STABILITY AND PROPERTIES OF
SUPERSATURATED VANADIUM ELECTROLYTES FOR HIGH ENERGY DENSITY VANADIUM REDOX BATTERY
A thesis submitted as part of the requirements for the degree of
Doctor of Philosophy (Ph.D.)
by FAIZUR RAHMAN M.S. (Chem. Eng.)
School of Chemical Engineering and Industrial Chemistry The University of New South Wales Sydney 2052 Australia
March 1998 U N S W 1 < JUL 1999 LIBRARY CERTIFICATE OF ORIGINALITY
I hereby declare that this submission is my own work and that, to the best of my knowledge and belief, it contains no material previously published or written by another person nor material which to a substantial extent has been accepted for the award of any other degree or diploma of a university or other institute of higher learning, except where due acknowledgement is made in the text. I also declare that the intellectual content of this thesis is the product of my own work, even though I may have received assistance from others on style, presentation and language expression.
ii Dedicated to my wife Aliya
and my children Ejaz, Sameera, Abdurrahaman & Saeed
iii ACKNOWLEDGEMENTS
I am extremely thankful and deeply indebted to Professor Maria Skyllas- Kazacos for her guidance, constant support, patience and untiring effort during all the stages of this research.
I wish to express my appreciation and thanks for technical support and advice to Mr. M. Kazacos, Dr. C. Menictas, Mrs. K. Nasev, Mr. H. Chau, Mr. S. Jacenyik, Mr. Rui Hong and Mr. J. Wilson, and for typing to Mr. G. N. Dar. I also thank Dr. D. Finlayson and Dr. J. Hook, School of Chemistry, The University of New South Wales for conducting ICP analyses and NMR spectra respectively.
I would like to thank my fellow postgraduates A. Tham, V. Haddadi, T. Mohammadi, A. Moline, C. Peng, A. Smith, and A. Mousa for their help and suggestions.
I wish to thank the management of King Fahd University of Petroleum and Minerals for approving the study leave. Special thanks are due to Dr. A.G. Maadhah and Dr. Halim Hamid for their support and encouragement.
I wish to express sincere thanks to my parents, sisters, and brothers for all they have done. Finally, I would like to mention that, without the sacrifices, patience, prayers, encouragement and understanding of my wife and children it would not have been possible to complete this work.
The financial support provided by the Australian Research Council is gratefully acknowledged. PUBLICATIONS ARISING FROM THE STUDY
Rahman, F., C. Z. X. Peng and M. Skyllas-Kazacos, “Improved Additives for Supersaturated Vanadium(V)/Vanadium(IV) Electrolytes”, patent offered to Unisearch Ltd. and being under review, 1996.
Rahman, F., C. Z. X. Peng and M. Skyllas-Kazacos, “Stability of Supersaturated Vanadium Electrolytes for High Energy Density Redox Cell”, Chemica ‘96, 24th Australian New Zealand Chemical Engineering Conference and Exhibition, Sydney Australia, 30 September - 2 October 1996.
Rahman, F. and M. Skyllas-Kazacos, “Solubility of Vanadyl Sulfate in Concentrated Sulfuric Acid Solutions”, Journal of Power Sources, Vol. 72, pp. 105-110, 1997.
Rahman, F. and M. Skyllas-Kazacos, “Solubility of Vanadium Oxides in Sulfuric Acid Solutions”, in preparation.
Rahman, F. and M. Skyllas-Kazacos, “Properties and Electrochemical Behaviour of Supersaturated Vanadium(V) Electrolytes for Vanadium Redox Batteries”, in preparation.
Rahman, F. and M. Skyllas-Kazacos, “Stability Evaluation and Kinetics of Precipitation of Supersaturated Vanadium(V) Electrolytes”, in preparation.
Rahman, F. and M. Skyllas-Kazacos, “Evaluation of Additives to Prevent Thermal Precipitation of Supersaturated Vanadium(V) Electrolytes for High Energy Density Vanadium Redox Battery”, in preparation. ABSTRACT
The All Vanadium Redox Flow Battery being developed at The University of New South Wales is showing promising results for various stationary applications such as remote area power systems, load levelling at power plants and emergency back-up applications. The electrolyte is one of the important components of the vanadium redox battery. The V(V)/V(IV) redox couple in the positive half-cell and V(II)/V(III) redox couple in the negative half-cell are separated by an ion exchange membrane with sulfuric acid as the supporting electrolyte.
Demand for longer life, and high energy density batteries is increasing for mobile applications. This research was therefore undertaken to increase the energy density of the vanadium redox battery so as to reduce the weight and volume of the battery required for mobile applications. The main emphasis of the study was to prepare supersaturated vanadium(V) electrolytes and determine the optimum conditions at which these vanadium(V) electrolytes are stable.
Solubility data of V2O5 was generated in sulfuric acid solutions of concentrations ranging between 0-9 M and at temperatures from 10 °C - 50 °C.
The solubility of V2O5 was found to decrease with increasing temperature due to the endothermic nature of the precipitation reaction of V02+ ions. It was found that increasing the sulfuric acid concentration increases the solubility of
V205 because of several factors such as the increase in H+ ions, formation of vanadium and sulfate/bisulfate complexes and dimerisation/polymerisation of V02+ ions. A solubility correlation was developed to predict the solubility of
V205 as a function of sulfuric acid concentration and temperature with an absolute average deviation of about 9 %.
vi The solubility data for VOSO4 was also generated in sulfuric acid concentrations ranging from 0-9M and over the temperature range of 10 °C - 50°C. Total vanadium and total sulfur in the liquid samples at equilibrium were determined by Inductively Coupled Plasma analysis (ICP). Increasing sulfuric acid concentration decreases solubility sharply at lower sulfuric acid concentrations but decreases only slightly as the sulfuric acid concentration is further increased above 6M. In a similar manner, the increase in solubility with increasing temperature is more pronounced at lower H2S04 concentrations. The variation in solubility is due to the common ion effect and is strongly linked with the second dissociation constant of H2S04 at different temperatures and sulfuric acid concentrations. The solubility data and saturation ionic product
(Ksip) data of vanadyl sulfate was correlated using the Extended Debye-Huckel functional form. For both correlations, the average absolute deviation was found to be less than 4.5 %. A vanadium scaling index (VSI) has been defined to predict scaling tendencies of supersaturated V(IV) solutions using a saturation ionic product (KSip) correlation.
The solubility of V203 in sulfuric acid could not be determined because of transformation of V203 to V0S04, particularly in solutions above 5M H2S04. However, total vanadium concentrations as high as 2 M were achieved with reagent grade V203 in 5M H2S04 by simple dissolution at 20 °C.
After investigating various methods it is recommended to prepare supersaturated vanadium(V) solution by electrolytic oxidation of supersaturated
V(IV) solution obtained by reacting V205 and V203 in sulfuric acid solution. Since the supersaturated V(IV) solutions are very sensitive to agitation and the presence of undissolved particles, the stability of V(IV) solution needs to be improved by preheating for an hour at its boiling point of about 115 °C and filtering the V(IV) solution twice before electrolysis to V(V).
vii The properties of supersaturated vanadium(V) solutions such as density, viscosity and conductivity were studied for V(V) concentrations ranging from 2M - 5 M and total sulfate/bisulfate concentrations of 5, 6 and 7 M. Increasing the V(V) concentration increases density but decreases conductivity due to increased viscosity and lowering of free H+ ions.
The viscosity of V(V) solutions increases gradually with increasing V(V) concentration in the range of 2 M to 3.5 M, but a further increase in V(V) concentration up to 5 M increases viscosity sharply. This behaviour indicates that the supersaturated V(V) solutions remain in the hydraulic type flow region at V(V) concentrations below 3.5 M and transform to the plastic flow region with a further increase in vanadium(V) concentration. The increase in viscosity is due to the formation of large size extended chain polyvanadic molecules and vanadium-sulfate complexes. It was discovered during the course of the study that supersaturated V(V) solutions in H2S04 absorb sufficient moisture when exposed to atmosphere with a significant drop in viscosity. Cyclic voltammetry and 51V NMR studies confirmed that an increase in water content in the vanadium(V) solution breaks the large size vanadium-sulfate complex ions and generates smaller size V(V) ions resulting in a significant drop in viscosity and a corresponding increase in conductivity.
The cyclic voltammograms of the supersaturated vanadium(V) solutions indicated that the peak currents are a maximum at 3.5 M V(V) concentration in 6 M total sulfates. The ageing of the V(V) solutions or addition of precipitation inhibitors to the V(V) solutions does not influence the electrochemical behaviour.
The induction time for the precipitation of V2O5 from supersaturated V(V) solutions increases with increasing sulfuric acid concentration and decreasing temperature. The increase in induction time with increasing sulfuric acid
viii concentration is believed to be due to the presence of more H+ ions (increased ratio of H+ ions to V(V) ions) which shifts the V2O5 precipitation equilibrium towards the formation of V02+. The stability might also be improved because of excess S042 ions (increased ratio of S to V(V) ions) available at higher H2S04 concentration which can prevent precipitation of V02+ ions to V2O5 by forming sulfate complexes with V02+. Further, the increase in stability could also be attributed to the dimerisation of V02+ ions to V2042+ and V2034+ species.
The kinetic study of the thermal precipitation of V(V) solutions indicated that the growth rate follows first order reaction kinetics under the conditions of low supersaturations with an activation energy of about 9.0 kJmol1, indicating diffusion controlled growth. At high supersaturations the V(V) precipitation obeys a second order rate equation. The high activation energy of 77.2 kJmof1 during second order crystal growth confirms that the precipitation of V(V) solution in the high supersaturation region is surface reaction controlled.
From the overall evaluation of the desupersaturation experiments, viscosity and conductivity measurements, and electrochemical behaviour of V(V) solutions, it appears that a suitable composition of V(V) electrolyte for the high energy density vanadium redox battery may be 3 M V(V) solution in 6 M total sulfate/bisulfate up to a temperature of about 30 °C.
Comprehensive studies were carried out to increase the V(V) concentration above 3 M and extend the temperature over 30 °C by evaluating a large number of additives as precipitation inhibitors and developing different formulations. A formulation developed by blending sodium hexametaphosphate (SHMP) and tripotassium phosphate (K3P04) was found to show better performance against precipitation of 4 M V(V) solution in 6M total sulfates at 40°C for about 40 days. Dosage optimization studies of formulation SHMP + K3P04 indicated
ix that KS11 (lwt % SHMP + lwt % K3P04) exhibited superior performance over other additive blends. The performance evaluation of formulation KS11 was carried out using solutions of different V(V) concentrations in various total sulfate/bisulfate concentrations at temperatures of 30, 40 and 50 °C. It was found that 3.5 M V(V) solution in 5.7 M total sulfates precipitated in 25 days at 40 °C, whereas addition of KS11 to this solution extended the induction time to about 60 days. The addition of KS11 also increased the apparent equilibrium concentration of V(V) solution to 3.21 M as compared to blank V(V) solution equilibrium concentration of 2.72 M.
The influence of these inhibitors on the nucleation rates and crystal growth may be due to (i) direct chelation of phosphate ion with V02+ ions to form stable complex (V02)3P04 and (ii) adsorption of the additive onto the precipitating ion, thus inhibiting scale nucleation, or adsorption onto the growing crystals, thus distorting and/or inhibiting further precipitation. Structural matching between the functional groups of the additives and the cations at the crystal surface plays an important role in determining the effectiveness of the additives.
Preliminary evaluation of formulation KS11 to inhibit precipitation of supersaturated V(II), V(III) and V(IV) solution was carried out. The induction time of 4 M V(IV) solution in 6M total sulfate/bisulfate at 20 °C was increased from 2 days for the blank solution to 56 days with the addition of KS11. The performance of KS11 against V(III) solution was evaluated at 3 °C in the refrigerator. The blank V(III) solution of concentration 4 M in 6 M total sulfate/bisulfate as well as a sample with KS 11 surprisingly did not show any sign of precipitation for about 3 months. However, the induction time of 2 M V(II) solution in 5 M total sulfate/bisulfate with KS11 was found to be about 27 days while that of a blank V(II) solution was observed to be 5 days at 3 °C. It appears that the formulation KS11 may act as a comprehensive additive if it shows promising results after further investigations against the precipitation of V(II), V(III) and V(IV) solutions at temperatures of about 5 °C - 40 °C, higher vanadium concentrations of 3.5 M and total sulfate concentrations up to 6 M.
A solution of composition 3.5 M V(V) in total sulfate/bisulfate concentration of 5.7 M with additive formulation KS11 appears to be very attractive for a high energy density vanadium redox battery up to a temperature of 40°C. If 3.5 M V(V) solution in 5.7 M total sulfate/bisulfate takes two months before it starts discharging in the vanadium redox battery, the formulation KS 11 may be used safely to hold the precipitation of V(V) solution for about two months. The transformation of V(V) species to V(IV) during the discharge cycle of the battery will further enhance the stability of V(V) solution due to the lowering of state-of-charge. TABLE OF CONTENTS
Section Title Page
CERTIFICATE OF ORIGINALITY...... ii
ACKNOWLEDGEMENT...... iii
ABSTRACT ...... v
CHAPTER 1 INTRODUCTION...... 1
CHAPTER 2 LITERATURE REVIEW...... 8
2.1 ENERGY STORAGE SYSTEMS...... 8
2.1.1 Redox Flow Battery...... 9
2.1.2 Vanadium Redox Flow Battery...... 12
2.1.2.1 Advantages...... 16
2.1.2.2 Applications...... 17
2.2 SOLUBILITY OF VANADIUM COMPOUNDS...... 18
2.2.1 Solubility of V2Os...... 19
2.2.2 Solubility of VOSO4...... 21
2.2.3 Solubility of V203...... 21
2.3 VANADIUM(V) ELECTROLYTE...... 22
2.3.1 Aqueous Chemistry...... 22
2.3.2 Previous Work on Stability of Supersaturated V(V) Solutions...... 27
2.3.3 Additives for the Control of Thermal Precipitation of V(V) Solutions...... 28
2.3.3.1 Precipitation Inhibitors Used in Water Formed Scale Deposits...... 28
2.3.3.2 Precipitation Inhibitors for Vanadium(V) Solutions...... 34
CHAPTER 3 THEORETICAL CONSIDERATIONS...... 38
3.1 SUPERSATURATED SOLUTIONS...... 38
3.1.1 Theoretical Background and Solubility...... 38
3.1.2 Solubility and its importance in the precipitation...... 42
3.1.3 Maximum Supersaturation and Supersolubility...... 43
3.1.4 Methods of Preparing Supersaturated Solutions...... 45
3.2 KINETICS AND MECHANISM...... 46
3.2.1 Nucleation...... 47 xii 3.2.2 Induction Time...... 53
3.2.3 Crystal Growth...... 55
3.3 CYCLIC VOLTAMMETRY...... 59
CHAPTER 4 SOLUBILITY STUDIES...... 65
4.1 INTRODUCTION...... 65
4.2 EXPERIMENTAL PROCEDURE...... 66
4.3 RESULTS AND DISCUSSION...... 67
4.3.1 Solubility of V2Os...... 68
4.3.1.1 Effect of H2S04 Concentration...... 72
4.3.1.2 Effect of Temperature...... 75
4.3.1.3 Solubility Correlations of V205...... 76
4.3.2 Solubility of V0S04...... 79
4.3.2.1 Effect of H2S04 Concentration...... 84
4.3.2.2 Effect of Temperature...... 86
4.3.2.3 Solubility Correlations of VOS04...... 88
4.3.2.4 Saturated Ionic Product Correlations...... 90
4.3.3 Solubility of V203...... 91
4.3.3.1 Effect of H2S04 Concentration...... 93
4.3.3.2 Effect of Temperature on Saturation Concentration...... 96
4.3.3.3 Solubility Correlations of V203...... 96
4.3.4 Theoretical Equilibrium Calculations for System: V205 - H2S04 - H20...... 97
4.4 SUMMARY OF RESULTS...... 101
CHAPTER 5 STABILITY OF SUPERSATURATED VANADIUM(V) SOLUTIONS.. 105
5.1 INTRODUCTION...... 105
5.2 EXPERIMENTAL...... 105
5.2.1 Preparation of Supersaturated V(V) Solutions...... 105
5.2.1.1 Preparation of Vanadium(V) Solution by Electrolytic Oxidation of Vanadium(IV) Solution...... 106
5.2.1.2 Preparation of Supersaturated V(IV) Solutions...... 109
xiii 5.2.1.2.1 Factors Affecting Stability of Supersaturated V(IV) Solution...... 111
5.2.1.3 Preparation of Vanadium(V) Solution by Electrolytic Dissolution of V2O3 or V205...... 115
5.2.1.3.1 Electrolytic Oxidation of V203 Powder...... 115
5.2.1.3.2 Electrolytic Reduction of V205 Powder...... 115
5.2.2 Experimental Procedure for Cyclic Voltammetry...... 116
5.2.3 Experimental Procedure for Supersaturated V(V) Solutions Stability Evaluation and Kinetic Study...... 118
5.3 RESULTS AND DISCUSSION...... 119
5.3.1 Preliminary Investigation of the Stability of Supersaturated V(V) Solutions...... 119
5.3.2 Description of Supersaturated V(V) Solutions Prepared for Stability Evaluation and Kinetic Study...... 122
5.3.3 Properties of Supersaturated Vanadium(V) Solutions...... 123
5.3.3.1 Density of Vanadium(V) Solution...... 123
5.3.3.1.1 Density Correlation of V(V) Solution...... 125
5.3.3.2 Viscosity Behaviour of Supersaturated Vanadium(V) Solutions...... 128
5.3.3.2.1 Effect of Concentration on Viscosity...... 129
5.3.3.2.2 Effect of Temperature on Viscosity...... 133
5.3.3.2.3 Variation in Viscosity of V(V) Solutions with Time...... 134
5.3.3.2.4 Change in Viscosity of V(V) Solutions When Exposed to Atmosphere...... 135
5.3.3.2.5 Electrochemical Studies of V(V) Solutions With and Without Water Addition...... 137
5.3.3.2.6 51V NMR Studies of Vanadium (V) Solutions...... 137
5.3.3.2.7 Verification of Moisture Absorption of V(V) Solutions When Exposed to Atmosphere...... 139
5.3.3.3 Effect of Supersaturation on Conductivity...... 143
5.3.4 Effect of the State-of-Charge on Stability...... 148
5.3.5 Effect of Stirring on Stability...... 149
5.3.6 Electrochemical Behaviour of Vanadium(V) Solutions...... 150
5.3.6.1 Effect of Elapsed Time...... 150
5.3.6.2 Effect of V(V) Concentration...... 154
xiv 5.3.6.3 Effect of Total Sulfates/Bisulfate Concentration...... 157
5.3.6.4 Calculation of Diffusion Coefficients and Rate Constants...... 161
5.3.7 Desupersaturation Experiments of Vanadium(V) Solution...... 169
5.3.8 Induction time...... 178
5.3.9 Effect of Temperature on Stability...... 181
5.3.10 Effect of Sulfuric Acid Concentration on Stability...... 182
5.3.10.1 51V NMR Studies of Vanadium (V) Solutions with Different Total Sulfate/bisulfate...... 185
5.3.11 Kinetics of Thermal Precipitation of Vanadium(V) Solutions...... 187
5.3.11.1 Kinetics of Crystal Growth...... 187
5.3.11.2 Evaluation of Rate Constants...... 188
5.3.11.3 Dependence of Rate Constants on Temperature...... 197
5.4 SUMMARY OF RESULTS...... 198
CHAPTER 6 EVALUATION OF ADDITIVES TO INHIBIT VANADIUM(V) PRECIPITATION...... 205
6.1 INTRODUCTION...... 205
6.2 EXPERIMENTAL PROCEDURE...... 207
6.3 RESULTS AND DISCUSSION...... 207
6.3.1 Preliminary Screening of Additives...... 208
6.3.2 Development of Additive Formulations...... 215
6.3.3 Evaluation of Different Additive Formulations...... 216
6.3.4 Dosage Optimization of Formulation KS...... 222
6.3.5 Performance Evaluation ofKSll...... 224
6.3.5.1 Long Term Performance Evaluation of KS 11...... 224
6.3.5.2 Effect of Vanadium(V) concentration...... 226
6.3.5.3 Effect of Temperature...... 227
6.3.5.4 Effect of total Sulfate/bisulfate Concentration...... 230
6.3.6 Effect of Additive Addition on Electrochemical Behaviour...... 232
6.3.7 Evaluation of the Stability ofV(II), V(III) and V(IV) Solutions using KS11...... 234
6.4 SUMMARY OF RESULTS...... 236
xv CHAPTER 7 CONCLUSIONS...... 242
CHAPTER 8 REFERENCES...... 250
APPENDICES
APPENDIX A: CALIBRATION CURVE FOR ICP ANALYSIS AND SAMPLE CALCULATION
APPENDIX B: CALCULATION OF ACTIVITY COEFFICIENT USING BROMLEY CORRELATION
APPENDIX C: COMPUTER PROGRAM IN FORTRAN TO CALCULATE EQUILIBRIUM COMPOSITION OF VARIOUS SPECIES FOR THE SYSTEM: V205-H2S04-H20
APPENDIX D: PROCEDURE TO ADJUST TOTAL VANADIUM AND TOTAL SULFUR CONCENTRATION OF A GIVEN V(V) SOLUTION IN SULFURIC ACID
APPENDIX E: CALIBRATION CURVE FOR ATOMIC ABSORPTION ANALYSIS AND SAMPLE CALCULATION
APPENDIX F: FORTRAN PROGRAM TO CALCULATE DENSITY OF SULFURIC ACID SOLUTIONS AS A FUNCTION OF TEMPERATURE AND CONCENTRATION
APPENDIX G: PLOTS OF GROWTH RATE OF V(V) SOLUTIONS IN 5M AND 6M TOTAL SULFATE/BISULFATE AT 20, 30, 40 AND 50 °C
xvi LIST OF FIGURES
Title Page
Figure 1.1. Schematic of all vanadium redox flow battery being developed at The University of New South Wales...... 4
Figure 2.1. A typical diagram showing redox flow cell set-up...... — 10
Figure 2.2. Potential - pH diagram of V-H20 system at 25°C...... - 24
Figure 2.3. Distribution of vanadium(V) species as a function of pH at 1 molal ionic strength and 25°C. (a) 0.1 molal V(V) (b) 0.001 molal V(V)...... — 25
Figure 2.4. Predominance diagram of vanadium(V)-OH' species as a function of pH at 1 molal ionic strength and 25°C...... —...... — 26
Figure 3.1. A typical diagram showing states of solution. -...... 44
Figure 3.2. Supersolubility (dashed) and solubility (solid) curves of solutions of three salts: (1) KN03; (2) KC1 ; (3) KC103 [Tovbin and Kransnova, 1951]...... 45
Figure 3.3. Schematic representation of different categories of nucleation [Garside, 1985]...... 48
Figure 3.4. (a) Cyclic potential sweep; (b) resulting cyclic voltammogarm...... 61
Figure 3.5. Typical cyclic voltammogram showing peak currents (Ip) and peak potentials (Ep)...... 61
Figure 3.6. Schematic of cyclic voltammogram for the three different redox systems: (a) reversible; (b) irreversible; (c) quasi-reversible...... -...... 63
Figure 4.1. XRD spectra of pure V205 powder used in the solubility experiments.------70
Figure 4.2. XRD spectra of V205 solids collected from solubility experiment...... 71
Figure 4.3. Solubility data of V205 as a function of equilibrium total sulfate/bisulfate at temperatures between 10 -50 °C...... 73
Figure 4.4. Variation in colour of saturated V205 solubility samples with increasing sulfuric acid concentration at 50°C...... 73
Figure 4.5. Effect of temperature on the solubility of V205 at different sulfuric acid concentration.------75
Figure 4.6. XRD spectra of VOS04 solids collected from solubility experiment.------81
Figure 4.7. XRD spectra of pure VOS04 solids used in the solubility experiment...... 82
Figure 4.8. Variation in solubility of VOS04 with concentration of total sulfur at equilibrium...... -...... 85
Figure 4.9. Variation in solubility of VOS04 with initial concentration of sulfuric acid at different temperatures...... 86
Figure 4.10. Saturation ionic product(KSiP ) of VOS04 as a function of total sulfur concentration at equilibrium...... 87
xvii Figure 4.11. Effect of temperature on solubility of V0S04 in various sulfuric acid concentrations.-...... —------88
Figure 4.12. Saturation concentration of vanadium trioxide as V203 (measured after 45 days) versus initial sulfuric acid concentration at different temperatures.------94
Figure 4.13. Effect of temperature on saturation concentration of vanadium (as V203) obtained by the dissolution of V203 in various H2S04 concentrations...... 97
Figure 5.1. Schematic diagram of electrolytic cell for the preparation vanadium(V) solution.------107
Figure 5.2. Design details of the electrolytic cell used for the preparation of vanadium(V) solution.------—...... 108
Figure 5.3. Conductivity of supersaturated V(IV) solution with time at a stirring speed of 200 rpm at room temperature.------112
Figure 5.4. Cyclic voltammetry apparatus.------117
Figure 5.5. Variation in concentration of V(V) solutions with time in different total sulfate/bisulfate at 20°C...... 120
Figure 5.6. Effect of vanadium concentration on density of the supersaturated V(V) solutions at 20°C...... —124
Figure 5.7. Effect of total sulfate/bisulfate concentration on density of the supersaturated V(V) solutions at20°C...... 125
Figure 5.8. Typical diagram showing effect of supersaturation on viscosity of concentrated solutions [Source [Nyvlt, 1971]]...... 129
Figure 5.9. Variation in viscosity of 5M vanadium(V) solutions with total sulfate/bisulfate at 20°C...... 130
Figure 5.10. Variation in viscosity of 2M-5M vanadium(V) solutions in 5M-7M total sulfate/bisulfate at 20°C...... 130
Figure 5.11. Variation in viscosity of sucrose solutions with increase in concentration at 20°C...... 132
Figure 5.12. Effect of temperature on viscosity of 4.5M V(V) solution in 7M total sulfate/bisulfate...... 133
Figure 5.13. Cyclic voltammograms of 5M V(V) solution in 7M total sulfur (5V7S), and 5V7S solution with 1% distilled water at an scan rate of 0.02v/s...... 138
Figure 5.14. 51V NMR spectra of various V(V) solutions in different supporting electrolyte concentrations...... 138
Figure 5.15. Mass gain comparison of 5M, 6M and 7M sulfuric acid...... -140
Figure 5.16. Mass gain comparison of 3M V(V) solution in 5, 6, and 7M total sulfate/bisulfate...... 141
Figure 5.17. Mass gain comparison of 2M, 3M and 4M V(V) solution in 6M total sulfate/bisulfate...... 142
Figure 5.18. Conductivity of vanadium(V) solutions in sulfuric acid at 20°C...... 144
xviii Figure 5.19. Conductivity of H2S04 solutions with concentration at 0°C...... 145
Figure 5.20. Conductivity of aqueous electrolytes of various concentration of KOH and NaOH at constant temperature [Bowen, 1943].------146
Figure 5.21. Variation in 5M V(V) solution in 6.0M H2S04 with different SOC at room temperature...... 149
Figure 5.22. Cyclic voltammogram of 3M V(V) solution in 5M total sulfate/bisulfate at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C (Initial potential: 1.45V; Electrode Area: 0.1cm2)...... 151
Figure 5.23. Cyclic voltammogram of 4M V(V) solution in 6M total sulfate/bisulfate as a function of time at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C...... 153
Figure 5.24. Cyclic voltammogram of 2 - 5M V(V) solution in 6M total sulfate/bisulfate at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C...... 155
Figure 5.25. Effect of V(V) concentration on peak currents at an scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C...... -156
Figure 5.26. Effect of V(V) concentration on peak potential separation at an scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C...... —157
Figure 5.27. Effect of V(V) concentration on peak currents at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C...... 158
Figure 5.28. Cyclic voltammogram of 4M V(V) solution in 5, 6 and 7 M total sulfate/bisulfate at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C.------159
Figure 5.29. Effect of total sulfate/bisulfate concentration on peak currents at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C.------160
Figure 5.30. Cyclic voltammogram obtained for the first cycle at the glassy carbon electrode for 2M V(V) solution in 6M total sulfate/bisulfate.------162
