Study of Decarbonization Reaction of Sodium Carbonate by Sodium Borates

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4-2006

Zaki Yusuf Western Michigan University

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Recommended Citation Yusuf, Zaki, "Study of Decarbonization Reaction of Sodium Carbonate by Sodium Borates" (2006). Dissertations. 1007. https://scholarworks.wmich.edu/dissertations/1007

This Dissertation-Open Access is brought to you for free and open access by the Graduate College at ScholarWorks at WMU. It has been accepted for inclusion in Dissertations by an authorized administrator of ScholarWorks at WMU. For more information, please contact [email protected]. STUDY OF DECARBONIZATION REACTION OF SODIUM CARBONATE BY SODIUM BORATES

Zaki Yusuf

A Dissertation Submitted to the Faculty of The Graduate College in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Department of Paper Engineering, Chemical Engineering and Imaging Science Advisor: Dr. John H. Cameron

Western Michigan University Kalamazoo, Michigan April 2006

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. STUDY OF DECARBONIZATION REACTION OF SODIUM CARBONATE BY SODIUM BORATES

Zaki Yusuf, Ph.D.

Western Michigan University, 2006

Today, the chemical process industries are facing many challenges in the wake of

skyrocketing energy price. Paper industry as a whole is also not only looking into

improving the process efficiency of its chemical recovery process but also is exploring to

meet these challenges with gasification based energy/chemical recovery process. Borate

based autocausticizing technology appears promising, provided it could be effectively

integrated into both types of chemical recovery processes based on the principles of

chemistry and chemical engineering.

My research was focused on the decarbonization reactions of sodium carbonate

by sodium metaborate (NaB 0 2 ) and sodium diborate (Na 4 B2 0 5 ) and drew a parallel

between organo-borate complexes and sodium metaborate occurring in the recovery

boilers. The primary objectives of this study is to provide information on the

stoichiometry and the effect of the rate controlling parameters on the decarbonization

reaction between sodium borates and sodium carbonate both above and below the melting

points of the reactants. Another objective of the study was to verily the melting/freezing

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. point of trisodium borate (Na 3 BC>3 ), which is the reaction product of the decarbonization

reactions. The final objective of the study was to critically examine the stoichiometry of

the causticization reaction of Na 3 BC>3 in the aqueous phase since its reaction behavior

would provide clue for its viability in various pulping processes.

Efforts were also undertaken to obtain the phenomenological rate parameters from

the reaction data. The heat of reaction of metaborate-based decarbonization was also

estimated at various temperatures. A major finding of the study is that reaction occurs

below the melting points of the reactants. However, the reactions are rapid above the

pooled meting point of the system. The decarbonization reactions are reversible in nature

and carbon dioxide removal is necessary for a high-degree of conversion. Trisodium

borate shows incongruent melting/freezing point characteristics. The causticization

reaction of Na 3 BC>3 is reversible in nature. Finally, it is recommended that a superheated

steam line (with substantial degree of superheat) should be integrated inside the molten

bed to periodically sweep out the CO 2 released from the decarbonization reaction to

attain quick, efficient and complete conversion of the decarbonization reactions inside the

smelt bed or gasification bed.

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGMENTS

I would like to commence by acknowledging Dr. Cameron’s early publication on

borate based chemical recovery which inspired me to pursue this experimental research

and led to the culmination of the work contained in this dissertation. I would also like to

express my sincere gratitude for Dr. John Cameron for his extreme patience and

thoughtful guidance throughout the course of this work. My appreciation will continue to

grow for him because this work has opened up new vistas for my upcoming research

endeavors.

Secondly, I would like to thank everybody beginning with my committee

members Dr. Peter Parker and Dr. John B. Miller for their support and help during this

work with their thoughts, wisdom and valuable time. Dr. Miller was incredibly generous

to provide me with packages like Cerisus 2 and CAChe and helped me with DFT

calculation.

I would also like to thank the department chair, Dr. Said Abu Bakr for his

continuous support during the dissertation writing process. I would also like to express

my deep appreciation for Dr. Paul D. Fleming, III for inspiring me to undertake

molecular modeling (ab intio and semi-empirical) based thermodynamic property

estimation. I would like to thank him for initiating interesting discussions on chemical

reaction rate theories from molecular level which helped me understand chemical

dynamics more intuitively.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgments — Continued

I would also like to thank Ms. Barbara Vilenski (Administrative Assistant) for her

patience, untiring and silent support and help on various aspects of my dissertation

writing process. I also extend my deepest appreciation for Mr. Matthew Stoops for his

help on fixing the furnace and my experimental setup. Mr. Richard Reames, the director

of Paper Pilot Plant was always extremely gracious to me to use his instruments and

supplies. My deepest appreciation also goes to Glen Hall from the engineering

department for fabricating the cap of my reactor without which the experimentation

would have been impossible.

Mr. Abu Sayeed Mia, my old friend from Microsoft Corporation, was the

invisible pillar of strength for me and provided me with softwares and all kinds of

logistical support from the very beginning of the work. He always emerged from

nowhere and was instrumental in sharing even the most difficult of personal problems

and vanished immediately without waiting for appreciation. I would also like to thank

Dr. Muhammad Razi for providing me with an excellent book on statistics to deal with

the nonlinear regression analysis. My deepest appreciation goes to Mr. Tamim Quader,

Manager, ASMO Manufacturing, my childhood friend for encouraging me to pursue

graduate program at W.M.U. Messer’s Mohammad Shahjahan (Bulldog) and Hussam

Alkhasawneh was sent as a blessing for me.

111

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgments — Continued

I would like to express my deepest gratitude for my parents, in-laws and my uncle

Mr Ziauddin Yusuf, P.E. for their constant and silent encouragement. I would also like to

pay tribute to my deceased uncle, Mr. Nizamuddin Yusuf for his impact in converting my

dreams into reality. The main thrust for the work came mainly came from my only son

Sulayman and his mother- Yasmin, the love and poem of my life.

Zaki Yusuf

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS

ACKNOWLDGEMENTS...... ii

LIST OF TABLES...... viii

LIST OF FIGURES...... ix

CHAPTER

I. INTRODUCTION...... 1

II. LITERATURE REVIEW...... 20

Boron-Oxygen Chemistry ...... 20

Structure and Properties of Various Borate Salts ...... 23

Structure and Properties of Various Borate Ions ...... 25

Complex Formation of Various Carbohydrates with Tetrahydroxy Borate Ions ...... 28

Classification and Properties of Lignocellulosics ...... 32

Kraft Recovery Boiler ...... 43

Green Liquor Properties ...... 54

White Liquor Properties ...... 55

Black Liquor Properties ...... 57

Modified Cooking Processes ...... 59

Black Liquor Gasification Technology ...... 61

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CHAPTER

Deacarbonization Reaction with Sodium Metaborate ...... 64

Causticization Reaction of Trisodium Borate ...... 66

Estimation of Thermodynamic Properties ...... 68

Reaction Rate Theories of Solid and Molten Phase Reactions 74

III. METHODOLOGY AND EXPERIMENTAL PROCEDURE...... 83

Salt Preparation for Decarbonization Reaction Involving Sodium Metaborate ...... 84

Sodium Diborate Preparation for Decarbonization Reactions 84

Experimental System for the Decarbonization Reactions ...... 85

Experimental System for Melting Point Determination of Trisodium Borate ...... 87

pH Determination of Aqueous Trisodium Borate ...... 89

IV. EXPERIMENTAL RESULTS AND DISCUSSIONS...... 90

Melting Point Verification and Solidification (Freezing) Point Observation of Trisodium Borate ...... 92

Decarbonization Reaction with Sodium Metaborate ...... 93

Extent of Reaction in the Solid Phase (Sodium Metaborate) ...... 95

Molten Phase Decarbonization Reaction and Stoichiometry with Sodium Metaborate ...... 101

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CHAPTER

Reaction without Carbon Dioxide Sweeping (Sodium Metaborate) ...... 105

Decarbonization Reaction with Sodium Diborate ...... 106

Molten Phase Decarbonization Reaction and Stoichiometry with Sodium Diborate...... 113

Reaction without Carbon Dioxide Sweeping (Sodium Diborate) ...... 115

Causticization Reaction of Trisodium Borate ...... 117

Implications in the Modified Continuous Cooking Processes ...... 121

Implications in the Chemical Recovery Process ...... 123

Implications in the Gasification Processes ...... 128

V. CONCLUSIONS AND RECOMMENDATIONS...... 132

APPENDICES

A. Figures of Sodium Metaborate based Decarbonization Reactions 135

B. Figures of Sodium Diborate based Decarbonization Reactions ...... 145

C. Calculation of Total Lattice Potential Energy of Trisodium Borate ...... 156

D. Estimation o f Heat of Reaction of Sodium Metaborate based Decarbonization Reactions ...... 160

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents—Continued

APPENDICES

E. JMP Results (Non-Linear Fit) from the Decarbonization Reactions When Sodium Metaborate and Sodium Diborate Were the Decarbonizing Agents...... 165

F. Heat of Formation Result of Trisodium Borate and B(OH)4 _ Ion from MOP AC Calculation ...... 189

BIBLIOGRAPHY...... 259

vii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES

2.1 1 *B NMR Results for Determination of Equilibrium Constants of Complexation ...... 31

2.2 Typical Inorganic Composition of Green Liquor ...... 55

2.3 Typical Inorganic Composition of White Liquor ...... 56

2.4 Typical Inorganic Composition of Black Liquor ...... 58

4.1 Reaction Conditions and Results with Respect to Carbon Dioxide Generation during Solid Phase Reaction (Sodium Metaborate as the Decarbonization Agent) ...... 99

4.2 Reaction Conditions and Results with Respect to Carbon Dioxide Generation during Molten Phase Reaction (Sodium Metaborate as the Decarbonization Agent) ...... 102

4.3 Reaction Conditions and Results with Respect to Carbon Dioxide Generation during Molten Phase Reaction (Sodium Diborate as the Decarbonization Agent) ...... 107

4.4 Gibbs Free Energy Change o f Reaction (4.1) at V arious T emperatures ...... 127

viii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES

1.1 Kraft Pulping Chemical Recirculation Loop ...... 7

2.1 Hybridization Scheme of Boron ...... 22

2.2 Various Forms of Monoborate Ions ...... 22

2.3 Structures of Metaborate, Diborate/Pyroborate, Monoborate and Carbonate Ions ...... 22

2.4 Infinite Borate Chain Ion of Calcium Metaborate and Lithium Metaborate ...... 25

2.5 Distribution of Various Polyborate and Monoborate Ions in the Aqueous Phase ...... 27

2.6 Distribution of Hydrolysis Species of Borate Ions ...... 28

2.7 Trends Showing the Shift in Equilibria to Higher Hydroxide Concentration with Increasing Temperature ...... 29

2.8 Complex Formation Scheme Between B(OH) 4 _ Ions and Carbohydrates/Polyols ...... 30

2.9 The p-1,4 Linkage of Cellulose Molecule ...... 34

2.10 The Reducing and Non-reducing End Group of Cellulose Molecule ...... 34

2.11 Common Sugars Found in Hemicelluloses ...... 36

2.12 The Structures of Coniferyl, Sinapyl and p-Coumaryl Alcohols ...... 37

2.13 The Structures of Guaicyl- and Syringyl Groups...... 38

2.14 The Structure of Spruce Lignin...... 39

2.15 The Structures of Some Terpene Compounds ...... 41

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures—Continued

2.16 The Structures of Abietic and Pimaric Acid ...... 42

2.17 The Structures of Some Lignan Compounds ...... 44

2.18 The Sulfate-Sulfide Cycle ...... 53

3.1 Experimental System Showing Alumina Reactor, Thermocouple, Electric Furnace, Gas Flow Meter, Gas Analyzer, and Data Acquisition System ...... 86

4.1 Carbon Dioxide Generation Rate and T emperature versus Time ...... 94

4.2 Cumulative Carbon Dioxide and Temperature versus Time ...... 94

4.3 Carbon Dioxide Generation Rate and T emperature versus T ime ...... 98

4.4 Cumulative Carbon Dioxide and Temperature versus Time ...... 98

4.5 Effect of Initial Mole Fraction of Sodium Metaborate on Carbon Dioxide Generation in the Solid Phase ...... 99

4.6 Effect of Sodium Metaborate Level on Moles of Carbon Dioxide Released per Mole Initial Metaborate ...... 103

4.7 Carbon Dioxide Generation Rate and Temperature versus T im e ...... 106

4.8 Cumulative Carbon Dioxide and Temperature versus Time ...... 108

4.9 Carbon Dioxide Generation Rate and Temperature versus T im e ...... 108

4.10 Cumulative Carbon Dioxide and Temperature versus Time ...... 109

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES—Continued

4.11 Carbon Dioxide Generation Rate and Temperature versus Time ...... 109

4.12 Carbon Dioxide Generation Rate and Temperature versus Time ...... 110

4.13 Cumulative Carbon Dioxide and Temperature versus Time ...... 110

4.14 Cumulative Carbon Dioxide and Temperature versus Time ...... I l l

4.15 Carbon Dioxide Generation Rate and Temperature versus Time ...... I l l

4.16 Cumulative Carbon Dioxide and Temperature versus Time ...... 116

4.17 Carbon Dioxide Generation Rate and Temperature versus Time ...... 116

4.18 Stoichiometry and Reaction Steps of Causticization Reaction of Trisodium Borate in the Aqueous Phase ...... 120

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER I

INTRODUCTION

The unique features of borate chemistry [1-8] has drawn the attention o f many

researchers in the paper industry to explore various aspects of autocausticizing reactions

of borate compounds in order to partially or completely eliminate the lime cycle from the

chemical regeneration loop.

A comprehensive understanding and investigation of borate chemistry in the

solid, molten and aqueous phase, its thermodynamic and kinetic behavior in relation to

the various pulping processes, chemical regeneration environments and its interaction

with various components of wood is essential for the effective and optimal integration of

borates into conventional and modified pulping processes. Moreover, novel chemical

and energy recovery processes, such as gasification technology, may also demand in-

depth understanding of borate chemistry in order to explore the beneficial, adverse, or

synergistic effects of borates on the various facets of conventional and gasification

technology based chemical recovery processes when borate salts are integrated into the

system. The commercial viability of borate based pulping and chemical recovery

processes can only be reasonably justified if such interactive relationships can be

effectively explored and well understood.

Boron is a hypoelectronic element and its orbital electronic configuration and

hybridization scheme allows the borate ions to assume various types of ionic structures,

including some polyborate ions in the aqueous phase [1, 6 and 7]. Moreover, these

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. borate ions not only attain equilibrium with each other depending on the pH of the

solution, the equilibrium relationships between these ions are also temperature, pressure

and to some extent ionic concentration dependent phenomena [9]. Moreover, both at

• 2 normal and elevated temperature and pressure various borate ions, e.g., B 4 0 5 (0 H) 4 ',

B3 0 3 (0 H)5 2' and B(OH)4" have the ability to exchange OH' ions in the vicinity of pH~12

with their equilibrium relationships [10, 11]. This phenomenon is centered on boron’s

hypoelectronic configuration, hybridization scheme and the thermodynamic viability of

exchange reactions [6, 7]. Maeda [13] and Maya [14], based on Raman spectroscopic

studies, independently concluded that B(OH) 4 1 is the major borate ion at high alkalinity.

Salentine [15], using NMR studies, has also identified the presence o f B(OH) 4 _1 ion along

with other polyborate ions [16] in aqueous systems. Additionally, tetrahydroxy borate

(B(OH) 4 ) and other borate ions readily form complexes with various organic compounds

such as polysaccharides, dicarboxylic acid and polyhydroxy alcohols in the aqueous

phase [17-24],

However, such complex formation is dependent on the stereochemistry o f the

organics and pH of the solution [17-19], In some cases, some boron compounds also

demonstrate incongruent freezing point melting point characteristics [25]. Additionally,

the melting point of sodium metaborate (NaBCh), sodium diborate (N a ^ O s) and

trisodium borate (Na 3 B 0 3 ) are spread over a wide temperature range [25-27]. Therefore,

synchronized and detailed understanding of wood and borate chemistry allows one to

have a clearer perception how to control the reactions inside the conventional recovery

boilers and novel gasification processes by selecting the optimal operating parameters,

which in turn would maximize the total economics of the system. Additionally, the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. chemical behavior of the borate ions should also be critically evaluated along the

processing conditions of the available commercial pulping processes to explore the

positive, negative or synergistic effects on pulping variables to forecast whether the ions

can supplement hydroxyl ion, additional hemicellulose retention, boiling point

rise/depression etc. However, the process economics of the chemical recovery system

only may justify the viability of the entire process provided comparable pulp quality and

yield could be achieved when a particular sodium borate is integrated as a supplement in

the specific pulping conditions.

Wood is the primary source of cellulosic pulp. It is well known that the

composition of wood is complex and comprises of various types of organic components

and minor amounts of inorganics. The major organic components of wood are

polysaccharides, such as cellulose and hemicellulose and phenolic substances such as

lignin [28, 29]. Small amounts of pectic substances and water-soluble polysaccharides

such as arabinogalactans are also present. Other phenolic substances present in small

amounts are tannins, phlobaphenes, coloring matter and lignans. Other organics include

terpenes and terpenoid, higher fatty acids as their esters, aliphatic alcohols, sterols and

proteins. Trace amounts of inorganic constituents are also present. Other minute

amounts of organics include cyclic polyhydric alcohols, aldehydydes, hydrocarbons and

alkaloids [30-33].

The complex, aromatic, high molecular weight, amorphous, polymeric material,

which is a major component of vascular plant tissues and accumulates through

photosynthesis, is known as lignin. Lignin is the second most abundant renewable

organic material found in nature after cellulose. Lignin acts as a cementing agent and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. binds the carbohydrates present in the cell wall. Plant lignin is observed between the

cells where it is deposited during the lignification process. It has no regular polymer

structure and it is not possible to break its polymer structure to form monomeric units by

hydrolysis [34—36].

The primary goal of pulping is the delignification and recovery of cellulose from

wood. In the kraft process, debarked and chipped wood is submerged with sodium

hydroxide and sodium sulfide solution, known as the cooking liquor, in a pressurized

vessel. This cooking liquor, also known as the white liquor, is practically regenerated

from black liquor of the previous cook. During the delignification process, the digester

temperature attains 160-170°C. In batch cooking, the high temperature and pressure

combined with the presence of threshold concentration o f hydroxyl (OH ) and

hydrosulfide (SH') ions drives the delignification process forward. At the beginning of

the batch delignification process the pH of the white liquor is maintained in the range of

-13.5 or above so that the pH of the black liquor remains above -12 at the end of the

cook and prevents re-lignification or condensation of lignins on to the cellulose fiber.

During the process, lignin is solublized in the cooking liquor and some cellulose

molecules also undergo degradation due to the presence of a high concentration of OH'

ions. On the other hand, during modified continuous cooking, uniform and lower pH is

maintained throughout the process which significantly lessens cellulose degradation and

helps retain higher amount of hemicellulose.

Cellulose and these degradation products along with wood extractives, soluble

lignins and some inorganic is the end product of the cooking liquor. This liquor, known

as the black liquor, is fed to multiple effect evaporators for removal of water. The

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. concentrated black liquor comprised of sodium salts of lignins and other organics is the

major source of energy for the pulp mill. The black liquor is converted to pyrolized

organics by means of pyrolysis and subsequently the pyrolized organics obtained from

the concentrated black liquor are converted to heat in the recovery boiler furnace via

gasification reactions along with volatile matters of black liquor organics due to the

exposure to high temperature and oxidative environment of the upper furnace. The

energy released from the pyrolysis and the subsequent combustion process is used to

generate steam. During the process the sodium salts associated with lignins are converted

into sodium carbonate (Na 2 CC>3 ). A reducing atmosphere is maintained at the bottom

section of the recovery boiler to maximize the production of sodium sulfide (Na 2 S). It is

critical that the recovery boiler’s operating temperature is maintained high enough to

allow for the quick evaporation of free moisture of the black liquor droplets to prevent

any contact between water and accumulated molten salt. Any contact could result in

vigorous explosion [37-39],

The salt mixture is continuously collected in molten form from spouts located at

the bottom of the reactor and flows into a dissolving tank where it is exposed to weak

wash stream recycled from the mud washer. The resulting liquor is known as green

liquor and enters a clarification system to remove the dregs before it is sent for the

causticizing reaction. The green liquor is composed of dissolved sodium carbonate and

sodium sulfide in water [39—41].

Sodium carbonate (Na 2 CC>3 ) in green liquor is converted to sodium hydroxide

(NaOH) by reacting with slaked lime (Ca(OH) 2 ). The other reaction product is calcium

carbonate (CaC 0 3 ), which is sparsely soluble in water and its precipitation drives the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. causticizing reaction in the forward direction. The precipitated calcium carbonate is

dewatered and sent to lime kiln for regenerating calcium oxide (CaO) and subsequently

into slaked lime for next causticizing reaction. The regeneration of calcium oxide is an

endothermic reaction and thus consumes considerable amount of energy [42, 43]. The

kraft pulping regeneration loop is shown in Figure 1.1 [66].

In the late seventies, Janson [44-48] was searching for chemicals that would act

as autocausticizing agents for decarbonizing sodium carbonate in the kraft furnace and

generate sodium hydroxide on dissolution in the green-liquor dissolving tank. Several

inorganic salts were evaluated including sodium tetraborate (NaaE^Oy), sodium

metaborate (NaBCh), sodium diphosphate (Naft^Cb), sodium silicate (Na 2 Si2 0 7 ) and

alumina ( A I 2 O 3 ) , as potential autocausticizing agents. He recognized that sodium

aluminate and sodium silicate would cause major process instability in the kraft pulping

system. He also acknowledged that sodium metaborate seemed very weakly alkaline and

was more suitable for alkaline bleaching, although it was agreed that sodium

diborate/pyroborate (l^E^Os) might act as an effective causticizing agent [46, 47].

Janson proposed the following reaction for autocausticization when sodium borate was

used as autocausticizing agent [47]:

2NaBC>2 + Na2CC>3 »Na4 B2 0 5 + CO2 ...... 1.1

Na4B20 5 + H20 <-► 2NaOH + 2NaB02 ...... 1.2

Additionally, he recognized that the decarbonization reaction (1.1), is reversible in

nature, but he could not clearly confirm whether the reaction (1.2) goes to completion.

He further acknowledged that when borate salts go into solution they demonstrate

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Wash & Rebum

CaO CaC03

CaC03:_“ 3 Ca(OH)2 \ Recaust& / Chips YClarify J

Green LiquorWhite liquor Green LiquorWhite

Dissolve & Wash Clarify

Weak Liquor

I Smelt Evaporation 8 |II | Recovery furnace Dust recirculation Washed Pulp

------!

Figure 1.1. Kraft Pulping Chemical Recirculation Loop [66]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. complicated solution chemistry. He also agreed with Ingri [11, 12, 44] that

tetrahydroxyborate (B(OH) 4 _l) ion is the dominant species above pH 10.5-11.0.

Grace cautioned [49], based on the stoichiometry of reaction (1.2) proposed by

Janson, that the introduction of metaborate as an autocausticizing agent in kraft pulping

would double the inorganic deadload of black liquor. This would result in higher energy

consumption for fluid moving devices, lower heating value per unit mass and higher

sensible heat load during both the evaporation and the combustion of the resulting black

liquor. This finding made the feasibility of using borate in conventional kraft pulping

less attractive.

A major breakthrough came in the nineties when Tran et al. [50] corrected the

stoichiometry associated with reaction (1.1) and proposed the following:

N aB02 + Na2C 03 -► Na3B 0 3 + C 02 ...... 1.3

This new finding rejuvenated the borate-based kraft pulping research because reaction

(1.3) shows that metaborate requirement is half of that proposed by Janson. They further

added that on dissolving, the trisodium borate salt reacts with water to form sodium

hydroxide and regenerate sodium metaborate, given by the following reaction [50]:

Na3B03 + H20 -»■ 2NaOH + NaB02...... 1.4

However, previously it was affirmed by Edwards [51] that the cyclic borate ions

(or boroxol ring) in sodium metaborate never exist as B 0 2~ ion rather as B(OH)4" ion in

aqueous solution [52], Additionally, others have demonstrated that tetrahydroxyborate

(B(OH)4 _1) ion also has the potential to react with some the organic components of wood

resulting in organo-borate compounds at high pH [17-24, 53-57]. Therefore, it is also

crucial to undertake a thorough discussion on this phenomenon to understand its effect on

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. viscosity, boiling point of black liquor and its potential impact on the perturbation o f the

equilibrium of reaction (1.4). Additionally, such thorough discussion is essential to

uncover the form of borate ions and its complexes in the context of pH, pressure,

temperature and ionic concentration. The exploitation of these properties should be

critically explored in order to obtain the effectiveness or viability in various pulping

processes. In addition, those boron oxygen bonds in B(OH) 4 _1 ions are shorter [58] and

therefore it was assumed in the current study that they are comparatively stronger and

remain intact during the pulping reaction. Therefore, it is of central importance to have

an in depth understanding of borate chemistry to unravel additional information from

reactions (1.3) and (1.4) in relations not only to the conventional and novel pulping

processes but also from the chemical and recovery stand point.

It should be pointed out that the temperature in the conventional recovery boiler

ranges from 850°C to as high as the 1250°C [38, 59 and 60]. Therefore, the feasibility of

sodium metaborate as decarbonization agents in the chemical recovery boiler largely

depends on the understanding the stoichiometry and rate controlling parameters of

reaction (1.3) between these temperatures ranges. These include the combustion process

near the char/smelt bed, the temperature, inorganic and organic constituents and CO/CO 2

concentrations inside and near the bed surroundings. Additionally, it is also necessary to

understand the reaction conditions which forms various organo-borate complexes from

the pulping reaction products and tetrahydroxy borate (B(OH)T) or other borate ions if

present in the black liquor to understand the form of borate in the black liquor.

Moreover, it should be mentioned that very useful information is available regarding

B(OH)4‘ ion’s reactivity with other various carbohydrates and polyhydric alcohols [18-

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24]. The commercial viability of using sodium borates as decarbonizing agent during the

burning of black liquor in the recovery boiler furnace may also depend on other factors.

These include the lattice energy, melting points and the solubility data of the sodium

borates. Examination of these chemical and physical properties may provide useful

information such as, their effect on the pooled melting point of the bed and therefore on

the operational constraints/advantages of the recovery boilers and as well as the high

temperature gasification reactors. Moreover, the lattice energy of trisodium borate

should be compared with other sodium compounds, e.g., sodium sulfide, sodium sulfate,

sodium carbonate and sodium hydroxide present in the recovery boiler to have a relative

understanding on the sodium vapor formation from those salts.

However, it should be pointed out that even if reaction (1.3) is reversible in

nature, the final conversion would depend on rate, equilibrium of the reaction and also on

the equilibrium and rate of CO 2 /CO conversion near the vicinity of the reaction. Because

of the high level of carbon present in the char bed of the kraft furnace, any carbon dioxide

formed is converted to carbon monoxide and in such condition; the equilibrium o f

reaction (1.3) would shift towards the right depending on the rate of conversion of CO 2 to

CO.

Tran et al. [61] have expressed a concern that the reaction between carbonate and

metaborate may be slow and suggested that the conversion rate is faster in the mill trials

because the reaction may follow several different pathways. They proposed that near the

char bed, under strong reducing atmosphere and high temperature, sodium carbonate

might react with carbon and water vapor to form sodium hydroxide. The following

equation was proposed for such reaction:

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Na2C03 + H20 + C -»• 2NaOH + C02...... 1.5

It was also proposed that sodium hydroxide produced from reaction (1.5) reacts with

sodium metaborate to form trisodium borate given by the following equation:

2NaOH + NaB02 -»■ Na3B03 + C02 ...... 1.6

Additionally, they also proposed that sodium oxide formed from the reaction between

sodium vapor and oxygen also reacts with sodium metaborate to form trisodium borate

given by the following equation:

Na20 + NaB02 —> Na3B 0 3...... 1.7

Finally, they suggested that since reaction (1.6) occurs at a lower temperature it is likely

to be the main pathway for trisodium borate formation in the recovery boiler. However, a

systematic thermodynamic assessment is indispensable to verify such reaction pathways.

Additionally, a methodical and comprehensive approach is necessary to understand the

kinetics and the equilibrium behavior of reaction (1.3).

Since the late nineties, modified cooking became more prevalent and these

processes may become more advantageous with the use of borate based cooking.

Commercially, several cooking processes, such as, modified continuous cooking (MCC),

extended modified continuous cooking (EMCC), isothermal cooking (ITC) and Lo-solids

pulping processes have become emerging pulping processes. Studies have shown that

these processes selectively remove lignin while diminishing the degradation of

carbohydrate components. These processes are based on the following principles [62—

77]:

1) The concentration of dissolved lignin should be as low as possible toward the

end of the cook.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2) The concentration of the alkali should be low and uniform throughout the

cook.

3) The concentration of sulfide should be as high as possible especially at the

beginning of the bulk delignification.

4) The ionic strength of the liquor should be as low as possible especially at the

end of the cook.

Hartler [65] has shown that the delignification process is retarded by a high

concentration of lignin in the pulping liquor. Elsewhere it has been stated that the re

deposition o f lignin occurs at below a threshold pH [38]. On the other hand, the lower

pH is vital to the retention of hemicellulose on the cellulosic fiber. It has been already

mentioned that several researchers have found that the E^OHfi ' 1 ion has the ability to

form complexes with ds-hydroxy sugars and polysaccharides at pH greater than or equal

to 11.5 [78, 79]. However, it should be pointed out that such complexes relinquish the

B(OH)4 _1 ion at lower pH. Therefore, it is not only necessary to locate the pH of the

resulting solution at room temperature yet also to trace the direction of the reaction (1.4)

in terms of the equilibrium relationships between various borate ions at elevated

temperature and pressure to establish the viability reaction (1.4). Moreover, the

understanding of these relationships may also provide clues to the retention of some of

those hemicelluloses that contain 'ds-hydroxy sugars as their basic building blocks. It

should be pointed out that the lignin removal from the first part of the cook is diffusion

limited not chemically controlled. Therefore, it is crucial to understand the equilibrium

relationships between the borate ions may also provide another indication with regards to

the capabilities of borate ions that how quickly they are capable of delivering additional

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. OH' ions in inside the core of the wood chips to improve the kinetics of the

delignification process. Thus, the amphoteric property of some borate salts may

demonstrate its potential as an important chemical for supplementing sodium hydroxide

as a cooking chemical for certain (low OH' ion concentration) pulping processes.

In addition to that, it has been demonstrated by the Scandinavian researchers [62—

77] that the low initial alkali concentration of the cooking liquor results in higher

carbohydrate yield with low lignin content in the pulp. More specifically, lower hydroxyl

concentration results in deceleration in cellulose degradation rate. However, although

during batch cooking low pH (~11.5) of the liquor favors redepositon of xylans on the

cellulose fibers it also increases the probabilities of relegnification [38]. The

thermodynamic constraints of equilibrium exchange reactions between various borate

ions and their adjacent counterparts, such as, B 3 0 3 (0 H)4 2' and B(OH)4' ions which are

present in the aqueous phase should be critically analyzed with respect to temperature

and pressure to find out whether they are capable of maintaining the pH (near pH 12) o f

the liquor inside the wood chip by its buffering ability.

The successful incorporation and use of sodium metaborate as a decarbonization

agent in the various kraft pulping processes also demands a solid understanding of the

thermodynamic behavior of both the decarbonization (1.3) and causticizing (1.4)

reactions. The use of sodium metaborate becomes more practicable if it also reacts in the

solid phase with sodium carbonate and produces reaction intermediates such as sodium

diborate. If such a reaction occurs, it has several implications. The first one suggests

that metaborate based autocausticizing would be feasible in a fluidized bed (solid state

condition), i.e., in low temperature (600°C) solid phase gasification processes, the second

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. one implies that, in a molten system, such as kraft furnace or high temperature

gasification processes, the decarbonization reaction should be more favorable because

part would occur before the molten phase is reached. However, the rate and the extent of

decarbonization reaction (1.3) together would govern the overall feasibility of both the

processes. Moreover, it should be pointed out that presence of moisture and carbon

dioxide drives the gasification reactions. Since, carbon dioxide is the reaction product of

the decarbonization reaction, the rate of carbon dioxide consumption during gasification

reactions may drive the decarbonization reaction forward. However, the congruence

between freezing point and melting point (675°C) of trisodium borate should be verified

before any conclusion is drawn on low temperature gasification process. In case of such

incongruent behavior of the salt, i.e., when freezing point of trisodium borate is less than

its melting point it may positively affect both conventional recovery processes and high

temperature gasification process and would allow them to be operated at a wider

temperature gradient. On the contrary, in such situation, during low temperature

fluidized bed gasification, bed agglomeration may result and thus may destabilize the

entire process.

It is known that the sodium to borate ratio of sodium diborate lies between the

ratios of sodium metaborate and tridsodium borate. In the conventional kraft furnace, if

the reaction (1.3) produces sodium diborate (m.p. 622°C) as a low melting point

intermediate, the presence of both low melting point trisodium borate and sodium

diborate are going to contribute to the overall lowering o f the melting point of the smelt

bed. This may have several implications. Primarily, it may facilitate additional collision

between the reactant molecules even at lower temperatures during the decarbonization

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reaction inside the bed. Furthermore, the bed (only the lower part of the reactor) could be

maintained at a much lower temperature due to the presence of low melting point

trisodium borate and sodium diborate which may, in turn, diminish the chances of bed

solidification. However, the temperature should not be lowered at the expense of the rate

o f reaction of other reactions because it should be understood that the pre-exponential

constant, A, i.e., (collision factor between the molecules) and exponential temperature

dependency of the rate o f reaction are not of the order of identical magnitude and also the

reactions occurring near the bed are themselves highly endothermic in nature. Moreover,

even if the temperature of the bed is maintained at the existing temperature of the smelt

bed, the presence of these low melting point borate salts would allow the mobility o f the

immobized salts and make them available for additional collisions.

It should be understood that the rate of reaction of carbon dioxide to carbon

monoxide reaction may govern the extent an rate of conversion of the decarbonization

reaction (1.3). Finally, the lowering o f pooled melting points of the smelt bed would also

allow the reactor to be operated over a wider temperature gradient thereby allowing more

leeway and control over the reactions taking place inside the reactor. The understating of

these properties would also shed light to the furnace or reactor designers to allow minor

modifications, if required, to maximize the extent of conversion of reaction (1.3). This is

because the attractiveness of using sodium metaborate is greatly enhanced if the

residence time of the smelt in the conventional recovery boiler (without the presence of

sodium metaborate) is comparable to the complete or near complete decarbonization of

sodium carbonate by metaborate during the black liquor combustion. Moreover, the

estimated value of the heat of reaction of the decarbonization reactions is another

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. important factor that will provide important information about additional energy

requirements.

The decarbonization reaction product, trisodium borate (Na 3 BC>3 ) undergoes

hydrolysis during causticizing reaction (1.3) and produces sodium hydroxide (NaOH) and

sodium metaborate in the aqueous phase [44-50]. It is of fundamental importance to

determine the pH of the resulting solution to forecast the type of ion formation it favors at

corresponding pH not only at room temperature but also at elevated temperature and

pressure. Moreover, the thermodynamic spontaneity or speed of these exchange

reactions [9, 15] between the various borate ions (BfOHfr" , BiCbfOHfs2' etc.) and their

implications should be examined when the hydroxyl ions are depleted during the

unwanted neutralization reactions with polysaccharinic acids. As mentioned earlier, in

addition, the behavior of the exchange reactions may also provide indication whether

additional hydroxyl ions can be supplemented to maintain the pH inside the core of the

wood chips from those reactions. The occurrence such exchange reactions [9] between

various borate ions may also help contribute or enhance the transport o f OH" ions from

the bulk liquor to the core of the wood chip resulting in lower pulping reaction time. In

such condition it is also necessary to account for the ion balance from the hydrolysis of

trisodium borate and their complexation product with some other specific organics may

serve better to understand boiling point rise in black liquor. On the other hand, during the

pulping reaction, B(OH)T ion may demonstrate its potential to form complexes with

polyhydric alcohols and specific polysaccharides present in the wood. Such

understanding, in turn, may provide an insight not only into the energy requirement

during the cooking and evaporation of black liquor but also to the change in viscosity due

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to the presence of organo-borate complexes. With such understanding, a comparative

analysis among the various types of pulping processes could be realized to determine the

process and economic viability of the various cooking processes.

The process cost and energy waste associated with the chemical recovery and

potential elimination of calcining cycle may be reduced further, if significant hydroxyl

ion (OH ) concentration (pH~13) could be achieved from reaction (1.4) and also

maintained at elevated temperature and pressure. Moreover, it should be understood that

the formation of multiple moles of B(OH) 4 ~ ions in the aqueous phase, from one mole of

sodium metaborate or boroxol ring would contribute, to some extent, more to the boiling

point rise in the black liquor thereby increasing the energy demand in the multiple effect

evaporators, yet it may play a positive role in depressing the vapor pressure in the

digester. On the other hand, the formation of complexes with cz's-hydroxy compounds

and B(OH)4 _ ions may also compensate for the boiling point rise. Additionally, the

additional presence of sodium metaborate and organo-borate complexes in the aqueous

phase would also demand supplementary energy in other unit operations, such as

pumping and require extra sensible heat to reach desired temperature in the unit

operations such as heat exchangers and evaporators; unit processes such as recovery

boiler and both continuous and batch pulping digesters.

The goal of this work is to study the kinetics of reaction (1.3) concurrently

drawing a strong parallel between organo-borate complexes and sodium metaborate. The

viability o f using sodium metaborate as decarbonization agent becomes promising if the

rate of reaction of reaction (1.3) is comparable or faster than the residence time to carry

out the original chemical and energy recovery reactions of the recovery boiler with

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. significant portion of sodium metaborate getting converted into trisodium borate. It is

assumed in the current study that borates remain as both sodium salt of B(OH) 4 _ ion

(evidence provided in the discussion) and organic complexes of B(OH)4" ion and the

organic component o f the borate complexes are oxidized before it reaches the reactor bed.

The primary objective of this study is to provide information on the stoichiometry

and the effect of the rate controlling parameters on the decarbonization reaction between

sodium metaborate and sodium carbonate. Because this reaction occurs at high

temperatures and involves multiple phases, little information is available concerning its

nature or rate controlling parameters.

One specific objective of this study is to verify the stoichiometry of reaction (1.3)

proposed by Tran et al. [50] of the decarbonization reaction between sodium carbonate

and sodium metaborate in the molten state. Although Tran et al. [50] proposed the

corrected stoichiometry for this reaction, no data were presented to confirm this

stoichiometry and little information was provided concerning the rate controlling

parameters. Another objective of this study is to determine the effect of the rate-

controlling parameters, such as temperature and concentrations of the reactants as well as

the phenomenological rate expression of the reaction. The understanding of this reaction

will provide key information regarding its applicability in various chemical recovery

processes. The third objective of this study is to determine if there is any reaction occurs

between sodium metaborate and sodium carbonate below the melting points of the

reactants. The fourth objective of the work is to examine the decarbonization reaction

between sodium diborate/pyroborate (Na 4 B2 C>5 ) and sodium carbonate. This particular

study was undertaken because pyroborate is an intermediate between sodium metaborate

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and trisodium borate. The fifth objective of the study is to identify the governing

parameters that control the conversion rate of this reaction as well as the

phenomenological rate expression of the reaction. The final objective of the study is to

critically examine the stoichiometry of reaction (1.4) since its reaction behavior would

provide clue for its viability in various pulping processes.

It should be pointed out that, it is beyond the scope of the current study to

determine the mechanistic steps that are involved in the decarbonization reactions. The

first part of the experimental plan consisted of studying the reaction between sodium

metaborate and sodium carbonate at various molar ratios, from low temperature to

temperature above the salt mixture’s pooled melting point. The second part of the

experiment was conducted in a similar fashion except sodium metaborate was replaced

with sodium diborate/pyroborate as the decarbonization agent. However, critical

discussions on equations (1.3) and (1.4) would be carried out to understand their

interactive effects on various parts of the chemical recovery and pulping processes. A

critical evaluation o f the stoichiometric representation of reaction (1.4) will also be

presented. Such examination, based on the existing literature on borate chemistry will

facilitate the explanation of several other phenomena, such as boiling point rise of black

liquor, transport of OH' ions to the core of wood chip.

Several empirical equations will be selected to estimate the heat of formation,

lattice energy, heat of fusion and heat capacity of trisodium borate to predict the heat of

reaction of reaction (1.3) at various temperatures. MOP AC, a semi-empirical

thermodynamic property estimation method will be used to predict the thermodynamic

parameters, e.g., heats of formation and heat capacity of trisodium borate.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER II

LITERATURE REVIEW

An in-depth understanding of kraft pulping processes, both conventional and

modified ones, energy and chemical recovery through conventional recovery boilers and

novel gasification technology is essential to successfully implement the borate based

autocausticization technology in the paper industry. Additionally, the collective

knowledge of wood chemistry, the properties and chemistry of black liquor along with

borate chemistry and their interactive relationships and the thermodynamic properties of

borate salts provide a general outline of the economic benefits of the autocausticization

technology.

Boron-Oxygen Chemistry

Boron is never a monovalent element despite its 2s 2 2p structure [6 , 7]. This is

because, the total energy released in the formation of one bond in a BX 3 compound

exceeds the energy of formation of one bond in a BX compound by more than enough to

provide for promotion of boron to a hybridized valence state of the sp type, wherein the

three sp2 hybrid orbitals lie in one plane at angles 120° [7]. Additionally, the presence of

only three valence orbitals makes the example of hypoelectronic element, that is, an

element with fewer valence electrons than valence orbitals [ 6 ]. Such properties of boron

allow it to form three two center 2 electron bonds in addition to one coordinate bond.

Most boron compounds are based on the excited 4P state of the boron atom which has

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. three unpaired electrons and one unoccupied orbital. Boron is, in general, a trivalent

element in which the central atom is sp 2 hybridized with trigonal planar coordination and

unoccupied pz orbital of similar orbital energy which can also accept two electrons. The

hybridization scheme is shown in Figure 2.1 [ 6 ]. Therefore, BX 3 compounds are Lewis

acid [1], Hydrated or anhydrous borate salts include boron-oxygen species both in

synthetic and natural origin. Borate salts could be found in the crystalline or vitreous

state [2 ],

Monomeric, oligomeric and polyborates contain the trigonal BO 3 and/or the

tetrahedral BO 4 units [1], Monoborates consists of the anions as shown in Figure 2.2.

Both types of units may be either isolated or joined by their vertices to form islands,

chains, layers or three dimensional networks. The oxygen atoms which link the BO 3 and

BO4 units may belong to two or three (even four in some cases) boron atoms [80, 81].

The oligomeric borates contain the boroxol (B 3 O3 ) ring, either isolated as in sodium

metaborate (Na 3 B3 0 6 ), the sodium salt of cycloboric acid or condensed with a second

ring as in borax (Na 2 B4 C>7 , IOH2 O) [80], The diborate (or pyroborate) ion (B 2 O54 ) in

solids consists of two triangles joined by a common oxygen atom [2, 82]. Various borate

structures are shown in Figure 2.3. The main systematics of the structure of crystalline

metal borates can be summarized as follows [ 6 , 81]:

1) Boron can link either three oxygen atoms to form a triangle or four oxygen

atom to form a tetrahedron.

2) Polynuclear anions are formed by vertex a sharing only o f these boron-oxygen

triangles or tetrahedral to give compact insular groups.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ID t t T t t T 2p 2p sp -1 2s 2s

Promotion ’bridization

Figure 2.1. Hybridization Scheme of Boron [ 6 ]

Figure 2.2. Various Forms of Monoborate Ions [81]

a) metaborale ion b) diborate ion c) monoborate ion d) carbonate ion

Figure 2.3. Structures of Metaborate, Diborate/Pyroborate, Monoborate and Carbonate Ions [80]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3) Boron can link either three oxygen atoms to form a triangle or four oxygen

atom to form a tetrahedron.

4) Polynuclear anions are formed by a vertex sharing only of these boron-oxygen

triangles or tetrahedral to give compact insular groups.

5) In the hydrated borates, the protonable oxygen atoms will be protonated in the

following sequence :

i) available protons are first assigned to free O2’ ions to convert them to

OH’ ions;

j) additional protons are then assigned to oxygen first on tetrahedral

boron atoms and then on trigonal boron atoms to give B-OH units;

k) any remaining protons are assigned to free OH' groups to give H20

molecule.

1) The hydrated insular groups that may polymerize in various ways to

eliminate water; there may be B -0 bond formation within the

polyanion framework.

m) That complicated borate polyanions may be modified by the

attachment of individual side groups such as a borate tetrahedron or

triangle, two linked borate triangles and/or heteroatom tetrahedron.

Structure and Properties of Various Borate Salts

Trisodium borate crystals are monoclinic in the space group P 2 |/c-C5 2 h and the

unit cell parameters are reported as, a= 5 .6 8 7 , b=7.53o, c= 9 .9 9 3 , (3 = 1 2 7 . 1 5 . The Madelung

part of the lattice energy was reported as 3700 kcal/mol [83]. The melting point of

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. trisodium borate (3:1) was reported to be 675°C [25]. Sodium diborate (or pyroborate)

are biaxial, positive and the unit cell structure of sodium diborate (or pyroborate) is

expressed as a = 1.50o, [3 = 1.52o, y = 1.55o. The melting point of this borate compound

is 622°C [26]. Bray et a l [85] have reported that in glasses of molar composition

xR 2 0(1-x)B 2 0 3, the fraction N 4 of boron’s that are four coordinated to oxygen increases

with x as x/(l-x) up to 0.30 then increases more slowly with x, finally reaching a

maximum value of 0.45 in the range 0.35< x <0.45. With further increase in x, N 4

decreases rapidly and reaches zero near x=0.70. They further added that at least two

different types of three coordinated borons are present in the composition range 0 . 1 0 < x

<0.30 whereas, several types of three coordinated borons are present in the composition

range 0.35< x <0.45.

