑉 work. This equation allows for each of the involved properties to be simultaneously

optimized when fitting experimental data. When used to calculate , this is called the 𝑙𝑙 𝑝𝑝 Derivative method. 𝐶𝐶

The properties used to find in Equation 2-6 are calculated using the temperature- 𝑙𝑙 𝑝𝑝 dependent correlations listed (Table𝐶𝐶 2-1). The contribution of each of these properties and

respective calculation methods to the Derivative method has been investigated, and will be

given.

Table 2-1: Calculation methods for properties in the Derivative method for finding Symbol Property Primary Method 𝒍𝒍 𝑪𝑪𝒑𝒑 Ideal Gas Heat Derived from statistical mechanics and ab initio generated 𝑖𝑖𝑖𝑖 Capacity vibrational frequencies 𝑝𝑝 𝐶𝐶 Vapor Volume Soave-Redlich Kwong [4] Equation of State using Liquid Volume Inverse of Rackett [5] fit to density experimental points 𝑉𝑉vap 𝑃𝑃vap Heat of Vaporization Watson fit to Clapeyron [2] and experimental points 𝑉𝑉liq Vapor Pressure Riedel [6] predicted or fit to experimental points vap Δ𝐻𝐻 𝑃𝑃vap

3 LITERATURE REVIEW OF THERMOPHYSICAL PROPERTIES

3.1 Vapor Pressure

Of the properties investigated in this work ( , , , ), is the most 𝑙𝑙 𝑖𝑖𝑖𝑖 vap vap 𝑝𝑝 𝑝𝑝 vap commonly measured and the most commonly known.𝑃𝑃 AsΔ shown𝐻𝐻 𝐶𝐶in Chapter𝐶𝐶 𝑃𝑃 2, the derivative of

the correlation is used to obtain , and the derivative of is used to obtain . 𝑙𝑙 vap vap vap 𝑝𝑝 Theref𝑃𝑃 ore, accurate representation of Δthe𝐻𝐻 true behavior acrossΔ the𝐻𝐻 entire range of 𝐶𝐶

vap temperatures (from melting point to critical point)𝑃𝑃 is essential to obtaining the best

thermodynamically consistent derived values for and . As such, care must be taken 𝑙𝑙 vap 𝑝𝑝 when correlating to data to select the proper Δfunctional𝐻𝐻 form𝐶𝐶 of the equation and obtain the

vap best regression. 𝑃𝑃

3.1.1 Vapor Pressure Correlation Equations

Though there are numerous equations in the literature, only a few have gained

vap traction over time. They will be described𝑃𝑃 here with letters as fitting coefficients, as temperature, as reduced temperature, and as the critical𝐴𝐴 −pressure.𝐷𝐷 𝑇𝑇

𝑟𝑟 𝐶𝐶 The first𝑇𝑇 correlation form is the Antoine𝑃𝑃 equation [7], which is the simplest equation

which will be described here. It is derived from an Arrhenius rate equation describing the

equilibrium between vapor and liquid:

= exp + (3-1) + 𝐵𝐵 𝑃𝑃vap �𝐴𝐴 � At very narrow temperature ranges, the Antoine equation𝑇𝑇 works𝐶𝐶 well. In fact, it is common to report Antoine coefficients with vapor pressure data.

The Cox equation is another vapor pressure correlation:

1 = exp 1 exp( + + + ) (3-2) 2 vap 𝐶𝐶 𝑟𝑟 𝑟𝑟 𝑃𝑃 𝑃𝑃 �� − 𝑟𝑟� 𝐴𝐴 𝐵𝐵𝑇𝑇 𝐶𝐶𝑇𝑇 ⋯ � The Riedel equation is the primary vapor𝑇𝑇 pressure correlation within the DIPPR database, and has been around since 1954 [6]:

= exp + + ln( ) + (3-3) 𝐵𝐵 6 𝑃𝑃vap �𝐴𝐴 𝐶𝐶 𝑇𝑇 𝐷𝐷 𝑇𝑇 � It consists of an Antoine fit (parameters and𝑇𝑇 ) with correction terms ( and ) to help the vapor pressure curve extend out from a small𝐴𝐴 temperature𝐵𝐵 region to the whole𝐶𝐶 temperature𝐷𝐷 region from the triple point to the critical point. Traditionally, 6 has been assigned as the exponent on the final temperature term. Riedel also gave a predictive method when he introduced this correlation which will be further detailed in Section 6.2 [6].

The Wagner correlation was introduced in 1973 [8] as:

(1 ) + (1 ) . + (1 ) + (1 ) = exp 1 5 3 6 (3-4) 𝑟𝑟 𝑟𝑟 𝑟𝑟 𝑟𝑟 vap 𝐶𝐶 𝐴𝐴 − 𝑇𝑇 𝐵𝐵 − 𝑇𝑇 𝐶𝐶 − 𝑇𝑇 𝐷𝐷 − 𝑇𝑇 𝑃𝑃 𝑃𝑃 � 𝑟𝑟 � He developed this correlation form after analyzing 𝑇𝑇the statistical significance of different terms when compared to cryogenic data for argon and nitrogen. Others have used this form but with

2.5 and 5 as the last two exponents to fit measured vapor pressure data [9].

Sanjari gave a modified version of the Riedel equation with the exponent on the last temperature term changed from 6 to 2 [10]:

= exp + + ln( ) + (3-5) 𝐵𝐵 2 𝑃𝑃vap �𝐴𝐴 𝐶𝐶 𝑇𝑇 𝐷𝐷 𝑇𝑇 � He found that this form fit vapor pressure data𝑇𝑇 better than Riedel’s original correlation form and

Wagner’s correlation form for 66 of 75 compounds tested. The nine remaining compounds were

light gases like H2 and Ne that were best fit by Wagner’s correlation.

Other correlation forms exist, but none that have gained significant traction over the

vap correlations already𝑃𝑃 given. Of the correlations above, the Riedel and Wagner equation forms

performed best in fitting vapor pressure data for well-known organic compounds.

3.1.2 Vapor Pressure Data Availability

As stated earlier, is the most commonly measured property among those of interest

vap to this work. The most commonly𝑃𝑃 measured point on the curve is the normal boiling point

vap because it is the temperature at which the compound boils𝑃𝑃 at atmospheric pressure. More

complex methods like ebulliometry and calorimetry may be used to measure around and

vap including the normal boiling point. As such, most data are concentrated around𝑃𝑃 the normal

vap boiling point. Several studies have found that measurements𝑃𝑃 at pressures below 1000 Pa contained significant uncertainty [11, 12].

3.2 Heat of Vaporization

Heat of vaporization, a temperature dependent quantity, is the heat required to vaporize a liquid. It is defined as a positive quantity here. Heat of vaporization decreases with increasing temperature until it reaches zero at the critical temperature where the liquid and vapor phases converge. The shape of the decreasing curve varies across chemical types. Functional groups that

hydrogen bond in the liquid phase increase the energy requirement for escape into the vapor

phase.

3.2.1 Heat of Vaporization Correlation Equations

A commonly used empirical, temperature-dependent form for [13] is:

Δ𝐻𝐻vap = (1 ) (3-6) 2 𝐵𝐵+𝐶𝐶𝑇𝑇𝑟𝑟+𝐷𝐷𝑇𝑇𝑟𝑟 +⋯ vap 𝑟𝑟 where are fitting coefficientsΔ𝐻𝐻 and 𝐴𝐴 is the− 𝑇𝑇reduced temperature. A must be positive since

𝑟𝑟 𝐴𝐴is −defined𝐷𝐷 as positive. The thermodynamically𝑇𝑇 derived value of 0 at = 1 is used to

vap 𝐶𝐶 justifyΔ𝐻𝐻 this otherwise empirical equation form. For some hydrogen bonding𝑇𝑇 compounds, more

fitting coefficients are needed to fully capture the shape of a curve derived from vapor pressure.

Although experimental data exist for , it is usually easier to calculate it from , , and

vap vap liq using the thermodynamically-exactΔ𝐻𝐻 Clapeyron equation than to perform experiments𝑃𝑃 𝑉𝑉 (See

vap 𝑉𝑉Equations 2-1 and 2-2).

3.2.2 Heat of Vaporization Data Availability

Much of the data in the literature were derived from other thermophysical

vap properties. Figure 3-Δ1 𝐻𝐻shows the distribution of data points labeled “Experimental” in the DIPPR

database. About a quarter of the “Experimental” data were direct heat of vaporization

measurements, but nearly two thirds of the data were derived or secondhand. Direct calorimetric

measurements, which are usually grouped around room temperature or the normal boiling

vap point,Δ𝐻𝐻 were most commonly gathered before the 1990’s using the adiabatic or bomb calorimetry

[14-17], or Tian-Calvet drop calorimetry [18]. Most of the data gathered within the past couple

of decades are derived. The transpiration method can be used to obtain a vapor pressure correlation from which heat of vaporization is easy to derive [19-21]. Correlation gas

chromatography is another method often employed that also derives heat of vaporization from a

correlation of vapor pressure, but uses gas chromatography instead [22-24]. These derived or

10 secondary approaches are much more common today. Figure 3-2 shows the DIPPR heat of vaporization data for propylene and separates calorimetric data from derived data in the DIPPR database for propylene. Notice that derived data for propylene outnumber direct data nearly 10:1.

This is common for many compounds in the database.

ΔHvap "Experimental" Data in Database (6923)

Experimental (1627)

Clapeyron/Otherwise Derived (1455)

Cited Works (Books/Tables/etc.) (2868)

Other (973)

Figure 3-1: Pie chart of ΔHvap data labeled as “Experimental” in the DIPPR database

2.5

2 ) - 1 1.5

(kJ mol DIPPR Correlation

vap 1 Calorimetric Data ΔH Derived Data 0.5

0 50 100 150 200 250 300 350 400 T/K

Figure 3-2: ΔHvap calorimetric and derived data with the DIPPR correlation for propylene

3.3 Ideal Gas Heat Capacity

The “ideal gas” is a condition that assumes no intermolecular interaction and is useful for

estimating the behavior of compounds in the vapor phase. As with many properties for ideal

gases, heat capacity can be derived using statistical mechanics, as shown in the Appendix, giving

the result:

/ , 7 = + 3𝑚𝑚−5 2 2 Θ𝑣𝑣𝑣𝑣 𝑇𝑇 (3-7) 𝑖𝑖𝑖𝑖 linear Θ𝑣𝑣𝑣𝑣 ( 𝑒𝑒 1) 𝐶𝐶𝑝𝑝 𝑁𝑁𝑁𝑁 � � � Θ𝑣𝑣𝑣𝑣 𝑗𝑗 𝑇𝑇 𝑇𝑇 2 for a linear molecule, and 𝑒𝑒 −

/ , = 4 + 3𝑚𝑚−6 2 Θ𝑣𝑣𝑣𝑣 𝑇𝑇 (3-8) 𝑖𝑖𝑖𝑖 nonlinear Θ𝑣𝑣𝑣𝑣 ( 𝑒𝑒 1) 𝐶𝐶𝑝𝑝 𝑁𝑁𝑁𝑁 � � � Θ𝑣𝑣𝑣𝑣 𝑗𝑗 𝑇𝑇 𝑇𝑇 2 for a nonlinear molecule where is temperature, is the number𝑒𝑒 of− atoms in a single molecule,

and is the vibrational frequency𝑇𝑇 for linear 𝑚𝑚and nonlinear molecules with m atoms, 𝑡𝑡ℎ 𝑣𝑣𝑣𝑣 respectivelyΘ [25]𝑗𝑗 . The vibrational modes may be found from experimental vibrational

𝑣𝑣𝑣𝑣 spectra or from quantum mechanical calculationsΘ using a program such as Gaussian [26]or

NWChem [27]. Once the vibrational modes are obtained, values for the heat capacity may be

generated at any temperature of interest using Equation 3-7 or 3-8.

3.3.1 Ideal Gas Heat Capacity Correlation Equations

Ideal gas heat capacity data may fit to the 4 parameter Aly-Lee correlation [28]:

= + 2 + 2 (3-9) 𝐶𝐶 𝐸𝐸 𝑖𝑖𝑖𝑖 sinh� � cosh� � 𝐶𝐶𝑝𝑝 𝐴𝐴 𝐵𝐵 � 𝑇𝑇 � 𝐷𝐷 � 𝑇𝑇 � 𝐶𝐶 𝐸𝐸 � � � � where are fitting coefficients. In𝑇𝑇 essence, the Aly𝑇𝑇-Lee correlation simplifies the statistical

mechanical𝐴𝐴 − 𝐸𝐸 equations (Equations 3-7 and 3-8) to one internal rotational contribution A, one

vibrational characteristic temperature contribution C, and one electronic contribution E with fitting coefficients B and D. The maximum average deviation for the Aly-Lee correlation for 𝑖𝑖𝑖𝑖 𝑝𝑝 at low temperatures should be <10% assuming the vibrational frequencies found for Equations𝐶𝐶

3-7 and 3-8 are well known [28].

The derived data can also be fit to a 6 parameter equation: 𝑖𝑖𝑖𝑖 𝐶𝐶𝑝𝑝 exp exp exp = + 2 + 2 + 2 (3-10) 𝐶𝐶 𝐶𝐶 𝐸𝐸 𝐸𝐸 𝐺𝐺 𝐺𝐺 𝑖𝑖𝑖𝑖 �exp� �1� �exp� �1� �exp� �1� 𝐶𝐶𝑝𝑝 𝐴𝐴 𝐵𝐵 � 𝑇𝑇 𝑇𝑇 2� 𝐷𝐷 � 𝑇𝑇 𝑇𝑇 2� 𝐹𝐹 � 𝑇𝑇 𝑇𝑇 2� 𝐶𝐶 𝐸𝐸 𝐺𝐺 � � � − � � � � − � � � � − � where are fitting coefficients.𝑇𝑇 This correlation is𝑇𝑇 an expanded version𝑇𝑇 of the Aly-Lee

correlation𝐴𝐴 − 𝐺𝐺that adds an extra vibrational frequency contribution. This correlation works better at

low temperatures compared to the Aly-Lee form because of the added flexibility of that vibrational contribution.

Both of these correlations are simplified versions of Equations 3-7 and 3-8. Simple

polynomials have also been used to fit DIPPR data [29]. However, polynomials are 𝑖𝑖𝑖𝑖 𝑝𝑝 susceptible to interpolation error and extrapolation𝐶𝐶 error outside the temperature region of the data when too many terms are used in the polynomial (“over-fitting” the data).

3.3.2 Ideal Gas Heat Capacity Data Availability

The DIPPR database contains many data which were labeled as “Experimental” that 𝑖𝑖𝑖𝑖 𝑝𝑝 are not from experimental measurements. The𝐶𝐶 2805 data points labeled as “experimental” were

evaluated and the sources were assessed, with results given in Figure 3-3. Over half of the data

were from tables or books—which could not be traced to primary source experiments—and

about a quarter of the data were from a vibrational analysis from an ab initio computational

calculation as described previously. As shown, only 10% of the data were actually experimental,

13 and the experimental data can be broken down into three measurement techniques: calorimetric, speed of sound, and hot wire.

ig Cp "Experimental" Data in Database (2805)

Experimental (289) Unable to Access (314) Vibrational Analysis (751) TRC/Books/Tables (1373) Liquid (47) Other (53)

ig Figure 3-3: Pie chart of Cp data labeled as “Experimental” in the DIPPR database

Calorimetry, speed of sound, and hot wire techniques measure the heat capacity in three different ways. In calorimetry, the heat capacity of a vapor is measured directly to determine how much heat is needed to increase the temperature [30]. In speed of sound measurements, ideal gas heat capacity is found indirectly. First, the ratio of constant pressure and constant volume ideal gas heat capacities is defined:

1 = = 𝑖𝑖𝑖𝑖 2 (3-11) 𝐶𝐶𝑝𝑝 1 𝑣𝑣𝑠𝑠 𝜌𝜌 𝑖𝑖𝑖𝑖 𝛾𝛾 ≡ 𝑔𝑔 𝑣𝑣 𝑅𝑅 𝑃𝑃 𝐶𝐶 − 𝑖𝑖𝑖𝑖 𝐶𝐶𝑝𝑝 where is the universal gas constant, is the constant volume ideal gas heat capacity, as 𝑖𝑖𝑖𝑖 𝑔𝑔 𝑣𝑣 𝑠𝑠 the velocity𝑅𝑅 of sound through the ideal gas,𝐶𝐶 as the density of the gas, and as the pressure𝑣𝑣 of

𝜌𝜌 𝑃𝑃

the system. Rearranging Equation 3-11 gives a method to calculate ideal gas heat capacity from

simultaneous speed of sound, density, and pressure measurements:

= 2 (3-12) 𝑣𝑣𝑠𝑠 𝜌𝜌 𝑖𝑖𝑖𝑖 𝑁𝑁𝑁𝑁 1 𝐶𝐶𝑝𝑝 2 𝑃𝑃 𝑣𝑣𝑠𝑠 𝜌𝜌 − Hot wire measurements combine a transport equation𝑃𝑃 to identify both thermal conductivity and

ideal gas heat capacity simultaneously [31].

As shown in Figure 3-4, about half of the truly experimental data in the DIPPR database were calorimetric, about 40% were from speed of sound measurements, and the remaining 10% were hot wire measurements.

ig Breakdown of True Experimental Cp Data (280)

Calorimetric (130) Speed of Sound (126) Hot Wire (24)

ig Figure 3-4: Pie chart of measurement techniques used for actual experimental Cp data in the DIPPR database

With these experimental data in hand, the performance of the predictive capabilities of

Equations 3-7 and 3-8 were checked. Ideal gas heat capacity values were generated using

quantum mechanical calculations for compounds at temperatures where experimental data exist,

and these values were compared to experimental data. Figure 3-5 shows the results with the % errors plotted as a function of temperature. Most of the quantum mechanical values fell within

10% of the experimental values with a couple of exceptions, as circled in the figure. N2O4 had the greatest deviation, but that was because the compound decomposed into two NO2 molecules.

C2F5H had the second greatest deviation, but another experimental data set covered the same

temperature range with less than 2% difference from the ab initio values. (CF2H)2O had the next

most error, followed by Cl2, HCN, and CF3H. Notice that for all of these, the ab initio values

were too high.

For further analysis, the erroneous data sets described for N2O4 and C2F5H were

removed, and a histogram of the remaining error values is given in Figure 3-6. The data skew

towards positive error, but 88% of the data were contained within the DIPPR assigned

uncertainty of 10%. This means that quantum mechanical calculations will generate values for

slightly larger than, but within 10% of, the real values. 𝑖𝑖𝑖𝑖 𝑝𝑝 𝐶𝐶

80% 70% 60% N2O4

Error 50% 40% C2F5H 30% (CF2H)2O 20% Cl2 HCN 10% CF3H

Quantum Mechanical Quantum 0% 100 200 300 400 500 600 -10% -20% T/K Calorimetric Data Hot Wire Data Speed of Sound Data

ig Figure 3-5: Quantum mechanical calculation error versus temperature for Cp compared to true experimental data in the literature

140

120

100

40 Number of DataNumber Points 20

0 <-20% -20 - 15% -15 - 10% -10 - 5% -5 - 0% 0 - 5% 5 - 10% 10 - 15% 15 - 20% >20% Quantum Mechanical Error Bins

ig Figure 3-6: Error distribution for quantum mechanical values compared to experimental Cp data

3.4 Liquid Heat Capacity

Due partially to size and intermolecular interactions, some molecules absorb more heat than others when exposed to heat and raised to the same temperature. describes this difference 𝑙𝑙 𝑝𝑝 by quantifying the amount of heat required to increase the temperature𝐶𝐶 of 1 mole of a liquid-

phase compound by 1 K in temperature. As the temperature increases, the ability to absorb more

heat also increases since the population of excited states changes.

At the most basic mathematical level described above, heat capacity is defined by the change in isobaric enthalpy for a change in temperature, or the slope of the enthalpy-temperature curve, where enthalpy is the sum of internal energy and the product of pressure and volume. As a convention, is defined at 101,325 Pa from the triple point to the normal boiling point, since 𝑙𝑙 𝑝𝑝 the correction𝐶𝐶 of saturation pressure to atmospheric pressure is negligible (See Chapter 2). Above

the normal boiling point, is defined at the vapor pressure. As the temperature approaches the 𝑙𝑙 𝑝𝑝 critical temperature, approaches𝐶𝐶 to positive infinity. 𝑙𝑙 𝐶𝐶𝑝𝑝 17

3.4.1 Liquid Heat Capacity Temperature Behavior

Liquid heat capacity exhibits a wide variety of temperature-dependent behavior. As such,

the liquid heat capacity curve shape can be difficult to predict in the absence of experimental

data. A corresponding states method has been developed that has been shown to work well [2] in

certain regions. Beyond that, the actual shape of the temperature-dependent liquid heat capacity

curve can vary widely.

Figure 3-7 shows the liquid heat capacity data and DIPPR correlations for n-butane, 1-

butene, 1-propanol, and ethylene glycol. All of these compounds are about the same size, but 1-

butene contains a double bond, 1-propanol contains an alcohol group instead of a carbon, and

ethylene glycol contains two alcohol groups in place of carbon atoms. Using n-butane as a baseline for the curve shape, 1-butene curls up at its triple point (87.8 K), 1-propanol crosses through all the other compounds’ data, and ethylene glycol contains a strong inflection point around its normal boiling point (470.38 K) before curling up at its critical point (719 K).

Intermolecular interactions cause this change in shape since other alkenes, alcohols, and glycols exhibit the same shapes [9, 32-37]. This is why it is important to understand where the experimental data exist, and how to correctly predict liquid heat capacity in temperature regions where there are no experimental data.

Experimental data are much more common from the triple point to the normal boiling 𝑙𝑙 𝑝𝑝 point than from the normal𝐶𝐶 boiling point to the critical point. When such data are available, the

Derivative method should match the experimental data well in that temperature region. At the

start of this project, however, the Derivative method tended to undershoot experimental data as

shown in Figure 3-8 for propylene. In 2013, the Derivative method was not used above the

18 normal boiling point, so the Derivative method curve in Figure 3-8 stops before the end of the

DIPPR correlation. As is shown in later chapters, this research reconciled these differences.

Butane Correlation 3.5 1-Butene Correlation

) 1-Propanol Correlation - 1

K 3

- 1 Ethylene Glycol Correlation

(Jg Butane Data l

p 2.5 C 1-Butene Data 1-Propanol Data 2 Ethylene Glycol Data

1.5 50 150 250 350 450 550 650 T/K

l Figure 3-7: Cp data and DIPPR correlations for butane, 1-butene, 1-propanol, and ethylene glycol 150 140 Experimental Data 130 DIPPR Correlation 120 Derivative Method (2013) ) 1 -

K 110 1 - 100 (J mol l

p 90 C 80 70 60 50 75 125 175 225 275 325 375 T/K

l Figure 3-8: Cp Data and DIPPR correlation for propylene, along with the Derivative method prediction from the start of this project

3.4.2 Liquid Heat Capacity Data Availability

Liquid heat capacity is most commonly measured near the triple point. Adiabatic

calorimetry [38, 39] and differential scanning calorimetry [40, 41] are the most common

techniques for measuring liquid heat capacity. As with most experimental methods, these

techniques are most easily performed at atmospheric pressure. Above the normal boiling point,

the material vaporizes, so pressure needs to be added to the experimental setup, and the

compound in the vapor phase needs to be accounted for [42]. Since high temperature measurement is difficult, it is much less common than measurements below the normal boiling point. Above the normal boiling point, saturated heat capacity is measured instead of constant pressure heat capacity. In order to compare these literature values to a Derivative method prediction, the data must be converted to isobaric heat capacity using:

= + (3-13) 𝑙𝑙 liq 𝜕𝜕𝑉𝑉liq 𝑑𝑑𝑃𝑃vap 𝐶𝐶𝑝𝑝 𝐶𝐶𝜎𝜎 �𝑇𝑇 � � − 𝑉𝑉liq� 𝜕𝜕𝜕𝜕 𝑃𝑃 𝑑𝑑𝑑𝑑 where is the data point from literature, is the liquid volume, and is the vapor liq 𝜎𝜎 liq vap pressure.𝐶𝐶 A derivation of Equation 3-13 is given𝑉𝑉 in the Appendix within a𝑃𝑃 derivation of the

Derivative method.

3.5 Analysis of Experimental Data and Correlations

A qualitative description of the data available for vapor pressure, heat of vaporization,

ideal gas heat capacity, and liquid heat capacity is given by Figure 3-9. In this figure, the x-axis is the reduced temperature, and the y-axis indicates the frequency of data available at each temperature. The vertical line represents the normal boiling point, and the other lines indicate data-temperature availability of the vapor pressure, heat of vaporization, and liquid heat capacity.

Several important observations may be made from this figure. First, compounds most frequently contain experimental vapor pressure data around the normal boiling point. Second, enthalpy (or heat) of vaporization data occur with less frequency than vapor pressure data, but are also centered near the normal boiling point. Third, most compounds have no experimental ideal gas heat capacity data. Fourth, liquid heat capacity data are fairly common near the triple point but less as the normal boiling point is approached.

The uncertainties for each property can be described as the inverse of Figure 3-9. Vapor pressure contains the lowest uncertainty at the normal boiling point and increases in both directions toward the triple point and critical point. Heat of vaporization is sometimes known experimentally at the normal boiling point, but is zero by definition at the critical point.

Generally, heat of vaporization isn’t known very well away from the critical point. Ideal gas heat capacity is generally derived with about 10% uncertainty at all temperatures. Liquid heat capacity uncertainty is lowest below the normal boiling point and gradually increases until the critical point, where liquid heat capacity is indeterminate.

More Frequent Vapor Pressure Heat of Vaporization Liquid Heat Capacity Normal Boiling Point

Less Frequent

0 Reduced Temperature 1

Figure 3-9: A qualitative look at the relative frequency of experimental data for vapor pressure, heat of vaporization, and liquid heat capacity around the normal boiling point

These properties can be optimized in a couple of ways, both revolving around the vapor

pressure correlation. One way is to minimize an objective function with temperature dependent

weighting. This allows the user to build uncertainty in measurements into the optimization.

Another way is to find the best vapor pressure correlation form to fit the data, which can be done

easily using the Riedel equation. These two multi-property optimization methods will be discussed in further detail in Chapters 4 and 5.

4 MULTI-PROPERTY OPTIMIZATION – TEMPERATURE DEPENDENT

ERRORS

This work has been published in Fluid Phase Equilibria and will be summarized here

[43]. As has been shown qualitatively in Figure 3-9, the availability and accuracy of

experimental data for the different thermophysical properties vary widely over the temperature

region from the triple point to the critical point. This perspective can be used are most likely to

be trustworthy, and which data are less reliable. Next, the mathematical methodology will be

discussed.

4.1 Weight Model

An optimization process was setup as a sum of weighted sum squared errors, with each

given by

( , ) ( ) = 2 (4-1) 𝑖𝑖 𝑖𝑖 𝑖𝑖 𝐽𝐽 𝐴𝐴 𝑇𝑇 − 𝐽𝐽 𝑆𝑆𝑆𝑆𝑆𝑆 𝐴𝐴 � �𝑤𝑤 𝑖𝑖 � 𝑖𝑖 𝐽𝐽 with as the weight of data point , ( , ) as the predicted property with optimization

𝑖𝑖 𝑖𝑖 parameters𝑤𝑤 at temperature , and𝑖𝑖 𝐽𝐽 as𝐴𝐴 the𝑇𝑇 th experimental data point𝐽𝐽 of property . The choice

𝑖𝑖 𝑖𝑖 of can greatly𝐴𝐴 affect the optimized𝑇𝑇 𝐽𝐽 fit. This𝑖𝑖 weighting can be chosen to emphasize𝐽𝐽 the fitting of certain𝑤𝑤 properties. For example, a large weight for compared to the weights of and

vap vap would ensure that data are fit well. However, 𝑃𝑃using one constant weighting forΔ each𝐻𝐻 𝑙𝑙 𝑝𝑝 vap property𝐶𝐶 is not entirely𝑃𝑃 reasonable when trying to find the multi-property optimal fit. For actual

measurements of small organic compounds, is very well known at temperatures around the

vap normal boiling point. Likewise, at the critical𝑃𝑃 point, is generally known because of the

vap prediction methods that have been developed for compounds𝑃𝑃 that do not thermally decompose.

For these temperature regions, for should be large. However, at very low temperatures

vap and pressures, say 100 Pa, accurate𝑤𝑤 measu𝑃𝑃 rements are much more difficult, so lower weight

should be given to those data.

Two schemes for were used for the optimizations done here: constant for each sum

of squared error, and temperature𝑤𝑤 -dependent for each sum of squared error. Table𝑤𝑤 4-1

summarizes the constant scheme which places𝑤𝑤 equal emphases on and . The 𝑙𝑙 vap 𝑝𝑝 temperature-dependent 𝑤𝑤 models were given as Lagrange polynomials𝑃𝑃 which𝐶𝐶 run through

rel assigned at different temperatures,𝜖𝜖 resulting in the curves given in Figure 4-1 which reflect the

true nature𝑤𝑤 of the uncertainty in , , and from the triple point to the critical point. In 𝑙𝑙 vap vap 𝑝𝑝 other words, , , and are𝑃𝑃 areΔ𝐻𝐻 given larg𝐶𝐶er weight in temperature regions where they 𝑙𝑙 vap vap 𝑝𝑝 are known with𝑃𝑃 higherΔ𝐻𝐻 certainty. For𝐶𝐶 and , this is around the normal boiling point. For

vap vap , this is below the normal boiling point.𝑃𝑃 Δ𝐻𝐻 𝑙𝑙 𝑝𝑝 𝐶𝐶 Table 4-1: Summary of the sum squared errors used in the multi-property optimization J Method Data Fitting 100 Clapeyron 33𝒘𝒘 𝑃𝑃vap Derivative Method 100 Δ𝐻𝐻vap 𝒍𝒍 𝐶𝐶𝑝𝑝

150

100 Vapor Pressure

w Heat of Vaporization 50 Liquid Heat Capacity Normal Boiling Point 0 0 1 Tr

Figure 4-1: Temperature dependent weight model used in the multi-property optimization for vapor pressure, heat of vaporization, and liquid heat capacity around the normal boiling point

Propylene can be used as a case study. Below the normal boiling point, propylene has

very small vapor pressures, culminating in the triple point pressure recommended by DIPPR,

, of 0.00117 Pa. To be able to measure a vapor pressure within 20% of 10-4 Pa would be a

TP decided𝑃𝑃 success. To echo this optimistic view, the weight at for was 100/20, or 5.

TP vap vap is rarely directly measured, but if it is, it is measured around 𝑇𝑇 with𝑃𝑃 much more error awayΔ𝐻𝐻

NB from . Hence, the weight at is highest, and decreases𝑇𝑇 towards both and . is 𝑙𝑙 NB NB TP c 𝑝𝑝 commonly𝑇𝑇 measured to 𝑇𝑇, but above , it must be converted from 𝑇𝑇 , introducing𝑇𝑇 𝐶𝐶

TP NB NB sat progressively larger potential𝑇𝑇 𝑇𝑇 error up to .𝑇𝑇 Thus, the weight is around 100𝐶𝐶 up to , and

c NB shrinks to 40 towards . 𝑇𝑇 𝑇𝑇

𝑇𝑇c 4.2 Results/Discussion

The DIPPR expression was used to predict and through the Clapeyron 𝑙𝑙 vap vap 𝑝𝑝 equation and the Derivative𝑃𝑃 method, giving a “starting fit.”Δ𝐻𝐻 This prediction𝐶𝐶 was compared to

optimizations of the Riedel and Wagner expressions with the constant and temperature

vap dependent weightings given in the previous𝑃𝑃 section. For convenience, these correlation forms are

given here with simplified symbols:

R1: = exp + + ln( ) + (4-2) 𝐵𝐵 1 𝑃𝑃vap �𝐴𝐴 𝑇𝑇 𝐶𝐶 𝑇𝑇 𝐷𝐷𝑇𝑇 � R2: = exp + + ln( ) + (4-3) 𝐵𝐵 2 𝑃𝑃vap �𝐴𝐴 𝑇𝑇 𝐶𝐶 𝑇𝑇 𝐷𝐷𝑇𝑇 � R6: = exp + + ln( ) + (4-4) 𝐵𝐵 6 vap 𝑃𝑃 �𝐴𝐴 (𝑇𝑇 𝐶𝐶) ( 𝑇𝑇 ) . 𝐷𝐷𝑇𝑇( � ) . ( ) = exp W2: 1 5 2 5 5 (4-5) 𝐴𝐴 1−𝑇𝑇𝑟𝑟 +𝐵𝐵 1−𝑇𝑇𝑟𝑟 +𝐶𝐶 1−𝑇𝑇𝑟𝑟 +𝐷𝐷 1−𝑇𝑇𝑟𝑟 vap 𝑐𝑐 𝑇𝑇𝑟𝑟 𝑃𝑃 𝑃𝑃 � ( ) ( ) . ( ) ( ) � = exp W3: 1 5 3 6 (4-6) 𝐴𝐴 1−𝑇𝑇𝑟𝑟 +𝐵𝐵 1−𝑇𝑇𝑟𝑟 +𝐶𝐶 1−𝑇𝑇𝑟𝑟 +𝐷𝐷 1−𝑇𝑇𝑟𝑟 𝑃𝑃vap 𝑃𝑃𝑐𝑐 � 𝑇𝑇𝑟𝑟 � where are fitting coefficients. Note that R1, R2, and R6 only differ by the final exponent.