Figure 5.31. Cyclic voltammogram obtained for the first cycle at the glassy carbon electrode for 3M V(V) solution in 6M total sulfate/bisulfate...... -163
Figure 5.32. Cyclic voltammogram obtained for the first cycle at the glassy carbon electrode for 4M V(V) solution in 6M total sulfate/bisulfate...... 164
Figure 5.33. Anodic peak currents versus scan rate of V(V)/V(IV) couple at the glassy carbon electrode for 3M V(V) solution in 6M total sulfate/bisulfate...... 165
Figure 5.34. Cathodic peak currents versus scan rate of V(V)/V(IV) couple at the glassy carbon electrode for 3M V(V) solution in 6M total sulfate/bisulfate...... -165
Figure 5.35. Anodic peak currents versus (Epa - E°) for V(V)/V(IV) couple at the glassy carbon electrode using 3M V(V) solution in 6M total sulfate/bisulfate...... -...... 167
Figure 5.36. Cathodic peak currents versus (Epa - E°) for V(V)/V(IV) couple at the glassy carbon electrode for 3M V(V) solution in 6M total sulfate/bisulfate...... -...... —168
xix Figure 5.37. Variation in concentration of 2M vanadium(V) solution in 5M total sulfate/bisulfate at different temperatures...... ------170
Figure 5.38. Variation in concentration of 3M vanadium(V) solution in 5M total sulfate/bisulfate at different temperatures...... 170
Figure 5.39. Variation in concentration of 4M vanadium(V) solution in 5M total sulfate/bisulfate at different temperatures.------171
Figure 5.40. Variation in concentration of 5M vanadium(V) solution in 5M total sulfate/bisulfate at different temperatures.------171
Figure 5.41. Variation in concentration of 2M vanadium(V) solution in 6M total sulfate/bisulfate at different temperatures.------—172
Figure 5.42. Variation in concentration of 3M vanadium(V) solution in 6M total sulfate/bisulfate at different temperatures...... 172
Figure 5.43. Variation in concentration of 4M vanadium(V) solution in 6M total sulfate/bisulfate at different temperatures. —...... 173
Figure 5.44. Variation in concentration of 5M vanadium(V) solution in 6M total sulfate/bisulfate at different temperatures...... 173
Figure 5.45. Variation in concentration of 2M vanadium(V) solution in 7M total sulfate/bisulfate at different temperatures.------...... -174
Figure 5.46. Variation in concentration of 3M vanadium(V) solution in 7M total sulfate/bisulfate at different temperatures...... 174
Figure 5.47. Variation in concentration of 4M vanadium(V) solution in 7M total sulfate/bisulfate at different temperatures...... -...... —175
Figure 5.48. Variation in concentration of 5M vanadium(V) solution in 7M total sulfate/bisulfate at different temperatures...... 175
Figure 5.49. Apparent equilibrium concentration of vanadium(V) solutions in 5M total sulfate/bisulfate at different temperatures after 1000 hours.------177
Figure 5.50. Apparent equilibrium concentration of vanadium(V) solutions in 6M total sulfate/bisulfate at different temperatures after 1000 hours...... 177
Figure 5.51. Apparent equilibrium concentration of vanadium(V) solutions in 7M total sulfate/bisulfate at different temperatures after 1000 hours...... -178
Figure 5.52. Induction times of V(V) solutions in 5M total sulfate/bisulfate at different temperatures.------180
Figure 5.53. Induction times of V(V) solutions in 6M total sulfate/bisulfate at different temperatures...... 180
Figure 5.54. Induction times of V(V) solutions in 7M total sulfate/bisulfate at different temperatures...... -...... 181
Figure 5.55. Effect of total sulfate/bisulfate concentration on stability of 3M V(V) solution after 1000 hours at different temperatures...... 184
Figure 5.56. Effect of total sulfate/bisulfate concentration on stability of 4M V(V) solution after 1000 hours at different temperatures...... 184
xx Figure 5.57. 51NMR spectra of 2M V(V) solution in 5, 6 and 7M total sulfate/bisulfate at room temperature.------186
Figure 5.58. Plot of growth rate of 4M V(V) solution in 5M total sulfates against relative supersaturation at 40°C (see Figure 5.39 for Cone vs time).------189
Figure 5.59. Plot of growth rate of 4M V(V) solution in 5M total sulfates against relative supersaturation at different temperatures...... 190
Figure 5.60. Concentration profiles of 3M V(V) solution in 5M total sulfate/bisulfate with and without stirring at 30°C...... 196
Figure 5.61. Arrhenius plot for the precipitation of V(V) solution using second order rate constants in 5M total sulfate/bisulfate.------—197
Figure 6.1 Structural characteristics of antisealants—...... —...... — 209
Figure 6.2. Precipitation behaviour of 4M V(V) solution in 6M total sulfate/bisulfate with and without inhibitor at 40°C...... -...... -218
Figure 6.3. Effect of different formulations on precipitation of V(V) solution at 40°C.—219
Figure 6.4. Effect of different blends of formulation KS on precipitation of V(V) solution at 40°C...... 223
Figure 6.5. Effect of KS11 on the precipitation of 4M V(V) solution in 6M total sulfate/bisulfate at 40°C...... -...... 225
Figure 6.6. Effect of initial V(V) concentration on performance of KS 11 to prevent precipitation of different V(V) solutions in 6M total sulfate/bisulfate at 40°C.------226
Figure 6.7. Effect of temperature on performance of formulation KS11 using 4M V(V) solution in 6M total sulfate/bisulfate...... 229
Figure 6.8. Effect of temperature on performance of formulation KS11 using 3M V(V) solution in 6M total sulfate/bisulfate...... -229
Figure 6.9. Stability of 3.5M V(V) solution in 5.7M total sulfate/bisulfate with additive formulation KS11 at 40°C.—...... — 232
Figure 6.10. Cyclic voltammogram of 4M V(V) solution in 5M total sulfate/bisulfate with and without additive.------233
Figure 6.11. Performance of KS11 to inhibit precipitation of 4M V(IV) solution in 6M total sulfate/bisulfate at 20°C...... -234
xxi LIST OF TABLES
Title Page
Table 4.1. Solubility of vanadium pentoxide (V2O5) in various sulfuric acid concentrations at temperatures from 10°C to 50°C...... 69
Table 4.2. Regression constants for solubility correlations of V2O5 in H2S04.------78
Table 4.3. Solubility of vanadyl sulfate (VOSO4) in various sulfuric acid concentrations at temperatures from 10°C to 50°C. —...... — 80
Table 4.4. Regression constants of solubility correlations and ionic product correlations for VOSO4...... -...... 89
Table 4.5. Saturation concentration of vanadium trioxide (V2O3) in various sulfuric acid concentrations at temperatures from 20°C to 50°C...... 92
Table 4.6. Vanadium trioxide (V2O3) concentration in 5M H2S04 measured under different experimental conditions...... 95
Table 4.7. Free energy of formation for the species considered in the above system at 25 °C...... 99
Table 4.8. Equilibrium composition of various species for 2m total V(V) solution in different H2S04 concentrations at 25°C...... 100
Table 5.1. Stability of supersaturated V(V) solutions at 50°C over a period of 30 days.-120
Table 5.2. Stability of different V(V) solutions in 7.0M total sulfate observed for 30 days at 50°C.------...... 121
Table 5.3. Densities of vanadium(V) solutions in various concentrations of total sulfate/bisulfate at 20°C (gm/cc)...... -...... —124
Table 5.4. Effect of temperature on viscosity of various vanadium (V) solutions.------134
Table 5.5. Viscosity variation of vanadium(V) solutions with time when stored in air tight containers...... —...... -135
Table 5.6. Variation in concentration of H2S04 and vanadium(V) solutions in H2S04 when exposed to atmosphere for 240 hours...... 142
Table 5.7. Diffusion coefficient for V(V)/V(IV) redox couple obtained from cyclic voltammogram at glassy carbon electrode at different scan rates using various V(V) concentrations in 6M total sulfate/bisulfate...... 166
Table 5.8. Rate constants for V(V)/V(IV) redox couple obtained from cyclic voltammogram at glassy carbon electrode at different scan rates using V(V) solution of various V(V) concentrations in 6M total sulfate/bisulfate...... 168
Table 5.9. Induction times of vanadium(V) solutions at various temperatures...... 179
Table 5.10. Summary of supersaturations of V(V) solutions and slope (g’) and kg’ calculated from intercept...... 192
xxii Table 5.11. Summary of supersaturations of V(V) solutions and corresponding reaction order and rate constants...... —...... 193
Table 6.1. List of additives studied for preventing V(V) precipitation in —...... 4.7 M V(V) solution in 6.0M H2S04at 50°C...... 211
Table 6.2. Effectiveness of additives studied for preventing precipitation of 4 M V(IV) solution in 6.0M H2S04at 20°C.------213
Table 6.3. Performance of various additives studied for preventing precipitation of 4.0 M V(V) solution in 6.0M H2S04 at 50°C.------214
Table 6.4. List of various formulations prepared for the prevention of V(IV)/V(V) precipitation...... -...... -...... 216
Table 6.5. Performance of Various formulations studied for inhibiting precipitation of 4.0 M V(V) solution in 6.0M H2S04 at 50°C...... 216
Table 6.6. Effectiveness of various formulations to inhibit precipitation of 4 M V(IV) solution in 6.0M H2S04 at 20°C...... 217
Table 6.7. Details of different mixtures of SHMP and K3P04 investigated to develop optimum blend of formulation KS at 40°C.-...... — 223
Table 6.8. Summary of induction times and final V(V) concentration of V(V) solutions without additive and with additive KS11 in various total sulfate/bisulfate concentrations at different temperatures...... 228
xxiii LIST OF SYMBOLS
Symbol Definition
A Debye-Huckel coefficient
Ae surface area of the electrode [cm ]
Ag pre exponential factor An crystal surface area [cm2]
AS absolute supersaturation [(C - Ceq), molar]
As specific crystal surface area [m gm' of solid] a ion size parameter
B Debye-Huckel coefficient
B° rate of nucleation
C concentration at any time [molar]
Ceq equilibrium saturation concentration [molar]
Co bulk concentration [molcm'3]
AC concentration difference [molar]
C, regression constant
C2 regression constant
C3 regression constant
^H20 density of water [gmcm'3]
^H2S04 density of sulfuric acid [gmcm'3]
D0 diffusion coefficient [cmV1]
^soln solution density [gmcm'3] dv(v) density of V(V) solution in sulfuric acid [gmcm'3]
Eg activation energy for crystal growth [kJmol1]
Ej initial potential [V]
En activation energy of nucleation [kJmol1]
E° formal potential [V]
xxiv peak potential [V] anodic peak potential [V] cathodic peak potential [V]
AEP peak potential separation [V] g or n order of reaction
I ionic strength [molal]
Im ionic strength [molal] peak current [A]
Ipa anodic peak current [A]
Ipc cathodic peak current [A]
Jd rate of diffusion
■Idep rate of deposition
Jdiss rate of dissolution
Jn rate of nucleation kb backward rate constant kf forward rate constant kg rate constant for crystal growth kn nucleation rate constant
KSp solubility product
Ksp° equilibrium constant log is natural logarithm (loge) M2 molarity of solution mi molal concentration of ion in solution n2 normality of solution
Na Avagadro’s number na number of electrons in rate determining step nc number of cycles ne number of electrons
XXV PS percent supersaturation [molar] R gas constant [8.314 J K'1 mol'1 ]
Rg crystal growth rate S solubility [molar] s surface area soc state-of-charge SR supersaturation ratio [C / Ceq] SS supersaturation [(C-Ceq), molar] T temperature [°C] time needed for a nucleus to grow
tn formation of stable nucleus to a detectable size
tr relaxation time
Vm molar volume of solid
^soln molar volume of solution
Zi charge number of an ion in the solution
a transfer coefficient
X number of building units arriving at a nucleus in a given time
5 effective thickness of diffusion layer
Y± mean activity coefficient viscosity of solution [centipoise]
^lsoln viscosity of solution [cP]
V scan rate [V/s ]
a interfacial energy
T induction time [hours]
Aoo equivalent conductivity at infinite dilution
Ae equivalent conductance of solution
xxvi Chapter 1 Introduction
CHAPTER 1 INTRODUCTION
Energy storage has long been recognised as a means of reducing petroleum demand and air pollution problems. Presently the development of efficient and environmentally safe energy storage systems is an important and urgent issue to save our society from potentially serious damage due to various pollutants in the atmosphere. The major chemical species involved in depleting ozone by catalytic reactions are CFC from refrigerants and CO, C02, S02, NOx, lead oxide and so on from exhaust of cars and power plants. Current measurements confirm that such depletion is taking place on a global scale and is specially pronounced in the Antarctic stratosphere resulting in the increased UV radiation reaching the earth’s surface. This increased UV radiation damages human health, plant and animal life and materials exposed to sunlight.
The expected increase in the number of cars in the world may increase pollution to intolerable levels. Increasing concern of public about better air quality have led to the new requirements for zero-emission and low-emission vehicles. Serious efforts are needed from all sectors to develop electric vehicles and renewable energy systems. One of the critical obstacles in the implementation of electric vehicles and alternative energy technologies to date is the lack of suitable energy storage systems. Advanced batteries with high energy density, durability, and low cost are being developed to provide electric vehicles with the higher mileage range, acceleration, and low life-cycle costs necessary to compete in the commercial markets [Takehara, 1994]. Throughout the world, therefore, enormous effort and funding is currently being diverted for the development of suitable battery systems for these applications. The world market for batteries estimated in year 1988 was in excess of 23 billion dollars [Gupta, 1988].
1 Chapter 1 Introduction
Demand for new energy storage systems is increasing for applications such as remote area power systems, wind turbine generators, load levelling at electric power stations, as well as emergency back-up applications. The use of batteries as portable electrical power sources has increased and to some extent technology has not been able to keep pace with the demands. Longer lifetime and higher volumetric energy densities are needed for electric vehicles while load levelling applications are more sensitive to cost than to the gravimetric or volumetric energy densities. Computers, other electronic equipment and defense industries require higher safety and shelf life whereas the space stations are demanding enormous amounts of power storage capacity in a small volume and weight. The ideal high energy density battery has to meet many of the above demands and efforts are being made to meet these stringent requirements.
Redox batteries have received considerable interest over the last 20 years as potentially low cost and highly efficient energy storage systems for large scale applications. Preliminary work on redox cells was conducted initially by Kangro and Pieper [1962] and Boeke [1970] to provide an electrically rechargeable bulk energy storage system which is economically feasible and have a high overall efficiency, extended cycle life, and high reliability. Thaller [1976] proposed a practical redox flow battery based on the redox couples Fe2+/Fe3+ and Cr2+/Cr3+. Unfortunately, the Fe/Cr flow cell had problems like cross contamination of the electrolyte and poor reversibility of the chromium half-cell. To overcome these problems Skyllas-Kazacos and co-workers [1985, 1986, 1988] suggested an All Vanadium Redox Flow Battery (AVRFB) employing V(n)/V(in) and V(IV)/V(V) redox couples in the negative and positive half-cell electrolytes respectively. The vanadium redox cell presently under development at The University of New South Wales by Skyllas-Kazacos and co-workers, is showing great promise as an efficient new energy storage system for a wide range of applications. They identified sulfuric acid as a suitable supporting electrolyte to prepare concentrated vanadium solutions for
2 Chapter 1 Introduction
the vanadium redox battery. The main features of the AVRFB are shown in Figure 1.1.
The system consists of two compartments separated by a selective ion-exchange membrane which prevents cross mixing of the electrolytes. Each side of the cell contains an inert electrode made of highly porous carbon felt. The electrolyte, both anolyte and catholyte are stored in two large external reservoirs. During the charge or discharge cycle, the rechargeable electrolytes are circulated through the redox flow cell from the reservoirs. The electrolyte is pumped through the inert electrode where the electrochemical reactions occur. A stack of these energy producing cells can be connected in series in a bipolar manner.
In this cell, the electrolyte is one of the most important components, being not only the conductor of the ions, but also the energy storage medium. Increasing the concentration of vanadium electrolyte increases the energy density of the battery. Therefore an effort was made to study the stability of supersaturated vanadium solutions with a view to improve the vanadium concentration.
Kazacos [1989] pointed out that modification of the electrolyte composition from 2M vanadium in 2M H2S04 to 2M vanadium in 3M H2S04 demonstrated much higher energy efficiencies and greater electrolyte stability.
Cheng [1991] recommended that concentrations of 2M V(V) in 4M H2S04 could be safely employed in applications where the battery undergoes continuous cycling and if high temperatures are not experienced over long periods. In applications where high temperatures and/or infrequent cycling are expected, the recommended electrolyte composition is 1.5M V(V) in 3-4M H2S04.
3 Chapter 1 Introduction
Pp|| QtopV (two cells) V(II) ^ V(III) + e
Figure 1.1. Schematic of all vanadium redox flow battery being developed at The University of New South Wales.
4 Chapter 1 Introduction
An interesting finding of Kazacos et al. [1990] is that the stability of supersaturated V(V) solutions at increased temperatures is highly dependent on the state-of-charge (SOC) of the solution thus suggesting interaction between the V(IV) and V(V) ions in the positive half-cell electrolyte, to form more stable ionic species.
Recent studies carried out by Skyllas-Kazacos et al. [1996] showed that V(V) solutions of concentration between 3M-5M V(V) in higher sulfuric acid concentrations (5M - 7M) are more stable at elevated temperatures than the original 2M V(V) electrolyte in 4M H2S04. Detailed investigations are still required to fully understand the phenomena and to determine the stability region of V(V) as a function of vanadium concentration, H2S04 concentration and temperature.
To define the supersaturation of vanadium solutions, knowledge of the saturation concentration of vanadium compounds is important. Meyer and Aulich [1930] published solubility data of V205 in H2S04 concentrations between 0 -16M but this is limited to a temperature of 25°C only. Recently Djong-Gie [1985] reported the saturation concentration of V205 as 0.165M in 1M H2S04 and 0.245M in 3M H2S04 solution. The solubility data of vanadyl sulfate (V0S04) and vanadium trioxide (V203) is practically non-existent in the published literature. However, Cheng [1991] reported solubility data of vanadium sulfates of V(II), V(III), and V(IV) in sulfuric acid concentrations of 0 - 5M over a temperature range of 10°C - 60°C. While the temperature range was covered very well for vanadium battery applications, solubility data is needed still at H2S04 concentrations above 5M. Moreover, the saturation concentrations of the sulfates was not reported which makes the data of limited use. At present, the solubility product of vanadium sulfates can not be calculated and this is needed to predict the precipitation potential of supersaturated vanadium sulfate solutions.
5 Chapter 1 Introduction
To establish the level of supersaturation in vanadium solution and to be able to predict the precipitation potential, it is necessary to systematically generate the solubility data of V205 in H2S04 at various concentrations and temperatures desired for the operating range of the vanadium battery. Since the V(V) species in the positive half-cell electrolyte undergoes transformation to the V(IV) oxidation state during the discharge cycle of the battery, the solubility data of vanadyl sulfate (VOSO4) is also required in H2S04 concentrations above 5M.
To investigate the viability of using V203 as a starting material to prepare supersaturated vanadium electrolytes, a solubility study of V203 was also needed in similar H2S04 concentrations and temperature range as selected for v2o5
This project concentrates on studies which are being undertaken to increase the energy density of the vanadium redox cell so as to reduce the weight and volume of the battery required for mobile applications. The main emphasis has been on preparing supersaturated vanadium(V) electrolytes, evaluating their properties, and determining the optimum conditions for stabilising these solutions.
The overall aim of this research is to systematically generate the solubility data of different vanadium compounds in H2S04 solutions and to study the properties, stability, electrochemical behaviour and kinetics of precipitation of supersaturated vanadium(V) solutions. The performance of additives or precipitation inhibitors on the rate of precipitation of vanadium(V) ions has also been investigated in an effort to extend the operating temperature range of the vanadium redox battery employing supersaturated vanadium solutions.
The specific objectives of the study are:
• Determine the solubility of vanadium compounds (V203, V205 V0S04) in different concentrations of sulfuric acid ranging from 0 to 9M and in the
6 Chapter 1 Introduction
temperature range 10°C to 50°C. Develop solubility correlations to predict the scaling potential of various vanadium compounds in the vanadium electrolyte.
• Prepare supersaturated vanadium(V) solutions in various sulfuric acid concentrations to study the properties, stability and kinetics of precipitation of supersaturated vanadium(V) solutions and determine the optimum conditions for a stable vanadium(V)-sulfuric acid system.
• Study the electrochemical behaviour of the supersaturated vanadium(V) electrolytes.
• Identify and evaluate the performance of suitable additives to prevent the thermal precipitation of vanadium(V) ions from supersaturated V(V) solutions so as to improve the energy density of the battery.
7 Chapter 2 Literature Review
CHAPTER 2 LITERATURE REVIEW
2.1 ENERGY STORAGE SYSTEMS
Batteries are the most familiar and most common of all energy-storage devices. They are available in different types and a variety of sizes and capacities depending on various applications. In terms of proven reliability and cost, nickel-cadmium and lead-acid batteries are still the only commercially available energy storage systems [Skyllas-Kazacos, 1996]. The lead-acid battery suffers from a number of problems in deep-discharge applications. Furthermore, environmental problems associated with the mining, smelting and disposal of lead are likely to adversely affect the lead-acid battery industry in the future. Similar problems are associated with nickel-cadmium battery and is also not very cost effective for most energy storage applications.
Attention has therefore focused on the development of the advanced batteries and new battery systems have been investigated such as zinc/chlorine, zinc/bromine, sodium/sulfur, and redox flow systems. Extensive research and development efforts were undertaken by the National Aeronautical and Space Administration (NASA) at the Lewis Research Center in the United States from about 1973 [Schainker, 1991; Hagedorn and Thaller, 1982]. The development of advanced batteries as a part of the Moonlight Project has been promoted by New Energy Development Organisation (NEDO) under the sponsorship of Agency of Industrial Science and Technology (AIST) in Japan [Furuta et al., 1991]. The total budget for the “Moonlight Project”, which include four battery systems, the sodium/sulfur battery, zinc/chlorine battery, zinc/bromine battery and iron/chromium redox flow battery, was about 17 billion yen for 12 years [Kazacos, 1989].
8 Chapter 2 Literature Review
2.1.1 Redox Flow Battery
The redox flow battery concept was first proposed by Thaller [1976] as an alternative storage battery to meet the requirements for remote area energy storage applications.
The term “redox” is obtained from a contraction of the words “reduction” and “oxidation” [Linden, 1984]. A typical redox flow battery system is shown in Figure 2.1. The anode and cathode reactions takes place in solution, on the surface of inert electrodes serving as current collectors. The reactants flowing across these electrodes are stored externally in the containers outside the cell. The reactant solutions themselves serve as the electrolyte, being prevented from mixing together by a highly specialised, semipermeable membrane. The cell is charged with the input of electric energy to drive the overall cell reaction in the thermodynamically uphill direction and the oxidised species produced at an inert electrode in one half-cell and the reduced form in the other. Electricity is produced in these cells upon discharge, when the electrogenerated species react at the electrodes. Thus these cells are of great interest as secondary or rechargeable batteries.
The inherent characteristics of redox flow cells offer a number of advantages compared to more conventional batteries. In such a system the electrochemical reactor unit is decoupled from the storage unit, yielding advantages in ease of design and in costs of both operation and maintenance of the system. Another advantage is the fact that both the reactant and reaction products are soluble and thus posses no physical form to be maintained. As a result, there are no inherent life-limiting factors associated with electrode morphology changes. Since the electrochemical reactions do not involve solid state processes, their rates and consequent efficiencies are higher than those of conventional batteries. The system storage capacity and the system power, can be independently sized.
9 Chapter 2 Literature Review
vT ' ~~~~—
Anode Cathode fluid fluid
Power conversion section
Figure 2.1. A typical diagram showing redox flow cell set-up.
10 Chapter 2 Literature Review
Most redox flow batteries operate at room temperature thus allowing the use of inexpensive construction materials. Mild reaction conditions contribute to the longer equipment life. The absence of traditional electrode manufacturing and forming steps in redox flow batteries along with the possibility of mass production of energy storage systems may result in the lower cost in terms of dollars per kilowatt-hour [Thaller, 1974, 1979].
Redox batteries thus possess many features that make them suitable for large scale energy storage applications in remote areas and load levelling. The redox couples selected after initial screening were Fe2+/Fe3+ and Cr2+/Cr3+ on the basis of availability and cost [Giner et al., 1980; Shimada et al., 1988; Gahn et al., 1985a; Cnobloch et al., 1988; Hamamoto, et al., 1985]. In the Iron-chromium (Fe/Cr) redox battery, the species formed during charging are Fe3+ and Cr2+ and during discharging the reactants are converted to Fe2+ and Cr3+ respectively. The concentration of the respective electrolytes was in the range of 1-2M Fe and 1-1.8M Cr both prepared in the 1-4M HC1 supporting electrolyte.