Certain metaborate compounds originally formulated as the hydrated metaborates

contain tetrahydroxoborate, i.e., B(OH) 4 _ ions, e.g., NaB02. 4H20 is Na+B( 0 H)4 '.2 H2 0 .

However, the normal forms of these salts under normal atmospheric pressure contain -5 either the cyclic/ring B 3 O6 " ion as in Na 3 B3 C>6 and K3 B306 or the infinite linear

metaborate (B 02)nn~ ion as in lithium and calcium metaborate is shown in Figure 2.4 [ 8 6 ].

Sodium metaborate has a planar ring structure with (B3CV ) comprised of three B 0 3

triangles with two of three comers shared. Each boron atom is bonded to one Oi atom

with a bond length of 1.280 ± 0.016 A and to two On atoms with B-On 1.433 ± 0.009 A,

while each sodium atom forms bonds with five Oi atoms and two On atoms, the Na-0

distance ranging from 2.461 A to 2.607 A. The large difference in the B - 0 bond lengths

is attributed to an unequal distribution of the boron valence strength between the three

bonds [84-89]. The melting point of sodium metaborate is 922°C [27]. The high

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.4. Infinite Borate Chain Ion of Calcium Metaborate and Lithium Metaborate. (Small Black Circles Represent Boron Atoms) [ 8 6 ]

melting point o f sodium metaborate compared to other sodium borate compounds may be

attributed to its highly symmetrical structure [90]. Sodium metaborate (NaBC> 2 . 4FLO) or

1:1:8 compound is the stable phase with its saturated solution between 11.5 and 53.6°C.

Sodium metaborate dihydrate (NaBC> 2 . 2 H2 O) or 1:1:4 compound becomes the stable

phase with its saturated solution between 53.6 and 105°C [25, 91 and 92], The heat of

hydration o f dihydrate to tetrahydrate is 52.51 kJ/mol, whereas the heat of dehydration of

dihydrate to NaBO 2 .0 .5 H2 O is 58.1 kJ/mol. Thermogravimetric study shows that the last

molecule of water associated with sodium metaborate is released up to 800°C [91, 92],

The Infra-red and other studies have confirmed the presence o f discrete tetrahedral

B(OH)4' ions [14-16, 25, 52],

Structure and Properties o f Various Borate Ions

Borate ions demonstrate complicated chemistry in aqueous solution [9-16]. The

presence of various polyborate [52] and monoborate species have been detected at

various levels o f pH at higher concentration [9]. However, it should be pointed out that

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Edwards [16] et al. has ruled out the possibility of formation of BO 2 " ion in the aqueous

phase. Moreover, Edwards et al. [52] have suggested that the metaborate ion (B 3 O6 3’)

hydrates very rapidly in water and loses its ring structure. Raman spectroscopic

measurements reveal that monomeric B(OH)4' and B(OH ) 3 species in the aqueous phase

have regular tetrahedral and equilateral triangular structure respectively [91]. The

principal polyborate species in water is B 3 0 3 (0 H)4 ' [10-16, 94 and 95], Other

polyborates [14] are also found in relatively minor quantities are B 5 0 6 (OH)4 ‘,

B4 0 5 (0H )42' and B 3 0 3 (0 H)52' when the concentration of boric acid is above 0.025

mol.dnT3. However, at room temperature and above pH 12, B(OHV ions are only

present in the aqueous solution [10, 11, 13 and 90] and at low ionic concentration

polyborates do not exist [9]. Cryoscopic evidence also shows sodium metaborate only

assumes B(OH) 4 ~ structure [96]. Ingri assumed that aqueous polyborate all remains in

the forms o f [B(OH) 3 ]

[10-12, 92]:

p O K + ^B(OH) 3 ~ [B(OH)3 k ( O H ) /...... 2.1

The variation of mol fraction of various monoborate and polyborate species with

respect to pH at room temperature are shown in Figures 2.5 and 2.6 [13, 91]. Maya and

Ingri have demonstrated that the equilibrium between these polyborate species is very

fast and changes in the equilibrium compositions do not take place [10, 11, 14].

Salentine and Maya [14, 15] also independently reported the formation constants for

several polyborate ions, such as, BsC^OH^', B 4 0 s(0 H)4 2' and B 3 0 3 (0 H)4‘ in the

aqueous phase. The equilibrium constants have been calculated for various polyborate

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ions and B(OH)4‘ ions [84]. Examples of such equilibrium relationships are given by the

following two equations [84]:

4 B(OH)4' B4 0 5 (OH)42' + 20H ’ + 5H20 ...... 2.2

Where, lo g ^ = -7.34 ± 0.109

3 B(OH)4- <-► B3 03(0H )52' + OH' + 3H20 ...... 2.3

Where, lo g £ = -4.64 ± 0.19

Moreover, Mesmer et al. [9] have studied the B(OH) 3 -B(OH)4" equilibria at

elevated temperatures. Their results show that in dilute boric acid solution, the

equilibrium quotient has a slight dependence on the ionic strength (I) and it decreases

slightly with temperature. Additionally, the pressure dependence o f the equilibrium

quotient is

0 4 f, ; 4

Figure 2.5. Distribution of Various Polyborate and Monoborate Ions in the Aqueous Phase [91]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X x

C 0

ix j | f%.| /* m w, M'

ti.

,.Q 2 E

11 PH

Figure 2.6. Distribution o f Hydrolysis Species of Borate Ions (Calculated Using Ingri’s Data) [10-13]

shown in Figure 2.7 [9]. The results demonstrate that there is a trend in increasing OH'

ion concentration with increasing temperature due to the shift in reaction equilibria.

Momii et al. [94] observed that the monomer-polymer anion distribution in the aqueous

phase depends on B 2 O3 /M2 O ratio.

Complex Formation of Various Carbohydrates with Tetrahvdroxv Borate Ions

It is a well established fact that B(OH)zt‘ ion readily forms complexes with

carbohydrates and polyols [97-113]. However, the complex formations are pH

dependent phenomena and for carbohydrates and polyols are favored at higher pH [21,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.7. Trends Showing the Shift in Equilibria to Higher Hydroxide Concentration with Increasing Temperature (Where n Represents B(OH,4 ‘ Ion) [9]

99]. Generally, the c/s-hydroxy groups form various complexes with B(OH)4" ions. The

complexation scheme is shown in Figure 2.8 [99]. Dawber et al. concluded that although

the complexation phenomena with B(OH) 4 ~ ion is commonly assumed across adjacent

hydroxy groups, it is now obvious that complexation is also possible across alternate

hydroxyl groups [22]. They have demonstrated through nB NMR and 13C NMR and

polarimetry that the B(OH)4‘ ion has almost universal ability of complexation with polyol

and carbohydrates. They considered three general reaction equilibria for comparing with

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. complexation between B(OH) 4 _ ion and carbohydrates/polyols. The first two represent

complexation across adjacent carbon atoms and the other represents complexation across

alternate carbon atoms. They have also reported the formation constants for various

carbohydrates which are shown in Table 2.1. Their findings show that in general, the

magnitudes of complexation constants are in the order K[>K2.>Kan showing that

complexation is more facile across adjacent OH groups than that across alternate OH

OH K O OH i / X X R + B(OH)4 ;...... R H + 2HzO OH o OH

(A) (H) (AB‘, 1/1-Complex)

OH * O. O .X' X. 2R + B(OH)4 — —- R R. R + 4H20 Oil o O

(A) (H) (A2B% 2/1-Complex)

O Oil Oil _ O O X / / ^ / \ X X B + R — —*■ R" B_ R + 2H20 Vx " X. V / x / X. / X _ X V / x /• O OH OH () o

(AjH, 1/1-Complex) (A) (A2B, 2/1-Complex)

Figure. 2.8. Complex Formation Scheme Between B(OH) 4 " Ions and Carbohydrates/Polyols [99]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 2.1: 1 *B NMR Results for Determination of Equilibrium Constants of ______Complexation [22] ______Carbohydrate/Polyol Complexation Constants k 2 x * D(+)-glucose 17 8 2

D(+)-galactose 113 15 - D(+)-mannose 199 6 46

L(+)-rhamnose 44 3 - D(+)-xylose 347 31 167

D(-)-arabinose 246 32 -

L(+)-arabinose 246 26 - xvlitol 126 15 17

D-arabitol 540 68 -

propane-1,3-diol -- 2.9 mannitol 232 32 15

groups. Malcolm et al. [24] asserted that the type of complex present can be influenced

by changes in the ratio of carbohydrate to borate. With suitable changes the borate

system can be used to give widely different results, such as gelation or solvation [55, 56].

Pezron et al. [78, 79] has indicated that the formation of complexes are possible both or

either intra-chain or inter-chain polymers. Finally, it should be understood that only cis-

hydroxy groups are responsible for the crosslinking or complexation with borate ions and

this phenomena is dependent on the types ligands present in the system [97-113].

However, for high molecular weight polymer, the formation of intra-chain loops

is highly dependent on the presence of passive salts leading to decrease in the intrinsic

viscosity o f the solution. On the other hand, this behavior is absent with low molecular

weight polymers. Moreover, at higher B(OH) 4 ~ concentration, demixing of polymers

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. occurs for both dilute and semidilute solution [78, 79], The demixing is induced from

increased number of cross links between interchain complexes for both types of solution.

In dilute solution, polymer chains precipitate and then form a dense gel, which is in

equilibrium with very dilute solution. The inception of demixing becomes noticeable

when progressive expulsion of solvent and simultaneous appearance of opaque gel takes

place from concentrated solution [55, 56].

Classification and Properties of Lignocellulosics

Plants are classified on the basis of their physical and chemical structures, growth

pattern, lifespan and method of reproduction (seed or spore). Plants are categorized into

four major subdivisions [28], They are known as (a) Thallophytes (b) Bryophytes (c)

Pteridophytes and (d) Spermatophytes.

The last group encompasses the majority of vegetation. Spermatophytes are

further subdivided into two groups: the gymnosperm (Gr., yuvoq, naked and cjTtsppa,

seed) and the angiosperm (Gr., ayyeiov, vessel and gtsppa, seed). The gymnosperms are

grouped into four orders: cycadeles, ginkgoales, coniferals and gnetales. The coniferals

order is the group which contains softwood coniferous wood and gymnosperm wood.

The angiosperms are the most abundant plants today and include both woody and

herbaceous species. Angiosperms are divided into two orders: monocotyledons (one seed

leaf) and dicotyledons (two-seed leaf).

The major organic constituents of wood are polysaccharides namely cellulose and

hemicellulose as well as phenolic substances known as lignin [29]. Minute amounts of

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pectic substances and water soluble polysaccharides such as arabinogalactans are also

present. Other phenolic substances present in small quantities are tannins, phlobaphenes,

colloring matters and lignans. In addition, other organics include terpenes and terpenoid

(containing volatile components), esters of higher fatty acids, aliphatic alcohols, sterols

and proteins. Cyclic polyhydric alcohols, aldehydes, hydrocarbons, alkaloids etc are also

found in minute quantities [29-33].

Cellulose is a polymer which is synthesized in plants from glucose, the

photosynthesis product of plants. Two glucose monomers are connected together by

condensation (the elimination of one molecule of water) reaction and each local molecule

is added to the polymer chain with a 180° rotation. The empirical formula for cellulose is

(C6 Hio 0 5 )n , where n is the degree of polymerization (DP). The DP ranges between

8000-10,000 for wood [31, 114].

The cellulose chain consist of only anhydrous -0-glucopyranose units except for

the end groups; however all other glucosidic bonds are identical to each another [115].

One of the end groups contains a reducing hemi-acetal group, also known as the reducing

end group and the other contains an extra hydroxyl group, also known as the reducing

end group [116]. The 0-1,4 linkage and end groups are shown in Figures 2.9 and 2.10,

respectively.

The infrastructure of wood is composed of cellulose molecules. The length of a

cellulose molecule is 5pm with a typical DP of 10,000. A cylindrical shaped microfibril

is a bundle of cellulose molecules with a diameter between 10-30 pm. Although the

cellulose molecules that are arranged longitudinally with respect to the microfibril axis,

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. OH OH

OH OH CHjOH n-2

Figure 2.9. The (3-1,4 Linkage of Cellulose Molecule [115]

OH OH

,OH O--- OH

Figure 2.10. The Reducing and Non-reducing End Group of Cellulose Molecule [115]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. in some segments they are parallel to each other. In these parts, molecules are

interconnected to each other by hydrogen bonding. The paracrystalline or amorphous

regions where the molecules are randomly oriented are small compared to the crystalline

regions [117]. In general, cellulose is highly crystalline in nature and it is exclusively an

isotactic polymer. The micro-crystals in cellulose are linked together by true covalent

bonds. Mechanical beating of cellulose cannot break the P-1,4 glucosidic bonds in the

molecular chain which link one crystallite to another [33].

The basic structure of cellulose fiber is known as an elementary fibril and

microfibrils and is assembled from these smaller units. Elementary fibrils are 2-6 nm

wide and larger are either continuous structures or bundles of elementary fibrils

withdimensions between 3.5-10 nm thick and 10-30 nm wide [118]. van der Hart et al.

[119] reported that native cellulose is a composite of two crystalline allomorphs, Ia and

Ip-

Hemicellulose is a mixture of nonglucose (pentose sugars) polysaccharides found

in plant cells. They are soluble in alkali, mostly insoluble in water and are readily

hydrolyzed by acid. The DP of the anhydro sugars in hemicellulose is noticeably lower

than cellulose. The following sugars are derived from hemicellulose in softwood [120]:

D-mannose 7-16%

D-galactose 6-17%

D-xylose 9-13%

L-arabinose >3.5%

Additionally, small amounts of L-rhamnose (>1%), sometimes L-fucose and 3-O-methyl -

L-rhamnose are also present. Uronic acids are also present in the form of 4-O-methyl-D-

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. glucuronic acid and galaturonic acid. In the hardwoods, the following sugars are derived

from hemicellulose [120, 121]:

D-xylose 20-39%

D-galactose 1-4%

Small amounts of L-rhamnose, L-arabinose and 4-O-methyl-D-glucouronicacid are also

present in hardwood. Common sugars found in hemicelluloses are shown in Figure 2.11.

COOH

PH HQHC

H OH H OH

l~*ttAilH0ru»ANOSt P-XttPPtfMiNOSE 0 •QLumFfnmo^mmmc ACiO L- Af o - x . 0-GU*

PH CM*OM

f \ A tv n m \ §H y jOH OH

N OH H OH 0*si.ucorrttANO$i 0 - WAMHOPfftAIWSf: D'OAUMSTOrrilAMOSt Q-G* o* m$ 0>GA*

iOH m HO

OH OH

«- FU C O PY SA M O Sg

Figure 2.11. Common Sugars Found in Hemicelluloses [120]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The complex, aromatic, high-molecular-weight, amorphous polymeric material which is a

major component (17-30%) accumulates through photosynthesis is known as lignin.

Lignin is the second most abundant renewable organic found in nature after cellulose.

Lignin acts as a reinforcing agent and binds the carbohydrates present in the cell. Plant

lignin is observed between the cells where it is deposited during the lignification process.

It has no regular polymer structure and moreover it is not possible to rupture its polymer

structure to form monomeric units by hydrolysis or any other means [34-36],

Lignins are classified into three major group on the basis of their monomer units.

Gymnosperm lignin is formed from the dehydrogenation of coniferyl alcohol.

Angiosperm lignin is formed from the mixed dehydrogenation o f coniferyl and sinapyl

alcohols. Grass lignin is a mixed dehydrogenation polymer o f coniferyl, sinapyl and p-

coumaryl alcohols. The structures o f coniferyl, sinapyl and p-coumaryl alcohols are

shown in Figure 2.12 [122].

tCH*OH CM* OH CH ) OH I * (#C« CH CH y II ll \\ oeCH CH CH l l 2 f l \ 3 QCHS CH30 ^ 5 y A o c H , J4 OH OHOH 111 121 13) tie a te i SInapfi alcohol p-Coumaryl ateishol

Figure 2.12. The Structures of Coniferyl, Sinapyl and p-Coumaryl Alcohols [122]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. It is well known that phenyl propane is the building block of plant lignins.

Gymnosperm lignins are known to be composed of polymers containing guaiacylpropane

units and angiosperm lignins contain both guaiacyl- and syringylpropane units. In the

later case, it is a random copolymer of guaiacyl- and syringylpropane monomers or it

may have an ordered structure of the two. The guaiacyl- and syringylpropane groups are

shown in Figure 2.13. The structure of spruce lignin is also shown in Figure 2.14 [123].

CHiQ h o / y h o /\ \ / CHjO'“ CH,o'W Gutkcyl Sym iyl

C m m yl ■ CH r CH* • CHjOH ^ y n«|y i • CH* * C H* • C H|0 H

Syrutfyl • CH* ■ CH* • CH* GuaiMyl ■ CHs - CH* - CH}

C tmkcyl • CH* * CHGH • CH* O m u y l * CO • CH(OCjH») ■ C H*

Cutiacyl-CH(OC,Hd*CO-CHi G m m yl ■ CO - CO ■ CH*

Guiiicyt-CHrCO-CH* 3yrin|yl.C0*CH«X:,H«)-CH,

% nafyl * CO * CO«CH* Sydhfyl • CH|* CO ■ CH,

Figure 2.13. The Structures of Guaicyl- and Syringyl Groups [123]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. *• J** I H *C D H , I; •»*** cm *f~° OHC

*>£' CH

OM* QM

! ;§***,!

Figure 2.14. The Structure of Spruce Lignin [122]

The food reserves in the wood such as starchy materials and fats are distributed

in the sapwood. Phenolic substances are also found in the heartwood. The exudates

secreted from sapwood and inner bark of a tree contains polysaccharide gums, resins and

volatile oils. The mixture containing volatile oils and resins is known as oleoresin.

Volatile components consist of the following compounds from among the terpene,

sesquiterpene and diterpene groups and their derivatives [125]:

a) Hydrocarbon

1) Terpenes (C6 H]6), sesquiterpenes (C 15H2 4 ) and diterpenes (C 2 0 H3 2 ).

2) Other cyclic and non cyclic hydrocarbons

b) Acids and phenols

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. c) Alcohols: derivatives of terpene, sesquiterpene, diterpene and other alcohols

d) Esters

e) Ethers

f) Aldehydes and ketones

g) Oxides and lactones

h) Sterols

The monoterpenes consists o f two isoprene (2-methylbutadiene) units while

sesquiterpene contain three units and diterpenes contain four units, a-pinene (b.p.l56°C),

p-pinene, (b.p.l64°C) and A3 carene (b.p.l68-9°C) are some examples of monoterpenes

found in wood. Oxygenated monoterpenes such as terpenoids are also sometimes

present. These are mainly a-terpinol (b.p.219°C) and bomeol (b.p.212°C). Cadinene

(b.p.l34-6°C) and cedrene (b.p.l21°C) are some examples of sesquiterpene [124]. The

structures of some terpenes compounds are shown in Figure 2.15.

Oleoresins, which are found in the resin ducts, are excreted from the wood as a

solution in a volatile terpene solvent. The empirical formula of resin acid is C 2 0 H3 0 O2

and it is subdivided into two groups: abietic acid-type and pimaric acid-type. The abietic

acid-type class includes levopimaric, abietic, neoabietic and palustric acid. The pimaric

acid-type includes dextropimaric acid and isodextropimaric acid. The structures of

abietic and pimaric acid are shown in Figure 2.16. The abietic acid is usually unstable in

contrast to the pimaric acid and undergoes structural changes (isomerization) in the

presence of acid, heat and atmospheric oxygen. The nonvolatile part of the oleorosin is

known as gum rosin and is a mixture of approximately 90 percent resin acids and 10

percent neutral oils. The composition of gum rosin and wood rosin are similar.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. !o h

a-Terptneol, Borneo!, m.p. ;ifjcC,, m.p, m*a b.p. 2irc. b.p. 212#C.

^ | \ 0 H CH* M/

Fenchyl alcohol, Camphor, b.p. 2 § rc . m.p. m*c.t b.p, 209*C.

Figure 2.15. The Structures of Some Terpene Compounds [124]

Approximately 10-11 percent of gum rosin is comprised of neutral components.

It is a heterogeneous mixture of 60 percent esters of fatty and resin acids and alcohols of

diverse molecular weight. The liquid unsaturated fatty acids include oleic acid, linoleic

acid and minute amounts of solid, while the saturated fatty acids include stearic and

palmitic acids. Resin is also found in the ray parenchyma cells in softwoods. In

hardwoods, resins and found almost entirely in the ray parenchyma cells. Parenchyma

resins are a mixture of fatty acids and unsaponifiables. Very small amounts o f resin acids

are found both in the ray parenchyma softwoods and hardwoods. The major portion of

parenchyma cell resins are saturated and unsaturated fat the acid resins. There also found

in the form of esters [125-127].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Another group of organic compounds known as tannins are also found in plants.

The tannin is complex polyhydric phenols that are present in wood. They are generally

an amorphous, non-crystalline material although that some crystalline tannins have been

'COOK

Abietic acid, m.p, 174X1

CH;

coon

Pim arie acid, m.p, 211 (218)X ,

Figure 2.16. The Structures of Abietic and Pimaric Acid [126]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reported. They are classified into two groups [128, 129]:

a) Hydrolyzable tannins

1) Gallotanins

2) Ellagitannins

b) Condensed tannins

1) Consists of monomer flavan-3-ols

2) Consists of monomer falvan-3,4 -diols

3) Consists of monomer polyphenol hydroxystilbenes.

Other organics such as cyclic polyhydric alcohols (cyclitols) lignans composed of C 6 .C3

units, organic acid such as acetic and formic acid and their salts and organic nitrogenous

compounds are also found in plants [130, 131]. The structure of lignan compounds are

shown in Figure 2.17.

Kraft Recovery Boiler

The multiple purposes of the recovery boiler furnace make its operation complex.

A black liquor recovery boiler serves both as a chemical reactor and a steam boiler. It

produces steam from the energy liberated during the combustion of organic components

of black liquor. On the other hand, chemicals from pulp digesting, such as sulfur and

sodium, are extracted as smelt in order to recycle and regenerate as effective pulping

chemicals [39].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C H ,O j ^ ' ' Y

CoBidencirin

X„

H , \ i / H

Figure 2.17. The Structures of Some Lignan Compounds [131]

A number of complex and intricately related physicochemical phenomena take

place during the combustion of combustion of black liquor in the recovery boiler furnace

and they include [132, 133]:

- injection and mixing of air with the furnace gases

- spraying of black liquor and its droplet formation

- drying of black liquor droplets

- pyrolysis of the black liquor and combustion of the pyrolyzed gases

- gasification and combustion of the residual char

- reduction of the sulfur compounds to sulfide

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. - recovery of the molten salt mixture comprising of sodium sulfide and sodium

carbonate.

Black liquor is the spent liquor generated from the chemical pulping o f wood. It

is a complex mixture of water, inorganic salts and organic matter. Each of these

components is very important in determining the transport and combustion properties of

the black liquor hence governing the operating condition of the recovery boilers. Other

factors that control the chemistry and properties of black liquor are the use o f bleach

plant filtrates in brown-stock washing. The dissolved organic solids from oxygen

delignification or alkaline extraction stages are partially oxidized compared with the

organic matter in kraft black liquor. The increase in oxidized organic solids and chloride

salts impact the composition of the final black liquor, its properties and heating values

[40, 134 and 135],

Black liquor is composed of the inorganic cooking chemicals in addition to lignin

and other organic constituents separated from the wood during pulping in the digester.

The inorganic cooking chemical is comprised of aqueous solution of sodium hydroxide

and sodium sulfide. The organic portion of the black liquor is comprised of dissolved

wood components. Both the inorganic and dissolved organic matter from wood

determines its physicochemical and transport properties [132, 135].

The substances in black liquor derive mainly from two sources: wood and white

(cooking) liquor. The dissolved wood substances comprises of the following classes

[135, 136]:

- Ligneous materials (polyaromatics)

- Saccharinic acids (degraded carbohydrates)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. - Low molecular weight organic acids

- Extractives (fatty acids and resins).

These organic constituents are combined chemically with sodium hydroxide in the form

o f sodium salts. The inorganic components in black liquor are sodium hydroxide, sodium

sulfide, sodium carbonate, sodium sulfate, sodium thiosulfate and sodium chloride etc

[60, 134-136],

The inorganic matter in kraft black liquor consists mainly of a variety of sodium

salts with smaller amounts potassium and minor quantities of calcium, magnesium,

aluminum, silicon, iron and other metals. The solubility of the sodium and potassium

salts is much greater than those of the other metallic salts. At concentrations below about

fifty percent total dry solid content, the sodium salts are completely dissolved in the

aqueous portion of the liquor. When the total solids content is increased above sixty

percent after evaporation of the water, a double salt of sodium carbonate and sodium

sulfate is formed, also known as Burkeite. In kraft black liquor, sodium sulfate and

sodium carbonate are part of the aqueous solution. The total concentration of the sodium

ion in black liquor influences the solubility o f these two salts through the common ion

effect [39, 136].

Black liquor releases heat when it bums in the recovery boiler furnace. The

higher heating value (HHV) of kraft black liquor is in the range o f 5,800 Btu/lbm. Both

the organic component and the reduced sulfur in the black liquor contribute to the HHV.

Other inorganic components act as diluent, lowering the HHV of black liquor. The net

heating value (NHV) of the black liquor calculated from HHV reflects the actual energy

release from the black liquor combustion [60].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Black liquor is concentrated by multiple effect evaporators. It is introduced to the

recovery boiler furnace through spray nozzles that produces relatively coarse droplets in

the range o f 0.5- 5 mm size. Sizes of the droplets are controlled in order to prevent those

from entrainment by the air and other gases. The combustion of black liquor takes place

in four overlapping stages. They are as follows [137-141]:

- Drying

- Devolatization

- Char burning

- Smelt coalescence and reactions

The black liquor solids undergo thermal degradation at combustion temperatures.

The droplet swells considerably during the devolatization process and the organic

material breaks down into tar and then decomposes further into gases and light

hydrocarbon. A large portion of carbon, hydrogen, sulfur and nitrogen in the black liquor

solids are released during this stage. The residue, remaining after the devolatization

process, contains fixed organic carbon and inorganic matter from the pulping chemicals.

The fixed organic carbon is consumed or burned during the char burning process.

Additionally, a small portion o f sodium, potassium, chloride and sulfur is vaporized as

fumes. The extent of this process is governed by the size of the droplets. Droplets that

are larger than 2.5-3 mm reach the char bed before most of the char reaction occurs [140,

141].

The upward moving air/combustion gas mixture entrains the smaller droplets.

The combustibles in smaller droplets are consumed during this process and finally the

coalescence of remaining inorganic takes place. The sodium sulfide in coalesced molten

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. bed, which is formed by reduction in char burning, may get oxidized due to the exposure

to the surrounding air/gas mixture [142].

Although there are significant similarities in solid fuel combustion and black

liquor combustion there are some differences. The black liquor during its combustion

process swells by a factor of ~ 1 0 0 in a reducing environment, although the volume

expansion for black liquor droplets are in the range between 20-50 when they are exposed

to usual furnace environment. These swelling properties have an impact on the internal

and external transport properties inside the droplets as well as the fluidization or

entrainment characteristics [137-141].

The mass/energy transport from the droplets is a strong function of its size and

porosity (swelling characteristics). The increase in particle swelling simultaneously

increases the porosity and surface area available for transport processes, which in turn

increases the apparent reactivity. The swelling phenomenon takes place mainly due to

the release of gases while the droplet is in plastic state. The degree of swelling is

governed by the rate of gas release and the polymeric properties of the organic material

present in the droplet. Swelling during the devolatization enhances external transport o f

oxygen and also increases the internal transport mechanism by opening the pore

structure. Swelling also has an impact on the droplet trajectories and the moisture

content of the droplets reaching the char bed. The black liquor composition that is

dependent primarily on the pulping conditions, wood species and other process

conditions [41,139-141].

The other major reason for difference between solid fuel and black liquor is the

presence of significantly higher concentration of low melting point inorganic material. It

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. acts as diluents for the combustible matter in the black liquor. Although the black liquor

contains -65% solids and 35% moisture, the black liquor contains 45% inorganic which

is equivalent to -64% moisture content on an ash free basis in comparison to 45-65%

moisture content present in other biomass.

The relative amount of volatiles and char depends on the black liquor

composition, transport properties and heating conditions. Less volatile materials are

released at lower temperature and lower heating rate. This phenomenon is observed in

most organic materials. The heating rate is also dependent on the size of the droplets.

Such particles, which are smaller than 2 mm size, if exposed to heating rates in excess of

300 ° C/second, half of the black liquor solids are volatilized during devolatization. Half

o f the original fixed carbon from the black liquor solids remains at the end o f the

devolatization process. The composition of inorganic materials after the devolatization

process depends on the volatization of sulfur and sodium [143, 144].

The next stage after the devolatization process is the droplet combustion process

during which heterogeneous chars combustion takes place. The solid organic that

remains in the droplets after the devolatization process reacts with oxygen. Carbon

dioxide and water vapor from the combustion process react to form carbon monoxide and

hydrogen via shift reaction. Carbon monoxide from the water gas then bums in the gas

phase. The droplet sizes continue to decrease during the char burning process. At the

end of the combustion process the carbon matrix collapses and the molten smelt

coalesces to a bead o f inorganic salt mixture. Generally, the reduced sulfur compounds

in the smelt beads are oxidized when exposed to surrounding gas containing high oxygen

partial pressure.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The presence of inorganic materials in the char increases the reactivity of the

organic char. This inorganic sodium salts acts as catalytic agent during the gasification

o f black liquor and burning of the organic char. Black char is several orders of

magnitude more reactive with carbon dioxide in the presence of inorganic salts. Sodium

sulfate (Na 2 S0 4 ) and sodium sulfide (Na 2 S) also accelerate carbon oxidation through a

redox cycle that transports oxygen to the char surface.

Transport phenomena are the key process in each stages black liquor combustion

process. Heat is transferred to and from the core of the droplets to evaporate water from

the droplets and move forward the pyrolysis of the organics in the droplets. The

oxidizing gases diffuse through the external surface of the char to the internal surfaces

within the pore structure. Although, when the furnace temperature reach near 1000°C,

the chemical reactions proceed at a much faster rate than the transport phenomena (rate

limiting step), therefore, the net effect of transport processes are more important than

reaction kinetics [39, 41, 139, 143].

The main function of the char bed is to create an environment for recovering the

inorganic chemicals used in the pulping process. The char bed is located at the bottom of

the black liquor recovery furnace. It mainly consists of carbon, partially pyrolyzed black

liquor solids and molten and solidified smelts. Generally, it covers the entire floor

surface area. In ideal case, all the inorganic pulping chemicals should reach the char bed

separate from the burning char in a molten, reduced state and flow out of the smelt spouts

without getting re-oxidized. Moreover, all the carbon present in the char bed should get

converted into carbon monoxide and carbon dioxide or react to form sodium carbonate

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. during the combustion process. It should also maintain a reducing environment to lower

the chances of formation of sodium sulfate from sodium sulfide [142, 143].

The materials that reach the char bed are partially dried, pyrolyzed and burned

black liquor solids and inorganic residue after complete combustion of black liquor

droplets. The materials reach the char bed surface as droplets or smelt particle, as char

sloughed from liquor sprayed on the furnace walls, as smelt running down the furnace

walls, or as deposits falling from the screen or super heater tubes. The larger droplets of

black liquor reach the bed partially dried and partially devolatilized. Smaller droplets

may arrive on the char bed as partially or completely burned particles. The distribution

o f residence times of the inorganic salts shed some light on the path of the sodium salts

from the liquor guns to the smelt spouts. Boiler size, char bed size, shape, permeability,

smelt flow path within the boiler and spout location are the main governing factors that

determine the residence time of the inorganic salts [137, 143, 144].

The combustion of char and the reduction of sulfates are the two most important

chemical processes that take place simultaneously in the char bed. Carbon present in the

char is converted to carbon monoxide by reacting with oxygen, carbon dioxide, water

vapor and sulfate. During this process sulfates reacts with carbon in the kraft char and is

reduced to sulfide. Some elemental sodium vapor may also form from the reaction

between sodium carbonate and carbon char. The above mentioned reactions are shown

below [133, 145 and 146]:

c + y2 o2 <-► co 2.4

C + C 0 2 <-► 2CO 2.5

c + h 2o CO + h 2 2.6

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4C + Na 2 S 0 4 <-► Na2S + 4C 0 ...... 2.7

2C + Na 2 C 0 3 <-► 2Na (vap) + 3C O ...... 2.8

The rate of burning in the bed is governed by the rate of transport of oxidizing

gases such as oxygen, carbon dioxide and water vapor to the bed surface. A number of

other factors are also important during the char burning process. They are as follows:

a) Oxidation of carbon by oxygen, carbon dioxide and water vapor at the char bed

surface, to produce mainly carbon monoxide and hydrogen.

b) Carbon monoxide and hydrogen are burned to form carbon dioxide and water

in the boundary layer, consuming oxygen that would diffuse to the char

surface and react with carbon and other organic and inorganic materials.

c) Oxidation of carbon monoxide in the gas boundary layer is catalyzed by water

vapor, so that carbon monoxide is burnt nearly to its completion to form

carbon dioxide when water vapor is present.

In short, oxygen present in the lower furnace would increase the rate of char

burning. With higher concentration of oxygen present, higher amount o f carbon

monoxide and hydrogen produced in the oxygen limited environment of the furnace are

burned to carbon dioxide and water vapor. This phenomenon leads to higher heat release

thereby increasing the char bed temperature, rate of gasification reaction and the rate of

sulfate and carbonate reduction in the bed.

Another mechanism of char burning involves a redox cycle based on sodium

sulfide and sodium sulfate as shown in Figure 2.18. It involves transport o f oxygen to the

char surface followed by reaction of oxygen with sulfide to form sulfate and reaction of

sulfate with carbon to form carbon monoxide, carbon dioxide and sulfide. During this

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Char surface

2 O2 + Na2S— Na2S04 4C + Na 2 S 0 4 -» Na2S . 4CO

4C + Na;S(C -> Na2S +4C0 2

Figure 2.18. The Sulfate-Sulfide Cycle [139]

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission process, when the temperature is high enough, the rate-limiting step is the transport of

oxygen to the char surface. When oxygen reaches the char surface, it can react with

sulfide or carbon dioxide directly. Both of these reactions are fast at char bed

temperatures. This reaction takes place both on the char bed and in flight burning

process. It occurs on the subsurface region o f the active char layers and which results in

the formation of sodium fume. Sulfates are reduced to sulfide by several possible ways:

a) Reaction with carbon to form sulfide, carbon monoxide and carbon dioxide.

b) Yet another mechanism by which carbon burning takes place is the reduction

of sodium carbonate by carbon forming sodium vapor, carbon monoxide and

carbon.

c) Reaction with carbon monoxide to from sulfide and carbon dioxide.

d) Reaction with hydrogen to form sulfide and water vapor.

The rate o f reduction of sulfate with carbon is more than two orders of magnitude

faster in comparison to carbon monoxide and hydrogen. Neither hydrogen nor carbon

monoxide plays a major role in sulfate reduction in recovery boilers [133, 142-149].

Green Liquor Properties

The inorganic smelt produced from the recovery boiler furnace is dissolved in

water to produce the green liquor. The solution thus obtained is green in color due to

presence o f small amounts of iron sulfide present in the solution. The major inorganic

components of green liquor are presented in Table 2.2. It should be noted that the main

components of green liquor are sodium carbonate and sodium sulfide [37—42, 134]. The

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. level o f sodium hydroxide present in the liquor is low in comparison to sodium sulfide

and sodium carbonate.

Table 2.2. Typical Inorganic Composition of Green Liquor [134-136]

Components Median c Range c Percent of Totalc

g/liter g/liter

NaOH 15 10-18 8

Na2S 37 35-40 2 0

Na 2 C 0 3 107 78-135 60

Na 2 S 0 3 6 . 1 4.2-7. 6 3

Na 2 SC>4 1 1 7.4-24 6

Na 2 S2 0 3 5.5 4.3-6.5 3

c g/liter as Na 2 0

White Liquor Properties

White liquor is used for cooking the wood chips in the kraft pulping process. It is

the aqueous solution of sodium hydroxide and sodium sulfide and the approximate

concentration are 1.0 molar in sodium hydroxide and 0.2 molar of sodium sulfide. For

batch cooking, the pH of this relatively colorless liquor is in the range of 13.5-14.0. The

major inorganic components of white liquor are presented in Table 2.3. Sodium sulfate is

present due to the incomplete reduction in the furnace, sodium carbonate due to the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. incomplete causticization of sodium carbonate and sodium thiosulfate due to the

oxidation o f sulfide in air. Moreover, other components such as iron, calcium,

magnesium and silicate also present in the white liquor. Apart from sodium hydroxide

and sodium sulfide rest of the components in white are collectively known as the

deadload [42, 43].

Green liquor contains significant amounts of sodium sulfide in addition to sodium

carbonate. The molar solubility o f calcium sulfide is six times higher than the molar

solubility of calcium hydroxide; therefore the causticization of sodium sulfide does not

proceed unless the concentration of sodium sulfide is very high. Nevertheless, during the

white liquor preparation steps the hydrolysis of sodium sulfide takes place by the

following reaction.

Table 2.3: Typical Inorganic Composition of White Liquor [134-136]

Components Median c Range c Percent o f Total c

g/liter g/liter

NaOH 95 81-120 53

Na2S 38 30-40 2 1

Na 2 C 0 3 26 11-44 15

Na 2 S 0 3 4.8 2 .0 -6 .9 3

Na 2 S 0 4 9.1 4.4-18 5

Na 2 S2 Q3 6 . 0 4.0-8.9 3

c g/liter as NaaO

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Na2S + H20 <-► NaOH + NaHS ...... 2.9

The hydroxyl ions produced from the resulting sodium hydroxide tend to suppress the

causticization of sodium carbonate. Due to this hydrolysis reaction the equilibrium

causticizing efficiency drops as the sulfidity of the liquor is increased. The hydroxyl ion

and the hydrosulfide ions are the main inorganic components in the kraft pulping.

Sodium hydroxide, being a strong electrolyte completely dissociates into hydroxyl ion.

The concentration of the HS' and OH' are the key elements in the lignin removal kinetics,

cellulose degradation reaction and other reactions that govern the quality of the pulping

process [41, 134].

The effective alkali charge, effective alkali concentration, sulfidity and sulfide

charge have a significant effect on delignification rate and pulp yield. The major portion

of alkali consumption in soda pulping is related to the dissolution of lignin, followed by

hydrolysis of formyl and acetyl groups present in the wood. A small part is retained or

used in the degradation of carbohydrates. During batch cooking, a minimum alkali

charge with certain pH is a prerequisite and for effective delignification and retention of

dissolved lignin salts in the cooking liquor minimum of pH~12 is indispensable [135].

Black Liquor Properties

The liquor that remains in the digester after the cooking of the wood chips is dark

in color and is known as black liquor. It contains both inorganic and organic material

removed from the wood during its cooking process in addition to the inorganic

components of the white liquor. The major difference between black and white liquor is

the presence o f dissolved organic solids. They are mainly present in the form o f organic

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. acids and alcohols. Some organics may be recovered as tall oil (mixture of fatty acid and

resins) or turpentine in liquid-liquid separation process. The inorganic composition of

typical black liquor is shown in Table 2.4.

Table 2.4: Typical Inorganic Composition of Black Liquor [134-136]

Components Median c Range c Percent of Total c

g/liter g/liter

NaOH 1.4 1.0-4.5 6-7

Na2S 4.2 1.5-5.6 19

Na 2 C 0 3 7.8 5.0-12 36

Na 2 S 0 3 2 . 0 0.4-3. 8 9

Na 2 SC>4 2 . 8 0.5-6.0 13

Na 2 S2 0 3 3.4 1.8-6.5 16

c g/liter as Na20

During the kraft pulping, the hydroxide and sulfide present in white liquor attack

the lignin and polysaccharides (cellulose and hemicelluloses) in wood chip and reduce

their molecular size and dissolving them to some extent. Lignin is degraded by liberation

o f phenolic groups from a- and b- aryl ether structures. Both the hydroxide and sulfide

present in white liquor contribute to the lignin degradation but hydroxyl ions are

responsible for the polysaccharide degradation.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The main degradation of the polysaccharides are saponification o f the acetyl

groups in hemicelluloses; the peeling of sugar units and random cleavage of the main

polysaccharide chains and removal of the methoxyl and other groups from xylans. The

hydroxide ion is consumed in neutralizing the acidic phenolic groups on the lignin and its

degradation products; the organic acid formed from the polysaccharides and the resin

acids form sodium salts o f the organic compounds. The dissolved organic material

consists of alkali lignin and the sodium salts of the polysaccharinic acids, resin acids and

fatty acids [39, 41, 134 and 136].

Modified Cooking Processes

Sulfidity has a profound effect on the delignification process; which increases

with an increase in sulfidity until a threshold value (pH ~13) is reached. Beyond this

threshold sulfidity, there is little effect on the delignification rate. The increase in

sulfidity also reduces the cost of causticizing, since no additional causticizing is required

for sodium sulfide [150, 151].

The modified continuous cooking became more prevalent since late seventies and

it has added some more advantage to the use of borate based cooking. Commercially,

several cooking processes, such as, modified continuous cooking (MCC), extended

modified continuous cooking (EMCC), isothermal cooking (ITC) and Lo-solids™

pulping processes have become emerging pulping processes. Studies have shown that

these processes selectively remove lignin while diminishing the degradation of

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. carbohydrate components. These processes are based on the following principles [62-67,

150, 151]:

1) Concentration of dissolved lignin should be as low as possible toward the end

of the cook.

2) Concentration of the alkali should be low and uniform throughout the cook.

3) Concentration of sulfide should be as high as possible especially at the

beginning of the bulk delignification.

4) Ionic strength of the liquor should be as low as possible especially at the end

of the cook.

The amphoteric property of borate salts thus makes it a potentially important

chemical for supplementing sodium hydroxide as cooking chemical(s) for the above-

mentioned modified continuous cooking processes due to the unique features of its

chemistry at higher temperature and pressure. It has been reported that Aurell and

Harder [38, 6 6 ] have shown that during the initial phase of delignification there is a drop

in alkali concentration due to the saponification of acetyl groups in xylan, neutralization

of extractives and reaction with easily removable carbohydrate materials. It has also been

suggested that the initial phase of the cook is diffusion controlled rather than rate

controlled process. Harder [65, 6 6 ] has also shown that delignification process is

retarded by high concentration of lignin in the pulping liquor. Elsewhere it has been

proven that the re-deposition of lignin occurs at below a threshold pH. On the other

hand, during batch cooking, low pH (~11.5) of the cooking liquor results in redepositon

of xylans on the cellulose fibers. Thus, the amphoteric property of B(OH) 4 _ ion makes it

a potentially important chemical for eliminating lime cycle as cooking chemical

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. regeneration process for both batch and modified (low pH) continuous processes. In

addition to that, it has been demonstrated by the Scandinavian researchers [62-67, 150,

151] that the low initial alkali concentration of the cooking liquor results in higher

carbohydrate yield. More specifically, lower hydroxyl concentration results in

deceleration in cellulose degradation.

Black Liquor Gasification Technology

Currently, black liquor gasification technology (BLGCC) is in the evolving stage

for commercial implementation. Gasification is a term which refers to the overall process

of thermochemical conversion of carbonaceous material to carbon monoxide, carbon

dioxide, hydrogen and other light gases in the presence of an oxidizing gas that the such

as water vapor, carbon dioxide etc. Carbon gasification refers to the conversion of fixed

carbon to carbon monoxide via oxidation with water vapor, carbon dioxide.

Devolatization process also takes place during gasification when volatile matters are

present in the fuel [152, 153].

Larson et al. have done a comparative study between Tomlinson furnaces and

various gasification technologies, its cost benefit assessment and the potential advantages

[154]. The process has been classified on the basis of operating temperature or by the

physical state of the inorganic constituents exiting the reactor. The operating temperature

of Low-temperature gasifiers is maintained below 700°C to ensure that the inorgaincs

leave as dry solids and the high-temperature gasifiers operate not exceeding 1000°C to

allow the inorgaincs to exit the reactor in the molten state [154, 155].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Black liquor gasification is a process whereby black liquor is partially burned

with a sub-stoichiometry amount of air or oxygen to recover process chemical and

convert the organic fraction of the liquor into a useable fuel gas. If the resulting gas is

pressurized and coupled with gas turbines, gasification systems may provide more

efficient energy utilization of black liquor fuel value and produce more electrical power

relative to steam [154-156]. Coupling gasification plants coupled with water gas shift

reactors and pressure swing absorbers can produce hydrogen or syngas for methanol or

dimethyl ether production [152]. However, the formation of semi-volatile and

nonvolatile (condensable) organics (tar) that during gasification poses a problem when

the product gas is used as a fuel in gas turbines or as syngas for methanol production.