For future𝐴𝐴 − reference,𝐷𝐷 this exponent will be symbolized as so that R1 can also be described as a

Riedel correlation with = 1, R2 as a Riedel correlation 𝐸𝐸with = 2, and R6 as a Riedel

correlation with = 6. 𝐸𝐸The data used in this process are referenced𝐸𝐸 in [43]. For each

vap correlation, the temperature𝐸𝐸 dependent weight did better than the constant temperature𝑃𝑃 weight optimizations at matching the experimental data, even though the constant temperature weight 𝑙𝑙 𝑝𝑝 scheme gave and equal𝐶𝐶 weights. 𝑙𝑙 vap 𝑝𝑝 To compare𝑃𝑃 these𝐶𝐶 fits, the average absolute deviation (AAD) was used as defined by:

1 ( ) = (4-7) 𝐽𝐽𝑖𝑖 − 𝐽𝐽̂ 𝑇𝑇𝑖𝑖 𝐴𝐴𝐴𝐴𝐴𝐴 � � 𝑖𝑖 � 𝑁𝑁 𝑖𝑖 𝐽𝐽 where is the experimental value for the property (vapor pressure, heat of vaporization, or liquid

𝑖𝑖 heat capacity),𝐽𝐽 ( ) is the model prediction for the property at temperature , and is the

𝑖𝑖 𝑖𝑖 number of experimental𝐽𝐽̂ 𝑇𝑇 points for that property. The AAD’s of the “starting𝑇𝑇 fit” and𝑁𝑁 each

optimized correlation with the temperature dependent weight from experimental data were

compared in Figure 4-2. The R6 temperature dependent weight optimization did worse than R1

and R2, and the W2 and W3 temperature dependent weight optimizations performed about

equally for propylene.

14 12 Starting Fit 10 Riedel: E=1 8 Riedel: E=2 6

AAD (%) Riedel: E=6 4 Wagner: 2.5,5 2 Wagner: 3,6 0 Vapor Pressure Heat of Vaporization Liquid Heat Capacity

Figure 4-2: Average absolute deviation (AAD) for propylene across vapor pressure, heat of vaporization, and liquid heat capacity data with the starting fit, the R1 fit, the R2 fit, the R6 fit, the W2 fit, and the W3 fit with temperature dependent weights

Of all the correlation forms, it appears that using the temperature dependent weight on

the R2 correlation gives the best fit for propylene. The optimized R2 correlation and

vap predicted and correlations through the Clapeyron equation and𝑃𝑃 Derivative method are 𝑙𝑙 vap 𝑝𝑝 given for propyleneΔ𝐻𝐻 in𝐶𝐶 Figure 4-3. In this optimization, the curve was allowed to deviate

vap from data at low temperatures to accommodate data𝑃𝑃. This tradeoff can be justified when 𝑙𝑙 vap 𝑝𝑝 the accuracy𝑃𝑃 of low temperature data are suspect𝐶𝐶 and the uncertainties of data are low at 𝑙𝑙 vap 𝑝𝑝 low temperatures. Additionally, the𝑃𝑃 curve changed significantly towards𝐶𝐶 (which

vap TP occurs as = 0.24) from the initialΔ Clapeyron𝐻𝐻 expression. 𝑇𝑇

𝑟𝑟 This𝑇𝑇 optimization was done with the same temperature dependent weighting for four

other compounds (propane, pentane, hexafluoroethane, and ammonia) using the data given in

[43], and the averages of the absolute average deviations (AAD) as defined by:

+ + (4-8) Average AAD = l vap 3 vap p 𝐴𝐴𝐴𝐴𝐷𝐷P 𝐴𝐴𝐴𝐴𝐷𝐷ΔH 𝐴𝐴𝐴𝐴𝐷𝐷C

are given for the expressions in Equations 4-2 through 4-6. For each of these compounds,

vap the “starting fit” refers𝑃𝑃 to the vapor pressure correlation fit using only experimental data.

vap Generally, the optimized correlations did not fit data as closely𝑃𝑃 as the “starting fits,”

vap vap but when used with the Clapeyron𝑃𝑃 equation and Derivative𝑃𝑃 method, the correlations fit

vap and much better. 𝑃𝑃 𝑙𝑙 vap 𝑝𝑝 Δ𝐻𝐻 𝐶𝐶

5 a) 20 b) 4 Data 15 3 10

(MPa) Starting Correlation 2 ) (ln(Pa)) 5 vap vap P Optimized 0 1 P Correlation ln( -5 0 -10 0 0.5 1 0 2 4 6 Tr 1/Tr 30 250 ) 1 -

25 c) ) (d) 1 - 200 20 K 1 - 15 (kJ mol 150 (J mol vap 10 l p H 100 C

Δ 5 0 50 0 0.5 1 0 0.5 1 Tr Tr Figure 4-3: Experimental data for propylene with the starting and optimized Riedel 2 fits for (a) vapor pressure, (b) natural log of vapor pressure, (c) heat of vaporization, and (d) liquid isobaric heat capacity

Notably, the R6 expression did the worst of any of the expressions for each of the

compounds studied. The choice of final exponent in the Riedel correlation, , greatly affects the

ability of the vapor pressure curve to be consistent with the other properties.𝐸𝐸 The correlation

vap used must be flexible enough to accommodate data at low temperature, so the 𝑃𝑃type of 𝑙𝑙 𝐶𝐶𝑝𝑝 28

correlation chosen will influence the ability of to be thermodynamically consistent with

vap and data. The predicted triple point pressures𝑃𝑃 are given for the optimized correlation 𝑙𝑙 vap 𝑝𝑝 Δwith𝐻𝐻 the lowest𝐶𝐶 average AAD for each of these compounds in Table 4-2.

7 Start Riedel: E=1 6 Riedel: E=2 Riedel: E=6 5 Wagner: 2.5,5 Wagner: 3,6 4

Average AAD (%) Average 2

0 Propylene Propane Pentane Hexafluoroethane Ammonia

l Figure 4-4: The average AAD from Pvap, ΔHvap, and Cp using the starting fit to Pvap data only and the optimized R1, R2, R6, W2, and W3 fits for the five compounds studied

Table 4-2: Optimized vapor pressure correlations with triple point pressures Compound ( ) ( ) Correlation A B C D Propylene 87.89 6.72×10-4 R2 63.335 -3550.3 -6.7797 1.3053×10-5 𝑻𝑻𝑻𝑻 𝑻𝑻𝑻𝑻 Propane 𝑻𝑻85.47𝑲𝑲 1.70×10𝑷𝑷 𝑷𝑷𝑷𝑷-4 R2 59.477 -3498.8 -6.1377 1.1167×10-5 Pentane 143.42 7.51×10-2 W3 -7.5454 2.1047 -3.6957 -1.0530 Hexafluoroethane 173.1 2.64×104 W2 -7.3650 1.8621 -2.2999 -2.7328 Ammonia 195.41 6.07×103 R2 69.276 -4343.7 -7.3461 1.0858×10-5

4.3 Conclusions

A multi-property optimization was created that enhanced the shape of the curve to

vap be more thermodynamically consistent with and data. The motivation for𝑃𝑃 developing 𝑙𝑙 vap 𝑝𝑝 an optimization was introduced with the ofΔ𝐻𝐻 propylene.𝐶𝐶 The weight model used in the 𝑙𝑙 𝑝𝑝 𝐶𝐶 29

optimization was discussed, with the best results coming from a temperature dependent model

for each property that quantifies the degree to which each property is accurate at each

temperature.

Three forms of the Riedel expression and two forms of the Wagner expression

vap vap were optimized for five compounds:𝑃𝑃 propylene, propane, pentane, hexafluoroethane,𝑃𝑃 and

ammonia. Of the Riedel expressions, R6 performed the worst, and R2 seemed to perform the

best, leading to a discussion of the parameter in the Riedel equation. The two Wagner

expressions performed about as well𝐸𝐸 as R2. The best optimized curve for propylene

vap changed significantly towards the triple point temperature. TheseΔ 𝐻𝐻optimizations changed the

vap expression for each compound to fit more accurate data, whether it be , , or based𝑃𝑃 𝑙𝑙 vap vap 𝑝𝑝 on the temperature for propylene, propane, pentane, hexafluoroethane, 𝑃𝑃and ammonia.Δ𝐻𝐻 From𝐶𝐶 these

optimizations, new thermodynamically consistent triple point pressures and expressions

vap were found that can be used in process design with these chemicals. 𝑃𝑃

5 MULTI-PROPERTY OPTIMIZATION – THE RIEDEL EQUATION

Upon completing the previous work comparing the Riedel correlation with the coefficient set to 1, 2, or 6, the overall effect of the coefficient on the vapor pressure 𝐸𝐸fit was further investigated. The Riedel correlation was generalized𝐸𝐸 to the form:

= exp + + ln( ) + (5-1) 𝐵𝐵 𝐸𝐸 𝑃𝑃vap �𝐴𝐴 𝐶𝐶 𝑇𝑇 𝐷𝐷𝑇𝑇 � and the parameter was changed in integer steps𝑇𝑇 from 1 to 6. The ability of those vapor pressure expressions𝐸𝐸 to predict liquid heat capacity data for many compounds was assessed.

5.1 Methods

The multi-property optimization proposed here involves fitting experimental data for vapor pressure and liquid heat capacity to Equations 2-1 and 2-6, respectively, using the generalized Riedel equation with different values. The experimental data were obtained from the DIPPR database [44]. Seven different chemical𝐸𝐸 families were used — n-alkanes, 2-methyl alkanes, 1-alkenes, n-aldehydes, aromatics, ethers, and ketones, with specific compounds listed in Table 5-1 for the hydrocarbons and Table 5-2 for the non-hydrocarbons. By changing , the heat of vaporization derived through the Clapeyron equation was changed at low temperatures.𝐸𝐸

However, there exist few experimental heat of vaporization data in the low temperature range to provide sufficient insight because most heat of vaporization values are derived through the

Clapeyron equation from a fit of experimental vapor pressure data. Therefore, vapor pressure and

liquid heat capacity data were used to determine the best fit for .

Although the thermodynamic procedure is rigorous, preliminary𝐸𝐸 analysis showed that

alcohols and other strongly hydrogen bonding families were not well identified using this

particular method. Previous studies have shown that extra terms can be added to the Riedel form

to improve the fit of alcohols [45], or that another equation form should be used altogether [46].

Other studies suggest changes to the cubic equation of state for compounds that dimerize in the vapor phase [47-49]. Due to these complications, strongly hydrogen bonding families were omitted from the current study.

Table 5-1: A list of hydrocarbons investigated in this study, grouped by chemical family n-Alkanes 2-Methyl Alkanes 1-Alkenes n-Aldehydes Aromatics Ethane Isobutane Propylene Butanal Benzene Propane 2-Methyl Butane 1-Butene Propanal Toluene Butane 2-Methyl Pentane 1-Pentene Pentanal Ethylbenzene Pentane 2-Methyl Hexane 1-Hexene Hexanal Propylbenzene Hexane 2-Methyl Heptane 1-Heptene Butylbenzene Heptane m-Xylene Octane o-Xylene p-Xylene

Table 5-2: A list of non-hydrocarbons investigated in this study, grouped by chemical family Ethers Ketones Dimethyl Ether Methyl Ethyl Ketone Diethyl Ether Methyl Isopropyl Ketone Ethyl Propyl Ether Methyl Isobutyl Ketone Di-n-Propyl Ether 2-Pentanone Methyl t-Butyl Ether 2-Hexanone 2-Heptanone 2-Octanone

A summary of the data for the vapor pressure and liquid heat capacity data for these

compounds are detailed in the Appendix.

The number of vapor pressure data points was usually more than double that of the heat

capacity data points for each compound. However, the vapor pressure data were composed

mostly of higher-temperature data while the heat capacity data were usually in the lower

temperature range, and often extended down to the triple point. Herein lies the strength of this

analysis—the liquid heat capacity data can be used to influence the second derivative of the

vapor pressure curve in a region where there is little to no experimental vapor pressure data.

Alternatively, if is known for a chemical family, then the ability to predict liquid heat capacity

from vapor pressure𝐸𝐸 would be more accurate.

Another advantage of the method is also related to the data. Experimental vapor pressure

data are limited and uncertain at subambient pressures [50, 51]. It has been repeated that

uncertainty in vapor pressure experimental data increases from as low as 0.00001% at 105 Pa to

at least 100% at 1 Pa. To circumvent the dearth and uncertainty of vapor pressure data, Perkins

et. al. [52] measured heat capacity to influence the vapor pressure equation for propane. Duarte-

Garza and Magee [50] used internal energy changes in the two phase region to derive vapor pressure for three refrigerants. They even checked the thermodynamic consistency of a previously published equation of state and re-evaluated the uncertainties of previously reported

subambient vapor pressures. Poling [45] also checked the efficacy of different vapor pressure

equation forms using vapor pressure and calorimetric data simultaneously, finding that heat

capacity data dominate the lower temperature region and vapor pressure data dominate the high

temperature region.

This project sought to use available heat capacity data to influence the vapor pressure fit,

since heat capacity can be measured with a comparatively high degree of accuracy. Low

temperature liquid heat capacity data were used to select the vapor pressure correlation form.

For each compound, the vapor pressure data were fitted to Equation 5-1 by a least squares

regression for a given value of ranging from 1 to 6 in integer values and for = 0.5. This

correlation was then used to obtain𝐸𝐸 the heat of vaporization through Equation 2𝐸𝐸-1, which was

then used in Equation 2-6 to generate a correlation for liquid heat capacity. The resulting liquid

heat capacity correlations obtained with each value of were then compared to liquid heat

capacity experimental data. 𝐸𝐸

As stated previously, the vapor volumes were calculated with the Soave-Redlich-Kwong

(SRK) equation of state [4], and the liquid volumes were calculated from the liquid density

correlations given in the DIPPR database [44]. The ideal gas heat capacities used in Equation 2-6 were calculated from vibrational frequencies generated by ab initio methods with appropriate scaling factors for the basis sets and levels of theory used.

5.2 Results

As mentioned above, the first step in the optimization was to fit the vapor pressure data to

Equation 5-1 with different values of . Table 5-3 shows the absolute average deviation between the resulting correlations and the data 𝐸𝐸for n-butane for = 1 through 6. Notice that changing has little effect on the absolute average deviation ( 𝐸𝐸) of the fit. 𝐸𝐸

𝐴𝐴𝐴𝐴𝐴𝐴

Table 5-3: Absolute average deviation of Equation 5-1 fit to vapor pressure data for n-butane while varying E n-Butane E=1 E=2 E=3 E=4 E=5 E=6 Pvap AAD 0.340% 0.328% 0.326% 0.331% 0.345% 0.367%

Next, heat of vaporization was derived using the Clapeyron equation for each value of ,

which are shown in Figure 5-1 for n-butane as temperature-dependent lines. The triple point 𝐸𝐸

occurs at = 0.33. Even for a compound such as n-butane, there exist few actual experimental

𝑟𝑟 heat of vaporization𝑇𝑇 data points, with one point given in Figure 5-1 [53].

In the case of n-butane, the lowest experimental vapor pressure data point was at =

𝑟𝑟 0.45. Below this temperature, the different predictions of heat of vaporization fan out 𝑇𝑇 considerably. As increases, the heat of vaporization curves dip lower at low temperatures.

Specifically, from𝐸𝐸 = 0.33 to = 0.5, the higher the value of the lower the value of the

𝑟𝑟 𝑟𝑟 heat of vaporization𝑇𝑇 at a given temperature.𝑇𝑇 However, this difference𝐸𝐸 does not occur in the

temperature range where experimental heat of vaporization data exist. In this instance, there was only one calorimetrically determined heat of vaporization data point for n-butane. Other n-

alkanes, 2-methylalkanes, n-aldehydes, 1-alkenes, ethers, ketones, and aromatics tested in this

work gave similar results and had few experimental heat of vaporization data points. Therefore, comparing heat of vaporization data to the Clapeyron derived curves provided little insight in choosing the best value for .

Finally, liquid heat capacity𝐸𝐸 was derived from vapor pressure and heat of vaporization using the Derivative Method (Equation 2-6) for each value of , as shown in Figure 5-2 for n- butane as temperature-dependent lines. Experimental data from𝐸𝐸 multiple sources are depicted as points. As increases, the predicted liquid heat capacity curves dips lower at low temperatures.

Specifically,𝐸𝐸 from = 0.33 to = 0.6, the higher the value of , the lower the value of the

𝑟𝑟 𝑟𝑟 heat capacity at a given𝑇𝑇 temperature.𝑇𝑇 The best fit to the data occurs𝐸𝐸 for = 2.

𝐸𝐸

28 temperature range of vapor pressure data ) 1 - 26 E=1 E=2 (kJ mol(kJ

vap 24 E=3 H

Δ E=4 E=5 22 E=6 Experimental Data 20 0.3 0.4 0.5 0.6 0.7 0.8 Tr

Figure 5-1: Heat of vaporization experimental data and Clapeyron equations using the Riedel equation with E = 1 through with the temperature range of vapor pressure data shown

𝟔𝟔 Also depicted in Figure 5-2 is an indication of the temperature range for the experimental

vapor pressure data. In the case of n-butane, the lowest experimental vapor pressure data point

was for = 0.45. Below this temperature, the different predictions of liquid heat capacity fan

𝑟𝑟 out considerably.𝑇𝑇 However, the fanning out actually begins at higher temperatures

(approximately = 0.6) where adequate experimental data exist. Other n-alkanes,

𝑟𝑟 2-methylalkanes,𝑇𝑇 n-aldehydes, 1-alkenes, aromatics, ethers, and ketones tested in this work gave

similar results. This is evidence that using the incorrect value for , even if experimental data for

the vapor pressure are available, can drastically affect properties based𝐸𝐸 on vapor pressure despite

the vapor pressure correlation itself appearing statistically accurate (See Table 5-3 for n-butane).

In order to determine if an optimal value exists, an analysis similar to what was just

presented for n-butane was performed for all𝐸𝐸 of the n-alkanes, 2-methylalkanes, 1-alkenes, n-

aldehydes, aromatics, ethers, and ketones listed in Table 5-1 and Table 5-2. The results are

contained in Figure 5-3 through Figure 5-9. Figure 5-3a through Figure 5-9a contain the absolute

average deviations ( ) between the experimental vapor pressure data and the fit to the Riedel

equation for = 0.5𝐴𝐴𝐴𝐴𝐴𝐴6. Similarly, Figure 5-3b through Figure 5-9b give the ’s between

the experimental𝐸𝐸 values− for liquid heat capacity and those predicted using Equation𝐴𝐴𝐴𝐴𝐴𝐴 2-6. Figure

5-3 is for the n-alkanes, Figure 5-4 for the 2-methylalkanes, Figure 5-5 for the 1-alkenes, Figure

5-6 for the n-aldehydes, Figure 5-7 for the aromatics, Figure 5-9 for the ketones, and Figure 5-8 for the ethers.

160

150 temperature range of vapor pressure data

140 ) 1 - K

1 Experimental Data - 130 E=1 mol

(J 120 E=2 l p

C E=3 110 E=4 100 E=5 E=6 90 0.3 0.4 0.5 0.6 0.7 0.8 Tr

Figure 5-2: Liquid heat capacity data and Derivative method predictions from the Riedel equation with E = 1 through 6 with the temperature range of vapor pressure data shown

While the best values for the vapor pressure fits vary from 0.5 to 6, the best values for the liquid heat capacity𝐸𝐸 range from 1 to 3, with 2 as the overall best performer for n𝐸𝐸-alkanes,

2-methyl alkanes, 1-alkenes, aromatics, and ether. For the n-aldehydes and ketones, an value from 1 to 3 generally gives the best heat capacity fit. Additionally, the absolute average𝐸𝐸 deviations do not increase by more than 0.5% for the vapor pressure fit, but the absolute average deviations for the liquid heat capacity fit increase by as much as 10% suggesting that the value

𝐸𝐸 37

affects the liquid heat capacity fit more than the vapor pressure fit. This shows that liquid heat

capacity data should be considered when trying to determine the best value of .

Another test of the low-temperature performance of the vapor pressure 𝐸𝐸correlation is its

ability to predict the triple point pressure ( ) of the compound. This test was applied to

validate the multi-property optimization approach𝑇𝑇𝑇𝑇𝑇𝑇 to fitting the Riedel equation presented above.

Specifically, the vapor pressure fit with the best value for each compound was extrapolated to

the triple point temperature, which was approximated𝐸𝐸 as the melting points for these pure

compounds, to predict the triple point pressure.

1.2% 16%

14% 1.0% 12% 0.8% 10% AAD

0.6% AAD 8% l p vap C P 6% 0.4% 4% 0.2% 2%

0.0% 0% 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 E Value E Value Figure 5-3: Absolute average deviation of a) vapor pressure data and b) liquid heat capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the n-alkanes ethane ( ), propane ( ), butane ( ), pentane ( ), hexane ( ), heptane ( ), and octane ( ) 𝑬𝑬

0.5% 14%

12% 0.4% 10%

0.3% 8% AAD AAD l p vap C

P 6% 0.2%

4% 0.1% 2%

0.0% 0% 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 E Value E Value Figure 5-4: Absolute average deviation of a) vapor pressure data and b) liquid heat capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the 2-methylalkanes isopropane ( ), 2-methylbutane ( ), 2-methylpentane ( ), 2-methylhexane ( ), and 2-methylheptane ( ) 𝑬𝑬

1.0% 20% 0.9% 18% 0.8% 16% 0.7% 14% 0.6% 12% AAD 0.5% AAD 10% l p vap C P 0.4% 8% 0.3% 6% 0.2% 4% 0.1% 2% 0.0% 0% 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 E Value E Value Figure 5-5: Absolute average deviation of a) vapor pressure data and b) liquid heat capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the 1-alkenes propylene ( ), 1-butene ( ), 1-pentene ( ), 1-hexene ( ), and 1-heptene ( ) 𝑬𝑬

1.6% 16%

1.4% 14%

1.2% 12%

1.0% 10% AAD 0.8% AAD 8% l p vap C P 0.6% 6%

0.4% 4%

0.2% 2%

0.0% 0% 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 E Value E Value Figure 5-6: Absolute average deviation of a) vapor pressure data and b) liquid heat capacity data of fits with the use of the Riedel equation with = 0.5 through E=6 for the n-aldehydes butanal ( ), pentanal ( ), hexanal ( ), and heptanal ( ) 𝑬𝑬

1.8% 8%

1.6% 7% 1.4% 6% 1.2% 5% 1.0% AAD AAD 4% l p vap 0.8% C P 3% 0.6% 2% 0.4%

0.2% 1%

0.0% 0% 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 E Value E Value Figure 5-7: Absolute average deviation of a) vapor pressure data and b) liquid heat capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the aromatic compounds benzene ( ), toluene ( ), m-xylene ( ), o-xylene ( ), p-xylene ( ), ethylbenzene ( ), propylbenzene ( ), and butylbenzene ( 𝑬𝑬 )

1.4% 20% 18% 1.2% 16% 1.0% 14% 12% 0.8% AAD AAD 10% l p vap C

P 0.6% 8%

0.4% 6% 4% 0.2% 2% 0.0% 0% 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 E Value E Value Figure 5-8: Absolute average deviation of a) vapor pressure data and b) liquid heat capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the ethers dimethyl ether ( ), diethyl ether ( ), ethyl propyl ether ( ), di-n-propyl ether ( ), and methyl tert-butyl ether ( ) 𝑬𝑬

3.0% 16%

14% 2.5% 12% 2.0% 10% AAD 1.5% AAD 8% l p vap C P 6% 1.0% 4% 0.5% 2%

0.0% 0% 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 E Value E Value Figure 5-9: Absolute average deviation of a) vapor pressure data and b) liquid heat capacity data of fits with the use of the Riedel equation with =0.5 through E=6 for the ketones methyl ethyl ketone ( ), methyl isopropyl ketone ( ), methyl isobutyl ketone ( ), 2-pentanone ( ), 2- hexanone ( ), 3-hexanone ( ), 2-heptanone𝑬𝑬 ( ), and 2-octanone ( )

The resulting values are given in Table 5-4 for the n-alkanes, Table 5-5 for the

2-methylalkanes, Table 5-6 for the 1-alkenes, Table 5-7 for the n-aldehydes, Table 5-8 for the

41 aromatics, Table 5-9 for the ethers, and Table 5-10 for the ketones along with the database values from DIPPR [44] and REFPROP [54]. These tables also give the number of coefficients in

Equation 5-1 fit to vapor pressure data. In all cases, the of this work are consistent to that in the literature. The n-alkane data also follow the characteristic𝑇𝑇𝑇𝑇𝑇𝑇 saw-tooth pattern as seen in Figure

5-10. These results further increase confidence in the method – specifically that optimizing the value of does not compromise the correlation’s ability to predict .

𝐸𝐸 𝑇𝑇𝑇𝑇𝑇𝑇

Table 5-4: Summary of triple point pressures (in Pa) from literature and this work for the n-alkanes DIPPR DIPPR [44] RefProp [54] Fitting This Work Carbon # Source Coefficients 2 Cited [55] 1.13 1.14 3 4 1.13 3 Cited [56] 1.69E𝑻𝑻𝑻𝑻𝑻𝑻-04 1.72E𝑻𝑻𝑻𝑻𝑻𝑻-04 𝑬𝑬2 4 2.20E𝑻𝑻𝑻𝑻𝑻𝑻-04 4 Cited [57] 0.674 0.666 2 4 0.653 5 Predicted 6.86E-02 7.63E-02 2 4 6.88E-02 6 Predicted 0.902 1.28 2 4 1.12 7 Predicted 0.183 0.175 2 4 0.187 8 Predicted 2.11 1.99 1 4 2.17

Table 5-5: Summary of triple point pressures (in Pa) from literature and this work for the 2-methylalkanes DIPPR DIPPR [44] RefProp [54] Fitting This Work Carbon # Source Coefficients 3 Predicted 1.21E-02 2.29E-02 2 4 2.65E-02 𝑻𝑻𝑻𝑻𝑻𝑻 𝑻𝑻𝑻𝑻𝑻𝑻 𝑬𝑬 𝑻𝑻𝑻𝑻𝑻𝑻 4 Predicted 1.21E-04 8.95E -05 2 4 1.26E-04 5 Predicted 2.07E-05 3 4 7.50E-06 6 Predicted 4.30E-03 2 4 2.01E-03 7 Predicted 1.06E-03 1 4 9.96E-04

Table 5-6: Summary of triple point pressures (in Pa) from literature and this work for the 1-alkenes DIPPR DIPPR [44] RefProp [54] Fitting This Work Carbon # Source Coefficients 3 Predicted 1.17E-03 7.47E-04 2 4 5.83E-04 𝑻𝑻𝑻𝑻𝑻𝑻 𝑻𝑻𝑻𝑻𝑻𝑻 𝑬𝑬 𝑻𝑻𝑻𝑻𝑻𝑻 4 Predicted 6.94E-07 2 2 8.24E-07 5 Predicted 3.70E-05 3 2 1.76E-05 6 Predicted 5.16E-04 2 2 2.51E-04 7 Predicted 1.86E-03 2 2 1.30E-03

Table 5-7: Summary of triple point pressures (in Pa) from literature and this work for the n-aldehydes DIPPR DIPPR [44] Fitting This Work Carbon # Source Coefficients 4 Predicted 0.697 3 2 0.341 5 Predicted 𝑻𝑻𝑻𝑻𝑻𝑻1.16 𝑬𝑬2 2 0.241𝑻𝑻𝑻𝑻𝑻𝑻 6 Predicted 1.86 3 2 1.365 7 Predicted 2.56 2 2 0.671

Table 5-8: Summary of triple point pressures (in Pa) from literature and this work for the aromatics DIPPR DIPPR [44] RefProp [54] Fitting This Work Compound Source Coefficients Benzene Predicted 4760 4790 2 4 4770 Toluene Predicted 0.0475𝑻𝑻𝑻𝑻𝑻𝑻 0.0406𝑻𝑻𝑻𝑻𝑻𝑻 𝑬𝑬2 4 0.0478𝑻𝑻𝑻𝑻𝑻𝑻 Ethylbenzene Predicted 4.39E-03 2 4 3.99E-03 Propylbenzene Predicted 1.814E-04 2 2 1.98E-04 Butylbenzene Predicted 1.54E-04 2 2 1.47E-04 m-Xylene Predicted 3.14 2 4 3.08 o-Xylene Predicted 23.8 2 4 22.6 p-Xylene Predicted 586 2 4 574

Table 5-9: Summary of triple point pressures (in Pa) from literature and this work for the ethers DIPPR DIPPR [44] Fitting This Work Compound Source Coefficients Dimethyl Predicted 3.05 1 2 2.50 Diethyl Predicted 0.395𝑻𝑻𝑻𝑻𝑻𝑻 𝑬𝑬2 2 0.639𝑻𝑻𝑻𝑻𝑻𝑻 Ethyl Propyl Predicted 1.61E-03 1 2 2.33E-03 Di-n-Propyl Predicted 7.63E-04 2 2 3.32E-04 Methyl t- Predicted 0.494 2 2 0.385 Butyl

Table 5-10: Summary of triple point pressure (in Pa) from literature and this work for the ketones DIPPR DIPPR [44] Fitting This Work Compound Source Coefficients Methyl Ethyl Ketone Predicted 1.42 2 2 1.02 Methyl Isopropyl Predicted 0.214𝑻𝑻𝑻𝑻𝑻𝑻 𝑬𝑬1 2 0.145𝑻𝑻𝑻𝑻𝑻𝑻 Ketone Methyl Isobutyl Predicted 0.0672 5 2 0.0636 Ketone 2-Pentanone Predicted 0.752 1 2 0.749 2-Hexanone Predicted 1.45 2 2 1.44 3-Hexanone Predicted 2.22 1 2 1.88 2-Heptanone Predicted 3.55 0.5 2 3.29 2-Octanone Predicted 4.68 0.5 2 3.46

2.5 DIPPR 2 RefProp This Project 1.5

0.5 Triple Point Pressure (Pa) Pressure Point Triple

0 0 2 4 6 8 10 Carbon Number

Figure 5-10: Triple point pressures versus carbon number for n-alkanes comparing DIPPR values [44], REFPROP values [54], and values from this work

5.3 Conclusions

Liquid heat capacity data for several n-alkanes, 2-methylalkanes, 1-alkenes, n-aldehydes,

ketones, ethers, and aromatics were used to determine the selection of the Riedel coefficient

for vapor pressure via the Derivative Method for predicting liquid heat capacity. This𝐸𝐸 analysis

showed that an of 2 fits these families much better than the traditional of 6. Additionally,

𝐸𝐸 𝐸𝐸 44 this method increased confidence in vapor pressure extrapolation to the triple point temperature, resulting in new triple point pressures comparable to those in the literature.

6 NEW THERMODYNAMICALLY CONSISTENT VAPOR PRESSURE

PREDICTION

This work has been published [58] and will be summarized here. Although vapor

pressure is the most commonly measured property of those discussed here, many compounds do

not have any data outside of the normal boiling point. Since is an important property

vap vap for a variety of𝑃𝑃 chemical processes, and other properties can be derive𝑃𝑃 d from it, predicting vapor

pressure well as a function of temperature could drastically improve the reliability, safety, and

profitability of chemical processes.

For many years, the Riedel equation has been considered an excellent and simple choice

among vapor-pressure correlating equations [59], but this work shows that it requires modification of the final coefficient to provide thermodynamic consistency with thermal data [60]. Specifically,

Riedel’s prediction method sets the final coefficient to a constant value of 6, but this restricts the shape of the correlation at low temperatures, which in turn severely restricts the ability of the model to produce accurate liquid heat capacity values below the normal boiling point.

This chapter will: 1) explain newly created predictive correlations where this final coefficient is changed from 1 to 6 in integer steps and 2) demonstrate how these correlations give improved prediction of vapor pressures for compounds with limited or no experimental data. The methodology followed is that originally proposed by Riedel [6] but the last coefficient was chosen based on its ability to simultaneously represent vapor pressure and liquid heat capacity. This

procedure improves the average absolute deviation of the fit to the liquid heat capacity data from

9% to 3%, while maintaining the fit to vapor pressure and heat of vaporization data similar to other

prediction methods. This procedure also greatly improves the ability to predict low-temperature vapor pressure by using liquid heat capacity data.

6.1 Introduction

The Riedel equation [6] for fitting and predicting the temperature dependence of vapor pressure is

= exp + + ln( ) + (6-1) 𝐵𝐵 𝐸𝐸 𝑃𝑃vap �𝐴𝐴 𝐶𝐶 𝑇𝑇 𝐷𝐷𝑇𝑇 � where are fitting coefficients. Recently, it𝑇𝑇 has been found that changing the value – the

5th parameter𝐴𝐴 − 𝐸𝐸 – can improve both the vapor pressure fit [10] and the thermodynamic𝐸𝐸 consistency

with other properties—specifically heat of vaporization and liquid and ideal gas heat capacities

[60]. The Riedel equation was originally published with a method to predict vapor pressure for

compounds without experimental data [6]. However, this method restricted the ability of the

prediction of liquid heat capacity by keeping at 6. This study created a series of new predictive

vapor pressure equations with =1,2,3,4,5, and𝐸𝐸 6 to improve the flexibility of the correlation

and increase thermodynamic consistency𝐸𝐸 with liquid heat capacity data while increasing the

training set to include a more diverse group of compounds. Only integer values were selected

because the data rarely justified increasing the precision on . Then, a larger set of compounds

was tested to see which value works best for each chemical𝐸𝐸 family. The previous chapter

shows best values for 𝐸𝐸alkanes, alkenes, aldehydes, aromatics, ethers, and ketones families [60].

This report 𝐸𝐸expanded this analysis into alkynes, esters, light gases, halogenated compounds,

multifunctional compounds, ring alkanes, silanes, and sulfides as well. Using this prediction

along with methods established in Chapter 2 extends the prediction into heat of vaporization and

liquid heat capacity as well, effectively turning one predictive correlation into three.