The electrode reactions are
At anode Cr ^------Cr3+ + e (2-1)
At cathode Fe + e ------^ Fe2+ (2-2)
One of the main disadvantages of the Fe/Cr system is that cross-mixing of the electrolytes occurs through the membrane separator in the redox cell, resulting in a permanent loss in energy storage capacity for the system because of the dilution of the active materials. Migration of other ions (H+ and/or Cl ) for charge balancing, however, must be permitted and therefore ion-selective membranes are required.
11 Chapter 2 Literature Review
Large-area carbon felts are used as inert current collectors. Charge and discharge reactions of the Fe2+ and Fe3+ ion are highly reversible, however, for the Cr reactions a catalyst is needed. Problems related to the irreversibilities of the chromium half cell and poor selectivities associated with the membrane separator have limited the commercial development of the iron-chromium redox cell [Linden, 1984].
Considerable attention was focused on the development of other flow batteries such as Zn/Cl2, Zn/Br2, Fe/Ti [Savinell et al., 1978; Liu et al., 1982; Wang et al., 1984]. Since all battery systems employ more than one redox couple, similar problems of electrolyte contamination was experienced apart from other problems like toxicity of bromine gas, high self-discharge rates, non-uniform zinc plating and pH variations caused by H2 and 02 evolution.
To overcome the deficiencies and problems associated with the above mentioned battery systems, Skyllas-Kazacos and co-workers [1986a, 1986b] proposed the All-Vanadium Redox Flow Battery (AVRFB) which employs V(II)/V(III) and V(IV)/V(V) redox couples in the negative and positive half-cell electrolytes respectively. By using the same metal ion in different oxidation states on either side of the membrane, problems related to cross contamination are thus eliminated. In the AVRFB the energy is stored in the vanadium solution. Excellent performance characteristics have been obtained with the all vanadium redox flow cell [Skyllas-Kazacos and Grossmith, 1987]. A brief description of the all vanadium redox flow (AVRFB) is given in the following subsection.
2.1.2 Vanadium Redox Flow Battery
The concept of the all vanadium redox flow battery was first proposed by Skyllas-Kazacos and co-workers [1986a, 1986b] and has been under development at The University of New South Wales (UNSW) since 1984.
12 Chapter 2 Literature Review
The main features of the all vanadium redox flow battery are shown in Figure 1.1. The V(V)/V(IV) redox couple is used in the positive half-cell and V(II)/V(III) redox couple is used in the negative half-cell separated by an ion selective membrane with sulfuric acid as the supporting electrolyte. An inert electrode made of highly porous carbon felt is placed in each side of the cell. During the charge or discharge cycle, the rechargeable electrolytes are circulated through the redox flow cell stored in the external reservoirs. The electrolyte is pumped through the inert electrode where the electrochemical reactions occur. The redox reactions which occur in the vanadium redox flow cell system are as follows:
At the positive electrode
discharge V02+ + 2H+ + e V02+ + H20 E°=1.00V (2-3) charge
At the negative electrode
charge V3+ + e =F==i V2+ E° = -0.26 (2-4) discharge
The standard cell potential is thus E° (cell) = 1.26 Volts at concentrations of 1 mole per litre and at 25 °C. Under actual cell conditions, however, an open- circuit voltage of 1.45 Volts is observed at 50% state-of-charge, while a fully charged cell produces over 1.6 Volts at open-circuit [Skyllas-Kazacos, 1996].
Initially the composition of electrolyte used in the vanadium redox battery was 2M VOSO4 in 2-3 M H2S04 as reported by Kazacos and Skyllas-Kazacos [1989] to have an overall efficiency up to 86% with a coulombic efficiency of about 97% over a temperature range of 5°C - 45 °C. The cost of vanadium electrolyte initially prepared from VOSO4 was quite high and it was necessary to investigate the possibility of using other low price vanadium compounds for
13 Chapter 2 Literature Review the vanadium redox battery system to be commercially viable. The use of the more readily available and lower cost V205 was thus considered essential for the successful commercialisation of the vanadium redox battery. Vanadium pentoxide, however, has a very low solubility in sulfuric acid solutions, and high vanadium concentrations are required for increased energy densities. Kazacos [1989] conducted studies to prepare vanadium electrolyte using both chemical and electrolytic reduction of V2O5 powder and found that vanadium solutions of 2M concentration can be prepared in sulfuric acid, thus allowing a significant reduction in the cost of the vanadium battery electrolyte.
Recently Kaneko et al. (1993) suggested a similar method for producing concentrated vanadium electrolyte. A vanadium electrolytic solution containing highly concentrated and dissolved vanadium was produced by a method wherein a vanadium pentoxide was subjected to a reduction operation in the presence of inorganic acids. At this time, by repeating the addition of the concentrated inorganic acids and the vanadium compound, a tetravalent and pentavalent vanadium solution of 3.4 M was obtained.
The other important components of the vanadium redox battery system are electrode and membrane. The electrodes used for a redox flow cell must be inert, conductive, chemically stable and cheap [Gahn and Hagedorn, 1985b; Inoue et al., 1987]. Different electrode materials including graphite rod and plate, carbon cloth, carbon fibres and graphite felts have been evaluated. Zhong et al. [1991] and Zhong [1992] developed conducting plastic electrodes from mixtures of carbon black, graphite fibre and low density polyethylene. Haddadi [1995] continued the optimization work on the conductive graphite felt-bonded carbon polymer composite material and achieved voltage efficiencies of up to 90% during charge-discharge cycling. The new electrodes developed at the UNSW have superior mechanical properties, and are impermeable to the
14 Chapter 2 Literature Review vanadium electrolyte, making them more desirable for use in the vanadium redox battery.
Another major component of a vanadium redox flow battery is an ion selective membrane which is required to separate the positive and negative electrolytes while still permitting the transport of charge balancing ions. A number of ion- selective membranes were investigated by Skyllas- Kazacos and co-workers [Grossmith et al., 1988; Zhong et al. 1991; Chieng et al., 1991] for use in the vanadium redox flow battery. The various membranes tested were Selemion CMV, DMV, AMV and New Selemion (Type 2), of Asahi Glass Co., Japan, Nafion 112, 117 and 324 of Dupont, U.S.A. and RAI RIO 10 and R4010 of Pall RAI Inc., U.S.A. Although most of these membranes showed good selectivity and conductivity, none of these had acceptable volumetric solution transfer behaviour. The Selemion CMV showed lowest chemical stability while Nafion 112 and New Selemion (Type 2) membranes exhibited excellent stability in the vanadium solution. A new composite membrane prepared by crosslinking divinyl benzene into a Daramic microporous polyethylene separator was developed by Mohammadi [1995] and showed promising results in the AVRFB. Sulfonation of the composite membrane and the AMV membrane led to a slight decrease in their chemical stability, however, a cycle life up to three years could be expected from the modified composite membranes developed by Mohammadi [1995].
The vanadium battery is now at a relatively advanced stage of development with several 1-3 kW prototype batteries already constructed and tested. Overall energy efficiencies as high as 90% have been achieved to date, not including pumping energy losses. These have been estimated at 2-3%, so that even at 87- 88% overall energy efficiency, the vanadium battery is proving to be one of the most efficient energy storage systems currently under development [Skyllas- Kazacos, 1996].
15 Chapter 2 Literature Review
2.1.2.1 Advantages
The all vanadium redox flow battery retains the properties of most redox flow systems and, in addition possesses the following advantages.
By employing the same element (vanadium) on both sides of the membrane, the major problem of cross contamination of electrolyte is eliminated.
The solution life is indefinite and can be recycled continuously, so that replacement costs are low and there are no waste disposal problems. Therefore, the vanadium battery system is considered as environmentally friendly.
It can be fully discharged or left at any state-of-charge without any detrimental effects unlike lead acid batteries. Instant recharge is possible by replacing discharged electrolyte with fresh charged solution or the solution can be electrically recharged at high rates about 5-10 times faster than lead-acid batteries.
High energy efficiencies are possible because of the relatively fast kinetics of the vanadium redox couples.
System capacity depends on the volume and concentration of vanadium solution stored in external tanks. As energy storage capacity increases the cost per kWh decreases.
The capacity of the battery can be measured and easily controlled by simply monitoring the state-of-charge of the solutions.
16 Chapter 2 Literature Review
The AVRFB reactions do not involve complex solid phase changes during charging and discharging which lead to shedding or shorting in conventional batteries.
Since vanadium is readily available at a favourable price, the cost of the vanadium battery is expected to be half that of the lead acid battery for most applications.
2.1.2.2 Applications
The all vanadium redox flow battery has potential for wide range of stationary as well as mobile applications due to its great flexibility, low maintenance and simplicity. The various applications include:
Load-levelling - in which any excess power generated by power plants during off-peak hours may be stored in the battery and can be used when needed in peak hours. A consortium comprising Mitsubishi Petrochemicals and Kashima Power Corporation of Japan has been licensed to further develop and commercialise the vanadium redox battery world-wide (excluding South-East Asia, China and Australia) in large scale load-levelling systems. A 200 kW/800 kWh demonstration battery was commissioned in Japan in 1997 and their plans are to construct and test a 2MW demonstration vanadium battery system for load-levelling purposes in the Tokyo area by 1999.
Independent emergency power source - it can provide a good back up source for hospital equipment, lighting, telecommunications, military installations etc.
Remote area power supply system (RAPSS) - Most RAPSS employ a diesel generator with or without solar panels or wind generator and a battery for storage. Due to poor performance and short cycle life of the lead-acid
17 Chapter 2 Literature Review
battery under deep discharge cycling, vanadium redox batteries are well suited for RAPSS applications.
Large scale photovoltaic applications - the electrical energy generated by photovoltaic cell from solar energy needs to be stored in a battery. The Vanadium battery can be used as an efficient and low cost energy storage system. A solar demonstration house was built at the site of the Thai Gypsum Factory in Thailand in 1993 and a lkW/12kWh vanadium battery was installed in the Solar Demonstration House by the UNSW Vanadium Battery Development Group in collaboration with the UNSW Centre for Photovoltaic Devices and Systems and Thai Gypsum Products Co. Ltd. Thailand.
Mobile applications - it has attracted considerable interest for mobile applications such as fork lifts, light rail, city buses and so on. With increased vanadium concentrations it may be possible to design a battery for passenger cars also.
2.2 SOLUBILITY OF VANADIUM COMPOUNDS
A comprehensive literature survey was carried out to collect the solubility data of vanadium compounds such as V205, V203 and VOSO4 in sulfuric acid solutions which are of interest in the vanadium battery electrolyte optimization studies. Since sulfuric acid is employed as the supporting electrolyte in the vanadium redox battery, a literature review related to the solubility of vanadium compounds in sulfuric acid for the operating temperature range is presented. The published solubility data was compiled to find out the saturation concentrations of these vanadium compounds in H2S04 solutions in order to determine the degree of supersaturation of vanadium electrolyte in the vanadium redox battery as well as to establish the H2S04 concentration at which the solubility of various vanadium compounds is maximum. It is also possible to
18 Chapter 2 Literature Review predict the precipitation potential of supersaturated solutions if solubility data is available.
2.2.1 Solubility of V205
A survey of the literature indicated that solubility of V205 has been reported by many authors in different acidic medium. Meyer and Aulich [1930] determined the solubility of V2O5 in solutions containing 0 - 98% sulfuric acid. The maximum solubility of V205 was reported to be about 1.5M in 88% H2S04 at 25°C. They also presented solubility data at 100°C for the above mentioned sulfuric acid concentration range. Marakov and Repa [1938] determined the solubility of V205 in H2S04 in the concentration range of 0 - 90 % at 25°C and 75°C and found four stable solid phases of V205 at equilibrium. They concluded that the solubility of V205 has a maximum value of about 0.9M in 60% H2S04. Although large variations are observed between the solubility data of Meyer and Aulich, and Marakov and Repa, the trend was still found to be similar. The solubility of V205 increases with increasing H2S04 concentration and decreasing temperature.
Britton and Welford [1940] generated the solubility data of V205 in the range of 0.180 - 1.800N H2S04 at 18°C by shaking the solutions with excess of the pure dry oxide for a month. At 100°C, the solubility was determined by heating the solutions for 3 hours in a steam oven. They also reported solubility data of V205 in HNO3, HC104, NaHS04, CCI3COOH and CH3COOH. They concluded that V205 is amphoteric, for it dissolves in solutions of acids to an extent depending upon the strength of the acid and the temperature. Their data is of little use in the present studies because the sulfuric acid concentration and temperature does not cover the useful range for the vanadium redox battery.
19 Chapter 2 Literature Review
Lanford and Kiehl [1940] evaluated the previous solubility data of V2O5 in sulfuric acid solutions [ Meyer and Aulich, 1930] and mentioned that these data are not satisfactory because, no sulfate determinations were made at equilibrium and only initial sulfuric acid concentrations were given. No information was provided regarding the nature of the solid phase in contact with these vanadium pentoxide-sulfuric acid solutions. They considered a three component system, V2O5-SO3-H2O at 30°C and reported equilibrium concentrations of V2O5 and S03 in mole percent. The solubility of V2O5 was reported to be 0.011 mole % and 1.4 mole% corresponding to the S03 concentration of 0 mole % and 11.3 mole % at 30°C. The solubility data shows that it was increasing continuously with increasing SO3 concentration.
Linke [1965] presented an excellent compilation of solubility data of inorganic and metal-organic compounds. He presented the solubility data of V205 published by various authors till year 1965 in an organised manner. In addition to the solubility data discussed above, he reported the solubility data of V2O5 determined by Nikolaev and Buslaev [1955, in Linke, 1965] in hydroflouric acid at 16°C and 25°C. Recently Djong-Gie [1985] reported that the concentration of a saturated V2O5 solution is 0.165M in 1M H2S04 and 0.245M in 3M H2S04 solution while presenting the permeation of vanadium cations through anionic and cationic membranes in vanadium redox fuel cell.
Sum and Skyllas-Kazacos [1985] found that the dissolution rate of V205 in sulfuric acid is very low. It needs 30 days to fully dissolve 2 gm of V2O5 in 1.8M sulfuric acid. More recently Cheng [1991] carried out preliminary studies of solubility of V2O5 in sulfuric acid and found that the solubility of V2O5 varied between 3.44 to 5.08 gm/100 ml for acid concentrations ranging from 1M to 5M during the period of 41 days.
20 Chapter 2 Literature Review
From the literature review presented above it appears that the available
solubility data of V2O5 adequately covers the sulfuric acid range from 0-98%, but the data is limited by the temperature range between 18°C to 30°C and equilibrium concentration of sulfate/bisulfate is also not reported. Furthermore, the data shows large discrepancies mainly because of differences in equilibrium
times, purity of V2O5, different solid phases of V2O5, sampling technique and analytical methods.
2.2.2 Solubility of VOSO4
The solubility data of vanadium compounds compiled by Linke [1965] does not report any data on solubility of vanadyl sulfate (VOSO4). A literature search conducted on CD ROM by scanning various scientific databases also indicated that the solubility data of VOSO4 is not available in the published literature. However, Cheng [1991] determined the solubilities of all vanadium sulfates in various concentrations of sulfuric acid at different temperatures. It was found that in the case of V(II), V(III) and V(IV) species, solubility increases with increasing temperature and decreasing sulfuric acid concentration while V(V) solubility increases with increasing sulfuric acid concentration and decreasing temperature. The temperature range was well covered from 10°C to 60°C but the initial sulfuric acid concentration was in the range of 2M to 5M and needs further investigations at higher concentrations. Also equilibrium sulfate/bisulfate concentrations are not reported which will enable the prediction of precipitation potential of supersaturated V(IV) solutions.
2.2.3 Solubility of V203
It appears from the literature review that the solubility data of vanadium trioxide
(V203) is practically non-existent. Linke [1965] has reported the melting points
of systems V203 - CaO and V2O3 - Si02 determined by Morozov [1939].
21 Chapter 2 Literature Review
The reliable solubility data of vanadium compounds (V203, V205 and VOS04) are not adequately available for the sulfuric acid concentration and temperature range required for the vanadium redox battery. It is therefore, important to systematically generate solubility data of vanadium compounds namely V203,
V205 and VOSO4 in the sulfuric acid concentration range of 0 - 9 M and over the temperature range of 10°C - 50°C to fully understand the solubility behaviour of these compounds for application in vanadium redox battery.
2.3 VANADIUM(V) ELECTROLYTE
2.3.1 Aqueous Chemistry
Vanadium was first discovered in 1801 by del Rio while he was examining a lead ore obtained from Zimapan, Mexico. It belongs to 3d-transition series of metals and occurs naturally in over 65 known vanadium bearing minerals. Important minerals containing vanadium are patronite, bravoite, sulvanite, davidite, and roscoelite. Deposits of sulvanite and davidite are available in Australia and U.S.A. Other deposits that are mineable for vanadium are found in South Africa, U.S.A., China, Finland and former USSR [Kirk and Othmer, 1980]. Vanadium is also contained in petroleum coke, ashes of oil and assorted slags and residues [Okuwaki et al., 1988; Shigendo, 1995; Zhang et al., 1995].
The relatively complex chemistry of vanadium arises from its electronic configuration 3d 4s , which is responsible for the existence of the oxidation states +5 to -1. Detailed discussion on properties, thermodynamic data, electrochemical behaviour and manufacturing processes of vanadium are given by many authors like Clark [1968], Baes and Mesmer [1976], Bard [1976], and Kirk and Othmer [1980].
The oxidation states of vanadium that occur in aqueous solutions are +2, +3, +4, and +5. Vanadium(II) or V2+ is the least stable, easily oxidised by air while vanadium(III) or V3+ undergoes slow oxidation in the presence of air. The
22 Chapter 2 Literature Review vanadium(IV) or V02+ ions are the most stable under many conditions whereas, vanadium(V) or V02+ is a mild oxidising agent and is also stable in the presence of air. Figure 2.2 shows potential-pH diagram for dilute vanadium solution at 25 °C illustrating the existence of different aqueous species of vanadium [Pourbaix, 1966].
The two most common compounds of vanadium(V) are vanadium pentoxide
(V205) and ammonium metavanadate (NH4VO3). Vanadium pentoxide is sparingly soluble in water (0.7 gm/1) giving a slight yellow solution. It is more soluble in strong acids like HC1, H2S04, and HN03 forming lightly coloured greenish yellow solution [Strehlow and Wendt, 1963]. It also readily dissolves in basic medium producing a colourless solution containing the vanadate ions [Cotton and Wilkinson, 1976].
Numerous vanadium(V) species are formed in the acidic medium depending on the pH of the solution. The pervanadyl or vanadic ion (V02+) is the principal species in the pH range of 0.5 to 1.3 and is easily protonated to form VO(OH)22+ species. At moderate acidities (1< pH <6) and V(V) concentrations, V02+ polymerises to form decavanadates, V10O28.z(OH)z(6 z)'. At pH less than neutral, metavanadates are formed, principally V3093 and V40124'. In the basic region, pyrovanadates are formed and finally the most basic orthovanadate, V043 [Baes and Mesmer, 1976].
Summary of various reactions and corresponding aqueous species is reported by Baes and Mesmer [1976] and Pourbaix [1966] along with the equilibrium constants at 25°C. The distribution of vanadium(V) species at different pH’s is shown in Figure 2.3 and regions of predominance of the vanadium(V) species as a function of pH is illustrated in Figure 2.4.
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-2 -1 3 4 5 6 7 8 9 10 1! 12 13 14 15 16
Hvor
E(V)
-2 -1 10 1! 12 13 14 15 16 PH
Figure 2.2. Potential - pH diagram of V-H20 system at 25°C (Source: Pourbaix, 1966).
24 Chapter 2 Literature Review
Silva et al. [1987] developed Eh-pH diagrams for the V-H20 system at high temperatures for vanadium molar activities in the range of 1.0-0.0001M. Silva and Ogasawara [1993] discussed the relationship between molar activities (av) and pH of the V-H20 and V-Na-H20 system. They developed logav-pH diagrams for the V-H20 and V-Na-H20 system to evaluate the influence of temperature and ionic activities in solution on the precipitation of vanadium compounds (polyoxides and/or polyvanadates). While studying the thermodynamics of precipitation in sodium vanadate solutions, they pointed out that presence of phosphorus tends to inhibit vanadium precipitation, probably owing to the formation of stable neutral complexes with V02+, such as (V02)3P04 (aq) or V02 H2P04 (aq).
Vanadium(V) may be complexed with several anions such as [V02C14]3, [V02EDTA] and [V02ox2] Oxohalides of vanadium may also exist as V02F or V02C1 [Kantner, et.al., 1983]. Studies of vanadium(V) complexes in the presence of sulfates were conducted by many researchers [Ivakin, 1966; Madie et al. 1984] and will be discussed later in section 4.3.1.1.
VO,(OH):
VQztOHM \ v206(0H)' vckoh:
(a) 0.1 m VCV) (b) 0.001 m V(V)
Figure 2.3. Distribution of vanadium(V) species as a function of pH at 1 molal ionic strength and 25°C. (a) 0.1 molal V(V) (b) 0.001 molal V(V). (Source: Baes and Mesmer, 1976)
25 Chapter 2 Literature Review
10 26
VO,(OH)
^-VO (OH)Jaq)
pH
Figure 2.4. Predominance diagram of vanadium(V)-OH species as a function of pH at 1 molal ionic strength and 25°C. (Source: Baes and Mesmer, 1976)
26 Chapter 2 Literature Review
2.3.2 Previous Work on Stability of Supersaturated V(V) Solutions
As mentioned earlier, the vanadium redox flow battery uses the V(V)/V(IV) redox couple in the positive half cell and V(II)/V(III) redox couple in the negative half cell. Skyllas-Kazacos and co-workers [1985, 1988, 1990] studied various alkaline and acidic supporting electrolytes and identified sulfuric acid as a suitable supporting electrolyte to prepare supersaturated vanadium(V) solutions for the vanadium redox battery.
Evaluation of the stability of vanadium electrolyte in H2S04 was initiated by Sum and Skyllas-Kazacos [1985] and the composition of vanadium electrolyte initially employed by Skyllas-Kazacos et al. [1987, 1988] was 2M vanadyl sulfate in 2M H2S04. Results from the conductivity and electrolyte stability tests at elevated temperatures have led to the modification of the electrolyte composition from 2M vanadyl sulfate in 2M H2S04 to 2M vanadyl sulfate in 3M H2S04 demonstrating higher energy efficiencies and greater V(V) electrolyte stability [Kazacos, 1989]. However, 2M V(V) solution in 3M H2S04 has shown that precipitation of V(V) solution can occur if it is stored for extended periods of time at elevated temperatures.
Cheng [1991] indicated that vanadium electrolyte of composition 2M V(V) in 4M H2S04 were found to be more stable than 2M V(V) in 3M H2S04 previously employed. They recommended that concentrations of 2M V(V) in 3-4M H2S04 could be safely employed in applications where the battery undergoes continuous cycling and if high temperatures are not experienced over long periods. In applications where high temperatures and/or infrequent cycling are expected, the recommended electrolyte composition is 1.5M V(V) in 3-4M H2S04.
An interesting finding of Kazacos et al. [1990] is that the stability of supersaturated V(V) solutions at increased temperatures is highly dependent on
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state-of-charge (SOC) of the solution thus suggesting that presence of small percentage of V(IV) species makes the V(V) solution more stable at elevated temperatures.
Recent studies carried out by Skyllas-Kazacos, Menictas and Kazacos [1996] showed that V(V) solutions of concentration between 3M-5M V(V) in higher sulfuric acid concentrations (5M - 7M) are more stable above 40°C for a period of 30 days. Detailed investigations are still required to fully understand the phenomena and determine the optimum sulfuric acid concentration and temperature range.
2.3.3 Additives for the Control of Thermal Precipitation of V(V) Solutions
To increase the energy density of vanadium battery, the induction times of supersaturated vanadium solutions can be increased by use of appropriate additives, thus enabling the prevention of precipitation. A review of the literature is presented first on the performance of antisealants conventionally used in preventing precipitation in desalination plants, oil wells, and cooling towers. The precipitation inhibitors investigated so far to specifically prevent thermal precipitation of supersaturated V(V) solutions, will also be discussed.
2.3.3.1 Precipitation Inhibitors Used in Water Formed Scale Deposits
The early work on threshold agents has been extensively reviewed by Elliott [1970]. The mode of action of these threshold agents has not yet been fully explained but would appear to be due to adsorption of the additive on the growing crystal nuclei which inhibits growth at the preferred nucleation sites and results in the formation of irregular, distorted crystals. Addadi [1982] noticed that the required dosages of these additives vary from 5 wt.% in solution for the objective of habit modification up to 10 wt.% for total inhibition. In the water treatment industry these additives have been used successfully to control carbonate as well as sulfate scales.
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Buehrer et al.[1940] discussed the effect of small quantities of sodium-hexa- meta-phosphate (SHMP) and mentioned that 2 ppm of SHMP can completely prevent precipitation of 200 ppm of calcium carbonate at room temperature. Much work was carried out [Herbert et ah, 1965; Hasson, et al., 1970; Flesher et al., 1970] with homopolymers and copolymers of acrylic acid, which were used for the prevention of scale in industrial water recirculation systems. Scale formation was prevented to a certain extent but none of the additives tested had a greater activity than polyphosphate.
Reddy and Nancollas [1973] studied several phosphonates to inhibit the crystal growth of calcite in evaporative desalination processes. The various additives included in the study were N,N,N’,N’-ethylenediaminetetra (methylenephosphonic) acid (ENTMP, Dequest-2041R, Monsato Company), N,N,N’,N’-hexamethylenediaminetetra(methylenephosphonic) acid (HTMP, Dequest-2051R, Monsanto Company), nitroli(methylenephosphonic) acid (NTMP, Dequest-2001R, Monsanto Company), 1-hydroxyethylene 1,1- diphosphonic acid (HEDP, Dequest-2011R, Monsanto Company), without any purification. They reported that the addition of phosphonic derivatives to a supersaturated calcium carbonate solution greatly reduces the rate of growth of calcite seed crystals at 25°C. At a fixed weight concentration of 0.5 ppm, the calcite growth inhibition effectiveness was found to be in the order HEDP > HTMP > ENTMP > NTMP. The growth-rate inhibition was found to be a function of phosphonate dosage at levels below 2.5 ppm. Reddy et al. [1976] investigated the inhibiting action of SHMP and several other inhibitors at ambient temperature. They observed that SHMP provides maximum gypsum scale inhibition compared with seven other additives.