Additionally, these compounds may also contaminate that the alkali recovery process and

gas cleanup operations upstream of the turbine or chemical plant, resulting in potential

loss of fuel. However, between 900 and 1000°C, with a longer residence time, tar

destruction is dominated by tar formation in the presence of oxidizing gases [153]. At

this higher temperature range the dioxin destruction could be realized provided the

residence time is maintained about~ 2 seconds. NO* control can also be achieved by

utilizing ammonia and urea based technology developed by Exxon and Electric Power

Research Institute (EPRI) respectively. The reactions used in these two technologies are

given by the following [157]:

Thermal DeNOy ® process

4NO + 4NH3 + 0 2 -*• 4N 2 + 6H20 ...... 2.10

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. EPRI process

2NO + (NH2) 2CO + 120 2 -»■ 2N2 + 2H20 + C0 2 ...... 2.11

On the other hand, in the low-temperature gasification alkali vaporization is less

prevalent, less consumption of black liquor is necessary to drive the endothermic

gasification reactions. It also lowers the air requirement thereby reducing product gas

dilution, sensible heat loss and the absence of molten smelt increases the life o f metal and

refractory materials inside the reactor [155]. However, low temperature results in slower

kinetics and favors formation of H 2 S, tar and high molecular weight sulfur compounds

[155],

In partial oxidation gasifiers, the oxygen supplied is consumed rapidly and

completely as the pyrolysis product are oxidized and reformed. Gasification proceeds

through the following two reactions [155, 156, 158-160]:

C + C 0 2 —► 2 CO...... 2.12

C + H20 (yap) —> CO + H2 ...... 2.13

The water gas shift reaction takes place resulting in the formation of hydrogen. The

reactor temperature, residence time and catalytic activity of the char determine the

equilibrium condition [157, 158].

CO + H20 (vap ) <-► C 0 2 + H2 ...... 2.14

Although, the yield of hydrogen is higher with low-temperature/partial oxidation

gasification process, it produces less process steam. Moreover, the overall energy

efficiency is higher with high-temperature/partial oxidation gasification process [155,

156, 158-162]. On the other hand, the water gas shift reaction becomes prominent at

higher temperature (900-1000°C) and determines the distribution of carbon between CO

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and CO2 [151, 152 and 160], It has also been reported that water vapor increased the

oxidation of char carbon more than CO 2 [160]. However, the alkali vapor and other

particulates must be cleaned or removed before it can be used in the integrated

gasification combined-cycle (IGCC) power generation system [163]. Encinar et al. has

discussed various aspects of alkali catalyzed and uncatalyzed steam gasification of

eucalyptus char [164]. They found out that both types of steam gasification are equally

efficient at higher temperature (~ 950°C).

Decarbonization Reaction with Sodium Metaborate

Autocausticizing based causticizing processes are non-conventional causticizing

reactions based on the use of amphoteric salts to release carbon dioxide directly from

sodium carbonate. The most promising autocausticizing processes is boron-based

autocausticizing. Such processes can be incorporated in kraft recovery boilers to strip

carbon dioxide from sodium carbonate. It is economically attractive because it could

supply either part or all of the hydroxide requirements in the kraft pulping process. If

autocausticizing supplies the total hydroxide requirement, the calcining/causticizing

process calcining/causticizing process is eliminated thereby significantly reducing the

fixed capital, working capital and energy requirement of a conventional kraft process.

On the other hand, if it meets part of the hydroxide requirement the material and energy

cost could be partly reduced for calcining/causticizing process.

Janson [44-48] was first to recognize that borate could directly form caustic in

aqueous solution would generate a pH high enough for use in the kraft process.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. However, the kinetics and stoichiometry of the autocausticization (decarbonization and

causticization) reactions were not well understood and the concept did not progress

further. In the nineties, Tran et al. [50] proposed that the actual autocausticization

reaction follows a different stoichiometry and is more effective than the stoichiometry

originally proposed by Janson. They also concluded that sodium metaborate based

autocausticizing reactions are proceeds through the reaction of sodium metaborate and

sodium carbonate in the furnace to form trisodium borate and carbon dioxide (reaction

1.3). On dissolving, the trisodium borate in water trisodium borate reacts to form sodium

hydroxide and regenerate sodium metaborate (reaction 1.4).

NaB02 + Na2C03 *-*■ Na3B03 + CO2 ...... 1.3

Na 3 B 0 3 + H20 —> 2NaOH + NaB0 2 ...... 1.4

Reactions (1.3) and (1.4) demonstrate that the requirement of borate is actually half the

amount originally proposed by Janson [50].

The integration of sodium metaborate as an autocausticizing agent largely

depends on the careful investigation of both the solid and molten phase reactions and

understanding its rate conversion controlling parameters. The commercial viability o f

using sodium metaborate as autocausticizing agent during the burning of black liquor in

the recovery boiler furnace depends on various factors. Although the magnitude of rate

o f reaction in the molten state would govern the feasibility of the autocausticizing

reaction, the effective removal of carbon dioxide from the reaction bed would also

control and shift forward the equilibrium of the reaction towards its completion.

The use o f sodium metaborate becomes more practicable if it also reacts in the

solid phase with sodium carbonate. No literature was found indicating that such a

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reaction would occur in the solid phase. If such a reaction occurs, it has two

implications. The first one indicating borate based autocausticizing is feasible in a

fluidized bed and the second one indicates that, in a molten system, such as kraft furnace,

the autocausticizing should be balanced because part would occur before the molten

phase is reached. The attractiveness of using sodium metaborate greatly enhances if the

residence time of the smelt in the conventional recovery boiler (without the presence of

sodium metaborate) is comparable to the complete autocausticization of sodium

carbonate when metaborate is present during the black liquor combustion.

Kingery and Arrowsmith et al. [165, 166] have suggested that any solid phase

reactions are complicated by an intricate relationship between solid phase diffusion and

reaction processes. During any reactions, the particles change their shape and a

nonuniform layer of products is formed around and between the particles. It has also

been suggested that the solid phase reactions are governed by three dependent or

independent diffusion processes, namely, volume diffusion, within the individual

crystals, boundary diffusion, along the grain of the polycrystalline materials and pore

surface diffusion along porous solids. Smith suggested that the understandings o f the

kinetics of solid-solid reactions are difficult since it is difficult to measure the diffusion

effects along the reacting interfaces of the solids [167, 168].

Causticization Reaction of Trisodium Borate

Tran et al. [50] proposed that trisodium borate upon dissolution forms sodium

metaborate. Very little is known about the kinetic and thermodynamic behavior of this

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reaction (1.4). However, various researchers over the last few decades have done

extensive and fundamental work on aqueous borate chemistry. A critical discussion

could be ensued from their work and which may lead to more scrupulous stoichiometry

for equation (1.4). Edwards et al. [52] have affirmed metaborate loses its ring structure

upon hydration and forms B(OH)4~ ions in the aqueous phase. Additionally, elsewhere he

stated that sodium metaborate never assumes BO 2 ' ion in the aqueous phase [51].

Moreover, Ingri [10-12] and subsequently others [13-15] have affirmed that above pH

12 borates only remain as B(OH)4' ion at room temperature. Moreover, during the

hydration of cyclic metaborate ion three molecules of water is required. These

phenomenon demands a modified stoichiometry for the trisodium borate hydrolysis

reaction (1.4) based on the pH value of the resulting solution.

As indicated by Ingri [10-12] and Mesmer et al. [9] at room temperature, in the

vicinity o f pH 12 it is in equilibrium with some polyborate ions, e.g., B 3 0 3 (0 H) 5 ‘ ion.

Therefore it has the potential to supply one mole of OH' ion per one mole of B(OH)4‘ ion

without sacrificing the pH which is also evident from Figure. 2.6. Moreover, Mesmer et

al. has done some extensive work on B(OH) 3 /B(OH)4‘ equilibria and shown that B(OH)4'

ions gives off additional OH' ion at higher temperature by shifting the entire equilibria of

equation (2.2) and (2.3) [9], Such behavior has positive implications in modified

continuous cooking processes where temperature and pressure of the system is

maintained constant continuously and constant and low alkali strength is considered

crucial right above a threshold value to maximize the economics of the process. Besides

that, the chemical similarity between the (HS‘ ion) from sodium sulfide and B(OH)4' ions

are very noticeable since they both are nucleophiles.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The hydration of borates and its both its positive and negative consequences will

be discussed in depth in the discussion section. Besides that, the chemical similarity

between the (HS' ion) from sodium sulfide and B(OH) 4 _ ions are also very noticeable.

Estimation of Thermodynamic Properties

Very few thermochemical and thermodynamic data are available for trisodium

borate. Therefore, appropriate empirical equations should be selected to estimate heat of

formation, heat capacities and heat of fusion of trisodium borate both in the solid and

molten state in order to approximately account for the solid and molten phase heat of

reaction for reaction (1.3) at a number of points along the temperature silhouette of the

reactor.

The enthalpy o f formation (kJ/mol) of a compound can be calculated by the

following empirical equation given by Pauling [169]:

A H/= 23I(Xa-Xb)2 -55.4nN -26.0no ...... 2.15

In which (Xa-Xb)is the electronegativity difference between the adjacent atoms, nN is the

number o f nitrogen atoms in the molecule and no is the number of that oxygen atom. The

value of A Hf is expressed in kJ/mol. However, this equation is not valid for substances

that contain multiple bonds. Moreover, the previous equation should not be

indiscriminately used and a comprehensive discussion is required to avoid any erroneous

result.

Electronegativity was originally defined as being the tendency for an atom in a

molecule to attract electrons to it [170]. Pauling viewed it as an atomic property and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. deemed it to be constant even for different oxidation states [171]. Mulliken’s values

represent an average o f the binding energy of the outer electrons in atom and its

corresponding negative ion. His view introduced the idea that electronegativity

represents an average of a property over a range of ionization potential [172]. He

concluded that electronegativity of an element A is proportional to

XA = (IsA + EsA)/2 = -p s...... 2.16

where IsA and EsA are the appropriate valence state ionization potential and electron

affinity respectively. Electronegativity has been also interpreted as the negative of the

chemical potential (ps) of the electrons [172]. It has the much of the same connotation as

the chemical potential in the classical thermodynamics of macroscopic systems [172].

On the other hand, Pauling verbally defined electronegativity (xp) as the power of an

atom in a molecule to attract electron to itself [174]. It should be mentioned that

electronegativities obtained from the Mulliken definition is approximately proportional to

Pauling’s values. The Pauling and Mulliken electronegativities (xm) are related to each

other by the following equation [174, 175]:

X p = 0.336(x m - 0.615)...... 2.17

Iczkowski et al. also defined electronegativity, based on the assumption that the energy

of an atom is a single valued function of its charge although differing valence state has

different energy and they used the following equation [175]:

E = a*q + b*q 2 + c*q 3 +d*q 4 + ...... 2.18

Where q is the number of electrons in valence shell (or integer charge) of nucleus A and

a, b, c, d are coefficients. E is a good approximation to the true equation for the energy

o f atoms in various states o f ionization (all the electrons belong to the same n -1 shell).

Differentiating equation with respect to q gives

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. dE/ 3q = a+ 2b*q +3c*d 2 + 4d*q 3 + ...... 2.19

It is possible to determine the coefficients a, b, c, d from the relationship between the

energy increments and q. Since these relationships are linear, equations 2.18 and 2.19 can

be rewritten by the following two equations:

E = a*q + b*q 2 ...... 2.20

dE/ dq = a+ 2b*q ...... 2.21

When q = 1 (valence state of A),

E = a + b = Is...... 2.22

When q = 2 (valence state of A"),

E = 2a + 4b=Is + Es ...... 2.23

Solving, a= (3 Is - Es) and b = (Es - Is)-

Therefore, when q = 1, (valence state of A) the absolute electronegativity is given by

equation the following equation:

Xa= (SE/ 3q) | q = i = a+ 2b = ((Is + Es)/2 ...... 2.24

Hence, the above equation is similar to the equation proposed by Mulliken (equation

2.16) [175]. Although, Klopman added that in order to correctly represent the

electronegativity of an atom in a molecule, the atom must be considered in its valence

state and which requires the introduction of electron spin. He has also given a parallel

definition of electronegativity by including all the electrons of the system in the energy

equation [176].

Hinze and Jaffe [173] also concluded that on the basis of Mulliken definition, that

it is not a property of atoms in their ground state, but of atoms in the same conditions in

which they are found in molecules, the valence state. They calculated and reported

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. valence state promotion energies for variety of states of the atom and ions of first and

second period. The combined promotion energies, ionization potentials and electron

affinities lead to the electronegativities of a number of valence states. However, they

pointed out that this definition of electronegativity should be coined as “orbital

electronegativity”.

Hinze, Whitehead and Jaffe [171, 173] also proposed electronegativity by the

following equation:

X = 3E(n)/ dn...... 2.25

where, E(n) is the energy of an atom in its valence state as a function of its occupation, n,

o f the orbital for which the electronegativity is expressed. They also determined that

singly occupied orbitals are identical with Mulliken definition. They further proposed the

concept of “bond electronegativity” based on Sanderson’s [177-182] electronegativity

equalization principle.

Although Clifford [183] suggested that reasonable values o f group

electronegativity may be obtained by averaging the individual electronegativity values of

the atoms comprising the group. Huheey [174, 184] proposed a more comprehensive

calculation scheme by assuming variable electronegativity of the central atom and using

Sanderson’s [177-182] electronegativity equalization principle. However, in some cases,

Sanderson’s [177-182] electronegativity equalization principle ignores the energies

arising from electrostatic interactions and changes in overlap. This might consequently

transpire into incorrect result for bonds with high degree of ionic character. Bratsch

[185], based on similar argument, has also indicated that this principle is mostly valid

with few exceptions. Mullay has also presented calculation procedures for group

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. electronegativity based on electronegativity equalization within each bond in the group

[186]. Reed, from his calculation procedures concluded that electronegativities of

isolated atom and atom in molecules are quite similar, although he acknowledged that the

proposition of equalization is strictly true. However, he also pointed out that

electronegativity equalization is approximately true for isolated atom [187]. He proposed

an extended electronegativity function based on LCAO-MO theory to predict the atomic

charges and core ionization energies for atoms, ions, coordination compounds [188-190]

and demonstrated its usefulness. He concluded that this extended electronegativity

function retains the intuitive nature of the Pauling’s original electronegativity concept

[190],

However, Murphy et al. [191] have given general guidelines for accepting any

electronegativity scale. They concluded that, for Pauling electronegativity, the

electronegativities of groups 1 and 17 in addition to the second and third rows of p-block

element could be accepted. On the other hand, Matsunaga et al. have showed that

Pauling’s original electronegativity equation can accurately describe the homolytic bond

dissociation enthalpies of common covalent bonds, including highly polar ones, with an

average deviation of ±1.5 kcal.mole ' 1 [192], Therefore, equation (2.15) could be

accepted to predict the heat of formation of trisodium borate at standard state. Additional

information and arguments on electronegativity and bond energies could be found

elsewhere [193-200].

Other empirical equations are also required in order to predict the enthalpy of

formation of trisodium borate in other states. There are no rigorous empirical

relationships available for predicting enthalpy (A H fus) and entropy (A Sfus) of fusion for

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. inorganic compounds. Several people have presented different methods for estimating

entropies of solid compounds [201-204]. However, the following equation is offered by

Moiseev et al. for estimating the entropy of fusion (A S/Ms) [201]:

A Sfus = Z ni A Sfus ( i) ...... 2.26

where, n; is the number of moles of ith sample substance

and A S/t„. is the entropy change at melting

The Neumann-Kopp rule (NKR) is the simplest method for estimating molar heat

capacity (Cpm) for binary oxides both at standard state Cpm (298.15 K) and higher

temperature (Cpm (7)) [205], The molar heat capacity of a mixed oxide is the weighted

sum of the constituent binary oxide. The primary advantage o f NKR is due to the

availability of experimental temperature dependencies of individual oxides [205].

However, a general expression for estimating heat capacity between room

temperature and melting point of inorganic compounds is given by the following [206,

207]:

Cp = a +b*10 "3 T+ c* 10 5 r 2...... 2.27

The expressions for the constants in equation (2.27) are given by the following [206-

208]:

a = { Tm* 10'3(EH + 4.7n) - 1.25n * 10 5 Tm ' 2 - 9.05n} / { Tm * 10'3-0.298 } ...... 2.28

b = {25.6n + 4.2n*10 5 rm "2 -X H }/{rm *10'3-0.298} ...... 2.29

c = - 4.184n ...... 2.30

Where n is the number of ions in the molecule, Tm is the absolute melting temperature and

E is the anionic/cationic contributions for the molar heat capacity. The values for E, for

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. both anionic and cationic contributions can be obtained from Spencer [208]. The above

expression is not valid for compounds melting above 2000°C [206].

According to Kubaschewski, the heat capacity of solids is approximately the

same, per atom or ion, at the melting point is approximately (30.3 ± 2 .1 ) that J/K.mole

[208]. It should be mentioned that compounds, which undergo solid-solid transformation

below the melting point and compounds with melting points lower than ca. 420 K were

not included in evaluating this value [206].

The heat capacities of molten inorganic substances do not substantially vary from

those of the corresponding solid materials and the heat capacity of an inorganic liquid

ranges between 29.3 to ca. 33.5 J/K.mol per atom or ion, to some extent depending on the

atomic weight of the substance concerned. The value 31.4 J/K.mol per atom or ion may

be used if measurements are unavailable [208].

Reaction Rate Theories of Solid and Molten Phase Reactions

Brief discussions of the rate constant in the light of early and contemporary

theories are essential in understanding and explaining the kinetic results obtained from

any chemical reaction. The dependency of specific rate constant, k(T) on temperature for

an elementary reaction follows the Arrhenius equation [209-211]

k(T) = A exp(-Ea/R7) ...... 2.31

where, A is the preexponential factor, Ea is the Arrhenius activation energy and R

is the universal gas constant. Burnham and Braun [212] have pointed out that although

the above equation is widely used, many fail to recognize that it is an empirical equation

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. with only qualitative justification. Smith [167] has also emphasized that this equation is

limited to elementary processes only. Although, the exponential effect of temperature

often accurately represents experimental data for an overall reaction, the observed the

activation energy may be a combination of Ea values for several of the elementary steps.

Zewail [213], in his Nobel lecture, pointed out that the rate constant, k(T), does not

provide a detailed molecular picture of the reaction. This is because k(T) was obtained

from an analogy o f van’t H offs description of the change with T o f the equilibrium

constant K, is essentially an average of the microscopic, “reagent-state to product-state”

rate coefficients o f all possible encounters. This might include different relative

velocities, mutual orientations, vibrational and rotational phases and impact parameters.

He further added that even in thermal reactions, there is of an enough energy distribution

to ensure many types of trajectories.

Moore and Pearson [209] have agreed on the existence of competing reactions in

such circumstances and given additional explanations for the varying nature of the

Arrhenius or experimental activation energy (Eexp). According to them, the same reaction

occurring in homogeneous and heterogeneous states is going to give different values of

Ea.

Logan [214] and Masel [215] separately asserted that, over a limited temperature

range (50-100K), In (k) vs. T l is acceptably linear. However, they never discussed the

effect of external colored noises on the activation energy. Masel [215] has pointed out

that most simple and elementary reactions follow the Arrhenius law. However, the

overall rate o f most industrially important reactions cannot be accurately fit with the

Arrhenius law since they are complex in nature. Moreover, Logan [214] has argued that

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. equation (2.31) is not in general obeyed, even by elementary chemical reactions, in the

sense that unique constant A and Ea do not exist for each reaction. In addition to that, he

has pointed out even when the Arrhenius plot is apparently linear and Ea should be best

regarded as an empirical or phenomenological quantity, defined by the following

equation:

Ea = -Rdln£(7)/d(l/7)...... 2.32

Karplus et al. [216] and Truhlar [217] share similar views with Logan about the

Arrhenius energy (Ea), suggesting that it is no more than an empirical parameter

correlating the specific reaction rate to temperature. Logan further went on arguing that

it is a quantity with no (not even approximate) physical significance [214]. Pacey also

pointed out that activation energy is not a single concept rather a series of related

concepts [218].

Kramers [219], in his seminal paper, pioneered concept of the effect of solvent

motion, i.e., thermal noise could affect the solute reaction rates in high-density solvents

as well as low-density gases. He introduced this thermal noise effect, finding that the rate

is controlled by spatial diffusion of the particle and falls off at a rate inversely

proportional to the viscosity of the solvent with increasing viscosity (q) [ 2 2 0 ] which was

also acknowledged by Zewail [213]. His work was followed by Chandrasekhar work and

in turn, introduced the Fokker-Planck equation, which essentially describes passage

across the barrier resembling Brownian motion [220-222]. Hanggi [223] addressed the

problem of surmounting fluctuating potential barriers associated with thermal white noise

and environmental variation (colored noise) of finite correlation. It was also concluded

that the Kramers theoretical results are analogous to variational transition state theory.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Karpal suggested [224] that the phenomenological description o f the transition rate

processes may break down due to the introduction of external noise induced processes.

Moreover, since the attracting states may possess complex intrinsic dynamics, these

dynamical features may interact with external noise to create unexpected transition rate

dynamics. The extension of Kramers’ theory has been reviewed in detail by Hanggi and

Talkner [225].

Bolhuis et al. [226-229] have recognized and eventually proposed, in the

condensed phase, for any reaction system comprised of large polyatomic molecules or

large clusters containing solvent, supportive motions of the condensed phase molecules

can create multiple saddle points on the potential energy surface. The presence of

ensembles of transition states, for such reactions, is very much likely on the

multidimensional potential energy surface. They further added that this high-dimensional

complicated topography of such energy surface is also almost impossible to visualize.

Reactions in solution [222], in general, are non-Markovian in nature and a solvent

may have a chemical effect on the reaction rate. The generalized Kramers’ problem [220]

with an exponential memory friction exhibits an additional oscillatory behavior in the

high friction regime. Elsewhere, it has been also shown that the rate of reaction between

ions may depend on the dielectric properties of the medium [222, 230]. In such cases the

rate constant is given by the following equation [28]:

k= k° exp[zA zB e 2 /(skBI)]...... 2.33

where zA and zB are the number of charges on the ion, 1/b is known as the Debye

screening length, e is the electronic charge, s is the dielectric constant of the medium and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ke is the Boltzman constant. Schroeder and Troe [231] also identified a variety o f solvent

effects, more static or dynamic character that influence the barrier crossing.

Lately, Vyazovkin [230], based on historical and contemporary information, has

summarized that the condensed phase reactions and also has recognized that significant

variations in observable (experimental) activation energy (Eexp) since the time of the

earliest kinetic measurements. He agreed that the reaction medium may induce

significant variations in the experimental activation energy (due to the physical or

chemical effects) even if a reaction involves a single chemical step reaction. He further

added that this observable fact is not consistent with the concept of constant activation

energy; therefore, it is reasonable to introduce the concept of variable activation energy

(experimental, Eexp) for both liquid and solid phase reactions.

Davidov et al. [232] are in agreement with the above discussion and further point

out that for the elementary reactions, the surrounding molecules in condensed phases

have decisive influence on all chemical reactions ranging from the approach o f the

reacting particle through the reaction medium to actual chemical transformation. They

further asserted that, for the solid phase reactions, the time of passage through all possible

states for a reacting particle is much greater than the characteristic time o f the chemical

reaction. Because of the hindrance of the molecular motion, particles have a distribution

of reactivities in the solid state. Thus, they are kinetically non-equivalent and demonstrate

an unusual kind of structural memory connected due to the initial distribution of

reactivities. Prodan [233] has emphasized on the gradation of the solid state to have a

better understanding of the reactivity of the solids. He has classified the solid state in

three mains groups such as, crystalline, non- crystalline, pseudo- crystalline or quasi-

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. crystalline. He also states that the variation in reactivity of solid may be the result of its

gradation.

According to Boldyvera [234], the result of the solid-state reaction depends on

various factors, which in turn determine its kinetics and spatial picture. Temperature,

environment, mechanical stress, crystal structure, type and distribution of defects and

particle size are important factors that have positive or negative feedback effect on the

reactivity of the solids. Moreover, she has emphasized on the qualitative and quantitative

studies of complete feedback loop to understand the course of the reaction. Lyakhov

[235] also, underlined that the correct interpretation of solid-state kinetic parameter is

very confusing and difficult to interpret. He further added that the reaction velocity is

dependent of morphological properties of the solid product and the reaction condition

may control crack per unit area through the reaction rate (ft) or diffusion. Additionally,

Schmalzried [236] has discussed the resting and moving interfaces in heterogeneous

solid-state reactions. Brown et al. [237, 238] have noticed the variation in kinetic triplets,

i.e., the Arrhenius parameters, A (frequency factor) and E (activation energy) for

numerous rate processes in the solid-state reaction kinetics.

Moreover, the critical understanding of topochemistry (spatial orientation) and

topochemical reactions [239-242] in the solid state is fundamental to the mechanism o f a

reaction and its rate since solid state reactions are coupled with the limited mobility o f the

reacting particles. From the postulate [240-242], it is suggested that fixed distances and

orientation, which in effect is controlled by the physical structure of the distinct media

and hence control the reactions in solids. However, Kaupp has pointed out with the

advent of atomic force microscopy (AFM), it can detect the long range molecular

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. movements for nontopotactic reactions and these far reaching molecular migrations are

controlled by crystal lattice and occur anisotropically (direction dependent) [243].

Therefore, solid-state nontopotactic reactions can occur. It has been also concluded this

lattice deformation energy can be related to the energetics of the solid state reaction and

can lead to phase transitions [244, 245].

The solid-state kinetics also follows Arrhenius behavior. The basic equation for

solid-state reaction is given by the following [246]:

da/dt = k(T) f(a ) ...... 2.34

where t represents time, T is the temperature, k(T) is the temperature dependent

rate constant and f(a) is a function called the reaction model, which describes the

dependence of the reaction rate on the extent of reaction (a). According to Galwey and

Brown [247], although the Maxwell-Boltzmann energy distribution function is the

foundation of the theoretical basis of Arrhenius behavior in homogenous system and

hence inappropriate for immobilized constituents of a solid, yet, the distribution function

for both the electronic energy (Fermi-Dirac statistics) and phonon energy (Bose-Einstein

statistics) approximate the same form of the Maxwell-Boltzmann energy distribution.

Thus, Arrhenius type equations are capable of justifying the fit of k-T kinetic data.

However, it should be understood that there have been ongoing controversies concerning

the variable nature of the activation energy [248, 249]

The Prout-Tompkins equation has attained an interesting and exclusive position

in solid-state decomposition and solid-solid reaction, yet it is not always convenient for

kinetic analysis because o f its indeterminate nature at small and large extremities of

extent of reaction [250]. Apart from P-T equation other equations has also been

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. introduced for various models for solid-state kinetics. Some researchers have

recommended the isoconversional model free kinetic studies to obtain the kinetic triplets

for solid state reactions over isothermal, nonisothermal kinetics [252-264],

However, the Arrhenius parameters obtained from nonisothermal kinetic data

have shown considerable variations. The kinetic triplets obtained from nonisothermal,

model-fitting approach may not be meaningfully compared to the parameters obtained

from isothermal kinetics [252], Elsewhere, these inconsistencies have been defended in

relation to kinetic compensation effect which can be the result of differences in sample

(particle sizes, packing) or experimental conditions [237, 238]. One of the proponents of

nonisothermal kinetics has emphasized on the exploration of the constituents of the solid-

state landscape in terms of crystallographic and other information [254]. Agrawal, in

such cases, also suggested the identification of physical factors that may result in the

variation in kinetic parameters [265, 266]. Gam, in general, has critically analyzed the

situations where the use of Arrhenius type equations is justifiable (i.e., in homogenous

system). Additionally, he also gave a clear indication where the use of such equations

would become theoretically sterile (i.e., for non-homogenous systems). The reaction

fronts, reversible/irreversible processes, atmosphere effects, particles size, homogeneity

of energy, are going to define the validity of homogenous kinetics [267, 268]. Kemeny

has recommended verifying the basic assumption of nonisothermal kinetics, i.e., whether

the fractional conversion is solely functions of time and temperature before reaching any

conclusion [269]. The isothermal kinetic protocol has also been criticized for its inability

to recognize any multiple steps that are present in the reaction [255, 263]. Vyazovkin &

Dollimore have observed the ambiguity associated with the kinetic triplet (E, A. f(a))

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. obtained from nonisothermal kinetics which creates problem predicting the behavior of

the reacting system over the experimental temperature range [264],

Others [270, 271] have acknowledged that isoconversional method is more

consistent in obtaining and evaluating kinetic parameters. Vyazovkin & Wight et al.

have deemed the isoconversional method to be the most promising and capable o f

unraveling at least some clues connected to any complex kinetics o f a solid-state reaction

and it is capable of analyzing both isothermal and nonisothermal data [252, 258 and 263].

Vyazovkin & Lesnikovich have developed an algorithm for obtaining such parameters

from isoconversional method provided heating rate is known for such reactions [258].

Vyazovkin & Dollimore have presented a nonlinear protocol for isoconversional kinetics

that produces low errors [264],

Flynn suggested that researchers, while reporting multiple or differing activation

energies of any solid-state reaction, should always present pertinent explanations [272],

Dunn has presented recommendations for methodically presenting thermal analysis data

to avoid confusion [273].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER III

METHODOLOGY AND EXPERIMENTAL PROCEDURE

The current chapter presents the experimental procedure and methodology o f the

decarbonization reaction study of sodium carbonate to obtain its rate controlling

parameters and phenomenological rate expressions. In the first set of experiments

sodium metaborate was used as the decarbonizing agent while in the second set of

experiments sodium diborate/pyroborate was used as the decarbonizing agent. The

reaction involving sodium metaborate included salt mixture preparation at various salt

ratios while the reaction involving sodium diborate, no special steps were undertaken to

obtain intimate contact between the salts. Various ratios of sodium carbonate and

diborate salts were physically mixed right before the reaction.

Separate, yet similar experimental setup was used to prepare trisodium borate to

verify its melting point, determine its solidification point to determine its

congruent/incongruent behavior. Additionally, the pH of the aqueous solution of the salt

was determined at room temperature. The pH of trisodium borate was determined in

order to extract supplementary information regarding the causticization reaction of

trisodium borate (reaction 1.4).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Salt Preparation for Decarbonization Reaction Involving Sodium Metaborate

In order to ensure good mixing between the reactants, different ratios of reagent

grade sodium metaborate to sodium carbonate were prepared by dissolving sodium

carbonate and sodium metaborate in a glass beaker with deioninized water. The solution

was subsequently evaporated over magnetically stirred electrical heater until the all the

free water was vaporized. The crystals formed form this process was collected for

grinding. The salt was then ground to coarse powder and mixed. The ground crystals

were placed inside a convection oven for removing the water of crystallization from the

salt crystals. The temperature inside the convection oven was maintained over 130°C.

The dried salts were kept in the oven over 48 hours.

Sodium Diborate Preparation for Decarbonization Reactions

Sodium diborate was prepared by the protocol used by Morey and Merwin, where

borax was fused with sodium carbonate in stoichiometric proportions [26]. The reaction

stoichiometry is given by the following:

Na2B4C>7 + Na 2 CC>3 > Na4B205 + CO2 ...... 3.1

The salt mixture was mixed and placed in an alumina crucible and heated inside a

muffle furnace1. The salt mixture started to react as soon as the mixture reached molten

state. The reaction was carried out above 940 °C for a minimum of 4 hours to ensure

complete conversion of sodium tetraborate (Na 2 B4 0 /) to sodium diborate (Na 4 B2 0 5).

Nitrogen was introduced as a sweep gas only after the mixture reached molten state and

1 Thermolyne® Convection Oven

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. was well passed the melting points of the reactants. Such conditions were imposed to

speed up the rate of reaction and complete removal of any water of crystallization from

the salts because borates have high affinity for water even at high temperature [92].

Continuous supply of sweep gas was maintained to purge out the reaction product gas

(carbon dioxide) from the system in order to attain complete conversion o f sodium

diborate. The product from the reaction was allowed to cool and attain solid state.

Experimental System for the Decarbonization Reactions

The experimental system for the two sets of decarbonization reactions used in this

study is shown in Figure 3.1. The experimental system consists of an alumina reactor

heated by a circular electric furnace, mass flow meter, carbon dioxide/carbon monoxide

analyzer and data acquisition system. After placing the mixed salts in the alumina

crucible, the salts were heated and sweep gas (nitrogen) was flowed through the reactor at

a rate of ~61iters/minute. This particular flow rate was adjusted in order to maintain a

positive pressure inside the reactor throughout the reaction and swiftly remove carbon

dioxide from the system without any entrainment of reactant particles. Such measure was

•i adopted also to ensure disruption of the equilibrium of the reaction. A mass flow meter

was used to monitor the sweep gas flow rate. The composition o f the off-gas (product)

was measured with an infrared gas analyzer4. The reaction rate was then followed using a

2 Coors Tek® AD-998 3 Omega® FMA-1900 4 MEXA-554 JU (Horiba) gas analyzer

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Data Storage & Retrieval Temperature Data Acquisition System Acquisition Board B oard

Gas Analyzer Thermocouple Sweep Gas & C 02 Out (To Vent) FAlumina Reactor

■ > Furnace

Flow M eter Sweep Gas

Figure 3.1: Experimental System Showing Alumina Reactor, Thermocouple, Electric Furnace, Gas Flow Meter, Gas Analyzer and Data Acquisition System

material balance on the system. The temperature of the salt mixture was measured with a

K- type thermocouple5.

The sweep gas flow rate, system temperature and off-gas composition were

continuously monitored and acquired using a computer and data acquisitions system6.

The data were recorded every two seconds into an Excel 7 spreadsheet and continuously

5 Medtherm® 6 Measurement Computing Corp., Middleboro, Massachusetts. 7 MS Office 97

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. integrated (with respect to time) to determine the total amount of product gas (carbon

dioxide) produced.

The melting point of the salt mixture was evident by a rapid increase in reaction

rate often accompanied by an inflection point on the temperature versus time curve and a

bubbling sound. In the initial experiments, it was observed that the reaction began before

the salts melted. To confirm this solid phase reaction, in the later experiments, the

temperature of the system was held for a long period at a constant temperature below the

melting points of the reactants, until the generation of carbon dioxide ceased.

Experimental System for Melting Point Determination of Trisodium Borate

Equimolar ratio of reagent grade sodium metaborate to sodium carbonate was

placed in an alumina crucible. The experimental system used in this study is similar to

that shown in Figure 3.1. The experimental system consists of an alumina reactor heated

by an electric convection oven and mass flow meter. No lid was placed on the top of the

crucible to allow for the efficient removal of carbon dioxide. An alumina tube, which

supplied nitrogen, as sweep gas was completely immersed inside the salt mixture. The

sweep gas not only ensured good contact or collision between the reactants but also

enhanced efficient removal of carbon dioxide which nullified any possibility of

equilibrium of the reaction. However, the sweep gas (nitrogen) flow was not allowed to

until the salt mixture completely reached molten state. The salt mixture was heated until

the mixture went past 966 °C. Identical mass flow meter was used to monitor the sweep

gas flow rate. The sweep gas flow rate was maintained approximately lliter/min in order

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to prevent any entrainment of any salt particles. The temperature of the salt mixture was

measured with a K-type thermocouple.

The reaction was continued for four hours although the sweep gas flow was

stopped periodically to check whether spontaneous release of carbon dioxide from the

reaction has ceased. It should be mentioned that through the entirety of the reaction the

visual state o f the melt was visually observed and monitored visually from the opening at

the top of the oven. Periodically, the purge gas was stopped to verify the complete

cessation of carbon dioxide bubbling through the melt to confirm the completion of the

reaction. At this point only the oven was turned off. However, the thermocouple

continued to detect the temperature of the system and the data acquisition system was still

recording the temperature drop of the mixture. Few salt flake formation was noticed on

the top surface of the melt approximately around 672°C. The thermocouple was

manually and continuously used to stir the mixture. As the temperature of the system

dropped the bulk of the salt mixture still remained in the molten state (flowed) although

gradual increase in the viscosity was felt during stirring. The salt became completely

immobile approximately between 500-520°C and the thermocouple got trapped inside the

salt. The system was heated again and the trapped thermocouple got released around

500°C when the thermocouple got released from the salt bed. The average solidification

point o f the salt was recorded.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pH Determination of Aqueous Trisodium Borate

Measured amount of trisodium borate was dissolved in deionized water inside a g polypropylene beaker and the pH of the solution was determined by a pH meter . The pH

and the temperature of the solution were recorded.

8 Coming

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER IV

EXPERIMENTAL RESULTS AND DISCUSIONS

This chapter presents the experimental results obtained from the decarbonization

reactions. A comprehensive discussion is initiated from the experimental results to

determine the feasibility of the reactions when integrated into conventional chemical

recovery processes. A follow-up discussion will ensue to investigate the viability o f the

decarbonization reaction in gasification processes in relation to the operating conditions

o f the process based on thermodynamics and kinetics of the decarbonization reactions,

chemical and physical properties of borate and borate complexes.

Additionally, the interactive relationship between pulping products and borate

salts and their ions will also be critically analyzed to unravel the positive, negative or

synergistic effects on pulping processes based on aqueous phase borate chemistry at

elevated temperature and pressure and their resulting impact on chemical recovery, black

liquor evaporation and calcium oxide based causticizing reaction. The transport

phenomena of hydroxyl ion from bulk liquor to the inside the wood chips and in situ

hydroxyl ion contribution inside the core of the wood chips are also going to be explored

from the B(OH) 4 -B(OH ) 3 reaction equilibria at elevated temperature and pressure and

their potential impact on various pulping processes. The formation of complexes with

various ligands and borate ions will also be discussed to forecast its impact on additional

hemicellulose retention, black liquor droplet stability, black liquor vapor pressure

depression and increase in the viscosity of black liquor.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In the first part of the decarbonization study sodium metaborate and sodium

carbonate were used as the reactants. In the second part, sodium diborate/pyroborate was

used as decarbonizing agent. In order to correctly explain the results of the

decarbonization reactions it is necessary to understand the nature of borate physical

properties. Therefore, melting/freezing points of some borate compounds are discussed

in the following section.

A major assumption in this current study is that apart from free sodium

metaborate, organo-borate complexes are also present in the black liquor. The organic

constituents of the organo-borate compounds react with oxygen from air when it is

exposed to the hot environment (800-1200°C) of the chemical recovery boiler.

Moreover, it was also assumed that these boron-oxygen bonds in B(OH)4" ions are never

cleaved during the pulping reactions and subsequent evaporation process. However, the

hydrogen atoms get substituted during complex formation and hydrogen and oxygen

atoms are removed when water of crystallization is expelled from the EfrOHjT ions to

form metaborate and this phenomenon begins at lower temperature and continues until it

reaches approximately 800°C [92]. Therefore, it is assumed that the borate salts keep

their identity as borate (EfrOHjT) ions in anhydrous form before they take part in the

decarbonization of sodium carbonate.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Melting Point Verification and Solidification (Freezing) Point Observation of Trisodium Borate

Some boron based compounds, such as boric oxide (B 2 O3 ) do not have distinct

melting point. The softening point (346°C), freezing point (275°C) and melting point

(543°C) of boric oxide are incongruent with each other. Moreover, the presence of

residual water content and the increase in its amount in boric oxide results in the

consistent elevation of the softening point (352°C), freezing point (275°C) and melting

points (543°C) of boric oxide. Most chemical literature reported the melting point of

anhydrous sodium metaborate as 966°C [27, 274]. This behavior led to the verification of

the melting point and solidification (freezing point) of trisodium borate. The melting

point (~672°C) of trisodium borate, determined during the current study, is consistent

with the result reported in the literature, which is 675°C [25]. During the study it was

observed that around 672°C, few salt flake formation was noticed on the surface of the

melt. As the temperature was decreasing the formation of the flakes increased.

However, the salt mixture continued to behave like a melt with increasing viscous

behavior until it reached the solidification or freezing point. The solidification point or

the freezing point of trisodium borate recorded was between 500 and 510°C. This

behavior is going to be used to explain the solid phase decarbonization reactions.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Decarbonization Reaction with Sodium Metaborate

In the initial experiments, the reaction mixture was gradually heated and the

product gas continuously analyzed. It was observed during the initial experiments that

carbon dioxide was the only product gas from the reaction. Representative data obtained

during these initial experiments are shown in Figures 4.1 and 4.2. All the experimental

results are presented in Appendix A. Figure 4.1 shows the product gas generation rate

and temperature versus time, while Figure 4.2 shows the cumulative carbon dioxide

versus time. Both the solid and molten state reactions can be followed from these

graphical representations. The first peak in Figure 4.1 signifies the maximum carbon

dioxide generation rate below the melting points of the reactants. Eventually, the rate of

carbon dioxide generation declined asymptotically to a non-detectable level due to the

creation o f non-equilibrium condition resulting from the continuous sweep of carbon

dioxide. The formation of reaction product along the reaction front and the immobility of

the reactants in the solid state could have resulted in the cessation of the solid phase

reaction. The second peak is observed after the system melted. A sudden release of

carbon dioxide was evident from the sharp and large second peak as the salt mixture

melted. This could result from the increased reactant mobility in the molten phase.

One of the surprising findings from these initial experiments is that the reaction

begins around 600°C, which is well below the melting point of the individual reactants,

(the melting points of sodium carbonate and sodium metaborate are 851°C and 966°C,

respectively). However, it should be pointed out that this solid phase reaction may have

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidfaed Bed Reactions Sodium Carbonate (0.4717 moles) and Sodium Metaborate (0.0821 moles). Metaborate Mole Fraction=fl.l48. September 18.2000

1000 n T 0.00035 900 -- 0.0003 800 700 0.00025 600 - 0.0002 Rate of Carbon 500 Temperature . Dioxide Released - 0.00015 400 (moles/second)

300 -- 0.0001 200 - 0.00005 100

0 500 1000 1500 2000 2500 3000

Time (seconds)

- Temperatute - Rate of Carbon dioxide

Figure 4.1. Carbon Dioxide Generation Rate and Temperature versus Time

Nonfluidized Bed Reactions Sodium Carbonate (0.4717 moles) and Sodium Metaborate (0.0821 moles). Metaborate Mole Fraction~0.148, September 18, 2000

0.1 0.09 0.08

0.07 Cumulative 0.06 Moles of Temperature 0.05 Carbon dioxide (Degree Celsius) 0.04 Released 0.03 (moles/second) 0.02 0.01 0 1500 2000

Time (seconds)

-Temperature - Cumulative Carbon dioxide

Figure 4.2. Cumulative Carbon Dioxide and Temperature versus Time

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. been initiated due to the initial juxtaposition of the reactants. Several workers have

pointed out that the initial topochemical orientation of the molecules may set off such

reactions [239-242]. Moreover, the reaction may have propagated to some extent due to

the presence of mobile and unfrozen trisodium borate molecules along the reaction

boundary which may have facilitated to some extent molecular lattice vibrations [243-

245]. Therefore, the movement o f the reactant molecules across the reaction boundary

may have been facilitated by the presence of low melting point trisodium borate

molecules. As the temperature of the furnace was gradually increased, the rate of carbon

dioxide generation increased during the solid phase reaction until a maximum point was

reached and gradually decreased and temporarily ceased before the salt mixture reached

its pooled melting point.

Extent o f Reaction in the Solid Phase (Sodium Metaborate)

In the later experiments, to determine the extent of the reaction in the solid phase,

the system was heated to a point where carbon dioxide was evolved but was below the

melting points of the concerned reactants. The temperature was then held constant and

the reaction allowed to continue until the generation of carbon dioxide ceased. At this

point, the system’s temperature was again increased. As soon as the temperature began

to increase, immediate generation of carbon dioxide commenced and noticed although the

temperature o f the system was well below the melting points of the reactants. This

phenomenon could have resulted from due to one or combined effects of the following

reasons [239-245]:

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a) increased diffusion of the reactant molecules along the reaction front,

b) lattice controlled long range molecular vibrations,

c) migrating molecules may have used “easy ways” due to the induction o f

mechanical stress and subsequent stress release and further facilitated

by the presence of mobile trisodium borate molecules, and

d) initial packing or orientations of the reactant molecules.

A sharp increase in the carbon dioxide generation rate was observed as the

reaction mixture melted when it reached its pooled melting point, normally between

850°C and 900°C. The reaction was continued until the carbon dioxide generation ceased

while continuously maintaining the reaction temperature above the melting points o f the

reactants. This phenomenon also raises two points. The first one indicates that the extent

o f reaction in the so called solid phase is indeterminate in nature and is function of

temperature of the system. The second one implies that the extent of reaction in the solid

phase is a function of the mole fraction of sodium metaborate and can be followed from

the following discussion.

In order to determine the effect of the sodium metaborate to sodium carbonate

ratio on the reaction rate and extent of the reaction in the solid phase, the reactions were

studied at different sodium metaborate to sodium carbonate ratios. The experiments

conducted in this phase are shown in Table 4.1. One such experimental result is also

shown in Figures 4.3 and 4.4. These figures show that the generation of carbon dioxide

begins at about 600°C. The reaction continues as the temperature of the system is held at

728°C (well below the melting point of the both the reactants), but eventually ceased. In

this case, it could be observed that approximately fifty percent of the metaborate was

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. converted based on reaction (1.3) during the solid phase reaction. Although, the release

o f carbon dioxide during the solid phase reaction ceased at a given temperature, the

reaction started immediately as soon as the temperature of the system was further

increased as earlier mentioned. Such phenomenon has been attributed to the previously

mentioned reasons and due to the increment in the kinetic energy of the reactant

molecules resulting from the temperature increase and subsequent stress release (due to

the thermal expansion) of the reactants thus aiding the rearrangement and movement of

the molecules through the reaction front. Additionally, it may have been further assisted

by presence of mobile trisodium borate molecules to promote ion transfer. As mentioned

earlier, the salt does not become completely immobile until it falls in the vicinity of

~500°C although the melting point of trisodium borate is 675°C. Moreover, during the

melting point verification study it was observed that only few salt flakes began to form

around ~672°C. As the temperature gradually receded viscosity increase was felt during

the stirring o f the melt. The salt remained in a very highly viscous state even around

600°C. Therefore, true solid state is in no way attained until it reaches 500°C. In the

context of previous observation it could be concluded that it may have been possible for

sodium metaborate and carbonate ions to diffuse through the viscous trisodium borate

across the reaction boundary due to the additional vibration of the ions thus allowing

additional contact between the reactants which might have resulted in the immediate

release of carbon dioxide as evident from the results.