The rest of this chapter will go as follows. First, existing vapor pressure prediction methods will be introduced from the literature. Then, the theory linking vapor pressure, heat of vaporization, and ideal gas and liquid heat capacities will be explained along with the theory behind this new predictive method. After that, the steps used to create the new method are outlined along with the compounds used to train the method. Finally, the new method is compared to other prediction methods and tested using a different set of compounds with favorable results.

6.2 Overview of Vapor Pressure Prediction and Correlation Methods

Several prediction methods are in use today. Riedel’s original prediction method,

vap established in 1957𝑃𝑃 [6], has the form:

ln( ) = + + ln( ) + (6-2) 6 𝑟𝑟 𝐵𝐵 𝑟𝑟 𝑟𝑟 𝑃𝑃 𝐴𝐴 𝑟𝑟 𝐶𝐶 𝑇𝑇 𝐷𝐷𝑇𝑇 where and are reduced temperature and 𝑇𝑇vapor pressure, respectively, are fitting

𝑟𝑟 𝑟𝑟 parameters,𝑇𝑇 and𝑃𝑃 of Equation 6-1 is set to 6. This value of was chosen because𝐴𝐴 − 𝐷𝐷 it appeared to

give a favorable 𝐸𝐸shape towards the critical point compared to𝐸𝐸 enthalpic data [6, 61]. Coefficients

are found using the following three constraints:

𝐴𝐴 −1.𝐶𝐶 force Equation 6-2 to give 1 atm at the normal boiling point ( )

𝑁𝑁𝑁𝑁 2. force Equation 6-2 to give the critical pressure ( ) at the critical𝑇𝑇 temperature ( )

𝑐𝑐 𝑐𝑐 3. set the slope of the Riedel parameter to zero at the𝑃𝑃 critical point 𝑇𝑇

The Riedel parameter, , is defined as:

𝛼𝛼

ln = + + 6 (6-3) ln 𝑟𝑟 6 𝜕𝜕 𝑃𝑃 𝐵𝐵 𝑟𝑟 𝛼𝛼 ≡ 𝑟𝑟 − 𝑟𝑟 𝐶𝐶 𝐷𝐷𝑇𝑇 The last coefficient is found from fitting𝜕𝜕 to𝑇𝑇 experimental𝑇𝑇 data. Specifically, the parameter is constrained to relate to the Riedel parameter (α), evaluated at the critical point, according𝐷𝐷 to:

= ( ) (6-4)

𝑐𝑐 𝑐𝑐 where and were found to be 0.0838𝐷𝐷 and− 3.758,𝐾𝐾 𝑋𝑋 −respectively,𝛼𝛼 from a fit of data for the

𝑐𝑐 vap compounds𝐾𝐾 listed𝑋𝑋 in Table 2-1. 𝑃𝑃

Unfortunately, this formulation, where the parameter is fixed at 6, has been shown to cause the liquid heat capacity ( ) curve obtained from𝐸𝐸 the Derivative method (See Chapter 2) to 𝑙𝑙 𝑝𝑝 dip too low at the triple point temperature𝐶𝐶 ( ) [60]. To correct for this, the Derivative Method

𝑇𝑇𝑇𝑇 can be paired with a corresponding states method𝑇𝑇 (explained below) to predict [2]. The 𝑙𝑙 𝑝𝑝 former is used at higher temperatures and the latter at lower temperatures. Unfortunately,𝐶𝐶 this does not ensure thermodynamic consistency between and . 𝑙𝑙 vap 𝑝𝑝 𝑃𝑃 𝐶𝐶 Table 6-1: Compounds originally investigated by Riedel, grouped by chemical family Training Set Family Number of Compounds Alkane 4 Alkene 2 Ester 5 Ether 1 Gas 5 Halogenated 3

Lee and Kesler introduced a corresponding states prediction method (Lee-Kesler) in

vap 1975 [62] of the form: 𝑃𝑃

ln( ) = ln ( ) + ln ( ) (6-5)

𝑃𝑃𝑟𝑟 𝑃𝑃0 𝑇𝑇𝑟𝑟 𝜔𝜔 𝑃𝑃1 𝑇𝑇𝑟𝑟

49 where is the acentric factor predicted using the normal boiling point, and ln ( ) and

0 𝑟𝑟 ln ( 𝜔𝜔) are empirically fit equations with the same form as the Riedel predictive𝑃𝑃 𝑇𝑇 method with

1 𝑟𝑟 𝑃𝑃= 6𝑇𝑇. This method was proposed as a thermodynamically robust correlation and drew favorable c𝐸𝐸omparisons to previous methods.

Citing a need for a better predictive form, Vetere published a method using the

vap Wagner correlation (Vetere-Wagner)𝑃𝑃 in 1991 [63]. This approach related the temperature to the vapor pressure according to:

1 ln( ) = [ (1 ) + (1 ) . + (1 ) ] (6-6) 1 5 3 𝑟𝑟 𝑟𝑟 𝑟𝑟 𝑟𝑟 𝑃𝑃 𝑟𝑟 𝐴𝐴 − 𝑇𝑇 𝐵𝐵 − 𝑇𝑇 𝐶𝐶 − 𝑇𝑇 where the coefficients were𝑇𝑇 calculated using the following constraints:

1. Forcing Equation𝐴𝐴 6−-6 𝐶𝐶to give 1 atm at the normal boiling point

2. Fitting a predicted Riedel parameter, defined in Equation 6-3, at the critical point

3. Fitting a predicted Riedel parameter, also defined in Equation 6-3, at the normal boiling point

These Riedel parameters were predicted using correlations from an empirical study of different chemical families. The authors admitted, at the time of its publication, that this method was only an initial attempt to make the Wagner correlation fully predictive [63], but no other major improvements have been made since.

Seeking to improve on the Riedel predictive method, Vetere [61] kept Equation 6-2 with

at 6 but changed how the empirical constant was calculated. Instead of using only vapor

𝐸𝐸pressure data to fit Equation 6-4, he used the normal𝐾𝐾 boiling point, critical point, acentric factor, reduced temperature, and chemical family. Initially, the selected families were nonpolar compounds, acids, alcohols, glycols, and other polar compounds [61]. Fifteen years later in 2006,

Vetere improved upon his previous method by segregating the chemical families further and increasing the mathematical complexity of the parameter calculations [64]. This Vetere-Riedel

𝐾𝐾 50 method gave better results when predicting the vapor pressures of saturated and branched hydrocarbons, olefins and aromatic compounds, alcohols, and other compounds [64] compared to the original Riedel prediction and the Lee-Kesler prediction.

These methods predict vapor pressure well. However, none of them could adequately replicate liquid heat capacity data below the normal boiling point, where the majority of heat capacity data exist. At these temperatures, few experimental vapor pressure data typically exist, and when they do, they suffer from high uncertainties [50, 51]. Therefore, liquid heat capacity data can be used to formulate a better vapor pressure prediction at low temperatures. A new prediction is necessary to achieve thermodynamic consistency by matching both and 𝑙𝑙 vap 𝑝𝑝 data. 𝑃𝑃 𝐶𝐶

6.3 Theory

6.3.1 Thermodynamic Relationships

In order to overcome the limitations explained in the previous section, a new

vap prediction method was created in order to predict both and correctly. is related𝑃𝑃 to 𝑙𝑙 vap 𝑝𝑝 vap through rigorous thermodynamic equations involving𝑃𝑃 the first𝐶𝐶 and second 𝑃𝑃temperature 𝑙𝑙 𝑝𝑝 derivatives𝐶𝐶 of as shown by the Clapeyron equation and Derivative method in Equations 2-1

vap and 2-6. 𝑃𝑃

6.3.1 New Predictive Vapor Pressure Method

The new predictive method for was created using the same methodology laid out by

vap Riedel with one crucial exception: the exponent𝑃𝑃 on in the final term, of Equation 1, was

𝑟𝑟 changed from 6 to other integer values. Specifically,𝑇𝑇 the general Riedel𝐸𝐸 equation was used in the linearized and reduced form

ln( ) = + + ln( ) + (6-7) 𝐸𝐸 𝑟𝑟 𝐵𝐵 𝑟𝑟 𝑟𝑟 𝑃𝑃 𝐴𝐴 𝑟𝑟 𝐶𝐶 𝑇𝑇 𝐷𝐷𝑇𝑇 where is the reduced pressure, is 𝑇𝑇the reduced temperature, are fitting parameters, and

𝑟𝑟 𝑟𝑟 is changed𝑃𝑃 from 1 to 6 in integer𝑇𝑇 steps. Changing has been found𝐴𝐴 − 𝐷𝐷 to improve the ability of

the𝐸𝐸 correlation to successfully predict using 𝐸𝐸the Derivative method for compounds with 𝑙𝑙 vap 𝑝𝑝 𝑃𝑃 and data in the previous chapter. Therefore,𝐶𝐶 the best will be determined by the 𝑙𝑙 vap 𝑝𝑝 predictive𝑃𝑃 𝐶𝐶 correlation’s ability to fit and data. 𝐸𝐸 𝑙𝑙 vap 𝑝𝑝 Four constraints are necessary𝑃𝑃 to calculate𝐶𝐶 coefficients . Three constraints are the exact same as Riedel’s original prediction method: 𝐴𝐴 − 𝐷𝐷

1. force Equation 6-7 to give 1 atm at the normal boiling point ( )

𝑁𝑁𝑁𝑁 2. force Equation 6-7 to give the critical pressure ( ) at the critical𝑇𝑇 temperature ( )

𝑐𝑐 𝑐𝑐 3. set the slope of the Riedel parameter to zero at the𝑃𝑃 critical point (See Equation 𝑇𝑇6-10)

Solving in terms of gives:

𝐴𝐴 − 𝐶𝐶 ln(𝐷𝐷) ln( ) ln( ) = ln( ) + ( ) ( ) (6-8) ln( 𝑟𝑟 ) ln( 𝑟𝑟 ) 𝑟𝑟 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑇𝑇 𝑟𝑟 𝑛𝑛𝑛𝑛𝑛𝑛 𝑇𝑇 𝑃𝑃 𝑃𝑃 � 𝑛𝑛𝑛𝑛𝑛𝑛 � 𝐷𝐷 �𝜙𝜙 𝑇𝑇 − 𝜙𝜙 𝑇𝑇 � 𝑛𝑛𝑛𝑛𝑛𝑛 �� where 𝑇𝑇 𝑇𝑇

( ) = 1 ( + 1) ln( ) + (6-9) 2 2 𝐸𝐸 𝑟𝑟 𝐸𝐸 𝑟𝑟 𝑟𝑟 𝜙𝜙 𝑇𝑇 𝐸𝐸 − − 𝑟𝑟 − 𝐸𝐸 𝐸𝐸 𝑇𝑇 𝑇𝑇 and and are the reduced atmosphere𝑇𝑇 the reduced normal boiling point, respectively.

𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑛𝑛𝑛𝑛𝑛𝑛 To obtain𝑃𝑃 the fourth𝑇𝑇 constraint, the Riedel parameter is defined:

ln 𝛼𝛼 = + + (6-10) ln 𝑟𝑟 𝐸𝐸 𝜕𝜕 𝑃𝑃 𝐵𝐵 𝑟𝑟 𝛼𝛼 ≡ 𝑟𝑟 − 𝑟𝑟 𝐶𝐶 𝐷𝐷𝐷𝐷𝑇𝑇 which is the same as Riedel’s predictive𝜕𝜕 𝑇𝑇 method,𝑇𝑇 except it has been generalized for all values of

. At the critical point, the Riedel parameter reduces to:

𝐸𝐸

= + + (6-11)

𝑐𝑐 or 𝛼𝛼 −𝐵𝐵 𝐶𝐶 𝐷𝐷𝐷𝐷

ln( ) ( ) = (6-12) ln( 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎) ln( 𝑛𝑛𝑛𝑛𝑛𝑛 ) 𝑐𝑐 𝑃𝑃 𝜙𝜙 𝑇𝑇 𝛼𝛼 𝑛𝑛𝑛𝑛𝑛𝑛 − 𝐷𝐷 𝑛𝑛𝑛𝑛𝑛𝑛 when and are substituted using Constraints𝑇𝑇 1-3. is found𝑇𝑇 following Riedel’s original methodology𝐵𝐵 𝐶𝐶 by fitting Equation 6-4 to experimental𝐷𝐷 data to find and , fitting parameters

𝑐𝑐 describing a corresponding states analysis. Substituting Equation 𝐾𝐾6-12 into𝑋𝑋 Equation 6-4 and

rearranging allows to be rewritten in terms of and according to:

𝑐𝑐 𝐷𝐷 ln( ) +𝐾𝐾 𝑋𝑋( ) = (6-13) ln(𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 ) + 𝑐𝑐( 𝑛𝑛𝑛𝑛)𝑛𝑛 𝑃𝑃 𝐾𝐾𝑋𝑋 𝜙𝜙 𝑇𝑇 𝑐𝑐 𝐷𝐷 𝐾𝐾 � 𝑛𝑛𝑛𝑛𝑛𝑛 𝑛𝑛𝑛𝑛𝑛𝑛 − 𝑋𝑋 � Substitution of Equation 6-13 into Equation𝑇𝑇 6-8 yields𝐾𝐾𝐾𝐾 𝑇𝑇the desired predictive correlation:

ln( ) ln( ) + ( ) ln( ) ln( ) = ln( ) + ( ) ( ) ( ) ( ) ( ) ( ) (6-14) ln 𝑟𝑟 ln 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 + 𝑐𝑐 𝑛𝑛𝑛𝑛𝑛𝑛 ln 𝑟𝑟 𝑟𝑟 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑇𝑇 𝑃𝑃 𝐾𝐾𝑋𝑋 𝜙𝜙 𝑇𝑇 𝑐𝑐 𝑟𝑟 𝑛𝑛𝑛𝑛𝑛𝑛 𝑇𝑇 𝑃𝑃 𝑃𝑃 � 𝑛𝑛𝑛𝑛𝑛𝑛 � 𝐾𝐾 � 𝑛𝑛𝑛𝑛𝑛𝑛 𝑛𝑛𝑛𝑛𝑛𝑛 − 𝑋𝑋 � �𝜙𝜙 𝑇𝑇 − 𝜙𝜙 𝑇𝑇 � 𝑛𝑛𝑛𝑛𝑛𝑛 �� where each value of requires𝑇𝑇 a unique𝑇𝑇 set 𝐾𝐾of𝐾𝐾 𝑇𝑇, , and . The parameter 𝑇𝑇 is defined as:

𝑐𝑐 𝐸𝐸 𝐾𝐾 𝑋𝑋 𝜙𝜙 𝜙𝜙 ( ) = 1 ( + 1) ln( ) + (6-15) 2 2 𝐸𝐸 𝐸𝐸 𝜙𝜙 𝑇𝑇𝑟𝑟 𝐸𝐸 − − − 𝐸𝐸 𝐸𝐸 𝑇𝑇𝑟𝑟 𝑇𝑇𝑟𝑟 𝑇𝑇𝑟𝑟 6.4 Methods

6.4.1 Regression of K and Xc as a Function of E

Recall (See Section 6.2) that Riedel set = 6 and found by fitting Equation 6-8 to

experimental data. He then found and (0.0838𝐸𝐸 and 3.758, respectively)𝐷𝐷 that satisfied

𝑐𝑐 Equation 6-4 so that the method could𝐾𝐾 be𝑋𝑋 predictive. The same procedure was followed here

using Equation 6-13 with = 1, 2, 3, 4, 5, and 6.

The training set in 𝐸𝐸this study, used to fit the coefficient, consisted of 37 compounds

from the eight chemical families listed in Table 6-2.𝐷𝐷 These compounds were selected because: 1)

they contained considerable data over a wide temperature range, and 2) they were a

vap chemically diverse set. Summaries𝑃𝑃 of the data used for these compounds are given in the

Appendix. In each case, the coefficient was fit to experimental data for a training set of

vap compounds and the corresponding𝐷𝐷 and were found. Thus, six𝑃𝑃 sets of and values were

𝐶𝐶 𝐶𝐶 obtained—one set for each value.𝐾𝐾 𝑋𝑋 𝐾𝐾 𝑋𝑋

Table 6-3 contains the𝐸𝐸 results. Notice that decreases rapidly (orders of magnitude) with increasing values. also decreases with increasing𝐾𝐾 , but much more slowly.

𝐶𝐶 The𝐸𝐸 dependence𝑋𝑋 of and on is displayed 𝐸𝐸graphically in Figure 6-1. The behavior of

𝐶𝐶 is exponential in nature, while𝐾𝐾 that𝑋𝑋 of 𝐸𝐸 is quadratic. Thus, the behavior of each can be fit

𝐶𝐶 reliably𝐾𝐾 ( = 0.9990 for both) to the following𝑋𝑋 correlations (displayed as lines on the figure). 2 𝑅𝑅 = 4.96465 . (6-16) −2 29195 = 4.14524𝐾𝐾 0.0818433𝐸𝐸 + 0.00310685 (6-17) 2 𝑐𝑐 With these equations, non𝑋𝑋 -integer values− of may be𝐸𝐸 chosen to fit vapor𝐸𝐸 pressure data when the

and data quantity and quality merit. 𝐸𝐸A sample calculation using this predictive method is 𝑙𝑙 vap 𝑝𝑝 given𝑃𝑃 in the𝐶𝐶 Appendix.

The last two rows of

Table 6-3 are significant. These show the and values for = 6 for the new method

𝐶𝐶 and Riedel’s original method. Notice that when 𝐾𝐾= 6, 𝑋𝑋 and for the𝐸𝐸 new method are nearly

𝑐𝑐 identical to those from Riedel’s original work. Even𝐸𝐸 though𝐾𝐾 the𝑋𝑋 training set for the new method

contains nearly double the number of compounds as Riedel’s original training set, the results are

similar.

Table 6-2: Training set of compounds for the new predictive Pvap correlation, grouped by chemical families Training Set Family Number Alkane 11 Alkene 1 Aromatic 5 Ester 3 Ether 1 Gas 5 Halogenated 4 Ketone 7

Table 6-3: Summary of prediction constants for the original Riedel Pvap prediction and this new Pvap prediction Source K Xc This 1 5.0398 4.065 Work 2𝑬𝑬 1.0048 3.996 3 0.3931 3.928 4 0.2045 3.867 5 0.1244 3.812 6 0.0836 3.767 Riedel [6] 6 0.0838 3.758

6 4.10

5 4.05 4.00 4 3.95 K

3 Xc 3.90 2 3.85 1 3.80 0 3.75 1 2 3 4 5 6 E Value

Figure 6-1: Fitting parameters K and Xc as functions of E

6.4.2 E Training Method

As is apparent from Figure 6-1, must be selected before the vapor pressure can be

predicted. It was hypothesized that an optimal𝐸𝐸 value could be found for families of

compounds. This was tested using a set of 106 𝐸𝐸compounds from the families listed in Table 6-4 which includes the 36 compounds used to generate and in Figure 6-1. Summaries of the

𝑐𝑐 data used for these compounds are given in the Appendix𝐾𝐾 . 𝑋𝑋The best value was found for each

compound by minimizing the average absolute deviation ( ) of the𝐸𝐸 predictions from the

experimental data for and simultaneously. Heat of 𝐴𝐴𝐴𝐴vaporization𝐴𝐴 could also have been 𝑙𝑙 vap 𝑝𝑝 used, but most 𝑃𝑃data in the𝐶𝐶 literature were derived from vapor pressure fits using the

vap Clapeyron equation.Δ𝐻𝐻 When calorimetric data were present in the literature, they were usually at temperatures where vapor pressure data were plentiful with low uncertainty. Therefore,

vap was not used to find the best in this analysis. Specifically, for the property was definedΔ𝐻𝐻 as: 𝐸𝐸 𝐴𝐴𝐴𝐴𝐴𝐴

1 ( , ) = (6-18) 𝐽𝐽𝑖𝑖 − 𝐽𝐽̂ 𝐸𝐸 𝑇𝑇𝑖𝑖 𝐴𝐴𝐴𝐴𝐴𝐴 � � 𝑖𝑖 � 𝑁𝑁 𝑖𝑖 𝐽𝐽 where is the experimental value for the property (vapor pressure, heat of vaporization, or liquid

𝑖𝑖 heat capacity),𝐽𝐽 ( , ) is the model prediction for the property for a certain and temperature

𝑖𝑖 , and is the𝐽𝐽 ̂number𝐸𝐸 𝑇𝑇 of experimental points for that property. The “best” 𝐸𝐸value of was

𝑖𝑖 defined𝑇𝑇 𝑁𝑁 as the value that minimized the average of and for each compound.𝐸𝐸 𝑙𝑙 vap 𝑝𝑝 Although propyl formate was used to create𝑃𝑃 this 𝐶𝐶 prediction𝐴𝐴𝐴𝐴𝐴𝐴 method, it was omitted

vap from this analysis because it did not have sufficient experimental𝑃𝑃 data. Only one alkyne and 𝑙𝑙 𝑝𝑝 one silane were included because few compounds in those families𝐶𝐶 contained and data. 𝑙𝑙 vap 𝑝𝑝 Of noticeable omission are the alcohols and acids, families where self-association𝑃𝑃 has been𝐶𝐶 well

documented [49, 65-67]. For these compounds, more data are necessary along with a separate

analysis scheme that may require a different correlation form and a modified equation of

vap state to calculate the vapor volumes. Due to these𝑃𝑃 complications, strongly hydrogen bonding

families will not be discussed here.

6.5 Results

6.5.1 Optimized E by Family

The last two columns of Table 6-4 contain the average ’s for all of the compounds tested in each chemical family using the best , which was found𝐴𝐴𝐴𝐴 𝐴𝐴by minimizing the average of the and for each compound. The𝐸𝐸 for was not used in the optimization 𝑙𝑙 vap 𝑝𝑝 vap scheme𝑃𝑃 because𝐶𝐶 𝐴𝐴𝐴𝐴 only𝐴𝐴 74 of the compounds contained𝐴𝐴𝐴𝐴𝐴𝐴 experimentalΔ𝐻𝐻 data (see the

vap Appendix). When data did exist, changing the value did notΔ𝐻𝐻 change the ability of the

vap correlation to Δfollow𝐻𝐻 the experimental values.𝐸𝐸 The new predictive method predicts

vap vap 𝑃𝑃 for all families below 5% , and predictsΔ𝐻𝐻 for all but the light gases below 5% on 𝑙𝑙 vap 𝑝𝑝 average.𝑃𝑃 Members of the light gas𝐴𝐴𝐴𝐴 𝐴𝐴group include several𝐶𝐶 noble gases and diatomic compounds𝐴𝐴𝐴𝐴𝐴𝐴

with triple point temperatures between 10 and 70 K, and critical temperatures between 30 and

160 K. The triple point temperatures for nearly all the other compounds were above 200 K, so it appears that this method works better at temperatures above about 150 K. The other predictive methods gave similar results for the light gases as well.

l Table 6-4: Average Pvap, ΔHvap, and Cp absolute average deviations (AAD) for the compounds in each chemical family using the best value for each compound Family Number of Compounds Avg (%) Avg (%) Avg (%) 𝑬𝑬 𝒍𝒍 Aldehyde 4 𝑷𝑷𝐯𝐯𝐯𝐯𝐯𝐯1.42𝐴𝐴𝐴𝐴𝐴𝐴 𝚫𝚫𝑯𝑯𝐯𝐯𝐯𝐯𝐯𝐯1.35𝐴𝐴𝐴𝐴 𝐴𝐴 𝑪𝑪𝒑𝒑4.21𝐴𝐴𝐴𝐴𝐴𝐴 Alkane 15 1.06 1.72 3.23 Alkene 9 4.43 0.91 4.64 Alkyne 1 1.52 0.92 2.84 Amine 8 3.18 0.82 2.18 Aromatic 12 4.73 0.52 2.58 Ester 6 4.46 0.45 1.64 Ether 5 1.97 1.26 3.70 Light Gases 5 0.59 1.43 6.81 Halogenated 8 1.65 0.95 3.62 Ketone 8 1.52 1.15 2.64 Multifunctional 14 2.26 0.44 2.43 Ring Alkane 5 2.41 2.22 2.10 Silane 1 2.49 -- 2.38 Sulfide 5 0.95 1.27 2.78

Figure 6-2 shows the distribution of best values for the 106 test compounds separated

into chemical families. The majority of compounds𝐸𝐸 were best optimized using = 3 or = 4,

though amines seem to do best with = 2 and aromatics seem to favor = 4 𝐸𝐸and above.𝐸𝐸

The best integer value for each𝐸𝐸 family was chosen by finding the𝐸𝐸 integer that best fits

the most compounds in each𝐸𝐸 family. These recommended values are summarized in Table 6-5.

The five light gases showed a spread in best value, with 𝐸𝐸a much larger average than 𝑙𝑙 𝑝𝑝 the other families. In this case, a value of was𝐸𝐸 chosen as it was closest to the average𝐶𝐶 𝐴𝐴𝐴𝐴 best𝐴𝐴

value. For compounds outside of the families𝐸𝐸 listed, should be set to 3 or 4, unless the 𝐸𝐸

compounds strongly self-associate. As was explained𝐸𝐸 in Section 4 above, alcohols and acids

were not included.

50 Aldehyde (4) 45 Alkane (15)

40 Alkene (9) Alkyne (1) 35 Amine (8) 30 Aromatic (12)

25 Ester (6) Ether (5) 20 Gas (5)

Number Compounds of 15 Halogenated (8) Ketone (8) 10 Multifunctional (14) 5 Ring Alkane (5) 0 Silane (1) 1 2 3 4 5 6 Sulfide (5) Best E

Figure 6-2: Distribution of best E values using the new predictive Riedel Pvap method on the test compounds

In general, the best values used to predict are 3 or 4 for all but the amine and gas

vap families. 𝐸𝐸 𝑃𝑃

Contrast these results to a previous study that found that a value of 2 should be used for

these same exact families [60]. The key difference here is that the previous article did not use the

Riedel parameter constraint (Constraint 3), while this prediction does. Adding an additional

constraint at the critical point changed the shape of the curve in a way that the best

vap correlations required a larger value. For compounds with𝑃𝑃 extensive data, Constraint 3 is

vap not needed. In those cases, a sm𝐸𝐸 aller value works better. However, for𝑃𝑃 compounds with limited

or no data, an value one integer𝐸𝐸 larger works better.

𝑃𝑃vap 𝐸𝐸

Table 6-5: Recommended E values for each of the chemical families tested Family Best Aldehyde 4 𝑬𝑬 Alkane 3 Alkene 3 Alkyne 3 Amine 2 Aromatic 4 Ester 4 Ether 3 Gas 5 Halogenated 4 Ketone 3 Multifunctional 3 or 4 Ring Alkane 4 Silane 3 Sulfide 3

6.5.2 Comparison to Other Predictive Methods

The new prediction method was compared to Riedel’s original method [6], the Lee-

Kesler corresponding states method [62], Vetere’s Wagner correlation prediction method [63],

and Vetere’s newest Riedel correlation prediction method [64]. The recommended values in

Table 6-5 were applied to each of the 106 compounds analyzed. The distribution𝐸𝐸 of the

vap test compounds is given in Figure 6-3 for the five prediction methods.𝑃𝑃 This𝐴𝐴𝐴𝐴 bar𝐴𝐴 chart shows the number of compounds on the y-axis for each range of on the x-axis and each

vap prediction method, shown with different color bars. The𝑃𝑃 red,𝐴𝐴𝐴𝐴 orange,𝐴𝐴 yellow, and green bars

show the results for the Riedel, Lee-Kesler, Vetere-Wagner, and Vetere-Riedel methods,

respectively. The blue dotted bars show the results for this new predictive method. For example,

this chart shows that 70 compounds were predicted with a in the range 0-2% using this

𝑃𝑃vap 𝐴𝐴𝐴𝐴𝐴𝐴 60

new predictive method. This new method performs at least as well as the other methods since the

distribution for this method is bunched slightly more toward zero than the other

vap prediction𝑃𝑃 𝐴𝐴𝐴𝐴𝐴𝐴 methods. The distribution for the new method is not discernably different

vap from the best of other methods𝑃𝑃 𝐴𝐴𝐴𝐴 (Riedel).𝐴𝐴 Therefore, this new method retains but does not

noticeably improve the fit of where the data are located. is greater than 10%

vap vap vap using this work for three compounds:𝑃𝑃 1,3-trans𝑃𝑃-pentadiene, pyrene,𝑃𝑃 and 𝐴𝐴𝐴𝐴octyl𝐴𝐴 acetate. In these cases, the majority of data are under 1000 Pa where uncertainty in measurements

vap vap grows [50, 51]. 𝑃𝑃 𝑃𝑃

70 Riedel

60 Lee-Kesler Vetere-Wagner 50 Vetere-Riedel 40 This Work 30

20 Number Compounds of 10

0 0-2% 2-4% 4-6% 6-8% 8-10% 10-12% 12-14% 14-16% 16-18% 18-20% >20% Pvap

Figure 6-3: The distribution of Pvap AAD for 106 test 𝐴𝐴compounds𝐴𝐴𝐷𝐷 using Pvap prediction methods: Riedel’s original method, Lee-Kesler, Vetere’s Wagner method, Vetere’s Riedel method, and this work

The distribution of the test compounds is given in Figure 6-4. Notice that the

vap x-axis extendsΔ𝐻𝐻 to 10%𝐴𝐴𝐴𝐴 𝐴𝐴instead of 20% as shown in Figure 6-3. Although the scale is different, the message is the same: these prediction methods are not discernible when looking at

𝑃𝑃vap Δ𝐻𝐻vap 61

data. However, the distributions for the Riedel prediction and this prediction (solid

vap red and blue dottedΔ bars,𝐻𝐻 respectively)𝐴𝐴𝐴𝐴𝐴𝐴 are slightly bunched closer to zero than the other three

methods. Although looking towards does not give much new information, the

vap vap distribution indicates that the originalΔ 𝐻𝐻Riedel prediction and this work may do slightlyΔ𝐻𝐻 better𝐴𝐴 𝐴𝐴for𝐷𝐷

vap Δ𝐻𝐻

30 Riedel Lee-Kesler 25 Vetere-Wagner 20 Vetere-Riedel 15 This Work 10 Number Compounds of 5

0 0-1% 1-2% 2-3% 3-4% 4-5% 5-6% 6-7% 7-8% 8-9% 9-10% >10% Δ vap

Figure 6-4: The distribution of ΔHvap for 106 test 𝐻𝐻compounds𝐴𝐴𝐴𝐴𝐷𝐷 using Pvap prediction methods: Riedel’s original method, Lee-Kesler, Vetere’s Wagner method, Vetere’s Riedel method, and this work

The distribution of the test compounds is given in Figure 6-5 and demonstrates 𝑙𝑙 𝑝𝑝 how the new𝐶𝐶 method𝐴𝐴𝐴𝐴𝐴𝐴 excels. This distribution for this new method (again, the blue 𝑙𝑙 𝑝𝑝 dotted bars) is bunched much closer𝐶𝐶 to𝐴𝐴𝐴𝐴 0%𝐴𝐴 than any of the other prediction methods. Only

vap one compound has an greater than 12% for the new method𝑃𝑃 compared to 11 for Vetere-

Wagner, 18 for Vetere𝐴𝐴𝐴𝐴-Riedel,𝐴𝐴 21 for the original Riedel method, and 24 for Lee-Kesler. The

method developed in this work does a much better job predicting thermodynamically consistent

and data than the other prediction methods found in the literature. 𝑙𝑙 vap 𝑝𝑝 vap 𝑃𝑃 50 𝐶𝐶 𝑃𝑃 45 Riedel 40 Lee-Kesler 35 Vetere-Wagner 30 25 Vetere-Riedel 20 This Work 15

Number Compounds of 10 5 0 0-2% 2-4% 4-6% 6-8% 8-10% 10-12% 12-14% 14-16% 16-18% 18-20% >20% l Cp

l Figure 6-5: The distribution of Cp AAD for the test compounds𝐴𝐴𝐴𝐴𝐷𝐷 using Pvap prediction methods within the Derivative method: Riedel’s original method, Lee-Kesler, Vetere’s Wagner method, Vetere’s Riedel method, and this work

6.5.3 Testing the Methods with Compounds Not Used in the Training Set

To fully test the applicability of the method, five sets of 40 compounds were randomly

chosen from the 70 compounds not used to train the and values, and the average ,

𝑐𝑐 vap , and ’s were found for the five prediction𝐾𝐾 methods𝑋𝑋 (four previous methods𝑃𝑃 and 𝑙𝑙 vap 𝑝𝑝 Δthat𝐻𝐻 of this work).𝐶𝐶 𝐴𝐴𝐴𝐴 𝐴𝐴Only 70 compounds were used for this analysis because the 36 other

compounds were used to fit the correlations, and including these would bias the

vap vap results in favor of the new method.𝑃𝑃 𝑃𝑃 𝐴𝐴𝐴𝐴𝐷𝐷

The average , , and absolute average deviations ( ) of the five sets of 𝑙𝑙 vap vap 𝑝𝑝 compounds for the five𝑃𝑃 Δ𝐻𝐻 prediction𝐶𝐶 methods are given in Figure 6-𝐴𝐴𝐴𝐴6 with𝐴𝐴 95% confidence

vap intervals. The values are𝑃𝑃 ordered on the X-axis by chronological order of publication. The new

method significantly decreased from around 7% to 3% without significantly increasing 𝑙𝑙 𝑝𝑝 and . Since almost𝐶𝐶 𝐴𝐴𝐴𝐴 all𝐴𝐴 of the data in the literature are just above the triple 𝑙𝑙 vap vap 𝑝𝑝 point𝑃𝑃 temperatureΔ𝐻𝐻 𝐴𝐴𝐴𝐴 (𝐴𝐴 ) and most of the data𝐶𝐶 in the literature are bunched around for

𝑇𝑇𝑇𝑇 vap 𝑁𝑁𝑁𝑁 each compound, an𝑇𝑇 improvement in 𝑃𝑃 corresponds to an improvement in the 𝑇𝑇 and 𝑙𝑙 𝑝𝑝 vap correlations near the where𝐶𝐶 it𝐴𝐴𝐴𝐴 is 𝐴𝐴difficult to measure accurately [50, 𝑃𝑃51].

vap 𝑇𝑇𝑇𝑇 vap ΔTherefore,𝐻𝐻 this new method 𝑇𝑇predicts vapor pressure at lower temperatures𝑃𝑃 with lower uncertainty

than any other prediction method tested.