Jacques et al. [1979] conducted a laboratory comparison of two inhibitors, a commercially available phosphate ester and COREXIT 7647, a low molecular weight polymer for control of SrS04 scale. The onset of SrS04 precipitation was found to be a strong function of degree of supersaturation and compared
29 Chapter 2 Literature Review with phosphate ester, COREXIT 7647 was more effective against SrS04 precipitation.
The relationship between structure and performance of high-temperature MSF plant scale control additives was studied by Walinsky et al. (1981). They evaluated low molecular weight polymers (Mw = 500 - 10,000) of maleic, fumaric, itaconic, methacrylic, acrylic, and vinylsulfonic acid to prevent alkaline scale formation. The major findings are as follows:
1. The overall scale control was most effectively demonstrated by low molecular weight maleic-based polymers.
2. Monomeric antisealants and polyvinylsulfonic acids were mostly ineffective against magnesium hydroxide.
3. Hydroxyethylidene diphosphonic acid and polyitaconic acid (Mw - 7,000) formed insoluble calcium and sodium complexes which precipitated out from seawater probably due to poor compatibility or temperature- dependent solubility in seawater.
The performance evaluation of a polyphosphate-based formulation known as Shuwaik Mix (49% sodium tripolyphosphate, 49 % lignin sulfonate derivative and an anti-foam agent about 2%) was evaluated by Butt and Bou-Hassan (1981) to prevent scaling in MSF desalination plant at about 85°C. They reported that the additive was only moderately effective over a period of 8 months. Busch [1981] developed a formulation to control scale build-up on metallic surfaces. Principle components of the formulation include a chelant, polymeric conditioners, a gluconate, a triazole and sodium sulfate.
Davey [1982] presented an excellent review on the role of additives in precipitation processes. He pointed out that most of the literature available is regarding the precipitation inhibition of sparingly soluble inorganic substances.
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He classified the various additives studied into the following 4 groups: (i) low molecular weight organic substances, e.g. citric, succinic, tartaric acids, nitrilotrimethylene phosphonic acid, (ii) low molecular weight inorganic materials, such as sodium triphosphate and sodium pyrophosphate, (iii) long chain polymeric materials with acidic and hydroxylic side groups e.g. polyacrylic acid, polyglutamic acid and alginic, and (iv) proteinaceous materials, e.g., gelatin, statherin, phosphoproteins, and polyribonucleotides. He reviewed the effect of various additives (polyacrylic acid, sodium triphosphate, polymethacrylic acid, sodium pyrophosphate) on the precipitation behaviour of different supersaturated solutions (strontium sulfate, gypsum, calcium oxalate) and concluded that the active additives invariably extend the induction time. He explains that the presence of active additive in the system may result in adsorption onto embryos that reduce the speed at which they pass through the critical size barrier and thus reduces the rate of nucleation. Leung and Nancollas [1978] reported the results of adsorption of nitrilotrimethylenephosphonic acid on barium sulfate crystals and concluded that only 5% surface coverage is necessary for complete inhibition of crystal growth.
Harris [in Porteous, 1983] discussed the effect of various additives in retarding the precipitation of alkaline scale (e.g. calcium carbonate, magnesium hydroxide) and sulfate scale in desalination plants. He mentioned that the use of threshold quantities of polyphosphates could prevent or reduce the formation of calcium carbonate scale. However, the polyphosphates are susceptible to hydrolysis, and the rate of hydrolysis increases with temperature. Polymaleic acid was found to overcome the disadvantage of polyphosphate and has the ability to withstand high temperatures and prevents the formation of alkaline scales. Harris believes that the only additive which appears to be in commercial use to retard calcium sulfate, strontium sulfate or barium sulfate scale formation
31 Chapter 2 Literature Review is polyphosphate, although investigations have shown that many chemicals can effect the rate of crystallisation of calcium sulfate.
Reitz [1984] developed a broad spectrum antisealant for reverse osmosis desalination plants. The additive (FLOCON 100) was designed specifically to control calcium sulfate, calcium carbonate, and strontium sulfate scaling. He presented operating data from reverse osmosis plant and showed that FLOCON 100 performed better than SHMP.
Amjad [1985] presented an excellent laboratory comparison of an advanced additive (a formulated polyelectrolyte called AF-400) with the conventional SHMP for control of gypsum scale in reverse osmosis desalination plant. He found that, at a dose level of 0.5 ppm, the induction period achieved with AF- 400 was about twice as long as that with SHMP. Smith [1985] discussed the effectiveness of a modern additive consisting of a blend of phosphonate and polycarboxylates called EL-5600. He reported that 8 ppm of EL-5600 when added to a solution of 2000 ppm NaCl brine containing gypsum can increase the soluble level of gypsum by a factor of 2.
Gill and Varsanik [1986] pointed out that a close comparison of the inhibitors and the mineral they inhibit or regulate shows some structural correlation. Various inhibitors have differing degrees of effectiveness even for different hydration forms of the same scale. Two crystallographic forms of calcium sulfate, dihydrate and hemihydrate have been shown to have markedly distinct interactions with inhibitors like polyvinyl sulfonate (PVS) and polyglutamic acid (PGA) with respect to change of the crystal habit. PGA is more effective than PVS for dihydrate phase while the reverse is true for the hemihydrate phase. They attributed the changes in morphologies and inhibition to the close association of the negatively charged groups on the inhibitor and positively charged calcium ions in the crystal lattice of calcium sulfate hemihydrate/dihydrate.
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Van Der Leeden and Rosemalen [1987] presented a comprehensive survey of various types of additives in relation to their application. They reported that the effective growth retarders at pH 5 were unsubstituted low molecular weight poly aery lates. At pH 8, the performance of these poly acrylates was substantially reduced. Combination of the inhibitor polyacrylic acid and a small amount of dispersant polystyrene sulfonic acid gave rise to a synergistic effect on gypsum growth retardation at pH 5.
Amjad [1989] examined a variety of polymeric inhibitors to prevent gypsum scale formation on heat exchange surfaces. He reported that scale growth experiments in the presence of low levels of acrylic acid-based copolymers clearly indicate that acrylic acid copolymer showed excellent inhibitory property compared to acrylic acid/acrylate ester, acrylic acid/2-acrylamido-2-methyl propane sulfonic acid, maleic acid copolymer, and maleic anhydride/sulfonated styrene.
Klepetsanis and Koutsoukos [1990] studied the precipitation of calcium sulfate from supersaturated aqueous solutions with and without inhibitors. Examination of hydroxyethylidene 1,1 diphosphonic acid (EHDP), ehtylenediamine tetramethylenephosphonic acid (ENTMP), and nitrilo tetramethyl phosphonic acid (NTMP) showed that these organophosphorus compounds prolong the induction periods preceding precipitation and reduce the rates of spontaneous precipitation in the order: ENTMP > NTMP > EHDP.
Polycarboxyl type antisealants in general have a tendency to become less effective in the presence of multi-valent metal ions such as Ca++ and Mg++ in sea water. Fukumoto et al. [1991] developed a new antisealant “AQUAKREEN KC-550” by the copolymerisation technology and has much higher stability against such multi-valent ions.
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Amjad and Pugh [1995] studied the influence of polymeric antisealants on the kinetics of crystal growth of calcium carbonate at pH 8.5 and 30°C. The antisealants evaluated contained various functional groups e.g. carboxyl, sulfonic, pyrolidone, and quarterenized ammonium, and different ionic charge like negative, neutral or cationic. It has been found that among the homopolymeric antisealants, carboxyl-group containing antisealants polyacrylic acid shows the best performance in inhibiting calcite crystal growth. Butt and Rahman [1997] carried out laboratory evaluation of SHMP, EL-5600 (of Calgon) and FLOCON-lOO (of FMC) using brackish water supersaturated with CaC03, SrS04 and CaS04.2H20. The results showed that the relative performance of the additives could be rated as EL-5600 > SHMP > FLOCON- lOO.
2.3.3.2 Precipitation Inhibitors for Vanadium(V) Solutions
The effect of antisealant on the precipitation of supersaturated vanadium solutions is not available in the published literature. However, some work on interaction between vanadium(V) and chelating agents related to the biological systems is reported due to increasing interest in metal-amino acid as well as peroxo-metal systems for understanding biologically important molecules. Vanadium is found in very low concentrations in most living organisms, but its biological function is still unclear. Yamada and coworkers [1976] studied kinetically the complex formation of some aminocarboxylates with V(V) and showed that dechelation is dependent on H+ concentration. Lagrange et al. [1984] discussed the kinetic study of acid dechelation of some vanadium(V) complexes of ethylenediamine-tetra-acetic acid, nitrilotriacetic acid, and ethylenediamine-N, N’-diacetic acid in aqueous solution. Bhattacharjee et al. [1990] described the synthesis, characterisation and properties of peroxo- vanadium(V) complexes with glycine as the hetero-ligand. Domingo et al. [1990] studied 18 chelating or reducing agents and determined their relative efficacy as antagonists in acute intramuscular vanadyl sulfate intoxication in
34 Chapter 2 Literature Review mice. Tiron followed by ascorbic acid and 2-mercaptosuccinic acid were found to be increasing the solubilising effect of vanadium. Branca et al. [1992] reported the binding of oxovanadium(IV) to simple sugars in neutral or basic solution. They found that the complexation is favoured in basic media and involves the co-ordination of the metal ion to couples of adjacent deprotonated hydroxyls of the sugar molecules. Sreedhara et al. [1994] while discussing the synthesis and characterisation of vanadyl saccharides mentioned that all the saccharide complexes are stable in solution for long periods under ambient conditions without being oxidised and showed no hydrolysis in the pH range 2-12.
The need to stabilise supersaturated vanadium solutions using antisealants was realised after the inception of the all vanadium redox flow battery concept by Skyllas-Kazacos and coworkers. Therefore, studies on the effect of scale inhibitors and complexing agents to stabilise vanadium solution to achieve higher energy densities were initiated by Skyllas-Kazacos. Cheng [1991] tested various dispersants and complexing agents like Teric BL8, Teric 16A16, Teric PE61, EDTA and so on. They used 10% of these dispersants to investigate the effectiveness against thermal precipitation of V(V) solutions at 25 °C and 40°C and reported that none of these chemicals were suitable for V(V) electrolyte stabilisation.
Skyllas-Kazacos and Kazacos [1994] conducted comprehensive studies on inhibitor evaluation against precipitation of all vanadium species (V(II), V(III), V(IV) and V(V)) involved in the vanadium redox battery. They discovered that 2-3 wt% of solid ammonium oxalate can stabilise 3M V(III) and V(IV) electrolyte for long periods of time over a temperature range of 5°C to 45 °C. In the V(II) oxidation state the same electrolyte with stabilising agent was stable at high temperatures, but at low temperatures after an extended period it formed crystals of V(II) complexes. The concentration of vanadium was found to be
35 Chapter 2 Literature Review
1.8M after 20 days at a temperature of 5°C. In the V(V) oxidation state, the same electrolyte solution forms an oxalate complex very rapidly at 100% state- of-charge. This orange oxalate complex is completely different from V205 precipitates. At 80-90% state-of-charge of V(V) electrolyte solution, the cell can be operated for a long time at room temperature with improved efficiency compared to cells having electrolyte not containing stabilising agent.
The effect of the addition of thiourea, a known stabilising agent, was compared to the effect of ammonium oxalate for the stabilisation of V(V) solution. Thiourea solution of concentration 1M was added to 2M V(V) solution in different quantities at room temperature. It was observed that the V(V) solution was reduced to V(IV) state even at a dose level of 5% by volume. Similarly the effect of addition of 1 to 20% by volume of glycerol to 2M V(V) electrolyte at room temperature was observed to change the yellow colour of V(V) solution to blue colour V(IV) solution.
When 1% fructose was added to the 6M V(V) solution during its preparation by electrolytic oxidation, it was found that the V(V) solution remained stable for about 3 weeks at room temperature. The addition of 1 % sorbitol also stabilised 5M V(V) solution at room temperature for 3 weeks. A large number of chemicals were investigated to inhibit the precipitation of 2M V(V) solution at room temperature. It was found that ascorbic acid and tri-sodium citrate when added in small quantities (1-5 % wt./vol.) have a slightly reducing effect on V(V) solution.
A mixture of 1% glycerine and 2% ammonium oxalate gave better inhibition results against V(II) and V(V) precipitation. At room temperature, 2.24M blank V(V) solution dropped in concentration to 2.03M while the addition of the mixture of additive prevented the precipitation of V(V) solution for about 20 days. When evaluated at 48°C, the 2.24M blank V(V) solution precipitated after one day (the concentration dropped to 1.36M) whereas 2.66M V(V)
36 Chapter 2 Literature Review solution with additive mixture (1% glycerine and 2% ammonium oxalate) slightly improved the stability (after one day the concentration was found to be 1.65M) and the V(V) concentration remained at about 1.6M for up to 20 days. With only 1% glycerine, the 2.96M V(V) solution decreased its concentration to 2.64M after one day and 1.8M after 20 days when tested at 48°C. The induction time of 2.7 - 3.0M V(V) solution with additive is therefore about one day at 48°C.
Further additive evaluation studies were conducted by Skyllas-Kazacos and Kazacos [1996] using 2M V(V) solution in 4M H2S04 at 45°C. They investigated the performance of many additives at a dose level of 1.5% wt./vol. and the concentration of V(V) solutions were measured after 15 or 16 days. Glycerol, lactose and asparagine showed promising results and the concentration of V(V) solution was found to be 1.6M, 1.63M and 1.4M after 20 days compared to 0.83M for blank solution over the same period at 45°C.
Sodium hexametaphosphate (SHMP) and Briquest 301-50A (nitrilotris (methylene phosphonic acid) of Albright and Wilson) also exhibited good inhibiting effect against the precipitation of 2M V(V) solution in 4M H2S04 at a dose level of 1 wt.% and 44°C. The colour of the solution was dark yellow, no precipitate was noticed for 3 days and very slight precipitate was observed after 16 days in the case of Briquest 301-50A while addition of SHMP showed no precipitate till 3 days and very slight precipitate developed after 8 days at 44°C.
37 Chapter 3 Theoretical Consideration
CHAPTER 3 THEORETICAL CONSIDERATIONS
This section presents the theoretical background of topics relevant to this study such as saturation and supersaturation, solubility and supersolubility, kinetics and mechanism and electrochemical methods.
3.1 SUPERSATURATED SOLUTIONS
3.1.1 Theoretical Background and Solubility
When a sufficiently large amount of solute is maintained in contact with a limited amount of solvent, dissolution occurs continuously till it reaches a state when the reverse process becomes increasingly important. This is the return of dissolved species (atoms, ions, or molecules) to the undissolved state, a process called precipitation. When dissolution and precipitation occur continuously and at the same rate, the amount of dissolved solute present in a given amount of solvent remains constant with time. The process is one of dynamic equilibrium and the solution in this state of equilibrium is known as a saturated solution. The concentration of the saturated solution is referred to as the solubility of the solute in the given solvent. Thus solubility of a solute is defined as its maximum concentration which can exist in solution under a given set of conditions of temperature, pressure and concentration of solution. A solution that contains less solute than required for saturation is called an unsaturated solution. A solution whose concentration is higher than that of a saturated solution due to any reason(s), such as change in solvent concentration, temperature and so on, is said to be supersaturated. When the temperature or concentration of a solvent is increased, the solubility may increase, decrease, or remain constant depending on the nature of the system. For example, if the dissolution process is exothermic, the solubility decreases with increased temperature; if endothermic, the solubility increases with temperature [Mullin, 1972; Khamskii, 1969].
38 Chapter 3 Theoretical Consideration
Both unsaturated and saturated solutions are stable and can be stored indefinitely whereas supersaturated solutions are generally unstable. However, in some cases, supersaturated solutions can be stored for a long time without exhibiting any change and the period for which a supersaturated solution can be stored depends on the degree of departure of such a solution from saturated concentration and on the nature of the substances in the solution [Khamskii, 1969]. The degree of supersaturation can be defined in two ways. One method is to measure the absolute supersaturation (AS) which can be represented as:
AS = C - Ceq (3-1) where C is the concentration of the dissolved substances in a given supersaturated solution and Ceq is its normal equilibrium saturation concentration.
The other method of expressing the degree of supersaturation is by defining in terms of percent supersaturation as stated below:
PS(%) = [(C - Ceq)/ Ceq ]*100 (3-2) and supersaturation ratio as:
SR = C / Ceq (3-3)
Solubility data of solutes provide a basis to establish saturation concentration. A convenient method of discussing the solubility (S) of a solute is by means of a solubility product (Ksp). Consider the addition of a solute MX (s) to distilled water. At the limit of solubility, there is a dynamic equilibrium which can be represented as follows:
MX(s) M+(aq) + X'(aq) (3-4) and the equilibrium constant, Ksp0, for the solubility process is given as
39 Chapter 3 Theoretical Consideration
Ksp° = [a(M+ ) a(X')] / a(MX) (3-5)
Since the activity of pure solid MX(s) is unity, the equilibrium expression simplifies to
Ksp° = a(M+ ) a(X') (3-6)
Ksp° is known as Solubility Product or sometimes Thermodynamic Solubility Product’ and it is a function of temperature and invariant with the ionic strength of the solution [Atkins, 1995].
In any aqueous solution containing M+ and X' ions, as long as the activities a(M+) and a(X‘) are such that their product is greater than Ksp° then some solid MX(s) should precipitate until the product of a(M+) and a(M~) becomes equal to Ksp°.
For a general case :
MpXq(s) pMq (aq) + qXp (aq) (3-7)
Ksp° = a(Mq+ )p a(Xp‘ )q (3-8)
Ksp° = [C(Mq+ )p C(XP' )q ] [7(Mq+ )p y(Xp' )q] (3-9) where y(Mq+ )p and y(Xp~ )q are the activity coefficient of species M and X. If C(Mq+ ) and C(XP' ) are the concentrations, the mean activity coefficient of
MpXq is denoted as then
Ksp° = [C(Mq+ )p C(XP' )q ] f+q (3-10)
The solubility product expression now can be modified as follows
40 Chapter 3 Theoretical Consideration
Ksp = [C(Mq+ )p C(XP‘ )q ] (3-11) where Ksp is known as the Apparent Solubility Product and is related to Thermodynamic Solubility Product as follows:
Ksp = Ksp°//+q (3-12)
If the ionic strength of the aqueous environment is low, the activity coefficient (y) is unity (i.e. ideal behaviour of solution is approached, in which activities and concentration can be equated) and the above expression reduces to an approximate form.
Ksp° ~ Ksp (3-13)
Ksp - [C(Mq+ )p C(XP‘ )q ] (3-14)
This form is frequently used in practice, in which the true solubility product is expressed simply in terms of concentration of the ions. However, it should be noted that, in aqueous systems of significant ionic strength the activity coefficient is not equal to one and thus Ksp is not equal to Ksp°. Then Ksp is a function of both temperature and ionic strength while Ksp0 is invariant with ionic strength. In such circumstances, the use of Equation 3-13 is likely to introduce significant errors. The calculation of activity coefficients (y+) becomes necessary at higher ionic strengths. A number of correlations are available in the literature to estimate activity coefficients and Horvath [1985] has given an excellent review of these. Pytkowicz [1980] suggested the following form for high ionic strength solutions:
logy± = AVl/(l + BaVl) + C, + C2I15 + C3I2 (3-15) where I = 1/2 X nij Zj2 ionic strength = molal concentration of ion T in the solution
41 Chapter 3 Theoretical Consideration
Zj = ionic charge of ion ‘i’ in the solution a = ion size parameter A,B = Debye-Huckel coefficients Ci - C3= Regression constants
Substituting equation 3-15 in equation 3-12 after taking log on both sides and assuming p = q =1 will give the following equation for Ksp. logKsp = logKsp0 + 2AVl / (1 + BaVl) + 2C,I + 2C2IL5 + 2C3I2 (3-16)
3.1.2 Solubility and its importance in the precipitation
The solubility of a salt as discussed earlier is defined as its maximum concentration which can exist in solution under given solution concentration, temperature and pressure. At this condition of saturation, the solution is said to be in equilibrium with respect to the salt. As long as the salt concentration in the solution is equal to or below its saturation concentration, it will not precipitate out of the solution, and no scale will form. If, however, the concentration of the salt exceeds its saturation concentration due to any reason(s), such as change in solution concentration, temperature, pressure, etc., the solution is said to be supersaturated. The excess salt in the saturated solution tends to precipitate and probably deposit as scale. The higher the degree of supersaturation, the greater is the driving force for precipitation to occur. Therefore the basic condition required for scale formation is attainment of ‘supersaturatin’ [Cowan and Weintritt, 1976]. As a consequence of supersaturation, nuclei will form and lead to crystal growth and precipitation or scale formation. Solubility of the scale-forming salts is, therefore, like a border between the scale and no-scale regimes and its knowledge is fundamental to the prediction and control of scale. So, the knowledge of solubility data is of vital importance for the prediction of scaling.
42 Chapter 3 Theoretical Consideration
3.1.3 Maximum Sup er saturation and Sup ersolubility
It is important to know the maximum supersaturation of a substance and the stability of the solution that can be achieved under given conditions. The maximum supersaturation represents the limit at which spontaneous crystallisation begins [Khamskii,1969]. The value of maximum supersaturation can be measured either in terms of absolute supersaturation or percent supersaturation. The value of maximum supersaturation depends primarily on the nature of solute and the solvent. However, other factors such as temperature, impurities, the rate of cooling of a solution and various other mechanical effects (filtration, stirring, irradiation with ultrasound etc.) have a significant influence on the value of maximum supersaturation. In view of the above mentioned factors, the method of preparation of a solution and the degree of its purity may be very important in achieving a high level of supersaturation.
The phenomenon of maximum supersaturation is closely related to the stability of supersaturated solutions, which is governed by the metastability limit also known as supersolubility. The supersolubility represents the maximum concentration, obtained at a given set of conditions of temperature, ionic strength etc., at which spontaneous crystallisation begins [Mullin, 1961]. The supersolubility (metastability limit) separates the region of supersaturated solutions into two parts. The supersaturated solutions with concentrations above the supersolubility limit crystallise instantaneously while those whose concentrations are below the limit can be stored without inducing crystallisation for some time. The first mentioned region is known as labile region or unstable zone; the second region as the metastable zone as shown in Figure 3.1 [Ostwald, 1900].
43 Chapter 3 Theoretical Consideration
Labile zone
Metastable zone
Stable (Unsaturated) solution zone
TEMPERATURE
Figure 3.1. A typical diagram showing states of solution.
Miers and Isaac [1906] has defined the supersolubility as the maximum concentration at which large scale crystallisation of a solution begins. The supersolubility curve resembles the solubility curve and the two are usually almost parallel to each other. Tovbin and Kransnova [1951] plotted the solubility and supersolubility data of three salts as shown in Figure 3.2. For KN03 and KC103, these curves are practically parallel while in the case of KC1, the solubility curve is steeper than the supersolubility curve. However, the difference between the two curves is relatively small and the two curves are in fact straight lines. In contrast to the solubility curve, the supersolubility curve does not depend just on the temperature and composition of the solution but, also on the elapsed time, other conditions being equal. The period during which the concentration of a solution remains constant is known as the induction period or latent period [Khamskii, 1969]. The duration of the induction period depends on the degree of supersaturation of a solution, the nature of the solute and the solvent, the vigour of stirring of the solution, the presence of impurities and on other factors. Studies of induction period are important not only from
44 Chapter 3 Theoretical Consideration the point of view of practical information on the crystallisation process but also because they can yield information about the crystallisation mechanism, the nature of the various stages of the crystallisation process, and about some of the properties of the crystalline substances.
------X
Z 2 <>'•
TEMPERATURE (C)
Figure 3.2. Supersolubility (dashed) and solubility (solid) curves of solutions of three salts: (1) KN03; (2) KC1; (3) KC103 [Tovbin and Kransnova, 1951]
3.1.4 Methods of Preparing Supersaturated Solutions
A supersaturated solution can be prepared by the following four methods. The first three methods are described in Khamskii [1969] and the fourth method is adopted from the procedure used by Sum and Skyllas-Kazacos [1985] for the vanadium system.
Method 1: If the solubility of a substance increases with increase in temperature, a supersaturated solution can be prepared by dissolution of the solute at higher temperature and then cooling it.
45 Chapter 3 Theoretical Consideration
Method 2: The second method can be applied to any substance and it involves the removal of a solvent at a constant temperature. The gradual loss of the solvent by evaporation increases the concentration of the solute in a solution resulting in supersaturation.
Method 3: This method is based on the principle of chemical equilibrium between substances. When a new compound is formed by a chemical reaction and the concentration of this compound is higher than its solubility in a given solution, such a solution becomes supersaturated with respect to the new compound. Generally, supersaturation by this method is obtained by mixing two or more solutions of relatively easily dissolved substances.
Method 4 The fourth method involves electrolytic dissolution of substances which exists in more than one oxidation state. Electrolytic oxidation or reduction of the solution can be carried out in an electrolytic cell which consists of two compartments separated by an ion-exchange membrane. The solute slowly dissolves in the solvent and simultaneously converted to the other oxidation state, thereby increasing the concentration of the solution. A higher degree of supersaturation can be achieved using this method.
3.2 KINETICS AND MECHANISM
Scale formation or precipitation is a complex process, commencing with the attainment of supersaturation, and the degree of supersaturation or deviation from equilibrium condition is the prime factor responsible for precipitation. The theory and application of precipitation and crystallisation processes has been the subject of several monographs which review the various aspects of the subject [Becker and Doring, 1935; Gordon, 1959; Van Hook, 1961; Nielsen, 1964; Walton, 1967; Khamskii, 1969; Mullin, 1972]. However, there is no universal theory which can be used to explain the various rate determining steps involved in different precipitation processes.
46 Chapter 3 Theoretical Consideration
It is generally agreed that crystallisation involves three basic stages: (1) the achievement of supersaturation, (2) the formation of nuclei of the precipitate or nucleation, and (3) growth of crystals. The supersaturation of a system may be achieved by concentrating the solution, raising the temperature, and so on. The state of supersaturation has already been discussed in the previous section. The other two factors, nucleation and crystal growth will be briefly described in the following paragraphs.
3.2.1 Nucleation
Nucleation is a rather complicated process with the result that it is the most controversial and least understood stage of crystallisation. However, the first step in nucleation is the attainment of supersaturation which represents a non equilibrium state. When the departure from the equilibrium is sufficient a new phase appears spontaneously which tends to bring the system to an equilibrium state [Khamskii, 1969]. The formation of this new phase is manifested by the appearance of a nucleus of definite volume. The minimum amount of a new phase capable of independent existence is known as nucleus. A nucleus is a crystallisation centre of the new phase. The nucleation stage is generally divided into three categories [Mullin, 1972; Garside, 1985]: primary homogeneous, primary heterogeneous and secondary nucleation, and Figure 3.3 shows these stages schematically.