It was observed during the solid-state reaction that (44.64 + 10.79) % of the total

metaborate reacted based on the stoichiometry shown in reaction (1.3). Additionally, it is

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.4243 moles) and Sodium Metaborate (0.040 moles). Metaborate Mole Fracti»n=0.086l. December 14.2000

1200 -i T 0.00016

0.00014 1000

-- 0.00012 800 Rate of Carbon Dioxide Temperature (Degree 600 -- 0.00008 Released Celsius) * (moles/second) - 0.00006 400 - 0.00004

200 0.00002

Tune (seconds)

Temperature Rate of Carbon dioxide

Figure 4.3. Carbon Dioxide Generation Rate and Temperature versus Time

Nonfliidized Bed Reactions Sodium Carbonate (0.4243 moles) and Sodum Metahorate<0.040 molest. Metaborate Mole FractionFO.0861, December 14,2000 1200 0.04

0.035 1000 -- 0.03 800 -- 0.025 Cumilative Moles of Tenfierature (Degree 600 0.02 Carbon Dioxide Celsius) Released 0.015 400

- 0.01 200 0.005 0 0 2000 4000 6000 8000 lime (seconds)

Tenure rature - Qumlative Carbon dioxide

Figure 4.4. Cumulative Carbon Dioxide and Temperature versus Time

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Moles Carhon Dioxide Release in the Solid Phase per Mole Initial M etaborate veisiB Initial Mole Fraction of Soduni Metaborate

0 .7 0.6

0 .5 M oles Carbon Dioxide Released 0 .4 per M ole Irrtial M e ta b o ra te 0 3

0.2 0.1 v = -1.218.\ + 0.627? R 2 = 0 .5 4 2

0 0 .0 5 0.1 0 .1 5 0.2 0 .2 5 0 3 5 Iirtial M ole Fraction of M etaborate

Figure 4.5. Effect of Initial Mole Fraction of Sodium Metaborate on Carbon Dioxide Generation in the Solid Phase

Table 4.1. Reaction Conditions and Results with Respect to Carbon Dioxide Generation during Solid Phase Reaction (Sodium Metaborate as the Decarbonization Agent)

Average Temperature Initial Reactants Mole Fraction Cumulative Percent Flow Rate of the Reaction Solid phase Metaborate to Sodium Sodium M etaborate C 0 2 Conversion Date Melting Point Carbonate M etaborate Produced in Terms of Liters/mi it Reg. C. Moles Moles Moles Reaction (1.3)

18-Sep-00 6 892 0.472 0.082 0.148 0.040 48.780

19-Oct-OO 6 909 0.426 0.038 0.081 0.025 66.310

*10/24/2000 0.6 815 0.472 0.189 0.286 0.054 28.560

* “ 10/28/2000 6.4 -■ 0.485 0.095 0.164

13-Dec-00 6.3 907 0.436 0.041 0.086 0.020 49.030

14-Dec-00 6.2 902 0.424 0.040 0.086 0.020 49.260

20-Dec-00 6.5 880 0.467 0.100 0.176 0.041 41.040

23-Dec-00 6.4 875 0.459 0.100 0.178 0.044 44.250

26-Dec-00 6.1 860 0.466 0.101 0.178 0.041 40.760

27-Oct-Ol 5.7 820 0.527 0.075 0.124 0.025 33.780 Avg. 44.641 Std. Dev. 10.794 * Reaction w as stopped before completion ** The purge tube end was placed above the salt mixture

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. evident from Table 4.1 and Figure 4.5 that as the mole fraction of sodium metaborate was

increased; it was noticed that there was a tendency for the percentage conversion to

decrease during the solid phase reaction. Such behavior may be attributed to the

inadequate juxtaposition of the reactant molecules during the salt preparation which may

have resulted from the dissimilar solubility properties of sodium metaborate and sodium

carbonate. The rupture of the cyclic ring structure of metaborate (boroxol group) during

this apparent solid phase decarbonization reaction with sodium carbonate may not

necessarily solely have led to the formation of trisodium borate. Sodium diborate, which

is an intermediate between trisodium borate and sodium metaborate, may also get formed

during such reaction since monoborate ( B O 3 ) are the basic building block for both these

borate salts.

A brief outline of the theory behind the isothermal and non-isothermal solid-state

kinetics was presented in Chapter II. Isoconversional methodology for non-isothermal

kinetics was also mentioned to extract kinetic triplets for the solid state kinetics.

However, as the reaction does not take place truly in conventional solid state no attempt

was made to mine out the kinetic parameters from the solid (pseudo) state reaction data.

Essentially, for the current scenario, any solid-state decarbonization reactions should be

considered to be occurring in the solid state only when it takes place below the

solidification point (520°C) of trisodium borate. Therefore, reaction (1.3) should be

considered to be occurring in pseudo solid state.

100

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Molten Phase Decarbonization Reaction and Stoichiometry with Sodium Metaborate

Once the solid phase reaction ceased, the temperature of the system was increased

again. Immediate evolution of carbon dioxide was noticed followed by the complete

termination o f carbon dioxide release in some cases and for other cases, considerable

decline was observed, as the temperature approached the pooled melting point.

Subsequently, for all cases, as the salt mixture reached its pooled melting point, a

vigorous increase in the rate of carbon dioxide evolution was observed. It is also

observed from Table 4.2 that the melting point of the salt mixture tended to decrease with

increasing mole fraction of metaborate. The variation of melting point o f the mixture did

show anomalous behavior signifying complex relationship with heat of reaction, mole

fraction of the initial reactants and intermediate product and due to the incongruency of

freezing point and melting point of trisodium borate as well as other unknown factors.

Tran et al. [50] proposed that the decarbonization reaction follows reaction (1.3)

which implies that one mole of sodium metaborate reacts with one mole o f sodium

carbonate resulting in the release of one mole of carbon dioxide. The results, in this

particular case (Figure 4.5), show that complete conversion of initial reactant (sodium

metaborate) was achieved in terms o f carbon dioxide generated, which confirms the

stoichiometry of reaction (1.3). The results for the molten phase reactions, the reaction

temperatures and amount of reactants are shown in Table 4.2 and Figure 4.6. Here, the

data presented in Table 4.2 reveals that one mole of carbon dioxide is released per mole

of sodium metaborate reacted (reaction 1.3) rather than half mole of carbon dioxide

released per mole of sodium metaborate originally proposed by Janson (reaction 1.1).

These results as evident from Table 4.2 and Figure 4.6 confirm the stoichiometry

101

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. proposed by Tran et al. [50]. The average (103 %) and standard deviation (5.9 %) of the

percent conversion, achieved from reaction (1.3) are also shown in Table 4.2. Moreover,

it could be also observed by comparing all the other results that the solid-state rate of

Table 4.2. Reaction Conditions and Results with Respect to Carbon Dioxide Generation during Molten Phase Reaction (Sodium Metaborate as the Decarbonization Agent)

Average Avg. Initial Reactants Mole Fraction Cumulative Percent Flow Rate Pooled Molten Phase Molten phase Metaborate M elting Point Reaction Sodium Sodium M etaborate C 02 Conversion Date Temperature Carbonate M etaborate Produced in Term s of l.itervm in Deg. C. Deg. C. (approx.) Moles Moles Moles Reaction (13)

18-Sep-OO 6 892 910 0.472 0.082 0.148 0.084 97.671

19-Oct-OO 6 909 1050 0.426 0.038 0.081 0.036 103506

*24-Oct-00 6.6 815 976 0.472 0.189 0.286 0.16622*

* “ 2 8 -Oct-OO 6.4 - 1055 0.485 0.095 0.164

13-Dec-00 6.3 907 1000 0.436 0.041 0.086 0.036 111.218

14-Dec-OO 6.2 902 950 0.424 0.040 0.086 0.035 111.924

20-Dec-00 6.5 880 910 0.467 0.100 0.176 0.101 98.990

23-Dec-00 6.4 875 920 0.459 0.100 0.178 0.101 98.265

27-Oct-Ol 5.7 820 1000 0.527 0.075 0.124 0.071 104.654 Avg. 103.613 Std. Dev. 5.960 * Reaction was stopped before completion ** The purge tube end was placed above the salt mixture

102

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Moles Carbon Dioxide Release in the Molten Phase per Mole Initial Metaborate vers ib Initial Mole Fraction of Sotinn Metaborate

1.1 1 0 .9 0.8 0 .7 Moles Carton o.6 Dioxide Released q g per Mole Initial M e ta b o ra te 0 3 0.2 y=1 1643*+ 0.8161 0.1 R2 = 0.6997 0 0 0.05 0.1 0.15 0.2 Initial Mole Fraction of M etaborate

Figure 4.6. Effect of Sodium Metaborate Level on Moles of Carbon Dioxide Released per Mole Initial Metaborate

reactions was very slow compared to the molten phase reactions irrespective of the

(higher/lower) mole fraction of metaborate. It could be also observed that the solid phase

reactions were atleast an order of magnitude slower than the molten phase reaction for all

cases. The results also show that the reaction is extremely rapid above its melting point

and goes to completion in about ten to fifteen minutes once the system melts.

The data obtained from the molten phase reaction were used to obtain the

experimental activation energy (Eexp), order of reaction with respect to sodium carbonate

(m) and sodium metaborate (n). It should be pointed out that since metaborate is a cyclic

compound involving three boron, six oxygen and three sodium atoms and sodium

carbonate contains three different atoms, therefore, it is reasonable to assume that

reaction (1.3) is not an elementary reaction by any standard and may be occurring in

multiple steps.

103

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A set of experimental Arrhenius constants obtained from the representative data

sets from the molten phase decarbonization reaction (1.3) involving sodium metaborate

are presented in Appendix E. It should be noted that JMP9®, a statistical package was

used to carryout the statistical nonlinear curve fitting. The values of the model constants

were obtained by manually minimizing the root mean squared error (rms error) [222].

The nonlinear model fitting approach from JMP® resulted in multiple solutions.

Therefore, root squared error were minimized to obtain the order of reaction with respect

to sodium carbonate (m) and sodium metaborate (n) concentration, pre-exponential

constant (A) and experimental activation energy (Eexp). Apart from rms error, Steinfeld

et al. also have emphasized the testing of significance of correlation coefficient (r)

between the experimental data and calculated data from the kinetic model. According to

them, for a reasonably fitted kinetic data, r value should be greater than 0.95 [222]. From

Appendix E, it can be observed that for all the treated data, for metaborate based

reactions, the correlation coefficients were greater than 0.98 during kinetic modeling.

Myers has also discussed the complexity associated with non-linear regression [278].

The pre-exponential constant values (A) demonstrated considerable variation with

different experimental data set. The order of reaction with respect to metaborate

concentration was order 2 and the order of reaction with respect to carbonate

concentration was order 1 and the experimental activation energy (Eexp) was obtained in

the range of ~(30-60) kJ/mol. This experimental activation energy (Eexp) obtained from

the study may be a combination of several elementary reactions or activation energy of

the rate limiting elementary reaction(s) and may have been convoluted with the energy

associated with viscous momentum transfer.

9 SAS® Institute

104

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reaction without Carbon Dioxide Sweeping (Sodium Metaborate)

It was observed from the results that the reaction takes place both in the solid

(below the melting points of the reactants) and molten phase. Once the system melts, the

reaction is extremely rapid. However, it should be pointed out that inefficient removal of

carbon dioxide could markedly reduce the rate of carbon dioxide evolution and hence the

rate of reaction. This was observed when the purge tube was placed above the salt

mixture. Here, the carbon dioxide was not effectively removed which significantly

decreased the reaction rate, although the flow rate of the sweep gas was maintained in the

range o f ~6 liters/min as also in other cases.

The carbon dioxide generation rate from this experimental arrangement is shown

in Figure 4.7. This suggests that the reaction (1.3) is reversible in nature and for this

reaction to go to completion the carbon dioxide must be removed. This is a critical

finding of the study since it provides vital evidence that even if the reactant mixture is

well past its pooled melting point, the reaction (1.3) may only reach a dynamic

equilibrium at any temperature unless carbon dioxide released from the reaction is

completely swept away from the reactant mixture or converted to other reaction

product(s). In the present case as it will be noticed later from one of the sodium diborate

based decarbonization reaction that if proper measures are not taken to eliminate carbon

dioxide, such decarbonization reaction might reach equilibrium very quickly and thus

result in the very poor yield of the product.

105

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Noafliitfaed Bed Reactions SodimCaitoonate (0.4851 moles) and Sodun Metaborate (0.0951 moles). Metaborate Mol Fraction=0.164. October28.2000

1200 0.0001 0.00009 1000 0.00008 -- 0.00007 0 .0 0 0 0 6 ^ Dioxide Tenperature (Degree 0.00005 Released Celsius) 0.00004 (moles/second) - 0.00003

- 000002 1 0.00001 0 oe

lim e (seconds)

Tenperatwe Rate of Carbon dtoxide

Figure 4.7. Carbon Dioxide Generation Rate and Temperature versus Time

Decarbonization Reaction with Sodium Diborate

It is evident from Table 4.1 that 29 to 66 % of the total carbon dioxide was

generated depending on the mole fraction of metaborate in the salt mixture during the

solid phase reaction. It is proposed that sodium diborate may be an intermediate product

resulting from the solid phase reaction in reaction (1.3). Incomplete reaction between

sodium carbonate and sodium metaborate may also result in the formation of sodium

diborate. However, the assumed intermediate borate could not be isolated or detected

due to the lack of availability of instrumentation. This diborate may circulate within the

chemical regeneration loop and eventually participate in the secondary decarbonization

106

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reaction. Thus, it was decided to study the decarbonization reaction involving sodium

diborate. The following stoichiometry was proposed for such reaction:

Na4B20 5 + Na2C 03 <-► 2Na3B0 3 + C 02 ...... 1.3.a

The primary goal of this study to verify the whether this reaction follows the

above mentioned stoichiometry (1.3.a). It may also be valuable to study this reaction and

investigate its rate controlling parameters. Several separate decarbonization reactions

were carried out with sodium carbonate as excess reactant and sodium diborate as

decarbonizing agent. Identical experimental setup (Figure 3.1) was used to monitor this

reaction. Representative real time data, for the molten state reaction, such as the rate of

carbon dioxide evolution, temperatures, the rate and cumulative carbon dioxide

generation are shown in Figures 4.8 through Figure 4.15 and summarized in Table 4.3.

Table 4.3. Reaction Conditions and Results with Respect to Carbon Dioxide Generation during Molten Phase Reaction (Sodium Diborate as the Decarbonization Agent)

Average Avg initial Reactant Mole Fraction Cumulative Percent Closure Flow R ate Molten Phase Molten phase (approx.) Temperature Sodium Sodium D iborate C 0 2 Date Deg. C. C arbonate D iborate Produced L iters/m in (A pprox.) Moles Moles M oles

15-Sep-02 800 0.506 0.102 0.1678 0.107 95.12

17-Oct-02 800 0.508 0.055 0.0972 0.059 92.20

i9-Oct-Q2 800 0.508 0.055 0.0974 0.052 105.95

2 l-Sep-02 800 0.509 0.054 0.0965 0.053 103.00

22-Sep-02 800 0.507 0.109 0.1766 0.102 106.27

29-Oct-02 810 0.512 0.055 0.0965 0.056 97.67

31-Oct-02 810 0.509 0.109 0.1762 0.094 113.62

5-Nov-02 700 0.507 0.105 0.1720 0.082 121.91

10-Nov-02 800 0.504 0.105 0.1720 0.087 117.06

* 7/3/2002 850 0.504 0.105 0.1720 0.110 94.87 Avg. 104.77 Std. Dev. 10.16 * The purge tube end was improperly j inside the salt mixture

107

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidizcd Bed Reaction Sodium Carbonate (0.5065 moles) and Sodium Diborate (0.1021 moles). Diborate Mole Kraction=O.I677. September 15.2002

1200 0.12

1000 - 0.1

800 0.08 Cumulative Moles of Temperature (Degree 600 0.06 Carbon Dioxide Celsius) Released 400 0.04

200 0.02

2000 4000 6000 8000 Time (seconds)

Temperature Cumulative Carbon dioxide

Figure 4.8. Cumulative Carbon Dioxide and Temperature versus Time

Nonfltidred Bed Reaction S ottnn Carbonate (0.5065 nries) and Sodim Diborate (0.1021 males). Diborate Mole FractknFO.1677. Septenfcer 15.2002

1200 t

1000 wmmmmmwmmmmmmw : 0.00025 800- aooo^ a te of Carbon Dioxide T enperatue (Degree Released Gelsiie) 600 - ■ 0.00015 (moles/second) (X000I

200 0.00005

Time (seconds)

Tenperatwe — Rate of Carbon (loxide

Figure 4.9. Carbon Dioxide Generation Rate and Temperature versus Time

108

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NorfMjBEd Bed Reactions Socirm Carbonate (0.5082 moles) and Soduan Diborate (0.0547 molest. Diborate Mole RactiorFO.0972. Sente nirer 17,2002

1200

1000 0.05 000 Tenperatwe (Degree - - 0,04 Q m iative Moles Celsius) 600 Carbon Dioxide Released 400

200 0l01

1000 2000 3000 4000 Time (seconds)

Q m iative Carlxm (foxkle

Figure 4.10. Cumulative Carbon Dioxide and Temperature versus Time

Nonfludbcd Bed Reactions Sodaan Carbonate (0.50821 moles) and Soditan Diborate (0.0547 males). Diborate Mole FractiorrO.0972. Septenfcer 17.2002

1200 i T 0.0003

1000 0.00025

800 0.0002 Rate of Garbon Dioxide Temrerature (Degree Released Celsius) 600 0.00015 (moles/second)

400 0.0001

200 0.00005

tune (seconds) Tenjaeratiac — Rate of Carbon cioxide

Figure 4.11. Carbon Dioxide Generation Rate and Temperature versus Time

109

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Norlhlrfced Bed Reactions Sodirm Carbonate (0.5091 males) and Sodun Diborate (0.0544 moles). Diborate Mole Kracti(HF0.096& S erten t)er2 l. 2002

1200

1000 ftOS

800 okm Cimlalive Moles of Tenperatree 600 0.03 Carbon Dioxide (Degree Celsius) Released 400 0.02

200 aoi

0 1000 2000 3000 4000 line (seconds)

- Terrperatwe - Q m iative Carbon dksxkfc

Figure 4.12. Cumulative Carbon Dioxide and Temperature versus Time

Nonlliirfced Bed Reactions Sodren Carbonate (0.5091 moles) and Sodren Diborate (0.0544 moles). Diborate Mole lraction=0.(1965. Sentenber21.2002

1 2 0 0 -i T 0.0003

1000 0.00025

800 0.0002 T enperatiie (Degree Rate of Garbon Dioxide Celsius) 600 0.00015 Released (imles/second) 400 0.0001

200 0.00005

oe o m

Tenperatree — Rate of Carbon cioxide

Figure 4.13. Carbon Dioxide Generation Rate and Temperature versus Time

110

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonflindbed Bed Reactions Sod m i Carbonate (0.5074 nules) and Sodren Dihorate (0.1088iroles). Diborate Mole Fraction=0. 17658. Septenber22. 2002

1200 0.12

1000 0.1

800 0.08 Q m ia tiv e Males of Tenperatine 600 Carbon Dioxide (Degree Celsius) Released 0.04 200

0 2000 3000 4000 5000 60001000 Time (seconds) - Tenperatine - Q m iative Carbon doxide

Figure 4.14. Cumulative Carbon Dioxide and Temperature versus Time

Nonfliidized Bed Reactions Sodum Carbonate (0.5074 moles) and Sodium Diborate (0.1088moles). Diborate Mole ITactiomO.17658. Septeniier22.2002

1200 i T 0.0003

1000 0.00025

800 0.0002 Tenpeiature (Degree Rate of Caibon Dioxide Celsius) 600 0.00015 Released (moles/second) 400 0.0001

200 0.00005

oe es

Time (seconds)

— Rate of Carbon dioxideTenpeiature

Figure 4.15. Carbon Dioxide Generation Rate and Temperature versus Time

111

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. All the experimental results are presented in Appendix B. The reactants were

physically mixed and placed in the reactor in granular form. No special steps were taken

to bring the reactants within its reaction proximity in order to carry forward the solid-

state reaction.

The results demonstrate that solid phase reaction was absent for all the cases

where sodium diborate was used as the decarbonizing agent. This could be due to the

nonexistence o f the intimate contact between the reactants at molecular level. The

reaction commenced at a much lower temperature in the vicinity of the melting point

(622°C) of diborate. The reaction gathered momentum as the temperature was further

increased and went passed the melting point of sodium carbonate. It should be

mentioned that the reaction mechanism of sodium diborate based decarbonization

reaction was beyond the scope of the current work. However, it should be reiterated that

the sodium diborate based decarbonization reaction is assumed to be occurring in

multiple steps. This implies that the reaction is rather a combination of several

elementary reactions. The experimental activation energies (Eexp), obtained from

nonlinear regressions for various experimental runs are presented in Appendix E. It can

be observed that the correlation coefficients were greater than 0.98 for the data obtained

after the inflection point. The experimental activation energy (Eexp) obtained from the

data treatment may be the summation of several elementary reactions or the activation

energy of the rate limiting elementary reaction(s). The pre-exponential constant values

(A) demonstrated considerable variation with different experimental data set. The order

of reaction with respect to sodium diborate concentration was of order (n) 2 and the order

112

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of reaction with respect to carbonate concentration was of order (m) 1 and the

experimental activation energy (Eexp) was obtained in the range o f-30 kJ/mol.

The experimental activation energies (Eexp) from sodium diborate based reaction

showed consistent trend. Experimental activation energy (Eexp) was determined both

from the data obtained before the reaction reached the peak and data obtained after it

went passed the peak. Experimental activation energies (Eexp) from both groups were

compared and it was found out that the activation energies after the peak were

considerably lower than the group of data obtained right before the inflection point. This

could be the result of the heterogeneous nature of the reactant mixture or result of the

higher initial viscosity during the initial period of the reaction (before it reached the

inflection point) or the combination of both. In the high viscosity regime, the ions and

particles (even in the case o f non homogeneity) may have required higher momentum to

cross the barrier over the potential energy surface even when the system temperature

attained the melting point of sodium diborate however it remained below the melting

point of sodium carbonate. However, the correlation coefficients were comparatively

inferior to the other results obtained after the inflection point as evident from the results

presented in Appendix E.

Molten Phase Decarbonization Reaction and Stoichiometry with Sodium Diborate

Therefore, the consistent decrease in experimental activation energy (Eexp) right

after it crossed the inflection point may have resulted from the decrease in the overall

viscosity o f the molten mixture as the temperature passed the pooled melting point.

113

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. However, as the temperature is further increased the activation energy (Eexp) decreased to

some extent. This could have been the result of either due to the change in the dielectric

properties of reaction medium resulting from the formation (trisodium borate) and release

o f products (carbon dioxide) with concurrent depletion of the reactants and/ or increasing

sodium and monoborate ion concentration which might have restricted the movements of

electrons. Additionally, Bolhuis et al. [226-229] have pointed out that, in the condensed

phase, for any reacting system comprised of large polyatomic molecules or large clusters

containing solvent, supportive motions of the condensed phase molecules can create

multiple saddle points on the potential energy surface. Therefore, the increase in the

activation energy (Eexp) in this case could have been resulted from the change of the

trajectory of the transition state complex followed by crossing the barrier over a different

saddle point on the potential energy surface for the rate limiting elementary steps of

reaction (1.3a) and may have been convoluted with the effects of viscosity.

Moreover, diborate and carbonate ions are the reacting ions and since both are

negatively charged, the reaction rate should increase due to the primary salt effect as

demonstrated by equation 2.33. Moreover, it should be mentioned again that although

the change in viscosity (decrease) during the progress of the reaction with respect to

increasing temperature and as a result should have a positive effect on the rate of reaction

and nevertheless may have been eclipsed by the above mentioned factors. The depletion

o f the reacting ions and formation of monoborate ions may have decelerated the

movements of the reacting particles and thus may be one o f the factors that could have

also decreased the collision frequency, i.e., the probability of encounters between the

114

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ions. However, it should also be pointed out that viscosity vs. temperature dependency

could not be isolated or mined out from the current reaction.

It could be also seen from the observed from Table 4.3 that the pooled melting

point for these reactions was approximately 810 °C. However, additional study is

required to find out whether the pooled melting point varies with respect to the mole

fraction o f components in the reacting system. From the results presented in Table 4.3, it

could be established that the stoichiometry of reaction between sodium carbonate and

sodium diborate is indeed identical to reaction proposed by equation 1.3.a.

Reaction without Carbon Dioxide Sweeping (Sodium Diborate)

The reversible nature of this reaction 91.3a) was also observed from Figures 4.16 and

4.17. In this particular case, the experimental system failed to sweep away the released

carbon dioxide completely from the system that resulted in gradual decline in carbon

dioxide release and subsequently very insignificant release of carbon dioxide was

realized giving strong indication that the reaction (1.3.a) is also reversible in nature.

Such incident occurred due to the incomplete submergence of the sweep gas tube, deep

inside the reacting mixture. The level o f the reacting mixture dropped when it attained

complete homogeneity in the molten state and due to the disappearance of its void

volume. When this was observed additional steps were taken to push back the tube into

the molten mixture that resulted in further carbon dioxide release and completion o f the

reaction. This is one of the other vital findings of the study since it provides conclusive

evidence that even if the reactant mixture is well past its pooled melting point the

reaction may not proceed further and may only reach a dynamic equilibrium at any

115

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.5056 moles) and Sodium Dihorate (0.1042moles). Diborate Mole Fraction=Q.I720, July 03.2002

Tenperature (Degree 0.08 Cumilative Moles of Carbon Dioxide Celsius) 0.06 Released 0.04

1000 2000 3000 4000 5000 6000 7000 Time (seconds)

Temperature - Cumilative Carbon dioxide

Figure 4.16. Cumulative Carbon Dioxide and Temperature versus Time

Nonflujdbed Bed Reactions SodhanCarbonate (0.5056 malesl and Sociim Diborate (0.1042molesl Dflxnate Mole FractioiFO. 172(1 July 03.2002

<100016 0.00014 000012 0.0001 Date of Carbon Dioxide Tenperatine (Degree Released 0.00008 Celsius) (moles/second) (100006 0.00004 0 .0 0 0 0 2 2

Time (seconds)

- Tenperatine - Rate of Carbon doxide

Figure 4.17. Carbon Dioxide Generation Rate and Temperature versus Time

116

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. temperature unless the released carbon dioxide from the reaction is completely swept

away from the reactant mixture or converted to other reaction product(s). The

implication of this situation will be discussed in the context of recovery boiler reactions

and gasification reactions.

Causticization Reaction of Trisodium Borate

The causticizing reaction (1.4) of trisodium borate was proposed by Tran et al.

[50]. However, they did not focus on the equilibrium behavior of the reaction at normal

temperature as well as high temperature and pressure. Therefore, a comprehensive

discussion is indispensable on this topic. This is because; during this reaction trisodium

borate forms sodium metaborate and sodium hydroxide in the aqueous phase and sodium

metaborate and immediately becomes available for pulping at elevated temperature and

pressure. Subsequently it becomes available in the chemical recovery loop for

decarbonization reaction in the chemical recovery boiler. Therefore, it is necessary to

discuss the causticization reaction (1.4) in terms of the structural form o f sodium

metaborate to get a better understanding of the decarbonization reaction in the actual

chemical recovery process. The resulting sodium metaborate from causticizing reaction

(1.4) undergoes transformation and should lose its ring structure consistent with the

argument provided by Edwards et al. [2, 16, 51, 52] to form (B(OH)T) ion in the aqueous

phase because the aqueous solution of trisodium borate produces pH -13.1 which was

also found from the current study. Elsewhere, Edwards [16] has also pointed out that the

borate ions from sodium metaborate never assume BO 2 structure. Ingri and others have

117

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. also shown that the majority of the borate ion remains as B(OH) 4 ' ions only when the pH

of the system is above -12 [9-16].

Therefore, reaction (1.4) should be expressed in a different form to have a more

comprehensible understanding of its equilibrium behavior during pulping process and

decarbonization reaction in the chemical recovery boiler. As mentioned earlier, it was

also observed from the current pH measurement study that trisodium borate in aqueous

phase generates pH in the range of -13.1 at room temperature. Therefore, the final form

of borate ion from trisodium borate is going to be B(OH ) 4 ion after it undergoes

hydrolysis in the aqueous phase. The sequence of the reaction is as follows:

a) Trisodium borate initially forms orthoboric acid, B(OH ) 3 and three moles of

sodium hydroxide.

b) The resulting borate ion should transform into B(OH)4 ion, since the pH of

solution reaches around -13.1. The resulting compound from the

causticization/hydrolysis reaction is sodium tetrahydroxyborate, Na+[B(OH)] 4 _

or NaBC> 2 , 4 H2 O, which is also known as sodium metaborate [88].

c) Since the final pH of the solution from reaction (1.4) did not reach 14 at 23°C,

it is suggested that the reaction is reversible in nature.

Various workers also have independently predicted the presence of monoborate

and polyborate ions in the aqueous phase [9-16, 51, 52]. Based on the results of their

work it could be concluded that the existence of the equilibrium between B 4 C>5 (OH)4 2' ion

and tetrahydroxy borate B(OH) 4 ~ ion in the aqueous phase signifies buffering capability

in the vicinity of pH -12 at room temperature. Examples of such equilibrium

relationships are given by the following two equations [84]:

118

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 B(OH)4‘ <-► B40 5(0H )42' + 20H' + 5H20 ...... 2.2

Where, lo g £ = -7.34 ±0.109

3 B(OH)4' <-► B30 3(0H )52' - + OH' + 3H20 ...... 2.3

Where, log#- = -4.64 ±0.19

However, Mesmer et al. have presented a more comprehensive relationship

between various borate ions [9]. Moreover, in order to explain the equilibrium behavior

of borate ions at elevated temperature and pressure it is indispensable to follow Mesmer’s

work. Mesmer et al. have also pointed out, based on their work on B(OH)4-polyborate-

B(OH)3 equilibria, it could be concluded that the additional OH' ion could be obtained

from B(OH)4 ions at elevated temperature i.e., between 50 and 200°C, due to the shift in

equilibria towards the right for equations (2.2), (2.3) and similar equations mentioned by

Mesmer. They developed equilibrium quotient (Q) relationships between various borate

ions with respect to ionic strength (I) and temperature (7) [9]. Efforts were also taken to

estimate the heat of formation of B(OH)4' using MOP AC. The results are shown in

Appendix F.

Therefore, causticization reaction (in the aqueous phase) is given by reaction

equation (1.4) and therefore should be expressed in a different form. The causticization

reaction is more clearly shown in Figure 4.18. It shows that three moles of water is

required for the causticizing reaction instead of one as originally proposed by Tran et al.

[50]. Therefore, with two additional moles of water getting tied up with borates to form

B(OH)4' ion in the aqueous phase, and subsequently, as the solution becomes more

concentrated with hydroxyl ions, the solution should adjust its pH through its

thermodynamic constraints and the equilibrium relationship. However, the sign and the

119

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Na

O Na

Na H

pH>12 Na' OH

Figure 4.18. Stoichiometry and Reaction Steps of Causticization Reaction of Trisodium Borate in the Aqueous Phase

magnitude of the heat of reaction of causticization reaction shown in Figure 4.18 will

govern the equilibrium and therefore the pH of the solution until it reaches the critical

temperature of water [3].

However, such buffering capability or the potential to supply extra OH' ion is

possible only in the vicinity of pH 12 which as evident from Figures 2.5 and 2.6 [9-13,

91]. In actual practice, the bulk pH of the white/cooking liquor is never allowed to drop

below pH 12 to prevent redeposition of lignin; however, the pH inside the wood chips

may fall below 12 due to the unwanted neutralization reactions. Therefore, inside the

core of the wood chips, the presence of tetrahydroxy borate B(OH) 4 _ ions has the

potential to buffer the local liquor pH by supplying it with additional OH' ions from the

equilibrium reaction (2.2 and 2.3) which is also evident from Figure 2.7 [9].

120

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Implications in the Modified Continuous Cooking Processes

These borate equilibria presented by Mesmer et al.'s [9] work supports the claim

mentioned earlier that it may have a positive impact on causticization and hence speed up

delignification process. Modified cooking processes were developed among many other

reasons to cut down the mass transfer limitations of hydroxyl ions to the wood chips [66,

150]. Modified continuous cooking process demands continuously maintaining a flat,

low and yet threshold pH value not only in the bulk liquor but also inside the core of the

wood chips [151]. Therefore, borate equilibria at elevated temperature and pressure

could be effectively utilized in the modified continuous pulping processes to maintain a

constant hydroxyl concentration profile because in such processes, essentially, white

liquor is supplied and black liquor is removed at different points of the process on a

continuous basis to operate the process on the principles of a maintaining a constant OH-

concentration profile with lower dissolved lignin concentration throughout the reactor.

Moreover, early impregnation of wood chips with trisodium borate is also going to

further facilitate the process by reducing the mass transfer related transport of hydroxyl

ions [150]. Therefore, during the modified continuous cooking processes, at the

downstream side of the delignification, where black liquor is not saturated with dissolved

lignin only trisodium borate has the potential to maintain the pH of the liquor.

Additionally, in case of pH drop inside the wood chips, these borate ions might

also act as a bridge to transport OH' ion to the core of the wood chips to prevent lignin

redeposition on to the cellulosic fibers and expedite the delignification process.

121

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Moreover, B(OH)4' ions also have the potential to form complexes with polyhydric

alcohol and some carbohydrates with cA-hydroxy groups, thus helping to retain

additional hemicelluloses due to the demixing and gelation phenomena resulting from the

complexation phenomenon [78, 79]. Several such examples of these types of

complexation are shown in Figure (2.8) and Table 2.1. However, the hemicellulose

retention will be more likely to occur in the less harsh pulping processes such as modified

continuous cooking processes where hemicellulose degradation is minimal. Moreover, it

should be understood that the complexes from low molecular weight czs-hydroxy

polyhydric alcohols and other carbohydrates should stay in the black liquor and has the

potential to contribute to the increase in the viscosity rise of black liquor. Additionally, it

should also be pointed out that polysaccharinic acids are released as a result of the

polysaccharide degradation due to the presence of higher initial pH during batch

delignification. However, it should be mentioned that although some o f these acids

containing hydroxy groups (acid ligands) yet they may not form complexes with B(OH)4

ions due to the thermodynamic constraints imposed by higher pH of the liquor [18, 101].

It is also understandable that the presence of sodium metaborate is going to

contribute to the vapor pressure depression (boiling point rise) of the black liquor. This

may demand additional heat demand during black liquor evaporation. However, the

formation of borate and m-hydroxy sugar complexes may compensate for the boiling

point rise o f black liquor. As pointed out earlier, the B(OH)4 -polyborate-B(OH ) 3

equilibria is a function o f temperature and pressure. The degree of complex formation

will be dictated by the concentration of cA-hydroxy sugar, stereochemistry of the

organics, temperature & pressure of the system and pH of the black liquor. In the same

122

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. context, the degree of viscosity increase will also be controlled by the same parameters in

addition to the chain length of the czs-hydroxy sugar polymers.

Therefore, although the addition of sodium metaborate would result in higher

energy demand in fluid moving devices, evaporators, in addition to the higher sensible

heat demand to sustain the correct temperature of green, white and black liquor although

major part of the capital could be recovered because of the presence of trisodium borate

in the recovery boiler would increase the efficiency of the process. This is more

elaborately discussed in the following section.

Implications in the Chemical Recovery Process

As mentioned earlier, the organo-borate complexes formed with B(OH)4" ions

may significantly increase the viscosity of the black liquor. However, such complexes

may also play several crucial role in maintaining the stability and integrity of the black

liquor droplets due to the complexation with some m-hydroxy organics and subsequent

gel formation. It is also recalled that the bed reactions (equations 2.4-2.7) are essentially

gasification type reactions and some may require water vapor to carry forward water-gas

shift reaction. The water molecules which remain chemically tied up with borate ions

may get released at high bed temperature [92] and may synergistically contribute to the

shift reactions. Additionally, when some water molecules are chemically linked with

borate ions as water of crystallization it reduces the heat requirement for the multiple

effect evaporators for evaporation, although it is understandable that additional presence

of borate would increase the sensible heat requirement in the overall system. However,

123

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. this reduced evaporation requirement may significantly compensate for the additional

sensible heat because the heat of vaporization of water is very high compared to the

sensible heat demand for the sodium metaborate salt on a molar basis depending on the

concentration of borate ions present in the black liquor and the degree of boiling point

rise.

On other account, it was also observed from the results that the decarbonization

reactions take place both in the molten phase and apparently in the solid phase. Once the

system that melts, the reaction is extremely fast. However, it has been observed earlier

that inefficient removal of carbon dioxide could noticeably reduce the rate o f reaction.

This was observed when the purge tube was placed above the salt mixture. Here, the

carbon dioxide was not effectively removed which significantly decreased the reaction

rate, although the flow rate of the sweep gas was maintained in the range o f ~6 liters/min

as also in other cases.

This implies that the product formation rate would decrease in the presence of

high carbon dioxide concentration. Or in other words, the higher product yield may

demand higher residence time inside the boiler to compensate for the low yield if the

carbon dioxide is not efficiently removed from the bed of the recovery boiler. However,

it should be pointed out that the presence of carbon (char) on the smelt bed should act as

a sink for the carbon dioxide released from reaction (1.3) by converting it to carbon

monoxide and thus increasing the rate and extent of conversion. The potential for this

phenomenon to occur is significant because the char or carbonaceous matter present in

the char bed of the recovery boiler generally converts the carbon dioxide to carbon

monoxide in this reducing atmosphere [38, 59]. It also implies that such reaction may be

124

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. more feasible in the reducing zone of the recovery boiler. Since the surface of the smelt

bed temperature ranges from 900°C to 1100°C, the reaction (1.3) is viable in the recovery

boiler and the rate would be governed by conversion of carbon dioxide to carbon

monoxide. However, it should be understood that this conversion rate is much lower than

the rate of carbon dioxide generation obtained from the current study. Therefore,

additional steps are required to make reaction (1.3) commercially more attractive.

It should also be pointed out that the melting/freezing point behavior of trisodium

borate may have several connotations in the chemical recovery processes. Primarily, it

has the potential to lower the overall freezing point and pooled melting point of the smelt

bed in the conventional chemical recovery boiler resulting in additional contact between

other immobilized salts in the smelt bed and increased collision between the reactants

thereby increasing the rate of reaction. However, the bed temperature should always be

maintained above the threshold temperature (900°C) otherwise it may compromise the

rate o f reaction (equations 2.4-2.8). Moreover, it should be pointed out that the

depression of the pooled melting point of smelt bed would also depend on the mole

fraction of trisodium borate and unreacted sodium metaborate present in the system.

Moreover, for Babcock & Wilcox (B&W) recovery boilers the reduced pooled

melting point of smelt would result in the release of trapped, idle chemicals in the smelt

bed thus freeing up a considerable amount of capital and reactor space/volume for

additional black liquor processing inside the reactor even if the lower bed temperature

drops to 760°C (surface temperature ~ 1000-1200°C). The underutilized sensible heat

associated with such immobilized salt mixture also gets released when trisodium borate is

present in the system. Moreover, during the emergency shut down, when the idle salts

125

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. are present the cooling of the bed demands much longer time which together with the

inactive capital depresses the economics of the pulping process. The operation o f the

reactor bed around 800°C also allows minimal sodium vapor formation on the bed surface

and reduced hydrogen sulfide (H 2 S) formation. However, the reaction rates, NOx, and

dioxin destruction should also be taken into account when selecting the operating

temperature of the bed [157, 275-277].

On the other hand, for the case of CE boiler, the temperatures of the bed (surface

temperature ~1050°C) are never allowed to fall below the melting point o f the smelt as

the sulfate reduction takes place during the descent of the sprayed black liquor to the bed

surface. This facilitates the prevention of the drop in temperature inside the bed which

results in lower bed height in the reactor allowing lower down time during cooling and

lower inventory of the salts and thus making these types of boilers economically more

attractive [38, 59]. Therefore, when trisodium borate is present in the boiler it may allow

further lowering of the pooled melting point of the salt bed and thus may allow carrying

out the recovery boiler reactions also at a lower temperature without bed solidification.

Therefore, with trisodium borate present in the system the CE boilers could also be

operated at a slightly lower temperature with reduced sodium vapor generation. Thus, for

almost all of the recovery boiler type can be operated over a larger temperature gradient

resulting in more flexible operation.

A very important discussion is necessary on an important issue raised by Tran et

al. [61]. They proposed a different reaction pathway that for the rapid formation of

trisodium borate based on reaction (1.5). The major premise behind their conclusion

resulted from the state of the phase of the system which was found to be in the melt state

126

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. at a very lower temperature. However, it should be mentioned that it was found from the

current study that trisodium borate behaves as a melt because it has a low freezing point

~520°C and shows melt characteristics although it was below its melting point is 675°C.

This anomalous behavior of trisodium borate was not taken into account by Tran et al.

[61] and might have resulted in reaching this incorrect conclusion. Moreover, when

reaction (1.5) was examined it was observed that the reaction stoichiometry was not

balanced. The corrected stoichiometry is given by the following:

Na2C 03 (liq) + H20 (vap) + C(s) «-» 2NaOH liq)( + 2CO (gas)...... 4.1

The feasibility of reaction (4.1) was investigated by computing the Gibbs free energy

change at various temperatures using data obtained from NIST-JANAF Thermochemical

tables [279] and the results of these calculations are shown in Table 4.4.

Table 4.4 Gibbs Free Energy Change of Reaction (4.1) at Various Temperatures [278]

Gibbs Free Energy of Foramtion Gibbs Free Sodium Carbon Water Sodium Carbon Energy Change Temperature Carbonate Hydroxide Monoxide For Reaction (4.1) (Liquid) (Solid) (Vapor) (Liquid) (Gas) AG (kJ/mol) DegC kJ/mol kJ/mol kJ/mol kJ/mol kJ/mol annrox.

727 -850.159 0 -192.59 -282.478 -200.275 77.243

1027 -760.294 0 -175.774 -236.877 -226.509 9.296

1227 -684.221 0 -164.376 -198.087 -243.74 -35.057

Interpolation of the above data shows that the change in Gibbs free energy is zero

at approximately 1070°C. Although the A G «~ -35 kJ/mol for reaction (4.2) at 1227°C,

suggesting that reaction (4.1) is favorable above 1070°C, the large levels o f carbon

monoxide in the vicinity of the char bed should suppress reaction (4.1). Additionally,

since the maximum surface temperature of the char bed is between 900°C and 1100 °C,

127

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59], any sodium hydroxide present below the surface of the char bed would tend to

convert back to sodium carbonate as the temperature falls below 1070°C due to the

thermodynamic constraint (positive Gibbs free energy change). Therefore, the reaction

pathways (reaction 1.5 and 1.6 or 4.1) proposed by Tran et al. [61] is only possible if

both the temperature is above 1070°C and the carbon monoxide concentration is

negligible near the vicinity of the reaction. On the contrary, the carbon monoxide

concentration is large near the vicinity of the char bed and there exists a decreasing

temperature gradient from its surface (~1100°C) to its bottom (~760°C). Therefore, it is

proposed that the major conversion to trisodium borate within the char bed would follow

reaction (1.3) when the carbon monoxide concentration near the surroundings and the

temperature profile of the bed are considered.

Implications in the Gasification Processes

The chemical behavior of trisodium borate and sodium metaborate also makes

them potentially important chemicals in the gasification processes. It is recalled that the

usual gasification reaction requires carbon dioxide whereas the steam gasification

reactions requires water vapor and carbon dioxide. Decarbonization reaction has the

potential to supply carbon dioxide for such reactions in the gasification processes.

Additionally, the presence of alkali metal (sodium) in borate salt may promote catalytic

steam gasification. Moreover, the release of chemically tied water vapor from B(OH) 4 ~

ions and carbon dioxide from decarbonization reaction (1.3) makes it an attractive

chemical for high temperature gasification processes. However, it (reaction 1.3) may

128

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. impose a negative constraint on low temperature gasification processes because although

the decarbonization reaction (1.3) with sodium metaborate begins at low temperatures

(~600°C), apparently in the solid state, a closer examination of its melting and freezing

points reveal that it may form low melting point sodium diborate and low freezing point

trisodium borate as its products and thus may destabilize the fluidized bed low

temperature gasification processes by agglomerating the bed [276]. Several gasification

processes with more efficient energy recovery have been proposed with operating

temperature between 600 and 1000°C [152-164]. Above 850°C, most of the metaborate

should get converted to trisodium borate since the reaction occurs at reducing

environment [155]. However, the residence time of the salts inside the reactor and

conversion rate of carbon dioxide to carbon monoxide may dictate the yield of trisodium

borate from reaction (1.3). Another important point should be mentioned about the

environmental constraints; that is hydrogen sulfide (H 2 S), SOx and NOx which are formed

depending on the type of black liquor gasification processes, demand scrubbing of these

product (nuisance) gases, usually by caustic solution. Trisodium borate, which

spontaneously produces caustic upon hydrolysis, should reduce additional caustic

demand in such processes. However, additional research is needed to determine the

feasibility of decarbonization reaction during the black liquor gasification.