12 Vapor Pressure AAD 10 Heat of Vaporization AAD Liquid Heat Capacity AAD 8

6 AAD (%) 4

0 Riedel (1954) Lee-Kesler (1975) Vetere-Wagner (1991) Vetere-Riedel (2006) This Work (2017) Pvap Prediction Method

l Figure 6-6: Average Pvap, ΔHvap, and Cp AAD for five sets of 40 compounds using different Pvap prediction methods

6.6 Conclusions

Predictive methods for the Riedel equation with different final coefficient values were

created. In summary, the coefficients for Equation 6-7 are calculated using , , and

𝑐𝑐 as follows: 𝐴𝐴 − 𝐶𝐶 𝐷𝐷 𝐸𝐸 𝛼𝛼

= ( 1) (6-19) 2 𝐴𝐴 =𝐸𝐸 − 𝐷𝐷 (6-20) 2 = 𝐵𝐵 −(𝐸𝐸 𝐷𝐷+ 1) (6-21)

𝑐𝑐 The coefficient and the Riedel parameter𝐶𝐶 𝛼𝛼 at− the𝐸𝐸 critical𝐸𝐸 𝐷𝐷point are calculated from the

𝑐𝑐 reduced normal 𝐷𝐷boiling point ( ), , , and : 𝛼𝛼

𝑛𝑛𝑛𝑛𝑛𝑛 𝑐𝑐 𝑇𝑇 ln𝐾𝐾 𝑋𝑋 , + 𝐸𝐸 ( , ) = (6-22) ln( ) + ( , ) �𝑃𝑃atm 𝑟𝑟� 𝐾𝐾𝑋𝑋𝑐𝑐𝜙𝜙 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 𝐸𝐸 𝐷𝐷 𝐾𝐾 � − 𝑋𝑋𝑐𝑐� 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 𝐾𝐾𝐾𝐾 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 𝐸𝐸 ln , + ( , ) = (6-23) ln(atm 𝑟𝑟 ) + 𝑐𝑐( 𝑛𝑛𝑛𝑛, 𝑛𝑛 ) 𝑐𝑐 �𝑃𝑃 � 𝐾𝐾𝑋𝑋 𝜙𝜙 𝑇𝑇 𝐸𝐸 𝛼𝛼 𝑛𝑛𝑛𝑛𝑛𝑛 𝑛𝑛𝑛𝑛𝑛𝑛 where , is the reduced atmosphere (or,𝑇𝑇 1 atmosphere𝐾𝐾𝐾𝐾 𝑇𝑇 divided𝐸𝐸 by the critical pressure),

atm 𝑟𝑟 𝑛𝑛𝑛𝑛𝑛𝑛 is the reduced𝑃𝑃 normal boiling point, and is given as: 𝑇𝑇

𝜙𝜙 ( , ) = 1 ( + 1) ln( ) + (6-24) 2 2 𝐸𝐸 𝑛𝑛𝑛𝑛𝑛𝑛 𝐸𝐸 𝑛𝑛𝑛𝑛𝑛𝑛 𝑛𝑛𝑛𝑛𝑛𝑛 𝜙𝜙 𝑇𝑇 𝐸𝐸 𝐸𝐸 − − 𝑛𝑛𝑛𝑛𝑛𝑛 − 𝐸𝐸 𝐸𝐸 𝑇𝑇 𝑇𝑇 Equations 6-16 and 6-17 are used to calculate𝑇𝑇 and , respectively. Equations 6-19 through

𝑐𝑐 6-24 provide a set of predictive correlations𝐾𝐾 with𝑋𝑋 values from 1 to 6 in integer steps.

vap These correlations𝑃𝑃 were compared to experimental𝐸𝐸 vapor pressure and liquid heat

capacity data. Vapor pressure and liquid heat capacity data for aldehydes, alkanes, alkenes,

alkynes, amines, aromatics, esters, ethers, gases, halogenated compounds, ketones,

multifunctional compounds, ringed alkanes, silanes, and sulfides were used to determine the

selection of the Riedel coefficient for vapor pressure via the Derivative Method for predicting liquid heat capacity. In 𝐸𝐸this procedure, families such as alcohols and acids were not included because they may require modifications to the vapor pressure correlation form and the equation of state to account for self-association. This analysis showed that an of 2-5 fits these families

much better than the traditional of 6. This method fit vapor pressure𝐸𝐸 as well as other predictive

𝐸𝐸 65 methods, but it fit liquid heat capacity much better than other vapor pressure predictive methods using randomized samples of the compounds with data. Since most liquid heat capacity data are at temperatures close to the triple point, this method improves the shape of the and

vap vap curves at low temperatures where they are difficult to measure. Therefore, this 𝑃𝑃method predictsΔ𝐻𝐻 thermodynamically consistent vapor pressure temperature-dependent correlations over wider temperature ranges than any currently available correlation.

7 EXPERIMENTAL WORK

Many chemical processes operate at the saturation curve of the involved compounds

including distillation, condensation, and boiling. Optimal design of such operations requires

accurate, pure-component, thermodynamic data describing the physical phenomena. In order to

more fully understand these thermophysical properties and to fill gaps in data, experimental

measurements were performed throughout the course of this project. These measurements have

been submitted for publication.

7.1 Compounds

Nineteen industrially important compounds were investigated via DSC to determine melting temperature, enthalpy of melting, and liquid heat capacity. These measurements can be used to derive heat of vaporization and vapor pressure [43]. This work reports the results of DSC

experiments performed on nineteen industrially important compounds to determine melting

temperature, enthalpy of fusion, and liquid heat capacity. The compounds studied are members

of the DIPPR database,[44] which selects compounds based on the needs of leading industrial

companies (url: https://www.aiche.org/dippr) in fields such as energy, pharmaceuticals, chemicals, semiconductors, oil and gas, and risk management.

Some of these compounds are found in the energy industry. o-Tolualdehyde, m-tolualdehyde, and p-tolualdehyde are all auto exhaust pollutants [68, 69]. 2,5-Dimethylfuran has been identified as a cheap alternative liquid fuel [70-72]. 5-Methylfurfural is also an

important biofuel intermediate [73], but is also used in pharmaceutical synthesis [74, 75] and

may have anti-tumor properties [76]. n-Hexylcyclohexane is a pyrolysis product of certain oils

[77]. 2,6-Dimethoxyphenol is a byproduct of the pulp and paper industry [78] that could be used to improve renewable energy storage materials [79].

Other compounds are important to biological systems. m-Tolualcohol is a metabolite of

xylene [80] and a precursor to amides, which are biologically important [81].

1-Phenyl-2-propanol is a useful pharmaceutical intermediate [82]. 2-Phenyl-1-propanol is an

ingredient in fragrances and food flavorings [83] that has been used as a representative drug in

new characterization method studies [84]. 2-Isopropylphenol is an important biochemical [85,

86]. Phenyl acetate is a biochemical that has been linked to depression [87]. Ethyl 2- phenylacetate is naturally occurring in both rice wine and grape wine [88, 89].

1H-Perfluorooctane is a member of the perfluorinated compound family, which are environmentally persistent and important to understand [90-92]. trans-Isoeugenol can be found naturally in plants [93] and has been used as a precursor to antioxidants [94] and biovanillin, a synthetic flavor [95].

The rest of the compounds studied have miscellaneous uses. p-Toluic acid is an OECD high production volume chemical that serves as an intermediate for polyethylene terephthalate production. It also serves as an anticorrosion additive [96]. 1-Phenyl-1-propanol is used as a test compound for racemic mixture separation techniques [97, 98]. 1-Propoxy-2-propanol is used as a cleaner for its quick evaporation and non-polar solvation [99, 100].

There exist few data in the literature about these compounds. Table B-72 through B-75 summarize the data with sources for melting point and enthalpy of fusion, vapor pressure, heat of

68 vaporization, and liquid heat capacity, respectively. A summary and analysis of the existing data appear below.

• Melting Point ( ): Extensive melting point data exist for 2,6-dimethoxyphenol and p-toluic acid.

𝑚𝑚 Two of these melting𝑇𝑇 point data sets are 100 K apart for p-toluic acid, while the data for 2,6-

dimethoxyphenol differ by 4 K at most. Several melting point data exist for p-tolualdehyde, n-

hexylcyclohexane, 6-undecanone, and trans-isoeugenol. The data for p-tolualdehyde range from

320.15 K to 512.15 K, while the data for 6-undecanone only differ by several degrees. The data

for trans-isoeugenol span 8 K, including room temperature. Only one melting point was found in

the literature for 2-phenyl-1-propanol, 2-isopropylphenol, and ethyl 2-phenylacetate.

• Enthalpy of Fusion ( ): Of all 19 compounds, only p-toluic acid has experimental enthalpy

fus of fusion data, whichΔ range𝐻𝐻 from 165 to 208 J g-1.

• Vapor Pressure ( ): Fifteen of the 19 compounds have experimental vapor pressure data,

vap consistent with the𝑃𝑃 idea that vapor pressure is the most commonly measured of these properties.

Of these, 1-phenyl-1-propanol, 2-phenyl-1-propanol, 2-isopropylphenol, 2,5-dimethylfuran, 5-

methylfurfural, phenyl acetate, ethyl 2-phenylacetate, n-hexylcyclohexane, and 1-propxy-2-

propanol contain several sets of independent data. m-Tolualdehyde, p-tolualdehyde, p-toluic acid,

6-undecanone, 1H-perfluorooctane, and trans-isoeugenol only have a few vapor pressure data

points, while o-tolualdehyde, m-tolualcohol, 1-phenyl-2-propanol, and 2,6-dimethoxyphenol did

not have any data.

• Heat of Vaporization: 5-Methylfurfural and n-hexylcyclohexane each contain one calorimetric

heat of vaporization data point around room temperature.

• Liquid Heat Capacity: Ethyl 2-phenylacetate, 2,5-dimethylfuran, and p-toluic acid each have one

liquid heat capacity experimental data point.

Vapor pressure literature data will be fit to a correlation, and the resulting derived heat of vaporization and liquid heat capacity will be compared to both those in literature and new values

measured in this report. Literature melting points and enthalpies of melting will be compared to

new values reported here.

Table 7-1 lists the compounds (with CAS number) examined in this study. Also found in the table are the molecular weight of the compounds, the supplier, the supplier-stated purity,

measured purities, and the expected compounds comprising any impurities (when known). All

samples were used “as is” without further purification. The data found in the Measured Purities

column were measured “in-house” to verify the supplier impurities. These experiments were

performed using an Agilent Technologies 7890A gas chromatograph system coupled with a

7683B series injector and 5975C inert XL EI MSD. Each compound ran through the GCMS

multiple times, with the results converted to mass fractions and compared to the supplier lot

analyses (See Table 7-1). The solid samples were dissolved in acetone before running through

the GCMS. Besides n-hexylcyclohexane, all of the compounds were above 98.0% pure. Eleven

of the nineteen compounds were above 99.0% pure. Eight compounds used for verification are

similarly listed in Table 7-2. All of these compounds were above 99.0% pure.

7.2 Calibrations/Verifications

The melting points, enthalpies of fusion, heat capacities, and glass transition temperatures

were measured using a TA Instruments Q2000 MDSC (Modulated Differential Scanning

Calorimeter). The temperature can range from 183 K to 823 K. The accuracy on temperature

measurement was ± 0.1 °C, while the precision of temperature appears to be within ± 0.01 °C.

This DSC takes advantage of patented Tzero technology, which incorporates cell resistance and

capacitance characteristics, therefore pinpointing heat flow with greater sensitivity and flatter

baselines.

Table 7-1: Purities of compounds measured in this study Compound CAS No. MW Supplier Supplier Measured Main Impurity o-Tolualdehyde 529-20-4 120.15 Sigma Aldrich 98.9% 98.3% m-, and p- tolualdehyde m-Tolualdehyde 620-23-5 120.15 Sigma Aldrich 98.9% p-Tolualdehyde 104-87-0 120.15 Sigma Aldrich 98.8% m-Tolualcohol 587-03-1 122.17 Sigma Aldrich 98.9% 99.7% Benzylalcohol p-Toluic Acid 99-94-5 136.15 Sigma Aldrich 99.5% 98.9% 2,2-dimethoxypropane 1-Phenyl-1-propanol 93-54-9 136.19 TCI America 99.4% 99.8% Propylbenzene 1-Phenyl-2-propanol 698-87-3 136.19 TCI America 99.9% 99.98% 1,2-ethanediol-1,2-diphenyl 2-Phenyl-1-propanol 1123-85-9 136.19 TCI America 99.8% 99.7% 2-cyclohexyl-1-propanol 2-Isopropylphenol 88-69-7 136.19 TCI America 99% 99.2% m-, and p- isopropylphenol 2,5-Dimethylfuran 625-86-5 96.13 Sigma Aldrich 99.8% 5-Methylfurfural 620-02-0 110.11 Sigma Aldrich 99.5% 99.5% 5-methyl-2(3H)furanone Phenyl acetate 122-79-2 136.15 Sigma Aldrich 99.8% Ethyl 2-phenylacetate 101-97-3 164.20 Sigma Aldrich 99.8% n-Hexylcyclohexane 4292-75-5 168.32 TCI America 98.6% 97.9% 3-methylpentylcyclohexane 1H-Perfluorooctane 335-65-9 420.07 Aldrich 99.9% 2,6-Dimethoxyphenol 91-10-1 154.17 Sigma Aldrich 99.1% trans-Isoeugenol 5932-68-3 164.20 Sigma Aldrich cis+trans: trans: 99.3% >98.5% 1-Propoxy-2-propanol 1569-01-3 118.18 Sigma Aldrich 99.8% 98.6% 6-Undecanone 927-49-1 170.29 Sigma Aldrich 98.6%

Table 7-2: Purities of verification compounds used in this study Chemical Name CAS no. Supplier Supplier Measured Main Impurity Naphthalene 91-20-3 Fluka Analytical 99.9% 99.84% thionaphthene Toluene 108-88-3 Sigma Aldrich 99.96% 99.93% ethylbenzene 1-Octanol 111-87-5 Fischer Scientific 99.8% 99.2% other alkanols n-Eicosane 112-95-8 Alfa Aesar 98.7% n-Decane 124-18-5 Alfa Aesar 99.3% 98.9% branched decanes n-Heptane 142-82-5 Sigma Aldrich 99.9% 99.86% methylcyclohexane 1,6-Hexanediol 629-11-8 Aldrich Chemistry 99.7% 99.92% water n-Pentacosane 629-99-2 Alfa Aesar 99.4%

Several calibrations were performed to ensure low uncertainty measurement. The

baseline was calibrated using sapphire disks. The temperature was calibrated using indium,

water, and adamantane with ASTM standard E967-08, through which the measured melting

temperatures were compared to literature values, and a cubic spline was fit to the calibration

curve over that range. The heat flow was calibrated using indium with ASTM standard E968-02,

through which the measured enthalpy of fusion was compared to literature enthalpy of fusion

values, and the measured heat flow was scaled. The temperature and heat flow calibrations were

verified by comparing melting points and enthalpies of fusion of several well-known compounds

to that in the literature, with results given in Table 7-3 and shown graphically in Figure 7-1 [44].

Each compound was taken to at least 15 °C below the literature melting point, then heated at 2

°C/min to at least 15 °C above the literature melting point. The melting temperatures and

enthalpies of fusion were determined graphically from the melt endotherm using TA

Instruments’ Universal Analysis toolkit in conjunction with ASTM standards E793-06 and E794-

06.

Table 7-3: Temperature and heat verification of melting point (Tm/K) -1 and enthalpy of fusion (ΔHfus/J g ) a b a b Chemical Name Literature Tm Experimental Tm Literature ΔHfus Experimental ΔHfus n-Decane 244±2.4[101] 243.03±0.04 202±2.0[102] 196.66±0.70 1-Octanol 257.7±0.5[103] 256.5±0.2 174±1.7[104] 176±4.4 n-Eicosane 309.6±0.6[102] 308.7±0.1 247±2.5[102] 243±4.8 1,6-Hexanediol 315±3.2[102] 312.6±0.4 206±6.5[105] 208±4.3 n-Pentacosane 327±3.3[106] 326.6±0.5 164±4.9[106] 157±3.0 Naphthalene 353±3.5[107] 353.0±0.4 148±1.5[107] 146±3.9 aUncertainty based on the DIPPR uncertainty bUncertainty given as the 95% confidence interval

3 10

2 ) - 1 6

(K) (Jg m

fus 4

1 H Δ 2

0 0 Literature T Literature

- 220 270 320 370 120 170 220 270 Literature

- -2 -1 -4

Measured -6 -2 Measured -8

-3 -10 Literature Enthalpy of fusion (J g-1) Literature Melting Point (K)

Figure 7-1: Verification results for a) temperature and b) heat calibrations, with the average difference for each compound from the DIPPR value [44] ( ) and 95% confidence intervals on the measurements, and the uncertainties from this study ( )

The MDSC heat capacity was calibrated using toluene and naphthalene with ASTM

standard E2716-09. The modulation frequency was lengthened to accommodate the slow thermal reaction of the liquid samples. Additionally, the isothermal time was increased from 20 to 30 minutes to allow the heat capacity to equilibrate. Each day before heat capacities were measured, the heat flow and heat capacity were calibrated by indium and toluene or naphthalene, depending on the temperature of the heat capacity measurement. Toluene was used to calibrate below 363

K, and naphthalene was used to calibrate 363 K to 473 K. This ensured that no calibration was

performed too close to the normal boiling point. The calibration method was verified by

measuring the heat capacity of n-heptane at -25, 25, and 75 °C as shown in Figure 7-2 with the

DIPPR correlation, DIPPR uncertainty, and literature data. This gave a bias of -0.05% with an average 95% confidence interval of 1.59%. The high temperature calibration method was verified by measuring the heat capacity of sapphire at 100, 140, 180, and 200 °C as shown in

Figure 7-3 with the DIPPR correlation, DIPPR uncertainty, and literature data. This gave a bias

of -0.34% with an average 95% confidence interval of 1.19%. Note that DIPPR gives two

correlations for the solid heat capacity of sapphire that meet at 400 K, giving a discontinuity in

the correlations that doesn’t appear in the literature. The average 95% confidence intervals for

both the low and high temperature verifications are within the 3.2% mean repeatability value

given in ASTM 2716-09.

2.6 DIPPR Correlation 2.5 1% Uncertainty 2.4 )

1 Verification Data - K 2.3 1 - Literature Data (J g

l 2.2 p C 2.1

2.0

1.9 175 225 275 325 375 T/K

Figure 7-2: Verification results for heat capacity of n-heptane with 95% confidence intervals compared to the DIPPR correlation, DIPPR uncertainty, and literature data

A glass transition was observed for several of the compounds. In these cases, ASTM

standard E1356-08 was followed with a 2 °C/min heating rate. Since these compounds have low molecular weights compared to polymers, and the measured glass transition temperatures were sub-ambient, it is assumed that no other reactions occurred.

1.10

1.05

1.00 ) 1 - K 1 - 0.95 (J g

l DIPPR Correlation p C 0.90 Literature Data

0.85 3% Uncertainty Verification Data 0.80 350 400 450 500 T/K Figure 7-3: Verification results for heat capacity of sapphire with 95% confidence intervals compared to the DIPPR correlation, DIPPR uncertainty, and literature data

7.3 Uncertainties

Based on the stated purities (see Table 7-1), and the calibration/verification tests

described in the previous section, the process uncertainty in melting point and glass transition temperature measurements were determined to be ± 1.0 K each, and the process uncertainty in the enthalpy of fusion measurements was determined to be ± 5 J/g. The uncertainties were found

by comparing the measured values and 95% confidence intervals to experimentally verified

DIPPR values and uncertainties. For the compounds measured in this study, enough melting

point and enthalpy of fusion replicates were performed so that the 95% confidence intervals were

smaller than the process uncertainties from the verification results. The impurities measured via

GCMS were estimated to affect the melting point and enthalpy of fusion to within the

uncertainties found in the verification. These uncertainties were used to fit experimental data that

allows thermodynamic analysis for each compound, for vapor pressure, heat of vaporization, and

liquid heat capacity.

7.4 Property Selection for Thermodynamic Analysis

For the compounds in this study, there are not enough vapor pressure experimental data

points to fit all four parameters in the Riedel equation (Equation (5-1). The three techniques used

to fit the data are summarized in Table 7-4, and will be explained here. When there exist reliable

data over a wide temperature range, two of the fitting coefficients are fit using the normal boiling

point and the critical point, leaving two coefficients to fit to data. When there exist only a couple

of vapor pressure data points, the derivative of the Riedel parameter (explained in Chapter 6) is

set to zero as well, leaving only one coefficient to fit to data. When no reliable experimental data

exist, the fully predictive correlation from Chapter 6 is used.

Table 7-4 Summary of vapor pressure fitting techniques Technique Name Coefficients Fit to Data When Used Riedel 3 2 Reliable data over a wide temperature range Riedel 2 1 Few data over a small temperature range Predictive 0 No reliable experimental data

7.5 Results

Melting point, enthalpy of melting, and liquid heat capacity results of these compounds

were compared to similar compounds not measured in this report, with values and uncertainties

from the DIPPR database. Liquid heat capacity was measured at discrete temperatures and

repeated as often as time allowed, resulting in average 95% confidence intervals of ±0.031 J g-1

K-1 or 1.52% over all temperatures and compounds. Enough melting point and enthalpy of

melting replicates were performed so that the 95% confidence intervals were smaller than the

process uncertainties from the verification results. Some compounds were unable to freeze

within the temperature range of the DSC, so their melting points were not measured. Compounds

that were solid at room temperature were pre-melted before melting point and enthalpy of fusion

measurements were taken. Liquid heat capacity was measured at discrete temperatures and

replicated as time permitted until the 95% confidence intervals shrunk to within 3% of the

average value. All liquid heat capacity measurements were done below the DIPPR-assigned normal boiling point for each compound so that vapor heat capacity could be ignored. For convenience, all the liquid heat capacity, melting point, and enthalpy of fusion measurements are summarized in Table 7-5, Table 7-6, and Table 7-7, respectively. The compounds measured are given below, grouped by common functional groups.

Table 7-5: Summary of liquid heat capacity measurements with uncertainties Compound T/K Cp/(J g-1 K-1) Replicates o-Tolualdehyde 238.16 1.535±0.027 15 293.16 1.661±0.027 7 348.15 1.813±0.020 15 403.13 1.920±0.023 9 458.11 2.173±0.038 16 m-Tolualdehyde 273.17 1.577±0.032 10 313.16 1.714±0.041 11 353.15 1.829±0.023 11 393.14 1.961±0.035 9 453.11 2.148±0.043 12 p-Tolualdehyde 273.17 1.593±0.016 16 313.16 1.700±0.020 17 353.15 1.800±0.023 12 393.14 1.934±0.027 16 453.11 2.089±0.032 8 m-Tolualcohol 266.15 1.819±0.019 6 306.15 2.053±0.031 5 356.15 2.301±0.022 16 406.15 2.417±0.022 12 456.15 2.522±0.015 18

p-Toluic acid 458.15 2.433±0.044 10 473.15 2.485±0.016 8 488.15 2.553±0.029 9 503.15 2.600±0.020 8 523.15 2.659±0.019 5

Table 7-5: continued Compound T/K Cp/(J g-1 K-1) Replicates 1-Phenyl-1-propanol 273.15 2.053±0.055 13 323.15 2.349±0.046 13 373.15 2.482±0.067 13 423.15 2.589±0.058 12 473.15 2.709±0.080 16 1-Phenyl-2-propanol 273.15 2.071±0.033 10 323.15 2.284±0.027 11 373.15 2.418±0.042 11 423.15 2.537±0.023 17 473.15 2.605±0.065 6 2-Phenyl-1-propanol 273.15 2.007±0.037 10 323.15 2.210±0.054 13 373.15 2.393±0.051 19 423.15 2.511±0.066 6 473.15 2.583±0.029 16 2-Isopropylphenol 273.15 2.070±0.026 9 323.15 2.257±0.039 11 373.15 2.361±0.022 8 423.15 2.481±0.057 14 473.15 2.602±0.047 9 5-Methylfurfural 250.15 1.639±0.008 12 300.15 1.748±0.017 9 350.14 1.839±0.008 9 400.13 1.992±0.022 10 450.10 2.121±0.019 13 2,5-Dimethylfuran 213.15 1.657±0.019 12 253.15 1.706±0.024 8 293.15 1.775±0.018 8 333.15 1.924±0.017 9 Phenyl acetate 253.15 1.619±0.015 14 293.15 1.651±0.027 13 333.15 1.763±0.012 16 373.15 1.876±0.025 13 413.15 1.979±0.034 11 Ethyl 2-phenylacetate 253.15 1.655±0.019 13 293.15 1.759±0.051 11 333.15 1.783±0.021 12 373.15 1.869±0.024 12 413.15 1.987±0.024 12 n-Hexylcyclohexane 228.16 1.735±0.020 14 288.16 1.962±0.031 15 348.14 2.146±0.044 22 408.13 2.429±0.032 19 468.09 2.755±0.042 8

Table 7-5: continued Compound T/K Cp/(J g-1 K-1) Replicates 6-Undecanone 293.16 2.136±0.039 9 343.16 2.241±0.027 16 373.15 2.363±0.025 9 423.13 2.481±0.021 12 473.10 2.719±0.022 12 1H-Perfluorooctane 258.16 1.062±0.015 9 273.16 1.092±0.011 11 298.16 1.143±0.009 7 323.16 1.178±0.018 11 373.14 1.254±0.008 11 2,6-Dimethoxyphenol 333.16 2.058±0.031 8 373.15 2.190±0.049 9 413.14 2.163±0.056 9 453.12 2.252±0.042 10 493.10 2.318±0.052 9 trans-Isoeugenol 298.15 1.991±0.064 7 323.15 2.049±0.058 8 373.15 2.122±0.028 20 423.15 2.324±0.031 8 473.15 2.358±0.041 17 1-Propoxy-2-propanol 193.19 2.009±0.018 7 223.15 2.098±0.011 10 273.16 2.294±0.013 11 323.16 2.455±0.019 12 373.15 2.663±0.018 17

Table 7-6: Summary of experimental melting point measurements a Chemical Name Tm/K Replicates o-tolualdehyde 233.4 6 m-tolualdehyde 224.7 3 p-toluladehyde 263.1 5 m-tolualcohol 264.3 10 p-toluic acid 452.1 10 1-phenyl-1-propanol 262.6 3 2-isopropylphenol 285.0 8 5-methylfurfural 240.5 20 phenyl acetate 266.0 4 ethyl 2-phenylacetate 244.0 3 hexylcyclohexane 224.9 23 6-undecanone 286.0 5 1H-perfluorooctane 254.3 8 2,6-dimethoxyphenol 326.4 5 trans-Isoeugenol 294.7 12 a Uncertainty of 1 K

Table 7-7 Summary of experimental enthalpy of fusion measurements a -1 Chemical Name ΔHfus /(J g ) Replicates o-tolualdehyde 84.8 11 p-toluladehyde 91.9 5 m-tolualcohol 111 28 p-toluic acid 158 9 2-isopropylphenol 80.6 8 5-methylfurfural 105 20 phenyl acetate 94.1 4 ethyl 2-phenylacetate 110 3 hexylcyclohexane 122 23 6-undecanone 184 5 1H-perfluorooctane 23.5 8 2,6-dimethoxyphenol 326 5 trans-Isoeugenol 71.3 13 a Uncertainty of 5 J/g

7.5.1 Toluene Derivatives

The melting points, enthalpies of fusion, and liquid heat capacities of several phenolic

compounds were measured. These included toluenes with alcohol, aldehyde, or acid groups on

the meta-, ortho-, or para- positions, as pictured in Figure 7-4. Table 7-8 and Figure 7-5 show

the experimental melting points obtained in this work with the values from chemically-similar compounds, like the xylenes. The uncertainties are also depicted. The values for the similar compounds came from the DIPPR database. Notice that the meta- compounds all melt at lower temperatures for each family (alcohol, aldehyde, acid). Also note that for each of the group

positions (meta-, ortho-, para-) the melting point order is tolualdehyde, xylene, tolualcohol,

toluic acid. Of particular note is the melting point for p-toluic acid. This study places the value at

452.1 K, within several degrees of some studies [108-112] but 100 K lower than others [113,

114]. The value measured was about 70 K above that for m-toluic acid, which is close to the

same difference between the melting points of p- and m- xylene. It therefore appears that the

higher values [113, 114] are in error.

O O O

m-tolualdehyde o-tolualdehyde p-tolualdehyde

p-toluic acid m-tolualcohol

Figure 7-4 The toluene derivatives measured in this study

Table 7-8: Summary of experimental melting points for the toluene derivatives Chemical Name Tm/K (Reps) Type Source o-xylene 247.98±0.5 Experimental DIPPR m-xylene 225.3±0.45 Experimental DIPPR p-xylene 286.40±0.57 Experimental DIPPR o-tolualdehyde 233.4±1.0(6) Experimental This Report m-tolualdehyde 224.7±1.0(3) Experimental This Report p-toluladehyde 263.1±1.0(5) Experimental This Report o-tolualcohol 309.15±3 Experimental DIPPR m-tolualcohol 264.3±1.0(10) Experimental This Report p-tolualcohol 332.65±3.3 Experimental DIPPR o-toluic acid 377±11 Experimental DIPPR m-toluic acid 384.15±3.8 Experimental DIPPR p-toluic acid 452.1±1.0(10) Experimental This Report

500

450

400

(K) 350 m T 300

250

200 ortho- meta- para-

Figure 7-5 Melting points for xylenes ( ), tolualdehydes ( ), tolualcohols ( ), and toluic acids ( ) with uncertainties contained within the size of the markers, open symbols represent new data from this study

Table 7-9: Summary of enthalpy of fusion experimental results for the toluene derivatives -1 Chemical Name ΔHfus /(J g ) (Reps) Type Source o-xylene 128.16±0.26 Experimental DIPPR m-xylene 109.7±1.1 Experimental DIPPR p-xylene 161.2±1.6 Experimental DIPPR o-tolualdehyde 84.8±5(11) Experimental This Report m-tolualdehyde 90±23 Predicted [115] DIPPR p-toluladehyde 91.9±5(5) Experimental This Report o-tolualcohol 106±26 Predicted [116] DIPPR m-tolualcohol 111.0±5(28) Experimental This Report p-tolualcohol 98±25 Predicted [115] DIPPR o-toluic acid 148.1±1.5 Experimental DIPPR m-toluic acid 115.3±1.1 Experimental DIPPR p-toluic acid 158.3±5(9) Experimental This Report

Figure 7-7 shows the newly-measured experimental liquid heat capacity data for the

toluenes. The position of the aldehyde group on the tolualdehydes does not clearly affect heat

capacity, which is the same conclusion drawn from a review of m-, o-, and p- xylene heat

capacities. The tolualcohol heat capacity shows a curve shape reminiscent of other alcohols [32,

117], and the heat capacity for p-toluic acid fell within 5% of the literature value [118].

180

160

140 ) 1 -

(Jg 120 fus H Δ 100

60 ortho- meta- para-

Figure 7-6 Enthalpies of fusion for xylenes ( ), tolualdehydes ( ), tolualcohols ( ), and toluic acids ( ) with uncertainties from DIPPR and this study, open symbols represent new data from this study

Table 7-10 gives vapor pressure curve summaries. The vapor pressure data and critical

constant prediction methods were re-evaluated, and best fits were found that went through the

newly-measured heat capacity data when the Derivative method was used. Each of the vapor

pressure curves had Riedel E values of 3, which is consistent with the results of Chapters 5 and

6. Of note, the average absolute errors (AAD’s) of the vapor pressure fits to data for m-

tolualdehyde and o-tolualdehyde were above 10%. However, the DIPPR vapor pressure

correlations for these two compounds both gave AAD’s above 10% as well, so this large number

was a result of scatter in the data.

2.8

2.6

2.4 ) 1 -

K 2.2 1 - (J g

l 2 p C 1.8

1.6

1.4 200 250 300 350 400 450 500 550 T/K

Figure 7-7 Liquid heat capacity measurements for m-tolualdehyde ( ), o-tolualdehyde ( ), p-tolualdehyde ( ), m-tolualcohol ( ), and p-toluic acid ( ) with experimental uncertainty from this study

Table 7-10: Summary of best critical constants and vapor pressure coefficients for the tolualdehydes Property m-Tolualdehyde o-Tolualdehyde p-Tolualdehyde Tc Method Lydersen [119] Lydersen [119] Lydersen [119] Tc/K 691.2 694.2 703.3 Pc Method Lydersen [119] Lydersen [119] Lydersen [119] Pc/MPa 3.671 3.671 3.671 Tnb Method DIPPR DIPPR DIPPR Tnb/K 472.15 474.15 480.4 Fitting Method Riedel 2 Riedel 2 Riedel 3 Ptp/Pa 0.96 0.11 2.0 Pvap(A) 87.605 112.37 82.487 Pvap (B) -9133 -10409 -9074 Pvap (C) -9.2902 -12.922 -8.4971 Pvap (D) 4.445E-9 6.8329E-9 3.553E-9 Pvap (E) 3 3 3 Pvap AAD 18.1 10.2 3.19 ΔHvap AAD ------l Cp AAD 2.3 0.94 0.61

7.5.2 Phenyl Propanols

The structures of four of the measured compounds—1-1-Phenyl-1-propanol, 1-phenyl-2- propanol, 2-phenyl-1-propanol, and 2-isopropylphenol—are found in Figure 7-8. 2-

Isopropylphenol froze and melted like other compounds in this study, but the other phenyl propanols each formed an amorphous glass, similar to glycerol [120]. As in other studies, these glass transitions were identified by a step change in the baseline, or heat capacity [40, 121].