Homogeneous nucleation is the spontaneous formation of new crystals from the liquid phase, induced by the state of supersaturation alone. Heterogeneous nucleation is influenced by the presence of foreign insoluble material in the crystal suspension, in addition to the supersaturation. Heterogeneous nucleation requires lower levels of supersaturation than does homogeneous nucleation. Secondary nucleation refers to nucleation induced by the presence of the suspended solute crystals themselves given the state of supersaturation.
47 Chapter 3 Theoretical Consideration
Nucleation in absence of > homogeneous solid interface primary or spontaneous
foreign interface > heterogeneous Nucleation in presence of solid interface apparent »■crystal of solute secondary true
contact
Figure 3.3. Schematic representation of different categories of nucleation [Garside, 1985].
There is no general agreement about the exact nature of nuclei; some researchers believe that a nucleus is a very tiny crystal while, others are of the opinion that a nucleus need not be a crystal and it may be either a stable complex of ions and molecules, capable of further growth, or an amorphous particle [Khamskii, 1969]. Mullin [1972] and Konak [1974] define a nucleus as a particle which has reached a certain size known as critical cluster. These particles (or embryos) below this size will dissolve, whereas others above it will grow to become crystals. Christiansen and Nielsen [1951] calculated that nuclei of low solubility compounds consists of several molecules, but La Mer and Dinegar [1951] and Frenkel [1955] consider nuclei to consist of several hundred atomic size particles.
According to cluster formation theory developed by Becker and Doring[1935], clusters of particles are formed in a solution based on the following scheme:
Ai + Ai ■ ■ A2
A2 + Ai A3
An_! + Ai „ An (critical cluster or nucleus) (3-17)
48 Chapter 3 Theoretical Consideration in which An is a cluster of ‘n’ molecules. The rate of nucleation is essentially the rate at which clusters An of nuclear size are formed by the successive reactions of Equation 3-17 [Reiss, 1977].
Classical theories of primary or spontaneous homogeneous nucleation assume that in supersaturated solutions, solute atoms or molecules combine in a series of bimolecular reactions to produce ordered aggregates or ‘embryos’. The overall free energy of these embryos goes through a maximum at some critical size which can be shown to be inversely proportional to the logarithm of the solution supersaturation [Walton, 1969]. Embryos larger than this critical size will decrease their free energy by further growth; they are ‘stable nuclei’ and grow to form macroscopic crystals. Formation of new nuclei is determined by the rate at which embryos surmount the maximum in the free energy curve and the resulting nucleation kinetic equation is of the form
J„ = C, exp [-C2 03 / T3 (InSS)2 ] (3-18) where Q and C2 are constants a Interfacial energy T Temperature SS Supersaturation
This equation indicates that three main variables govern the rate of nucleation: temperature, T; degree of supersaturation, SS and interfacial energy g. The primary nucleation rate is highly non-linear in solution supersaturation, being near-zero for low values of SS (the metastable region) but increasing extremely rapidly once some critical supersaturation is reached (the labile region). However, the increase in rate of formation of nuclei with increasing supersaturation is not indefinite, at very high supersaturation the rate begins to decrease due to increase in viscosity of solution, which impedes the nucleation of the new phase. It has been observed that the dependence of primary
49 Chapter 3 Theoretical Consideration nucleation rates on the supersaturation is closely approximated by a power-law relationship of the form [Mina-Mankarios, 1991]:
Jn = kn(SS)n (3-19) where SS is the supersaturation (C - Ceq), the driving force and ‘n’ is the kinetic order of nucleation and kn is the nucleation rate constant with temperature dependency usually modelled as an Arrheneus type relationship
kn = An exp (- En/RT) (3-20) where En is the activation energy of nucleation.
Another kinetic approach for homogeneous nucleation of crystals from ionic solution was suggested by Christiansen and Nielsen [1951]. Unlike classical theory which predicted that the critical size and rate of nucleation are highly dependent on supersaturation, their model suggested that the rate of nucleation is not a strong function of supersaturation, and that the critical cluster size is always a constant. According to Christiansen and Nielsen, the nucleation rate can be expressed as a power law,
Jn = kn (SR-1)P (3-21) where ‘p* is the number of ions in the critical sized cluster, SR is the supersaturation ratio and ‘kn’ is a constant. In order to relate the nucleation time with the observed induction time for appearance of visible precipitation, they also suggested that the induction time t, is inversely proportional to Jn. Hence,
1/T ~ kn(SR-l)p (3-22)
Several sparingly soluble salts have been shown to follow Equation 3-22 with values for p in the range of 2 to 9 [Turnbull, 1953; Christiansen and Nielsen, 1951]. By plotting induction times versus supersaturation n and p can be determined. This model stresses a weak dependence of the nucleation rate on
50 Chapter 3 Theoretical Consideration
the supersaturation which is inconsistent with some experimental findings [Nielsen, 1964]. It is suggested that the induction period, which may range from seconds to days depending on supersaturation, represents the time needed for the assembly of a critical nucleus.
Chiang et al. [1988b] have developed a novel theory to describe the kinetics of homogeneous nucleation of crystals from the ionic solution. The theory separates those aspects of the nucleation process that are inherently kinetic from those that are inherently thermodynamic. The supposition that an expression for crystal nucleation rate can be adopted “by analogy” to vapour condensation is unnecessary and they showed that to be incorrect. The main assumption in their theory is that the crystals grow primarily by the addition of ions rather than molecules and any cluster containing two or more molecules is a potential nucleus. The kinetics according to Chiang et al. [1988b] is represented as
(AB)! + A+ + B (AB)2
(AB)2 + A+ + B (AB)3
(AB)i + A+ + B (AB)i+1 (nucleation)
(AB)i + A+ +B" (AB)i+2 (growth) (3-23) where AB denotes the monomer or “molecule” of AB.
Thus, the net rate, J(i), that clusters of size i grow to size, i+1, is the difference between the rate that clusters of size i add an additional molecule (more correctly, the corresponding ion pair) and the rate at that clusters of size i +1 lose a molecule (or ion pair); that is,
J(i) =f(i) n(i,t) - b(i+l) n(i+l,t) (3-24)
51 Chapter 3 Theoretical Consideration where/f/J, the forward rate, and b(i), the backward rate, are the rates of arrival and departure of an ion pair from a cluster containing i molecules.
Different mathematical equations have been developed for surface reaction/molecule integration mechanism and the sequential ionic-integration mechanism. The present approach indicates that the nucleation rate can be related to the growth rate by a power law with an order greater than two. This happens when the forward rate is a weak function of size but backward rate depends on size through the Freudlich-Oswald equation [in Chiang, Donohue and Katz, 1988b]. Also, whenever the forward and backward rates have the same size dependence the nucleation rate will obey the power law dependence, on growth rate.
The kinetics of nucleation of alumina trihydrate was studied by Ang and Loh [1990] utilising a Coulter-Counter as the particle size measuring equipment. The kinetic data were correlated using the following equation:
B° = knAa„ACb (3-25) where B° = rate of nucleation kn = nucleation rate constant An = crystal surface area (As * crystal concentration) AC = supersaturation difference (C-Ceq) C = concentration at any time Ceq = equilibrium concentration a = exponent of A b = exponent of AC As = the specific crystal surface area(m2/gm of solids) was calculated by the method recommended in the Coulter- Counter Model D Operating Manual.
52 Chapter 3 Theoretical Consideration
3.2.2 Induction Time
It has been noticed that usually a period of time elapses between the achievement of supersaturation and the detection of a new phase in a given system [Sohnel et ah, 1988]. This time is more commonly known as “induction period”. A great deal of experimental information is available about induction periods for a wide variety of systems, but very conflicting interpretations of these data have been put forward in terms of crystal nucleation and growth.
The induction time is undoubtedly related in some way to the size and complexity of the critical nucleus. It should be emphasised however, that the induction period is not a fundamental property of a system, since the term “new phase detection” is open to a variety of interpretations such as the first appearance of crystals, the onset of a change of solution property, etc.
Initially Mullin [1972] defined induction time by the following equation,
T = tr + tn + tg (3-26) where tr is the relaxation time required for the system to achieve quasi-state distribution of molecular clusters, tn is the time required for the formation of stable nucleus, and tg is the time needed for the nucleus to grow to a detectable size. It is difficult to isolate and measure these times, but the nucleus formation time tn, is believed to be the largest.
Despite its complexity and uncertainty, induction time has frequently been used as a measure of the nucleation rate. Many researchers [Christiansen and Nielsen, 1951; Turnbull, 1953; Dunning, 1969; Khamskii, 1969] agreed on the assumption that the induction period is essentially devoted to nucleus formation and can therefore be considered inversely proportional to the rate of nucleation and using the classical theory concept the relationship between induction time and supersaturation is as follows:
53 Chapter 3 Theoretical Consideration
log(l/T) °c [(03 / T3) (logSR)2 ] (3-27)
Thus for a given temperature, a plot of log x versus (logSR)"2 should yield a straight line whose slope will give the value for interfacial energy a. Chepelevski suggested [in Mullin, 1972] that solution viscosity should also be taken into account such that the slope of the line log t versus (logSR)2 is given by (Kr|2 /T3 ), where K is a constant for the system and the resulting equation will have the following form,
log(x) = [(Ktf/T3)/ (logSR)2] (3-28) where r| is the viscosity of the solution.
Recently Sohnel et al. [1988] interpreted induction time as the sum of the time for critical nucleus formation tn, and growth to detectable size, tg and can be written as follows:
T — tn + tg (3-29)
Expressions describing the dependence of t on supersaturation are derived for the cases tn » tg , tn ~ tg and tn « tg , taking into account different possible nucleation and growth mechanisms, and their validity was assessed on the basis of experimental evidence.
Gutzow and Toshev [in Sohnel and Mullin, 1988] indicated that non-steady- state nucleation may become influential in viscous solutions. The number of building units arriving at the nucleus decreases with increasing viscosity according to the relationship:
x = RTNA2/3/TlVra5/3 (3-30) where % = Number of building units arriving at nucleus in a unit time R = Gas constant T = Absolute temperature
54 Chapter 3 Theoretical Consideration
Na = Avogadro Number r| = Viscosity of solvent Vm = Molar volume of solid
3.2.3 Crystal Growth
Once stable crystal nuclei are produced in a supersaturated solution they begin to grow. Nancollas and Purdie (1964) presented an excellent review on kinetics of crystal growth. They mentioned that the growth of crystals takes place through number of steps:
(i) the diffusion of solute to the crystal-solution interface (ii) the adsorption of solute at the surface (iii) the building of the units into the lattice, and (iv) the opposing process of dissolution
If steps (ii) to (iv) were sufficiently rapid to maintain an effective concentration corresponding to saturation at the surface, then the diffusion of material to the surface would be rate determining. The flux of solute, is given by
JD = D s (C-Ceq)/5 (3-31) where D is the diffusion coefficient, s the surface area, 5 the effective thickness of the diffusion layer at the surface, and C the solute concentration.
In reaction-controlled precipitation an analogy may be made to the kinetics of homogeneous solution reaction, the ions being incorporated at growth sites directly from solution. For deposition, the flux
Joep = ksCn (3-32)
where kg is the rate constant, and n the order of reaction. For dissolution
JDiss = k’s (3-33)
and in saturated solution these rates are equal, giving k’ = kCeqn
55 Chapter 3 Theoretical Consideration
In a supersaturated solution, assuming that diffusion is not exerting any influence, they proposed the net rate of deposition to be
-dC/dt = Jöep " Jöiss — ks( Cn - Cgq11) (3-34)
However, this above equation does not fit the results of growth experiments. Davies and Jones (1949) have pointed out that the analysis of the process into two opposing reactions will not give the correct picture since it is the net change at a fixed reaction site in which we are interested and not just the statistical result of a number of isolated chemical actions. While discussing the crystal growth during precipitation of binary electrolyte, Davies and Nancollas [1955] suggested that in crystallisation experiments, the area s available for reaction could be taken as constant. The use of traditional kinetics in terms of forward and a reverse (growth and dissolution) elementary processes (Nielsen, 1979) lead to expressions like
r = rg - rd = k (Cn - Cneq) (3-35) where r is the net reaction rate, rg and rd are growth rate and dissolution rate, and k is the rate constant. Nielsen pointed out however that Equation 3-35 has not been fully verified and that empirical data usually agree far better with
r = k (C - Ceq)n (3-36) with values of n close to 2.
Liu and Nancollas [1973] studied the crystal growth of calcium sulfate dihydrate using seed crystals and they expressed the growth rate with the following equation:
dC/dt = kcS„ (C - Ceq)2 (3-37) where kc is the rate constant for growth and sn is a function of the number of growing sites added as seed crystals. An advantage of utilizing the seeded technique is that crystal growth occurs on well defined surfaces of known area
56 Chapter 3 Theoretical Consideration and morphology. The effective rate constant kcsn were reported as litres mole1 min'1. Campbell and Nancollas [1969] reported kinetics of strontium sulfate in aqueous solution using Equation 3-37. They mentioned that changes in surface area of the crystals during the precipitation experiments usually amounted to less than 1% of the total seed crystals present and could thus be neglected.
Nancollas and Purdie (1964), Mullin (1980) and Mina-Mankarios et al.( 1991) described the dependence of the growth rate on supersaturation by the semi- empirical power law relation as follows
Rg = -dC/dt = kg (C-Ceq)g (3-38) where C the concentration at any time t, Ceq the equilibrium concentration, RG is overall growth rate, k Rd = kd (C - Ceq) diffusion reaction (3-39) Rs = (ks) (C - Ceq)2 surface reaction (3-40) where is the diffusion rate constant and (ks) is the effective surface reaction rate constant in which s is a parameter proportional to the total number of available growth sites. Crystal growth from ionic solution occurs by a series of consecutive steps: bulk diffusion, surface adsorption, surface diffusion, surface reaction, and finally integration of ions or molecules into the crystal lattice [Mullin, 1972; Konak, 1974; Lee et al., 1988]. When the rate of any of these steps is much slower than all others, the growth kinetics can be modeled by considering that process. Conversely, if two or more processes have similar rates, one must derive the growth rate expression taking all of the slow steps into account [Chiang et al. 1988a]. 57 Chapter 3 Theoretical Consideration The effect of supersaturation and temperature on the growth rate of alumina trihydrate was studied by Misra and White [1971]. They correlated their measured growth rates using the kinetic relation of the form Rg =-dC/dt = kg (C-Ceq)2 (3-41) The distinction between surface reaction control and diffusion control has been explained by Nielsen [1979]. For the growth of microcrystals, the distinction can be achieved comparing the actual growth rate, RG, with the stagnant diffusion growth rate RD. Rg = ko (C-Ceq)n (3-42a) Rd = DV(C - C*)/r (3-42b) where D is the diffusion coefficient, V is the molar volume of the crystal, and r is the radius of the crystal. For Rg/Rd < 1 the kinetics is surface-reaction controlled and, for Rg/Rd ^ 1 the kinetics is probably diffusion controlled. Equation 3-38 can be used to analyse the experimental results by rewriting as: -log(-dC/dt) = -log kc - g log(C-Ceq) (3-43) Thus, a plot of -log(-dC/dt) vs -log(C-Ceq) if linear, gives ‘g’ as the order of the reaction rate, and the intercept determines the effective rate constant kG. Values of g determined experimentally for different crystal systems have often been close to 1 and many inorganic salts give an overall growth rate order in the range 1.5 to 2 [Mullin, 1972; Chiang and Donohue, 1988a]. In an earlier study, the growth rate order for the thermal precipitation of V(V) ions was found to be 1 by Cheng [1991]. Yeboah et. al. [1994] determined the order of the reaction rate for the precipitation of strontium sulfate from electrolyte solutions at various temperatures by using the following equation: 58 Chapter 3 Theoretical Consideration dC/dt = (ks)c (C - Ceq)n (3-44) where (ks)c is the effective rate constant based on concentration driving force and n is the order of the reaction. They found that over a wide range of the experimental conditions, the order was consistently around two within a period representing approximately 90 percent of the concentration range covered. After the second order growth rate period, the first order precipitation rate was evident in some experiments. They concluded that the circumstances leading to first order dependence may be due to a diffusion-controlled step when the crystal are larger and supersaturations very low. They then estimated the accurate rate constants using the integrated form of Equation 3-44 with n=2 in the following manner: 1/(C - Ceq) - 1/(C - Ceq)t=0 = (ks)c t (3-45) The relationship between an effective reaction rate constant, (ks)c and the absolute temperature, T is given by the Arrheneus equation (ks)c = A0 exp (- Eg / RT) (3-46) where EG is the activation energy for crystal growth and AG is the preexponential factor. If the Arrheneus equation applies, a plot of ln(ks)c against 1/T should give a straight line of slope (-EG/R) and intercept In AG. 3.3 CYCLIC VOLTAMMETRY Cyclic voltammetry is an effective electroanalytical technique for studying the electrochemical behaviour of a compound, a biological material, or an electrode surface. The complete behaviour of the system can be investigated by sweeping the potential linearly with time and measuring the corresponding current in the form of a curve (current versus potential) which characterises the presence of redox reactions [Skoog, 1985]. 59 Chapter 3 Theoretical Consideration Bard et al. [1980] and Kissinger et al. [1983] presented an excellent review on the fundamentals of cyclic voltammetry. The potential of the working electrode is controlled versus a reference electrode such as a saturated calomel electrode (SCE). The current required to sustain the electrolysis at the working electrode is provided by the counter electrode. The voltage applied to the working electrode is scanned linearly with time from an initial value E* to a predetermined limit E^, where the direction of the scan is reversed. This triangular potential excitation signal [Figure 3.4(a)] which sweeps the potential of the electrode between two values, is known as the switching potential. The application of switching potentials results in a repetitive triangular sequence as the potential of the working electrode sweeps back and forth and the resultant current response can be plotted as a function of the applied potential as shown in Figure 3.4(b). The important parameters of a cyclic voltammogram are the magnitudes of anodic peak current (Ipa) and cathodic peak current (Ipc) and the peak potential separation [AEp = (Epa - Epc) ] obtained by the difference of anodic peak potential (Epa) and cathodic peak potential (Epc) as illustrated in Figure 3.5. Redox reactions may be classified into the following three main categories: (i) Reversible Systems or Nerstian Systems (ii) Irreversible Systems (iii) Quasi-Reversible Systems Consider a general redox reaction kf O + ne R (3-47) kb where kf and kb are the heterogeneous rate constants for the forward and backward reactions respectively. 60 Chapter 3 Theoretical Consideration 0 Switching time. X Figure 3.4. (a) Cyclic potential sweep; (b) resulting cyclic voltammogarm. 0.8 0.6 Potential (V) vs SCE Figure 3.5. Typical cyclic voltammogram showing peak currents (Ip) and peak potentials (Ep). 61 Chapter 3 Theoretical Consideration Figure 3.6 shows typical voltammograms corresponding to each of the three systems mentioned above. By obtaining the cyclic voltammogram at different scan rates, a redox system can be identified as reversible, irreversible or quasi- reversible system. For a reversible system, the peak potential Ep is independent of the scan rate, whereas Ep changes with scan rate if the system is irreversible. The system is quasi-reversible when the situation is between the reversible and irreversible state and the reverse reaction is also taken into account. The redox reaction is said to be reversible, if the peak potential separation is: AEp = (Epa - Epc) ~ 0.057/n (V) at 25°C (3-48) If AEp > 0.059/n, then the system is totally irreversible or quasi-reversible. The peak current Ip for the reversible system ( kf = kb ) and totally irreversible system ( kf» kb ) may be given by the following equations [Skoog, 1985] at 25°C: Reversible system: ip = (2.69 x 105) ne3/2AeC0v1/2D01/2 (3-49) Irreversible system: ip = (2.99 x 105) ne(ana)1/2Ae D01/2C0v1/2 (3-50) where ip is the peak current (A) a is the transfer coefficient v is the scan rate (V/s) Ae is the surface area of electrode (cm2) D0 is the diffusion coefficient (cm2/s) C0 is the bulk concentration (mol/cm3) ne = number of electrons na = number of electrons in the rate determining step 62 Chapter 3 Theoretical Consideration Potential E Potential E ( b) Potential E Figure 3.6. Schematic of cyclic voltammogram for the three different redox systems: (a) reversible; (b) irreversible; (c) quasi-reversible. 63 Chapter 3 Theoretical Consideration Quasi-reversible reactions involve the consideration of both the forward and the backward reactions, where kf > kb. The mathematical expressions of these systems have been presented in detail by Bard et al. [ 1980]. For an irreversible system, if ip is plotted against v1/2 (Equation 3-50), the slope of the line if linear gives the diffusion coefficient. The diffusion coefficient is a measure of the mobility of electroactive species in a solution under the influence of a gradient of chemical potential, that is a concentration gradient [Bard et al., 1980]. In supersaturated solutions viscosity also affects the diffusion coefficient. The Peak potential is given as: Ep = E°’ + RT/ anF [-0.78 + ln(k°/D„ m) - 0.5 ln(anFv/ RT)] (3-51) where k° is the heterogeneous rate constant E°’ is the formal potential, E° = [ X (Epa + Epc)/2 ] / nc (3-52) Epa is the anodic peak potential Epc is the cathodic peak potential nc is the number of cycles F is Faradays constant In terms of peak potential Ep and formal potential E°\ ip can be evaluated as: ip = 0.227nFAC0k°exp [ -(ocnaF/ RT)(Ep - E0’) ] (3-53) A plot of ln( ip ) versus (Ep - E°) if straight line gives an intercept equal to ln(0.227nFACok°), thus providing a value for the rate constant (k°). 64 Chapter 4 Solubility Studies CHAPTER 4 SOLUBILITY STUDIES 4.1 INTRODUCTION The availability of solubility data of vanadium compounds in sulfuric acid is of considerable interest for the All Vanadium Redox Flow Battery (AVRFB). In this battery, the electrolyte is one of the most important components, as discussed earlier. It employs V(II)/V(III) and V(V)/V(IV) redox couples in the negative and the positive half-cells respectively. The power output of the system is determined by the size of the battery stack while the capacity is set by the concentration and volume of the electrolytes in the tanks. Earlier studies [Kazacos et al., 1990; Skyllas-Kazacos, Menictas and Kazacos, 1996] suggested that 2M V(IV) in 3-4M H2S04 could be safely employed in applications where the battery undergoes continuous cycling. Precipitation of V(II), V(III) and V(IV) ions from 2 molar vanadium solutions in 3-4M H2S04 is observed at lower temperatures, below about 10°C whereas V(V) solution precipitates above 40°C. The precipitation of various vanadium species occurs during the battery operation depending on their solubility limits and induction times. Once precipitation begins, it continues until stability have been achieved. Higher sulfuric acid concentration favours the precipitation of V(II), V(III) and V(IV) ions but stabilises V(V) ions [Cheng, 1991 and Rahman et al., 1996]. Precipitation can be eliminated over a wider temperature range by reducing the vanadium concentration below 2M. However, while concentrations as low as 1.5M are acceptable for stationary applications, a minimum vanadium concentration of 3M is required to make the vanadium battery suitable for electric vehicles. To find out the optimum conditions of H2S04 concentration and temperature where all the vanadium species are most stable, the solubility of these 65 Chapter 4 Solubility Studies compounds was studied systematically. Such studies are required, since reliable solubility data which permits the determination of degree of supersaturation and prediction of precipitation of vanadium species is not readily available in the literature. This section presents the results of the solubility study of vanadium pentoxide (V205), vanadyl sulfate (VOS04) and vanadium trioxide (V203) over a wider range of H2S04 concentrations, from 0 to 9 M and at temperatures from 10°C to 50°C. 4.2 EXPERIMENTAL PROCEDURE A solution saturated with a given solute is one that is in equilibrium with the solid phase, and it is the achievement of true equilibrium which presents one of the biggest difficulties. To achieve equilibrium saturation, prolonged and intimate contact is required between excess solid and solution at a constant temperature for several hours or in certain cases many days [Mullin, 1972]. Sample glass bottles of size 40 ml capacity with teflon stoppers containing sulfuric acid of desired concentration in the range 0 - 9 M were brought to a constant temperature of the desired value (10°C - 50°C) in the water bath. A temperature controlled immersion circulator (Thermoline) capable of controlling temperature to an accuracy of ± 0.5°C was used to maintain the constant temperature. Solids of high purity reagent grade V205, V203 or V0S04*5H20 from Aldrich Chemicals were added in sufficient quantity so that excess solids remained at the bottom when the system reached equilibrium. Preliminary experiments indicated that the equilibration time for the V205 and V203 in H2S04 was about 12 days while VOS04 - H2S04 system reached equilibrium in about 10 days. However, shaking of the bottles was carried out on daily basis for about 45 days. Equilibrium was thus achieved from the unsaturated state [Marshall and Gill 1961; Butt et al. 1995a]. Britton and Welford [1940] determined the solubility of V205 in various acids (including H2S04) by shaking the solutions with excess of the pure V205 for a month at 18°C. 66 Chapter 4 Solubility Studies Liquid samples were collected after keeping the solution for about three days without shaking so that the fine particles could settle down completely. A membrane filter (Millipore ready-to-use filters in plastic assembly) of size 0.45 pm and plastic syringe was used to collect the liquid samples. The filtered liquid samples were immediately diluted in 0.02M HC1 and the dilution factor was adjusted to bring the approximate amount of vanadium and sulfur in the range of 50 -100 mg/1. For example, a sample of V205 in distilled water was diluted by about 25 times whereas the dilution factor for a VOSO4 sample in distilled water was about 1250. The dilution factors were selected on the basis of preliminary experiments of all the three compounds conducted in distilled water, 1, 3 and 6M H2S04 at 20°C. The liquid samples were then analysed using Inductively Coupled Plasma analysis (ICP, Labtam, Australia) to determine the equilibrium of total vanadium and total sulfur (S042' and HS04) concentrations. Three replicates were taken for each sample by ICP and the mean reading was taken when the relative standard deviation (RSD) of the three readings was less than 1.0%. The ICP was operated through an IBM computer and software provided by Labtam, Australia. A typical calibration curve and sample calculation are given in Appendix A. Calibration of the ICP instrument was done periodically using standards prepared from 1000 mg/1 vanadium standard solution (Spectrosol, BDH Laboratories Supplies) and a calibration curve was developed to take care of any drift in the instrument. At the end of the experiment, the solid phase from a few selected experiments was collected, and after washing with distilled water many times and by acetone, the solids were dried for three days in the oven at 50°C and analysed by XRD. 4.3 RESULTS AND DISCUSSION The solubility data of the vanadium compounds (V203 V205 and VOS04) in sulfuric acid solutions of various concentrations and at different temperatures 67 Chapter 4 Solubility Studies are presented in the following sub-sections. Solubility correlations were developed using solubility data generated in this study to predict the scaling potential of various vanadium species in the vanadium redox battery electrolyte. 