The total lattice potential energies of major compounds present in the recovery

boiler is shown in Table C.l of Appendix C. The calculated lattice energy of trisodium

borate is 14177.795 kJ/mol and is presented in Appendix C. Comparison of the lattice

energy values of other sodium compounds suggests that, at higher temperatures, sodium

vapor formation from trisodium borate is less likely to occur compared to other major

129

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. sodium compounds. Moreover, the result is also substantiated by the diffusivity values

provided by Cable. According to his result, the diffusivity values of borates varies from

9*19~9 to 5*1 O'8 cm2/s at 1000°C at different Na 2 0 /B 2 0 3 ratios [280].

The heat of formation for solid phase trisodium borate at 25°C is calculated by

Pauling’s equation [169]. The gas phase heat o f formation of trisodium borate by

MOP AC is also presented in Appendix F [281, 282]. The estimated heat of reaction of

reaction (1.3) presented in Table D.l of Appendix D suggests that the reaction becomes

endothermic ~ 900°C when sodium carbonate (solid) transforms into liquid phase.

However, it should be borne in mind that since sodium carbonate already remains in the

liquid state at 900°C; therefore, the additional heat consumption from the system by

reaction (1.3) would be minimal.

Finally, it should be remembered that in order to achieve the completion of the

decarbonization reaction (1.3) in the chemical recovery boiler and gasification processes

it is imperative to ensure conditions that would allow efficient sweeping of carbon

dioxide from the close proximity of the reaction. Such condition can only be

implemented when the smelt bed is integrated with a superheated steam line with

substantial degree of superheat associated with so that it may periodically act as a sweep

gas to remove carbon dioxide. It was earlier mentioned that the recovery boiler bed

reactions are essentially gasification reactions (equations 2.4-2.7) and therefore, such

condition would further facilitate steam gasification over carbon dioxide based

gasification on the smelt bed and compensate for heat loss through the endothermic

reactions taking place on the bed. This requirement will demand only minimal design

changes since the recovery boiler itself produces superheated steam.

130

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Determination of the “true” activation energy for these reactions was difficult due

to the following: (a) there are multiple elementary reactions occurring (solid and liquid

phase), (b) the reaction appears to be reversible when carbon dioxide is not continuously

swept away from the reactor (c) when the temperature reaches a steady state and the

system is fully melted, a substantial amount of metaborate has already reacted with

carbonate and only a small fractions o f metaborate remains in the system, (d) the

viscosity plays a role in the reaction rate, and (e) the energy associated with the reactants

movement through the viscous medium is convoluted with true activation energy of the

rate limiting reactions. Thus, determination of true activation energy becomes a daunting

task.

More simplistically, the point (a) implies that the probability of sodium diborate

formation during the solid phase reaction along with unreacted sodium metaborate may

have resulted in two parallel reactions which in turn, created problems in separating the

variables from these two parallel reactions. Furthermore, the seclusion, isolation,

detection or mining of viscous effects (point (e)) and elementary steps were the main

constraints behind finding the true reaction orders, pre-exponential constant (A) and true

activation energy (Ea) from a nonlinear fit. In such situation, it is essential to separate

these convoluted reactions by simultaneously collecting real-time concentration o f the

elementary reactions using isotopes and employing other data mining methods.

131

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER V

CONCLUSIONS AND RECOMMENDATIONS

The results from the decarbonization studies demonstrate that it has considerable

promise if the technology is correctly integrated into the conventional recovery boilers

and as well as high temperature gasification processes. The unique physical and

chemical features o f trisodium borate have the potential to compensate for the additional

energy and heat demand when sodium metaborate is integrated into the chemical

recovery processes for autocausticization. The following conclusions are made from the

current study:

a) A major finding in this study is that the reaction (1.3) starts in the solid phase

(~600 °C) and a considerable amount of metaborate reacts before it reaches

the melting points of the reactants. There is a strong indication that the

resulting borate salt product is a mixture of trisodium borate and sodium

diborate.

b) Reaction (1.3) is rapid as soon as it reaches its pooled melting point (~ 850°C)

and can easily account for the higher rate of reaction; no additional reaction

mechanism is required to support the high rate of reaction.

c) The extent of conversion reaction (1.3) is governed by the effective removal

of carbon dioxide from the system.

d) For the solid-state reactions, the extent of conversion varied in the opposite

direction with respect to the increase in mole fraction of sodium metaborate.

132

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. e) The stoichiometry of the reaction between sodium metaborate and sodium

carbonate reaction has been reconfirmed (1.3).

f) The decarbonization reaction (1.3a) involving sodium diborate began in the

vicinity of its melting point.

g) This reaction was rapid after it went passed its pooled melting point.

h) The rate of conversion and yield involving both sodium metaborate and

sodium diborate based decarbonization reactions demand efficient removal of

carbon dioxide.

i) Trisodium borate demonstrates incongruent melting/freezing point behavior.

j) The melting point of trisodium borate was found to be ~672°C.

k) The freezing point of trisodium borate was found to be ~510°C.

1) The stoichiometry of the reaction between sodium diborate and sodium

carbonate reaction has been reconfirmed (1.3a).

m) The causticization reaction (1.4) is reversible in nature and should be

expressed as shown in Figure 4.18.

The following recommendations are offered to successfully integrate the borate

based autocausticization technology into chemical recovery and gasification based energy

recovery processes on the basis of borate chemistry:

a) It is recommended and suggested that a superheated steam line (with

substantial degree of superheat associated with it) should be integrated deep

inside the molten smelt bed to periodically sweep out the carbon dioxide

133

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. released form the decarbonization reaction in order to quickly and efficiently

achieve complete conversion of the decarbonization reactions (1.3) inside the

smelt bed or gasification bed.

b) This would also simultaneously boost the water-gas shift reactions both near

the smelt bed and gasification reactors.

c) The bed temperature should always be maintained above 850°C.

d) Sodium borates could be used in alkali catalyzed; non-catalyzed high

temperature gasification processes because it has alkali metal associated with

it and it also has the potential to catalyze gasification reactions by supplying

CO2 and water vapor for shift reactions respectively.

e) The aqueous solution of borate salts can be used for scrubbing acid gases

(H2 S, SOx and NOx) produced during various types of gasification processes.

134

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. \

APPENDIX A

Figures of Sodium Metaborate based Decarbonization Reactions

135

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonflridbed Bed Reactions Sodnn Carbonate (0.4717 moles) and Sodim Metaborate (0.0821 males). M etaborate Mole Fraction=0.148. Septenber 18.2000

0.1 0.09 0.08 0.07 ( iilllativc 0.06 M oles o f Tenperature 0.05 Carbon doxide (Degree Celsius) 0.04 R e le ased 0.03 (moles/second) 0.02 0.01 0 1500 2000

Time (seconds)

- Tenperatue - O nnlative Carbon doxide

Figure A. 1. Cumulative Carbon Dioxide and Temperature versus Time

Nonfliadred Bed Reactions Sod tsn Carbonate (0.4717 males) and Sodnm Metaborate (0.0821 moles). M etaborate Mole Fhrction=0. 148. Septenber 18.2000

1000 T 900 800 700 600 - 0.0002 Rate of Cuban 500 Tenperature .Dioxide Released 0.00015 (Degree Celsiis) 400 (mnles/second) 300 0.0001 200 100 0.00005

0 500 1000 1500 2000 2500 3000 lim e (seconds) - Tenperatrtc - Rate of Carbon doxide

Figure A.2. Carbon Dioxide Generation Rate and Temperature versus Time

136

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Norihitfeed Red Reactions Sodun Carbonate (0.4255 males) and Sodun Metaborate (0.037 moles). IVfctaboiate Mole Ptaction=ft0814& October 19.2000

i z o o 0.045 0.04 0.035 0.03 0 0 2 5 Om Jatfve Moles oi Tenperatue 02 C arbon Dioxide (Degree Celsius) R eleased / 0.015 0.01 0.005 0 0 1000 2000 3000 4000 5000 6000 lim e (seconds)

♦ Tenperatue - a — G m iative Carbon doxide

Figure A.3. Cumulative Carbon Dioxide and Temperature versus Time

Norfludzed Bed Reactions Sodun Carbonate (0.4255 moles) and Sodun Metaborate (0.037 moles). M etaborate Mole Fraction=0.0814& October 19.2000

1200 0.00005 a000045 aooooi 0.000035 0.00003 ^ate tarhon Dioxide Tenperatue R eleased 0.000025 (Degree Gelsiis) (moles/second) 0.00002 aoooois n aooooi 0.000005 h ■» \e oe X XI X N O » ^ n » in *i m i/i 5ot o4 «* 4 o Xr- r~» » M oh er- m X. 2^ » » — n— « N orj tn rx m x t tr, ir, sC

lime (second)

- Tenperatue — Rate of Carbon doxide

Figure A.4. Carbon Dioxide Generation Rate and Temperature versus Time

137

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfliidbed Bed Reactions SodimCarbonate (0.4721 moles) and Sodun Metaborate (0.1890 moles'). Metaborate Mole Ftaction=0.286. October24.2000

0.18 0.16 0.14 0-12 QmJative Moles ol 0.1 Gartxm Dioxide 0.08 Released 0.06 0.04 0.02

0 2000 4000 6000 8000 Time (seconds)

Tenperatue Gmiative Carbon doxide

Figure A. 5. Cumulative Carbon Dioxide and Temperature versus Time

Nonfludbed Bed Reactions SodumCaifconate (0.4721 molest and Sodun Metaborate (0.1890 moles). M etaborate Mole FractiotFO.286. October24.2000

1000 - : 0.0005 800

Tenperatue (Degree , R eleased ^ , 6UU C c Is i i r ) -- 0.0003 (moles/second) 400 200 ^ 0 90

Tenperatue - Rate of Cartxai doxide

Figure A.6. Carbon Dioxide Generation Rate and Temperature versus Time

138

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nnrihitfeed Bed Reactions Sodun Carbonate (0.4851 moles) and Sodun Metaborate (0.0951 moles). Metaborate Mol Fraction=0.164. October28.2000

1200 0.12 1000 0.1

800 0.08 Qiireitative Moles of Tenperature (Degree 600 0.06 Carton Dioxide C elsius) R eleased 400 0.04

200 0.02 0 0 1000 2000 3000 4000 5000 lim e (seconds)

- Tenperatue - Qm Jadve Carton doxide

Figure A.7. Cumulative Carbon Dioxide and Temperature versus Time

Nnnfliirfced Bed Reactions SodumCaitonate (0.4851 moles) and Sodum Metaborate (0.0951 moles). Metaborate Mol FractiorF<).164. October28.2000

Tenperature (Degree Celsius)

Dme (seconds)

-♦-Tenperature — Rate of Carton doxide

Figure A.8. Carbon Dioxide Generation Rate and Temperature versus Time

139

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfliidaed Red Reactions Sodun Carhonalr (0.4717 moles) and Sodun Me taboratefQ.041 molest Metaborate Mol Fraction =0.086. Decenfcer 13.2000

1200 ft(M5 0.04 1000 (1035 800 a«3 Tenperatue (Degree 0.025 O m lative Moles of 600 Geisius) ft02 Carbon doxide R eleased 400 aois aoi 200 0.005 0 1000 2000 3000 4000 5000 6000 7000 lime (seconds)

- Tenperatue - Crm iative Carbon doxide

Figure A.9. Cumulative Carbon Dioxide and Temperature versus Time

N orihitfad Red Reactions Sodun Gaibonate (0.4717 moles) and Sodun Metaborate(0.04i moles). Metaborate Mol Fraction =0.086. Decenber 13.2000

1000

800 . Rate of Carbon Dioxide Tenperatue (Degree 600 R eleased G elsiis) (moles/second)

200 aooooi

. . . . _ .. -g'rroaotojttocjtb

Time (seconds)

- Tenperatue — Rate of Carbon doxide

Figure A. 10. Carbon Dioxide Generation Rate and Temperature versus Time

140

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Norfhidzed Bed Reactions SodunCarbonato (0.4243 males) and Sodun Me taboratetO.040 moles). Metaborate Mole Fractional.0861. Dc center 14.2000 1200 U.1H 1000

800 G m iative Moles of Tenperatue (Degree 0.02 Carbon Dioxide G elsiis) R eleased 400 200 0 0 2000 4000 6000 8000 H ire (seconds)

♦ Tenperatue Gmiative Carbon dioxide

Figure A. 11. Cumulative Carbon Dioxide and Temperature versus Time

Nonfltidzed Bed Reactions Sodun Carbonate (0.4243 moles) and Sodun Metaborate (0.040 moles), M etaborate M tie Fraction=0.0861, Deoeirfter 14.2000

1200 t 0.00016 1000 - 0.00014 0.00012 800 of Carbon Dioxide Tenperatue (Degree 600 0.00008 Released G e lsiis) (moles/second) + 0.00006 400 0.00004 200 - 0.00002

lim e (seconds)

-Tenperatue Rate of Carbon doxide

Figure A. 12. Carbon Dioxide Generation Rate and Temperature versus Time

141

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonflridzed Bed Reactions Sodum Carbonate (0.4667 males) and Sodum Metaborate (0.0999 moles). Metaborate Mol Fraction=0.1764. Decenfcer20.2000

1000 0.12 900 800 0.1 700 0.08 000 Gm iiative Moles ol Tenperature (Degree ! 500 0.06 Carbon Dioxide Oelsius) 400 G enerated 300 200 0.02 100

0 2000 4000 6000 8000 lime (seconds)

-Tenperature - Qmulative Carbon dioxide

Figure A. 13. Cumulative Carbon Dioxide and Temperature versus Time

Nonfliitfaed Bed Reactions Sodrmi Carbonate (0.4667 moles) and Sodum Metaborate (0.0999 moles). Metaborate Mol Fractiore=0.1764, D ecenber20.2000

1000 0.0004

900 0.00035 800 0.0003 700 0.00025 600 Tenperature (Degree Rate of Carbon Dioxide 500 0.0002 Released Celsius) 400 0 00015 (moles/second) 300 0.0001 200 100 0.00005

Time (seconds)

Tenperature — Rate of Caibon doxide

Figure A. 14. Carbon Dioxide Generation Rate and Temperature versus Time

142

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Noriharfced Bed Reactions Sodun Carbonate (0.4588 moles) and Sodun Metaborate (0.0996 moles). Metaborate Mole Fraction=0.178. Decenber23 .2000 1000 0.12 900 800 0.1

700 0.08 600 G m iative Moles ol Tenperatue (Degree ' 500 0.06 G ls h s ) 400 R e le ased 0.04 300 200 100

0 2000 6000 8000 10000 12000

Time (seconds)

- Tenperatue - Gmiative Carbon doxide

Figure A. 15. Cumulative Carbon Dioxide and Temperature versus Time

Nonfludzed Bed Reactions Sodun Carbonate (0.4588 moles) and Sodun M etaborate (0.0996 moles). Metaborate Mole Fraction=0.178. Decenber 23,2000 1000 7 ...... -...... — ...... - ...... T 0.0003

0.00025

0.0002

Tenperatue (Degree Rate of Gnbon Dioxide 0.00015 Released G e lsiis) (moles/second) 0.0001

oj««*r'r-hr-hr''e«in('«ONin n — -

Time (seconcb)

- Tenperatue — Rate of Carbon doxide

Figure A. 16. Carbon Dioxide Generation Rate and Temperature versus Time

143

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.5027 moles) and Sodium Metaborate (0.075 moles). M etaborate Mole l''ractHin=0.12426. October 27.2001

1200 0.09 4- 0.08 1000 - 0.07 800 - 0.06 0 Cumulative Moles of Temperature (Degree Carbon Dioxide Celsius) ^00 - 0.04 R eleased 400 0.03 - 0.02 200 - 0.01

500 1000 1500 2000 2500 Tune (seconds)

u u a ie C r o i x dTmperature Cumulative Carbon dioxideTem

Figure A. 17. Cumulative Carbon Dioxide and Temperature versus Time

Nonfhmdzed B ed Reactions Sodium Carbonate 10.5027 moles) and Sodium Metaborate (0.075 moles). M etaborate Mole Fraction=0.12426. October 27.2001

1200 T 0.0006

1000 0.0005

800 Dioxide Teiqxiature (Degree R eleased Celsius) 600 0.0003 (moles/second)

400 0.0002

200 0.0001

Time (seconds)

— Rate of Carbon doxide

Figure A. 18. Carbon Dioxide Generation Rate and Temperature versus Time

144

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX B

Figures of Sodium Diborate based Decarbonization Reactions

145

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfltitfacd Bed Reaction S odun Carbonate (0.5065 moles) and.Sodun Dihorate <0.1021 molesX Diborate Mole FractkarO.1677. Septenber 15. 2002 1200 1000 ai

800 0.08 G m iative Moles of Tenperatue (Degree^ '600 0.06 C arbon Dioxide C elsius) R e le ased 0.04 200

2000 6000 8000

G m iative Carbon doxide

Figure B .l. Cumulative Carbon Dioxide and Temperature versus Time

Nonftitfoed Bed Reaction Sodum Carbonate (0.5065 moles) and Sodun Dihorate (0.1021 moles). Diborate Mole FractionO. 1677. Septenber 15.2002 1200 1000 : 0.00025 800 Tenperatue (Degree o.ooo^ate Ca,^onI*ox*‘fe R eleased G elsiis) 600 -- 0.00015 (moles/second)

200 000005

Tenperatue - Rate of Carbon doxide

Figure B.2. Carbon Dioxide Generation Rate and Temperature versus Time

146

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfliidbed Bed Reactions Sodhm Gubonale (0.5082 moles ) and Sodlun Diborate (0.0547 moles ). Dihorate Mole Ftactjon=0.0972, Septenter 17.2002

1200 0.07

1000 ao6 0.05 800 Tenperatue (Degree 0,04 Gm iative Moles Celsius) 600 Cartnn Dioxide a 03 Released 400 0.02 200 aoi 0 0 0 1000 2000 3000 Time (seconds)

-♦—Tenperatue CunJative Carbon doxide

Figure B.3. Cumulative Carbon Dioxide and Temperature versus Time

Nonfliidbcd Bed Reactions S odU nC artxw ate (0150821 m ales) a n d ,S o d u n U flm ate (01(1547 moles), D ihorate M ole rVactk>n=0.(W72. Septenfcer 17.2002

1200 n T 0.0003

1000 - 0.00025

800 0.0002 Rate of Cariwn Dioxide Tenperature (Degree R eleased C elsius) 600 0.00015 (moles/second)

400 0.0001

200 0.00005

Time (seconds) Tenperatue — Rate of Caiton dkreide

Figure B.4. Carbon Dioxide Generation Rate and Temperature versus Time

147

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfludfoed Bed Reactions Sndhn Cartionate (0.5083 nales) and Sodim Dihorate (0.0548 molest. Dihorate Mole Iraction=0.0974. Septerrtier 19.2002

1200 0.06

1000 0lQ5

800 0.04 G m iative Moles Tenperatue 0.03 G irb o n Dioxide (Degree Celsius) R eleased 400 0.02

200 0.01 0 0 1000 2000 3000 4000 Time (seconds)

- Tenperatue Gm iative Carbon doxide

Figure B.5. Cumulative Carbon Dioxide and Temperature versus Time

Nonfltidzed Bed Reactions Sodun Carbonate (0.5083 moles) and Sodun Diborate (0.0548 moles). Dihorate Mole Fractional0974. Septenber 19.2002

1200 0.00035

1000

800

Tenperature 600 R eleased (Degree Celsius) 0.00015 (molcs/second) 400 0.0001 200

r r r~ o \ ^ vfi oe th ir , vD — X t~ h . 3C X c rN T t -C O' r* tn in oo

Time (seconds)

- Tenperatue - Rate of Carbon doxide

Figure B.6. Carbon Dioxide Generation Rate and Temperature versus Time

148

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfltidzed Bed Reactions Sodun Carbonate (0.5091 moles) and Sodun Diboiate (0.0544 moles). Diborate Mole Kraction=0.0965. Septenfccr21,2002

1200 0.06

1000 0.05

800 0.04 O m iative Moles of T e n p e ra tu e _ „.. . 600 0.03 O aibon Dioxide (Degree Celsius) R e le ased 400 002

200 0.01

0 1000 2000 3000 4000 Tine (seconds)

Tenperatue Omiative Cartnn doxide

Figure B.7. Cumulative Carbon Dioxide and Temperature versus Time

Nonfliidzed Bed Reactions Sodun Cartionate (0.5091 moles) and Sodun Diborate (0.0544 moles). Diborate Mole FractjMF=0.0965. Septenber21.2002

1200 T 0.0003

1000 0.00025

800 Tenperatue (Degree Rate of Carbon Dioxide G elsiis) 600 000015 R eleased (moles/second) 400 0.0001

200 0.00005

lim e (seconds)

Tenperatue - Rate of Carbon doxide

Figure B.8. Carbon Dioxide Generation Rate and Temperature versus Time

149

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NonfltidiBd Bed Reactions SodunCarhnnate (0J074 moles) and Sodun Diborate (0.1088ni)lesl. Diborate Mole Fraction=0.17658, Septenber 22.2002

1200

1000 0.1

800 0.08 O m iative Moles ol T en p eratu e 600 Carbon Dioxide (Degree Celsius) R eleased 400

200

0 1000 2000 3000 4000 5000 6000 lim e (seconds)

- T en p era tu re - O m iative Carbon doxide

Figure B.9. Cumulative Carbon Dioxide and Temperature versus Time

Nmihidbed Bed Reactions Sodun Carbonate (0.5074 moles) and Sodun Diborate (0. IQSSmoles). Diborate Mole Fraction=0.17658. Septenber 22.2002

12 0 0 -i

1000

800 0.0002 Tenperatue (Degree Rate of Carbon Dioxide CelsitB) 600 0.00015 Released (moles/second) 0.0001

200 0.00005

- Rate of Carbon doxide

Figure B.10. Carbon Dioxide Generation Rate and Temperature versus Time

150

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nnnfliadred Bed Reactions Sodun Carbonate (0.5121 moles) andSodunDiborate (0.0S47mplesl Diborate Mole FractioiFO.0965. October29.2002

1000 900 800 ' 0.05

700 0.04 600 O m iative Moles of Tenperature 500 0.03 C arbon D ioxide (D egree Celsius) 400 R e le ased 300 - 0.02 200 0.01 100

0 1000 2000 3000 Time (seconds)

- Tenperatue - O m iative Carbon doxide

Figure B. 11. Cumulative Carbon Dioxide and Temperature versus Time

IVotdluidzed Bed Reactions Sodun Carbonate (0.5121 moles) and Sodun Diborate (0.0547moles). Diborate Mole Fraction=0.0965. October 29,2002

1000 0.00035

0.0003

- 0.00025 Rate of Carbon Dioxide Tenperatue 0.0002 Released (Degree Celsits) ■ - a00015 (males/second) •=- 0.0001 - 0.00005 0 B « « N B in P o <*> * Time (seconds)

-Tenperatue - Rate of Carbon doxide

Figure B.12. Carbon Dioxide Generation Rate and Temperature versus Time

151

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonflrirfced Bed Reactions Sodun Carbonate (0.5088 moles) and Sodun Dihorate (0.1088 moles). Diborate Mole Fraction=0.176Z October31.2002

1UUU 0.1 0.09 0.08 0.07 0-06 Om iative Moles T e n p e ra tu e 0.05 Carbon Dioxide (Degree Celsius) 0.04 Released 0.03 0.02 0.01 0 0 1000 2000 3000 4000 5000 6000 7000

Time (seconds)

Tenperatue Gmiative Carbon doxide

Figure B. 13. Cumulative Carbon Dioxide and Temperature versus Time

Norfhidbed Bed Reactions Sodun Carbonate (0.5088 molest and Sodium Diborate (0.1088 moles). Diborate Mole FYaction=O.I762. October 31.2002

1000 a00025

aooo2

Tenperatute ft0

000005

S r 8 - S rsi * 1 in m lime (seconds)

- Tenperatue Rate of Carbon doxide

Figure B.14. Carbon Dioxide Generation Rate and Temperature versus Time

152

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfliidzed Bed Reactions Sodun Cartxmate (0.5071 moles) and Sodun Diborate (0.1053moles). Diborate Mole lbactioirO.1719, NoventierOS. 2002

O m iative Moles le n p e r a tu e Cartxm Dioxide (Degree CelsitE) 4 0 0 R eleased

1000 2000 3000 4000 5000 6000 7000

Time (seconds)

- Tenperatue - O m iative Cartxm doxide

Figure B. 15. Cumulative Carbon Dioxide and Temperature versus Time

Nonfliidzed Bed Reactions S odun Cartionate (0.5071 moles) and Sodum Diborate (0.1053moles), Diborate Mole FractiotFO.1719, Noyenfcer05.2002

900 0.0003

800 h 0.00025 700 —

600 0.0002 Tenperatue Rate of Cartxm Dioxide (Degree Celsius) 500 R eleased ;; ' (moles/second) 400

300 ao o o i

200 0.00005 100 \

0 J ______- 0 Ol 1/1 O V) M 1 /1 OO P S n » e j n pa sc n««pi»Spp tt oe m-h »i-i ram ps ® t'ti/i/i/i4«PTf Wl lim e (seconds)

- Tenperatue - Rate of Cartxm doxide

Figure B.16. Carbon Dioxide Generation Rate and Temperature versus Time

153

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonflukfccd Bed Reactions SnriuriCaibonate (0 l5037 moles') and SodhraDiborate (0.1046moles). Dihorate Mole Fiaction=O.I719. Novenfcer ig 2002

0.1 0.09 0.08 ao7 0.06 Tenperatue 500 a os O „ m iative . ... Moles .. (Degree Gelsiis) 400 Carbon Dioxide 0.04 Released 0.03 002 0.01 0 0 1000 2000 3000 4000 5000 6000 7000 lim e (seconds)

Tenperatue * Omiative Gabon dioxide

Figure B. 17. Cumulative Carbon Dioxide and Temperature versus Time

Nonftudbed Bed Reactions S o tiu n C arix m ate (Q.5CD7 m oles) an d Sodum Diborate (OLlQ46moles). D iborate M ole Fractkm=0.1719. NoventierlO. 2002

MMMMMMMWIMIMMM

600 0.0002 Tenperatue 5 0 0 Rate of Cartxm Dioxide (Degree OelsiiB) ^ 0.00015 Released „ _____ (moles/sccond) 300 0.0001

- 0 .0 0 0 0 5

N(nOV'eNON(f|l/)1C»«\OHNe« \e — (N M

lim e (seconds)

- Tenperature - Rate of Cartxm dioxide

Figure B.18. Carbon Dioxide Generation Rate and Temperature versus Time

154

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidzed Bed Reactions Sodum Carbonate (0.5056 moles) and Sodum Diborate (Q.I042mples), Diborate Mole Iraction=0.1720, July 03,2002

1000 0.14 900 - 0.12 800 700

600 0.08 Temperature (Degree 500 Carbon Dioxide C elsius) - 0.06 400 R e le ased 300 0.04 200 - 0.02 100 0 0 1000 2000 3000 4000 5000 6000 7000

Time (seconds)

• Tenperature - G im d ativ e C arbon doxide

Figure B. 19. Cumulative Carbon Dioxide and Temperature versus Time

Norihatiaed Bed Reactions Soduan Carbonate (0.5056 moles) andSodunDiborate tftl042mplesl. Diborate Mole F>actiorF0.1720. Jiiv 03.2002

1000 0.00016 900 1 aoooi4 800 0.00012 700 A OlOOOI 8 ^ of Carbon Dioxide 600 / i Tenperatue (Degree R eleased 500 / 0.00008 CfelsiiB) (moles/second 400 I\ 0.00006 300 J aooooi 200 100 P W 0.00002 0 0

0H 6 I® " A ~ A§ Time (seconcfc)

- Tenperatue - Rate of Carbon doxide

Figure B.20. Carbon Dioxide Generation Rate and Temperature versus Time

155

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX C

Calculation of Total Lattice Potential Energy of Trisodium Borate

156

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Calculation of Total Lattice Potential Energy of Trisodium Borate [271

Ionization Energies Element Energy, (eV/mol)

First Ionization Energy Na(I) 5.139

First Ionization Energy B (I) 8.298

Second Ionization Energy B (II) 25.154

Third Ionization Energy B (III) 37.93

Therefore, the lattice enthalpy can be calculated using Bom-Fajans-Haber cycle.

B (g) = B+ (g) + e' A Hi = 8.298 eV/mol

B+ (g) = B2+ (g) + e A Hu = 25.154 eV/mol

B2+ (g) = B3+ (g) + e A H„i = 37.93 eV/mol

B( g) = BJ+ (g) + 3e‘ A H,.m= 71.328 eV/mol

and,

Na (g) = Na+ (g) + e' A Hr^ 5.139 eV/mol

Therefore,

3Na (g) = 3Na+ (g) + 3e A Hi = 15.417 eV

157

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Electron Affinity Element Energy. kJ/mol

First O (EA) -142

Second O (2EA) 844

Therefore,

O (g) + e" = O' (g) A Heai=-142 kJ/mol

O’ (g) + e" = O2' (g) A Heaii — 844 kJ/mol

O (g) + 2 e‘ = Ol~ (g) AHea„=702 kJ/mol

3Na (s) + B (s) + 3/20 2 (g) = Na3 B 0 3 (s) A Hi/= -2064.95 kJ/mol

3Na (g) = 3Na (s) AH2/= -323.1 kJ

3Na+(g) + 3e’ = 3Na (g) A H3/= -1487.49 kJ

B(g) = B(s) A H4/= -562.748 kJ/mol

B 3 +(g) + 3e’ = B (g) A HS/= - 6887.292 kJ/mol

302’ = 30(g) +6 e’ AH6/= -2106 kJ

3Na (g) + B (g) + 30 (g) = Na3 B 0 3 (s) A H°R = -14179.0395 kJ/mol

Since, A H lattice A H r

Therefore, Lattice enthalpy for trisodium borate [Na 3 B 0 3 (s)],

A H iattiCe = 14179.039 kJ/mol

It should be pointed out that Konig and Hoppe [83] reported that the Madelung part o f the

lattice energy for trisodium borate as,

A H lattice =15480.8 kJ/mol

158

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The total lattice potential energy, U p o t , of crystalline salts, M aXb, is related to lattice

enthalpy by the following relationship:

A H lattice = Upo t+ [a{nM/2 - 2} + b{nx/2 - 2 }]RT

where nM and nx equal 3 for monoatomic ions, 5 for linear polyatomic ions and 6 for

polyatomic non linear ions.

Since BO3 '3 is a nonlinear polyatomic ion inside trisodium borate,

nM = 3 and nx = 6

and U p o t = A H lattice - [a{nM/2 - 2} + b{nx/2 - 2}] RT

= 14179.039 - [3 {3/2 - 2} + 1 {6/2 - 1}]*8.314*10‘3 * 298.16 \

= 14177.795 kJ/mol.

The total lattice potential energy (Bom-Fajans-Haber) of sodium carbonate, sodium

sulfate, sodium sulfide and sodium hydroxide are shown in Table C.l.

Table C.l Total Lattice Potential Energies of Major Compounds Present in the Recovery Boiler [27]

Total Lattice Compound Potential Energy Born-Fajans-Haber kJ/mol

Sodium Carbonate 2016 Sodium Sulfide 2203 Sodium Hydroxide 892 Sodium Sulfate 1938

Therefore, it may be concluded that Na+ formation is less likely to occur from trisodium

borate compared to the other sodium compounds shown in Table C.l.

159

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX D

Estimation of Heat of Reaction of Sodium Metaborate based Decarbonization Reactions

160

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Heat of Foramtion Estiamtion at Standard State (Pauling)

Electronegativity of Sodium xl := 0.93

Electronegativity of Boron x2 := 2.04

Electronegativity of Oxygen x3 := 3.44 nl := 3

Q1 := 4.184[23[3[(xl - x3 )2 + (x2 - x3)2]] - 26-nl]

AH1 := -Q1 3 kJ AH1 = -2.058 x 10j ------mol

Heat Capacity Estimation of Solid and Melt

Trisodium Borate Has Three Na Atom Attached to Trigonal Planar BQ3 Ion Solid State

Properties of Trisodium Borate (Kubaschewski et al. and Spencer)

Tm := 675 + 273.16 Kelvin

( 0 2 , 0 3 , 64) represents contibutions from three sodium ions

0 j represents contibutions from one B03 ion

n := 4 6 , := ~ 0 2 := 25.94 0 3 := 0 2 0 4 := 0 2

0 , = 55.6 03 = 25.94 0 4 = 25.94

161

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [im -lO 3[(0] + 3-02) + 4.7-n] - 1.25-n-105-Tm 2 - 9.05-n] a := (Tm-10_3 - 0.298)

a = 165.456

[25.6-n + 4.2-n- 105-Tm 2 - (0i + 3-02)] b := ((Tm -10 ' 3 - 0.298)) b = -44 .8 3 7

c := -4 .2 n

c = -16.:

Cp(Tm) := a + b-10 3-Tm + c-105-Tm 2

Where Cp represents standard state to melting point Cp(Tm) = 121.074

Tm { \ AH2 := (a + b- 10_3-T + c- 10 5-T“2j- ] '(25+273.16 ) kJ AH2 = 85.522 mol

Heat Capacity of Molten State (Spencer)

Noxygen := 3 Nboron := 1 Nsodium := 3

Ntotal := Noxygen + Nboron + Nsodium Ntotal = 7

cpmelt := 33.5-Ntotal -10

kJ cpmelt = 0.235 K-mol

162

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Estiamtion of Enthalpy Change at Melting (Moiseev et al.)

The follwoing equation is for estimating the entropy change of complex inorganic compoung at melting:

m := 2 n, := 3 represents 3 moles sodium oxide

n2 := 1 represents 1 mole boric oxide

AS! := (253.773 - 219.829) represents the entropy change of sodium (K-mol) oxide at its melting (1405.2 K)

AS2 := (162.757- 129.464) represents the entropy change of boric (K-mol) oxide at its melting (723 K)

ASmelt := z [ ( ni)-(ASi)]-10-3 kJ i = 1 ASmelt = 0.135 (K-mol)

Enthalpy Change at Melting Point)

AHmelt := ASmelt-Tm kJ AHmelt = 128.12 mol

Enthalpy Change from Solid State (Standard State) to Melting Point

AHsm := AH1 + AH2 + AHmelt AHsm = -1.845 x 10 kJ mol

163

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Enthalpy Change from Solid (Standard State) Elevated Temeprature Beyond Melting Point of Trisodium Borate

j := 727,827.. 1127

Tj := j + 273.16

AHTotal j := AHsm + cpmelt-[Tj - (675 + 273.16)]

T j = K AHTotal j = 1000.16 -1.832-103 1100.16 -1.809-103 1200.16 -1.786-103 1300.16 -1.762-103 1400.16 -1.739-103

The heat of reaction from equation (1.3) is tabulated in the following table.

Table D.l Heat of Reaction for Equation (1.3) at Various Temperatures

H eat o f F o ra n tio n H eat Sodium Sodium T risodium C arb o n o f Temperature C arb o n ate Metaborate B o rate D inoxide Reaction (1.3) Crystal to liquid Crystal to Liquid Crystal to liquid (G as) AH (kJ/mol) D eg C elsius kJ/m ol kJ/m ol kJ/m ol kJ/m ol ap p ro x .

727 -1115.60 -973.79 -1832.17 -394.62 -137.40

827 -1119.78 -97231 -1808.72 -394.84 -111.47

927 -1268.59 -1067.56 -1785.27 -394.05 156.83

1027 -1261.47 -1029.33 -1761.82 -395.05 133.93

1127 -1254.43 -1023.07 -1738.37 -395.26 143.88

164

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX E

JMP Results (Non-Linear Fit) from the Decarbonization Reactions When Sodium Metaborate and Sodium Diborate Were the Decarbonizing Agents

165

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.4717 moles) and Sodium Metaborate(0.041 moles) Cumulative Moles of Carbon dioxide Genreated December 13, 2000

From JMP

Phenomenological Rate Expression: Rate=A[Carbonate]m[Metaborate]ne('E/RT) Nonlinear Fitting Control Panel _ Second Deriv. Method _ Continuous Update _ Iteration Log _ Loss is -LogLikelihood Report Converged in the Gradient

Current Limit Alpha Iteration 1 60 0.050 Shortening 0 15 O Criterion 0.0003468697 0.0000001 D Criterion 0.9997602072 0.0000001 G Criterion 0.0000000347 0.000001 CL Criterion 7 0 . 0 0 0 0 1

Parameter Current Value Lock SSE

A 2919186.7655 0.0000000001 m 1 X 7 n 2 X E 60000 X

Solution SSE DFE MSE RMSE 0.0000000001 61 1.728e-12 0.0000013

Parameter Estimate ApproxStdErr Lower CL Upper CL A 2919186.7655 20598.5013 ? 7

m 1 0 ? ?

n 2 0 ? 7

E 60000 0 7 7

166

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0.9861 1.0000 Correlations model rate 1.0000 0.9861 1250 model Variable rate 12301190 Temp 1220 P l a t 12 lO 12 1200 Figure E.l:Figure Rate Model and vs. (Kelvin)Temperature

'rate mocfel " 0.000025 0 .0 0 0 0 3 5 0.000020 0.000015 0.000030 Nonfluidized BedReactions Sodium (0.4717 Carbonate moles) Sodiumand Metaborate (0.041 moles) December 13, 2000 \ 0 -J

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.4667 moles) and Sodium Metaborate (0.099 moles). Metaborate Mol Fraction =0.1764, December 20, 2000

From JMP

Phenomenological Rate Expression: Rate=A [Carbonate]"1 [Metaborate] ”e('E/RT) Nonlinear Fitting Control Panel _ Second Deriv. Method _ Continuous Update _ Iteration Log _ Loss is -LogLikelihood Report Converged in the Gradient

Current Limit Alpha Iteration 1 60 0.050 Shortening 0 15 O Criterion 0.0000034087 0.0000001 D Criterion 0.0196306321 0.0000001 G Criterion 0.0000000003 0.000001 CL Criterion ? 0.00001

Parameter Current Value Lock SSE m 1 X 0.0000000017 n 2 X ? E 60000 X A 2941332.5871 _

Solution SSE DFE MSE RMSE 0.0000000017 76 2.258e-ll 0.0000048

Parameter Estimate ApproxStdErr Lower CL Upper Cl m 1 0 ? ? n 2 0 ? ? E 60000 0 ?? A 2941332.5871 14861.2192 ? ?

168

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1180 Correlations 1170 Variable Variable rate rate model model 1.0000 0.9839 0.9839 1.0000 Temp P ic * 1150 1 1 4 0 Figure E.2: Rate Modeland vs. (Kelvin)Temperature Metaborate MolMetaborate Fraction =0.1764, December 20, 2000 1130

'rate 'mocfel 00013 . 0.00014 0 . 0 0 00.00010 1 0.00009 0.00008 0.00016 0 0.00007 0.00006 0.00015 0.00012 Nonfluidized Bed Reactions Sodium (0.4667Carbonate moles) Sodiumand Metaborate (0.099 moles), ON VO

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.4588 moles) and Sodium Metaborate (0.0996 moles). Metaborate Mole Fraction=0.178. December 23. 2000

From JMP

Phenomenological Rate Expression: Rate=A [Carbonate]m [Metaborate] ne("E/RT) Nonlinear Fitting Control Panel _ Second Deriv. Method _ Continuous Update _ Iteration Log _ Loss is -LogLikelihood Report Converged in the Gradient

Current Limit Alpha Iteration 1 60 0.050 Shortening 0 15 O Criterion 0.0040482987 0.0000001 D Criterion 0.6476395261 0.0000001 G Criterion 0.0000004048 0.000001 CL Criterion ? 0 . 0 0 0 0 1

Parameter Current Value Lock SSE m 1 X 0.0000000009 n 2 X ? E 30000 X A 100260.71432 _

Solution SSE DFE MSE RMSE 0.0000000009 8 6 1.087e-ll 0.0000033

Parameter Estimate ApproxStdErr Lower CL Upper CL m 1 0 ? ? n 2 0 ?? E 30000 0 ? ? A 100260.71432 336.442286 ? ?

170

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1.0000 0.9935 Correlations model rate 0.9935 1.0000 11701160 Variable model rate Temp 1150 Plot 1 1 4 0 Figure E.3: Rate and Model vs. Temperature (Kelvin) Model vs. Temperature and Rate E.3: Figure Metaborate Mole 23, December Fraction=0.178, 2000 Metaborate 1130 1 7

mocfel 'rate 00 0 0 00013 . . 0.00014 0 . 0 00.0 0 00 1 10 0.00009 0.00008 0 0.00006 0 . 0 0 00.00016 1 7 0.00015 0 0.00012 Nonfluidized Bed Reactions Sodium Carbonate (0.4588 moles) and Sodium Metaborate (0.0996 (0.4588moles), Metaborate Sodium moles) and Carbonate Sodium Nonfluidized BedReactions

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate 10.4255 moles) and Sodium Metaborate (0.03702 moles). Metaborate Mole Fraction=0.08003. October 19, 2000

From JMP

Phenomenological Rate Expression: Rate=A[Carbonate]m[Metaborate]ne( E/RT) Nonlinear Fitting Control Panel _ Second Deriv. Method _ Continuous Update _ Iteration Log _ Loss is -LogLikelihood Report Converged in the Gradient

Current Limit Alpha Iteration 1 60 0.050 Shortening 0 15 O Criterion 2.584939e-21 0.0000001 D Criterion 6.339461e-16 0.0000001 G Criterion 2.685818e-38 0.000001

CL Criterion 7 0 . 0 0 0 0 1

Parameter Current Value Lock SSE A 2670700.7415 0.0000000004 m 1 X 7 n 2 X E 60000 X

Solution SSE DFE MSE RMSE 0.0000000004 99 3.97e-12 0 . 0 0 0 0 0 2

Parameter Estimate ApproxStdErr Lower CL Upper CL A 2670700.7415 20585.3752 ? 7 m 1 0 ? 7 n 2 0 ? 7 E 60000 0 7 7

172

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13 lO 13 Correlations Variable Variable rate model model 0.9838 1.0000 rate rate 1.0000 0.9838 1270 Temp Pic* 1230 Figure Figure E.4: Rate Modeland vs. (Kelvin)Temperature Metaborate MoleMetaborate Fraction=0.08003, October 19, 2000 1210

'rate macfe! ' 0.000030 0.000015 0.000005 0.000040 0.000025 0.000045 0.000035 0.000020 0.0000lO 0-000050 Nonfluidized BedReactions Sodium (0.4255Carbonate moles) Sodiumand Metaborate (0.03702 moles),

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reaction Sodium Carbonate (0.5065 moles) and Sodium Diborate (0.1021 moles). Diborate Mole Fraction=0.1677. September 15. 2002

From JMP

Phenomenological Rate Expression: Rate=A [Carbonate]m [Dibor ate] ne(E/RT) Nonlinear Fitting Control Panel _ Second Deriv. Method _ Continuous Update _ Iteration Log _ Loss is -LogLikelihood Report Converged in the Gradient

Current Limit Alpha Iteration 2 60 0.050 Shortening 0 15 O Criterion 0 0 . 0 0 0 0 0 0 1 D Criterion 2.091143e-16 0.0000001 G Criterion 9.426146e-38 0.000001 CL Criterion ? 0 . 0 0 0 0 1

Parameter Current Value Lock SSE A 123521.99373 _ 0.0000000075 m 1 X ? n 2 X E 30000 X

Solution SSE DFE MSE RMSE 0.0000000075 80 9.371e-ll 0.0000097

Parameter Estimate ApproxStdErr Lower CL Upper CL A 123521.99373 814.432268 ? ? m 1 0 ? ? n 2 0 ? ? E 30000 0 ? ?

174

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Correlations 1130 1140 Variable Variable rate model model 0.9950 1.0000 rate rate 1.0000 0.9950 1120 11 lO 11 T e m p llOO Riot 1090 1080 Diborate Mole Fraction=0.1677, September 15, 2002 Figure E.5: Figure E.5: Rate Modeland vs. (Kelvin)Temperature "rate ‘m o c f e l 0.00010 0.00020 0.00015 0.00025 NonfluidizedBed Reaction Sodium (0.5065Carbonate moles) Sodiumand Diborate (0.1021 moles), /1 C 'O

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.50836 moles) and Sodium Diborate (0.05486 moles'). Diborate Mole Fraction=0.0974. September 19, 2002

From JMP

Phenomenological Rate Expression: Rate=A[Carbonate]m[Diborate]ne( E/RT) Nonlinear Fitting Control Panel _ Second Deriv. Method _ Continuous Update _ Iteration Log _ Loss is -LogLikelihood Report Converged in the Gradient

Current Limit Alpha Iteration 1 60 0.050 Shortening 0 15 O Criterion 9.926167e-20 0.0000001 D Criterion 2.530257e-16 0.0000001 G Criterion 6.482492e-38 0.000001 CL Criterion ? 0.00001

Parameter Current Value Lock SSE A 239639.015 _ 0.0000000149 mlX? n 2 X E 30000 X

Solution SSE DFE MSE RMSE 0.0000000149 152 9.785e-ll 0.0000099

Parameter Estimate ApproxStdErr Lower CL Upper CL A 239639.015 2355.70795 ? ? m l 0 ? ? n 2 0 ? ? E 30000 0 ? ?