These glass transition temperatures were measured, and are given in Table 7-11.

OH HO

1-phenyl-1-propanol 1-phenyl-2-propanol 2-phenyl-1-propanol

2-isopropylphenol Figure 7-8: The phenyl propanols measured in this study

Table 7-11: Summary of experimental glass transition temperatures for the phenyl propanols Chemical Name Tg/K (Reps) Type Source 1-phenyl-1-propanol 198.8±1.0(5) Experimental This Report 1-phenyl-2-propanol 200.6±1.0(6) Experimental This Report 2-phenyl-1-propanol 197.6±1.0(8) Experimental This Report glycerol 190 Experimental [122]

The melting point of 1-phenyl-1-propanol was measured using methodology similar to glycerol which will be described here [123]. The DSC was cooled at a rate of 0.1 °C/min to just above the glass transition temperature at 203.15 K and held 3 hours. Then, it was heated at a rate of 1 °C/min to 218.15 K and held for 6 hours. Finally, the cell was heated at a rate of 0.5 °C/min to 288.15 K to observe the exothermic freezing and endothermic melting peaks. Unfortunately, the data produced from these runs were not sufficiently consistent to repeat for the other phenyl propanols.

Melting point results for 1-phenyl-1-propanol and 2-isopropylphenol are given in Table

7-12. When the alcohol group is moved from the propane chain to the benzene as in

2-isopropylphenol, no glass is observed, and melting point can be easily determined. The measured heat capacities are plotted in Figure 7-9 showing that the placement of the phenyl and alcohol groups had little effect on the measured values.

Table 7-12: Summary of experimental melting points for the phenyl propanols Chemical Name Tm/K (Reps) Type Source 1-phenyl-1-propanol 262.6±1.0(3) Experimental This Report glycerol 291.33±2.9 Experimental DIPPR 2-isopropylphenol 285.0±1.0(8) Experimental This Report

Table 7-13: Summary of enthalpy of fusion experimental results for the phenyl propanols -1 Chemical Name ΔHfus /(J g ) (Reps) Type Source 1-phenyl-1-propanol ------glycerol 198.5±6.0 Experimental DIPPR 2-isopropylphenol 80.6±5.0(8) Experimental This Report

2.7 ) 1

- 2.5 K 1 -

(J g 2.3 l p C 2.1

1.9 260 310 360 410 460 T/K

Figure 7-9 Liquid heat capacity measurements for 1-phenyl-1-propanol ( ), 1-phenyl-2-propanol ( ), 2-phenyl-1-propanol ( ), and 2-isopropylphenol ( ) with experimental uncertainty

7.5.3 Furans

2,5-Dimethylfuran and 5-methylfurfural (Figure 7-10) were measured to help understanding of the furan family. These were compared to existing data for furan and furfural whose structures are shown in Figure 7-11.

O O O

2,5-dimethylfuran 5-methylfurfural Figure 7-10: The furans measured in this study

O O O

furan furfural Figure 7-11: Comparison compounds for the furans

Table 7-14 summarizes the experimental data (from both DIPPR and this study) for the

four furans mentioned above. The measured melting point for 5-methylfurfural fell within the

DIPPR assigned uncertainty of the melting point for furfural. Unfortunately, the melting point

for 2,5-dimethylfuran was too low for the DSC to measure, so the reported value in the table is

the DIPPR value.

Table 7-14: Summary of experimental melting points for the furans Chemical Name Tm/K (Reps) Type Source 5-methylfurfural 240.5±1.0(20) Experimental This Report 2,5-dimethylfuran 210.4±2.1 Experimental DIPPR furfural 236.65±7.1 Experimental DIPPR furan 187.55±0.38 Experimental DIPPR

Table 7-15 lists the enthalpy of fusion results for the four furans. The value for 2,5- dimethylfuran is listed as predicted because, as just explained, the melting point was too low for

the DSC to measure. This predicted value came from the DIPPR database. The enthalpy of

fusion for 5-methylfurfural was measured to be 105.22 ± 5 J g-1 which is much lower than

furfural. This would indicate that the methyl group makes it difficult for the compound to pack

into a crystal lattice structure, so less energy would be needed to move to the liquid phase.

Table 7-15: Summary of enthalpy of fusion experimental results for the furans -1 -1 Chemical Name ΔHfus /(J g ) (Reps) Uncertainty/(J g ) Source 5-methylfurfural 105.22±5.0(20) Experimental This Report 2,5-dimethylfuran 83±21 Predicted [115] DIPPR furfural 149.9±4.5 Experimental DIPPR furan 55.87±0.56 Experimental DIPPR

Table 7-16 shows the results of the thermodynamic analysis using the reported liquid heat

capacity data for 5-methylfurfural and 2,5-dimethylfuran. In particular, the critical temperature,

critical pressure, normal boiling point, and Riedel E value were selected in order to

simultaneously fit vapor pressure and newly-measured heat capacity data. Both of these compounds used the same E value of 3, which follows the idea that compounds in the same family are best fit using the same E values.

Table 7-16: Summary of best critical constants and vapor pressure coefficients for the furans Property 5-Methylfurfural 2,5-Dimethylfuran nd Tc Method WJ 2 Order [2] Joback [2] Tc/K 692.5 558.2 nd Pc Method WJ 2 Order [2] Joback [2] Pc/MPa 4.407 4.173 Tnb Method DIPPR DIPPR Tnb/K 460.15 366.8 Fitting Method Riedel 3 Riedel 2 Ptp/Pa 0.285 7.96 Pvap(A) 91.042 83.895 Pvap (B) -9452.27 -6995.96 Pvap (C) -9.67447 -9.09288 Pvap (D) 3.54388E-9 8.00850E-9 Pvap (E) 3 3 Pvap AAD 1.64 0.068 ΔHvap AAD 0.89 -- l Cp AAD 0.53 2.082

7.5.4 Phenyl Acetates

The structures of the two phenyl acetates measured are shown in Figure 7-12. Figure 7-13

shows benzyl acetate and methyl benzoate, which are chemically similar to the phenyl acetates

measured.

O O O

phenyl acetate ethyl 2-phenylacetate

Figure 7-12: The phenyl acetates measured in this study

O O

benzyl acetate methyl benzoate Figure 7-13: Comparison compounds for the phenyl acetates

Table 7-17 summarizes the experimental melting point data (from both DIPPR and this study) for the four esters mentioned above. The measured melting point for ethyl 2-phenylacetate is higher than the DIPPR value for benzyl acetate, which would be consistent with a molecular weight argument. The measured melting point for phenyl acetate is slightly higher than the

DIPPR value for methyl benzoate, which means that the ester group packs better into a crystal lattice when the carbonyl group is moved away from the phenyl group. Table 7-18 shows the experimental enthalpy of fusion data for these esters. Both of the measurements by this study are higher than the DIPPR values for benzyl acetate and methyl benzoate.

Table 7-17: Summary of experimental melting points for the phenyl acetates Chemical Name Tm/K (Reps) Type Source phenyl acetate 266.0±1.0(4) Experimental This Report ethyl 2-phenylacetate 244.0±1.0(3) Experimental This Report benzyl acetate 221.65±2.2 Experimental DIPPR Methyl benzoate 260.75±2.6 Experimental DIPPR

Table 7-18: Summary of enthalpy of fusion experimental results for the phenyl acetates -1 Chemical Name ΔHfus /(J g ) (Reps) Type Source phenyl acetate 94.1±5.0(4) Experimental This Report ethyl 2-phenylacetate 110±5.0(3) Experimental This Report benzyl acetate 79±19 Predicted [115] DIPPR Methyl benzoate 71.5±0.715 Experimental DIPPR

Table 7-19 shows the results of the thermodynamic analysis done using the vapor pressure and liquid heat capacity data to find the best vapor pressure curve fit. Both of the compounds measured were best represented using a Riedel E value of 3, which has been a common result for many of these organic compounds.

Table 7-19: Summary of best critical constants and vapor pressure coefficients for the phenyl acetates Property Phenyl Acetate Ethyl Phenyl Acetate Tc Method Lydersen [119] Joback [2] Tc/K 687.1 702.4 Pc Method Lydersen [119] Joback [2] Pc/MPa 3.587 2.947 Tnb Method DIPPR DIPPR Tnb/K 468.85 498.55 Fitting Method Riedel 3 Riedel 2 Ptp/Pa 2.9 0.023 Pvap(A) 91.709 115.462 Pvap (B) -9642.6 -11507.2 Pvap (C) -9.7509 -13.1213 Pvap (D) 3.4375E-9 5.2518E-9 Pvap (E) 3 3 Pvap AAD 2.5 8.4 ΔHvap AAD -- -- l Cp AAD 0.70 2.69

7.5.5 n-Hexylcyclohexane

Recently, DIPPR performed a family review of the n-alkyl cyclohexanes. To help bolster that review, n-hexylcyclohexane, pictured in Figure 7-14, was measured. The experimental

melting point of this compound along with the accepted DIPPR values for ethyl-, butyl-, and

octylcyclohexane are found in Table 7-20. Table 7-21 contains the values for the enthalpy of fusion for the same compounds. Notice that the experimental melting point and enthalpy of fusion for n-hexylcyclohexane found in this work follows the family trends. Specifically, melting point appears to increase 20-30 K and enthalpy of fusion increases 20-30 J g-1 for every two

carbons added to the alkyl chain.

n-hexylcyclohexane Figure 7-14: n-hexylcyclohexane

Table 7-20: Summary of experimental melting points for the alkylcyclohexanes Chemical Name Tm/K (Reps) Type Source Ethylcyclohexane 161.5±0.5 Experimental DIPPR Butylcyclohexane 198.42±0.4 Experimental DIPPR Hexylcyclohexane 224.9±1.0(23) Experimental This Report Octylcyclohexane 252.75±2.5 Experimental DIPPR

Table 7-21: Summary of enthalpy of fusion experimental results for the alkylcyclohexanes -1 Chemical Name ΔHfus /(J g ) (Reps) Type Source Ethylcyclohexane 74.3±0.7 Experimental DIPPR Butylcyclohexane 101.0±0.2 Experimental DIPPR Hexylcyclohexane 122.1±5.0(23) Experimental This Report Octylcyclohexane 153.4±7.7 Experimental DIPPR

Figure 7-15 shows the experimental liquid heat capacity data as a function of temperature

for ethyl-, butyl-, and hexylcyclohexane. (No experimental values exist for octylcyclohexane.)

The family trends also hold for the newly-measured data. The magnitudes of the values for n-

hexylcyclohexane are comparable to those of the other to alkylcyclohexanes on a mass basis.

Table 7-22 summarizes the best vapor pressure fit that meets the newly-measured liquid heat capacity data using the Derivative method. A Riedel E value of 3 did the best job at fitting not just the data for n-hexylcyclohexane, but for the other alkyl cyclohexanes as well.

2.8

2.6

2.4 ) 1 - K 2.2 1 - (J g

l 2 p C 1.8

1.6

1.4 150 200 250 300 350 400 450 500 T/K

Figure 7-15: Liquid heat capacity data for n-ethyl- ( ) and n-butyl- ( ) with DIPPR uncertainty, and n-hexyl- ( ) cyclohexane and experimental uncertainty

Table 7-22: Summary of best critical constants and vapor pressure coefficients for n-hexylcyclohexane Property n-Hexylcyclohexane Tc Method Lydersen [119] Tc/K 686.6 Pc Method Lydersen [119] Pc/MPa 2.154 Tnb Method DIPPR Tnb/K 497.93 Fitting Method Riedel 2 Ptp/Pa 4.06E-3 Pvap(A) 108.850 Pvap (B) -1075.1 Pvap (C) -12.301 Pvap (D) 5.3750E-9 Pvap (E) 3 Pvap AAD 0.981 ΔHvap AAD -- l Cp AAD 2.729

7.5.6 6-Undecanone

The di-n-alkyl ketone family required more data to bolster a DIPPR family review, so

6-undecanone (or dipentyl ketone, as shown in Figure 7-16) was measured. Table 7-23 and Table

7-24 show that the measured melting point and enthalpy of fusion followed family trends of about 15-20 K and 10 J g-1 increments, respectively. The vapor pressure data were re-evaluated,

and the most thermodynamically consistent fit is summarized in Table 7-25. Once again a Riedel

E value of 3 gave the best vapor pressure fit for not just this compound, but the other compounds

in the family.

6-undecanone Figure 7-16: 6-undecanone

Table 7-23: Summary of experimental melting points for the di-n-alkyl ketones Chemical Name Tm/K (Reps) Type Source 3-Pentanone 234.2±2.3 Experimental DIPPR 4-Heptanone 240.7±2.4 Experimental DIPPR 5-Nonanone 267.3±2.7 Experimental DIPPR 6-Undecanone 286.0±1.0(5) Experimental This Report

Table 7-24: Summary of enthalpy of fusion experimental results for the di-n-alkyl ketones -1 Chemical Name ΔHfus /(J g ) (Reps) Type Source 3-Pentanone 134.5 Experimental DIPPR 4-Heptanone 163±41 Predicted [115] DIPPR 5-Nonanone 175.3 Experimental DIPPR 6-Undecanone 184±5.0(5) Experimental This Report

Table 7-25: Summary of best critical constants and vapor pressure coefficients for 6-undecanone Property 6-Undecanone Tc Method Experimental [124] Tc/K 678.5

Table 7-26: continued Property 6-Undecanone Pc Method Lydersen [119] Pc/MPa 2.052 Tnb Method DIPPR Tnb/K 500.55 Fitting Method Riedel 3 Ptp/Pa 2.6 Pvap(A) 133.55 Pvap (B) -12,486 Pvap (C) -15.754 Pvap (D) 6.729E-9 Pvap (E) 3 Pvap AAD 1.88 ΔHvap AAD -- l Cp AAD 1.04

7.5.7 1H-Perfluorooctane

Few data exist for the 1H-perfluoro family in the DIPPR database, so 1H-perfluorooctane

(as shown in Figure 7-17) was purchased and measured. It gave a slightly higher melting point than perfluorooctane, as shown in Table 7-26. The enthalpy of fusion measurement was the same as perfluorooctane, within the experimental uncertainty, as shown in Table 7-27.

F2 F2 F2 C C C CF3 HF2C C C C F F F 2 2 2 1H-perfluorooctane Figure 7-17: 1H-perfluorooctane

Table 7-26: Summary of experimental melting points for 1H-perfluorooctane and related compounds Chemical Name Tm/K (Reps) Type Source 1H-perfluorooctane 254.3±1.0(8) Experimental This Report perfluorooctane 250±2.5 Experimental DIPPR 1H-perfluorohexane 180.15±18 Not Specified [125] DIPPR

Table 7-27: Summary of enthalpy of fusion experimental results for 1H-perfluorooctane and related compounds -1 Chemical Name ΔHfus /(J g ) (Reps) Type Source 1H-perfluorooctane 23.5±5.0(8) Experimental This Report perfluorooctane 21.87±0.22 Experimental DIPPR 1H-perfluorohexane 16±8 Predicted [116] DIPPR

7.5.8 2,6-Dimethoxyphenol

2,6-Dimethoxylphenol (Figure 7-18) was measured because no liquid heat capacity data

exist in the literature for it nor chemically-similar compounds such as guaiacol or ethyl vanillin

(Figure 7-19). The measured melting point of 2,6-dimethoxyphenol was 326.4 K (see Table

7-28) and was within 1-2 K of other melting points for 2,6-dimethoxyphenol in the literature

[126-130]. Moreover, its value was between that of guaiacol and ethyl vanillin, which

relationship is reasonable considering the trends in molecular weight.

O O

2,6-dimethoxyphenol Figure 7-18: 2,6-dimethoxyphenol

Table 7-29 shows the measured enthalpy of fusion with that of the similar compounds.

Unfortunately, the uncertainties in the predicted DIPPR enthalpy of fusion values for the

comparison compounds were too high to make a worthwhile comparison, though they do lie in

the vicinity of the new experimental point for 2,6-dimethoxyphenol.

O OH

O H guaiacol ethyl vanillin Figure 7-19: Compounds compared to 2,6-dimethoxyphenol

Table 7-28: Summary of experimental melting points for 2,6-dimethoxyphenol and related compounds Chemical Name Tm/K (Reps) Type Source 2,6-dimethoxyphenol 326.4±1.0(5) Experimental This Report guaiacol 304.65±9.1 Not Specified [131] DIPPR ethyl vanillin 350.65±3.5 Not Specified [132] DIPPR

Table 7-30 gives the parameters for the best vapor pressure correlation that meets the measured liquid heat capacity data. Although there exist a couple of vapor pressure data points for 2,6-dimethoxyphenol, they vary from DIPPR’s current vapor pressure expression by an average of 60% error [127, 133, 134]. However, fitting these data did not produce a correlation that was consistent with the newly-measured liquid heat capacity data. Using the new prediction for vapor pressure described in Chapter 6 with an E value of 3 helped improve the consistency of the vapor pressure curve to within the error in the heat capacity data without significantly increasing the average vapor pressure error.

Table 7-29: Summary of enthalpy of fusion experimental results for 2,6-dimethoxyphenol and related compounds -1 Chemical Name ΔHfus /(J g ) (Reps) Type Source 2,6-dimethoxyphenol 113.7±5.0(5) Experimental This Report guaiacol 100±50 Predicted [116] DIPPR ethyl vanillin 113±28 Predicted [115] DIPPR

Table 7-30: Summary of best critical constants and vapor pressure coefficients for 2,6-dimethoxyphenol Property 2,6-Dimethoxyphenol Tc Method Nannoolal [135] Tc/K 752.2 Pc Method Nannoolal [135] Pc/MPa 3.785 Tnb Method DIPPR Tnb/K 534.15 Fitting Method Predictive Ptp/Pa 7.0 Pvap(A) 140.96 Pvap (B) -14490 Pvap (C) -16.4103 Pvap (D) 5.02938E-9 Pvap (E) 3 Pvap AAD -- ΔHvap AAD -- l Cp AAD 1.63

7.5.9 trans-Isoeugenol

trans-Isoeugenol (Figure 7-20) was selected for measurements due to lack of experimental data which caused a thermodynamic consistency problem when the compound was being initially reviewed for addition to the DIPPR database. No experimental melting point was used for the compound prior to this work, and the initial strategy for obtaining a value was to use the prediction method of Constantinou [136]. This gave a melting point value of 324.55 K meaning the compound was a solid at the standard state temperature of 298.15 K. The DIPPR researchers knew that this was unlikely based on the melting temperatures of comparison compounds—specifically eugenol and anethole—whose structures are found in Figure 7-21 and which were known to be liquids at room temperatures.

trans-isoeugenol Figure 7-20: trans-isoeugenol

O O

eugenol anethole Figure 7-21: Comparison compounds for trans-isoeugenol

The experiments performed on trans-isoeugenol found a melting temperature more in

line with expections. Table 7-31 contains the melting point measurements for all three

compounds. Notice that the melting point of trans-isoeugenol is 294.7 K, which means it is a liquid at the standard state condition of 298.15 K. This was especially important when calculating the standard state Gibb’s energy of the compound. Without this experimental value, the incorrect prediction using the Constantinou method resulted in a thermodynamically-

100 inconsistent Gibb’s energy of formation and standard state Gibb’s energy. The new experimental value yielded Gibb’s energies that were consistent with other data.

Table 7-31: Summary of experimental melting points for trans-isoeugenol and related compounds Chemical Name Tm/K (Reps) Type Source trans-isoeugenol 294.7±1.0(12) Experimental This Report eugenol 264±2.64 Experimental DIPPR anethole 294.5±8.8 Not Specified [137] DIPPR

Table 7-32 shows that the measured enthalpy of fusion for trans-isoeugnol was much lower than that of eugenol and anthole. This would indicate that the addition of the alcohol group from anethole to trans-isoeugenol makes it more difficult for the molecule to pack well in a lattice structure.

Table 7-32: Summary of experimental enthalpy of fusion for trans-isoeugenol and related compounds -1 Chemical Name ΔHfus /(J g ) (Reps) Type Source trans-isoeugenol 71.3±5.0(13) Experimental This Report eugenol 114±29 Predicted [115] DIPPR anethole 108.0±3.2 Experimental DIPPR

Table 7-33 gives the most thermodynamically consistent vapor pressure curve information. Note that although the vapor pressure absolute average deviation (AAD) seems a bit high at 8.10%, the current DIPPR vapor pressure curve (that is not thermodynamically consistent) gives an AAD of 7.27%. However, using the current DIPPR vapor pressure curve to predict liquid heat capacity gives a AAD of 4.7%. This means that a small sacrifice in vapor 𝑙𝑙 𝑝𝑝 pressure— AAD increased from𝐶𝐶 7.27% to 8.10%—led to a significant improvement in its

vap ability to fit𝑃𝑃 liquid heat capacity data— AAD decreased from 4.7% to 1.56%. 𝑙𝑙 𝐶𝐶𝑝𝑝 101

Table 7-33: Summary of best critical constants and vapor pressure coefficients for trans-isoeugenol Property trans-Isoeugenol Tc Method Nannoolal [135] Tc/K 751.9 nd Pc Method WJ 2 Order [2] Pc/MPa 3.007 Tnb Method DIPPR Tnb/K 539.15 Fitting Method Riedel 2 Ptp/Pa 0.615 Pvap(A) 155.72 Pvap (B) -14206 Pvap (C) -19.122 Pvap (D) 8.355E-6 Pvap (E) 2 Pvap AAD 8.10 ΔHvap AAD -- l Cp AAD 1.56

7.5.10 1-Propoxy-2-Propanol

1-Propoxy-2-propanol was also measured because the liquid heat capacity was not well known. Unfortunately, the thermodynamic analysis techniques developed within the course of this project were insufficient to provide a vapor pressure curve that could predict liquid heat capacity through the Derivative method. The alcohol group seems to influence the shape of the vapor pressure curve to the point that the Riedel equation equipped with SRK vapor volume calculations is inadequate.

1-propoxy-2-propanol Figure 7-22: 1-propoxyl-2-propanol

102

7.6 Conclusions

New melting point, enthalpy of fusion, and liquid heat capacity experimental data for nineteen industrially important compounds were measured via DSC. The compounds were:

• o-tolualdehyde (CAS 529-20-4)

• m-tolualdehyde (CAS 620-23-5)

• p-tolualdehyde (CAS 104-87-0)

• m-tolualcohol (CAS 587-03-1)

• p-toluic acid (CAS 99-94-5)

• 1-phenyl-1-propanol (CAS 93-54-9)

• 1-phenyl-2-propanol (CAS 698-87-3)

• 2-phenyl-1-propanol (CAS 1123-85-9)

• 2-isopropylphenol (CAS 88-69-7)

• 2,5-dimethylfuran (CAS 625-86-5)

• 5-methylfurfural (CAS 620-02-0)

• phenyl acetate (CAS 122-79-2)

• ethyl 2-phenylacetate (CAS 101-97-3)

• n-hexylcyclohexane (CAS 4292-75-5)

• 6-undecanone (CAS 927-49-1)

• 1H-perfluorooctane (CAS 335-65-9)

• 2,6-dimethoxyphenol (CAS 91-10-1)

• trans-isoeugenol (CAS 5932-68-3)

• 1-propoxy-2-propanol (CAS 1569-01-3).

The melting points and enthalpies of fusion were replicated enough times to yield 95% confidence intervals below 1 K and 5 J g-1, respectively, which values are below the process uncertainties determined by a verification study. Liquid heat capacity was measured at discrete 103

temperatures and repeated as needed to reduce the average 95% confidence intervals to ±0.031 J

g-1 K-1 or 1.52% over all temperatures and compounds. Vapor pressure data and critical point

pressure and temperature were chosen so that the Riedel vapor pressure correlation was able to

successfully predict liquid heat capacity for fourteen of the compounds through the Derivative

method to within the liquid heat capacity experimental error for several of the compounds. All of

the compounds’ properties were compared to similar compounds with favorable results. In

particular, family plots for the toluene-like compounds, alkylcyclohexanes, and di-n-alkyl ketones increased confidence in the experimental results. Additionally, a method for freezing and melting 1-phenyl-1-propanol was developed and used for DSC. These measurements represent a

step forward in understanding these industrially important chemicals so they can be more

effectively used in process design.

104

8 BEST PRACTICES, RECOMMENDATIONS, AND INCORPORATIONS INTO

THE DATABASE

8.1 Introduction

This chapter will detail several improvements made to the thermodynamic calculation procedure based on the findings in previous chapters. First, improvements in the ideal gas heat capacity calculation procedure will be explained. Then, two calculation methods for liquid heat capacity (the derivative and integral methods) will be discussed. Next, a methodology will be given for the thermodynamic analysis procedure when a chemical does not have heat capacity data. Best recommendations are then given as a result of these improvements, which were then used to improve the DIPPR 801 project database. Finally, some work has also been done for associating compounds, especially carboxylic acids, will be described herein.

8.2 Ideal Gas Heat Capacity Database Fixes

In order to calculate ideal gas heat capacity, , the vibrational frequencies for each 𝑖𝑖𝑖𝑖 𝑝𝑝 molecule are calculated by solving Schrodinger’s Equation.𝐶𝐶 Doing so requires selection of a level

of theory to account for electron correlation and a basis set which is used to approximate the

unknown wave function. Systematic errors are associated with each level of theory and basis set

selection, but scaling factors have been determined to account for these systematic errors in

certain cases. These scaling factors are found empirically with up to 3 significant figures [138]

and are readily available in the literature [139].

105

For some compounds, the vibrational frequency scaling factors needed to be updated. The

main basis sets and levels of theory used by DIPPR are HF/6-31G(d), BLYP/6-311G(df,p), and

B3LYP/6-311+G(3df,2p). When this work began, DIPPR procedures used with scaling factors of

0.8953, 0.9986, and 0.9986, respectively. This work has shown these factors was cause for concern because BLYP and B3LYP give different correlations with the same scaling factor. 𝑖𝑖𝑖𝑖 𝑝𝑝 The CCCBDB database from the National Institute𝐶𝐶 of Standards and Technologies

(NIST) [140] indicate scaling factors around 0.90 for the HF level of theory, 0.99 for the BLYP level of theory, and 0.965 for the B3LYP level of theory with comparable basis sets [140]. This means that the BLYP and B3LYP scaling factors should be different—with the BLYP scaling factor much closer to 1 and the B3LYP closer to 0.967 as given in the CCBDB database—than what the DIPPR procedures indicate.

The difference between the old and new B3LYP correlations are shown for methyl ethyl ketone with data and the BLYP correlation in Figure 8-1. Depicted is the ideal gas heat capacity obtained from experiment and that predicted by quantum mechanical calculations and Equation

3-8. The predictions for BLYP using a scaling factor of 0.9986 (BLYP NIST f), B3LYP using a scaling factor of 0.9986 (B3LYP old f), and B3LYP using a scaling factor of 0.967 (B3LYP

NIST f) are shown. Notice that using the incorrect scaling factor of 0.9986 with B3LYP (B3LYP old f) results in heat capacities that are outside of the experimental data in certain cases and is not consistent with the BLYP prediction. Using the correct factor of 0.967 remedies both problems.

This error was probably a remnant of a DIPPR programmer switching from BLYP to B3LYP without using a new scaling factor.

106

150

140 ) - 1

K 130 - 1 (Jmol

ig 120 BLYP (NIST f) p C B3LYP (old f)

110 B3LYP (NIST f) Experimental Data

100 325 345 365 385 405 425 445 465 T/K

Figure 8-1: The ideal gas heat capacity for methyl ethyl ketone with data and DIPPR uncertainty and different basis sets, levels of theory, and scaling factors

When incorrect scaling factors are used, the absolute error in is directly translated to 𝑖𝑖𝑖𝑖 𝑝𝑝 the calculation of . This means that if the old scaling factor was used𝐶𝐶 to calculate the ideal gas 𝑙𝑙 𝐶𝐶𝑝𝑝 heat capacity of methyl ethyl ketone, the curve would be about 5 J mol-1 K-1 lower than the 𝑖𝑖𝑖𝑖 𝐶𝐶𝑝𝑝 with the NIST scaling factor, as shown in Figure 8-1. From this, the calculated would be 𝑖𝑖𝑖𝑖 𝑙𝑙 𝑝𝑝 𝑝𝑝 𝐶𝐶about 5 J mol-1 K-1 lower than it should, which would correspond to a 2.8% error at 𝐶𝐶400 K. In

order to reduce these errors, the NIST scaling factors were used for all of the compounds

analyzed through the course of this project.

A couple of group contribution methods have been developed for [141, 142]. These 𝑖𝑖𝑖𝑖 𝑝𝑝 methods used experimental data down to 298.15 K to regress the groups. However,𝐶𝐶 the triple

point temperatures for smaller organic compounds extend much lower. Therefore, extrapolation

error has been inadvertently introduced into the Derivative method. Therefore, group 𝑙𝑙 𝐶𝐶𝑝𝑝

107 contribution methods were not recommended for compounds with low triple point temperatures.

The DIPPR policy was changed to use ab initio as the primary method for calculation. 𝑖𝑖𝑖𝑖 𝐶𝐶𝑝𝑝 Fortunately, these calculation improvements were found relatively early in this 𝑖𝑖𝑖𝑖 𝐶𝐶𝑝𝑝 project, so the results given in the previous chapters utilize these improvements. Since the 𝑖𝑖𝑖𝑖 𝑝𝑝 calculation methodology was improved and uncertainties reduced, it became easier to evaluate𝐶𝐶 the effectiveness of the calculation methods, which will be explained next. 𝑙𝑙 𝐶𝐶𝑝𝑝 8.3 Derivative vs. Integral Methods

At the start of this project, two methods existed to connect heat of vaporization with heat capacities: the Derivative and the Integral method. The Derivative method was introduced in

Chapter 2, and the Integral method was first implemented by DIPPR researchers within the last decade. The Integral method first assumes a correlation form for : 𝑙𝑙 𝑝𝑝 𝐶𝐶 ( ) = + + + + (8-1) 𝑙𝑙 𝐵𝐵 2 3 𝐶𝐶𝑝𝑝 𝑇𝑇 𝐴𝐴 𝐶𝐶𝐶𝐶 𝐷𝐷𝜏𝜏 𝐸𝐸𝜏𝜏 where are fitting coefficients and 𝜏𝜏 is defined as:

𝐴𝐴 − 𝐸𝐸 𝜏𝜏 = 1 (8-2) 𝑇𝑇 𝜏𝜏 − 𝐶𝐶 This correlation form is plugged into the integral𝑇𝑇 of the Derivative method from temperature 1

( ) to temperature 2 ( ):

𝑇𝑇1 𝑇𝑇2 ( ) ( , ( ) 𝑇𝑇2 ( ) = 𝑇𝑇2 ( ) + ( ) (T ) 𝑃𝑃vap 𝑇𝑇 𝑇𝑇2 2 𝑙𝑙 𝑖𝑖𝑖𝑖 𝜕𝜕 𝑉𝑉vap 𝑇𝑇 𝑃𝑃vap 𝑇𝑇 𝑝𝑝 𝑝𝑝 vap 1 vap 2 2 (8-3) � 𝐶𝐶 𝑇𝑇 𝑑𝑑𝑑𝑑 � 𝐶𝐶 𝑇𝑇 𝑑𝑑𝑑𝑑 Δ𝐻𝐻 𝑇𝑇 − Δ𝐻𝐻 − �𝑇𝑇1 𝑇𝑇 � � � 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑇𝑇1 𝑇𝑇1 0 𝜕𝜕𝑇𝑇 ( ) ( ) + ( ) 𝑇𝑇2 𝜕𝜕Δ𝑉𝑉 𝑇𝑇 𝑑𝑑𝑃𝑃vap 𝑇𝑇 �𝑇𝑇1 �Δ𝑉𝑉 𝑇𝑇 − 𝑇𝑇 � �𝑃𝑃� 𝑑𝑑𝑑𝑑 The coefficients for Equation 8-1 are calculated𝜕𝜕𝜕𝜕 𝑑𝑑 numerically𝑑𝑑 by fitting the integral of Equation 8-

1 to the right hand side of Equation 8-3.

108

At the time of its introduction, the Integral method was touted as the computationally

quicker of the two methods and superior because it relied less on derivatives of data. The Integral

method was also said to be more accurate since the slope of the curve goes to infinity with

vap the Derivative method. These calculation methods were bothΔ improved𝐻𝐻 through the course of 𝑙𝑙 𝑝𝑝 this project, which will be shown𝐶𝐶 with propylene as an example compound.

At the start of this project in 2013, the Derivative and Integral method calculations varied from one another, as shown in Figure 8-2 for propylene. As depicted, both the Derivative (red curve) and Integral (purple curve) methods undershoot the liquid heat capacity data (black points). The Derivative method increased smoothly but stopped at the normal boiling point,

while the Integral method showed a slight inflection point around the normal boiling point before

increasing towards the critical point. Since the methods undershot by almost a constant value, it

was hypothesized that something was wrong with the ideal gas heat capacity.

By taking a closer look at the ideal gas heat capacity, it was found that, similarly to what

was discussed in Section 8.1, the ideal gas heat capacity was predicted with a group contribution

method that was extrapolated below 298.15 K. To correct this, a quantum mechanical calculation

was used with experimental data to create a new ideal gas heat capacity correlation using the 6

parameter form in Equation 3-10. The new Derivative and Integral methods are given in Figure

8-3. Unfortunately, a better ideal gas heat capacity correlation slightly worsened the liquid heat

capacity predictions.