4.3.1 Solubility of V205 The solubility of V205 was determined according to the experimental procedure mentioned above. The saturation concentrations of total vanadium and total sulfur (S042 and HS04) analysed by ICP at temperatures of 10, 20, 30, 40 and 50°C in the initial sulfuric acid concentrations between 0 - 9M are tabulated in Table 4.1 It appears from the total sulfur (S042 and HS04 ) data that the initial and final total sulfate/bisulfate concentration remains constant and no sulfur has combined with vanadium to form any precipitate of vanadium and sulfur. The solubility of V205 in 1.0M H2S04 was found to be 0.163M at 20°C which is very close to the data reported by Djong-Gie [1985] as 0.165M The data reported by Meyer and Aulich [1930] was about 0.108M in H2S04 concentration of 0.869M. The solubility of V205 in 3.0M H2S04 was obtained in this study as 0.297M at 20°C as compared to 0.245M by Djong-Gie while Marakov and Repa [1938] reported a value of 0.278M at 3.185M H2S04 It appears that the solubility determinations from this study are comparable to the published data. The XRD of pure V205 powder from Aldrich Chemicals and a sample collected at the end of the solubility experiment from a sample bottle of V205 in 6M H2S04 is shown in Figure 4.1 and Figure 4.2 respectively. It can be observed that the XRD spectra of both the samples are identical, indicating that the solid phase in equilibrium with the sulfuric acid solutions in the solubility experiments was V205. The effect of sulfuric acid concentration and temperature on the solubility of V205 is discussed in the following paragraphs. 68 Chapter 4 Solubility Studies Table 4.1. Solubility of vanadium pentoxide (V2O5) in various sulfuric acid concentrations at temperatures from 10°C to 50°C. At Equilibrium Initial. H2SO4 Temp Total Sulfur* v2o5* Cone (°C) Cone Cone (mol/1) (mol/1) (mol/1) 0.0 10.0 0.0003 0.0068 1.0 10.0 1.0429 0.2282 3.0 10.0 3.0286 0.3615 5.0 10.0 5.0118 0.2770 6.0 10.0 6.0257 0.3029 7.0 10.0 6.9841 0.4074 8.0 10.0 7.9164 0.8801 9.0 10.0 8.8803 1.5117 0.0 20.0 0.0029 0.0060 1.0 20.0 0.9916 0.1630 3.0 20.0 3.0023 0.2966 5.0 20.0 5.0718 0.2233 6.0 20.0 6.0281 0.2489 7.0 20.0 6.9823 0.3095 8.0 20.0 8.0710 0.6778 9.0 20.0 8.9871 1.2887 0.0 30.0 0.0069 0.0053 1.0 30.0 1.0122 0.1491 3.0 30.0 3.0092 0.2552 5.0 30.0 5.0799 0.1860 6.0 30.0 6.0035 0.1898 7.0 30.0 7.0235 0.2296 8.0 30.0 7.9757 0.5104 9.0 30.0 8.9642 1.0969 0.0 40.0 0.0002 0.0042 1.0 40.0 1.0212 0.1352 3.0 40.0 3.0307 0.2069 5.0 40.0 5.0571 0.1545 6.0 40.0 6.0807 0.1606 7.0 40.0 6.8966 0.1739 8.0 40.0 7.9127 0.2907 9.0 40.0 9.0193 0.7605 0.0 50.0 0.0002 0.0027 1.0 50.0 1.0619 0.0964 3.0 50.0 3.0070 0.1672 5.0 50.0 5.0329 0.1421 6.0 50.0 5.9884 0.1480 7.0 50.0 7.0790 0.1573 8.0 50.0 7.9280 0.1888 9.0 50.0 9.0683 0.4933 * Saturation concentration at equilibrium 69 o CO experiment: o solubility vO the in o CD LTl (VI used C5 < 5 -J- 0 2 V pure O nn o f spectra o Csl 050 SI XRD 4.1. O Figure pucoas ja 70 800 n CD CD O puoDas jaj CD CD 71 s4uno] Cvl CD O 006 00912 0E CD CD rn C CD CD LT\ CD cd NO CD CO CD n J CD fNJ < CL CU cn Figure 4.2. XRD spectra o f V205 solids collected from solubility experiment. Chapter 4 Solubility Studies 4.3.1.1 Effect of H2S04 Concentration The effect of sulfuric acid concentration on the solubility of V2O5 is illustrated in Figure 4.3. The solubility of V2O5 was found to be very low in distilled water at all temperatures, and increasing sulfuric acid concentration in the beginning between 0 - 5M did not affected the solubility of V205 which remained almost constant. Further increases in H2S04 concentration increases the solubility and the effect is more pronounced above 7M. The proton concentration does not increase monotonically from about 1M because of formation of complex vanadium species which in turn consumes H+ ions, and dimerisation has been reported to be significant above 5-6M H2S04 concentration than in lower H2S04 concentration [Madie et al. [1984]]. The increase in solubility at higher H2S04 concentration is probably due to the presence of more H+ ions (increased ratio of H+ ions to V(V) ions) which favours the dissolution reaction in the forward direction [Kazacos et al., 1990; Baes and Mesmer 1976]. V205 (c) + H+ V02+ + H20 (4-1) The solubility might also be increasing because of complex formation between V02+ and sulfate/bisulfate ions making the solution undersaturated with respect to V02+ ions and increasing the solubility at higher sulfuric acid concentrations according to the following reactions [Kazacos et al., 1990; Ivakin, 1966]: vo2+ + hso4- ..... V02S04' + H+ (4-2) vo2+ + so42‘ •'«----- vo2so4 (4-3) vo2+ + vo2 so4 ------W (vo2)2so4 (4-4) The solubility samples were found to change colour from yellow in 3M H2S04 concentration to orange and orange-red for 5, 7 and 9M H2S04 as shown in Figure 4.4. This change in colour is probably due the formation of polyvanadic species of vanadium and sulfate/bisulfate complexes at higher sulfuric acid 72 Chapter 4 Solubility Studies INITIAL SULFURIC ACID CONC (M) Figure 4.3. Solubility data of V2O5 as a function of equilibrium total sulfate/bisulfate at temperatures bet ween 10 °C - 50 °C. Figure 4.4. Variation in colour of saturated V2^,05 solubility samples with increasing sulfuric acid concentration at 50°C. 73 Chapter 4 Solubility Studies concentration. The dark orange colour of OM H2S04 sample bottle is due to suspended V205 particles and not because of increased V(V) concentration. Studies conducted by Rossotti and Rossotti [1956] based on spectrophotometric and potentiometric measurements concluded that a decamer is predominant in the coloured solutions and that the equilibria involved are: [V|0O28f + H+ [HV10O28]5- (4-5) [HV,o028]5- + H+ - [H2V,o028]4' (4-6) [H2Vio028]4- + 14H+ ------10VO2+ + 8H20 (4-7) Connor and Ebsworth [1964] were also of the opinion that the V02+ is the main species in strongly acid solutions. Madie et al. [1984] studied the speciation of vanadium(V) in concentrated solutions of sulfuric acid using Raman, and NMR spectroscopy and by X-ray scattering and cyclic voltammetry. They mentioned that the yellow colour of V(V) solutions in dilute sulfuric acid corresponds to the presence of V02+ ions; but as the acid concentration was increased, they also observed the colour of the solutions gradually turned to orange and red. They associated this change in colour to the dimerisation of V02+ ions in the following manner. 2V02+ -----^ v2o42+ (4-8) 2V02+ + H+ v2o34+ + h2o (4-9) Therefore, further increases in solubility may be due to this dimerisation of V02+ ions. The mass action law constant (KD) values reported for the dimerisation of V02+ ions in 7, 8, 9 and 10M H2S04 were 0.26, 2.3, 19 and 83. The exponential increase in solubility at sulfuric acid concentrations of 8 and 9M could be attributed to the increase in the KD value by a factor of 10 and 73 between 7 and 8M, and 7 and 9M respectively. 74 Chapter 4 Solubility Studies Thus the increase in solubility of V2O5 with an increase in sulfuric acid concentration may be due to several factors such as the increase in H+ ions, formation of vanadium-sulfate/bisulfate complexes and dimerisation/ polymerisation of V02+ ions. 4.3.1.2 Effect of Temperature The solubility of V2O5 was found to decrease with increasing temperature as shown in Figure 4.5 because of the endothermic nature of the precipitation reaction of V02+ ions. The effect of temperature on solubility is more pronounced at sulfuric acid concentrations of 8 and 9M whereas the effect of temperature is minor in the sulfuric acid concentration range of 1 - 7M. < 0.6- 0.4 - TEMPERATURE (Q Figure 4.5. Effect of temperature on the solubility of V2O5 at different sulfuric acid concentration. 75 Chapter 4 Solubility Studies It can be observed that the solubility decreases gradually in the sulfuric acid concentration range of 1 - 9M with increase in temperature. This decrease in solubility of V2O5 in H2S04 with increase in temperature is due to the endothermic nature of reactions 4-1, but is also possible due to the sharply decreasing second dissociation constant of H2S04 with rising temperature [Marshall and Jones, 1966] resulting in a reduction of S042 ions. This reduction in S042 ions probably decreases the formation of V(V)-S042 complexes and in turn decreases the solubility. 4.3.1.3 Solubility Correlations of V205 If reliable solubility data are available, solubility correlations can be developed using the Extended Debye-Huckel equation or modifying it by additional constants. Marshall et al. [1964, 1966] determined the solubility of various forms of CaS04 (including gypsum) in NaCl solutions at various temperatures. They used the following form of relationship to correlate gypsum data: logKsp = logKsp0 + 8AVl / (1 + BaVl) + 2CI + 2DI2 (4-10) Ostroff and Metier [1966] presented gypsum solubility data in the mixture of NaCl + MgCl2 over the temperature range of 28°C - 90°C. They correlated their solubility data using the following regression equation: S = a + b(mn) + c(mn)2 + d(mn)3 + e(mn)4 (4-11) where S = gypsum solubility m = cone, of MgCl2 in the mixture (molal) n = cone, of NaCl in the mixture (molal) a, b, c, d, e = regression constants 76 Chapter 4 Solubility Studies Equation 4-10 or 4-11 can also be used with necessary modifications to develop solubility correlations for the vanadium compounds and the constants can be estimated by a Statistical Analysis System (SAS). The solubility correlation will help in predicting the solubilities of vanadium species for a desired sulfuric acid concentration and temperature. The applicability of solubility correlations depends on the temperature and H2S04 concentration range of the solubility data used to develop these correlations. Several relationships were evaluated to correlate the solubility data of V205 generated in this study. The major difficulty experienced in correlating the solubility data of V205 in sulfuric acid solutions was to find a suitable relationship as a function of temperature and H2S04 concentration, which can provide an almost constant solubility with increases in H2S04 concentrations up to 5M, while with further increases in H2S04 concentrations, it should increase the solubility significantly taking into account the effect of temperature. Normally increasing an independent variable either increases or decreases the dependent variable. The behaviour of the solubility data of V205 in sulfuric acid solutions is peculiar as it is almost constant in the H2S04 concentration range of 1M to 5M and then starts increasing. After testing a number of functional forms, the following equation was found to best correlate the solubility data of V205 when all the data points in the sulfuric acid concentration range of 0 - 9M and in the temperature range of 10°C - 50°C were considered. logs = Cl + C2*Vm rr2 + C3*(m)',3/T3 + C4Vm / (1 + CS'Jm ) + C6m2 + C7m3 (4-12) where S = solubility of vanadium pentoxide (molar) m = total sulfate concentration (molar) T = temperature (°C) C1-C7 = regression constants 77 Chapter 4 Solubility Studies The average absolute deviation obtained was 16% with a maximum deviation of about 77%. As mentioned above, because of the nature of the solubility data of V205 it was difficult to develop a suitable correlation. However, if the solubility data in the sulfuric acid concentration range of 3M to 9M were considered and the data of all the temperatures between 10°C - 50°C were taken, Equation 4-13 predicted the solubility data with an average absolute deviation of 9 % and a maximum deviation of about 31%. The regression constants for both Equations 4-12 and 4-13 are given in Table 4.2. logS = Cl + C2 m/T + C3 m/T2 + C4\m/(1 + C5Vm) + C6m2 + C7 Vm (4-13) where S = solubility of vanadium pentoxide (molar) m = total sulfate concentration (molar) T = temperature (°C) C1-C7 = regression constants Table 4.2. Regression constants for solubility correlations of V205 in h2so4. Regression Solubilitv Correlations Constants Initial H2S04 Cone Range 0-9M 3-9M (Eq. 4-12) (Eq. 4-13) Cl -2.319 -20.442 C2 65.05 2.995 C3 -656.9381 -18.698 C4 2.6765 58.966 C5 0.7823 1.294 C6 -0.0593 0.0627 Cl 0.00614 -7.21 No. of Data Points 40 30 Mean Dev(%) 16.11 8.96 Max. Dev(%) 77.6 30.7 Corr. Coeff.(R2) 0.76 0.91 78 Chapter 4 Solubility Studies 4.3.2 Solubility of VOSO4 This section presents the results of the solubility study of vanadyl sulfate (VOSO4) over a wider range of H2S04 concentration, from 0 to 9 M and at temperatures from 10°C to 50°C. The solubility experiments were conducted according to the experimental procedure described in Section 4.2. The saturation concentration of V0S04 in the samples was determined at 10, 20, 30, 40, and 50°C in sulfuric acid concentrations ranging from 0 to 9M. The saturation concentrations of total vanadium and total sulfur (S042 + HS04) as obtained from ICP are tabulated in Table 4.3. The solid V0S04 collected at the end of the experiment was analysed by XRD and the spectrum compared very well with that of pure V0S04 as shown in Figures 4.6 and 4.7 respectively. In order to calculate the solubility product of VOS04, the equilibrium concentrations of V02+ and S042 need to be determined. Unfortunately, neither ICP nor ion chromatography (IC) is able to distinguish between the S042 and HS04 in the solution. Furthermore, the chemistry of vanadium is complex, with a large number of different species existing at different potentials and pH’s. Ivakin and Voronova [1973] suggested the following reactions: V0S04.xH20 vo2+ + S042' + *H,0 (4-14) ------hso4 H+ + so42' (4-15) vo2+ + so42' voso4° (4-16) vo2+ + SO42- 5=5= V0(S04)22- (4-17) vo2+ + hso4' —- vohso4+ (4-18) 79 Chapter 4 Solubility Studies Table 4.3. Solubility of vanadyl sulfate (VOSO4) in various sulfuric acid concentrations at temperatures from 10°C to 50°C. At Equilibrium Initial. H2S04 Temp Total Sulfur* VOSO4* Ksip Cone (°C) Cone Cone (mol/1) (mol/1) (mol/1) (molar) 0.0 10.0 3.167 3.037 9.618 1.0 10.0 3.659 2.432 8.899 3.0 10.0 4.692 1.448 6.794 5.0 10.0 5.987 0.784 4.694 6.0 10.0 6.895 0.493 3.399 7.0 10.0 7.390 0.384 2.838 8.0 10.0 8.219 0.243 1.997 9.0 10.0 8.802 0.185 1.628 0.0 20.0 3.449 3.280 11.313 3.0 20.0 4.717 1.786 8.425 5.0 20.0 6.129 0.995 6.098 6.0 20.0 6.925 0.711 4.924 7.0 20.0 7.434 0.570 4.237 8.0 20.0 8.328 0.363 3.023 9.0 20.0 8.936 0.260 2.323 0.0 30.0 3.720 3.640 13.541 3.0 30.0 4.939 2.149 10.614 5.0 30.0 6.374 1.262 8.044 6.0 30.0 6.868 0.997 6.847 7.0 30.0 7.724 0.718 5.546 8.0 30.0 8.404 0.514 4.320 9.0 30.0 9.291 0.386 3.586 0.0 40.0 4.105 3.994 16.395 3.0 40.0 5.353 2.460 13.168 5.0 40.0 6.454 1.585 10.230 6.0 40.0 7.178 1.216 8.728 7.0 40.0 7.851 0.875 6.869 8.0 40.0 8.510 0.676 5.753 9.0 40.0 9.347 0.492 4.599 0.0 50.0 4.458 4.349 19.388 3.0 50.0 5.598 2.822 15.798 5.0 50.0 6.510 1.904 12.395 6.0 50.0 7.271 1.474 10.718 7.0 50.0 7.938 1.023 8.121 8.0 50.0 8.665 0.778 6.741 9.0 50.0 9.407 0.586 5.513 * Saturation concentration at equilibrium 80 CD CO experiment. o vJD solubility from CD LO CD rsi collected QJ cn solids c < 4 V 0 S 0 CD m of CD spectra Osl XRD 4.6. CD Figure puoDas J3J sjuno} 81 o CO o experiment. r- o solubility vO the in o LT1 CD used CsJ CD solids cn 4 CD r < V 0 S 0 CD pure m of CXI XRD 4.7. o Figure puoD95 jaj s4uno3 82 Chapter 4 Solubility Studies They calculated the stability constants of reactions 4-16, 4-17 and 4-18 as 55 ± 3, 320 ± 10 and 1.7 ± 0.3 respectively. Based on their experimental results they concluded that vanadium (IV) complexes do exist but are relatively unstable. Strehlow and Wendt [1963] reported the association constant of ion pair V0S04° in distilled water as 300. There exist discrepancies and uncertainties in the reported equilibrium constants of vanadium (IV) ions and sulfate ions, and because of the lack of availability of reliable data it is not possible to accurately calculate the distribution of the various species and thus the solubility product (Ksp) of VOSO4. An attempt was made to calculate the solubility product (Ksp) of vanadyl sulfate by considering reactions 4-14 and 4-15 according to the procedure outlined by Marshall and Jones [1966] for the determination of Ksp for gypsum in sulfuric acid solutions. They ignored the contribution of the gypsum concentration on the density of the solution and assumed the density of sulfuric acid equivalent to the density of the solution of gypsum and sulfuric acid. The set of mass action equations was then solved iteratively using Newton-Raphson technique to determine Ksp, the second dissociation constant of H2S04 (K2) and the ionic strength of the system (I). In the present system however, the solubility of VOSO4 is fairly high, so its contribution to the density cannot be ignored and hence a Ksp calculation could not be performed. In view of above mentioned difficulties for calculating Ksp, the term Ksp was replaced in this study by a new parameter, ‘saturation ionic product (KSip)’ defined as: (KSIP) = [V02+]*([ SO/ ] + [ HSO4- ]) (4-19) The KSip data are included in Table 4.3 along with the solubility data. Although it has no theoretical significance, it is believed that the saturation ionic product (KSip) will be of more practical utility. Thus, to determine the degree of 83 Chapter 4 Solubility Studies supersaturation or scaling potential of a given vanadium solution, the ionic product (KIP) of total vanadium and total sulfur of the solution (obtained from ICP), can be compared with the saturation ionic product (KSip). 4.3.2.1 Effect of H2S04 Concentration The solubility of VOS04 as a function of total sulfur (S042 + HS04 ) at equilibrium is presented in graphical form in Figure 4.8 and the variation in solubility with initial sulfuric acid concentration is shown in Figure 4.9. To discuss the experimental results, assumptions are made that (i) the first dissociation constant of H2S04 was infinite, which means there are no neutral H2S04 species, (ii) the vanadium(IV) and sulfate/bisulfate ion complexes are unstable resulting in unassociated vanadium (IV) ions. It can be observed from Figure 4.8 that the solubility of V0S04 decreases continuously with increasing H2S04 concentration and decreasing temperature. The effect of H2S04 concentration on V0S04 solubility is more pronounced at lower concentrations. The decrease in solubility is more sharp in the H2S04 concentration range of 0 - 7M and at 8M and 9M H2S04 concentration the rate of decrease in solubility is minor. The higher rate of decrease in solubility at lower sulfuric acid concentration may be due to a higher dissociation of bisulfate ions to sulfate ions which shifts the equilibrium towards the left in Equation 4-14, resulting in a faster drop in solubility. As the sulfuric acid becomes more concentrated, the dissociation of bisulfate ions becomes less [Cameron and Breazeale, 1903; Marshall and Jones, 1966] thus reducing the rate of decrease in VOS04 solubility. The experimental results of the present study confirm the findings of Ivakin and Voronova [1973] that vanadium (IV) ions and sulfate complexes are unstable, otherwise the solubility of V0S04 would have increased to a certain extent with increasing H2S04 concentration. 84 Chapter Figure V0S04SOLUBI 4 4.8. Variation in TOTAL solubility SULFUR at equilibrium. of AT VOSO4 EQUILIBRIUM 85 with (mol/l) concentration Solubility of total Studies sulfur Chapter 4 Solubility Studies ♦ IOC ■ 20C A 30C X 40C o 50C INITIAL H2S04 CONCENTRATION (M) Figure 4.9. Variation in solubility of VOSO4 with initial concentration of sulfuric acid at different temperatures. The variation in saturation ionic product (KSip) with total sulfur at equilibrium is shown in Figure 4.10. It can be observed that as total sulfur concentration increases KSIP drops almost linearly. This behaviour indicates a rapid increase in precipitation potential with increasing vanadium as well as sulfuric acid concentration. 4.3.2.2 Effect of Temperature The effect of temperature on the solubility of VOSO4 is shown in Figure 4.11. The solubility increases with an increase in temperature and the effect is more significant at lower H2S04 concentration. This could be due to the sharply decreasing second dissociation constant (K2) of H2S04 with rising temperature [Marshall and Jones, 1966] resulting in a reduction of S04 ' ions, allowing the solubility of VOSO4 to increase. 86 Chapter SATURATION IONIC PRODUCT ( Figure 4 4.10. Saturation sulfur TOTAL ionic concentration SULFUR product(K AT 87 EQUILIBRIUM S at ip ) equilibrium. of VOS0 (mol/I) 4 as a function Solubility of Studies total Chapter 4 Solubility Studies TEMPERATURE (°C) Figure 4.11. Effect of temperature on solubility of VOSO4 in various sulfuric acid concentrations. 4.3.2.3 Solubility Correlations of VOSO4 Solubility correlations were thus developed using solubility data generated in this study. Several relationships were investigated to best fit the data. The functional form similar to one suggested by Marshall and Slusher [1964] was finally selected to correlate the data. After screening different modified relationships, the following equation was found to provide a better representation of the data. logS = Cl + C2/T + C3*T + C4-Vms/(1 + C5Vms ) + C6msl/3 + C7*T/ms (4-20) where S = solubility of vanadyl sulfate (molar) ms = total sulfur concentration (S042 and HS04) in molar T = temperature (°C) Cl - C7 = regression constants 88 Chapter 4 Solubility Studies The constants Cl - C7 estimated after carrying out regression analysis using SAS are listed in Table 4.4 which covers all the 36 data points generated in this study. The average deviation obtained was about 4.5% and the maximum deviation was 12.0%. This maximum deviation was observed at the data point corresponding to 9M H2S04 concentration and at 10°C. At other temperatures also relatively high deviations were observed at 9M H2S04 concentration. Another improved correlation was therefore developed using the same equation (Equation 4-20) but considering the sulfuric acid concentration range of 3M - 7M which is of more practical utility and the regression constants Cl - C7 are given in Table 4.4. The average deviation was found to be about 3.0% with a maximum deviation of only 6.7%. Table 4.4. Regression constants of solubility correlations and ionic product correlations for V0S04. Regression Solubilitv Correlations Satd. Ionic Product Correlations Constants Initial H2S04 Cone Range Initial H2S04 Cone Range 0-9M 3-7M 0-9M 3-7M Cl -0.45 -4.33 0.454 -5.55 C2 0.017 0.017 0.017 0.017 C3 -1.2 -1.0 -1.2 -1.0 C4 11.63 19.76 8.265 21.58 C5 1.33 0.84 0.5 0.83 C6 -3.5 -6.39 -4.89 -6.169 C7 -0.04 -0.04 -0.04 -0.0406 No. of Data Points 36 20 36 20 Mean Dev(%) 4.5 3.0 4.0 3.1 Max. Dev(%) 12.1 6.7 12.6 7.1 Corr. Coeff.(R2) 0.999 0.999 0.996 0.998 89 Chapter 4 Solubility Studies 4.3.2.4 Saturated Ionic Product Correlations Regression analyses were also performed on the saturation ionic product (KSIP) as defined earlier in Equation 4-19. The functional form which was used for modelling of solubility data was found suitable for correlating saturation ionic product(Ksip) data also and is represented as a function of total sulfur concentration and temperature in the following manner. log Ksip = Cl + C2/T + C3*T + C4Vms/(l + C5Vms) + C6msl,3+C7*T/ms (4-21) where KSIP = saturation ionic product (molar) ms = total sulfur concentration (S042 and HS04) in molar T = temperature (°C) C1-C7 = regression constants The regression constants Cl - C7 for saturation ionic product (KSiP) correlation are also given in Table 4.4 and the average absolute deviation and maximum deviation was found to be 4.0% and 12.6% respectively. When regression was performed using KSiP data in 3M to 7M H2S04 concentration the average absolute deviation dropped again to 3.0% with a maximum deviation of 7.1%. The correlation coefficient in all four cases was excellent at about 0.99. To predict the scaling tendencies or precipitation potential of a supersaturated vanadium(IV) solution to be used in the battery, a scaling index has been defined as follows: Vanadium Scaling Index (VSI) = KIP /KSiP (4-22) VSI = 1 solution is saturated VSI < 1 solution is undersaturated VSI > 1 solution is supersaturated (scaling potential exist) 90 Chapter 4 Solubility Studies where KIP = product of total vanadium (V02+) and total sulfur (S042 and HS04) concentration of a given solution at a particular initial H2S04 concentration and temperature (obtained from the analysis of the solution by ICP). Ksip= product of total saturation vanadium V02+ and total sulfur (S042 and HS04 ) concentration at equilibrium at the same initial H2S04 concentration and temperature (from Equation. 4-21). If temperature and composition in terms of the total vanadium and total sulfur of a supersaturated vanadium(IV) solution can be analysed by ICP then at any desired temperature (between 10°C - 50°C) the scaling tendencies can be predicted using Equations 4-21 and 4-22. If the value of VSI is one or less than one, scale will not form. If VSI is greater than one, in that case the solution has the potential to form scale, but the start of precipitation will depend on the induction period of that solution and how fast it will precipitate depends on the kinetics. The scaling potential can thus be predicted from VSI by using KSIP correlation. 4.3.3 Solubility of V203 The solubility of V203 was determined according to the experimental procedure used for V205, as mentioned above in Section 4.2. The solubility experiments of V203 were carried out in sulfuric acid concentrations of 0 - 9M, at temperatures ranging from 20°C - 50°C. The saturation concentrations were measured after 45 days by shaking the solutions at various temperatures on a daily basis. The solubility experiments in 8M and 9M sulfuric acid concentration developed a thick precipitate after about two weeks and had to be terminated. The solubility data of V203 for sulfuric acid concentrations between 0 - 7M at 20, 30, 40 and 50°C are listed in Table 4.5. It is seen that the solubility of V203 is fairly high about 1.2M (or 2.4M as V) at 20°C in 5M H2S04 as compared to 0.22M V205 (or 0.44M as V) under identical conditions. 91 Chapter 4 Solubility Studies Table 4.5. Saturation concentration of vanadium trioxide (V2O3) in various sulfuric acid concentrations at temperatures from 20°C to 50°C. At Equilibrium Initial. H2S04 Temp Total Sulfur* V203* Cone Cone Cone (mol/1) (°C) (mol/1) (mol/1) 0.0 20.0 0.0004 0.0005 3.0 20.0 2.9787 0.9889 5.0 20.0 4.8947 1.2226 6.0 20.0 5.4144 0.6800 7.0 20.0 5.8411 0.4600 0.0 30.0 0.0004 0.0011 3.0 30.0 3.0349 1.1127 5.0 30.0 5.0527 1.5430 6.0 30.0 5.5597 0.7300 7.0 30.0 6.0090 0.5012 0.0 40.0 0.0003 0.0034 3.0 40.0 3.1346 1.3100 5.0 40.0 5.0420 1.7750 6.0 40.0 5.6074 0.8000 7.0 40.0 6.3064 0.5400 0.0 50.0 - - 3.0 50.0 2.9657 1.4400 5.0 50.0 5.1389 1.9671 6.0 50.0 5.6565 0.8600 7.0 50.0 6.5007 0.6002 * Saturation concentration at equilibrium 92 Chapter 4 Solubility Studies The solubility of V2O3 was found to be as high as 4M total vanadium just by dissolution in 5M H2S04 at 50°C. To confirm the high saturation concentration of vanadium observed, the solubility experiment of V203 (Aldrich Chemical) in 5M H2S04 at 20°C was repeated, and the saturation concentration of V203 was again found to be 1.154M (2.308M as V) when determined after 45 days. All the samples were collected using Millipore filter of size 0.45 micron. 