176

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Correlations 1180 Variable Variable model model rate rate 1.0000 0.9860 0.9860 1.0000 1140 1160 Temp Riot 1120 llOO Diborate Mole Fraction=0.0974, September 19,2002 Figure E.6: Rate Model and vs. (Kelvin)Temperature 1080 m odi rate 0.00020 0.00015 0.00010 0.00005 Nonfluidized Bed Reactions Sodium (0.50836Carbonate moles) Sodiumand Diborate (0.05486 moles),

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.5074 moles) and Sodium Diborate (0.1088 moles'). Diborate Mole Fraction=0.1765, September 22. 2002

From JMP

Phenomenological Rate Expression: Rate=A[Carbonate]m[Diborate]"e(‘E/RT) Nonlinear Fitting Control Panel _ Second Deriv. Method _ Continuous Update _ Iteration Log _ Loss is -LogLikelihood Report Converged in the Gradient

Current Limit Alpha Iteration 2 60 0.050 Shortening 0 15 O Criterion 2.481542e-20 0.0000001 D Criterion 3.289077e-16 0.0000001 G Criterion 1.731169e-37 0.000001 CL Criterion ? 0.00001

Parameter Current Value Lock SSE A 83920.996051 _ 0.0000000051 mlX? n 2 X E 30000 X

Solution SSE DFE MSE RMSE 0.0000000051 189 2.694e-ll 0.0000052

Parameter Estimate ApproxStdErr Lower CL Upper Cl A 83920.996051 344.354877 ?? M 1 0 ??

n 2 0 ? ?

E 30000 0 ??

178

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Correlations Variable Variable rate model rate rate model 1.0000 0.9906 0.9906 1.0000 Temp Riot 1120 1140 1160 1180 1200 llOO Figure E.7: Figure E.7: Rate Model and vs. (Kelvin)Temperature Diborate Mole Fraction=0.17658, September 22, 2002 1080 — — — model "rate O .O O O l V 0.00016 ~ — 0.00015 ~ 0.00014 — 0 . 0 0 0 1 1 0.00009 ~ 0.00008 — 0 . 0 0 0 1 0 0.00013 — 0.00012 0.00007 — 0.00006 — 0.00005 — NonfluidizedBed Reactions Sodium (0.5074Carbonate moles) Sodiumand Diborate (0.1088 moles),

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate ('0.5082 moles) and Sodium Diborate (0.0547 moles). Diborate Mole Fraction=0.0972, September 17. 2002

F r o m J M P

Phenomenological Rate Expression: Rate=A[Carbonate]m[Diborate]ne( E/RT)

N onlinear Fitting C ontrol Panel

_ Second D eriv. M ethod

_ C ontinuous U pdate

_ Iteration L og

__ Loss is -L ogL ikelihood

R e p o r t

C onverged in the G radient

Current Limit Alpha

I t e r a t i o n 1 6 0 0 . 0 5 0 S h o r t e n i n g 0 1 5 O C riterion 0 0.0000001

D C riterion 3.047088e-18 0.0000001

G Criterion 1.096609e-41 0.000001

C L C riterion ? 0.00001

Parameter Current Value Lock SSE

A 309296.11076 0.000000004

m 1 X ?

n 2 X

E 3 0 0 0 0 X

S o l u t i o n

SSE DFE MSE RMSE

0.000000004 68 5.835e-ll 0.0000076

P a r a m e t e r Estimate ApproxStdErr Lower CL Upper CL

A 309296.11076 2173.98729 ? ?

m 1 0 ? ? n 2 0 ? ?

E 30000 0 ? ?

1 8 0

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

1150 Correlations rate model 1.0000 0.9905 0.9905 1.0000 1140 model Variable rate 1130 1120 Temp R lc * 11 lO 11 1 1 OO 1 1 1090 Diborate Mole Fraction=0.0972, September 17,2002 Figure E.8: Rate andModel vs. Temperature (Kelvin) 0.00020 0.00010 0.00005 0.00025 + x rate model Nonfluidized BedReactions Sodium Carbonate (0.5082 moles) and SodiumDiborate (0.0547 moles), o o

From JM P (B efore the Inflection Point)

Phenomenological Rate Expression: Rate=A[Carbonate]"1 [Diborate]ne("E/RT)

N onlinear Fitting C ontrol Panel

_ Second D eriv. M ethod

_ C ontinuous U pdate

_ Iteration L og

_ Loss is -LogLikelihood

R e p o r t

C onverged in the G radient

C u r r e n t Lim it Alpha

I t e r a t i o n 1 6 0 0 . 0 5 0

Shortening 0 1 5

O C riterion 0 0.0000001

D C riterion 1.401945e-16 0.0000001

G C riterion 2.653065e-39 0.000001

C L C riterion ? 0.00001

P a r a m e t e r C urrent V alue Lock SSE

m 1 X 0.000000001

n 2 X ?

E 5 0 0 0 0 X

A 204599.03712

S o l u t i o n

SSE DFE MSE RMSE

0.000000001 6 3 1 . 5 7 e - l l 0 . 0 0 0 0 0 4

P a r a m e t e r E s t i m a t e A pproxStdErr L o w e r C L U p p e r C L

m 1 0 ? ? n 2 0 ? ? E 5 0 0 0 0 0 ? ?

A 204599.03712 2 2 0 6 . 6 9 7 9 1 ? ?

1 8 2

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Correlations 1030 1020 Variable Variable rate rate model model 1.0000 0.7895 0.7895 1.0000 1 0 1 0 Temp lOOO Riot 980 Diborate Mole Fraction=0.1677, September 15,2002 Figure E.9: Rate andModel vs. Temperature (Kelvin) "rate 'mocfel 0.000050 0.000045 0.000060 0.000040 0.000035 0.000055 (Before the Inflection Point) NonfluidizedBed Reaction Sodium Carbonate (0.5065 moles) and SodiumDiborate (0.1021 moles), oo

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.5082 moles') and Sodium Diborate (0.0547 moles'). Diborate Mole Fraction=0.0972, September 17. 2002

From JM P (B efore the Inflection Point)

Phenomenological Rate Expression: Rate=A[Carbonate]m[Diborate]ne('E/RT)

N onlinear Fitting C ontrol Panel

_ Second D eriv. M ethod

_ C ontinuous U pdate

_ Iteration Log

_ Loss is -LogLikelihood

R e p o r t

C onverged in the G radient

Current Limit Alpha

Iteration 1 60 0.050

S h o r t e n i n g 0 1 5

O C riterion 0.0003347799 0.0000001

D C riterion 0.7068188147 0.0000001

G C riterion 0.0000000335 0.000001

C L C riterion ? 0.00001

P a r a m e t e r Current V alue Lock SSE

m 1 X 0.0000000003

n 2 X ?

E 1 0 0 0 0 0 X

A 195190063.07 _

S o l u t i o n

SSE DFE MSE RMSE

0.0000000003 61 4.18e-12 0.000002

Parameter Estimate ApproxStdErr Lower CL U p p e r C L ml 0 ? ? n 2 0 ? ?

E 100000 0 ? ?

A 195190063.07 1541596.19 ? ?

1 8 4

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Correlations Variable Variable rate rate model model 1.0000 0.9272 0.92721.0000 Temp P ic * Diborate Mole Fraction=0.0972, September 17, 2002 Figure E.10: Rate andModel vs. Temperature (Kelvin) 955 960 965 970 975 980 985 990 995 lOOO mocfel rate 0.000040 0.000035 0.000030 0.000025 0.000020 (Before the Inflection Point) NonfluidizedBed Reactions Sodium Carbonate (0.50821 moles) and Sodium Diborate (0.054732moles),

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.5082 moles) and Sodium Diborate ('0.0547 moles). Diborate Mole Fraction=0.0972. September 17, 2002

From JM P (B efore the Inflection Point)

R esults not show n due to poor correlation coefficient.

1 8 6

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nonfluidized Bed Reactions Sodium Carbonate (0.5074 moles') and Sodium Diborate (0.1088 molest. Diborate Mole Fraction=0.17658. September 22.2002

From JM P (B efore the Inflection Point)

Phenomenological Rate Expression: Rate=A[Carbonate]m[Diborate]ne( E/RT)

N onlinear Fitting C ontrol Panel

_ Second D eriv. M ethod

_ Continuous U pdate

_ Iteration Log

_ Loss is -LogL ikelihood

R e p o r t

C onverged in the G radient

Current Limit Alpha

Iteration 1 60 0.050

Shortening 0 15

O Criterion 0.0040973419 0.0000001

D Criterion 0.6994044438 0.0000001

G Criterion 0.0000004097 0.000001

CL Criterion ? 0.00001

Parameter Current Value Lock SSE

m 1 X 0.0000000083

n 2 X ?

E 2 2 0 0 0 0 X

A 4.6687843el4 _

S o l u t i o n

SSE DFE MSE RMSE

0.0000000083 63 1.31 le-10 0.0000114

P a r a m e t e r E s t i m a t e ApproxStdErr Lower CL Upper Cl

m 1 0 ? ? n 2 0 ?? E 220000 0 ? ?

A 4.6687843el4 5 . 8 4 0 0 3 e l 2 ? ?

1 8 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

1.0000 0.9741 Correlations rate model 0.9741 1.0000 lOOO lOOO 1010 1020 model Variable rate Temp Flat 950 980 Diborate Mole Fraction=0.17658, September 22, 2002 Figure E .ll: Rate and Model vs. Temperature (Kelvin)

"rate ' mo cfel mo ' 0.00020 0.00015 0.00010 0.00005 (Before the Inflection Point) NonfluidizedBed Reactions Sodium Carbonate (0.5074 moles) and SodiumDiborate (0.1088 moles), o o o o

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A P P E N D I X F

H eat of Form ation R esult of Trisodium B orate and B (O H ) 4_ Ion from M O P A C

C alculation

1 8 9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Thermochemical Results for Trisodium Borate from MOPAC (AMI) at Elevated Temperature ■t. -I- .t. >l. .1. -t- ^ -la -t- —I. -I. -I- -I- -l< -la aL -L ala —fa —la -I- —fa —la —la —la -I# —la —la —la -la -I- —la —la —la —la —la4 * —la ^ ^ - 1* 4 a it -la -la -t -la -la —la —la —la -la 4 f ^ —la —la —la —la —la —la -la —la 4 - —la -la -la —la —la a|% aj% ap 5J- a|- ap aj— ap ^ ^ aj— a|- a[« a|- ap ^ ^ ap ^ ^ î ^ ap ap ap ^ ^ ^ ^ ap ap ap ^ ap ^ ^ ap ap ap ap ^ ^ ap ap ip ip î ^ ^ ap ^ ^ ^ î ^ ap ap ^ ap ^ ap a^ ap î ^

** FRA N K J. SEILER RES. LAB., U.S. A IR FORCE ACADEM Y, COLO. SPGS., CO.

8 0 8 4 0 * *

AM I CALCULATION RESULTS

* MOPAC: VERSION 6.00 CALC'D. 24-May-02

* GEO-OK - OVERRIDE INTERATOM IC DISTANCE CHECK

* GRAPH - GENERATE FILE FOR GRAPHICS

* T= -A TIME OF 24.0 HOURS REQUESTED

* DUM P=N - RESTART FILE W RITTEN EVERY 60.0 M INUTES

* FORCE - FORCE CALCULATION SPECIFIED

* AM I - THE AM I HAM ILTONIAN TO BE USED

* NOINTER - INTERATOM IC DISTANCES NOT TO BE PRINTED

* NOXYZ - CARTESIAN COORDINATES NOT TO BE PRINTED

* THERM O - THERM ODYNAM IC QUANTITIES TO BE CALCULATED

* ROT - SYM M ETRY NUM BER OF 3 SPECIFIED

0 0 B Y 1 0 0

AM I T=24.0H DUM P=60.0M NOXYZ NOINTER GRAPH GEO-OK FORCE

TH ERM O (200,600,10) +

R O T = 3

M O PA C C alculation from Cerius2

ATOM CHEMICAL BOND LENGTH BOND ANGLE TW IST ANGLE

NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES) (I) NA:I NB:NA:I NC:NB:NA:I NA NB NC

1 O * 2 B 1 . 3 4 7 9 0 1 * 3 O 1 . 3 4 7 8 4 120.01379 * 2 1 * 4 O 1 . 3 4 8 1 0 119.97309 * 179.88225 * 2 1 3 * 5 N a 2 . 2 9 4 1 4 119.45014 * -0.42161 * 3 1 2 * 6 N a 2 . 2 9 3 0 9 59.46676 *-179.40821 * 1 3 2 * 7 N a 2 . 2 9 2 4 1 89.47537 * -0.28954 * 4 2 1

B: (A M I): M .J.S. D EW AR, C. JIE, E. G. ZO EBISCH O RGA N OM ETALLICS 7, 513

( 1 9 8 8 )

1 9 0

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. O: (A M I): M .J.S. D EW A R ET AL, J. A M . CH EM . SOC. 107 3902-3909 (1985)

Na: (AM I): SODIUM -LIKE SPARKLE. USE W ITH CARE.

RHF CALCULATION, NO. OF DOUBLY OCCUPIED LEVELS = 12

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

HEAT OF FORMATION - -414.939297 KCALS/MOLE

INTERNAL COORDINATE DERIVATIVES

NUMBER ATOM BOND ANGLE DIHEDRAL

1 O

2 B - 0 . 1 2 6 4 3 9

3 O -0.078136 -0.004830

4 O 0.032737 -0.152215 -0.073126

5 N a - 0 . 0 5 2 0 1 4 0 . 0 2 2 4 5 2 - 0 . 0 9 3 6 5 8

6 N a -0.129891 -0.056678 0 . 0 4 9 5 8 9

7 Na -0.170005 -0.106322 -0.115911

GRADIENT NORM = 0.37399

TIM E FOR SCF CALCULATION = 0.08

TIM E FOR DERIVATIVES = 0.01

M OLECULAR W EIGHT = 127.78

PRINCIPAL M OM ENTS OF INERTIA IN CM (-l)

A = 0.059042 B = 0.059002 C = 0.029511

1 9 1

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PRINCIPAL M OM ENTS OF INERTIA IN UNITS OF 10**(-40)*GRAM -

C M * * 2

A = 474.113245 B = 474.433041 C = 948.537825

ORIENTATION OF M OLECULE IN FORCE CALCULATION

NO. A T O M X Y Z

1 8 -1.3480 0.0003 - 0.0022 2 5 - 0.0001 0 . 0 0 0 3 - 0.0022 3 8 0.6741 1.1674 - 0.0022 4 8 0 . 6 7 3 4 - 1 . 1 6 7 5 0.0002

5 11 2 . 6 4 9 6 0.0011 0 . 0 1 2 5

6 11 - 1 . 3 2 6 3 2.2932 -0.0226 7 11 - 1 . 3 2 2 8 -2.2945 0.0141

FIRST DERIVATIVES W ILL BE USED IN THE CALCULATION OF SECOND

DERIVATIVES

ESTIM ATED TIM E TO COM PLETE CALCULATION = 3.70 SECONDS

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 1 TIM E = 0.16 SECS, INTEGRAL = 0.16 TIM E LEFT: 86399.75

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=T0, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

1 9 2

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 2 TIM E = 0.16 SECS, INTEGRAL = 0.32 TIM E LEFT: 86399.59

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 3 TIM E = 0.16 SECS, INTEGRAL = 0.48 TIM E LEFT: 86399.43

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 4 TIM E = 0.16 SECS, INTEGRAL = 0.64 TIM E LEFT: 86399.27

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=T0, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

1 9 3

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 5 TIM E = 0.16 SECS, INTEGRAL = 0.80 TIM E LEFT: 86399.11

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

S T E P : 6 TIM E = 0.16 SECS, INTEGRAL = 0.97 TIM E LEFT: 86398.95

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 7 TIM E = 0.16 SECS, INTEGRAL = 1.12 TIM E LEFT: 86398.79

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

1 9 4

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT-10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

S T E P : 8 TIM E = 0.16 SECS, INTEGRAL = 1.29 TIM E LEFT: 86398.62

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SH IFT-10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 9 T IM E- 0.16 SECS, INTEGRAL = 1.45 TIM E LEFT: 86398.46

ALL CONVERGERS ARE NOW FORCED ON

SHIFT-10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SH IFT-10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 10 T IM E - 0.16 SECS, INTEGRAL = 1.61 TIM E LEFT: 86398.30

ALL CONVERGERS ARE NOW FORCED ON

SH IFT-10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 11 TIM E = 0.16 SECS, INTEGRAL = 1.77 TIM E LEFT: 86398.14

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 12 TIM E = 0.16 SECS, INTEGRAL = 1.93 TIM E LEFT: 86397.98

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=T0, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 13 TIM E = 0.16 SECS, INTEGRAL = 2.09 TIM E LEFT: 86397.83

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

1 9 6

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 14 TIM E = 0.16 SECS, INTEGRAL = 2.24 TIM E LEFT: 86397.67

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 15 TIM E = 0.09 SECS, INTEGRAL = 2.34 TIM E LEFT: 86397.58

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 16 TIM E = 0.16 SECS, INTEGRAL = 2.50 TIM E LEFT: 86397.42

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 17 TIM E = 0.16 SECS, INTEGRAL = 2.65 TIM E LEFT: 86397.26

ALL CONVERGERS ARE NOW FORCED ON

1 9 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 18 TIM E = 0.09 SECS, INTEGRAL = 2.74 TIM E LEFT: 86397.17

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 19 TIM E = . 0.16 SECS, INTEGRAL = 2.90 TIM E LEFT: 86397.01

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 20 TIM E = 0.16 SECS, INTEGRAL = 3.06 TIM E LEFT: 86396.85

ALL CONVERGERS ARE NOW FORCED ON

SHIFT=10, PULAY ON, CAM P-KING ON

AND ITERATION COUNTER RESET

STEP: 21 TIM E = 0.09 SECS, INTEGRAL = 3.15 TIM E LEFT: 86396.76

FORCE M ATRIX IN M ILLIDYNES/ANGSTROM

1 9 8

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 0 O 1 B 2 03 04 Na 5 Na 6

0 1 4 . 1 1 1 1 9 2 B 2 3 . 2 1 2 6 2 6 8 . 0 0 5 5 0 9

O 3 0.712685 3.213798 4.111795

O 4 0.713156 3.207386 0.712314 4.105623

N a 5 0.066002 0.232726 0.173843 0.172991 0 . 3 6 7 3 9 6

N a 6 0.174387 0.232947 0.173286 0 . 0 6 6 0 5 0 0.024254 0.368185

N a 7 0 . 1 7 3 5 2 5 0 . 2 3 3 0 4 7 0 . 0 6 6 0 5 5 0.174742 0.024273 0 . 0 2 4 2 7 7 0

N a 7

Na 7 0.368749

HEAT OF FORM ATION = -414.939297 KCALS/M OLE

ZERO POINT ENERGY 10.830 KILOCALORIES PER M OLE

T H E L A S T 6 VIBRATIONS ARE THE TRANSLATION AND ROTATION M ODES

THE FIRST THREE OF THESE BEING TRANSLATIONS IN X, Y, AND Z,

RESPECTIVELY

NORM AL COORDINATE ANALYSIS

R O O T N O . 1 2 3 4 5 6

8 8 . 7 3 7 1 1 88.98009 107.76231 126.51715 126.63210 242.57093

1 - 0.00022 -0.00069 -0.00033 0.02826 0.07007 - 0 . 0 0 2 6 4 2 - 0 . 0 0 1 9 3 0.00001 0.00057 0.06230 -0.02493 0 . 0 1 1 3 2

3 -0.31386 0.01423 0.13769 -0.00078 -0.00039 0 . 0 0 0 0 7

4 - 0 . 0 0 0 2 7 -0.00071 -0.00032 0 . 0 3 3 2 5 0.08258 -0.00081

5 - 0 . 0 0 0 6 6 0.00052 0.00062 0 . 0 8 2 8 0 - 0 . 0 3 3 2 0 - 0 . 0 0 0 3 9

6 - 0 . 0 0 1 0 8 -0.00005 0.16011 0 . 0 0 0 7 7 - 0 . 0 0 0 9 3 - 0 . 0 0 0 3 7

7 - 0 . 0 0 1 2 5 -0.00134 -0.00029 0 . 0 2 9 1 0 0 . 0 6 3 0 9 0 . 0 1 0 1 7

8 - 0 . 0 0 0 0 5 0.00092 0.00061 0.06979 -0.02419 - 0 . 0 0 4 7 5

9 0.16703 0.28057 0.14037 0.00076 0.00066 0 . 0 0 0 3 4

1 0 0 . 0 0 0 3 9 -0.00008 -0.00032 0 . 0 2 2 8 3 0 . 0 6 5 3 6 - 0 . 0 0 9 7 9

1 9 9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 - 0.00001 0 . 0 0 0 3 2 0.00061 0.06713 -0.03093 - 0 . 0 0 7 6 2 12 0.14390 -0.29471 0 . 1 4 0 2 9 0.00210 - 0 . 0 0 2 7 6 - 0 . 0 0 1 5 4

1 3 0.00106 -0.00077 0.00152 0.04170 0.10488 0 . 2 3 3 2 3

1 4 0 . 0 0 0 3 6 - 0 . 0 0 1 1 4 0 . 0 0 1 1 4 - 0 . 2 2 3 4 5 0 . 0 8 9 1 0 0 . 0 0 4 3 5

1 5 -0.10993 0.00489 -0.12274 0.00041 0.00092 0.00149

1 6 0.00041 0.00097 0.00107 -0.19871 .0.08444 -0.11949

1 7 0.00084 -0.00072 -0.00179 -0.03370 -0.15080 0 . 1 9 8 8 9

1 8 0.05220 -0.10435 - 0 . 1 2 1 8 6 -0.00113 0.00144 - 0 . 0 0 2 1 9

1 9 -0.00060 0.00160 -0.00179 0.08557 - 0 . 1 9 7 4 4 - 0 . 1 1 1 7 9

20 0 . 0 0 0 4 9 0.00074 -0.00088 0.07958 0 . 1 3 3 0 2 - 0 . 2 0 2 3 4 21 0 . 0 6 0 2 8 0 . 0 9 9 4 2 - 0 . 1 2 1 8 2 - 0 . 0 0 1 0 8 - 0 . 0 0 0 1 9 0 . 0 0 1 6 6

R O O T N O . 7 8 9 10 11 12

2 5 2 . 7 3 3 2 1 2 7 7 . 0 0 0 3 8 2 7 7 . 2 4 5 8 3 567.42563 567.69258 742.4

1 0.00059 -0.15399 -0.03568 -0.14806 0.07549 0 . 0 0 0 2 4 2 0.21462 0.02147 -0.09075 -0.12592 -0.24726 - 0.00001

3 -0.00172 -0.00059 0.00168 0.00013 0.00049 0 . 1 1 3 0 9

4 0 . 0 0 0 4 4 - 0 . 1 4 0 5 0 -0.03260 -0.10883 0.05551 0 . 0 0 0 2 5

5 - 0 . 0 0 0 0 7 0 . 0 3 2 4 3 -0.14109 0.05550 0 . 1 0 8 8 2 - 0 . 0 0 0 4 4

6 0.00002 - 0 . 0 0 0 8 7 0.00102 0.00023 0.00017 - 0 . 4 6 5 5 0

7 0.18631 -0.09925 -0.05237 0.23534 0.09566 - 0.00011 8 - 0 . 1 0 7 5 4 0 . 0 0 3 8 9 -0.14504 -0.14599 0.13647 - 0 . 0 0 0 1 9

9 0 . 0 0 1 6 5 - 0 . 0 0 1 5 3 0.00071 0.00050 -0.00009 0 . 1 1 3 1 0

10 -0.18558 -0.11328 0.00332 0.06124 -0.24681 - 0 . 0 0 0 3 7 11 -0.10734 0.05902 -0.13217 0.19632 -0.03788 0 . 0 0 0 6 3 12 0.00013 -0.00048 0.00066 -0.00029 - 0 . 0 0 0 1 7 0 . 1 1 3 1 6

1 3 - 0 . 0 0 9 6 4 0 . 1 9 0 9 5 0.04348 -0.02571 0.01300 0 . 0 0 0 0 6

1 4 0.07575 -0.00521 0.02230 0.00463 0.00899 0.00000

1 5 - 0 . 0 0 0 1 4 0 . 0 0 1 2 8 0.00020 -0.00013 0.00007 - 0 . 0 0 5 7 7

1 6 -0.06189 0.08152 - 0 . 0 5 8 2 6 - 0 . 0 1 6 8 3 - 0 . 0 0 0 5 4 0 . 0 0 0 0 3

1 7 -0.04509 -0.10838 0.13286 0.01823 0.01800 - 0 . 0 0 0 0 5

18 0.00007 0.00128 -0.00138 -0.00023 -0.00015 - 0 . 0 0 5 7 4

19 0.07040 0.04866 0.08908 -0.00964 0.01409 - 0 . 0 0 0 0 3

20 -0.03045 0.03963 0.16726 0.00366 0.02531 - 0 . 0 0 0 0 5 21 0.00002 - 0 . 0 0 0 3 4 - 0 . 0 0 1 4 1 0.00002 - 0 . 0 0 0 1 7 - 0 . 0 0 5 7 8

ROOT NO. 13 14 15 16 17 1 8

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1052.44446 1535.69892 1536.80953 0.00088 0.00044 0.00098

1 -0.25994 0.11895 -0.13720 0 . 1 3 3 6 9 0.00000 0.00000 2 0.00002 -0.01531 -0.01341 0.00000 0 . 1 3 3 6 9 0.00000 3 0.00003 0.00003 0.00001 0.00000 0.00000 - 0 . 1 3 3 6 9 4 - 0.00020 -0.29332 0.33916 0 . 1 3 3 6 9 0.00000 0.00000

5 0 . 0 0 0 3 6 0.33687 0.29533 0.00000 0 . 1 3 3 6 9 0.00000

6 -0.00078 -0.00065 - 0 . 0 0 0 1 4 0.00000 0.00000 - 0 . 1 3 3 6 9 7 0.13009 -0.01282 -0.09186 0 . 1 3 3 6 9 0.00000 0.00000

8 0 . 2 2 5 0 6 -0.06058 -0.14579 0.00000 0 . 1 3 3 6 9 0.00000 9 0.00003 0.00003 0.00000 0.00000 0.00000 - 0 . 1 3 3 6 9

10 0.13000 0.09193 0.00006 0.13369 0.00000 0.00000 11 -0.22532 -0.15156 -0.04022 0.00000 0 . 1 3 3 6 9 0.00000 12 0.00048 0.00024 0.00005 0.00000 0.00000 - 0 . 1 3 3 6 9

1 3 - 0 . 0 0 1 3 8 0.00378 -0.00437 0.13369 0.00000 0.00000 1 4 0.00001 0 . 0 0 4 2 7 0 . 0 0 3 7 4 0.00000 0 . 1 3 3 6 9 0.00000 1 5 - 0.00001 0 . 0 0 0 0 3 - 0 . 0 0 0 0 4 0.00000 0.00000 - 0 . 1 3 3 6 9

16 0.00069 0.00189 0.00540 0.13369 0.00000 0.00000

1 7 - 0.00121 -0.00544 0.00185 0.00000 0 . 1 3 3 6 9 0.00000

1 8 0.00000 0 . 0 0 0 0 6 0.00001 0.00000 0.00000 - 0 . 1 3 3 6 9

19 0.00069 -0.00559 -0.00113 0 . 1 3 3 6 9 0.00000 0.00000

20 0.00119 0.00105 -0.00567 0.00000 0 . 1 3 3 6 9 0.00000 21 - 0.00001 0.00001 0 . 0 0 0 0 6 0.00000 0.00000 - 0 . 1 3 3 6 9

ROOT NO. 19 20 21

■5.38835 -4.51718 - 4 . 9 0 2 7 4

1 0.00011 - 0.00021 - 0.00002 2 -0.00070 0.00076 -0.09469

3 - 0 . 0 6 4 6 1 0 . 1 2 9 6 2 0 . 0 0 0 6 6

4 0.00011 - 0.00021 - 0.00002 5 0.00020 0.00011 - 0.00001 6 0.00002 0 . 0 0 0 0 3 0.00000

7 -0.00067 0.00035 -0.08200

8 0 . 0 0 0 6 5 - 0.00021 0 . 0 4 7 3 5

9 0.13787 -0.00529 - 0 . 0 0 0 6 3

10 0 . 0 0 0 7 7 - 0 . 0 0 0 5 4 0 . 0 8 2 0 1 11 0.00043 -0.00033 0.04730

12 - 0 . 0 7 3 2 8 -0.12427 -0.00003

1 3 - 0 . 0 0 0 6 0 0.00120 - 0 . 0 0 0 0 7

1 4 0 . 0 0 0 6 3 - 0 . 0 0 1 9 1 0 . 1 8 6 1 2

15 0.12713 -0.25469 - 0 . 0 0 1 2 9

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 -0.00044 -0.00107 - 0 . 1 6 1 0 9

1 7 0 . 0 0 1 1 6 0.00179 -0.09317

1 8 0 . 1 4 3 7 5 0.24444 0.00006

1 9 0 . 0 0 0 8 5 0 . 0 0 0 2 5 0 . 1 6 1 1 8

20 -0.00215 - 0 . 0 0 0 0 8 - 0 . 0 9 2 9 2

21 -0.27088 0.01019 0 . 0 0 1 2 3

M ASS-W EIGHTED COORDINATE ANALYSIS

R O O T N O . 1 2 3 4 5 6

88.73711 88.98009 1 0 7 . 7 6 2 3 1 126.51715 126.63210 2 4 2 . 5 7 0 9 3

1 - 0 . 0 0 0 5 3 - 0 . 0 0 1 5 5 - 0 . 0 0 0 8 9 0.06794 0.16882 - 0 . 0 0 5 4 8

2 -0.00464 0.00003 0.00152 0.14975 - 0 . 0 6 0 0 6 0 . 0 2 3 4 7

3 - 0 . 7 5 3 2 3 0.03218 0.36799 -0.00189 -0.00095 0 . 0 0 0 1 5

4 -0.00052 -0.00132 -0.00071 0 . 0 6 5 6 9 0 . 1 6 3 5 5 - 0 . 0 0 1 3 9

5 -0.00131 0.00096 0 . 0 0 1 3 7 0.16362 -0.06575 - 0 . 0 0 0 6 7

6 -0.00214 -0.00009 0 . 3 5 1 7 4 0.00152 -0.00183 - 0 . 0 0 0 6 3

7 - 0 . 0 0 3 0 0 -0.00304 -0.00077 0.06996 0 . 1 5 2 0 1 0 . 0 2 1 0 9

8 - 0.00012 0.00207 0.00162 0.16776 -0.05829 - 0 . 0 0 9 8 5

9 0.40086 0.63428 0 . 3 7 5 1 7 0.00184 0.00158 0 . 0 0 0 7 1

10 0.00094 -0.00018 -0.00084 0.05487 0.15748 - 0 . 0 2 0 3 0

11 - 0.00002 0.00072 0.00164 0.16137 - 0 . 0 7 4 5 3 - 0 . 0 1 5 7 9

1 2 0 . 3 4 5 3 4 -0.66624 0.37494 0.00504 -0.00664 - 0 . 0 0 3 2 0

13 0.00304 -0.00208 0.00488 0.12015 0 . 3 0 2 9 2 0 . 5 7 9 4 9

14 0.00105 -0.00308 0.00364 -0.64390 0 . 2 5 7 3 4 0 . 0 1 0 8 2

15 -0.31625 0.01324 -0.39324 0.00118 0 . 0 0 2 6 5 0 . 0 0 3 7 0

16 0.00119 0.00263 0.00343 -0.57260 - 0 . 2 4 3 8 7 - 0 . 2 9 6 8 8

1 7 0 . 0 0 2 4 3 -0.00196 -0.00573 - 0 . 0 9 7 1 0 - 0 . 4 3 5 5 2 0 . 4 9 4 1 7

18 0.15017 -0.28277 -0.39042 -0.00326 0 . 0 0 4 1 5 - 0 . 0 0 5 4 5

19 -0.00172 0.00433 -0.00574 0.24659 - 0 . 5 7 0 2 2 - 0 . 2 7 7 7 5

2 0 0 . 0 0 1 4 0 0.00202 -0.00284 0.22930 0 . 3 8 4 1 8 - 0 . 5 0 2 7 2

21 0.17341 0.26940 -0.39029 -0.00313 -0.00054 0.00413

R O O T N O . 7 8 9 10 11 12

252.73321 277.00038 277.24583 567.42563 567.69258 742.41966

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 . 0 0 1 4 7 - 0 . 3 9 9 0 1 - 0 . 0 9 2 0 6 - 0 . 3 6 0 3 1 0 . 1 8 3 5 9 0 . 0 0 0 5 5 2 0 . 5 3 0 6 9 0 . 0 5 5 6 4 - 0 . 2 3 4 1 5 - 0 . 3 0 6 4 3 - 0 . 6 0 1 3 3 - 0.00002

3 - 0 . 0 0 4 2 5 - 0 . 0 0 1 5 4 0.00434 0.00031 0.00120 0 . 2 6 2 9 8

4 0 . 0 0 0 9 0 - 0 . 2 9 9 2 6 - 0 . 0 6 9 1 4 - 0 . 2 1 7 6 8 0 . 1 1 0 9 7 0 . 0 0 0 4 9

5 - 0 . 0 0 0 1 5 0 . 0 6 9 0 7 - 0 . 2 9 9 2 3 0.11101 0 . 2 1 7 5 4 - 0 . 0 0 0 8 3

6 0 . 0 0 0 0 4 - 0 . 0 0 1 8 5 0 . 0 0 2 1 5 0 . 0 0 0 4 5 0 . 0 0 0 3 5 - 0 . 8 8 9 7 5

7 0 . 4 6 0 6 7 -0.25717 -0.13511 0 . 5 7 2 6 9 0 . 2 3 2 6 5 - 0 . 0 0 0 2 6

8 - 0 . 2 6 5 9 0 0.01007 -0.37423 - 0 . 3 5 5 2 5 0 . 3 3 1 8 9 - 0 . 0 0 0 4 4

9 0 . 0 0 4 0 7 - 0 . 0 0 3 9 6 0 . 0 0 1 8 3 0.00121 - 0.00022 0 . 2 6 2 9 9

10 - 0 . 4 5 8 8 6 - 0 . 2 9 3 5 5 0 . 0 0 8 5 7 0 . 1 4 9 0 1 - 0 . 6 0 0 2 3 - 0 . 0 0 0 8 6 11 - 0 . 2 6 5 4 1 0.15293 -0.34101 0 . 4 7 7 7 4 - 0 . 0 9 2 1 2 0 . 0 0 1 4 7 12 0 . 0 0 0 3 3 -0.00124 0.00170 - 0 . 0 0 0 7 0 - 0 . 0 0 0 4 0 0 . 2 6 3 1 4

1 3 - 0 . 0 2 8 5 7 0 . 5 9 3 1 2 0 . 1 3 4 4 7 - 0 . 0 7 5 0 1 0 . 0 3 7 9 0 0 . 0 0 0 1 6

1 4 0.22452 -0.01619 0 . 0 6 8 9 8 0 . 0 1 3 4 9 0 . 0 2 6 2 1 0.00000

1 5 - 0 . 0 0 0 4 2 0 . 0 0 3 9 7 0 . 0 0 0 6 0 - 0 . 0 0 0 3 9 0.00020 - 0 . 0 1 6 0 7

1 6 - 0 . 1 8 3 4 4 0.25322 -0.18019 - 0 . 0 4 9 1 0 - 0 . 0 0 1 5 9 0 . 0 0 0 0 8

1 7 -0.13364 -0.33666 0 . 4 1 0 9 1 0 . 0 5 3 1 7 0 . 0 5 2 4 6 - 0 . 0 0 0 1 3

1 8 0.00021 0.00399 -0.00427 - 0 . 0 0 0 6 6 -0.00043 -0.01599

1 9 0 . 2 0 8 6 5 0.15116 0.27550 - 0 . 0 2 8 1 2 0.04108 -0.00009

20 - 0 . 0 9 0 2 6 0 . 1 2 3 0 9 0 . 5 1 7 3 0 0 . 0 1 0 6 6 0 . 0 7 3 7 8 - 0 . 0 0 0 1 5 21 0 . 0 0 0 0 5 - 0 . 0 0 1 0 6 - 0 . 0 0 4 3 8 0 . 0 0 0 0 5 - 0 . 0 0 0 4 9 - 0 . 0 1 6 1 2

ROOT NO. 13 1 4 1 5 1 6 1 7 1 8

1 0 5 2 . 4 4 4 4 6 1535.69892 1536.80953 0.00000 -0.00044 0.00116

1 - 0 . 5 7 7 1 9 0.27687 -0.31719 0 . 3 5 3 8 5 0.00000 0.00000 2 0 . 0 0 0 0 4 -0.03564 -0.03100 0.00000 0 . 3 5 3 8 5 0.00000

3 0.00007 0.00007 0.00002 0.00000 0.00000 - 0 . 3 5 3 8 5

4 - 0 . 0 0 0 3 7 - 0 . 5 6 1 1 8 0 . 6 4 4 5 0 0 . 2 9 0 8 6 0.00000 0.00000

5 0 . 0 0 0 6 6 0 . 6 4 4 5 1 0 . 5 6 1 2 1 0.00000 0 . 2 9 0 8 6 0.00000 6 - 0 . 0 0 1 4 3 -0.00125 -0.00026 0.00000 0.00000 - 0 . 2 9 0 8 6

7 0 . 2 8 8 8 7 -0.02983 -0.21237 0 . 3 5 3 8 5 0.00000 0.00000

8 0.49973 -0.14100 - 0 . 3 3 7 0 3 0.00000 0 . 3 5 3 8 5 0.00000 9 0.00008 0.00007 0.00000 0.00000 0.00000 - 0 . 3 5 3 8 5 10 0 . 2 8 8 6 5 0 . 2 1 3 9 7 0.00014 0.35385 0.00000 0.00000 11 - 0 . 5 0 0 3 1 -0.35276 -0.09299 0.00000 0 . 3 5 3 8 5 0.00000 12 0 . 0 0 1 0 8 0 . 0 0 0 5 5 0.00011 0.00000 0.00000 - 0 . 3 5 3 8 5

1 3 - 0 . 0 0 3 6 8 0 . 0 1 0 5 4 - 0.01211 0 . 4 2 4 1 7 0.00000 0.00000

1 4 0 . 0 0 0 0 3 0.01193 0.01037 0.00000 0 . 4 2 4 1 7 0.00000

15 -0.00003 0.00008 - 0.00012 0.00000 0.00000 - 0 . 4 2 4 1 7

16 0.00184 0.00528 0.01496 0 . 4 2 4 1 7 0.00000 0.00000

1 7 -0.00322 -0.01518 0.00511 0.00000 0 . 4 2 4 1 7 0.00000

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 8 0.00001 0 . 0 0 0 1 7 0 . 0 0 0 0 3 0.00000 0.00000 - 0 . 4 2 4 1 7

1 9 0 . 0 0 1 8 2 - 0 . 0 1 5 5 9 - 0 . 0 0 3 1 3 0 . 4 2 4 1 7 0.00000 0.00000

2 0 0 . 0 0 3 1 8 0 . 0 0 2 9 4 - 0 . 0 1 5 7 2 0.00000 0 . 4 2 4 1 7 0.00000 21 -0.00003 0 . 0 0 0 0 4 0 . 0 0 0 1 6 0.00000 0.00000 0 . 4 2 4 1 7

ROOT NO. 19 20 21

-5.38835 -4.51718 -4.90274

1 0 . 0 0 0 2 4 -0.00046 -0.00005 2 -0.00161 0.00165 -0.22560

3 -0.14943 0.28185 0.00156

4 0.00020 -0.00038 -0.00004

5 0 . 0 0 0 3 8 0.00020 - 0.00002 6 0 . 0 0 0 0 4 0 . 0 0 0 0 5 0.00000

7 -0.00155 0.00076 - 0 . 1 9 5 3 7

8 0.00150 -0.00046 0.11281

9 0.31889 -0.01150 -0.00150

10 0.00177 -0.00118 0.19539 11 0 . 0 0 0 9 9 - 0 . 0 0 0 7 2 0 . 1 1 2 6 9 12 - 0 . 1 6 9 4 9 -0.27022 -0.00007 13 -0.00166 0.00313 - 0.00020

14 0.00174 -0.00497 0.53154

15 0.35249 -0.66385 -0.00369

1 6 - 0.00122 -0.00280 -0.46006

1 7 0.00323 0.00466 -0.26609

1 8 0 . 3 9 8 5 6 0 . 6 3 7 1 4 0 . 0 0 0 1 6

19 0.00235 0.00066 0 . 4 6 0 3 2

20 - 0 . 0 0 5 9 7 - 0.00022 - 0 . 2 6 5 3 6 21 -0.75105 0.02656 0.00353 1

DESCRIPTION OF VIBRATIONS

VIBRATION 1 ATOM PAIR ENERGY CONTRIBUTION

RADIAL

FREQ. 88.74 O 1 - Na 7 22.4% (183.2%) 0.0%

T-DIPOLE 0.0396 O 1 - Na 6 22.3% 0.0%

TRAVEL 0.2115 0 1 - - B 2 20.9% 0.0%

RED. MASS 8.4956 O 3 - Na 5 7.3% 0.0%

2 0 4

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VIBRATION 2 ATOM PAIR ENERGY CONTRIBUTION

R A D I A L

FREQ. 88.98 O 4 - N a 7 18.3% (165.3%) 0.0%

T-DIPOLE 0.0252 O 3 - N a 6 1 6 . 8 % 0 . 0%

TRAVEL 0.2112 O 4 - N a 5 1 6 . 7 % 0 . 0 %

RED. M ASS 8.4904 B 2 — 0 4 1 6 . 7 % 0 . 0 %

B 2 — 0 3 1 5 . 1 % 0.0%

O 3 - Na 5 15.0% 0.0%

VIBRATION 3 ATOM PAIR ENERGY CONTRIBUTION

RADIAL

FREQ. 107.76 B 2 - Na 5 18.2% (213.3%) 0.0%

T-DIPOLE 5.1255 B 2 - Na 6 1 8 . 2 % 0. 0%

TRAVEL 0.1727 B 2 - Na 7 1 8 . 2 % 0. 0%

RED. M ASS 10.4892 0 1 - B 2 9 . 3 % 0 . 0 %

VIBRATION 4 ATOM PAIR ENERGY CONTRIBUTION

RADIAL

FREQ. 126.52 B 2 - N a 7 12. 0 % (186.2% ) 5 8 . 5 %

T-DIPOLE 2.0369 B 2 - Na 6 1 1 . 7 % 1 . 9 %

TRAVEL 0.1476 B 2 - Na 5 1 1 . 5 % 0 . 4 %

RED. M ASS 12.2372 0 1 - B 2 1 0 . 4 % 2 . 4 %

VIBRATION 5 ATOM PAIR ENERGY CONTRIBUTION

RADIAL

FREQ. 126.63 B 2 - Na 5 12.0% (185.4% ) 1 5 . 7 %

T-DIPOLE 2.0343 B 2 - Na 6 11.8 % 4 . 5 % TRAVEL 0.1475 B 2 ~ N a 7 1 1 . 5 % 0.1%

RED. M ASS 12.2341 B 2 - 0 3 11.0% 0.2%

V I B R A T I O N 6 ATOM PAIR ENERGY CONTRIBUTION

RADIAL

FREQ. 242.57 Na 5 - Na 6 13.8% (79.6% ) 100.0% T-DIPOLE 0.0304 Na 5 - Na 7 1 3 . 7 % 100.0% TRAVEL 0.1100 Na 6 - N a 7 1 3 . 7 % 100.0% RED. M ASS 11.4888 O 4 - Na 5 6.8 % 7 7 . 9 %

VIBRATION 7 ATOM PAIR ENERGY CONTRIBUTION

R A D I A L

FREQ. 252.73 O 3 - N a 5 11.4% (91.9% ) 9 3 . 7 %

T-DIPOLE 0.0161 O 1 - N a 6 1 1 . 4 % 9 3 . 3 %

TRAVEL 0.1253 O 4 - N a 7 1 1 . 4 % 9 3 . 5 %

RED. M ASS 8.4987 O 3 - N a 6 11.2% 9 0 . 7 % O 1 - N a 7 11.1% 9 0 . 6 % O 4 - N a 5 11.1% 9 0 . 3 % O 1 - B 2 1 0 . 4 % 0.0%

2 0 5

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. B 2 — 0 3 10.4% 0.0%

B 2 — 0 4 10.4% 0.0%

V I B R A T I O N 8 ATOM PAIR ENERGY CONTRIBUTION

RADIAL

FREQ. 277.00 B 2 - Na 5 12.9% (160.4%) 99.1%

T-DIPOLE 4.7637 B 2 - Na 6 11.8% 83.9%

TRAVEL 0.1097 B 2 - Na 7 10.9% 35.9%

RED. M ASS 10.1221 B 2 - - 0 3 9.8% 17.2% 1

VIBRATION 9 ATOM PAIR ENERGY CONTRIBUTION

RADIAL

FREQ. 277.25 B 2 - N a 7 12.9% (160.0% ) 9 8 . 5 %

T-DIPOLE 4.7626 B 2 - Na 6 12. 0% 8 7 . 0 %

TRAVEL 0.1096 B 2 - N a 5 10. 8 % 2 3 . 4 %

RED. MASS 10.1220 O 1 - B 2 9.9% 11. 0%

VIBRATION 10 A T O M P A I R ENERGY CONTRIBUTION

RADIAL

FREQ. 567.43 B 2 — 0 3 15.9% ( 84.6% ) 0 . 0%

T-DIPOLE 1.5509 O 1 - Na 6 8 . 8 % 5 8 . 1 % TRAVEL 0.0864 B 2 — 0 4 8 . 8 % 6 . 7 % RED. M ASS 7.9520 O 1 - N a 7 8 . 8 % 4 6 . 6 %