109

150 140 Experimental Data 130 120 Derivative Method (2013) ) 1 -

K 110

1 Integral Method (2013) - 100 (J mol l

p 90 C 80 70 60 50 75 125 175 225 275 325 375 T/K

Figure 8-2: Liquid heat capacity data for propylene with the derivative and integral methods from the start of this project (2013)

150 140 Experimental Data 130 120 Derivative Method (2014) ) 1 -

K 110

1 Integral Method (2014) - 100 (J mol l

p 90 C 80 70 60 50 75 125 175 225 275 325 375 T/K

Figure 8-3: Liquid heat capacity data for propylene with the derivative and integral methods with a better ideal gas heat capacity correlation (2014)

110

Upon further inspection, some differences appeared in the implementation of the

Derivative and Integral methods. First, the temperature ranges for each method were different, so

the Derivative method was extended up past the normal boiling point to a reduced temperature of

0.96 in order to match the temperature range of the integral method. Doing so revealed that the

two methods differed at high temperatures, as shown below in Figure 8-4.

The reason for this difference was found by investigating the computational form of the

Integral method. Figure 8-5 shows the pieces of the form used by the Integral method in 2014 to calculate the fitting coefficients of Equation 8-1 with the units displayed. Since these pieces came from the integral in Equation 8-3, they should have units of J mol-1. However, two of the

pieces ( – a correction to change an ideal gas heat capacity to a vapor heat capacity,

𝑣𝑣 𝑡𝑡𝑡𝑡 𝑖𝑖𝑖𝑖 and Δ𝐶𝐶 –𝑝𝑝 a correction to change a saturated liquid heat capacity to isobaric heat capacity) were

𝐿𝐿 implementedΔ𝐶𝐶𝑝𝑝 with inconsistent units compared to the other terms. The methods used to calculate

these corrections were corrected by double-checking them against rigorous thermodynamics.

Another problem was that only 40 temperature points were being generated for the

Integral method parameter fitting process, causing the curve to dip at high temperatures. When

the number of points was increased to 250, the Integral method came in line with the Derivative method at high temperatures where the corrective terms – labeled as , , and

𝑣𝑣 𝑡𝑡𝑡𝑡 𝑖𝑖𝑖𝑖 𝑉𝑉 𝐿𝐿 in Figure 8-5 – have the greatest effect. However, increasing the numberΔ𝐶𝐶𝑝𝑝 of parameterΔ𝐶𝐶𝑝𝑝 fittingΔ 𝐶𝐶𝑝𝑝

points also increased the calculation time for the Integral method coefficients, so it is

recommended that the Derivative method be used instead.

111

150 140 Experimental Data 130 120 Derivative Method (2015) ) 1 -

K 110

1 Integral Method (2014) - 100 (J mol l

p 90 C 80 70 60 50 75 125 175 225 275 325 375 T/K

Figure 8-4: Liquid heat capacity data for propylene with the Derivative and Integral methods with the Derivative method extended above normal boiling point (2015)

J J J J J = + + mol mol mol K mol m 𝑖𝑖𝑖𝑖 𝑑𝑑Δ𝐻𝐻vap 𝑦𝑦 𝐶𝐶𝑝𝑝 � � − � � Δ𝐶𝐶𝑝𝑝𝑣𝑣 𝑡𝑡𝑡𝑡 𝑖𝑖𝑖𝑖 � � Δ𝐶𝐶𝑝𝑝𝑉𝑉 � � − Δ𝐶𝐶𝑝𝑝𝐿𝐿 � 3� Figure 8-5 The equation𝑑𝑑𝑑𝑑 used to calculate coefficients for the integral method (2014)

With the Derivative and Integral methods in line, the multi-property optimization described in Chapter 5 could be performed for propylene. After looking over different vapor pressure correlation forms, it was found that a Riedel correlation fit to vapor pressure data with

= 2 gave a more thermodynamically consistent fit (2017) with liquid heat capacity data, as shown𝐸𝐸 in Figure 8-6 along with the original derivative and integral method fits (2013). This represents a drop in AAD from 27% to 2.8%, a full order of magnitude. These improvements gave the Derivative and Integral methods the ability to predict more effectively, which will be 𝑙𝑙 𝑝𝑝 discussed in the next section. 𝐶𝐶

112

150 140 Experimental Data 130 Derivative Method (2013) 120 Integral Method (2013) ) 1

- Derivative Method (2017)

K 110 1 - Integral Method (2017) 100 (J mol l

p 90 C 80 70 60 50 75 125 175 225 275 325 375 T/K

Figure 8-6: Liquid heat capacity data for propylene with the derivative and integral methods now (2017) compared to the start of this project (2013)

8.4 Compounds without Liquid Heat Capacity Data

It is common for niche chemicals to lack data. In these instances, the best 𝑙𝑙 𝑝𝑝 recommendation is to try to match the shape and/or𝐶𝐶 absolute values of the corresponding 𝑙𝑙 𝑝𝑝 states prediction given in [2], and shown as: 𝐶𝐶 𝑙𝑙 𝑝𝑝 𝐶𝐶 0.49 6.3 1 1 0.4355 ( ) = ( ) + 1.586 + + 4.2775 + 3 + ⎡ 𝑇𝑇 ⎤ (8-4) 𝑖𝑖𝑖𝑖 � − � 𝑙𝑙 ⎢ 1 ⎛ 𝑇𝑇𝑐𝑐 1 ⎞⎥ 𝐶𝐶𝑝𝑝 𝑇𝑇 𝐶𝐶𝑝𝑝 𝑇𝑇 𝑅𝑅𝑔𝑔 𝜔𝜔 ⎢ 𝑇𝑇 ⎜ 𝑇𝑇 𝑇𝑇 ⎟⎥ − − ⎢ 𝑇𝑇𝑐𝑐 𝑇𝑇𝑐𝑐 𝑇𝑇𝑐𝑐 ⎥ ⎣ ⎝ ⎠⎦ where is the universal gas constant, is the critical temperature, and is the acentric factor

𝑔𝑔 𝑐𝑐 for a given𝑅𝑅 compound. Though not thermodynamically𝑇𝑇 consistent, the corresponding𝜔𝜔 states prediction has proven better than the Ruzicka-Domalski method [143] time and again, especially above .

𝑇𝑇𝑁𝑁𝑁𝑁 113

As an example, consider the compound trans-1-chloro-3,3,3-trifluoro-1-propene, whose vapor pressure has been measured but lacks liquid heat capacity data. The vapor pressure data were fit using Riedel correlations with values of 1, 2, 3, and 6 for comparison. These

vap correlations were used to predict liquid𝐸𝐸 heat capacity with the derivative method. These 𝑃𝑃four

predictions were compared to the corresponding states method (CSP) and the Ruzicka-Domalski

method (RD) in Figure 8-7. The vapor pressure correlation with = 3 seems to agree with the

CSP curve the best, so an value of 3 was selected as the best option.𝐸𝐸 This chemical is

representative of other compounds𝐸𝐸 that lack data. When a compound does not have data, 𝑙𝑙 𝑙𝑙 𝑝𝑝 𝑝𝑝 the corresponding states method can be used𝐶𝐶 to identify an appropriate curve shape for 𝐶𝐶the

Derivative or Integral methods. This has been shown to work when fitting the Riedel equation to

vapor pressure data, and when predicting vapor pressure by the method described in Chapter 6.

300 CSP Der. E=1 )

1 Der. E=2 -

K Der. E=3 1 - Der. E=6 200 RD (J mol l p C

100 150 200 250 300 350 400 450 T/K

Figure 8-7: Liquid heat capacity for trans-1-chloro-3,3,3-trifluoro-1-propene with several prediction methods

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8.5 Recommendation Summary

This work developed tools to improve the correlations and thermodynamic consistency of

vapor pressure, heat of vaporization, and liquid heat capacity for individual compounds. Section

8.2 showed improvements made in calculations. Since Section 8.3 reconciled the differences 𝑖𝑖𝑖𝑖 𝑝𝑝 between the Derivative and Integral𝐶𝐶 methods, it is recommended that the Derivative method be

used in favor of the Integral method because the improved Integral method is more

computationally expensive. Section 8.4 laid out a methodology for compounds without data. 𝑙𝑙 𝑝𝑝 Chapters 4 and 5 explained how changing the Riedel correlation form to increased 𝐶𝐶

thermodynamic consistency from to . Chapter 6 gave a new prediction method that allows 𝑙𝑙 vap 𝑝𝑝 the same flexibility when data𝑃𝑃 do not𝐶𝐶 exist. All of these updates lead to a new

vap recommendation for a thermodynamic𝑃𝑃 consistency analysis procedure.

As compounds are investigated for addition to the DIPPR database, the following procedure should be followed:

1. Select normal boiling point, critical temperature, and critical pressure based on

DIPPR policy and procedure recommendations

2. Loop on the following:

a) Vapor pressure: select data and pick correlation value

b) Heat of vaporization: evaluate shape and compare𝐸𝐸 Clapeyron derived

curve to literature data.

c) Ideal gas heat Capacity: verify that the quantum mechanical calculations

(ab initio) are fit correctly from to . This includes fitting 𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇 𝐶𝐶 𝑝𝑝 experimental data when available.𝑇𝑇 𝑇𝑇 𝐶𝐶

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d) Liquid heat capacity: check shape of Derivative method curve and

compare to literature data and the shape of the corresponding states

method

Also, compounds will contain varying amounts of data. Table 8-1 summarizes the recommended methodology for all levels of and data. Generally, the amount of data available 𝑙𝑙 vap 𝑝𝑝 vap does not directly affect the methodology𝑃𝑃 𝐶𝐶 since data usually occur inΔ𝐻𝐻 temperature regions

vap where is already well-known. However, Δ𝐻𝐻 curves should still be compared and fit to

vap vap experimental𝑃𝑃 data, when available, in order toΔ create𝐻𝐻 correlations that give the best values through the whole temperature range. By following this methodology, the most thermodynamically consistent correlations can be developed.

Table 8-1: Summary of best recommendations for achieving thermodynamic consistency Data Data Section Recommendation 𝒍𝒍 Select the best value that minimizes and 𝑷𝑷Extensive𝐯𝐯𝐯𝐯𝐯𝐯 𝑪𝑪𝒑𝒑Yes Chapter 5 AAD while fitting 2 or 4 coefficients 𝑙𝑙 𝐸𝐸 𝑃𝑃vap 𝐶𝐶𝑝𝑝 Select the best value that minimizes and Sparse Yes Chapter 5 𝑃𝑃vap AAD while fitting 1 coefficient 𝑙𝑙 𝐸𝐸 𝑃𝑃vap 𝐶𝐶𝑝𝑝 Select the best valuevap while fitting 2 or 4 coefficients, guided 𝑃𝑃by the corresponding states Extensive No Section 8.4 vap correlation shape𝐸𝐸 for 𝑃𝑃 𝑙𝑙 Select the best value𝑝𝑝 while fitting 1 coefficient, Sparse No Section 8.4 guided by the corresponding𝐶𝐶 states correlation shape vap for 𝐸𝐸 𝑃𝑃 Use new𝑙𝑙 predictive Riedel equation with value that No Yes Chapter 6 𝑝𝑝 minimizes𝐶𝐶 AAD Use new predictive𝑙𝑙 Riedel equation with 𝐸𝐸 value No No Chapter 6 𝑝𝑝 selected according𝐶𝐶 to family in Table 6-5 𝐸𝐸

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8.6 DIPPR Database Improvements

The improvements found through the course of this project were implemented into the

DIPPR 801 database project. Unfortunately, 116 compounds were previously added to the

DIPPR database with the incorrect integral method liquid heat capacity correlations. Samples of five of those compounds were purchased for measurements. The correlations and recommended values for the other 111 compounds were updated and re-added to the database. Thermodynamic

analyses were performed following Table 8-1 to find the best Riedel equation form for 41

additional compounds in Chapter 5. An additional 70 compounds were analyzed in Chapter 6 in

order to create a new predictive vapor pressure calculation method. Fourteen of the 19

compounds measured and described in Chapter 7 were analyzed, and thermodynamically

consistent fits to vapor pressure were recommended. In all, over 200 compounds were directly

influenced as a result of this project.

The DIPPR vapor pressure correlations and subsequent Derivative method liquid heat

capacity curves were compared to these new correlations for 121 compounds. Figure 8-8 shows

the average absolute deviations for vapor pressure and Derivative method heat capacity fits

before and after analysis. Each point represents one compound. Red circles represent prior

DIPPR vapor pressure and Derivative method AAD’s. Blue diamonds represent vapor pressure

and Derivative method AAD’s as a result of this project. The red and blue squares represent the

average over all the compounds for DIPPR and this project, respectively. The x-axis shows the

AAD’s of the vapor pressure fits, while the y-axis gives the AAD of heat capacity fit when the vapor pressure correlation is used to get a Derivative method curve. The red and blue squares are at about the same x-position, but the blue square is about 4% lower than the red square on the y- axis. This means that on average, the compounds analyzed became more thermodynamically

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consistent through the Derivative method compared to liquid heat capacity data without

sacrificing the vapor pressure correlation fit to data.

30% DIPPR AAD l p

C DIPPR Avg 20% This Project This Project Avg 10% Derivative Method Derivative 0% 0% 10% 20% 30% 40% 50% 60% 70% 80% Pvap AAD

Figure 8-8: The average absolute deviations for the vapor pressure and Derivative method heat capacity fits before and after analysis

8.7 Association

Self-associating compounds, such as carboxylic acids, provide a major obstacle to

improving thermodynamic consistency because they constitute a mixture of “mers,” instead of a single molecule. The association reaction for such compounds (e.g. carboxylic acids) can be represented as follows:

2 (8-5)

where stands for monomer with the RCOOH𝑀𝑀 ↔ 𝐷𝐷 functional group, and stands for dimer where

the RCOOH𝑀𝑀 for each functional group has hydrogen bonded. The degree𝐷𝐷 of association varies

with temperature and pressure, meaning that the fractions of monomer and dimer shift along the

saturation curve. It is often assumed that the liquid phase consists solely of dimer because the

molecules interact with one another. For the vapor phase, however, the mole fractions of

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monomer and dimer need to be known in order to effectively represent the thermodynamic

properties along the saturation curve. For this purpose, an equilibrium constant is defined from

the fugacities of the mixture as:

= (8-6) 2 𝑇𝑇 𝑀𝑀 𝑃𝑃 𝐾𝐾 Φ 𝐾𝐾 𝐷𝐷 where is the temperature-dependent equilibriumΦ constant, and and are the fugacity

𝑇𝑇 𝑀𝑀 𝐷𝐷 coefficients𝐾𝐾 of the monomer and dimer, respectively. The fugacityΦ coefficientsΦ are calculated

using an equation of state with critical constants of the theoretical pure monomer and pure dimer,

respectively. These critical constants are taken from estimates in the literature [65], but the

fugacity coefficients are insensitive to these values.

The temperature-dependent equilibrium constant is:

= exp = exp + (8-7)

𝑇𝑇 Δ𝐺𝐺 −Δ𝐻𝐻 Δ𝑆𝑆 𝐾𝐾 � 𝑔𝑔 � � 𝑔𝑔� where is the universal gas constant,𝑅𝑅 𝑇𝑇 is the temperature,𝑅𝑅𝑅𝑅 𝑅𝑅 and is the Gibb’s energy of

𝑔𝑔 association,𝑅𝑅 which can be separated into𝑇𝑇 , the enthalpy of association,Δ𝐺𝐺 and , the entropy of

association. Δ𝐻𝐻 Δ𝑆𝑆

At this point, the monomer mole fraction given can be identified. The equilibrium

constant given in Equation 8-6 can also be defined in terms of the partial pressures of the

components:

= (8-8) 𝑃𝑃𝐷𝐷 𝑃𝑃 2 𝐾𝐾 𝑀𝑀 where and are the partial pressures of monomer𝑃𝑃 and dimer, respectively. These can be

𝑀𝑀 𝐷𝐷 related𝑃𝑃 to the mole𝑃𝑃 fractions using Dalton’s law:

= (8-9)

𝑃𝑃𝑖𝑖 𝑦𝑦𝑖𝑖𝑃𝑃 119

where and are the partial pressure and mole fraction of the component in the vapor th 𝑖𝑖 𝑖𝑖 phase with𝑃𝑃 total𝑦𝑦 pressure . Combining Equations 8-8 and 8-9 with𝑖𝑖 the summation of the monomer and dimer mole𝑃𝑃 fractions gives the following expression:

1 = + (8-10) 2 𝑀𝑀 𝑃𝑃 𝑀𝑀 where is the monomer mole fraction,𝑦𝑦 which𝐾𝐾 can𝑃𝑃𝑦𝑦 be isolated using the quadratic formula as:

𝑀𝑀 𝑦𝑦 1 + 1 + 4 = (8-11) 2 𝑃𝑃 𝑀𝑀 − � 𝐾𝐾 𝑃𝑃 𝑦𝑦 𝑃𝑃 The monomer mole fraction can be used𝐾𝐾 𝑃𝑃to adjust the volume from an equation of state to

that of an associating fluid found via experiment:

= = = (8-12) exp exp 2 𝐸𝐸+𝐸𝐸𝐸𝐸 2 𝐸𝐸𝐸𝐸𝐸𝐸 exp 𝑍𝑍 𝑅𝑅𝑇𝑇 𝑉𝑉 𝑉𝑉 𝑉𝑉 exp 𝐷𝐷 𝑀𝑀 𝑀𝑀 where is the experimental volume𝑃𝑃 at an experimental𝑦𝑦 𝑦𝑦 temperature,− 𝑦𝑦 , and pressure, .

exp exp exp The volume𝑉𝑉 using an equation of state, , is adjusted to fit the experimental𝑇𝑇 compressibility𝑃𝑃

𝐸𝐸𝐸𝐸𝐸𝐸 factor, . In this process, the enthalpy𝑉𝑉 and entropy of association from Equation 8-7 are used

exp to calculate𝑍𝑍 , which is then used to calculate using Equation 8-6. is used in conjunction

𝑇𝑇 𝑃𝑃 𝑃𝑃 with pressure𝐾𝐾 in Equation 8-11 to calculate the monomer𝐾𝐾 mole fraction.𝐾𝐾 In the end, the monomer

mole fraction in Equation is fit to P,V,T data by adjusting the enthalpy and entropy of

association in Equation 8-7.

8.7.1 Saturated Monomer Mole Fraction

Using Wiltec data [65], supplemented by DECHEMA equilibrium constant correlations

[144] where necessary, the monomer mole fractions were calculated along the saturation curve

by using the supplied equilibrium constant equation and saturation pressure from a fit of vapor

pressure data. The temperature dependent results are given in n-carboxylic acids from formic

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(C1) to octanoic acid (C8) in Figure 8-9, with curves spanning the triple point to the critical point for each compound. As expected, the smaller acids experience the most dimerization, and therefore have the smallest monomer mole fractions. As the acids increase in length, the vibrations in the hydrocarbon tails overcome the strength of the hydrogen bond, resulting in higher monomer mole fractions.

1 0.9 y.C1 0.8 y.C2 0.7 y.C3 0.6 y.C4 0.5 y.C5 0.4

y(Monomer) y.C6 0.3 y.C7 0.2 y.C8 0.1 0 200 300 400 500 600 700 T/ K

Figure 8-9: The monomer mole fractions for n-alkanoic acids along the saturation curve

It would seem intuitive that as the temperature increases, the fraction of monomer would also increase because the thermal energy would overcome any hydrogen bonding. For acids above 3 carbons in length, the mole fraction of monomer actually goes through a shallow minimum with respect to temperature. This can be explained by examining Equation 8-11 for the monomer mole fraction. In this equation, the equilibrium constant is multiplied by the pressure, which is the temperature dependent vapor pressure equation in this case. At a given temperature, the pressure – representing the ability of molecules to interact with each other – and the

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equilibrium constant – representing the affinity of molecules to hydrogen bond upon interaction

– are in competition. As temperature increases, the vapor pressure increases, but the equilibrium

constant decreases. This balance determines the fraction of monomer and dimer in the mixture.

For large acids at low temperatures, the vapor pressures are too small for the molecules to

interact, resulting in mostly monomer. This explains the shallow minima with temperature in

Figure 8-9 for larger compounds.

8.7.2 Heat of Vaporization

Using these temperature dependent mole fractions, the heat of vaporization can be

derived from a fit of vapor pressure and P,V,T data as:

( ) 1 = (8-13) 2 𝐸𝐸𝐸𝐸𝐸𝐸 ( ) 2 ( ) vap vap 𝑉𝑉 𝑇𝑇 𝑑𝑑𝑃𝑃 Δ𝐻𝐻 𝑇𝑇 � 𝑚𝑚 − 𝐿𝐿 � � � where ( ) is the temperature dependent− 𝑦𝑦 𝑇𝑇liquid molar𝜌𝜌 𝑇𝑇 density𝑑𝑑𝑇𝑇 correlation given by DIPPR [44].

𝐿𝐿 Because𝜌𝜌 most𝑇𝑇 of the liquid is associated into dimers, the liquid molar density is multiplied by 2

since the DIPPR correlation is per moles of monomer. The vapor volume is divided by 2

( ) to account for the volume of the mixture of monomers and dimers as shown by Equation−

𝑚𝑚 8𝑦𝑦-12𝑇𝑇. The association enthalpy and entropy from Equation 8-7 can be fit using vapor pressure

and heat of vaporization data in Equation 8-13. In this analysis, monomer mole fractions from

Figure 8-9 were fit to P,V,T data using Equation 8-12. Those mole fractions, along with DIPPR’s

liquid density correlations and vapor pressure correlations fit to data, were used in Equation 8-13 to calculate for n-propanoic (C3) to n-heptanoic (C7) acids in Figure 8-10. These curves

vap matched Δ𝐻𝐻 data for n-propanoic (C3) to n-hexanoic (C6) acids [65] well.

Δ𝐻𝐻vap

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90 C3 Associated Clapeyron C4 Associated Clapeyron 80 C5 Associated Clapeyron C6 Associated Clapeyron 70 C7 Associated Clapeyron C3 Data 60

) C4 Data - 1 C5 Data 50 C6 Data (kJ mol 40 vap H Δ 30

0 250 300 350 400 450 500 550 600 650 T/K

Figure 8-10: Heat of vaporization experimental data and curves derived using the Clapeyron equation for n-carboxylic acids with association

8.7.3 Future Work

Furthering this analysis, the slope of the curve can be used to relate the ideal gas

vap heat capacity and the liquid heat capacity. The DerivativeΔ𝐻𝐻 method, Equation 2-6, can be modified

for association, and the results can be compared to data to help improve thermodynamic 𝑙𝑙 𝑝𝑝 consistency for associating compounds. However, this𝐶𝐶 analysis procedure has yet to be adequately performed. Eventually, alcohols and amines, which weakly associate, will also be considered in like manner.

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9 CONCLUSIONS

The thermodynamic consistency among , , , and has been improved as a 𝑖𝑖𝑖𝑖 𝑙𝑙 vap vap 𝑝𝑝 𝑝𝑝 result of this project. A survey of the literature helped𝑃𝑃 Δ shape𝐻𝐻 this𝐶𝐶 story.𝐶𝐶 It was found that vapor

pressure, although the most commonly measured of the four properties, is generally not known

well at temperatures far below the normal boiling point. On the other hand, liquid heat capacity

is commonly measured at low temperatures, but not above the normal boiling point.

Thermodynamic relations were used to link these properties along the temperature region from

the triple point to the critical point. In so doing, both low temperature and high temperature

vap correlations were dramatically improved. Several methods were used𝑃𝑃 to improve the 𝑙𝑙 𝑝𝑝 𝐶𝐶thermodynamic consistency of these properties.

The most obvious way to improve these properties was to optimize them simultaneously.

This was done by changing the fitting coefficients of the Riedel vapor pressure correlation to fit

and data, weighted by temperature. This allowed the vapor pressure curve to fit vapor 𝑙𝑙 vap 𝑝𝑝 pressure𝑃𝑃 data𝐶𝐶 at high temperatures, and liquid heat capacity data at low temperatures. This

project used property uncertainties to inform the temperature dependent correlations.

Another way to improve the correlations for these properties is to change the vapor

pressure equation form. The exponent on the final temperature term of the Riedel correlation

(denoted as ) was changed from the traditional value of 6 to other integer values between 1 and

𝐸𝐸 124

6. By so doing, the thermodynamic consistency from vapor pressure to liquid heat capacity for

41 compounds over 7 families was improved. In particular, the different values changed the

shape below the normal boiling point so that the thermodynamically𝐸𝐸-derived Derivative

vap method𝑃𝑃 calculations went through data. This formed a manual optimization that was 𝑙𝑙 𝑙𝑙 𝑝𝑝 𝑝𝑝 simple to𝐶𝐶 implement into DIPPR procedures.𝐶𝐶

For compounds without experimental vapor pressure data, a state-of-the-art

vap prediction method was developed by taking advantage of the findings discussed in the𝑃𝑃 previous

paragraph. Riedel’s corresponding states methodology was used in conjunction with 37 well-

known compounds to generate predictive correlations with values ranging from 1 to 6.

vap These correlations were checked𝑃𝑃 against 106 compounds, and thermodynamic𝐸𝐸 analyses were

performed to determine which values worked best for which chemical families. This prediction

performed as well as other predictions𝐸𝐸 from the literature for vapor pressure and heat of

vaporization. However, the average error for dropped from 8% using predictions from the 𝑙𝑙 𝑝𝑝 literature, to around 3% using this new prediction.𝐶𝐶 This better agreement with corresponded 𝑙𝑙 𝑝𝑝 to an improvement in the low temperature vapor pressure prediction, precisely𝐶𝐶 the temperature

region where previous prediction methods had been inadequate.

A differential scanning calorimeter (DSC) was purchased in order to measure

thermophysical properties for pure compounds. Calibrations and verifications showed

uncertainties of 1 K for melting point, and 5 J g-1 for enthalpy of fusion. Adjustments to the

American Society for Testing and Materials (ASTM) methods for measuring heat capacity

reduced the uncertainty from 3.2% to 1.52% on average across all compounds and temperatures.

In the end, melting point was measured for 13 compounds, enthalpy of fusion for 12 compounds,

125

and liquid heat capacity for 19 compounds. These new experimental data were combined with the analysis procedures described in previous paragraphs to recommend improved, thermodynamically consistent vapor pressure expressions for 14 of the compounds. In particular,

, , and correlations for the tolualdehyde, furan, phenyl propanol, n-alkyl 𝑙𝑙 vap vap 𝑝𝑝 𝑃𝑃cyclohexΔ𝐻𝐻ane, phenyl𝐶𝐶 acetate, and di-n-alkyl ketone families were improved in this process.

In this project, the calculation methods for the thermodynamic relations linking these four

properties-- , , , and —were also improved. Ideal gas heat capacity uncertainty 𝑙𝑙 𝑖𝑖𝑖𝑖 vap vap 𝑝𝑝 𝑝𝑝 was reduced𝑃𝑃 by correctlyΔ𝐻𝐻 𝐶𝐶 implementing𝐶𝐶 the scaling factor within the statistical mechanics

derivation. Also, extrapolation error was avoided by not using group contribution methods to

calculate below 298 K. Also, the Derivative and Integral liquid heat capacity calculation 𝑖𝑖𝑖𝑖 𝑝𝑝 methods were𝐶𝐶 brought into alignment by careful mathematical investigation. These

improvements decreased the uncertainty in the Derivative method so that a) more successful 𝑙𝑙 𝑝𝑝 predictions could be made, and b) more thermodynamically consistent vapor pressures curves𝐶𝐶

could be found. A review of 121 compounds with all of the improvements from this project

dropped the average liquid heat capacity absolute average deviation by 4%. These improvements

triggered a full database review, which in turn increased the value of the DIPPR database.

9.1 Future Work

Although this project was able to improve the thermodynamic consistency among ,

𝑃𝑃vap , , and , it also introduced more topics that could be explored, as given in this list. 𝑖𝑖𝑖𝑖 𝑙𝑙 Δ𝐻𝐻vap 𝐶𝐶𝑝𝑝 𝐶𝐶𝑝𝑝

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9.1.1 Continue Liquid Heat Capacity Measurements

There exist many more compounds in the DIPPR database that do not have data. 𝑙𝑙 𝑝𝑝 Continuing these measurements could help improve the current understanding of the𝐶𝐶 correlation

forms for more chemical families similarly to the analyses done in Chapter 7 of this report.

Chemically similar compounds to 1H-perfluorooctane, 2,6-dimethoxyphenol, trans-isoeugenol, and 1-propoxy-2-propanol could be measured to improve the family trends and verify the results of the experiments listed in Chapter 7. To do this, octanal, 1,4-pentanediol, cyclopentyl acetic acid, 2-(5H)-furanone, 1-chloro-3-propanol, N-methylpiperidine, vanillin, guaiacol, and eugenol

have been purchased, and melting points, enthalpy of fusions, and liquid heat capacities will be

measured by future lab researchers.

9.1.2 Measure Vapor Pressure

The standards established by ASTM E1782-14 give a useful guideline to measuring

vap via DSC. This will include a couple of additions to the current setup (TA Instruments’ Q20 𝑃𝑃

DSC). Figure 9-1 shows the recommended setup, including A) the DSC, B) a pressure

transducer, C) a pressure or vacuum source, D) a pressure stabilizer, E) a pressure regulator, and

F) a relief value. The pan lids would need holes added—in the form of either smaller pinholes

made by laser according to ASTM standards, or larger holes with a metal ball on top—to ensure

slow mass release [145, 146]. The Q20P DSC pressure can range from 1 to 7,000,000 Pa with a

vacuum pump attached. To make the measurement, pressure is held constant, and temperature is

increased at a constant rate. As temperature increases, an endothermic peak appears as the

material boils for the solid to liquid phase transition. With more measurements done at low

vap pressures, current understanding of the low pressure portion of the𝑃𝑃 curve could be further

vap improved. 𝑃𝑃

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Figure 9-1: The experimental setup recommended by ASTM E1782-14 to measure Pvap via DSC

9.1.3 Improve the Multi-Property Optimization

As was mentioned in Chapter 4 and touch on in the conclusions, a multi-property optimization was developed with temperature-dependent weightings. Although some work has shown promising results, this procedure has not been adapted for use in DIPPR policies and procedures. The multi-property optimization could be adapted to include the Riedel coefficient

as one of the parameters. Doing so would require subtle mathematical manipulation 𝐸𝐸of the

optimization, since the value changes other Riedel fitting parameters by many orders of

magnitude. Furthermore,𝐸𝐸 optimization constitutes a major research area, with many techniques

and strategies that could be used to improve the procedures started in Chapter 4. If an automated

regression scheme could be developed, the time needed to perform these thermodynamic

analyses would plummet.

128

9.1.4 Measure the Solid Phase Properties

The experimental setup and procedure for measuring does not differ from that of . 𝑠𝑠 𝑙𝑙 𝑝𝑝 𝑝𝑝 The Q2000 DSC could be an incredible tool in improving the𝐶𝐶 data in the DIPPR database.𝐶𝐶 𝑠𝑠 𝑝𝑝 While measuring , a project could be used to improve the consistency𝐶𝐶 in solid-vapor properties 𝑠𝑠 𝑝𝑝 the same way this𝐶𝐶 project improved the consistency in solid-liquid properties. This could help

improve agreement among solid vapor pressure, heat of sublimation, and solid heat capacity.

9.1.5 Measure Ideal Gas Heat Capacity

Although ideal gas heat capacity can be derived via statistical mechanics, a complete understanding of especially low temperature behavior has not yet been achieved. Following experimental procedures for calorimetric [147], speed of sound [148], or thermal conductivity

[149] measurements could produce data necessary to fill gaps in data within the DIPPR database.

Also, the ab initio methods used to calculate ideal gas heat capacity require further attention.

Current DIPPR methods calculate vibrational frequencies for the torsion of dihedral angles and

treat them the same as other vibrational frequencies – constant through temperature. However, at

high temperatures, those torsional vibrations turn into internal rotations, commonly for

compounds with terminal methyl groups [150, 151]. This changes the contribution of the torsion

to the ideal gas heat capacity. Torsion calculations combined with the combinatorics for

configurational probabilities [152, 153], mean that ideal gas heat capacity prediction could use

some improvement.

9.1.6 Improve Methods for Associating Compounds

For the purposes of this discussion, associating compounds can be broken into two

groups: alcohols and acids. Alcohols strongly associate in the liquid phase, but only slightly

associate in the vapor phase. Even so, the Riedel equation does not seem to be the correct form to 129

predict heat capacity through the derivative method. For alcohols, a different vapor pressure

correlation should be used. A wider range of vapor pressure correlations in the literature could be

tested, or a new correlation form could be created. Acids strongly associate in the liquid phase,

and also associate in the vapor phase. This causes problems when trying to calculate vapor

volume from a cubic equation of state. As shown in Section 8.3, P,V,T measurements were used

to modify the equation of state to account for dimerization while using the Clapeyron equation.

Before vapor pressure, heat of vaporization, and ideal gas heat capacity can be used to

successfully predict liquid heat capacity, the temperature limits of the P,V,T measurements (and

subsequent equilibrium constant) need to be skillfully expanded to low temperatures where

liquid heat capacity data are common. Therefore, new P,V,T measurements or a careful extrapolation technique guided by thermodynamic principles will be needed. Currently, there do

not exist enough data to understand the acid dimerization equilibrium over the whole

temperature range from the triple point to the critical point.

9.1.7 Reduce Heat of Vaporization Uncertainty

Although heat of vaporization was discussed here, it is still a topic for future work. As

shown in Figure 5-1 for n-butane, changing the vapor pressure correlation has a dramatic effect

on the heat of vaporization curve. Few experimental heat of vaporization data exist near the triple

point temperature, so they could not be used to check the results of this work. An analysis of

measurements in this temperature region could prove useful in trying to determine the best vapor

pressure curve. Measurements could be done in this region at low pressures to verify this

thermodynamic consistency procedure.