4.3.3.1 Effect of H2S04 Concentration The solubility of V203 increases with an increase in sulfuric acid concentration between 0 and 5M but with a further increase in sulfuric acid concentration to 7M, the saturation concentration of V203 started to decrease sharply as shown in Figure 4.12. At the start of the experiment, it was observed that the colour of the solution was slightly blue typical of V(IV) species but it turned seagreen after a few days in the case of experiments containing 0 - 5M H2S04. This blue coloration was probably due to the presence of some percentage of V204 or V0S04 in the V203 powder used for the solubility experiment. When the sulfuric acid concentration was increased from 6M to 7M the solid phase was transformed from V203 to a mixture of V203, V2(S04)3, V204 and probably V0S04 which was obvious from the blue coloured solids at the bottom of the sample bottle. The colour of the solution was also observed to be a mixture of seagreen [typical of V(III)] and blue[typical of V(IV)] at the end of the experiment. When potentiometric titration was carried out to determine the amount of V(IV) present in the solubility sample, it was found that, of the total vanadium in the filtered solution from the 3M sulfuric acid sample bottle about 15 - 20% was in the form of V(IV) species. The decrease in saturation concentration of vanadium at higher H2S04 concentrations can be attributed to the transformation of the dark blackish blue V203 solids to the solids of V(III) and V(IV) sulfates leading to the decrease in the solubility as a result of the common ion effect. 93 Chapter 4 Solubility Studies —X— 50 C 1.50 - O 1.00 - < 0.50 -- INITIAL H2S04 CONC (M) Figure 4.12. Saturation concentration of vanadium trioxide as V2O3 (measured after 45 days) versus initial sulfuric acid concentration at different temperatures. Thus it can be concluded that it is not possible to determine the solubility of V203 in sulfuric acid as the solids cannot exist in the form of V203 in equilibrium with the sulfuric acid solution and transforms to V(III) and V(IV) sulfates. The above mentioned difficulties are probably the reason that solubility data of V203 is not available in the literature. The total vanadium concentrations from now on therefore will be referred to as saturation concentration of vanadium obtained from V203 dissolution and not as solubility of V203. However, these experiments revealed that total vanadium concentrations of about 2 M could be achieved by simple dissolution of reagent grade V203 in 5M sulfuric acid solution at 20°C after shaking for 45 days. Another set of experiments were conducted to find out if similar vanadium concentrations could be achieved using industrial grade V203 in 5M H2S04. 94 Chapter 4 Solubility Studies The V2O3 powder was added in enough quantity to the sulfuric acid solutions so that excess solids were present in the container at the time of sampling. The liquid samples were collected using 0.45 micron Millipore filters and the V203 concentrations achieved with different experimental conditions are tabulated in Table 4.6 along with their corresponding total sulfur (S042' and HS04) concentrations obtained by ICP. The saturation concentration of total vanadium when industrial grade V203 was used at 20°C [V3-20-I] was found to be 0.748M (or 0.374M as V203) after 45 days as compared to 2.308M (or 1.154M as V203) with Aldrich Chemicals V203. The total vanadium concentration of experiment V3-20-IS3 with stirring for three hours was found to be 0.492M (0.246M as V203) indicating that it did not reach saturation concentration after three hours of stirring. Table 4.6. Vanadium trioxide (V203) concentration in 5M H2S04 measured under different experimental conditions. Description of Experiment Total Sulfur v2o3 Cone Cone (mol/1) (mol/1) [V3-20-A] V203 (Aldrich) + 5M H2S04, hand shaking for 45 days at 20°C 4.853 1.154 [V3-20-I] V203 (Ind. grade) + 5M H2S04, hand shaking for 45 days at 20°C 4.525 0.374 [V3-20-IS3] V203 (Ind. grade) + 5M H2S04, stirring for 3 hours at 20°C 4.290 0.246 [V3-20-IB1] V203 (Ind. grade) + 5M H2S04, boiled for 1 hour, then cooled down to 20°C 4.579 0.615 [V3-20-IB3] V203 (Ind. grade) + 5M H2S04, boiled for 3 hours, then cooled down to 20°C 4.690 0.636 95 Chapter 4 Solubility Studies It was observed earlier that the solubility of V2O3 increases with increasing temperature therefore, to enhance the dissolution of industrial grade V203, the samples were boiled for one hour [V3-20-IB1] and three hours [V3-20-IB3] and the liquid samples were collected after cooling down to 20°C. The total vanadium concentrations after one hour boiling and three hours boiling were found to be 1.23 M (or 0.615M as V2O3) and 1.27M (or 0.636M as V2O3) respectively. Therefore, the saturation concentration of total vanadium in 5M H2S04 that can be obtained from industrial grade V2O3 was found to be 1.3M, about 56% of the total vanadium concentration of 2.3M with reagent grade (Aldrich Chemicals) V203 at 20°C. The lower solubility of industrial grade V203 is probably due to its crystalline nature and higher density compared to the lighter agglomerates of reagent grade V203. The higher level of impurities in the industrial grade V2O3 could be another factor for lower vanadium concentrations. 4.3.3.2 Effect of Temperature on Saturation Concentration The effect of temperature on the dissolution of V203 in different sulfuric acid concentrations is illustrated in Figure 4.13. The saturation V203 concentration linearly increases with increasing temperature. It can also be observed that the effect of temperature is more pronounced when H2S04 concentration is in the range of 3 - 5M and the effect is less significant at other H2S04 concentrations. 4.3.3.3 Solubility Correlations of V203 The solubility correlations for V2O3 in H2S04 were not developed because of the uncertainty of the solid phases existing at equilibrium. The potentiometric titrations did confirm the presence of V(IV) species in the solution. Bright blue colour solids of V0S04 were also observed in the solution after a few days probably due to the transformation of some portion of the blackish dark blue coloured V2O3 solids to bright blue coloured V0S04 solids. 96 Chapter 4 Solubility Studies Distilled water 3M H2S04 O 1.6 -- 5M H2S04 6M H2S04 U 1.2 - 7M H2S04 O 0.8 -- H 0.4 - TEMPERATURE (C) Figure 4.13. Effect of temperature on saturation concentration of vanadium (as V203) obtained by the dissolution of V203 in various H2S04 concentrations. 4.3.4 Theoretical Equilibrium Calculations for System: v2o5 - h2so4 - h2o Equilibrium calculations were performed for the system V205-H2S04-H20 to evaluate the effect of varying H2S04 concentration on the equilibrium composition of different vanadium(V) species. The equilibrium constant method [Ting and Nancollas, 1972] was used to estimate the equilibrium concentrations of solute components in a V(V) solution. It was assumed that (i) the first dissociation constant of H2S04 was infinite and (ii) because of the non availability of free energy of formation or Cp data for the V(V)-sulfate/bisulfate complexes, it was assumed that these complexes are not present in the system. A simplified system was thus considered with the following set of reactions. 97 Chapter 4 Solubility Studies Reactions Equilibrium constant h2o H+ + OH' K1=0.100E-13 (4-23) V205(c) + H+ vo2+ + h2o K2=0.03419+00 (4-24) HSCV ------H+ + soY K3=0.105E-01 (4-25) These reaction will show the effect of increasing H+, HS04' and S042' ions as a result of increasing H2S04 concentration on the equilibrium composition of vanadium species. The free energy of formation data of all the species present in the above system are listed in Table 4.7 and the equilibrium constants for the three reactions calculated using the data in Table 4.7 are included in the reactions (Equation 4-23 to 4-25). The activity coefficients of various species were calculated using the Bromley method [Horvath, 1985] and a sample calculation is presented in Appendix B. The mass action equations for the system under study are Kl = [H+] [OH ] (Gl) (4-26) K2 = ( [V02+] / [H+] ) (G2) (4-27) K3 = ( [H+] [S042 ] / HS04') (G3) (4-28) where Kl, K2 and K3 are equilibrium constants for reactions 4-23, 4-24 and 4- 25, respectively and Gl(y H+*y oh )5 G2 and G3 are lumped factors of activity coefficients for each reaction. 98 Chapter 4 Solubility Studies Table 4.7. Free energy of formation for the species considered in the above system at 25 °C. Species Name Free Energy of Formation AGf (Kcalmol1) H+ 00.0 OH' -37.6 h2o(1) -56.7 v205(c) -339.3 vo2+ -280.6 hso4 -190.2 so4 -187.5 Source: Bamer and Scheurman [1977]. The mass balance equations are VT= [V02+] + [V2Os(c)] (4-29) sx= [S042] +[HS04] (4-30) and the charge balance equation can be written as [V02+] + [H+] - [OH ] -2 [S042-] - [HSO4-] = 0 (4-31) where VT and ST are total vanadium and total sulfur concentration. The Equations 4-26 to 4-31 forms a set of non-linear algebraic equations that were solved by developing a FORTRAN program included in Appendix C. The equilibrium calculations were performed by assuming 2 molal supersaturated V(V) solution in different H2S04 concentrations reaching equilibrium. The equilibrium composition obtained by solving the above mentioned set of equations are tabulated in Table 4.8. 99 Chapter 4 Solubility Studies Table 4.8. Equilibrium composition of various species for 2m total V(V) solution in different H2S04 concentrations at 25 °C. Species Name Equilibrium Composition (m) @ 5m H2S04 @ 6m H2S04 @ 7m H2S04 Vanadium as V205(c) (1.68) (1.62) (1.55) vo2+ 0.32 0.38 0.45 hso4 4.95 5.96 6.97 so42' 0.05 0.04 0.03 H+ 4.73 5.66 6.59 Note: V(V) / S042’ complexation not included () Positive value of V205(c) concentration indicates precipitation. It is obvious from the equilibrium concentrations given in Table 4.8 that increasing the H2S04 concentration increases the concentration of V02+ ions confirming the earlier observations during solubility experiments of V205 in sulfuric acid solutions. The calculated equilibrium V02+ ions concentration is slightly higher than that of the experimental values obtained earlier in Section 4.3.1. This discrepancy is probably because of the approximate equilibrium constant values and activity coefficients calculated from the Bromley correlation. 100 Chapter 4 Solubility Studies 4.4 SUMMARY OF RESULTS The results of the solubility studies of V2O5, V203 and VOSO4 in various sulfuric acid concentrations and different temperatures as well as the equilibrium calculations for the system V205 - H2S04 - H20 are summarised below. 1. The solubility of V205 was determined in sulfuric acid concentrations between 0 - 9M and at temperatures ranging from 10°C - 50°C. It was found that the initial and final sulfate/bisulfate concentration in the liquid samples remain constant and no sulfur combines with vanadium to form any precipitate of vanadium and sulfur. Also the XRD of the starting material, pure V205 and a sample of V205 collected at the end of the solubility experiment showed very similar spectra indicating that the solid phase in equilibrium with liquid was V205. 2. It was found that increasing the sulfuric acid concentration increases the solubility of V205 gradually at first up to 5 - 6M H2S04 concentration followed by an exponential increase in solubility with a further increase in H2S04 concentration beyond 7M. Thus the increase in V205 solubility with increasing sulfuric acid concentration may be due to several factors such as the increase in H+ ions, formation of vanadium and sulfate/bisulfate complexes and dimerisation/polymerisation of V02+ ions. 3. The solubility of V205 was found to decrease with increasing temperature because of the endothermic nature of the precipitation of V02+ ions to V205, and the effect is more pronounced at higher sulfuric acid concentrations probably due to the sharply decreasing second dissociation constant of H2S04 with rising temperature resulting in a reduction of S04 ' ions. This will lead to a decrease in formation of 101 Chapter 4 Solubility Studies V02+ and S042 complexes with a subsequent decrease in solubility of V205. 4. A solubility correlation was developed to predict the solubility of V2O5 in sulfuric acid concentrations ranging from 3M to 9M covering the temperature range of 10 - 50°C. The overall average absolute deviation was about 9 % with a maximum deviation of 31% and a correlation coefficient of about 0.91. 5. The solubility data for vanadyl sulfate was generated in sulfuric acid concentrations ranging from 0 to 9 M and over the temperature range 10°C to 50°C. The effect of both sulfuric acid concentration and temperature on the solubility of vanadyl sulfate is significant. Increasing sulfuric acid concentration decreases solubility sharply at lower sulfuric acid concentrations but decreases only slightly as the sulfuric acid concentration is further increased above 6M. In a similar manner, the increase in solubility with increasing temperature is more pronounced at lower H2S04 concentrations. The variation in solubility is due to the common ion effect and is strongly linked with the second dissociation constant of H2S04 at different temperatures and sulfuric acid concentrations. The XRD analysis of the pure V0S04 and solids collected from the solubility experiment were found to be identical indicating that no phase change had occurred during the course of the experiment. 6. The solubility data and saturation ionic product (KSip) data of vanadyl sulfate was correlated using the Extended Debye-Huckel functional form. For both correlations, when all the 36 data points covering the sulfuric acid concentration range of 0-9M and a temperature range of 10°C to 50°C were considered, the average absolute deviation was 102 Chapter 4 Solubility Studies found to be less than 4.5% whereas if selected solubility data points were taken in the more useful sulfuric concentration range of 3M-7M, the average absolute deviation was estimated to be about 3%. A vanadium scaling index (VSI) has been defined to predict scaling tendencies of supersaturated V(IV) solutions using a saturation ionic product (KSip) correlation. 7. An attempt was made to determine the solubility of V2O3 in sulfuric acid solutions. It was also observed that the dark blackish blue coloured solids of V2O3 transformed to the bright blue colour of VOSO4 after 2-3 weeks during the solubility experiment resulting in a phase change. Hence the saturation concentrations of vanadium may not represent the solubility of V2O3 and therefore, this should be referred to as saturation concentration of vanadium obtained from V2O3 and not as the solubility of V2O3 in sulfuric acid. 8. The saturation concentration of V2O3 was determined in sulfuric acid concentrations ranging from OM to 7M over the temperature range of 20 - 50°C. It was observed that the saturation concentration increases initially with increasing H2S04 concentrations up to 5M and further increases in H2S04 concentrations decreases saturation concentration. The saturation concentration of vanadium was found to increase with an increase in temperature and the effect was more pronounced in the H2S04 concentration range of 3 - 5M. 9. Using the high purity reagent grade V203, a fairly high saturation concentration of about 2M total vanadium(III) was achieved in 5M H2S04 as compared with the very low value of about 0.22M of vanadium(v) (from V2O5) in 5M H2S04 concentration at 20°C. The saturation concentration of total vanadium obtained with industrial 103 Chapter 4 Solubility Studies grade V2O3, however, was found to be about 0.748M in 5M H2S04 at 20°C with hand shaking on a daily basis for 45 days. The total vanadium concentration obtained from industrial grade V203 in 5M H2S04 concentration at 20°C when stirring was done for three hours was found to be 0.49M and if boiled for one hour and three hours, the total vanadium concentrations achieved were 1.2M and 1.3M respectively. 10. The equilibrium calculations for the system V205 - H2S04 - H20 revealed that increasing H2S04 concentration increases the V02+ concentration, confirming the observations made in solubility experiment of V205 in H2S04 solutions. 104 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions CHAPTER 5 STABILITY OF SUPERSATURATED YANADIUM(V) SOLUTIONS 5.1 INTRODUCTION Depending on the concentration of the solute, a solution may be unsaturated, saturated or supersaturated. Supersaturation in solutions was first achieved by Lovitz [1795] as reported in Khamskii [1969] in an investigation of the crystallisation of salts and of the nature of supersaturation. Since then, the properties of supersaturated solutions have been and are still being investigated. Supersaturated Vanadium(V) electrolyte is employed in the positive half-cell of the vanadium redox battery. To increase the energy density of the battery, the electrolyte has to be more and more concentrated or supersaturated, but at the same time it has to be stable so as to provide reliable performance of the battery. Research work is therefore undertaken to evaluate the stability of V(V) solutions at different supersaturation levels by studying the various factors that affect the precipitation of V(V) species such as temperature, supporting electrolyte concentration, state-of-charge, stirring and so on. 5.2 EXPERIMENTAL 5.2.1 Preparation of Supersaturated V(V) Solutions Meyer and Aulich [1930] reported that the solubility of V205 in H2S04 increases with increasing H2S04 concentration and reaches a maximum value of about 1.5M in 16M H2S04. Marakov and Repa [1938] presented solubility data along with the information about type of solid phase of V205 in equilibrium with H2S04. They reported that the solubility of V205 in H2S04 gradually increases reaching a maximum of 0.98M at a sulfuric acid concentration of 7.7M and again decreases. 105 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Based on the published solubility data, the maximum V(V) concentration in the H2S04 concentration range 5M to 7M should be around 0.2M to 0.5M. The solubility data of V205 in 5M to 7M H2S04 generated in this study also indicates that the solubility of V205 is in the range of 0.2 to 0.3 M at 20°C. Using the electrolytic dissolution method (electrolytic oxidation of V(III) or V(IV) compounds) however, V(V) solutions of concentrations as high as 5.5M were achieved [Skyllas-Kazacos, Menictas and Kazacos [1996]]. Electrolytic oxidation of V2Ü3 powder or electrolytic reduction and reoxidation of V205 can be carried out to prepare supersaturated V(V) solution. 5.2.1.1 Preparation of Vanadium(V) Solution by Electrolytic Oxidation of Vanadium(IV) Solution To prepare V(V) solution from V(IV) solution by electrolytic oxidation, a two- compartment electrolytic cell separated by an anion selective AMV membrane and lead electrodes was used as shown in Figure 5.1 with design details given in Figure 5.2. The V(IV) solution was introduced in the positive half-cell and the same concentration of sulfuric acid was placed in the negative half-cell. A current of 3 - 4 amperes was applied so as to maintain a current density of 20 mA/cm2. Nitrogen was bubbled through the mixture of V(IV) solution in sulfuric acid to keep the solution well mixed and uniformly distributed over the whole lead electrode. The electrolysis was stopped when the theoretical time was completed and also it was visually observed that supersaturated V(V) solution had turned dark yellowish orange in colour. A small sample was tested by carrying out potentiometric titration to check the oxidation state of the prepared V(V) solution. 106 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Nitrogen Positive Electrode H2S04 Solution PL SO. + V (IV ) Solution Membrane Figure 5.1. Schematic diagram of electrolytic cell for the preparation of vanadium(V) solution. 107 d • o>H ~d LT) > ¥ G • *“H T3G G > Ui o OG G c3 0)ex, cxUi 3u JUO S a> -c•*—> u o G 'S 'O c W) •55oj Q 5.2. Figure 108 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions In the beginning, the electrolytic oxidation was continued for an extended period of time to ensure almost 100% V(V) species in the supersaturated V(V) solution. But these solutions were found to be highly unstable at high temperature as well as less stable at room temperature. Therefore, it was decided to terminate the electrolysis when the solution had about 97 - 98% V(V) species. The supersaturated V(V) solution with 2-3 % of V(IV) species was found to be relatively stable at room temperature as pointed out earlier by Kazacos et al [1990]. The V(V) solutions were analysed using ICP to determine the total vanadium and total sulfate in the solution. Usually slight vanadium and sulfur transfer occurs during the electrolysis and the final concentrations of vanadium and sulfur are different from those of the starting V(IV) solution, depending on the concentrations and membrane quality. Based on the ICP results the final vanadium and sulfur concentrations of the V(V) solutions were adjusted as described in the case of the V(IV) solutions in Appendix D. It is recommended to prepare V(V) solution having slightly higher V(V) concentration and lower sulfates than the desired value. This will facilitate the adjustment of concentrations of both total vanadium and total sulfur by solving concentration balance equations. 5.2.1.2 Preparation of Supersaturated V(IV) Solutions To prepare supersaturated vanadium(IV) solution, the two compounds (V203 and V2O5 powders) were mixed in sulfuric acid of the desired concentration in a conical flask at room temperature. Equimolar amounts of V2O3 and V2O5 are required to form V(IV) species according to the following reaction. V2O3 + V2Os + 4H2S04 =f== 4V02++ 4S042'+ 4H20 (5-1) While stirring at a very low speed, the temperature of the mixture was gradually increased till the solution started boiling (at about 115°C). In approximately 15 minutes concentrated V(IV) solution was prepared. Care must be taken while 109 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions preparing V(IV) solution by this method as overflowing occurs by the vigorous exothermic reaction when the solution approaches boiling point. The water produced during this process is simultaneously evaporated as boiling was continued for approximately one hour to ensure full dissolution of all the solid particles and increase the stability of the resultant V(IV) solution. The final vanadium and sulfur concentration was analysed by ICP and by considering concentration balance of vanadium and sulfur, the concentration of both vanadium and sulfur was adjusted to a required value as described in Appendix D. A peculiar observation was made when the V2O3 powder and V205 powder were added in stoichiometric quantity. Instead of obtaining blue V(IV) solution, the solution was green and about 15-20% extra V203 was required to prepare the blue V(IV) solution. When only V203 powder (industrial grade) was dissolved in sulfuric acid, in the beginning the solution appeared to be blue in colour and after some time turned slightly seagreen typical of the V(III) solution. Potentiometrie titration of the solution indicated that it comprised 18% V(IV) species and 82% V(III) species. Similar phenomena of blue coloration in the beginning, turning to the seagreen colour later was also observed during the solubility experiments of V203. The minor amount of V204 or VOSO4 present in the V203 powder will probably dissolve initially giving rise to V(IV) species so that a corresponding amount of V205 powder will remain unreacted in the solution. After adding extra V203 the remaining V205 reacted completely and a blue solution of about 98% V(IV) was obtained. The blue supersaturated V(IV) solution thus prepared was filtered through two sheets of Whatmann filter paper of size 2 microns to remove any unreacted particles and thus avoid crystallisation of the supersaturated V(IV) solution within a short period of time. 110 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5.2.1.2.1 Factors Affecting Stability of Supersaturated V(IV) Solution When V(IV) solutions were prepared in higher sulfuric acid concentrations, precipitation of V(IV) solutions occurred rapidly. Sometimes it was observed that when a freshly prepared V(IV) solution was stored in a beaker for a few hours and then a portion transferred to other test tube, the solution in the beaker precipitated earlier than that in the test tube. This is believed to be due to passage of fine unreacted V2O5 particles as well as impurities through the filter paper, which after storing for some time settled at the bottom of the beaker and acted as nucleating sites for earlier precipitation. The problem of transferring the fine V2O5 particles to the solution was minimised by filtering the solution twice. To prepare V(V) solution by electrolytic oxidation, the V(IV) solution has to be transferred to the electrolytic cell and nitrogen is bubbled through the solution to evenly distribute the solution over the electrodes and also to provide better mixing of the solution during electrolysis. This bubbling action however, was found to cause precipitation of the supersaturated V(IV) solution making the electrolysis process difficult. To verify that the cause of precipitation was due to agitation, a separate experiment was conducted to see the effect of stirring on the stability of 4M V(IV) solution in a solution of 6M total sulfate/bisulfate concentration. Two samples were monitored, one with stirring and the other without stirring. It was observed that the solution kept in the beaker without stirring did not show any sign of precipitation for about two weeks whereas the solution stirred at a speed of about 200 rpm started precipitating after 55 minutes. The precipitation process was monitored by measuring the conductivity of V(IV) electrolyte which is shown in Figure 5.3. The conductivity remained constant for about 55 minutes, then as the VOS04 precipitation begins the solution becomes less viscous and correspondingly the conductivity started increasing gradually. The whole solution precipitated completely in about 76 minutes. Ill Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The precipitate dissolved after adding some distilled water to the solution and re-heating for an hour at its boiling point. It was noticed that the heating of these V(IV) solutions for about an hour at boiling point improved the stability of the V(IV) solutions and no precipitation was observed for about 35 days when kept without stirring. Furthermore, the solution did not precipitate for about 30 hours even with stirring. This increased induction time of supersaturated V(IV) solution due to heat treatment facilitated greatly the electrolytic oxidation process to prepare supersaturated V(V) solutions. 