VIBRATION 11 ATOM PAIR ENERGY CONTRIBUTION

RADIAL

FREQ. 567.69 O 1 - B 2 13.8% ( 78.9%) 0 . 8 %

T-DIPOLE 1.5526 B 2 — 0 4 12.9% 1 . 3 %

TRAVEL 0.0864 O 3 - N a 6 9 . 6 % 3 . 4 %

RED. M ASS 7.9523 O 3 - N a 5 9 . 6 % 0 . 1%

VIBRATION 12 ATOM PAIR ENERGY CONTRIBUTION

RADIAL

FREQ. 742.42 B 2 — 0 4 17.9% ( 86.2%) 0 . 0%

T-DIPOLE 2.4025 B2 - 0 3 17.9% 0 . 0% TRAVEL 0.0877 O 1 - B 2 17.9% 0 . 0%

RED. MASS 5.9065 B 2 - Na 7 1 5 . 2 % 0. 0% B 2 —Na 5 15.2% 0. 0% B 2 - N a 6 1 5 . 2 % 0. 0%

VIBRATION 13 A T O M P A I R ENERGY CONTRIBUTION

RADIAL

FREQ. 1052.44 B 2 — 0 4 11.1% (50.7% ) 100. 0% T-DIPOLE 0.0084 O 3 - Na 6 11. 1% 0 . 0%

TRAVEL 0.0633 O 3 - N a 5 11. 1% 0. 0%

2 0 6

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RED. M ASS 7.9998 O 1 - Na 7 11.1% 0.0% O 1 - - N a 6 1 1 . 1 % 0.0% O 4 — Na 5 11.1% 0.0%

O 4 — Na 7 11.1% 0.0%

B 2 — 0 3 11.1% 100.0%

0 1 - B 2 1 1 . 1 % 100.0%

VIBRATION 14 ATOM PAIR ENERGY CONTRIBUTION

R A D I A L

FREQ. 1535.70 B 2 — 0 4 21.4% (91.6% ) 9 8 . 1 %

T-DIPOLE 7.0112 O 1 - - B 2 1 7 . 3 % 6 0 . 3 %

TRAVEL 0.0602 B 2 - ■ 0 3 1 4 . 8 % 1 9 . 1 %

RED. M ASS 6.0590 B 2 - N a 6 1 3 . 8 % 9 6 . 6 %

B 2 - N a 5 1 3 . 8 % 4 4 . 9 %

B 2 - N a 7 1 3 . 8 % 1 1 . 3 %

VIBRATION 15 ATOM PAIR ENERGY CONTRIBUTION

R A D I A L

FREQ. 1536.81 B 2 — 0 3 20.9% (90.5% ) 9 4 . 4 %

T-DIPOLE 7.0124 0 1 - B 2 1 8 . 4 % 7 2 . 5 %

TRAVEL 0.0602 B 2 — 0 4 1 4 . 2 % 7 . 1 %

RED. M ASS 6.0590 B 2 - N a 7 1 3 . 8 % 9 0 . 1 %

B 2 - N a 5 1 3 . 8 % 5 8 . 7 %

B 2 - N a 6 1 3 . 8 % 3 . 9 % 1

SYSTEM IS A GROUND STATE

M O PA C C alculation from Cerius2

M OLECULE IS NOT LINEAR

THERE ARE 15 GENUINE VIBRATIONS IN THIS SYSTEM

THIS THERM ODYNAM ICS CALCULATION IS LIM ITED TO

M OLECULES W HICH HAVE NO INTERNAL ROTATIONS

CALCULATED THERM ODYNAM IC PROPERTIES *

2 0 7

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TEMP. (K) PARTITION FUNCTION H.O.F. ENTHALPY HEAT CAPACITY ENTROPY KCAL/MOL CAL/MOLE CAL/K/MOL CAL/K/MOL

200 VIB. 46.93 1922.38134 16.89520 17.26014 ROT. 0.955E+05 596.178 2.981 25.769 INT. 0.448E+07 2518.559 19.876 43.029 TRA. 0.768E+27 993.630 4.968 38.448 TOT. -417.542 3512.1893 24.8442 81.4766

210 VIB. 59.68 2093.34312 17.29351 18.09418 ROT. 0.103E+06 625.987 2.981 25.914 INT. 0.613E+07 2719.330 20.274 44.008 TRA. 0.826E+27 1043.312 4.968 38.690 TOT. -417.291 3762.6415 25.2426 82.6983

220 VIB. 75.67 2268.18233 17.67103i 18.90747 ROT. 0.110E+06 655.796 2.981 26.053 INT. 0.834E+07 2923.978 20.652 44.960 TRA. 0.886E+27 1092.993 4.968 38.921 TOT. -417.037 4016.9711 25.6201 83.8813

230 VIB. 95.64 2446.70098 18.0297C 1 19.70096 ROT. 0.118E+06 685.605 2.981 26.185 INT. 0.113E+08 3132.306 21.011 45.886 TRA. 0.947E+27 1142.674 4.968 39.142 TOT. -416.779 4274.9802 25.9787 85.0280

240 VIB. 120.5 2628.71925 18.37122: 20.47557 ROT. 0.126E+06 715.414 2.981 26.312 INT. 0.151E+08 3344.133 21.352 46.788 TRA. 0.101E+28 1192.356 4.968 39.353 TOT. -416.517 4536.4889 26.3203 86.1409

250 VIB. 151.4 2814.07326 18.69708 ! 21.23217 ROT. 0.133E+06 745.222 2.981 26.434 INT. 0.202E+08 3559.296 21.678 47.666 TRA. 0.107E+28 1242.037 4.968 39.556 TOT. -416.253 4801.3333 26.6461 87.2219

260 VIB. 189.6 3002.61316 19.00861 21.97160 ROT. 0.142E+06 775.031 2.981 26.551 INT. 0.268E+08 3777.645 21.989 48.523 TRA. 0.114E+28 1291.719 4.968 39.750 TOT. -415.985 5069.3636 26.9576 88.2730

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 270 VIB. 236.7 3194.20150 19.30696 i 22.69463 ROT. 0.150E+06 804.840 2.981 26.663 INT. 0.355E+08 3999.042 22.288 49.358 TRA. 0.120E+28 1341.400 4.968 39.938 TOT. -415.713 5340.4423 27.2560 89.2959

280 VIB. 294.7 3388.71181 19.59316 i 23.40198 ROT. 0.158E+06 834.649 2.981 26.772 INT. 0.466E+08 4223.361 22.574 50.174 TRA. 0.127E+28 1391.082 4.968 40.118 TOT. -415.439 5614.4430 27.5422 90.2922

290 VIB. 365.8 3586.02735 19.86814 24.09436 ROT. 0.167E+06 864.458 2.981 26.876 INT. 0.610E+08 4450.485 22.849 50.971 TRA. 0.134E+28 1440.763 4.968 40.293 TOT. -415.163 5891.2489 27.8172 91.2635

300 VIB. 452.6 3786.04000 20.13271 24.77241 ROT. 0.175E+06 894.267 2.981 26.977 INT. 0.794E+08 4680.307 23.114 51.750 TRA. 0.141E+28 1490.445 4.968 40.461 TOT. -414.883 6170.7520 28.0818 92.2109

310 VIB. 558.6 3988.64928 20.38758 25.43674 ROT. 0.184E+06 924.076 2.981 27.075 INT. 0.103E+09 4912.725 23.368 52.512 TRA. 0.148E+28 1540.126 4.968 40.624 TOT. -414.601 6452.8517 28.3366 93.1358

320 VIB. 687.3 4193.76150 20.63340 i 26.08792 ROT. 0.193E+06 953.885 2.981 27.170 INT. 0.133E+09 5147.646 23.614 53.258 TRA. 0.155E+28 1589.808 4.968 40.782 TOT. -414.316 6737.4543 28.5824 94.0393

330 VIB. 843.5 4401.28894 20.87072 26.72650 ROT. 0.202E+06 983.694 2.981 27.262 INT. 0.171E+09 5384.983 23.852 53.988 TRA. 0.163E+28 1639.489 4.968 40.934 TOT. -414.029 7024.4721 28.8198 94.9224

340 VIB. 1032. 4611.14924 21.10005 27.35298 ROT. 0.212E+06 1013.503 2.981 27.351 INT. 0.219E+09 5624.652 24.081 54.704

209

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TRA. 0.170E+28 1689.171 4.968 41.083 TOT. -413.740 7313.8228 29.0491 95.7861

350 VIB. 1260. 4823.26479 21.32184 27.96783 ROT. 0.221E+06 1043.312 2.981 27.437 INT. 0.279E+09 5866.576 24.303 55.405 TRA. 0.178E+28 1738.852 4.968 41.226 TOT. -413.449 7605.4288 29.2709 96.6313

360 VIB. 1534. 5037.56216 21.53648 28.57151 ROT. 0.231E+06 1073.120 2.981 27.521 INT. 0.354E+09 6110.683 24.517 56.092 TRA. 0.185E+28 1788.534 4.968 41.366 TOT. -413.155 7899.2166 29.4855 97.4589

370 VIB. 1864. 5253.97173 21.74433 29.16444 ROT. 0.240E+06 1102.929 2.981 27.603 INT. 0.448E+09 6356.901 24.725 56.767 TRA. 0.193E+28 1838.215 4.968 41.502 TOT. -412.859 8195.1165 29.6934 98.2695

380 VIB. 2258. 5472.42724 21.94572 29.74701 ROT. 0.250E+06 1132.738 2.981 27.682 INT. 0.565E+09 6605.165 24.927 57.429 TRA. 0.201E+28 1887.897 4.968 41.635 TOT. -412.561 8493.0624 29.8948 99.0640

390 VIB. 2729. 5692.86548 22.14092 30.31960 ROT. 0.260E+06 1162.547 2.981 27.760 INT. 0.710E+09 6855.413 25.122 58.079 TRA. 0.209E+28 1937.578 4.968 41.764 TOT. -412.261 8792.9911 30.0900 99.8430

400 VIB. 3291. 5915.22600 22.33021 30.88256 ROT. 0.270E+06 1192.356 2.981 27.835 INT. 0.889E+09 7107.582 25.311 58.718 TRA. 0.217E+28 1987.260 4.968 41.890 TOT. -411.959 9094.8420 30.2793 100.6072

410 VIB. 3959. 6139.45084 22.51383 31.43622 ROT. 0.280E+06 1222.165 2.981 27.909 INT. 0.111E+10 7361.616 25.495 59.345 TRA. 0.225E+28 2036.941 4.968 42.012 TOT. -411.655 9398.5572 30.4629 101.3571

420 VIB. 4752. 6365.48431 22.69198 31.98090

210

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ROT. 0.291E+06 1251.974 2.981 27.980 INT. 0.138E+10 7617.458 25.673 59.961 TRA. 0.234E+28 2086.623 4.968 42.132 TOT. -411.350 9704.0811 30.6410 102.0932

430 VIB. 5693. 6593.27286 22.86487 32.51689 ROT. 0.301E+06 1281.783 2.981 28.051 INT. 0.171E+10 7875.056 25.846 60.568 TRA. 0.242E+28 2136.304 4.968 42.249 TOT. -411.043 10011.3601 30.8139 102.8162

440 VIB. 6804. 6822.76485 23.03270 33.04447 ROT. 0.312E+06 1311.592 2.981 28.119 INT. 0.212E+10 8134.356 26.014 61.164 TRA. 0.251E+28 2185.986 4.968 42.363 TOT. -410.734 10320.3425 30.9817 103.5265

450 VIB. 8116. 7053.91046 23.19562 33.56391 ROT. 0.322E+06 1341.400 2.981 28.186 INT. 0.262E+10 8395.311 26.177 61.750 TRA. 0.259E+28 2235.668 4.968 42.474 TOT. -410.423 10630.9785 31.1447 104.2245

460 VIB. 9661. 7286.66157 23.35382 34.07547 ROT. 0.333E+06 1371.209 2.981 28.252 INT. 0.322E+10 8657.871 26.335 62.327 TRA. 0.268E+28 2285.349 4.968 42.584 TOT. ■410.111 10943.2200 31.3029 104.9107

470 VIB. 0.1148E+05 7520.97162 23.50744 34.57S ROT. 0.344E+06 1401.018 2.981 28.316 INT. 0.395E+10 8921.990 26.488 62.895 TRA. 0.277E+28 2335.030 4.968 42.690 TOT. ■409.797 11257.0204 31.4565 105.5855

480 VIB. 0.1361E+05 7756.79559 23.65663 35.07f ROT. 0.355E+06 1430.827 2.981 28.379 INT. 0.483E+10 9187.623 26.638 63.454 TRA. 0.285E+28 2384.712 4.968 42.795 TOT. ■409.482 11572.3348 31.6057 106.2493

490 VIB. 0.1611E+05 7994.08987 23.80152 35.56f ROT. 0.366E+06 1460.636 2.981 28.440 INT. 0.590E+10 9454.726 26.782 64.005 TRA. 0.294E+28 2434.393 4.968 42.897 TOT. ■409.165 11889.1195 31.7506 106.9024

211

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 500 VIB. 0.1903E+05 8232.81220 23.94226 36.04742 ROT. 0.378E+06 1490.445 2.981 28.500 INT. 0.718E+10 9723.257 26.923 64.548 TRA. 0.304E+28 2484.075 4.968 42.998 TOT. -408.847 12207.3322 31.8913 107.5453

510 VIB. 0.2244E+05 8472.92165 24.07897 36.52289 ROT. 0.389E+06 1520.254 2.981 28.559 INT. 0.873E+10 9993.176 27.060 65.082 TRA. 0.313E+28 2533.756 4.968 43.096 TOT. -408.527 12526.9320 32.0280 108.1781

520 VIB. 0.2641 E+05 8714.37852 24.21176 36.99175 ROT. 0.400E+06 1550.063 2.981 28.617 INT. 0.106E+11 10264.441 27.193 65.609 TRA. 0.322E+28 2583.438 4.968 43.192 TOT. -408.206 12847.8793 32.1608 108.8013

530 VIB. 0.3103E+05 8957.14432 24.34077 37.45417 ROT. 0.412E+06 1579.872 2.981 28.674 INT. 0.128E+11 10537.016 27.322 66.128 TRA. 0.331E+28 2633.119 4.968 43.287 TOT. -407.884 13170.1355 32.2898 109.4151

540 VIB. 0.3640E+05 9201.18172 24.46610 37.91032 ROT. 0.424E+06 1609.681 2.981 28.730 INT. 0.154E+11 10810.862 27.447 66.640 TRA. 0.341E+28 2682.801 4.968 43.380 TOT. -407.560 13493.6633 32.4151 110.0198

550 VIB. 0.4263E+05 9446.45453 24.58787 38.36038 ROT. 0.436E+06 1639.490 2.981 28.784 INT. 0.186E+11 11085.944 27.569 67.145 TRA. 0.350E+28 2732.482 4.968 43.471 TOT. -407.236 13818.4265 32.5369 110.6156

560 VIB. 0.4985E+05 9692.92763 24.70618 38.80448 ROT. 0.448E+06 1669.298 2.981 28.838 INT. 0.223E+11 11362.226 27.687 67.643 TRA. 0.360E+28 2782.164 4.968 43.560 TOT. -406.910 14144.3900 32.6552 111.2029

570 VIB. 0.5819E+05 9940.56697 24.82114 39.24279 ROT. 0.460E+06 1699.107 2.981 28.891 INT. 0.267E+11 11639.674 27.802 68.134

212

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TRA. 0.369E+28 2831.845 4.968 43.648 TOT. -406.582 14471.5198 32.7702 111.7819

580 VIB. 0.6782E+05 10189.33950 24.93284 39.67544 ROT. 0.472E+06 1728.916 2.981 28.943 INT. 0.320E+11 11918.256 27.914 68.618 TRA. 0.379E+28 2881.527 4.968 43.735 TOT. -406.254 14799.7827 32.8819 112.3527

590 VIB. 0.7893E+05 10439.21320 25.04138 40.10259 ROT. 0.484E+06 1758.725 2.981 28.994 INT. 0.382E+11 12197.938 28.022 69.096 TRA. 0.389E+28 2931.208 4.968 43.820 TOT. -405.925 15129.1468 32.9904 112.9157

600 VIB. 0.9172E+05 10690.15698 25.14687 40.52435 ROT. 0.496E+06 1788.534 2.981 29.044 INT. 0.455E+11 12478.691 28.128 69.568 TRA. 0.399E+28 2980.890 4.968 43.903 TOT. -405.594 15459.5810 33.0959 113.4710

* NOTE: HEATS OF FORMATION ARE RELATIVE TO THE ELEMENTS IN THEIR STANDARD STATE AT 298K

TOTAL CPU TIME: 3.28 SECONDS

= MOP AC DONE ==

213

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Thermochemical Results for B(OH) 4_ from MOPAC (AMI) at Elevated Temperature

** FRANK J. SEILER RES. LAB., U.S. AIR FORCE ACADEMY, COLO. SPGS., CO. 80840 **

AMI CALCULATION RESULTS

5. IJ5 / 5%3*J5 47 |C. JJC vt« 4? |5. j3|C . JJ5 5|C 44 444. *I#J%a vl» »{, U# 9 4*|C 9|C Sp ^ 44 *1* •!#44 4^ *1* *1> *|« Sp ^ 44 .I# ^ 44 «L «1* ^^ 4^^ 44*L J*44 U#5|% 54*y* ^ ^ ^ ^ ^ ^ ^ ^ WU ^ ^ «1*^ 4* ^*1# 4^ ^ »p 4^ ^^ ^^ kl«^ 4* ^ *3* ip ^ ^ ^ ^ 4* ^ 'I 4* ' *1* v ^ V ^ V 4f V V V T *4**P 4* *p ^ip 4*^ ^ V 4« V 4f*P *P4U *p «lff *P ilf

* MOPAC: VERSION 6.00 CALC'D. 30-May-02 * GEO-OK - OVERRIDE INTERATOMIC DISTANCE CHECK * GRAPH - GENERATE FILE FOR GRAPHICS * * * * CHARGE ON SYSTEM = -1 * * * * T= -A TIME OF 24.0 HOURS REQUESTED * DUMP=N - RESTART FILE WRITTEN EVERY 60.0 MINUTES * FORCE - FORCE CALCULATION SPECIFIED * AMI - THE AMI HAMILTONIAN TO BE USED * NOINTER - INTERATOMIC DISTANCES NOT TO BE PRINTED * ENPART - ENERGY TO BE PARTITIONED INTO COMPONENTS * NOXYZ - CARTESIAN COORDINATES NOT TO BE PRINTED * THERMO - THERMODYNAMIC QUANTITIES TO BE CALCULATED * ROT - SYMMETRY NUMBER OF 1 SPECIFIED

00BY100 AMI FORCE T=24.0H DUMP=60.0M NOXYZ NOINTER GRAPH ENPART THERMO(200,600,10) + ROT=l GEO-OK CHARGE=-1 MOPAC Calculation from Cerius2

ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES)

214

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (I) NA:I NB:NA:I NC:NB:NA:I NA NB NC

1 O 2 B 1.45862 * 1 3 O 1.45655 * 109.17546 * 2 1 4 O 1.45672 * 109.69523 * 119.32335 * 2 1 3 5 H 2.51438 * 79.35810 * -29.57944 * 3 1 2 6 O 1.45342 * 109.55325 * -120.33031 * 2 1 3 7 H 0.87416 * 109.40635 * 179.89154 * 6 2 1 8 H 2.52049 * 19.76603 * .■127.38617 * 1 3 2 9 H 2.54247 * 49.04303 * 20.97864 * 4 2 1 H: (AMI): MJ.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985) B: (AMI): M.J.S. DEWAR, C. JIE, E. G. ZOEBISCH ORGANOMETALLICS 7, 513 (1988) O: (AMI): M.J.S. DEWAR ET AL, J. AM. CHEM. SOC. 107 3902-3909 (1985)

RHF CALCULATION, NO. OF DOUBLY OCCUPIED LEVELS = 16

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

HEAT OF FORMATION = -325.141057 KCALS/MOLE

INTERNAL COORDINATE DERIVATIVES

NUMBER ATOM BOND ANGLE DIHEDRAL

1 O 2 B 117.291763 3 O -109.768477 -53.356585 4 O 0.439868 92.213048 -9.084627 5 H -27.254719 -293.885862 -92.442592 6 O 10.753852 4.986073 -1.388437 7 H -93.567166 11.544657 0.384388 8 H -26.846665 -315.755078 -5.179256 9 H -27.931490 -234.430128 -160.025579

GRADIENT NORM = 568.96579

215

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ** GRADIENT IS TOO LARGE TO ALLOW FORCE MATRIX TO BE CALCULATED, (LIMIT=10) **

GEOMETRY WILL BE OPTIMIZED FIRST USING FLEPO CYCLE 1 TIME 0.04 TIME LEFT: 86399.7 GRAD. 77.014 HEAT:-346.8858 CYCLE 2 TIME 0.07 TIME LEFT: 86399.7 GRAD. 56.608 HEAT:-347.6225 CYCLE 3 TIME 0.02 TIME LEFT: 86399.6 GRAD. 39.861 HEAT:-348.4616 CYCLE 4 TIME 0.02 TIME LEFT: 86399.6 GRAD. 39.958 HEAT:-349.0289 CYCLE 5 TIME 0.02 TIME LEFT: 86399.6 GRAD. 29.171 HEAT:-350.0527

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 6 TIME: 0.22 TIME LEFT: 86399.4 GRAD.: 33.296 HEAT:-350.1850

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 7 TIME: 0.18 TIME LEFT: 86399.2 GRAD.: 20.510 HEAT:-350.5884

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 8 TIME: 0.18 TIME LEFT: 86399.0 GRAD.: 12.609 HEAT:-350.8217

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

216

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CYCLE: 9 TIME: 0.20 TIME LEFT: 86398.8 GRAD.: 13.505 HEAT:-350.9661

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 10 TIME: 0.36 TIME LEFT: 86398.5 GRAD.: 19.697 HEAT:-351.1510

ALL CONVERGERS ARE NOW FORCED ON SHIFT=T0, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 11 TIME: 0.37 TIME LEFT: 86398.1 GRAD.: 23.174 HEAT:-351.3731

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

217

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CYCLE: 12 TIME: 0.35 TIME LEFT: 86397.7 GRAD.: 30.526 HEAT:-351.6824

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 13 TIME: 0.18 TIME LEFT: 86397.6 GRAD.: 16.389 HEAT-.-351.8885

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 14 TIME: 0.18 TIME LEFT: 86397.4 GRAD.: 10.084 HEAT:-351.9891

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON SHIFT=T0, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 15 TIME: 0.37 TIME LEFT: 86397.0 GRAD.: 25.465 HEAT:-351.9992

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 16 TIME: 0.18 TIME LEFT: 86396.8 GRAD.: 21.328 HEAT:-352.1944

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

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CYCLE: 17 TIME: 0.34 TIME LEFT: 86396.5 GRAD.: 16.485 HEAT:-352.2394

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 18 TIME: 0.36 TIME LEFT: 86396.1 GRAD.: 15.478 HEAT:-352.3038

ALL CONVERGERS ARE NOW FORCED ON SHIFT=T0, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 19 TIME: 0.35 TIME LEFT: 86395.8 GRAD.: 11.839 HEAT:-352.3461

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

219

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CYCLE: 20 TIME: 0.34 TIME LEFT: 86395.4 GRAD.: 19.867 HEAT:-352.4022

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 21 TIME: 0.54 TIME LEFT: 86394.9 GRAD.: 8.958 HEAT:-352.4550

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 22 TIME 0.21 TIME LEFT 86394.7 GRAD. 6.911 HEAT:-3 52.4812 CYCLE: 23 TIME 0.02 TIME LEFT 86394.7 GRAD. 9.510 HEAT:-352.5533 CYCLE: 24 TIME 0.15 TIME LEFT 86394.5 GRAD. 122.061 HEAT:-352.7429 CYCLE: 25 TIME 0.15 TIME LEFT 86394.4 GRAD. 21.142 HEAT:-352.7627

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

220

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CYCLE: 26 TIME: 0.21 TIME LEFT: 86394.2 GRAD.: 9.784 HEAT.--352.7869

ALL CONVERGERS ARE NOW FORCED ON SHIFT=T0, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 27 TIME: 0.19 TIME LEFT: 86394.0 GRAD. 10.313 HEAT:-352.7993 CYCLE: 28 TIME: 0.03 TIME LEFT: 86394.0 GRAD. 6.942 HEAT:-352.8162 CYCLE: 29 TIME: 0.02 TIME LEFT: 86393.9GRAD. 8.121 HEAT:-352.8266

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 30 TIME: 0.18 TIME LEFT: 86393.7 GRAD.: 5.347 HEAT:-352.8349

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 31 TIME: 0.18 TIME LEFT: 86393.6 GRAD.: 4.618 HEAT:-352.8418

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 32 TIME: 0.17 TIME LEFT: 86393.4 GRAD.: 3.355 HEAT:-352.8491

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 33 TIME: 0.20 TIME LEFT: 86393.2 GRAD.: 3.916 HEAT:-352.7147

221

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 34 TIME: 0.20 TIME LEFT: 86393.0 GRAD.: 19.423 HEAT.--352.8352

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 35 TIME: 0.17 TIME LEFT: 86392 .8 GRAD. 23.100 HEAT:-352.7060 CYCLE: 36 TIME: 0.03 TIME LEFT: 86392 .8 GRAD. 24.133 HEAT:-352.7442 CYCLE: 37 TIME 0.04 TIME LEFT: 86392 .8 GRAD. 23.071 HEAT:-352.8605 CYCLE: 38 TIME 0.02 TIME LEFT: 86392 .7 GRAD. 12.588 HEAT:-352.9217 CYCLE: 39 TIME 0.03 TIME LEFT: 86392 .7 GRAD. 11.029 HEAT:-353.0657 CYCLE: 40 TIME 0.03 TIME LEFT: 86392 7 GRAD. 11.714 HEAT:-353.1641 CYCLE: 41 TIME: 0.10 TIME LEFT: 86392 .6 GRAD. 22.581 HEAT:-353.3241 CYCLE: 42 TIME: 0.02 TIME LEFT: 86392 .6 GRAD. 15.373 HEAT:-353.4374 CYCLE: 43 TIME: 0.10 TIME LEFT: 86392 .5 GRAD. 9.776 HEAT:-353.4830 HEAT OF FORMATION TEST SATISFIED HOWEVER, A COMPONENT OF GRADIENT IS LARGER THAN 0.10

CYCLE: 44 TIME 0.13 TIME LEFT: 86392. 3 GRAD. 9.528 HEAT:-353.4850 CYCLE: 45 TIME 0.06 TIME LEFT: 86392. 3 GRAD. 6.463 HEAT:-353.5050 CYCLE: 46 TIME 0.06 TIME LEFT: 86392. 2 GRAD. 8.599 HEAT-.-353.5196 CYCLE: 47 TIME 0.02 TIME LEFT: 86392. 2 GRAD. 4.506 HEAT.--353.5360 CYCLE: 48 TIME 0.02 TIME LEFT: 86392, 1 GRAD. 3.699 HEAT:-353.5535 CYCLE: 49 TIME 0.06 TIME LEFT: 86392, 1 GRAD. 4.538 HEAT:-353.5730 CYCLE: 50 TIME 0.13 TIME LEFT: 86392, 0GRAD. 4.419 HEAT:-353.5851 CYCLE: 51 TIME 0.12 TIME LEFT: 86391. 8 GRAD. 5.686 HEAT:-353.5940

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 52 TIME 0.18 TIME LEFT: 86391.7 GRAD. 5.823 HEAT:-353.6049 CYCLE: 53 TIME 0.02 TIME LEFT: 86391.6 GRAD. 4.210 HEAT:-353.6129 CYCLE: 54 TIME 0.10 TIME LEFT: 86391.5 GRAD. 3.481 HEAT:-353.6267 CYCLE: 55 TIME 0.06 TIME LEFT: 86391.5 GRAD. 4.256 HEAT:-353.6355 CYCLE: 56 TIME 0.09 TIME LEFT: 86391.4 GRAD. 4.671 HEAT:-353.6395

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CYCLE: 57 TIME 0.16 TIME LEFT: 86391.2 GRAD. 3.939 HEAT: -353.6701 CYCLE: 58 TIME 0.02 TIME LEFT: 86391.2 GRAD. 3.694 HEAT: -353.6895 CYCLE: 59 TIME 0.16 TIME LEFT: 86391.0 GRAD. 3.411 HEAT: -353.7073 CYCLE: 60 TIME 0.02 TIME LEFT: 86391.0 GRAD. 2.309 HEAT: -353.7127 CYCLE: 61 TIME 0.02 TIME LEFT: 86391.0 GRAD. 2.339 HEAT: -353.7179 CYCLE: 62 TIME 0.10 TIME LEFT: 86390.9 GRAD. 4.734 HEAT: -353.7256 CYCLE: 63 TIME 0.07 TIME LEFT: 86390.8 GRAD. 6.333 HEAT: -353.7386 CYCLE: 64 TIME 0.02 TIME LEFT: 86390.8 GRAD. 6.294 HEAT: -353.7468 CYCLE: 65 TIME 0.05 TIME LEFT: 86390.7 GRAD. 2.337 HEAT: -353.7538

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 66 TIME: 0.24 TIME LEFT: 86390.5 GRAD.: 3.392 HEAT:-353.7608

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 67 TIME: 0.35 TIME LEFT: 86390.2 GRAD.: 1.320 HEAT:-353.7674

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

HEAT OF FORMATION TEST SATISFIED HOWEVER, A COMPONENT OF GRADIENT IS LARGER THAN 0.10

CYCLE: 68 TIME: 0.18 TIME LEFT: 86390.0 GRAD.: 0.631 HEAT:-353.7684

ALL CONVERGERS ARE NOW FORCED ON

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CYCLE: 69 TIME: 0.21 TIME LEFT: 86389.8 GRAD.: 4.353 HEAT:-353.6728

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 70 TIME: 0.16 TIME LEFT: 86389.6 GRAD.: 3.829 HEAT.--353.6001

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 71 TIME: 0.16 TIME LEFT: 86389.4 GRAD.: 2.429 HEAT:-353.3562

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 72 TIME: 0.17 TIME LEFT: 86389.3 GRAD.: 20.991 HEAT:-353.7436

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

CYCLE: 73 TIME: 0.36 TIME LEFT: 86388.9 GRAD.: 0.976 HEAT:-353.7614

224

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CYCLE: 74 TIME 0.19 TIME LEFT 86388.7 GRAD. 0.657 HEAT:-353.5660 CYCLE: 75 TIME 0.02 TIME LEFT 86388.7 GRAD. 3.751 HEAT:-353.6512 CYCLE: 76 TIME 0.04 TIME LEFT 86388.7 GRAD. 6. 366 HEAT:-353.0748 CYCLE: 77 TIME 0.04 TIME LEFT 86388.6 GRAD. 21 .644 HEAT:-353.7029 CYCLE: 78 TIME 0.14 TIME LEFT 86388.5 GRAD. 13 .768 HEAT:-353.7353 CYCLE: 79 TIME 0.09 TIME LEFT 86388.4 GRAD. 7. 904 HEAT:-353.7524

HEAT OF FORMATION IS ESSENTIALLY STATIONARY

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

AMI FORCE T=24.0H DUMP=60.0M NOXYZ NOINTER GRAPH ENPART THERMO(200,600,10) + ROT=l GEO-OK CHARGE=-1 MOPAC Calculation from Cerius2

PETERS TEST WAS SATISFIED IN BFGS OPTIMIZATION SCF FIELD WAS ACHIEVED

AMI CALCULATION VERSION 6.00 30-May-02

FINAL HEAT OF FORMATION = -353.76292 KCAL

TOTAL ENERGY = -1414.29370 EV ELECTRONIC ENERGY = -3983.15282 EV

225

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CORE-CORE REPULSION = 2568.85913 EV

GRADIENT NORM = 3.60968 IONIZATION POTENTIAL = 5.51058 NO. OF FILLED LEVELS = 16 MOLECULAR WEIGHT = 78.839

SCF CALCULATIONS = 130 COMPUTATION TIME = 11.934 SECONDS

FINAL POINT AND DERIVATIVES

PARAMETER ATOM TYPE VALUE GRADIENT 1 2 B BOND 1.437230 0.927505 KCAL/ANGSTROM 2 3 O BOND 1.436806 0.223872 KCAL/ANGSTROM 3 3 O ANGLE 108.811101 1.257462 KCAL/RADIAN 4 4 O BOND 1.438368 1.039837 KCAL/ANGSTROM 5 4 O ANGLE 108.662946 1.625444 KCAL/RADIAN 6 4 O DIHEDRAL 121.051007 -0.060468 KCAL/RADIAN 7 5 H BOND 2.561147 0.009408 KCAL/ANGSTROM 8 5 H ANGLE 78.324737 0.038435 KCAL/RADIAN 9 5 H DIHEDRAL -22.923121 -0.341606 KCAL/RADIAN 10 6 O BOND 1.437690 0.137538 KCAL/ANGSTROM 11 6 O ANGLE 111.232455 0.021345 KCAL/RADIAN 12 6 O DIHEDRAL -119.596606 -0.072968 KCAL/RADIAN 13 7 H BOND 0.952542 -0.071300 KCAL/ANGSTROM 14 7 H ANGLE 102.133246 0.042980 KCAL/RADIAN 15 7 H DIHEDRAL 74.872922 0.032823 KCAL/RADIAN 16 8 H BOND 2.318197 -0.269681 KCAL/ANGSTROM 17 8 H ANGLE 23.630479 1.542464 KCAL/RADIAN 18 8 H DIHEDRAL -226.998531 -0.255159 KCAL/RADIAN 19 9 H BOND 2.324003 0.173123 KCAL/ANGSTROM 20 9 H ANGLE 54.012492 1.701376 KCAL/RADIAN 21 9 H DIHEDRAL 21.505132 1.103901 KCAL/RADIAN

ATOM CHEMICAL BOND LENGTH BOND ANGLE TWIST ANGLE NUMBER SYMBOL (ANGSTROMS) (DEGREES) (DEGREES) (I) NA:I NB:NA:I NC:NB:NA:I NA NB NC

226

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 O 2 B 1.43723 * 1 3 O 1.43681 * 108.81110 * 2 1 4 O 1.43837 * 108.66295 * 121.05101 * 2 1 3 5 H 2.56115 * 78.32474 * -22.92312 * 3 1 2 6 O 1.43769 * 111.23245 * -119.59661 * 2 1 3 7 H 0.95254 * 102.13325 * 74.87292 * 6 2 1 8 H 2.31820 * 23.63048 * 133.00147 * 1 3 2 9 H 2.32400 * 54.01249 * 21.50513 * 4 2 1

EIGENVALUES

-32.40151 -29.38108 -29.31323 -29.30425 -15.05991 -12.46939 -12.46212 -10.95643 -9.78595 -9.22509 -7.50740 -7.50028 -6.18798 -5.68148 -5.67673 -5.51058 9.67280 10.83968 10.84311 11.70888 11.71174 13.16111 13.91819 13.91894

NET ATOMIC CHARGES AND DIPOLE CONTRIBUTIONS

ATOM NO. TYPE CHARGE ATOM ELECTRON DENSITY 1 O -0.4473 6.4473 2 B 0.1200 2.8800 3 O -0.4482 6.4482 4 O -0.4492 6.4492 5 H 0.1681 0.8319 6 O -0.4491 6.4491 7 H 0.1682 0.8318 8 H 0.1688 0.8312 9 H 0.1686 0.8314 DIPOLE X Y Z TOTAL POINT-CHG. -6.901 0.020 -0.011 6.901 HYBRID 0.020 0.006 -0.009 0.023 SUM -6.881 0.026 -0.020 6.881

ATOMIC ORBITAL ELECTRON POPULATIONS

1.86281 1.38067 1.27243 1.93140 1.04834 0.61104 0.60777 0.61283 1.86283 1.63268 1.37049 1.58222 1.86275 1.23487 1.82157 1.53002 0.83190 1.86261 1.85960 1.45208 1.27477 0.83178 0.83118 0.83136

TOTAL ENERGY PARTITIONING IN AMI

227

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ONE-CENTER TERMS

E-E: ELECTRON-ELECTRON REPULSION E-N: ELECTRON-NUCLEAR ATTRACTION

ATOM E-E E-N (E-E + E-N) O 1 232.9649-541.0328 -308.0680 B 2 30.5160 -77.6132 -47.0972 0 3 233.0318-541.1040-308.0722 0 4 233.1038 -541.1803 -308.0766 H 5 2.2229 -9.4807 -7.2578 0 6 233.0920-541.1649-308.0729 H 7 2.2223 -9.4794 -7.2571 H 8 2.2191 -9.4725 -7.2535 H 9 2.2200 -9.4745 -7.2545

TWO-CENTER TERMS

J: RESONANCE ENERGY E-E: ELECTRON-ELECTRON REPULSION K: EXCHANGE ENERGY E-N: ELECTRON-NUCLEAR ATTRACTION N-N: NUCLEAR-NUCLEAR REPULSION C: COULOMBIC INTERACTION = E-E + E-N + N-N EE: TOTAL OF ELECTRONIC AND NUCLEAR ENERGIES

ATOM J K E-E E-N N-N C EE PAIR

B 2 O 1 -15.1189

O 3 O 1 0.1580 -0.1006 235.5834-440.5584 205.9881 1.0132 1.0706 O 3 B 2 -15.1237 -4.8236 142.0105 -283.7023 145.8983 4.2064-15.7409

O 4 O 1 0.1591 -0.1020 235.7195 -440.7586 206.0564 1.0173 1.0745 O 4 B 2 -15.0768 -4.8101 141.9520-283.5507 145.7816 4.1829-15.7040 O 4 O 3 0.1929 -0.1404 232.3036-434.8180 203.4762 0.9619 1.0143

H 5 O 1 -0.0297 -0.0266 23.5178 -50.2885 26.4665 -0.3042 -0.3606 H 5 B 2 -0.1771 -0.0193 15.2345 -34.2460 19.4146 0.4031 0.2067 H 5 O 3 -0.0124 -0.0017 27.9273 -59.6152 31.3004-0.3874 -0.4016 H 5 O 4 -14.5988 -5.4721 53.6667-115.8127 68.8021 6.6562-13.4147

0O 6 0O 1 0.1914 -0.1403 232.0969-434.4502 203.3129 0.9596 1.0107

228

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. O 6 B 2 -15.0963 -4.8146 141.9833 -283.6229 145.8322 4.1926-15.7184 0 6 0 3 0.1593 -0.1004 235.8555 -441.0311 206.1923 1.0166 1.0755 0 6 0 4 0.1603 -0.1020 235.9705-441.1798 206.2312 1.0219 1.0802 O 6 H 5 -0.0114 -0.0053 30.5113 -65.0451 34.1083 -0.4255 -0.4422

ATOM J K E-E E-N N-N C EE PAIR H 7 O 1 -0.0126 -0.0017 27.7171 -59.1774 31.0765 -0.3838 -0.3981 H 7 B 2 -0.1765 -0.0193 15.2300 -34.2387 19.4117 0.4029 0.2071 H 7 O 3 -0.0117 -0.0058 30.6139 -65.2705 34.2310-0.4256 -0.4431 H 7 O 4 -0.0299 -0.0265 23.5471 -50.3500 26.4970-0.3059 -0.3624 H 7 H 5 -0.0006 0.0000 3.0146 -7.2481 4.3562 0.1228 0.1222 H 7 O 6 -14.5986 -5.4715 53.6588 -115.8054 68.8031 6.6564-13.4137

ATOM J K E-E E-N N-N C EE PAIR H 8 O 1 -0.0103 -0.0052 30.4510 -64.9555 34.0789-0.4256 -0.4412 H 8 B 2 -0.1829 -0.0197 15.2408 -34.2766 19.4428 0.4070 0.2045 H 8 O 3 -14.5793 -5.4674 53.5930-115.7153 68.7628 6.6405-13.4062 H 8 O 4 -0.0124 -0.0016 27.9214 -59.6272 31.3156-0.3901 -0.4042 H 8 H 5 -0.0051 -0.0005 3.1322 -7.5335 4.5289 0.1276 0.1221 H 8 O 6 -0.0300 -0.0269 23.5163 -50.3049 26.4818 -0.3067 -0.3635 H 8 H 7 -0.0006 0.0000 3.0061 -7.2307 4.3476 0.1231 0.1225

ATOM J K E-E E-N N-N C EE PAIR H 9 O 1 -14.5758 -5.4675 53.5911 -115.7038 68.7503 6.6375 -13.4058 H 9 B 2 -0.1808 -0.0196 15.2353 -34.2598 19.4297 0.4053 0.2049 H 9 O 3 -0.0297 -0.0268 23.4948 -50.2547 26.4541 -0.3057 -0.3622 H 9 O 4 -0.0102 -0.0050 30.4021 -64.8357 34.0069-0.4267 -0.4419 H 9 H 5 -0.0005 0.0000 3.0000 -7.2148 4.3374 0.1226 0.1221 H 9 O 6 -0.0122 -0.0017 27.9790 -59.7399 31.3698 -0.3911 -0.4049 H 9 H 7 -0.0049 -0.0005 3.1186 -7.5004 4.5089 0.1271 0.1217 H 9 H 8 -0.0006 0.0000 2.9958 -7.2077 4.3350 0.1231 0.1225

*** SUMMARY OF ENERGY PARTITION ***

ONE-CENTER TERMS

ELECTRON-NUCLEAR (ONE-ELECTRON) -2280.0023 EV ELECTRON-ELECTRON (TWO-ELECTRON) 971.5927 EV

TOTAL OF ONE-CENTER TERMS -1308.4096 EV

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RESONANCE ENERGY -118.6892 EV EXCHANGE ENERGY -42.0506 EV

EXCHANGE + RESONANCE ENERGY: -160.7399 EV

ELECTRON-ELECTRON REPULSION 2596.7640 EV ELECTRON-NUCLEAR ATTRACTION -5110.7673 EV NUCLEAR-NUCLEAR REPULSION 2561.2538 EV

TOTAL ELECTROSTATIC INTERACTION 47.2505 EV

GRAND TOTAL OF TWO-CENTER TERMS -113.4893 EV

ETOT (EONE + ETWO) -1421.8990 EV

DATA FOR GRAPH WRITTEN TO DISK

GRADIENT NORM = 3.6096845

**** WARNING ****

GRADIENT IS VERY LARGE FOR A THERMO CALCULATION RESULTS ARE LIKELY TO BE INACCURATE IF THERE ARE ANY LOW-LYING VIBRATIONS (LESS THAN ABOUT 400CM-1) GRADIENT NORM SHOULD BE LESS THAN ABOUT 0.2 FOR THERMO TO GIVE ACCURATE RESULTS

TIME FOR SCF CALCULATION = 0.18

TIME FOR DERIVATIVES = 0.01

MOLECULAR WEIGHT = 78.84

PRINCIPAL MOMENTS OF INERTIA IN CM(-l)

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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A = 0.173792 B = 0.173565 C = 0.170370

PRINCIPAL MOMENTS OF INERTIA IN UNITS OF 10**(-40)*GRAM- CM**2

A = 161.069987 B= 161.280534 C= 164.304699

ORIENTATION OF MOLECULE IN FORCE CALCULATION

NO. ATOM X Y Z

1 8 -1.4392 0.0009 -0.0003 2 5 -0.0019 0.0009 -0.0003 3 8 0.4614 1.3610 -0.0003 4 8 0.4583 -0.7020 1.1671 5 1 1.3843 -0.8192 0.9766 6 8 0.5187 -0.6609 -1.1656 7 1 0.3647 -0.0149 -1.8484 8 1 -0.0808 1.7523 0.6792 9 1 -1.6362 -0.9140 0.1828

FIRST DERIVATIVES WILL BE USED IN THE CALCULATION OF SECOND DERIVATIVES

ESTIMATED TIME TO COMPLETE CALCULATION = 10.62 SECONDS

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 1 TIME = 0.37 SECS, INTEGRAL = 0.37 TIME LEFT: 86387.83

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ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 2 TIME = 0.37 SECS, INTEGRAL = 0.73 TIME LEFT: 86387.46

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 3 TIME = 0.36 SECS, INTEGRAL = 1.09 TIME LEFT: 86387.11

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 4 TIME = 0.35 SECS, INTEGRAL = 1.44 TIME LEFT: 86386.76

ALL CONVERGERS ARE NOW FORCED ON

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ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 5 TIME = 0.36 SECS, INTEGRAL = 1.80 TIME LEFT: 86386.40

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 6 TIME = 0.35 SECS, INTEGRAL = 2.15 TIME LEFT: 86386.05

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 7 TIME = 0.36 SECS, INTEGRAL = 2.51 TIME LEFT: 86385.68

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON

233

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON SHIFT=T0, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 8 TIME = 0.36 SECS, INTEGRAL = 2.87 TIME LEFT: 86385.32

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 9 TIME = 0.36 SECS, INTEGRAL = 3.23 TIME LEFT: 86384.96

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 10 TIME = 0.35 SECS, INTEGRAL = 3.58 TIME LEFT: 86384.61

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

234

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 11 TIME = 0.36 SECS, INTEGRAL = 3.95 TIME LEFT: 86384.25

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON SHIFT-10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 12 TIME = 0.37 SECS, INTEGRAL = 4.31 TIME LEFT: 86383.88

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 13 TIME = 0.37 SECS, INTEGRAL = 4.68 TIME LEFT: 86383.51

ALL CONVERGERS ARE NOW FORCED ON SHIFT-10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

235

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 14 TIME = 0.36 SECS, INTEGRAL = 5.04 TIME LEFT: 86383.15

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 15 TIME = 0.36 SECS, INTEGRAL = 5.40 TIME LEFT: 86382.80

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 16 TIME = 0.37 SECS, INTEGRAL = 5.77 TIME LEFT: 86382.43

ALL CONVERGERS ARE NOW FORCED ON SHIFT=T0, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

236

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 17 TIM E- 0.35 SECS, INTEGRAL - 6.13 TIME LEFT: 86382.07