130

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203

APPENDIX A. THERMODYNAMIC DERIVATIONS

A.1 Clapeyron Equation Derivation

Start with the relationship between Gibb’s energy, enthalpy, and entropy from elementary thermodynamics:

= (A-1)

At equilibrium, the Gibb’s energy Δis𝐺𝐺 the sameΔ𝐻𝐻 − in𝑇𝑇 Δthe𝑆𝑆 liquid and vapor phases, so is zero, resulting in: Δ𝐺𝐺

= (A-2)

From the partial derivative game, Δ𝐻𝐻 𝑇𝑇Δ𝑆𝑆

= (A-3) V Δ𝑆𝑆 Δ𝑃𝑃 Substituting from Equation A-3 intoΔ EquationΔ𝑇𝑇 A-2 gives the Clapeyron equation:

Δ𝑆𝑆 = (A-4) Δ𝑃𝑃 Δ𝐻𝐻 𝑇𝑇Δ𝑉𝑉 Δ𝑇𝑇 A.2 Derivative Method Derivation

First, start by recognizing that heat of vaporization is defined as the difference in enthalpies of the liquid and vapor phases:

(A-5)

vap vap liq Take the temperature derivative of𝛥𝛥𝐻𝐻 the previous≡ 𝐻𝐻 −equation𝐻𝐻 along the saturation curve:

= (A-6) 𝛥𝛥𝐻𝐻vap 𝐻𝐻vap 𝐻𝐻liq � � � � − � � 𝑑𝑑𝑑𝑑 𝜎𝜎 𝑑𝑑𝑑𝑑 𝜎𝜎 𝑑𝑑𝑑𝑑 𝜎𝜎

204 where signifies the slope along the saturation curve. The two terms on the right hand side of the previous𝜎𝜎 equation are the liquid and vapor saturation heat capacity, respectively:

= (A-7) vap 𝜎𝜎 𝜎𝜎 𝛥𝛥𝐻𝐻 vap liq � �𝜎𝜎 𝐶𝐶 − 𝐶𝐶 From this point, each saturation heat𝑑𝑑𝑑𝑑 capacity needs to be changed to an isobaric heat capacity, and the vapor must be transformed to ideal gas in order to compare the properties in question.

A.2.1 Saturation and Isobaric Heat Capacities

To derive the connection between saturation and isobaric heat capacity, first recognize that for a closed system:

= + = + (A-8) where is heat, is work, 𝑑𝑑 𝑑𝑑is entropy,𝑄𝑄 𝑊𝑊 is 𝑇𝑇volume,𝑇𝑇𝑇𝑇 𝑉𝑉 𝑉𝑉𝑉𝑉and is pressure. Since pressure, volume, and temperature𝑄𝑄 can𝑊𝑊 be measured,𝑆𝑆 they are𝑉𝑉 often picked as the𝑃𝑃 independent variables instead of entropy. It would be useful to have an expression linking to and . Write as a function of and : 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝑆𝑆

𝑇𝑇 𝑃𝑃 = ( , ) (A-9)

Then, use the chain rule of partial differentiation𝑆𝑆 𝑆𝑆 𝑇𝑇 𝑃𝑃 to obtain:

= + (A-10) 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑 � �𝑃𝑃 𝑑𝑑𝑑𝑑 � �𝑇𝑇 𝑑𝑑𝑑𝑑 Substitute = from the𝜕𝜕 𝜕𝜕Maxwell relation𝜕𝜕𝜕𝜕 in for the second partial derivative of 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 �𝜕𝜕𝜕𝜕�𝑇𝑇 − �𝜕𝜕𝜕𝜕�𝑃𝑃 Equation A-10:

= (A-11) 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑 � �𝑃𝑃 𝑑𝑑𝑑𝑑 − � �𝑃𝑃 𝑑𝑑𝑑𝑑 Now, break down the first partial derivative𝜕𝜕𝜕𝜕 of Equation𝜕𝜕𝜕𝜕 A-10 into parts:

205

= (A-12) 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕 � �𝑃𝑃 � �𝑃𝑃 � �𝑃𝑃 From Equation A-8 obtain: 𝜕𝜕𝜕𝜕= , and𝜕𝜕 from𝜕𝜕 the𝜕𝜕𝜕𝜕 definition of isobaric heat capacity obtain: 𝑑𝑑𝑑𝑑 1 �𝑑𝑑𝑑𝑑�𝑃𝑃 𝑇𝑇 = . Use these relationships in Equation A-11 to get: 𝜕𝜕𝜕𝜕 𝑃𝑃 𝐶𝐶 �𝜕𝜕𝜕𝜕�𝑃𝑃

= (A-13) 𝐶𝐶𝑃𝑃 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 − � �𝑃𝑃 𝑑𝑑𝑑𝑑 Plugging this equation into Equation A𝑇𝑇-8 gives:𝜕𝜕 𝜕𝜕

= + (A-14)

𝑃𝑃 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑 𝐶𝐶 𝑑𝑑𝑑𝑑 �𝑉𝑉 − 𝑇𝑇 � �𝑃𝑃� 𝑑𝑑𝑑𝑑 At this point, take the partial derivative of enthalpy𝜕𝜕 with𝜕𝜕 respect to temperature at saturation to get:

= = + (A-15)

𝜎𝜎 𝑑𝑑𝑑𝑑 𝑃𝑃 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑 𝐶𝐶 � �𝜎𝜎 𝐶𝐶 �𝑉𝑉 − 𝑇𝑇 � �𝑃𝑃� � �𝜎𝜎 or: 𝑑𝑑𝑑𝑑 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑

= + (A-16) vap 𝜎𝜎 𝑃𝑃 𝜕𝜕𝜕𝜕 𝑑𝑑𝑃𝑃 𝐶𝐶 𝐶𝐶 �𝑉𝑉 − 𝑇𝑇 � �𝑃𝑃� � � which is the relationship needed between saturation𝜕𝜕𝜕𝜕 and𝑑𝑑 isobaric𝑑𝑑 heat capacity.

A.2.2 Vapor and Ideal Gas Heat Capacities

Adjusting between vapor and ideal gas heat capacity is simply an adjustment from vapor pressure to zero pressure. To do so, the pressure dependence of isobaric heat capacity needs to be found. Start with the commutative property of Equation A-14:

= (A-17) 𝑑𝑑 𝑑𝑑𝑑𝑑 𝑑𝑑 𝑑𝑑𝑑𝑑 � �𝑇𝑇 � �𝑃𝑃 � �𝑃𝑃 � �𝑇𝑇 and substitute partial derivatives𝑑𝑑𝑑𝑑 on 𝑑𝑑both𝑑𝑑 sides𝑑𝑑 of𝑑𝑑 the equation𝑑𝑑𝑑𝑑 to get:

206

= (A-18)

𝑑𝑑 𝑃𝑃 𝑑𝑑 𝜕𝜕𝜕𝜕 � 𝐶𝐶 �𝑇𝑇 � �𝑉𝑉 − 𝑇𝑇 � �𝑃𝑃��𝑇𝑇 or 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝜕𝜕𝜕𝜕

= 2 (A-19) 𝑑𝑑 𝜕𝜕 𝑉𝑉 � 𝐶𝐶𝑃𝑃� −𝑇𝑇 � 2� 𝑇𝑇 𝑃𝑃 when simplified. Now, integrate𝑑𝑑 from𝑑𝑑 zero pressure𝜕𝜕𝑇𝑇 to the vapor pressure on both sides to get:

= 𝑃𝑃vap 2 (A-20) vap 𝑖𝑖𝑖𝑖 𝜕𝜕 𝑉𝑉 𝐶𝐶𝑃𝑃 − 𝐶𝐶𝑃𝑃 � −𝑇𝑇 � 2� 𝑑𝑑𝑑𝑑 0 𝑃𝑃 Solving for the isobaric vapor heat capacity shows: 𝜕𝜕𝑇𝑇

= 𝑃𝑃vap 2 (A-21) vap 𝑖𝑖𝑖𝑖 𝜕𝜕 𝑉𝑉 𝐶𝐶𝑃𝑃 𝐶𝐶𝑃𝑃 − � 𝑇𝑇 � 2� 𝑑𝑑𝑑𝑑 0 𝑃𝑃 which is the needed relationship. 𝜕𝜕𝑇𝑇

A.2.2 The Derivative Method

The pieces required to derive the derivative method are given by Equations AA-7,

AA-16, and AA-21. Plugging Equations AA-16 and AA-21 into Equation AA-7 gives:

= + 𝛥𝛥𝐻𝐻vap 𝑙𝑙 𝜕𝜕𝑉𝑉liq 𝑑𝑑𝑃𝑃vap � � −𝐶𝐶𝑃𝑃 �𝑉𝑉liq − 𝑇𝑇 � � � � � (A-22) 𝑑𝑑𝑑𝑑 𝜎𝜎 𝜕𝜕𝜕𝜕 𝑃𝑃 𝑑𝑑𝑑𝑑 + + 𝑃𝑃vap 2 𝑖𝑖𝑖𝑖 𝜕𝜕 𝑉𝑉vap 𝜕𝜕𝑉𝑉vap 𝑑𝑑𝑃𝑃vap �𝐶𝐶𝑃𝑃 − � 𝑇𝑇 � 2 � 𝑑𝑑𝑑𝑑 �𝑉𝑉vap − 𝑇𝑇 � � � � �� 0 𝑃𝑃 𝑃𝑃 This can be rearranged into the form given𝜕𝜕𝑇𝑇 by Equation 2-6: 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑

= 𝑃𝑃vap + (A-23) 2 𝑙𝑙 𝑖𝑖𝑖𝑖 𝜕𝜕 𝑉𝑉vap 𝑑𝑑𝑑𝑑𝐻𝐻vap 𝜕𝜕Δ𝑉𝑉 𝑑𝑑𝑃𝑃vap 𝑝𝑝 𝑝𝑝 2 𝐶𝐶 𝐶𝐶 − 𝑇𝑇 � � � 𝑑𝑑𝑑𝑑 − �Δ𝑉𝑉 − 𝑇𝑇 � �𝑃𝑃� 0 𝜕𝜕𝑇𝑇 𝑑𝑑𝑑𝑑 𝜕𝜕𝜕𝜕 𝑑𝑑𝑑𝑑

207

A.3 Ideal Gas Heat Capacity Derivation using Statistical Mechanics

As with most properties for ideal gases, heat capacity can be derived, starting with the definition of isobaric heat capacity:

(A-24)

𝑝𝑝 𝑑𝑑𝑑𝑑 𝐶𝐶 ≡ � �𝑃𝑃 with as the isobaric heat capacity, as the temperature,𝑑𝑑𝑑𝑑 as the pressure, and as the

p enthalpy𝐶𝐶 of the fluid. Enthalpy can be 𝑇𝑇broken down into parts:𝑃𝑃 𝐻𝐻

+ (A-25) with as the internal energy, as the pressure,𝐻𝐻 ≡ 𝑈𝑈and 𝑃𝑃𝑃𝑃 as the molar volume. Substituting this definition𝑈𝑈 into Equation AA-24𝑃𝑃 gives: 𝑉𝑉

= + (A-26)

𝑃𝑃 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑 𝐶𝐶 � �𝑃𝑃 𝑃𝑃 � �𝑃𝑃 From statistical mechanics, 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑

= 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 (A-27)

𝑈𝑈 � 𝑈𝑈𝑖𝑖 𝑖𝑖 with the modes of internal energy being translational, rotational, vibrational, and electronic. For each of these modes,

ln( ) = (A-28) , 2 𝑖𝑖 𝑖𝑖 𝑑𝑑 𝑞𝑞 𝑈𝑈 𝑘𝑘𝑇𝑇 � �𝑁𝑁 𝑉𝑉 where is the Boltzmann constant, is the number𝑑𝑑 𝑑𝑑of molecules, is the volume, and is the

𝑖𝑖 contribution𝑘𝑘 of mode to the partition𝑁𝑁 function. Putting all of these𝑉𝑉 concepts together gives𝑞𝑞 a form for heat capacity:𝑖𝑖

208

ln( ) , = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 2 𝑑𝑑 𝑞𝑞𝑖𝑖 + (A-29) 𝑑𝑑 �𝑘𝑘𝑇𝑇 � � � 𝑑𝑑𝑑𝑑 𝑁𝑁 𝑉𝑉 𝑃𝑃 ⎛ ⎞ 𝑑𝑑𝑑𝑑 𝐶𝐶 � 𝑃𝑃 � �𝑃𝑃 𝑖𝑖 ⎜ 𝑑𝑑𝑑𝑑 ⎟ 𝑑𝑑𝑑𝑑 𝑃𝑃 The ideal gas law, ⎝ ⎠

= (A-30)

with as pressure, as molar volume, as𝑃𝑃 temperature,𝑃𝑃 𝑁𝑁𝑁𝑁𝑁𝑁 as Avogadro’s number, and as the

Boltzmann𝑃𝑃 constant,𝑉𝑉 simplifies Equation𝑇𝑇 AA-29 for : 𝑁𝑁 𝑘𝑘 𝑖𝑖𝑖𝑖 𝑝𝑝 ln( ) 𝐶𝐶 , = modes 2 𝑑𝑑 𝑞𝑞𝑖𝑖 + = + (A-31) 𝑑𝑑 �𝑘𝑘𝑇𝑇 � � � 𝑖𝑖𝑖𝑖 ⎛ 𝑑𝑑𝑑𝑑 𝑁𝑁 𝑉𝑉 ⎞ 𝑖𝑖𝑖𝑖 𝐶𝐶𝑝𝑝 � 𝑁𝑁𝑁𝑁 𝐶𝐶𝑣𝑣 𝑁𝑁𝑁𝑁 𝑖𝑖 ⎜ 𝑑𝑑𝑑𝑑 ⎟ 𝑃𝑃 The partition function, in Equation⎝ AA-31, can be derived⎠ with statistical mechanics [154],

𝑖𝑖 giving: 𝑞𝑞

/ , 7 = + 3𝑚𝑚−5 2 2 Θ𝑣𝑣𝑣𝑣 𝑇𝑇 (A-32) 𝑖𝑖𝑖𝑖 linear Θ𝑣𝑣𝑣𝑣 ( 𝑒𝑒 1) 𝐶𝐶𝑝𝑝 𝑁𝑁𝑁𝑁 � � � Θ𝑣𝑣𝑣𝑣 𝑗𝑗 𝑇𝑇 𝑇𝑇 2 for a linear molecule, and 𝑒𝑒 −

/ , = 4 + 3𝑚𝑚−6 2 Θ𝑣𝑣𝑣𝑣 𝑇𝑇 (A-33) 𝑖𝑖𝑖𝑖 nonlinear Θ𝑣𝑣𝑣𝑣 ( 𝑒𝑒 1) 𝐶𝐶𝑝𝑝 𝑁𝑁𝑁𝑁 � � � Θ𝑣𝑣𝑣𝑣 𝑗𝑗 𝑇𝑇 𝑇𝑇 2 for a non-linear molecule with as temperature, as the number𝑒𝑒 of− atoms in a single molecule,

and as the vibrational frequency𝑇𝑇 for linear𝑚𝑚 and nonlinear molecules with m atoms, 𝑡𝑡ℎ 𝑣𝑣𝑣𝑣 respectivelyΘ [25]𝑗𝑗 .

209

APPENDIX B. DATA USED

Vapor pressure, heat of vaporization, and liquid heat capacity literature data were used throughout the course of this project. Chapters 4, 5, 6, and 7 were all published separately, but much of the literature data overlapped. Here, the data were separated by property, and then further separated into whichever chapter they were used.

B.1 Vapor Pressure Data

Vapor pressure data are summarized below. These tables are categorized into data used in

Chapter 5, and data used in Chapter 6.

B.1.1 Vapor Pressure Data for Riedel Equation Analysis

The following data were used to analyze which forms of the Riedel equation worked for which families, as described in Chapter 5.

211

Table B-1: Summary of vapor pressure data used in this work for the n-alkanes Carbon # # Pvap Data Pvap Low T Pvap High T Data Sources 2 278 92 K 305.42 K [55, 155-165] 3 120 163.15 K 368.75 K [164, 166-178] 4 200 195.1 K 425.07 K [53, 164, 169, 179-214] 5 108 223.05 K 468 K [147, 215-223] 6 228 239.55 K 503.15 K [223-260] 7 406 185.3 K 540 K [159, 214, 223, 229, 230, 233, 239, 241, 242, 246, 253, 255, 261-292] 8 162 263.15 K 568.74 K [187, 214, 223, 233, 244, 269, 272, 292-299]

Table B-2: Summary of vapor pressure data used in this work for the 2-methylalkanes Carbon # # Pvap Data Pvap Low T Pvap High T Data Sources 3 159 238.98 K 407.5 K [168, 180-182, 189, 190, 195, 199, 202, 203, 210-212, 300-318] 4 55 217.19 K 448.15 K [213, 214, 223, 319-321] 5 48 285.91 K 359.7 K [223, 260, 322-324] 6 34 273.13 K 530.3 K [244, 325] 7 50 233.15 K 559.56 K [223, 244, 326, 327]

Table B-3: Summary of vapor pressure data used in this work for the 1-alkenes Carbon # # Pvap Data Pvap Low T Pvap High T Data Sources 3 188 151.72 K 364.5 K [162, 174, 187, 247, 328-345] 4 143 198.15 K 420.37 K [174, 180, 182, 189, 190, 195, 202, 247, 315, 318, 334, 346-355] 5 88 218.35 K 463.4 K [247, 271, 356-360] 6 64 249.97 K 374.15 K [262, 278, 285, 361-364] 7 40 255.46 K 374.15 K [362-366]

Table B-4: Summary of vapor pressure data used in this work for the n-aldehydes Carbon # # Pvap Data Pvap Low T Pvap High T Data Sources 4 30 303.86 K 353.15 K [250, 367-375] 5 34 242.15 K 377.65 K [376-380]

212

Table B-4: continued Carbon # # Pvap Data Pvap Low T Pvap High T Data Sources 6 19 322.27 K 402.17 K [381-385] 7 30 310.15 K 453.15 K [379, 386, 387]

Table B-5: Summary of vapor pressure data used in this work for aromatic compounds Compound # Pvap Data Pvap Low T Pvap High T Data Sources Benzene 143 283.1 K 553.15 K [361, 388-393] Toluene 98 247.15 K 591.7 K [361, 388-394] Ethylbenzene 165 288.1 K 618 K [223, 271, 361, 389, 395-399] Propylbenzene 31 266.35 K 433.39 K [223, 271, 400] n-Butylbenzene 27 268.45 K 500.97 K [36, 400, 401] m-Xylene 123 273.15 K 617.05 K [223, 271, 288, 389, 397, 402-414] o-Xylene 145 273.15 K 630.2 K [223, 235, 271, 389, 402-404, 407, 410-422] p-Xylene 83 293.15 K 616.1 K [223, 271, 318, 397, 402, 403, 407, 410-414, 423-428]

Table B-6: Summary of vapor pressure data used in this work for the ethers Compound # Pvap Data Pvap Low T Pvap High T Data Sources Dimethyl- 20 261.37 K 335.66 K [257, 301, 370, 429-437] Diethyl- 55 250.05 K 466.85 K [296, 297, 316, 438-442] Ethyl propyl- 139 171.63 K 400.38 K [443, 444] Di-n-propyl- 40 299.74 K 323.15 K [378, 441, 445-448] Methyl tert-Butyl 250 273.15 K 496.4 K [214, 245, 247, 370, 446, 449-452]

Table B-7: Summary of vapor pressure data used in this work for the ketones Compound # Pvap Data Pvap Low T Pvap High T Data Sources Methyl Ethyl 175 265.15 K 536.78 K [214, 398, 453-476] Methyl Isopropyl 77 276.25 K 549.82 K [457, 458, 477-487]

213

Table B-7: continued Compound # Pvap Data Pvap Low T Pvap High T Data Sources Methyl Isobutyl 149 283.15 K 415.82 K [458, 479, 483, 487-495] 2-Pentanone 99 203.61 K 558.15 K [445, 477, 480, 496-500] 2-Hexanone 36 298.15 K 427.76 K [453, 483, 498, 501-504] 3-Hexanone 93 292.85 K 422.25 K [361, 396, 453, 503, 505, 506] 2-Heptanone 119 274 K 452.42 K [396, 453, 500, 507-510] 2-Octanone 52 260 K 630 K [453, 500, 501, 511-515]

214

B.1.2 Vapor Pressure Data for New Predictive Riedel Equation

The following data were used to generate and analyze the predictive Riedel equation as described in Chapter 6.

215

Table B-8: Summary of vapor pressure data used in this work for alkanes and alkenes Compound # Pvap Data Pvap Low T Pvap High T Data Sources Ethane 278 92 K 305.42 K [55, 155-165] Propane 120 163.15 K 368.75 K [164, 166-178] Butane 200 195.1 K 425.07 K [53, 164, 169, 179-214] Pentane 108 223.05 K 468 K [147, 215-223] Hexane 228 239.55 K 503.15 K [223-260] Octane 162 263.15 K 568.74 K [187, 214, 223, 233, 244, 269, 272, 292-299] Isopropane 159 238.98 K 407.5 K [168, 180-182, 189, 190, 195, 199, 202, 203, 210-212, 300-318] Isobutane 55 217.19 K 448.15 K [213, 214, 223, 319-321] 2-Methylhexane 34 273.13 K 530.3 K [244, 325] 2-Methylheptane 50 233.15 K 559.56 K [223, 244, 326, 327] Cyclohexane 109 280.05 K 560.07 K [223, 516-521] Ethylene 97 110 K 282.34 K [361, 522-526]

Table B-9: Summary of vapor pressure data used in this work for aromatic compounds Compound # Pvap Data Pvap Low T Pvap High T Data Sources Benzene 143 283.1 K 553.15 K [361, 388-393] Toluene 98 247.15 K 591.7 K [361, 388-394] m-Xylene 123 273.15 K 617.05 K [223, 271, 288, 389, 397, 402-414] o-Xylene 145 273.15 K 630.2 K [223, 235, 271, 389, 402-404, 407, 410-422] p-Xylene 83 293.15 K 616.1 K [223, 271, 318, 397, 402, 403, 407, 410-414, 423-428]

Table B-10: Summary of vapor pressure data used in this work for the esters and ethers Compound # Pvap Data Pvap Low T Pvap High T Data Sources Methyl Formate 62 198.95 K 487.15 K [361, 527, 528] Ethyl Acetate 272 229.75 K 523.3 K [187, 233, 248, 250, 288, 318, 401, 445, 529-543] Propyl Formate 87 302.43 K 370.61 K [544, 545] Diethyl Ether 55 250.05 K 466.85 K [296, 297, 316, 438-442]

216

Table B-11: Summary of vapor pressure data used in this work for the gases Compound # Pvap Data Pvap Low T Pvap High T Data Sources Hydrogen 23 15.1 K 33.18 K [361, 546] Neon 62 24.54 K 44.49 K [361, 527, 547-549] Argon 22 83.8 K 150.86 K [361, 445, 550] Oxygen 77 54.36 K 154.58 K [361, 526, 551] Carbon Monoxide 53 68.08 K 132.92 K [361, 548, 552-554]

Table B-12: Summary of vapor pressure data used in this work for the halogenated compounds Compound # Pvap Data Pvap Low T Pvap High T Data Sources Chlorotrifluoromethane 78 92.16 K 302 K [12, 555, 556] Carbon tetrachloride 84 252.65 K 556.3 K [361, 445, 528, 557] Hexafluoroethane 94 173.7 K 292.22 K [558-562] Fluorobenzene 33 255.3 K 560.07 K [445, 529, 563]

Table B-13: Summary of vapor pressure data used in this work for the ketones Compound # Pvap Data Pvap Low T Pvap High T Data Sources Methyl Ethyl 175 265.15 K 536.78 K [214, 398, 453-476] Methyl Isobutyl 149 283.15 K 415.82 K [458, 479, 483, 487-495] 2-Pentanone 99 203.61 K 558.15 K [445, 477, 480, 496-500] 2-Hexanone 36 298.15 K 427.76 K [453, 483, 498, 501-504] 3-Hexanone 93 292.85 K 422.25 K [361, 396, 453, 503, 505, 506] 2-Heptanone 119 274 K 452.42 K [396, 453, 500, 507-510] 2-Octanone 52 260 K 630 K [453, 500, 501, 511-515]

Table B-14: Summary of vapor pressure data used in this work for alkanes Compound # Pvap Data Pvap Low T Pvap High T Data Sources Heptane 406 185.3 K 540 K [159, 214, 223, 229, 230, 233, 239, 241, 242, 246, 253, 255, 261-292] 2-Methylpentane 48 285.91 K 359.7 K [223, 260, 322-324] 2,2-Dimethylpentane 43 285.34 K 453.15 K [223, 271, 364, 564]

217

Table B-14: continued Compound # Pvap Data Pvap Low T Pvap High T Data Sources 3-Ethylpentane 49 294.28 K 540.57 K [244, 271, 565] 3-Methylheptane 19 315.85 K 563.6 K [223, 244] 2,3,3-Trimethylpentane 41 309.9 K 573.49 K [223, 244]

Table B-15: Summary of vapor pressure data used in this work for multifunctional compounds Compound # Pvap Data Pvap Low T Pvap High T Data Sources 2-Aminobiphenyl 36 350 K 623.56 K [566] Aniline 53 343.16 K 498.85 K [36, 567-570] Dibenzofuran 34 358.15 K 602.59 K [571] Dimethyl isophthalate 32 349.98 K 607.23 K [34] Furan 42 275.7 K 483.15 K [572-574] Indane 57 284 K 482.44 K [575-578] Methyl Acrylate 17 278.15 K 353.15 K [574, 579] 2-Methylpyridine 61 295.24 K 441.52 K [580-582] 3-Methylpyridine 42 314.03 K 457.7 K [582-584] Piperazine 17 418 K 655 K [585, 586] Pyridine 50 310.64 K 616.48 K [573, 587-589] Pyrrole 77 338.15 K 615.15 K [235, 573, 589-591] Styrene 44 298.1 K 635.2 K [169, 592-594] Tetrahydrofuran 120 275.99 K 538.71 K [214, 283, 573, 595-600]

Table B-16: Summary of vapor pressure data used in this work for the 1-alkenes Compound # Pvap Data Pvap Low T Pvap High T Data Sources Propylene 188 151.72 K 364.5 K [162, 174, 187, 247, 328-345] Butylene 143 198.15 K 420.37 K [174, 180, 182, 189, 190, 195, 202, 247, 315, 318, 334, 346-355] 1-Pentene 88 218.35 K 463.4 K [247, 271, 356-360] 1-Heptene 40 255.46 K 374.15 K [362-366] trans-2-Pentene 30 273.15 K 343.15 K [601, 602] 1,3-Butadiene 50 193.1 K 423.1 K [180, 186, 196, 318, 370, 603, 604]

218

Table B-16: continued Compound # Pvap Data Pvap Low T Pvap High T Data Sources trans-1,3-Pentadiene 21 213.14 K 315.96 K [605] 2-Methyl-1,2-Butadiene 23 213.14 K 319.19 K [606]

Table B-17: Summary of vapor pressure data used in this work for the 1-alkenes Compound # Pvap Data Pvap Low T Pvap High T Data Sources Propylene 188 151.72 K 364.5 K [162, 174, 187, 247, 328-345] Butylene 143 198.15 K 420.37 K [174, 180, 182, 189, 190, 195, 202, 247, 315, 318, 334, 346-355] 1-Pentene 88 218.35 K 463.4 K [247, 271, 356-360] 1-Heptene 40 255.46 K 374.15 K [362-366] trans-2-Pentene 30 273.15 K 343.15 K [601, 602] 1,3-Butadiene 50 193.1 K 423.1 K [180, 186, 196, 318, 370, 603, 604] trans-1,3-Pentadiene 21 213.14 K 315.96 K [605] 2-Methyl-1,2-Butadiene 23 213.14 K 319.19 K [606]

Table B-18: Summary of vapor pressure data used in this work for the n-aldehydes Compound # Pvap Data Pvap Low T Pvap High T Data Sources Propanal 29 231.15 K 373.15 K [213, 250, 367, 371, 470, 607-611] Butanal 30 303.86 K 353.15 K [250, 367-375] Pentanal 34 242.15 K 377.65 K [376-380] Hexanal 19 322.27 K 402.17 K [381-385] Heptanal 30 310.15 K 453.15 K [379, 386, 387]

Table B-19: Summary of vapor pressure data used in this work for aromatic compounds Compound # Pvap Data Pvap Low T Pvap High T Data Sources Ethylbenzene 165 288.1 K 618 K [223, 271, 361, 389, 395-399] Propylbenzene 31 266.35 K 433.39 K [223, 271, 400] n-Butylbenzene 27 268.45 K 500.97 K [36, 400, 401] p-Cymene 35 263.15 K 633.15 K [543, 612, 613]

219

Table B-18: continued Compound # Pvap Data Pvap Low T Pvap High T Data Sources Ethylbenzene 165 288.1 K 618 K [223, 271, 361, 389, 395-399] Propylbenzene 31 266.35 K 433.39 K [223, 271, 400] n-Butylbenzene 27 268.45 K 500.97 K [36, 400, 401] p-Cymene 35 263.15 K 633.15 K [543, 612, 613] Naphthalene 100 353.33 K 745.9 K [586, 614-623] Phenanthrene 32 373.15 K 667.74 K [606, 624] Pyrene 8 425.65 K 458.15 L [625]

Table B-20: Summary of vapor pressure data used in this work for the ethers Compound # Pvap Data Pvap Low T Pvap High T Data Sources Dimethyl- 20 261.37 K 335.66 K [257, 301, 370, 429-437] Ethyl propyl- 139 171.63 K 400.38 K [443, 444] Di-n-propyl- 40 299.74 K 323.15 K [378, 441, 445-448] Methyl tert-Butyl 250 273.15 K 496.4 K [214, 245, 247, 370, 446, 449-452]

Table B-21: Summary of vapor pressure data used in this work for the ketones Compound # Pvap Data Pvap Low T Pvap High T Data Sources Methyl Isopropyl 77 276.25 K 549.82 K [457, 458, 477-487]

Table B-22: Summary of vapor pressure data used in this work for the amines Compound # Pvap Data Pvap Low T Pvap High T Data Sources Ethylamine 28 211.86 K 456.35 K [626, 627] Propylamine 13 296.12 K 350.74 K [299, 628] Butylamine 12 297.09 K 349.3 K [629, 630] Pentylamine 13 322.61 K 377.93 K [631] Isobutylamine 18 289.18 K 373.76 K [628] N,N-Diethylmethylamine 9 308.15 K 444.61 K [632-634] Triethylamine 36 273.04 K 423.15 K [214, 629, 635-637]

220

Table B-21: continued Compound # Pvap Data Pvap Low T Pvap High T Data Sources Isopropylamine 11 213.08 K 334.13 K [628]

Table B-23: Summary of vapor pressure data used in this work for the ringed alkanes Compound # Pvap Data Pvap Low T Pvap High T Data Sources Ethylcyclopentane 29 301.93 K 566.48 K [271, 638] Methylcyclohexane 113 298.74 K 443.15 K [214, 223, 288, 516, 639-642] Ethylcyclohexane 17 324.56 K 405.89 K [223] Propylcyclohexane 11 345.66 K 430.86 K [223]

Table B-24: Summary of vapor pressure data used in this work for the halogenated compounds Compound # Pvap Data Pvap Low T Pvap High T Data Sources 1,2-Dichloroethane 75 293.15 K 560.3 K [261, 636, 643-649] n-Butyl chloride 77 256.45 K 367.05 K [249, 364, 470, 650-658] Trifluoromethane 164 133.69 K 298.15 K [659-665] Perfluoro-n-heptane 72 271.26 K 473.94 K [666-670]

Table B-25: Summary of vapor pressure data used in this work for the esters Compound # Pvap Data Pvap Low T Pvap High T Data Sources Butyl Acetate 94 326.19 K 410.04 K [445, 671-676] Pentyl Acetate 75 274.2 K 508.85 K [9, 401, 677-682] Hexyl Acetate 21 274.5 K 380.55 K [679, 683-686] Octyl Acetate 21 274.5 K 484.95 K [683-686]

Table B-26: Summary of vapor pressure data used in this work for the sulfides Compound # Pvap Data Pvap Low T Pvap High T Data Sources Methyl mercaptan 8 221.88 K 288.16 K [687, 688] Ethyl mercaptan 33 273.15 K 373.15 K [169, 689-691]

221

Table B-25: continued Compound # Pvap Data Pvap Low T Pvap High T Data Sources Diethyl sulfide 54 283.15 K 395.58 K [182, 692-694] Methyl-n-butyl sulfide 30 346.9 K 435.83 K [690, 695] Methyl isopropyl sulfide 38 275 K 550 K [690, 696, 697]

Table B-27: Summary of vapor pressure data used in this work for the alkynes and silanes Compound # Pvap Data Pvap Low T Pvap High T Data Sources Ethylacetylene 35 204.23 K 353.15 K [636, 698, 699] Tetramethylsilane 34 208.94 K 450.4 K [700-702]

222

B.2 Heat of Vaporization Data

Heat of vaporization data were used in Chapter 6 to determine how well the new predictive vapor pressure method does with the Clapeyron equation. Those data are listed here.