ALL CONVERGERS ARE NOW FORCED ON SHIFT-10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 18 TIM E- 0.35 SECS, INTEGRAL = 6.47 TIME LEFT: 86381.72

ALL CONVERGERS ARE NOW FORCED ON SHIFT-10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 19 TIM E- 0.36 SECS, INTEGRAL = 6.83 TIME LEFT: 86381.36

ALL CONVERGERS ARE NOW FORCED ON SHIFT-10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

237

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 20 TIME = 0.36 SECS, INTEGRAL = 7.20 TIME LEFT: 86381.00

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 21 TIME = 0.36 SECS, INTEGRAL = 7.56 TIME LEFT: 86380.64

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 22 TIME = 0.36 SECS, INTEGRAL = 7.91 TIME LEFT: 86380.28

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 23 TIME = 0.35 SECS, INTEGRAL = 8.27 TIME LEFT: 86379.93

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 24 TIME = 0.36 SECS, INTEGRAL = 8.63 TIME LEFT: 86379.57

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 25 TIME = 0.36 SECS, INTEGRAL = 8.99 TIME LEFT: 86379.21

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

ALL CONVERGERS ARE NOW FORCED ON

239

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 26 TIME = 0.35 SECS, INTEGRAL = 9.35 TIME LEFT: 86378.85

ALL CONVERGERS ARE NOW FORCED ON SHIFT=10, PULAY ON, CAMP-KING ON AND ITERATION COUNTER RESET

STEP: 27 TIME = 0.36 SECS, INTEGRAL = 9.71 TIME LEFT: 86378.49

FORCE MATRIX IN MILLIDYNES/ANGSTROM 0 O 1 B 2 O 3 O 4 H 5 O> 6

o 1 5.005803 B 2 1.859010 6.038207 0 3 0.424512 1.868246 5.017441 O 4 0.426294 1.839517 0.424027 5.011557 H 5 0.071898 0.414355 0.029980 3.532480 3.674588 O 6 0.419892 1.852291 0.429175 0.429918 0.040458 5.020454 H 7 0.030358 0.414661 0.042723 0.071896 0.006460 3.532141 H 8 0.040524 0.416580 3.518353 0.029971 0.006754 0.072135 H 9 3.514645 0.415370 0.071802 0.039021 0.006421 0.029607

H 7 H 8 H 9

H 7 3.673987 H 8 0.006608 3.661811 H 9 0.006602 0.006480 3.657484

HEAT OF FORMATION = -353.762919 KCALS/MOLE

240

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ZERO POINT ENERGY 38.825 KILOCALORIES PER MOLE

THE LAST 6 VIBRATIONS ARE THE TRANSLATION AND ROTATION MODES THE FIRST THREE OF THESE BEING TRANSLATIONS IN X, Y, AND Z, RESPECTIVELY

NORMAL COORDINATE ANALYSIS

ROOT NO. 1 2 3 4 5 6

190.99490 193.46297 243.20896 288.86236 339.08192 341.09913

1 -0.00283 0.00440 0.00111 0.01601 -0.00055 0.00637 2 -0.00787 -0.00703 0.01656 0.03306 -0.06483 -0.09313 3 0.02546 -0.03320 0.02710 -0.01357 -0.11137 0.05978 4 -0.00800 0.01042 0.00319 0.02138 0.00154 0.01191 5 0.01127 0.00608 -0.00170 0.01474 0.00005 0.00863 6 -0.00226 -0.00658 0.00016 0.03112 0.00096 0.01648 7 -0.02325 -0.02132 -0.01689 -0.02209 0.06819 0.09003 8 0.01113 0.01071 0.00603 0.02381 -0.02127 -0.02352 9 -0.02586 -0.00378 -0.02363 0.01909 0.10798 -0.05999 10 0.00612 -0.00616 -0.01523 0.03867 0.05201 -0.09096 11 0.02883 0.01995 -0.03795 -0.01713 0.10422 0.02157 12 0.01024 0.01334 -0.01531 -0.00329 0.04511 0.05676 13 -0.09307 -0.09440 -0.06992 -0.02851 -0.01108 -0.11600 14 -0.40823 -0.38931 -0.29431 -0.29243 -0.14324 -0.17959 15 -0.20131 -0.16097 -0.11994 -0.16653 -0.10876 0.06563 16 -0.01275 0.03199 0.03914 -0.00899 -0.11722 0.00067 17 -0.01559 0.01089 0.01431 -0.02501 -0.01802 0.09847 18 0.00471 0.00603 0.00796 0.03195 -0.04330 -0.04684 19 0.47157 -0.40070 0.23902 -0.28125 0.10398 -0.21330 20 0.16979 -0.17439 0.09120 -0.15876 0.10873 0.08236 21 0.07190 -0.07162 0.03628 -0.03160 0.02655 -0.01576 22 0.20347 0.24168 -0.30426 -0.29612 -0.18143 0.00195 23 -0.06938 -0.11114 0.12639 0.10591 0.03800 0.11216 24 0.20128 0.27736 -0.32309 -0.24543 -0.12534 -0.21053 25 0.02323 0.00020 -0.02803 0.00189 0.03356 0.10269 26 -0.07491 0.06174 0.11171 -0.04666 -0.00548 -0.16143 27 -0.27865 0.30521 0.46661 -0.43276 0.22238 -0.17045

241

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ROOT NO. 7 8 9 10 11 12

460.44644 460.64151 485.26368 860.17169 1071.44802 1072.85803

1 -0.12408 -0.00514 0.08459 0.16275 0.04513 0.07770 2 -0.03852 0.08640 -0.03445 0.00285 -0.01730 0.01020 3 -0.05547 -0.05049 -0.08883 -0.00132 0.00241 -0.00240 4 -0.11263 -0.00691 0.06614 -0.00061 -0.04553 -0.14725 5 0.04076 -0.11935 0.04398 -0.00152 -0.13823 0.10238 6 0.06382 0.06435 0.08904 0.00080 0.12135 0.06087 7 0.08662 -0.06459 -0.02641 -0.04959 0.01792 -0.02654 8 -0.02911 -0.11192 0.09335 -0.15457 0.07643 -0.04169 9 -0.04428 -0.05952 -0.08072 -0.00183 0.00695 0.01357 10 0.08043 0.07602 -0.00508 -0.05437 -0.03488 -0.00208 11 -0.03152 0.00018 -0.12241 0.08031 0.03932 -0.02298 12 -0.05265 0.11687 0.04079 -0.13070 -0.06087 0.04412 13 0.05730 0.05689 0.03409 -0.04729 -0.04503 -0.03850 14 0.04823 -0.01494 0.02511 0.04420 0.08303 0.13386 15 -0.23478 0.02289 0.14446 -0.08449 -0.19976 -0.25106 16 0.02060 0.01032 -0.11732 -0.05845 0.02273 0.02705 17 0.06279 0.08864 0.02022 0.07232 -0.03710 -0.02886 18 0.12385 -0.05010 0.04339 0.13336 -0.02958 -0.07019 19 0.00438 -0.05458 0.03763 -0.02575 -0.11244 0.05933 20 -0.00435 0.22167 0.11533 0.04129 0.18038 -0.13303 21 0.06682 0.08463 0.09711 0.09392 0.20074 -0.15894 22 0.18647 0.00671 0.12977 -0.02961 0.10991 0.12733 23 0.14097 -0.05896 0.07632 -0.09827 0.19275 0.25107 24 -0.06852 -0.03614 0.05224 -0.01563 -0.00423 -0.03831 25 -0.04928 -0.19867 0.10859 0.10360 -0.27205 0.22263 26 -0.04472 0.12743 -0.00142 0.01474 0.05266 -0.02732 27 0.00507 -0.07528 0.10632 0.00522 -0.01109 0.03211

ROOT NO. 13 14 15 16 17 18

1168.69388 1302.53421 1347.75408 1439.51903 1440.56444 3596.19551

1 -0.09180 -0.01674 0.00852 -0.03580 0.01026 -0.01247 2 0.00713 0.02272 -0.02416 0.01450 -0.02892 -0.05546 3 -0.01019 -0.00191 0.00504 0.00039 0.00858 0.01114

242

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 0.16978 0.00174 0.04542 0.10891 0.04796 -0.00374 5 0.11930 0.00085 0.02872 -0.08623 0.10331 -0.00145 6 0.20933 0.00008 0.05563 0.04151 -0.08986 0.00114 7 -0.04001 0.01777 0.01886 -0.02527 -0.01817 -0.00890 8 -0.08194 0.01017 0.00330 -0.00297 -0.03227 0.00739 9 -0.00023 -0.01831 -0.01788 0.02044 0.01166 0.01163 10 -0.02155 -0.01593 -0.02112 -0.02322 -0.00217 0.00388 11 0.03605 -0.00930 -0.00384 -0.00237 -0.01944 -0.00057 12 -0.07912 0.01951 0.01749 0.02138 0.03158 -0.00094 13 0.01752 -0.05192 -0.05146 -0.05573 -0.02754 -0.06554 14 -0.03295 0.17194 0.18245 0.18761 0.10584 0.00911 15 0.13536 -0.34607 -0.34205 -0.37166 -0.20304 0.01205 16 0.02526 0.01333 -0.00987 -0.01872 0.00925 -0.00002 17 -0.04838 -0.02383 0.02478 0.02493 -0.03037 0.00056 18 -0.06730 0.00029 -0.00632 0.02107 0.00697 -0.00099 19 -0.00870 -0.14634 0.15141 0.08521 -0.16130 0.00265 20 0.07717 0.25063 -0.23577 -0.13681 0.26852 -0.01258 21 0.06567 0.27354 -0.26275 -0.14711 0.29465 0.01344 22 0.07703 -0.18934 -0.16611 0.20304 0.10516 0.14795 23 0.08522 -0.35152 -0.32723 0.38159 0.19842 -0.11907 24 0.00316 0.04818 0.05133 -0.05407 -0.03206 -0.18891 25 0.12655 0.39378 -0.36370 0.23452 -0.41754 0.23310 26 -0.02567 -0.07639 0.07128 -0.04873 0.08122 0.90134 27 0.04021 0.03008 -0.01661 0.01358 -0.02903 -0.17961 1

ROOT NO. 19 20 21 22 23 24

3598.67610 3604.35596 3605.72981 0.00120 0.00201 0.00076

1 -0.00364 0.00005 -0.00043 -0.13303 0.00000 0.00000 2 -0.01541 -0.00209 -0.00346 0.00000 0.13303 0.00000 3 0.00295 0.00044 0.00081 0.00000 0.00000 -0.13303 4 -0.00061 -0.00294 -0.00241 -0.13303 0.00000 0.00000 5 -0.00497 0.00122 0.00117 0.00000 0.13303 0.00000 6 -0.00110 0.00228 -0.00438 0.00000 0.00000 -0.13303 7 0.03213 -0.00245 0.00231 -0.13303 0.00000 0.00000 8 -0.02357 0.00195 -0.00194 0.00000 0.13303 0.00000 9 -0.04033 0.00333 -0.00302 0.00000 0.00000 -0.13303 10 0.00168 -0.03422 -0.04228 -0.13303 0.00000 0.00000 11 -0.00009 0.00461 0.00543 0.00000 0.13303 0.00000 12 -0.00056 0.00632 0.00870 0.00000 0.00000 -0.13303 13 -0.02778 0.55993 0.69492 -0.13303 0.00000 0.00000

243

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 0.00388 -0.08126 -0.10027 0.00000 0.13303 0.00000 15 0.00459 -0.09501 -0.11653 0.00000 0.00000 -0.13303 16 0.00090 0.00690 -0.00551 -0.13303 0.00000 0.00000 17 -0.00395 -0.02955 0.02323 0.00000 0.13303 0.00000 18 0.00508 0.03148 -0.02514 0.00000 0.00000 -0.13303 19 -0.01502 -0.10501 0.08266 -0.13303 0.00000 0.00000 20 0.06937 0.46753 -0.36887 0.00000 0.13303 0.00000 21 -0.07775 -0.53188 0.42131 0.00000 0.00000 -0.13303 22 -0.50948 0.03964 -0.03786 -0.13303 0.00000 0.00000 23 0.41406 -0.03333 0.03136 0.00000 0.13303 0.00000 24 0.65597 -0.05152 0.04894 0.00000 0.00000 -0.13303 25 0.06549 0.00881 0.01492 -0.13303 0.00000 0.00000 26 0.24889 0.03217 0.05605 0.00000 0.13303 0.00000 27 -0.04952 -0.00588 -0.01066 0.00000 0.00000 -■0.13303

ROOT NO. 25 26 27

14.39877 18.08850 14.30156

1 -0.00006 0.00000 0.00010 2 -0.09339 0.05988 0.12381 3 0.00938 0.15253 -0.06608 4 -0.00006 0.00000 0.00010 5 -0.00016 0.00007 0.00014 6 -0.00008 0.00018 -0.00015 7 -0.08829 0.05660 0.11713 8 0.02989 -0.01920 -0.03972 9 -0.13348 -0.07733 -0.06238 10 0.05321 0.09450 -0.11394 11 0.14159 0.00531 0.03221 12 0.06426 -0.03392 0.06412 13 0.05956 0.06943 -0.11529 14 0.18339 -0.03720 -0.05916 15 0.06941 -0.12962 0.11379 16 0.03520 -0.15105 -0.00340 17 -0.07806 -0.04593 -0.11619 18 0.05993 -0.04118 0.06437 19 -0.01119 -0.19654 0.08352 20 -0.15350 -0.05378 -0.14485 21 -0.00098 -0.03835 0.01764 22 -0.10920 0.14491 0.11962 23 0.05985 0.01755 0.04865

244

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 -0.16741 -0.02803 -0.11128 25 0.06049 -0.01866 -0.08703 26 -0.08862 0.07190 0.15201 27 0.09836 0.19252 -0.01896

MASS-WEIGHTED COORDINATE ANALYSIS

ROOT NO. 1 2 3 4 5 6

190.99490 193.46297 243.20896 288.86236 339.08192 341.09913

1 -0.01350 0.02118 0.00525 0.07690 -0.00200 0.02539 2 -0.03751 -0.03382 0.07855 0.15873 -0.23710 -0.37131 3 0.12128 -0.15975 0.12853 -0.06514 -0.40728 0.23836 4 -0.03131 0.04123 0.01245 0.08437 0.00464 0.03903 5 0.04411 0.02403 -0.00664 0.05818 0.00016 0.02827 6 -0.00885 -0.02602 0.00062 0.12283 0.00289 0.05401 7 -0.11077 -0.10261 -0.08012 -0.10608 0.24936 0.35894 8 0.05303 0.05152 0.02859 0.11433 -0.07779 -0.09377 9 -0.12318 -0.01818 -0.11206 0.09165 0.39489 -0.23917 10 0.02916 -0.02962 -0.07223 0.18571 0.19020 -0.36266 11 0.13733 0.09599 -0.18002 -0.08224 0.38113 0.08601 12 0.04877 0.06420 -0.07262 -0.01580 0.16496 0.22632 13 -0.11126 -0.11402 -0.08324 -0.03436 -0.01017 -0.11608 14 -0.48805 -0.47023 -0.35038 -0.35244 -0.13148 -0.17972 15 -0.24067 -0.19443 -0.14279 -0.20071 -0.09983 0.06568 16 -0.06075 0.15393 0.18563 -0.04318 -0.42870 0.00267 17 -0.07427 0.05243 0.06789 -0.12008 -0.06591 0.39262 18 0.02246 0.02902 0.03776 0.15342 -0.15836 -0.18674 19 0.56377 -0.48398 0.28456 -0.33897 0.09544 -0.21345 20 0.20299 -0.21064 0.10857 -0.19134 0.09980 0.08242 21 0.08595 -0.08650 0.04319 -0.03809 0.02437 -0.01577 22 0.24325 0.29191 -0.36222 -0.35689 -0.16654 0.00195 23 -0.08294 -0.13424 0.15047 0.12765 0.03488 0.11225 24 0.24063 0.33500 -0.38464 -0.29580 -0.11505 -0.21068 25 0.02778 0.00024 -0.03337 0.00228 0.03080 0.10276 26 -0.08956 0.07458 0.13299 -0.05624 -0.00503 -0.16155 27 -0.33313 0.36864 0.55551 -0.52157 0.20412 -0.17058 1

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ROOT NO. 7 8 9 10 11 12

460.44644 460.64151 485.26368 860.17169 1071.44802 1072.85803

1 -0.43656 -0.01809 0.29812 0.49395 0.18665 0.32148 2 -0.13554 0.30394 -0.12140 0.00865 -0.07156 0.04221 3 -0.19516 -0.17760 -0.31307 -0.00399 0.00999 -0.00994 4 -0.32574 -0.01997 0.19161 -0.00151 -0.15479 -0.50076 5 0.11788 -0.34512 0.12741 -0.00379 -0.46995 0.34817 6 0.18456 0.18608 0.25794 0.00200 0.41257 0.20702 7 0.30475 -0.22721 -0.09307 -0.15049 0.07411 -0.10982 8 -0.10243 -0.39374 0.32900 -0.46913 0.31611 -0.17248 9 -0.15578 -0.20939 -0.28446 -0.00555 0.02873 0.05615 10 0.28299 0.26744 -0.01792 -0.16500 -0.14426 -0.00862 11 -0.11090 0.00065 -0.43139 0.24373 0.16262 -0.09506 12 -0.18523 0.41114 0.14376 -0.39667 -0.25176 0.18252 13 0.05060 0.05023 0.03015 -0.03602 -0.04675 -0.03998 14 0.04259 -0.01319 0.02221 0.03367 0.08619 0.13900 15 -0.20733 0.02021 0.12778 -0.06436 -0.20737 -0.26071 16 0.07249 0.03631 -0.41347 -0.17740 0.09399 0.11193 17 0.22092 0.31184 0.07125 0.21950 -0.15346 -0.11939 18 0.43576 -0.17623 0.15293 0.40475 -0.12234 -0.29042 19 0.00387 -0.04820 0.03328 -0.01961 -0.11672 0.06161 20 -0.00384 0.19573 0.10202 0.03145 0.18725 -0.13814 21 0.05901 0.07473 0.08590 0.07154 0.20839 -0.16505 22 0.16467 0.00592 0.11479 -0.02255 0.11410 0.13223 23 0.12449 -0.05206 0.06751 -0.07486 0.20009 0.26072 24 -0.06051 -0.03191 0.04620 -0.01191 -0.00439 -0.03979 25 -0.04351 -0.17542 0.09605 0.07891 -0.28242 0.23119 26 -0.03949 0.11252 -0.00126 0.01123 0.05466 -0.02837 27 0.00448 -0.06647 0.09404 0.00398 -0.01151 0.03334

ROOT NO. 13 14 15 16 17 18

1168.69388 1302.53421 1347.75408 1439.51903 1440.56444 3596.19551

1 -0.29783 -0.08072 0.04098 -0.16192 0.04641 -0.04888 2 0.02312 0.10956 -0.11629 0.06558 -0.13081 -0.21732 3 -0.03304 -0.00921 0.02424 0.00174 0.03883 0.04365 4 0.45278 0.00688 0.17969 0.40496 0.17830 -0.01205 5 0.31815 0.00339 0.11361 -0.32062 0.38412 -0.00467

246

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 0.55825 0.00033 0.22005 -0.15433 -0.33411 0.00367 7 -0.12980 0.08570 0.09076 -0.11431 -0.08217 -0.03488 8 -0.26584 0.04905 0.01587 -0.01342 -0.14595 0.02895 9 -0.00076 -0.08828 -0.08604 0.09248 0.05272 0.04557 10 -0.06991 -0.07680 -0.10162 -0.10505 -0.00983 0.01519 11 0.11696 -0.04485 -0.01848 -0.01071 -0.08795 -0.00225 12 -0.25668 0.09409 0.08419 0.09670 0.14283 -0.00367 13 0.01426 -0.06285 -0.06216 -0.06327 -0.03126 -0.06447 14 -0.02683 0.20811 0.22038 0.21301 0.12017 0.00896 15 0.11022 -0.41887 -0.41316 -0.42196 -0.23052 0.01186 16 0.08196 0.06428 -0.04751 -0.08467 0.04185 -0.00007 17 -0.15697 -0.11492 0.11927 0.11277 -0.13739 0.00220 18 -0.21834 0.00139 -0.03044 0.09530 0.03155 -0.00387 19 -0.00709 -0.17713 0.18288 0.09674 -0.18313 0.00261 20 0.06284 0.30335 -0.28478 -0.15532 0.30486 -0.01237 21 0.05347 0.33107 -0.31737 -0.16702 0.33453 0.01322 22 0.06272 -0.22916 -0.20064 0.23052 0.11939 0.14553 23 0.06940 -0.42547 -0.39526 0.43324 0.22527 -0.11711 24 0.00257 0.05831 0.06200 -0.06139 -0.03640 -0.18582 25 0.10305 0.47661 -0.43930 0.26626 -0.47404 0.22928 26 -0.02090 -0.09246 0.08610 -0.05533 0.09221 0.88656 27 0.03274 0.03641 -0.02006 0.01542 -0.03296 -0.17666

ROOT NO. 19 20 21 22 23 24

3598.67610 3604.35596 3605.72981 0.00088 0.00211 -0.00076

1 -0.01451 0.00021 -0.00181 -0.45049 0.00000 0.00000 2 -0.06146 -0.00879 -0.01467 0.00000 0.45049 0.00000 3 0.01178 0.00184 0.00343 0.00000 0.00000 -0.45049 4 -0.00199 -0.01014 -0.00840 -0.37029 0.00000 0.00000 5 -0.01628 0.00420 0.00406 0.00000 0.37029 0.00000 6 -0.00361 0.00789 -0.01526 0.00000 0.00000 -0.37029 7 0.12814 -0.01029 0.00976 -0.45049 0.00000 0.00000 8 -0.09401 0.00819 -0.00823 0.00000 0.45049 0.00000 9 -0.16083 0.01398 -0.01278 0.00000 0.00000 -0.45049 10 0.00671 -0.14384 -0.17903 -0.45049 0.00000 0.00000 11 -0.00037 0.01939 0.02302 0.00000 0.45049 0.00000 12 -0.00224 0.02656 0.03684 0.00000 0.00000 -0.45049 13 -0.02780 0.59067 0.73864 -0.11307 0.00000 0.00000 14 0.00388 -0.08572 -0.10658 0.00000 0.11307 0.00000 15 0.00459 -0.10023 -0.12386 0.00000 0.00000 -0.11307

247

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 0.00359 0.02898 -0.02334 -0.45049 0.00000 0.00000 17 -0.01574 -0.12421 0.09839 0.00000 0.45049 0.00000 18 0.02027 0.13232 -0.10646 0.00000 0.00000 -0.45049 19 -0.01504 -0.11077 0.08786 -0.11307 0.00000 0.00000 20 0.06943 0.49319 -0.39207 0.00000 0.11307 0.00000 21 -0.07782 -0.56108 0.44781 0.00000 0.00000 -0.11307 22 -0.50998 0.04181 -0.04025 -0.11307 0.00000 0.00000 23 0.41447 -0.03516 0.03333 0.00000 0.11307 0.00000 24 0.65662 -0.05435 0.05202 0.00000 0.00000 -0.11307 25 0.06556 0.00929 0.01586 -0.11307 0.00000 0.00000 26 0.24914 0.03393 0.05958 0.00000 0.11307 0.00000 27 -0.04957 -0.00620 -0.01133 0.00000 0.00000 -0.11307

ROOT NO. 25 26 27

14.39877 18.08850 14.30156

1 -0.00022 0.00001 0.00034 2 -0.32720 0.20991 0.43209 3 0.03285 0.53472 -0.23061 4 -0.00018 0.00001 0.00028 5 -0.00046 0.00021 0.00042 6 -0.00023 0.00053 -0.00042 7 -0.30933 0.19841 0.40875 8 0.10474 -0.06733 -0.13862 9 -0.46766 -0.27111 -0.21770 10 0.18643 0.33130 -0.39764 11 0.49609 0.01860 0.11239 12 0.22515 -0.11892 0.22376 13 0.05238 0.06109 -0.10099 14 0.16127 -0.03273 -0.05182 15 0.06104 -0.11405 0.09967 16 0.12334 -0.52954 -0.01186 17 -0.27351 -0.16102 -0.40547 18 0.20998 -0.14436 0.22463 19 -0.00984 -0.17294 0.07315 20 -0.13498 -0.04733 -0.12687 21 -0.00086 -0.03374 0.01545 22 -0.09603 0.12751 0.10478 23 0.05264 0.01544 0.04261 24 -0.14722 -0.02467 -0.09747 25 0.05319 -0.01642 -0.07623

248

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 -0.07793 0.06327 0.13315 27 0.08649 0.16940 -0.01660 1

DESCRIPTION OF VIBRATIONS

VIBRATION 1 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 190.99 0 6 - H 7 23.9% (75.3%) 0.4% T-DIPOLE 0.6107 0 4 - H 5 23.7% 0.0% TRAVEL 0.3262 0 3 - H 8 14.1% 0.0% RED. MASS 1.6585 O 1 - H 9 12.0% 1.0%

VIBRATION 2 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 193.46 0 6 - H 7 21.5% (71.4%) 0.0% T-DIPOLE 0.6260 0 4 - H 5 19.1% 0.4% TRAVEL 0.3238 0 3 - H 8 17.9% 0.8% RED. MASS 1.6618 01 -H 9 15.5% 0.0%

VIBRATION 3 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 243.21 0 1 - H 9 30.7% (57.9%) 0.8% T-DIPOLE 0.1491 0 3 - H 8 26.6% 0.2% TRAVEL 0.2527 0 4 - H5 13.4% 1.7% RED. MASS 2.1708 O 6 - H 7 9.1% 0.5%

VIBRATION 4 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 288.86 B 2 - 0 4 19.7% (80.6%) 0.3% T-DIPOLE 0.9111 B 2 — 0 6 18.8% 0.3% TRAVEL 0.1238 0 1 - B2 18.5% 0.1% RED. MASS 7.6163 B 2 - O 3 17.6% 0.2%

VIBRATION 5 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 339.08 O 1 - B 2 17.7% (54.1%) 0.0% T-DIPOLE 0.0813 B 2 — 0 6 16.0% 0.0% TRAVEL 0.1056 B 2 — 0 3 12.9% 0.0% RED. MASS 8.9078 B 2 — 0 4 12.1% 0 .0% 0 3 - H 8 11.4% 1.5%

O 1 - H 9 11.3% 2.9%

VIBRATION ATOM PAIR ENERGY CONTRIBUTION RADIAL

249

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. FREQ. 341.10 B 2 - 0 3 23.4% (116.8%) 0.1% T-DIPOLE 0.5110 B 2 — 0 4 22.9% 0.1% TRAVEL 0.0599 B 2 - 0 6 22.1% 0.1% RED. MASS 27.5776 0 1 - B 2 21.7% 0.1%

VIBRATION 7 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 460.45 B 2 - 0 4 23.8% (118.5%) 0.0% T-DIPOLE 0.5677 B 2 - 0 3 23.7% 0.0% TRAVEL 0.0750 0 1 - B2 15.0% 5.6% RED. MASS 13.0327 B2-06 15.0% 4.9%

VIBRATION 8 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 460.64 B2-- 06 23.9% (118.9%) 0.0% T-DIPOLE 0.5582 O 1 - B 2 23.6% 0.0% TRAVEL 0.0749 B 2 - 0 4 15.2% 4.4% RED. MASS 13.0566 B2-03 14.8% 6.3%

VIBRATION 9 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 485.26 B 2 — 0 3 17.6% (80.3%) 2.4% T-DIPOLE 1.8609 O 1 - B 2 17.4% 2.8% TRAVEL 0.0923 B 2 — 0 6 17.4% 3.1% RED. MASS 8.1542 B 2 — 0 4 17.3% 3.5% 1

VIBRATION 10 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 860.17 B 2 — 0 4 13.2% (45.8%) 100.0% T-DIPOLE 0.0175 O 1 - B 2 13.2% 99.9% TRAVEL 0.0693 B 2 — 0 6 13.2% 100.0% RED. MASS 8.1695 B 2 — 0 3 13.0% 99.9% 0 3 - H 8 11.9% 4.2% O 1 - H 9 11.9% 4.2% 0 6 - H 7 11.8 % 4.3% 0 4 - H 5 11.8 % 4.2%

VIBRATION 11 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 1071.45 B 2 — 0 4 22.9% (77.8%) 84.8% T-DIPOLE 1.6266 B 2 — 0 3 22.7% 81.8% TRAVEL 0.0785 B 2 — 0 6 16.5% 31.9% RED. MASS 5.1047 O 1 - B 2 16.2% 26.7%

250

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VIBRATION 12 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 1072.86 B 2 — 0 6 23.0% (77.7%) 83.9% T-DIPOLE 1.6277 0 1 - B 2 22.6% 82.8% TRAVEL 0.0785 B 2 — 0 3 16.4% 30.1% RED. MASS 5.0973 B 2 — 0 4 16.3% 28.6%

VIBRATION 13 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 1168.69 0 1 - B 2 23.0% (77.8%) 56.3% T-DIPOLE 4.3597 B 2 — 0 3 22.9% 55.2% TRAVEL 0.0693 B 2 — 0 4 22.6% 54.6% RED. MASS 6.0080 B 2 — 0 6 22.5% 52.7%

VIBRATION 14 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 1302.53 O 1 - H 9 24.9% (51.1%) 2.2% T-DIPOLE 0.0167 0 3 - H 8 24.8% 2.3% TRAVEL 0.1755 0 6 - H 7 24.3% 2.2% RED. MASS 0.8401 0 4 - H 5 23.2% 2.2%

VIBRATION 15 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 1347.75 0 4 - H 5 20.9% ( 47.7% 3.8% T-DIPOLE 0.0907 0 6 - H 7 20.2% 3.7% TRAVEL 0.1471 O 1 - H 9 18.8% 3.9% RED. MASS 1.1562 0 3 - H 8 18.8% 3.8%

VIBRATION 16 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 1439.52 0 3 - H 8 16.9% (47.1%) 4.4% T-DIPOLE 1.4128 0 4 - H 5 15.7% 4.3% TRAVEL 0.1016 O 1 - B 2 15.2% 64.9% RED. MASS 2.2708 B 2 - 0 6 15.1% 68.5% B 2 — 0 3 12.9% 3.6% B 2 — 0 4 12.8 % 2.9%

VIBRATION 17 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 1440.56 0 6 - H 7 16.5% ( 46.5%) 4.2% T-DIPOLE 1.4093 O 1 - H 9 16.2% 4.4% TRAVEL 0.1016 B 2 — 0 3 15.3% 68 .8 % RED. MASS 2.2691 B 2 - - 0 4 15.0% 64.0% B 2 — 0 6 12.9% 2.6%

O 1 - B 2 12.8 % 4.1% 1

251

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VIBRATION 18 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 3596.20 O 1 - H 9 91.8% (96.0%) 99.9% T-DIPOLE 0.2197 0 3 - H 8 7.3% 99.8% TRAVEL 0.1166 0 4 - H 5 0.5% 100.0% RED. MASS 0.6891 0 1 - B 2 0.3% 2 .8 %

VIBRATION 19 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 3598.68 O 3 - H 8 91.1% (95.6%) 99.9% T-DIPOLE 0.2682 0 1 - H 9 7.3% 99.8% TRAVEL 0.1165 0 6 - H 7 1.2% 99.8% RED. MASS 0.6898 B 2 — 0 3 0.3% 2 .1%

VIBRATION 20 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 3604.36 0 6 - H 7 60.2% ( 77.7% 99.9% T-DIPOLE 0.2271 0 4 - H 5 38.7% 99.9% TRAVEL 0.1165 O 3 - H 8 0.6% 99.8% RED. MASS 0.6893 B 2 — 0 6 0.2% 2.3%

VIBRATION 21 ATOM PAIR ENERGY CONTRIBUTION RADIAL FREQ. 3605.73 0 4 - H 5 60.4% ( 77.8%) 99.9% T-DIPOLE 0.2773 0 6 - H 7 38.2% 99.9% TRAVEL 0.1164 0 3 - H 8 0.6% 99.8% RED. MASS 0.6904 O 1 - H 9 0.4% 100.0%

SYSTEM IS A GROUND STATE

MOP AC Calculation from Cerius2

MOLECULE IS NOT LINEAR

THERE ARE 21 GENUINE VIBRATIONS IN THIS SYSTEM THIS THERMODYNAMICS CALCULATION IS LIMITED TO MOLECULES WHICH HAVE NO INTERNAL ROTATIONS

252

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CALCULATED THERMODYNAMIC PROPERTIES * TEMP. (K) PARTITION FUNCTION H.O.F. ENTHALPY HEAT CAPACITY ENTROPY KCAL/MOL CAL/MOLE CAL/K/MOL CAL/K/MOL

200 VIB. 3.295 969.57098 11.65006 7.21722 ROT. 0.405E+05 596.178 2.981 24.065 INT. 0.134E+06 1565.749 14.631 31.282 TRA. 0.372E+27 993.630 4.968 37.009 TOT. -355.915 2559.3790 19.5991 68.2913

210 VIB. 3.726 1088.73030 12.17806 7.79849 ROT. 0.436E+05 625.987 2.981 24.211 INT. 0.162E+06 1714.717 15.159 32.009 TRA. 0.400E+27 1043.312 4.968 37.251 TOT. -355.716 2758.0287 20.1271 69.2603

220 VIB. 4.223 1213.06225 12.68508i 8.37679 ROT. 0.468E+05 655.796 2.981 24.349 INT. 0.197E+06 1868.858 15.666 32.726 TRA. 0.429E+27 1092.993 4.968 37.482 TOT. -355.513 2961.8511 20.6341 70.2083

230 VIB. 4.795 1342.37152 13.17396i 8.95151 ROT. 0.500E+05 685.605 2.981 24.482 INT. 0.240E+06 2027.976 16.155 33.433 TRA. 0.459E+27 1142.674 4.968 37.703 TOT. -355.304 3170.6507 21.1230 71.1362

240 VIB. 5.452 1476.48900 13.64710 i 9.52224 ROT. 0.533E+05 715.414 2.981 24.609 INT. 0.290E+06 2191.903 16.628 34.131 TRA. 0.489E+27 1192.356 4.968 37.914 TOT. -355.090 3384.2586 21.5961 72.0452

250 VIB. 6.206 1615.26775 14.10652. 10.08870 ROT. 0.566E+05 745.222 2.981 24.730 INT. 0.351E+06 2360.490 17.087 34.819 TRA. 0.520E+27 1242.037 4.968 38.117 TOT. -354.872 3602.5277 22.0556 72.9360

260 VIB. 7.071 1758.57917 14.55388 10.65072 ROT. 0.601 E+05 775.031 2.981 24.847 INT. 0.425E+06 2533.611 17.535 35.498

253

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TRA. 0.552E+27 1291.719 4.968 38.312 TOT. -354.649 3825.3296 22.5029 73.8097

270 VIB. 8.062 1906.30949 14.99049 ' 11.20821 ROT. 0.636E+05 804.840 2.981 24.960 INT. 0.513E+06 2711.150 17.971 36.168 TRA. 0.584E+27 1341.400 4.968 38.499 TOT. -354.422 4052.5503 22.9395 74.6671

280 VIB. 9.199 2058.35667 15.41740i 11.76112 ROT. 0.671E+05 834.649 2.981 25.068 INT. 0.618E+06 2893.006 18.398 36.829 TRA. 0.616E+27 1391.082 4.968 38.680 TOT. -354.190 4284.0879 23.3664 75.5090

290 VIB. 10.50 2214.62773 15.83538 12.30945 ROT. 0.708E+05 864.458 2.981 25.173 INT. 0.743E+06 3079.086 18.816 37.482 TRA. 0.650E+27 1440.763 4.968 38.854 TOT. -353.955 4519.8493 23.7844 76.3362

300 VIB. 11.99 2375.03650 16.24502 12.85322 ROT. 0.745E+05 894.267 2.981 25.274 INT. 0.893E+06 3269.304 19.226 38.127 TRA. 0.684E+27 1490.445 4.968 39.022 TOT. -353.715 4759.7485 24.1941 77.1494

310 VIB. 13.69 2539.50183 16.64675 13.39247 ROT. 0.782E+05 924.076 2.981 25.372 INT. 0.107E+07 3463.578 19.628 38.764 TRA. 0.718E+27 1540.126 4.968 39.185 TOT. -353.471 5003.7042 24.5958 77.9492

320 VIB. 15.64 2707.94605 17.04084 13.92722 ROT. 0.820E+05 953.885 2.981 25.466 INT. 0.128E+07 3661.831 20.022 39.393 TRA. 0.753E+27 1589.808 4.968 39.343 TOT. -353.223 5251.6389 24.9899 78.7363

330 VIB. 17.87 2880.29391 17.42750 14.45754 ROT. 0.859E+05 983.694 2.981 25.558 INT. 0.153E+07 3863.988 20.408 40.016 TRA. 0.789E+27 1639.489 4.968 39.496 TOT. -352.971 5503.4771 25.3765 79.5111

340 VIB. 20.41 3056.47166 17.80683 14.98345

254

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ROT. 0.898E+05 1013.503 2.981 25.647 INT. 0.183E+07 4069.974 20.788 40.630 TRA. 0.825E+27 1689.171 4.968 39.644 TOT. -352.715 5759.1453 25.7559 80.2742

350 VIB. 23.32 3236.40642 18.17891 15.50501 ROT. 0.938E+05 1043.312 2.981 25.733 INT. 0.219E+07 4279.718 21.160 41.238 TRA. 0.862E+27 1738.852 4.968 39.788 TOT. -352.456 6018.5704 26.1280 81.0262

360 VIB. 26.63 3420.02579 18.54376 16.02226 ROT. 0.979E+05 1073.120 2.981 25.817 INT. 0.261E+07 4493.146 21.525 41.840 TRA. 0.899E+27 1788.534 4.968 39.928 TOT. -352.193 6281.6802 26.4928 81.7673

370 VIB. 30.41 3607.25753 18.90139 16.53523 ROT. 0.102E+06 1102.929 2.981 25.899 INT. 0.310E+07 4710.187 21.882 42.434 TRA. 0.936E+27 1838.215 4.968 40.064 TOT. -351.926 6548.4023 26.8504 82.4980

380 VIB. 34.71 3798.02942 19.25179 17.04397 ROT. 0.106E+06 1132.738 2.981 25.979 INT. 0.368E+07 4930.768 22.233 43.022 TRA. 0.975E+27 1887.897 4.968 40.196 TOT. -351.656 6818.6646 27.2008 83.2186

390 VIB. 39.62 3992.26921 19.59496 17.54849 ROT. 0.110E+06 1162.547 2.981 26.056 INT. 0.437E+07 5154.816 22.576 43.604 TRA. 0.101E+28 1937.578 4.968 40.325 TOT. -351.382 7092.3948 27.5440 83.9296

400 VIB. 45.21 4189.90463 19.93091 18.04885 ROT. 0.115E+06 1192.356 2.981 26.131 INT. 0.518E+07 5382.261 22.912 44.180 TRA. 0.105E+28 1987.260 4.968 40.451 TOT. -351.105 7369.5206 27.8800 84.6311

410 VIB. 51.57 4390.86346 20.25965 18.54505 ROT. 0.119E+06 1222.165 2.981 26.205 INT. 0.613E+07 5613.028 23.241 44.750 TRA. 0.109E+28 2036.941 4.968 40.573 TOT. -350.824 7649.9699 28.2087 85.3235

255

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 420 VIB. 58.80 4595.07366 20.58119 19.03713 ROT. 0.123E+06 1251.974 2.981 26.277 INT. 0.725E+07 5847.047 23.562 45.314 TRA. 0.113E+28 2086.623 4.968 40.693 TOT. -350.541 7933.6705 28.5302 86.0071

430 VIB. 67.03 4802.46350 20.89558 19.52511 ROT. 0.128E+06 1281.783 2.981 26.347 INT. 0.856E+07 6084.246 23.876 45.872 TRA. 0.117E+28 2136.304 4.968 40.810 TOT. -350.254 8220.5507 28.8446 86.6821

440 VIB. 76.37 5012.96167 21.20287 20.00903 ROT. 0.132E+06 1311.592 2.981 26.416 INT. 0.101E+08 6324.553 24.184 46.425 TRA. 0.121E+28 2185.986 4.968 40.924 TOT. -349.964 8510.5393 29.1519 87.3487

450 VIB. 86.98 5226.49749 21.50313 20.48889 ROT. 0.137E+06 1341.400 2.981 26.483 INT. 0.119E+08 6567.898 24.484 46.971 TRA. 0.126E+28 2235.668 4.968 41.036 TOT. -349.671 8803.5655 29.4522 88.0071

460 VIB. 99.02 5443.00104 21.79643 20.96473 ROT. 0.141E+06 1371.209 2.981 26.548 INT. 0.140E+08 6814.210 24.777 47.513 TRA. 0.130E+28 2285.349 4.968 41.145 TOT. -349.375 9099.5594 29.7455 88.6576

470 VIB. 112.7 5662.40330 22.08289 21.43657 ROT. 0.146E+06 1401.018 2.981 26.612 INT. 0.165E+08 7063.422 25.064 48.049 TRA. 0.134E+28 2335.030 4.968 41.252 TOT. -349.076 9398.4521 30.0319 89.3004

480 VIB. 128.2 5884.63628 22.36260 21.90443 ROT. 0.151E+06 1430.827 2.981 26.675 INT. 0.193E+08 7315.463 25.343 48.579 TRA. 0.138E+28 2384.712 4.968 41.356 TOT. -348.774 9700.1755 30.3116 89.9355

490 VIB. 145.7 6109.63318 22.63569 22.36835 ROT. 0.155E+06 1460.636 2.981 26.736 INT. 0.226E+08 7570.269 25.617 49.105

256

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TRA. 0.143E+28 2434.393 4.968 41.459 TOT. -348.470 10004.6628 30.5847 90.5633

500 VIB. 165.6 6337.32847 22.90230 22.82835 ROT. 0.160E+06 1490.445 2.981 26.797 INT. 0.265E+08 7827.773 25.883 49.625 TRA. 0.147E+28 2484.075 4.968 41.559 TOT. -348.163 10311.8485 30.8513 91.1839

510 VIB. 188.0 6567.65800 23.16256 23.28445 ROT. 0.165E+06 1520.254 2.981 26.856 INT. 0.310E+08 8087.912 26.143 50.140 TRA. 0.152E+28 2533.756 4.968 41.657 TOT. -347.853 10621.6684 31.1116 91.7973

520 VIB. 213.5 6800.55911 23.41664 23.73670 ROT. 0.170E+06 1550.063 2.981 26.913 INT. 0.363E+08 8350.622 26.398 50.650 TRA. 0.156E+28 2583.438 4.968 41.754 TOT. -347.540 10934.0599 31.3657 92.4039

530 VIB. 242.2 7035.97063 23.66468 24.18510 ROT. 0.175E+06 1579.872 2.981 26.970 INT. 0.423E+08 8615.842 26.646 51.155 TRA. 0.161E+28 2633.119 4.968 41.848 TOT. ■347.22511248.9618 31.6137 93.0037

540 VIB. 274.7 7273.83303 23.90684 24.62971 ROT. 0.180E+06 1609.681 2.981 27.026 INT. 0.494E+08 8883.514 26.888 51.656 TRA. 0.165E+28 2682.801 4.968 41.941 TOT. ■346.90811566.3146 31.8559 93.5968

550 VIB. 311.3 7514.08837 24.14329 25.07055 ROT. 0.185E+06 1639.490 2.981 27.081 INT. 0.575E+08 9153.578 27.124 52.151 TRA. 0.170E+28 2732.482 4.968 42.032 TOT. ■346.588 11886.0604 32.0923 94.1835

560 VIB. 352.7 7756.68041 24.37421 25.50766 ROT. 0.190E+06 1669.298 2.981 27.134 INT. 0.670E+08 9425.979 27.355 52.642 TRA. 0.174E+28 2782.164 4.968 42.122 TOT. ■346.266 12208.1428 32.3232 94.7637

570 VIB. 399.3 8001.55457 24.59974 25.94107

257

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ROT. 0.195E+06 . 1699.107 2.981 27.187 INT. 0.779E+08 9700.662 27.581 53.128 TRA. 0.179E+28 2831.845 4.968 42.210 TOT. ■345.942 12532.5074 32.5488 95.3378

580 VIB. 451.9 8248.65797 24.82008 26.37082 ROT. 0.200E+06 1728.916 2.981 27.239 INT. 0.904E+08 9977.574 27.801 53.610 TRA. 0.184E+28 2881.527 4.968 42.296 TOT. -345.615 12859.1012 32.7691 95.9058

590 VIB. 511.1 8497.93940 25.03538 26.79695 ROT. 0.205E+06 1758.725 2.981 27.290 INT. 0.105E+09 10256.665 28.016 54.087 TRA. 0.189E+28 2931.208 4.968 42.381 TOT. ■345.286 13187.8730 32.9844 96.4677

600 VIB. 577.7 8749.34937 25.24581 27.21949 ROT. 0.211E+06 1788.534 2.981 27.340 INT. 0.122E+09 10537.883 28.227 54.560 TRA. 0.193E+28 2980.890 4.968 42.464 TOT. •344.956 13518.7734 33.1949 97.0238

* NOTE: HEATS OF FORMATION ARE RELATIVE TO THE ELEMENTS IN THEIR STANDARD STATE AT 298K

TOTAL CPU TIME: 21.72 SECONDS

= MOP AC DONE ==

258

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY

1) Steudel, R., Chemistry o f the Non-Metals, eds., F. C. Nachod, and J. J. Zuckerman, Walter de Gruyter & Co. Berlin, NY, pp. 361-383, 1977.

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