223

Table B-28: Summary of heat of vaporization data used in this work for alkanes and alkenes Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Ethane 18 133.15 K 301.3 K [703, 704] Propane 25 277.6 K 361 K [705-707] Butane 1 273.7 K 273.7 K [552] Pentane 56 259.54 K 455.37 K [147, 706, 708-711] Hexane 21 298.15 K 444.26 K [710, 712-715] Octane 4 298.2 K 298.2 K [14, 16, 17, 716] Isopropane 11 261.4 K 383.71 K [717, 718] Isobutane ------2-Methylhexane 5 298.15 K 353.15 K [325, 715] 2-Methylheptane 5 298.15 K 353.15 K [710, 715] Cyclohexane 20 310.93 K 537.04 K [719-723] Ethylene ------

Table B-29: Summary of heat of vaporization data used in this work for the aromatic compounds Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Benzene 24 273.1 K 553.1 K [714, 724-726] Toluene 26 298.15 K 521.13 K [425, 727, 728] m-Xylene ------o-Xylene ------p-Xylene 11 298.15 K 509.27 K [728]

Table B-30: Summary of heat of vaporization data used in this work for the esters and ethers Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Methyl Formate 3 293.3 K 313.5 K [723] Ethyl Acetate 8 320.57 K 363.4 K [729, 730] Propyl Formate* ------Diethyl Ether 5 293.15 K 313.15 K [731-733]

224

Table B-31: Summary of heat of vaporization data used in this work for the gases Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Hydrogen 20 13.96 K 32.87 K [546, 734] Neon ------Argon ------Oxygen 1 90.13 K 90.13 K [735] Carbon Monoxide ------

Table B-32: Summary of heat of vaporization data used in this work for the halogenated compounds Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Chlorotrifluoromethane ------Carbon tetrachloride 5 298.15 K 358.15 K [736] Hexafluoroethane 8 179.96 K 195.21 K [559] Fluorobenzene ------

Table B-33: Summary of heat of vaporization data used in this work for the ketones Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Methyl Ethyl 13 298.15 K 370.57 K [275, 454, 471, 737] Methyl Isobutyl 5 298.15 K 358.15 K [454, 737] 2-Pentanone 7 298.15 K 358.15 K [737-739] 2-Hexanone 17 298.15 K 368.15 K [737, 738, 740, 741] 3-Hexanone 5 298.15 K 368.15 K [737] 2-Heptanone 2 298.15 K 298.15 K [738, 742] 2-Octanone 1 298.15 K 298.15 K [738]

Table B-34: Summary of heat of vaporization data used in this work for alkanes Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Heptane 20 273.15 K 373.15 K [710, 714, 715, 743, 744] 225

Table B-86: continued Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources 2-Methylpentane 7 293.15 K 353.15 K [713, 745] 2,2-Dimethylpentane 9 298.15 K 368.15 K [746] 3-Ethylpentane 7 298.15 K 348.15 K [746] 3-Methylheptane 1 298.15 K 298.15 K [710] 2,3,3-Trimethylpentane 9 298.15 K 368.15 K [746]

Table B-35: Summary of heat of vaporization used in this work for the 1-alkenes Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Propylene 13 227.6 K 355.4 K [747] Butylene 20 202.31 K 377.59 K [346, 748, 749] 1-Pentene 15 283.96 K 410.93 K [358, 750] 1-Heptene ------trans-2-Pentene ------1,3-Butadiene 3 247.07 K 295.67 K [604] trans-1,3-Pentadiene ------2-Methyl-1,2-Butadiene ------

Table B-36: Summary of heat of vaporization data used in this work for the n-aldehydes Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Propanal 4 286.25 K 321.21 K [751, 752] Butanal 2 298.15 K 347.9 K [752, 753] Pentanal ------Hexanal ------Heptanal ------

226

Table B-37: Summary of heat of vaporization data used in this work for the aromatic compounds Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Ethylbenzene ------Propylbenzene ------n-Butylbenzene 3 343.15 K 368.15 K [754] p-Cymene ------Naphthalene ------Phenanthrene ------Pyrene ------

Table B-38: Summary of heat of vaporization data used in this work for the ethers Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Dimethyl- 1 248.3 K 248.3 K [429] Ethyl propyl------Di-n-propyl- 10 298.15 K 363.22 K [441, 731, 755] Methyl tert-Butyl 5 298.15 K 343.15 K [731, 756]

Table B-39: Summary of heat of vaporization data used in this work for the ketones Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Methyl Isopropyl 6 298.2 K 367.48 K [505, 737]

Table B-40: Summary of heat of vaporization data used in this work for the amines Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Ethylamine ------Propylamine 3 298.15 K 328.15 K [629] Butylamine 6 298.15 K 358.15 K [629, 757] Pentylamine 1 298.15 K 328.15 K [757] Isobutylamine 4 298.15 K 298.15 K [629, 757] 227

Table B-92: continued Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources N,N-Diethylmethylamine ------Triethylamine 7 298.15 K 362.15 K [629, 757] Isopropylamine 2 298.15 K 313.15 K [629]

Table B-41: Summary of heat of vaporization data used in this work for the ringed alkanes Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Ethylcyclopentane 5 313.15 K 368.15 K [758] Methylcyclohexane 11 298.2 K 493.15 K [710, 715, 727] Ethylcyclohexane 6 298.2 K 368.15 K [710, 758] Propylcyclohexane 1 298.2 K 298.2 K [710]

Table B-42: Summary of heat of vaporization data used in this work for the halogenated compounds Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources 1,2-Dichloroethane 7 298 K 358.15 K [736, 759, 760] n-Butyl chloride 11 298.15 K 358.15 K [752, 759, 761-763] Trifluoromethane 2 190.97 K 191.15 K [659, 764] Perfluoro-n-heptane 1 298.15 K 298.15 K [728]

Table B-43: Summary of heat of vaporization data used in this work for the esters Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Butyl Acetate 6 298.15 K 358.15 K [765-767] Pentyl Acetate ------Hexyl Acetate ------Octyl Acetate ------

228

Table B-44: Summary of heat of vaporization data used in this work for the sulfides Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Methyl mercaptan 1 279.11 K 279.11 K [688] Ethyl mercaptan 3 281.15 K 281.16 K [689] Diethyl sulfide 4 286 K 365.26 K [22, 692] Methyl-n-butyl sulfide 1 298.15 K 298.15 K [695] Methyl isopropyl sulfide 4 298.15 K 357.98 K [697, 768]

Table B-45: Summary of heat of vaporization data used in this work for the alkynes and silanes Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources Ethylacetylene 6 262.53 K 282.52 K [698] Tetramethylsilane ------

Table B-46: Summary of heat of vaporization data used in this work for multifunctional compounds Compound # ΔHvap Data ΔHvap Low T ΔHvap High T Data Sources 2-Aminobiphenyl ------Aniline 3 298.15 K 333.2 K [769-771] Dibenzofuran ------Dimethyl isophthalate ------Furan 3 279.15 K 304.51 K [572] Indane 51 284 K 500 K [577, 578, 772] Methyl Acrylate ------2-Methylpyridine 6 298.15 K 368.15 K [773] 3-Methylpyridine 6 298.15 K 368.15 K [773] Piperazine ------Pyridine 9 298.15 K 388.4 K [587, 773] Pyrrole 3 362.11 K 402.91 K [590] Styrene ------Tetrahydrofuran 3 301.8 K 339.1 K [774]

229

B.3 Liquid Heat Capacity Data

Liquid heat capacity data are summarized below. These tables are categorized into data used in Chapter 5, and data used in Chapter 6.

B.3.1 Liquid Heat Capacity Data for Riedel Equation Analysis

The following data were used to analyze which forms of the Riedel equation worked for which families, as described in Chapter 5.

230

Table B-47: Summary of liquid heat capacity data used in this work for the n-alkanes l l l Carbon # # Cp Data Cp Low T Cp High T Data Sources 2 33 91.59 K 290 K [55, 775] 3 21 89.66 K 229.75 K [776] 4 99 138.61 K 316.75 K [777] 5 17 148.6 K 302.87 K [778] 6 58 180 K 366.48 K [779-784] 7 47 182.55 K 370 K [325, 783-790] 8 50 222.61 K 386.09 K [779, 782, 784, 785, 791-795]

Table B-48: Summary of liquid heat capacity data used in this work for the 2-methylalkanes l l l Carbon # # Cp Data Cp Low T Cp High T Data Sources 3 27 113.55 K 380 K [796] 4 22 113.36 K 300 K [320, 797-800] 5 20 121.16 K 303.27 K [780, 801] 6 37 154.9 K 300 K [325, 501, 799] 7 26 164.19 K 370 K [710, 799]

Table B-49: Summary of liquid heat capacity data used in this work for the 1-alkenes l l l Carbon # # Cp Data Cp Low T Cp High T Data Sources 3 32 93.9 K 223.4 K [496, 802, 803] 4 128 88.5 K 299.83 K [346, 804, 805] 5 114 108.78 K 308.44 K [806-808] 6 55 136.19 K 308.16 K [809-811] 7 22 157.13 K 299.61 K [809]

Table B-50: Summary of liquid heat capacity data used in this work for the n-aldehydes l l l Carbon # # Cp Data Cp Low T Cp High T Data Sources 4 72 176.8 K 330.53 K [375, 812, 813] 5 2 270 K 298.2 K [814, 815]

231

Table B-49: continued l l l Carbon # # Cp Data Cp Low T Cp High T Data Sources 6 11 214.94 K 330 K [816] 7 8 230 K 300 K [375]

Table B-51: Summary of liquid heat capacity data used in this work for the aromatic compounds l l l Compound # Cp Data Cp Low T Cp High T Data Sources Benzene 37 278.68 K 500 K [361, 394] Toluene 52 278.15 K 503.15 K [790, 817-825] Ethylbenzene 37 184.4 K 373.15 K [826-834] Propylbenzene 29 180.87 K 391.4 K [831, 833, 835] n-Butylbenzene 45 193.81 K 640 K [36, 831, 833, 835] m-Xylene 39 231.4 K 540.15 K [405, 411, 817, 825, 831, 834] o-Xylene 17 251.99 K 413.18 K [415] p-Xylene 29 290 K 410.65 K [411, 825, 827, 834, 836, 837]

Table B-52: Summary of liquid heat capacity data used in this work for the ethers l l l Compound # Cp Data Cp Low T Cp High T Data Sources Dimethyl- 11 140 K 240 K [429] Diethyl- 42 164.39 K 300 K [501, 529, 838, 839] Ethyl propyl- 21 145.65 K 320 K [756] Di-n-propyl- 22 158.36 K 330 K [501, 755] Methyl tert-Butyl 65 168.32 K 325.15 K [756, 840-842]

Table B-53: Summary of liquid heat capacity data used in this work for the ketones l l l Compound # Cp Data Cp Low T Cp High T Data Sources Methyl Ethyl 69 186.47 K 335 K [814, 843-847] Methyl Isopropyl 21 184.43 K 440 K [496, 843] Methyl Isobutyl 6 190 K 450 K [496] 2-Pentanone 37 196.35 K 364.11 K [501, 843, 848-850]

232

Table B-52: continued l l l Compound # Cp Data Cp Low T Cp High T Data Sources 2-Hexanone 63 217.69 K 460 K [361, 496, 501, 849, 851] 3-Hexanone 39 220 K 460 K [496, 815, 851] 2-Heptanone 7 240 K 490 K [496, 500] 2-Octanone 25 252.86 K 500 K [361, 496, 848]

233

B.3.2 Liquid Heat Capacity Data for New Predictive Riedel Equation

The following data were used to analyze the predictive Riedel equation as described in

Chapter 6.

234

Table B-54: Summary of liquid heat capacity data used in this work for alkanes and alkenes l l l Compound # Cp Data Cp Low T Cp High T Data Sources Ethane 33 91.59 K 290 K [55, 775] Propane 21 89.66 K 229.75 K [776] Butane 99 138.61 K 316.75 K [777] Pentane 17 148.6 K 302.87 K [778] Hexane 58 180 K 366.48 K [779-784] Octane 50 222.61 K 386.09 K [779, 782, 784, 785, 791-795] Isopropane 27 113.55 K 380 K [796] Isobutane 22 113.36 K 300 K [320, 797-800] 2-Methylhexane 37 154.9 K 300 K [325, 501, 799] 2-Methylheptane 26 164.19 K 370 K [710, 852] Cyclohexane 37 279.99 K 366.48 K [781, 838, 853] Ethylene 27 103.97 K 252.7 K [361, 854]

Table B-55: Summary of liquid heat capacity data used in this work for the aromatic compounds l l l Compound # Cp Data Cp Low T Cp High T Data Sources Benzene 37 278.68 K 500 K [361, 394] Toluene 52 278.15 K 503.15 K [790, 817-825] m-Xylene 39 231.4 K 540.15 K [405, 411, 817, 825, 831, 834] o-Xylene 17 251.99 K 413.18 K [415] p-Xylene 29 290 K 410.65 K [411, 825, 827, 834, 836, 837]

Table B-56: Summary of liquid heat capacity data used in this work for the esters and ethers l l l Compound # Cp Data Cp Low T Cp High T Data Sources Methyl Formate 12 213.15 K 304.15 K [361, 501, 855, 856] Ethyl Acetate 25 189.3 K 330 K [813, 857] Propyl Formate* ------Diethyl Ether 42 164.39 K 300 K [501, 529, 838, 839]

235

Table B-57: Summary of liquid heat capacity data used in this work for the gases l l l Compound # Cp Data Cp Low T Cp High T Data Sources Hydrogen 20 14 K 32 K [546] Neon 9 24.6 K 40 K [858] Argon 6 83.8 K 130 K [526, 838] Oxygen 57 54.36 K 142 K [526, 735, 859] Carbon Monoxide 31 70 K 128 K [361, 553, 860-862]

Table B-58: Summary of liquid heat capacity data used in this work for the halogenated compounds l l l Compound # Cp Data Cp Low T Cp High T Data Sources Chlorotrifluoromethane 1 243.15 K 243.15 K [555] Carbon tetrachloride 6 293.15 K 333.15 K [850, 863-865] Hexafluoroethane 12 174.88 K 195 K [552, 559] Fluorobenzene 18 239.99 K 454.95 K [866, 867]

Table B-59: Summary of liquid heat capacity data used in this work for the ketones l l l Compound # Cp Data Cp Low T Cp High T Data Sources Methyl Ethyl 69 186.47 K 335 K [814, 843-847] Methyl Isobutyl 6 190 K 450 K [496] 2-Pentanone 37 196.35 K 364.11 K [501, 843, 848-850] 2-Hexanone 63 217.69 K 460 K [361, 496, 501, 849, 851] 3-Hexanone 39 220 K 460 K [496, 815, 851] 2-Heptanone 7 240 K 490 K [496, 500] 2-Octanone 25 252.86 K 500 K [361, 496, 848]

Table B-60: Summary of liquid heat capacity data used in this work for alkanes l l l Compound # Cp Data Cp Low T Cp High T Data Sources Heptane 47 182.55 K 370 K [325, 783-790] 2-Methylpentane 20 121.16 K 303.27 K [780, 801] 2,2-Dimethylpentane 17 154.68 K 298.36 K [325]

236

Table B-59: continued l l l Compound # Cp Data Cp Low T Cp High T Data Sources 3-Ethylpentane 7 250 K 300 K [361] 3-Methylheptane 28 157.2 K 376 K [710, 852] 2,3,3-Trimethylpentane 6 280 K 320 K [361]

Table B-61: Summary of liquid heat capacity data used in this work for the 1-alkenes l l l Compound # Cp Data Cp Low T Cp High T Data Sources Propylene 32 93.9 K 223.4 K [496, 802, 803] Butylene 128 88.5 K 299.83 K [346, 804, 805] 1-Pentene 114 108.78 K 308.44 K [806-808] 1-Heptene 22 157.13 K 299.61 K [809] trans-2-Pentene 35 134.98 K 301.68 K [806, 868] 1,3-Butadiene 16 164.24 K 300 K [604] trans-1,3-Pentadiene 16 189.2 K 316.41 K [869] 2-Methyl-1,2-Butadiene 18 161.86 K 314.56 K [869]

Table B-62: Summary of liquid heat capacity data used in this work for the n-aldehydes l l l Compound # Cp Data Cp Low T Cp High T Data Sources Propanal 2 298.2 K 298.2 K [814] Butanal 72 176.8 K 330.53 K [375, 812, 813] Pentanal 2 270 K 298.2 K [814, 815] Hexanal 11 214.94 K 330 K [816] Heptanal 8 230 K 300 K [375]

Table B-63: Summary of liquid heat capacity data used in this work for the aromatic compounds l l l Compound # Cp Data Cp Low T Cp High T Data Sources Ethylbenzene 37 184.4 K 373.15 K [826-834] Propylbenzene 29 180.87 K 391.4 K [831, 833, 835] n-Butylbenzene 45 193.81 K 640 K [36, 831, 833, 835]

237

Table B-62: continued l l l Compound # Cp Data Cp Low T Cp High T Data Sources p-Cymene 20 205.25 K 300 K [613, 870] Naphthalene 23 355 K 434.98 K [871-873] Phenanthrene 4 383.27 K 408.64 K [874] Pyrene 7 423.81 K 480 K [875]

Table B-64: Summary of liquid heat capacity data used in this work for the ethers l l l Compound # Cp Data Cp Low T Cp High T Data Sources Dimethyl- 11 140 K 240 K [429] Ethyl propyl- 21 145.65 K 320 K [756] Di-n-propyl- 22 158.36 K 330 K [501, 755] Methyl tert-Butyl 65 168.32 K 325.15 K [756, 840-842]

Table B-65: Summary of liquid heat capacity data used in this work for the ketones l l l Compound # Cp Data Cp Low T Cp High T Data Sources Methyl Isopropyl 21 184.43 K 440 K [496, 843]

Table B-66: Summary of liquid heat capacity data used in this work for the amines l l l Compound # Cp Data Cp Low T Cp High T Data Sources Ethylamine 2 293.15 K 293.15 K [627, 876] Propylamine 20 189.96 K 334.56 K [877, 878] Butylamine 2 298.15 K 298.15 K [878, 879] Pentylamine 1 298.15 K 298.15 K [878] Isobutylamine 1 298.15 K 298.15 K [877, 879, 880] N,N-Diethylmethylamine 2 283.15 K 298.15 K [881] Triethylamine 11 298.15 K 393.15 K [878, 882] Isopropylamine 25 177.99 K 353.15 K [877, 879, 880]

238

Table B-67: Summary of liquid heat capacity data used in this work for the ringed alkanes l l l Compound # Cp Data Cp Low T Cp High T Data Sources Ethylcyclopentane 50 140.23 K 301.82 K [529] Methylcyclohexane 14 155.09 K 298.15 K [883, 884] Ethylcyclohexane 32 167.35 K 560 K [885, 886] Propylcyclohexane 20 185.51 K 373.2 K [887]

Table B-68: Summary of liquid heat capacity data used in this work for the halogenated compounds l l l Compound # Cp Data Cp Low T Cp High T Data Sources 1,2-Dichloroethane 37 284.16 K 353.14 K [821, 865, 888] n-Butyl chloride 30 284.15 K 353.15 K [889] Trifluoromethane 15 117.97 K 240 K [659, 890] Perfluoro-n-heptane 20 221.87 K 470 K [666, 669]

Table B-69: Summary of liquid heat capacity data used in this work for the esters l l l Compound # Cp Data Cp Low T Cp High T Data Sources Butyl Acetate 25 193.15 K 373.15 K [891-895] Pentyl Acetate 15 300 K 580 K [9] Hexyl Acetate 6 193.15 K 423.15 K [895] Octyl Acetate 23 310.03 K 420.02 K [818]

Table B-70: Summary of liquid heat capacity data used in this work for the sulfides l l l Compound # Cp Data Cp Low T Cp High T Data Sources Methyl mercaptan 13 160 K 280 K [688] Ethyl mercaptan 21 130.04 K 315.25 K [689] Diethyl sulfide 15 181.95 K 322.08 K [692] Methyl-n-butyl sulfide 23 186.9 K 358.01 K [695] Methyl isopropyl sulfide 45 171.65 K 360 K [697]

239

Table B-71: Summary of liquid heat capacity data used in this work for the alkynes and silanes l l l Compound # Cp Data Cp Low T Cp High T Data Sources Ethylacetylene 14 150 K 280 K [698] Tetramethylsilane 28 174.79 K 290 K [701, 896, 897]

Table B-72: Summary of liquid heat capacity data used in this work for multifunctional compounds l l l Compound # Cp Data Cp Low T Cp High T Data Sources 2-Aminobiphenyl 44 322.28 K 800 K [566] Aniline 51 275.7 K 700 K [36, 857, 880, 898] Dibenzofuran 17 361.98 K 520.28 K [571] Dimethyl isophthalate 20 360 K 740 K [34] Furan 14 190.99 K 299.08 K [572] Indane 6 240 K 320 K [899] Methyl Acrylate 12 196.21 K 300 K [900] 2-Methylpyridine 70 209.9 K 570 K [580, 582] 3-Methylpyridine 70 257.52 K 595 K [582, 584] Piperazine 13 384.6 K 505 K [585, 901] Pyridine 30 231.49 K 560 K [587, 588, 902] Pyrrole 19 249.74 K 400 K [590] Styrene 6 250 K 300 K [903] Tetrahydrofuran 22 164.76 K 320 K [904-906]

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B.4 Compounds measured

Below is a compilation of the data in the literature for the compounds that were measured in Chapter 7.

Table B-73: Summary of melting point and melting enthalpy literature data -1 Formula Compound Cas No. Tm/K ΔHm/(J g ) Source C8H8O o-Tolualdehyde 529-20-4 -- -- C8H8O m-Tolualdehyde 620-23-5 -- -- C8H8O p-Tolualdehyde 104-87-0 356.65 -- [907] 356.65 -- [908] 320.15 -- [909] 512.15 -- [910] C8H10O m-Tolualcohol 587-03-1 -- -- C8H8O2 p-Toluic acid 99-94-5 455.15 -- [911] 555.1 -- [912] 555.1 165.9 [113] 452.34±0.22 165.11±0.81 [110] 450.15±1 -- [108] 452.75 166.9 [118] 455.15 -- [913] 453.65 -- [109] 452.75 -- [112] 456.70 208.6 [111] C9H12O 1-Phenyl-1-propanol 93-54-9 -- -- C9H12O 1-Phenyl-2-propanol 698-87-3 -- -- C9H12O 2-Phenyl-1-propanol 1123-85-9 399.15 -- [914] C9H12O 2-Isopropylphenol 88-69-7 288.65 -- [527] C6H8O 2,5-Dimethylfuran 625-86-5 -- -- C6H6O2 5-Methylfurfural 620-02-0 -- -- C8H8O2 Phenyl acetate 122-79-2 -- -- C10H12O2 Ethyl 2-phenylacetate 101-97-3 243.75 -- [915] C12H24 n-Hexylcyclohexane 4292-75-5 225.64 -- [916] 225.64 -- [917] C11H22O 6-Undecanone 927-49-1 285.65 -- [918] 287.65±0.5 -- [919, 920] 287.15 -- [126] C8HF17 1H-Perfluorooctane 335-65-9 -- -- C8H10O3 2,6-Dimethoxyphenol 91-10-1 328.65±0.1 -- [127] 328.65±0.6 -- [128] 326.15±1.5 -- [129]

241

Table B-72: continued -1 Formula Compound Cas No. Tm/K ΔHm/(J g ) Source C8H10O3 2,6-Dimethoxyphenol 91-10-1 328.65±0.5 -- [130] 324.95±0.7 -- [921] 327.65 [130] C10H12O2 trans-Isoeugenol 5932-68-3 298.15 -- [922] 303.33 -- [923] 306.05 -- [924] 304.65 -- [925] C6H14O2 1-Propoxy-2-propanol 1569-01-3 -- --

Table B-74: Summary of vapor pressure literature data Formula Compound CAS No. T range /K Pvap range /kPa Source C8H8O o-Tolualdehyde 529-20-4 ------C8H8O m-Tolualdehyde 620-23-5 468.15 99.3 [926] 357.15 1.9 [927] C8H8O p-Tolualdehyde 104-87-0 373.62-374.62 1.93? [928] 383.13 2.67? [929] 389.13 101.3 [930] C8H10O m-Tolualcohol 587-03-1 ------C8H8O2 p-Toluic acid 99-94-5 775 3800 [931] C9H12O 1-Phenyl-1-propanol 93-54-9 383.13 101.3 [930] 380.15 2 [932] 378.65 2.27 [933] 380.15 2.40 [934] 401.44 5.33 [935] 378.65 1.87 [936] 371.15 1.33 [937] C9H12O 1-Phenyl-2-propanol 698-87-3 ------C9H12O 2-Phenyl-1-propanol 1123-85-9 405.63 4.47 [938] 375.15 0.8 [939] 342.15 0.09 [940] 383.65 1.3 [941] 373.65 0.7 [942] C9H12O 2-Isopropylphenol 88-69-7 329.73-487.66 0.133-101.3 [527] 375.09-493.28 2.014-118 [943] 379.13 2.67 [944] 486.16 101.3 [945] 486.16 99.3 [946] 486.16 101.3 [947] 486.16 101.3 [948] 486.66 101.3 [949] C6H8O 2,5-Dimethylfuran 625-86-5 283.16-366.7 3.01-101.3 [950] 313.15-393.15 5.88-114 [951] 272.7-299.1 1.5-6.8 [952]

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Table B-73: continued Formula Compound CAS No. T range /K Pvap range /kPa Source C6H8O 2,5-Dimethylfuran 625-86-5 331.46-366.83 30.01-101.33 [953] 345.24-364.37 50-94 [954] 345.24-364.37 50-94 [955] C6H6O2 5-Methylfurfural 620-02-0 303.15-453.15 0.10-83.40 [956] 359.95-450.19 2.93-79.1 [957] 362.65 3.5 [958] 337.15 0.93 [959] 298.15 0.08 [960] C8H8O2 Phenyl acetate 122-79-2 465.8-685.2 93.08-3593 [961] 349.15 1 [962] 468.95 101.0 [963] 348.65 1 [964] 372.15 3.3 [965] C10H12O2 Ethyl 2-phenylacetate 101-97-3 393.23-475.15 3.13-52.5 [966] 288.2-328.2 0.0033-0.084 [967] 501.16 100 [968] 415.15 8 [969] 388.65 2.9 [970] 381.65 2 [971] 356.9 0.53 [972] C12H24 n-Hexylcyclohexane 4292-75-5 264.7-467.26 7.5E-4-47.38 [973] 497.94 101.3 [916] 497.94 101.3 [917] 497.86 101.3 [974] 375.12, 494.16 2.13, 101.3 [975] C11H22O 6-Undecanone 927-49-1 388.35-531.93 2.608-201.7 [453] 496.16 101.3 [976] 418.83 3.9 [918] C8HF17 1H-Perfluorooctane 335-65-9 298.15-413.15 0.24-75.0 [90] 346.15 6 [977] 330.65 2.7 [978] C8H10O3 2,6-Dimethoxyphenol 91-10-1 ------C10H12O2 trans-Isoeugenol 5932-68-3 414.15 2 [979] 359.45-515.45 0.13-53.3 [527] 414.15 2.13 [980] C6H14O2 1-Propoxy-2-propanol 1569-01-3 298.15-413.15 0.341-74.983 [981] 298.15-323.15 0.355-1.755 [982] 330.65 2.66 [978] 605.1 3051 [983] 421.93 97.3 [984]

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Table B-75: Summary of heat of vaporization literature data -1 Formula Compound CAS No. T range /K ΔHvap range /(J mol ) Source C8H8O o-Tolualdehyde 529-20-4 -- -- C8H8O m-Tolualdehyde 620-23-5 -- -- C8H8O p-Tolualdehyde 104-87-0 -- -- C8H10O m-Tolualcohol 587-03-1 -- -- C8H8O2 p-Toluic acid 99-94-5 -- -- C9H12O 1-Phenyl-1-propanol 93-54-9 -- -- C9H12O 1-Phenyl-2-propanol 698-87-3 -- -- C9H12O 2-Phenyl-1-propanol 1123-85-9 -- -- C9H12O 2-Isopropylphenol 88-69-7 -- -- C6H8O 2,5-Dimethylfuran 625-86-5 -- -- C6H6O2 5-Methylfurfural 620-02-0 298.15 55 800 [985] C8H8O2 Phenyl acetate 122-79-2 ------C10H12O2 Ethyl 2-phenylacetate 101-97-3 -- -- C12H24 n-Hexylcyclohexane 4292-75-5 298.14 56 500 [986] C11H22O 6-Undecanone 927-49-1 ------C8HF17 1H-Perfluorooctane 335-65-9 -- -- C8H10O3 2,6-Dimethoxyphenol 91-10-1 -- -- C10H12O2 trans-Isoeugenol 5932-68-3 -- -- C6H14O2 1-Propoxy-2-propanol 1569-01-3 -- --

Table B-76: Summary of liquid heat capacity literature data l -1 -1 Formula Compound Cas No. T range /K Cp range /(J mol K ) Source C8H8O o-Tolualdehyde 529-20-4 -- -- C8H8O m-Tolualdehyde 620-23-5 -- -- C8H8O p-Tolualdehyde 104-87-0 -- -- C8H10O m-Tolualcohol 587-03-1 -- -- C8H8O2 p-Toluic acid 99-94-5 452.75 321 [118] C9H12O 1-Phenyl-1-propanol 93-54-9 -- -- C9H12O 1-Phenyl-2-propanol 698-87-3 -- -- C9H12O 2-Phenyl-1-propanol 1123-85-9 -- -- C9H12O 2-Isopropylphenol 88-69-7 -- -- C6H8O 2,5-Dimethylfuran 625-86-5 298.15 149 [952] C6H6O2 5-Methylfurfural 620-02-0 -- -- C8H8O2 Phenyl acetate 122-79-2 -- -- C10H12O2 Ethyl 2-phenylacetate 101-97-3 298.15 338 [967] C12H24 n-Hexylcyclohexane 4292-75-5 -- -- C11H22O 6-Undecanone 927-49-1 -- -- C8HF17 1H-Perfluorooctane 335-65-9 -- -- C8H10O3 2,6-Dimethoxyphenol 91-10-1 -- -- C10H12O2 trans-Isoeugenol 5932-68-3 -- -- C6H14O2 1-Propoxy-2-propanol 1569-01-3 -- --

244

APPENDIX C. SAMPLE CALCULATION FOR PREDICTIVE METHOD

The vapor pressure of 2,2-dimethylpentane will be calculated at 285.34 K, where there exists a reliable data point to check the method [271]. The DIPPR critical constants and normal boiling point are given in Table C-1, from which the reduced properties can be calculated, given in Table C-2.

Table C-1: Summary of compound constants for 2,2-dimethylpentane Constant Symbol Value Unit Critical Temperature 520.5 K Critical Pressure 2.77E6 Pa 𝑐𝑐 Normal Boiling Point 𝑇𝑇 352.34 K 𝑐𝑐 𝑃𝑃 Table C-2: Summary of reduced properties𝑇𝑇𝑁𝑁𝑁𝑁 for 2,2-dimethylpentane Reduced Property Symbol Value / 0.54820 / 0.67693 𝒄𝒄 𝑟𝑟 𝑻𝑻 𝑻𝑻/ 𝑇𝑇 0.03658 𝑵𝑵𝑵𝑵 𝒄𝒄 𝑛𝑛𝑛𝑛𝑛𝑛 𝑻𝑻 𝑻𝑻 𝑇𝑇 𝒂𝒂𝒂𝒂𝒂𝒂 𝑷𝑷𝒄𝒄 𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 Start by selecting = 3, the recommended value for alkanes in Table 5-2. From this, calculate and using Equations𝐸𝐸 18 and 19, respectively:𝐸𝐸

𝑐𝑐 𝐾𝐾 𝑋𝑋 = 4.96465 3 . = 0.400268 −2 29195 = 4.14524𝐾𝐾 0.0818433∗ 3 + 0.00310685 3 = 3.92767 2 𝑐𝑐 With , , , and𝑋𝑋 , calculate− at the normal∗ boiling point using∗ Equation 6-24:

𝐾𝐾 𝑋𝑋𝑐𝑐 𝐸𝐸 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 3 𝜙𝜙 ( , ) = 3 1 3 (3 + 1) ln(0.67693) + 0.67693 = 0.30288 0.676932 2 3 𝜙𝜙 𝑇𝑇𝑛𝑛𝑛𝑛𝑛𝑛 𝐸𝐸 − − − ∗ ∗ − From these values, calculate and using Equations 6-22 and 6-23, respectively:

𝑐𝑐 𝐷𝐷 𝛼𝛼 245

ln(0.03658) + 0.400268 3.92767 ( 0.30288) = 0.400268 3.92767 = 1.3898 ln(0.67693) + 0.400268 ( 0.30288) ∗ ∗ − 𝐷𝐷 � − � ln(0.03658) + 0.400268 3.92767∗ − ( 0.30288) = = 7.3998 ln(0.67693) + 0.400268 ( 0.30288) ∗ ∗ − 𝛼𝛼𝑐𝑐 Now calculate correlation coefficients using Equations∗ − 6-19 through 6-21:

= (3𝐴𝐴 −1𝐶𝐶) 1.3898 = 11.118 2 𝐴𝐴 = 3− 1.∗3898 = 12.508 2 = 7.3998𝐵𝐵 −3 ∗(3 + 1) 1.3898− = 9.2778

We now have a temperature𝐶𝐶 dependent− correlation∗ for∗ the vapor −pressure of 2,2-dimethylpentane by substituting these coefficients into Equation 9:

12.508 ln( ) = 11.118 + 9.2778 ln( ) + 1.3898 3 𝑟𝑟 − 𝑟𝑟 𝑟𝑟 𝑃𝑃 𝑟𝑟 − ∗ 𝑇𝑇 ∗ 𝑇𝑇 or: 𝑇𝑇

12.508 = exp 11.118 + 9.2778 ln( ) + 1.3898 3 vap 𝑐𝑐 − 𝑟𝑟 𝑟𝑟 𝑃𝑃 𝑃𝑃 ∗ � 𝑟𝑟 − ∗ 𝑇𝑇 ∗ 𝑇𝑇 � Plugging in the reduced temperature for 314.86𝑇𝑇 K gives: = 7645 . This agrees to within

vap 1 % of experimental data from the literature at 7700 Pa. 𝑃𝑃 𝑃𝑃𝑃𝑃

246