160 - 120 - TIME (min) Figure 5.3. Conductivity of supersaturated V(IV) solution (4M V(IV) in 6M total sulfates) with time at a stirring speed of 200 rpm at room temperature. Similar observations were made by Kidyarov and Dandaron [1981] who reported the effects of heat treatment procedure, crystallisation temperature and supersaturation on the duration of crystallisation induction periods in potassium iodate solutions. They mentioned that the nucleation process was heterogeneous, and nuclei were formed on foreign nucleation centres; the main effect of heat treatment was the de-activation of these centres. Kubota and 112 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Kawakami [1986] when studying the primary nucleation of potassium nitrate from aqueous solution prepared the initial solutions in the same way in terms of filtration and heat treatment to ensure identical solution history. Nyvlt [1971] described in detail the effect of heat treatment on stability of solutions. He stated that extended pre-heating of a solution results as a rule in a significant widening of the domain of metastability. He explained that if a saturated solution is heated to a temperature above that at which saturation occurs and is then maintained at that temperature for some time, the size of the larger aggregates will be reduced. On subsequent cooling it will return to its initial value only slowly, and this delay results in the observation of a widened metastable region. He further explained that the widening of the metastable region will depend also upon the length of time over which the temperature was held at the higher level, i.e., on the degree of change of structure which the solution was allowed to attain. He expressed the width of the metastable zone to be a simple function of the relative distribution of aggregates of characteristic size, N, corresponding to the initial temperature of the solution and described the kinetics of change of the distribution of aggregates of characteristic size by the simple empirical equation dN/dt = Constant ( N - Nequii) (5-2) where N is the relative frequency of occurrence of aggregates of characteristic size at time t, Nequil is the corresponding value for aggregates of equilibrium size at the same temperature. Vacek, Pakarek and Nyvlt [1982] further investigated a number of systems regarding crystallisation of supercooled liquids. They found that the attainable degree of supercooling depends on the previous heat treatment of the system. The longer the liquid or solution has been kept, before being cooled down, at a certain temperature, and the higher this temperature is (at least within a certain temperature range which is specific for a given system) the lower the 113 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions temperature it can withstand without crystallisation within a constant time interval. This phenomenon is commonly used in practice to prevent undesirable nucleation. They explained this effect of preheating on its prolonged induction time by the following hypothesis: 1. A destruction (or melting) of various foreign particles (possibly with higher melting points than that of the main substance but lower than the preheating temperature) which, if remain unmelted could serve as crystallisation nuclei, 2. Deactivation of various active sites of the vessel walls of the system or of solid impurities already present in it, 3. Small crystals of the main substance, which have not had enough time to dissolve fully can act as centres for crystallisation. They concluded their discussion by mentioning that the thermal history can considerably affect the crystallisation of supercooled solution. However, the crystallisation kinetics and induction periods exhibit rather high scatter even under the identical experimental conditions. Sohnel et al. [1988] also pointed out that under special conditions, such as at low supersaturations or as a result of thermal pretreatment, induction periods may become extremely long e.g. BaS04, KI. Thus the recommended procedure of preparing more stable supersaturated V(IV) solutions may be (i) first prepare a solution approximately 75% of the desired concentration of vanadium and sulfate then heat the solution to boil off the water till the desired concentration of vanadium and sulfur is reached and (ii) filter the solution twice with double Whatmann ashless filter paper. By this method a more stable V(IV) solution of required specifications can be prepared. Care must be taken not to boil off too much water which results in high supersaturations and subsequent quick precipitation. This will usually happen 114 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions when a small quantity (about 100 ml) of solution is prepared. The stabilised V(IV) solutions thus prepared were used in the V(IV) solution additive evaluation experiments or oxidised electrolytically to prepare V(V) solutions according to the procedure described above in Section 5.2.1.1. 5.2.1.3 Preparation of Vanadium(V) Solution by Electrolytic Dissolution of V2O3 or V2O5 Alternatively supersaturated vanadium(V) solutions can be prepared either by electrolytic oxidation of V203 powder or by electrolytic reduction and reoxidation of V205 powder. Brief description of these two methods which were used in the initial stages of this study, are given below. 5.2.1.3.1 Electrolytic Oxidation of V203 Powder Electrolytic oxidation of V203 was carried out to prepare V(V) solutions of high concentrations. The electrolytic cell discussed above was used. A mixture of sulfuric acid and V203 powder was introduced in the positive half cell and the same concentration of sulfuric acid was placed in the negative half cell. A current of 3 - 4 amperes was applied so as to maintain a current density of 20 mA/cm2. Nitrogen was bubbled through the mixture of V203 powder and H2S04 to keep the V203 powder suspended in the solution and prevent it from settling down at the bottom. After completing the electrolysis for the predetermined time, the resulting supersaturated V(V) solution which is dark yellow in colour was filtered using Whatmann filter paper in a Buchner funnel. 5.2.1.3.2 Electrolytic Reduction of V205 Powder Preparation of vanadium(V) solution by electrolytic dissolution of V205 powder is very similar to that of electrolytic oxidation of V203 powder. While bubbling nitrogen through the sulfuric acid in the cathode side of the electrolysis cell, V205 powder was introduced. Electrolytic reduction was conducted for the required time. After visually observing the blue coloration or slightly seagreen 115 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions colour of the solution, the polarity was reversed. Electrolytic oxidation was then continued to obtain a dark yellow vanadium(V) solution. 5.2.2 Experimental Procedure for Cyclic Voltammetry The cyclic voltammetry was performed using a three electrode electrochemical cell and an EG&G Princeton Applied Research Model 273 potentiostat. An IBM computer was connected to the potentiostat through a GPIB communication interface card. The functions of the potentiostat were controlled by EG&G model M270 Electrochemical Analysis Software version 2.00. The three electrode cell consisted of a 50 ml beaker containing the V(V) solution under study with a saturated calomel reference electrode (SCE), a working electrode (glassy carbon, 0.1 cm2 area) and a counter electrode (graphite rod) immersed in it. These three electrodes were connected to the potentiostat as shown in Figure 5.4. About 40 ml of V(V) electrolyte was placed in the beaker and the three electrodes were immersed vertically in the electrolyte about 2 cm apart from each other, keeping some clearance from the bottom. The initial potential was set at 1.45V, and the upper and lower voltage scan limits at 1.45V and -0.85V respectively. The scan was initiated in the negative direction at a scan rate of 0.02V/sec. Each CV was scanned for four cycles and the fourth cycle was recorded on a HP 7475A plotter. To evaluate the reversibility of the V(V)/V(IV) redox couple and determine the diffusion coefficients and rate constants, cyclic voltammograms were obtained at different scan rates and the first cycle was recorded in each case. All the scans were recorded at about 20°C, and sufficient time was given between each scan. 116 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions EG & G POTENTIOSTAT GALVANOSTAT Working Electrode ■SBBBBhI (Glassy Carbon) ► Counter Electrode , ,s,n'\s>V „i;\„ ^ SjjvSäSfcSS»iw* 5SS §S§&§1 (Graphite) v* x. » si'C4l| Reference Electrode (SCE) Vanadium(V) solution Figure 5.4. Cyclic voltammetry apparatus. 117 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5.2.3 Experimental Procedure for Supersaturated V(V) Solutions Stability Evaluation and Kinetic Study Supersaturated vanadium(V) solutions of various vanadium concentrations 2M, 3M, 4M and 5M prepared in different sulfuric acid concentrations containing 5M, 6M and 7M total sulfate/bisulfate were used for studying the stability and kinetics of thermal precipitation. All of these vanadium(V) solutions were prepared by first reacting V203 powder and V2O5 powder in the desired concentration of sulfuric acid and then carrying out electrolytic oxidation of the resultant V(IV) solution (details in Section 5.2.1). From each vanadium(V) solution, samples of about 30 ml were taken in sample glass bottles of capacity 40 ml with teflon stoppers and placed in constant temperature water baths maintained at 20, 30, 40 and 50°C. A temperature controlled immersion circulator (Thermoline) capable of controlling the temperature to an accuracy of ±0.5°C was used to maintain the constant temperature. At the commencement of an experiment, after taking the initial sample of vanadium(V) solution the sample bottle was kept in the water bath of desired temperature. The rate of crystal growth was monitored by withdrawing the liquid samples through a 0.45|im filter (Millipore) fitted to a plastic syringe. Standard volumes of the liquid samples (0.2 ml) were diluted immediately in 500 ml 0.02 M HC1 and stored for analysis of vanadium concentration using an atomic absorption spectrophotometer Model Varian AA2 Plus. Acetylene and nitrous oxide was used to obtain a reducing red cone of about 1-1.5 cm. The analysis of total vanadium was carried out at a wave length of 306.6 nm with a slit width of 0.5 mm. Calibration was done before and after the analysis of the each set of vanadium samples. A calibration curve was developed to take care of any drift in the instrument as shown in Appendix E. The sampling was done at different intervals for a period of 1000 hours and the frequency was increased during initial precipitation after visual observation. A small amount of V(V) precipitate was dissolved in IM HC1 and the liquid sample was analysed by ICP. No sulfur was detected in the liquid sample indicating that the precipitate 118 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions is vanadium pentoxide without any vanadium-sulfur compound. Lu and Skyllas-Kazacos [1996] also confirmed in a recent spectroscopic study that the red precipitate obtained from supersaturated V(V) solution is V205. 5.3 RESULTS AND DISCUSSION 5.3.1 Preliminary Investigation of the Stability of Supersaturated V(V) Solutions Preliminary experiments were conducted to investigate the stability and precipitation behaviour of supersaturated V(V) solutions in concentrated sulfuric acid. These initial runs were necessary in order to be able to properly design the experiments for stability evaluation, studying kinetics of precipitation and inhibitor evaluation to increase the induction time. A range of vanadium(V) solutions of concentration around 4.0M were prepared using sulfuric acid solutions with initial concentrations of 5.0, 6.0, 6.5 and 7.0M. The concentration of all these solutions was monitored over a period of more than 30 days at 20°C and the results are shown in Figure 5.5. The concentration of the 4.0M V(V) solution in 5.0M total sulfate reached 3.8M V(V) after 30 days at 20°C, dropping by 5%. The concentration of the 4.2M V(V) solution in 6.0M total sulfate decreased to 4.1M, a decrease of about 2.4% while the 4.1M V(V) solution in 6.5M total sulfate showed a final concentration of 4.0M, a decrease of about 2.4%. In 7.0M total sulfate the V(V) concentration decreased from 3.9M to 3.8M, about 2.5% drop in V(V) concentration over the same period of 30 days. Although, the drop in concentration of V(V) in 5.0M total sulfate is slightly higher than that in higher total sulfate concentration, the difference is still minor, and for practical purposes, all the solutions can be considered as having similar stability at room temperature. 119 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions V(V) - 5M Total S V(V) - 6M Total S V(V) - 6.5M Total S V(V) - 7M Total S TIME (days) Figure 5.5. Variation in concentration of V(V) solutions with time in different total sulfate/bisulfate at 20°C. To evaluate the effect of increased temperature on the thermal stability of the V(V) solutions over an extended period of time, solutions having an initial V(V) concentration around 4 M in different H2S04 concentrations were kept in a hot water bath maintained at 50°C. Table 5.1 shows that at 50°C, the stability of V(V) solutions gradually improves with increasing total sulfate concentration. Table 5.1. Stability of supersaturated V(V) solutions at 50°C over a period of 30 days. Total 5.0M 6.0M 6.5M 7.0M Sulfate Cone. Time V(V) Time V(V) Time V(V) Time V(V) (days) Cone. (M) (days) Cone. (M) (days) Cone. (M) (days) Cone. (M) 0 4.0 0 4.2 0 4.1 0 3.9 1 ppt(5) 4 PPt(2) 15 PPt(l) 30 no ppt ppt precipitation (1) slight ppt on walls of tube (2) 25% solids in solution (3) 50% solids in solution (4) 75% solids in solutions (5) 100% solution precipitated 120 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The 4.0M vanadium(V) solution in 5M total sulfate showed the least stability as it precipitated completely within a day. The 4.2M V(V) solution in 6.0M total sulfate started precipitating after 4 days, 4.1M V(V) solution in 6.5M total sulfate developed a slight precipitate after 15 days while the 3.9M V(V) solution in 7.0M total sulfate did not show any sign of precipitation even after 30 days when observed visually. In view of the results obtained by studying the effect of H2S04 concentration on stability of V(V) solutions, both at room temperature and at 50°C, 7.0M total sulfate was selected to further investigate the stability of supersaturated V(V) solutions. Vanadium(V) solutions ranging in concentration from 2.0M to 4.5M were prepared in 7M total sulfate to study the stability and determine the optimum V(V) concentration. Table 5.2 shows the preliminary results of the effect of high temperature (50°C) on the stability of solutions at different V(V) concentrations. None of the solutions precipitated for a period of 20 days. Slight precipitation was observed on the walls of the tube of the 4.5M V(V) solution after 20 days and all other solutions showed no sign of precipitation when observed visually. Although, 4.2M V(V) solution in 7.0M total sulfate was found to drop in concentration to 4.0 M (about 5%) after 4 days, the 3.6 M V(V) solution showed absolutely no decrease in concentration at 50°C even after 30 days. Another solution of concentration 4.0M V(V) in 8M total sulfate/bisulfate was found to be very stable and did not precipitated for about two months even at 50°C. Table 5.2. Stability of different V(V) solutions in 7.0M total sulfate observed for 30 days at 50°C. V(V) Cone, Time for initial evidence Appearance of solution (moles/lit.) of precipitation (days) after 30 days 2.0 no ppt no ppt 2.8 no ppt no ppt 3.6 no ppt no ppt 4.2 no ppt no ppt 4.5 ppt(l) after 20 days PPt(2) ppt = precipitation (1) = slight ppt on walls of tube (2) = 25% solids in solution 121 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Skyllas-Kazacos and Peng [1996] studied the stability of supersaturated V(IV) electrolyte which represents the discharged state of the positive half cell of the vanadium redox battery. They found that the stability of V(IV) species in sulfuric acid is opposite to that of V(V) ions. The precipitation rate increases with increasing total sulfate concentration and in 7M total sulfate the precipitation is significant. To summarise the results of preliminary experiments, at room temperature, vanadium(V) solutions of concentration 3.9 - 4.2M in 5-7M total sulfate were found to decrease in concentration by 2 - 4 % after 30 days of storage. On the other hand, at 50 °C, in 7.0 M total sulfate the 3.9M V(V) solution did not show any sign of precipitation even after 60 days. The precipitation behaviour of V(IV) solutions however, indicated that lower sulfuric acid concentrations (<7M total sulfate) should be considered for increased stability. Since the V(V) solution is converted to V(IV) during discharge of the positive half-cell electrolyte in the vanadium battery, a sulfuric acid concentration which optimises the stability of both oxidation states must be selected. 5.3.2 Description of Supersaturated V(V) Solutions Prepared for Stability Evaluation and Kinetic Study After examining the results of preliminary experiments conducted earlier, various supersaturated vanadium(V) solutions were prepared to carry out the stability evaluation and study the kinetics of precipitation at different temperatures. The description of these solutions is as follows: 1. 2M V(V) solution in 5M total sulfate/bisulfate (2V5S) 2. 3M V(V) solution in 5M total sulfate/bisulfate (3V5S) 3. 4M V(V) solution in 5M total sulfate/bisulfate (4V5S) 4. 5M V(V) solution in 5M total sulfate/bisulfate (5V5S) 5. 2M V(V) solution in 6M total sulfate/bisulfate (2V6S) 6. 3M V(V) solution in 6M total sulfate/bisulfate (3V6S) 122 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 7. 4M V(V) solution in 6M total sulfate/bisulfate (4V6S) 8. 5M V(V) solution in 6M total sulfate/bisulfate (5V6S) 9. 2M V(V) solution in 7M total sulfate/bisulfate (2V7S) 10. 3M V(V) solution in 7M total sulfate/bisulfate (3V7S) 11. 4M V(V) solution in 7M total sulfate/bisulfate (4V7S) 12. 5M V(V) solution in 7M total sulfate/bisulfate (5V7S) 5.3.3 Properties of Supersaturated Vanadium(V) Solutions The structure of a supersaturated solution is probably more complex than that of an unsaturated or saturated solution. As reported by Khamskii [1969], a number of attempts have been made to find the distinguishing features of supersaturated solutions by investigating the dependences of various physical properties on concentration. Some of these important properties are density, viscosity and conductivity. 5.3.3.1 Density of Vanadium(V) Solution The approximate density of different vanadium(V) solutions were measured using 50 ml volumetric flask at 20°C. The densities of all the 12 solutions under study are listed in Table 5.3 and plotted in Figure 5.6. It can be observed from Figure 5.6 that the density of supersaturated vanadium(V) electrolytes increases linearly with increasing vanadium concentration. The effect of sulfate/bisulfate concentration on density is illustrated in Figure 5.7. The densities of vanadium(V) solutions do not change significantly with changes in total sulfate/bisulfate concentration however, densities of solutions in 7M total sulfate/bisulfate are distinctly higher than that in 5M and 6M total sulfate/bisulfate. The effect of vanadium concentration on density appears to be more pronounced than that of the sulfate/bisulfate concentration. 123 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Table 5.3. Densities of vanadium(V) solutions in various concentrations of total sulfate/bisulfate at 20°C (gm/cc). Total sulfate/bisulfate concentration 5M 6M 7M 2M V(V) 1.456 1.469 1.492 3M V(V) 1.527 1.541 1.579 4M V(V) 1.591 1.619 1.670 5M V(V) 1.657 1.721 1.789 7M Sulfates 1.8 -- 1.6 -- 5M Sulfates Z 1.4 -- 1.2 - V(V) CONCENTRATION (M) Figure 5.6. Effect of vanadium concentration on density of the supersaturated V(V) solutions at 20°C. 124 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5M V(V) 1.8 - 1.6 - Z 1.4 - 1.2 - TOTAL SULFUR CONC (M) Figure 5.7. Effect of total sulfate/bisulfate concentration on density of the supersaturated V(V) solutions at 20°C. 5.3.3.1.1 Density Correlation of V(V) Solution The density of multicomponent aqueous solutions of inorganic substances and its dependence on solution concentration and/or temperature plays an important role for chemical engineering and physical chemistry. It is useful in the conversion of concentration units and in the investigation of interactions in solution [Fabuss et al, 1966 and Millero, 1971]. Data of many binary aqueous solutions have been compiled [Weast, 1972; International Critical Tables, 1928; Novotny and Sohnel, 1988] but relatively few density measurements have been made on solutions containing more than one solute. Novotny and Sohnel [1988] collected existing density data for binary aqueous solutions of about 306 inorganic substances, evaluated them critically, selected reliable values and developed correlations in a consistent manner to predict densities of binary solutions. Mixing rules have been suggested by Millero [1972] and Potter and Hass [1978] to calculate mixture densities using binary density data. Very often mixture densities are needed and a rapid method of determination of mixture 125 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions density is essential. Sometimes the solute concentration available is in one unit and density correlation uses different units and causes difficulties. Millero [1971,1972] presented excellent reviews on the various aspects of molar volumes and densities of electrolyte solutions. Further reviews have been written by several investigators on the subject [Young and Vogel, 1932; Harned and Owen, 1958; Friedman & Krishnan, 1973] and more recently by Sohnel & Novotny [1985]. Shilovskaya & Lenkova [1974] showed that sometimes the simple equation can be used for representation of densities in the concentration interval of 0.1 - 4.0 M of solution at constant temperature. (5-3) where dsoin = density of the aqueous electrolyte solution, gm/cc dH2o = density of pure water, gm/cc Im = Ionic strength a, b = adjustable parameters A similar equation was used by Root [1933] and Bremner [1938] for the density of aqueous salt solution as a function of concentration in terms of normality (N2) as follows: 1 /2 dsoin = dito + a N2 + b N2 (5-4) where N2 = Normality a, b = adjustable parameters Watson and Felsing [1941] used an expression for the density of aqueous solutions as a function of the molarity: 1 /2 dsoin = dn2o + a M2 + b M2 (5-5) where M2 = Molarity 126 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions a, b = adjustable parameters An attempt has been made to correlate the density data of supersaturated vanadium(V) solutions in concentrated sulfuric acid. In this study, after investigating several functional forms the following equation was proposed and found to better represent the density data of vanadium(V) solutions in sulfuric acid: dv(v) - dn2so4 + Q Mi + C2 M2 (5-6) where dV(V) = density of the V(V) solution in sulfuric acid, gm/cc dH2so4 = density of sulfuric acid, gm/cc at cone. Mj Mj = sulfuric acid concentration, molarity M2 = V(V) concentration, molarity Ci, C2 = adjustable parameters The overall average absolute deviation of predicted values from measured data was about 0.95% with a maximum deviation of 2.5% and an excellent correlation coefficient (R2) of 0.99. The regression constant Q was estimated as -0.006857 and C2 was obtained as 0.0846 at 20°C using SAS. The density of sulfuric acid (dH2S04) required in the above equation can be calculated using an empirical equation suggested by Novotny and Sohnel [1988] which describes the concentration-temperature dependence of densities of binary aqueous solutions as follows: d = dH _ + Ac + Bet + Cct2 + Dc3/2 + Ec3/21 + Fc3'212 (5-7) where dH,Q = 999.65 + 2.0438 x 10-‘t - 6.1744 x 10‘2 t3/2 (5-8) is the density of pure water as a function of temperature. 127 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions t = temperature (°C) c = molar concentration d = density of binary solution as a function temperature and concentration in (Kg/m3) A, B, C, D, E and F are constants given by Novotny and Sohnel [1988]. A computer program developed in FORTRAN to calculate the density of H2S04 as a function of concentration and temperature is given in Appendix F. 5.3.3.2 Viscosity Behaviour of Supersaturated Vanadium(V) Solutions One of the important properties of concentrated vanadium solutions is viscosity and is of considerable interest as it affects the conductivity and electrochemical behaviour of V(V) solutions. Viscosity of supersaturated vanadium solutions were measured by flow through capillary method using a capillary viscometer of proper size to handle the relatively viscous vanadium(V) solutions. The viscosity of liquids generally decreases with increase in temperature. The molecules acquire more kinetic energy as the temperature increases and are able to move about more freely. This improves their ability to slide past each other and decreases the shear forces between layers and hence viscosity. Viscosity increases with increase in concentration of the electrolytes by increasing the intermolecular interactions and making the liquid more and more cohesive. In some types of electrolytes (KF, LiBr, etc) when a certain concentration of solid phase is attained, the viscosity may reach such high values that the hydraulic type flow is replaced by plastic flow [Nyvlt; 1971, Satoh and Hayashi; 1961] as shown in Figure 5.8. So, the maximum practical supersaturation is limited by the viscosity of the solution to be able to remain in the hydraulic flow region. 128 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions SUPERS ATURATION (s/1) Figure 5.8. Typical diagram showing effect of supersaturation on viscosity of concentrated solutions [Source [Nyvlt, 1971]]. 5.3.3.2.1 Effect of Concentration on Viscosity The viscosity behaviour of supersaturated vanadium(V) solutions was studied by measuring the viscosity of vanadium(V) solutions over the vanadium concentration range of 2M to 5M in solutions containing 5M-7M total sulfate/bisulfate. The effect of total sulfate/bisulfate concentration on the viscosity of vanadium(V) solutions is more pronounced at higher vanadium concentration as shown in Figure 5.9. The variation in viscosity of vanadium solutions with increasing vanadium concentration is presented in Figure 5.10. The viscosity increases linearly and gradually between 2M and 3.5M vanadium(V) concentration and then increases rapidly on further increasing the vanadium concentration to 5M. The V(V) solutions in the concentration range of 2M to 4M were observed to be not very viscous and can be considered as Newtonian. The 5M V(V) solution however, appears to be in the non- Newtonian region. 129 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 2M V(V) 160 - 3M V(V) 3.5M V(V) 4M V(V) 120 - 4.5M V(V) 5M V(V) 83 80- TOTAL SULFATE7BISULFATE CONC (M) Figure 5.9. Variation in viscosity of 5M vanadium(V) solutions with total sulfate/bisulfate at 20°C. 7M Total S 160 - 120 - 6M Total S 5M Total S V(V) CONCENTRATION (M) Figure 5.10. Variation in viscosity of 2M-5M vanadium(V) solutions in 5M- 7M total sulfate/bisulfate at 20°C. 130 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions A concentration of about 3.5M V(V) solution in 5-7M total sulfate/bisulfate concentration appears to be the limiting concentration to be able to remain in the hydraulic flow region and with further increase in V(V) concentration viscosity increases rapidly. This is probably due to the formation of extended chain polyvanadic molecules [Pozarnsky and McCormick, 1994], subsequently increasing the viscosity more steeply. Also at such high supersaturations, ion distribution attains a degree of order resembling crystallinity and the influence of ion-ion interaction on viscosity increases significantly [Beck; 1939 in Good, 1964]. Another reason for the exponential increase in viscosity could be the start of dimerisation of V02+ ions to V2042+ at sulfuric acid concentration of 7M as suggested by Madie et al. [1984]. They reported the mass action law constant for the dimerisation of V02+ in 7, 8, 9 and 10M H2S04 as 0.26, 2.3, 19 and 83 respectively. Additional complexation with sulfate and bisulfate ions at increased sulfuric acid concentrations is also possibly occurring. This change in structure of V02+ in higher vanadium as well as sulfuric acid concentrations is probably also contributing to the rapid increase in viscosities. Similar behaviour was reported by Stokes and Mills [1965] in the case of sucrose solutions shown in Figure 5.11, over the concentration range of 20% to 70%. Satoh and Hayashi [1961] discussed the viscosity behaviour of concentrated aqueous solutions of strong electrolytes from 0.5 to 5 mol/1 at room temperature. They found that the plots of viscosity against concentration were of two types. In the first type (KF, LiCl, LiBr, NaBr, etc), the viscosity rises almost linearly with concentration in the dilute range to a critical concentration or deflection point, above which the slope becomes increasingly positive. They explained that the normal water structure in concentrated solutions ( >1M ) is considered to be broken down due to interaction between ionic hydration shells. The ions can then be pictured as embedded in a different solvent from that in the dilute range. 131 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 400 - 300 - 200 - 100 - SUCROSECONC (%) Figure 5.11. Variation in viscosity of sucrose solutions with increase in concentration at 20°C. It has been pointed out that the viscosity of aqueous solutions of strong electrolytes can be expressed by the following empirical relationship given by Jones and Dole [1929]. r| / r|0 = 1 + A Vc +B c (5-9) where r| is the viscosity of the solution r|0 is the viscosity of pure water c concentration of the electrolyte A coefficient refers to the ion-ion interaction B coefficient, a measure of ion-solvent interaction Good [1964] conducted comprehensive studies to find out the effect of solute concentration on viscosity of aqueous electrolyte solutions. He mentioned that parameter A in Equation 5-9 is numerically smaller and less variable than B, 132 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions supporting the view that, in electrolyte solutions, ion-solvent interactions have a greater effect on fluid motion. 5.3.3.2.2 Effect of Temperature on Viscosity The effect of temperature on the viscosity was studied using 4.5M V(V) solution in 7M total sulfate/bisulfate. It was found that the variation in temperature affects viscosity quite significantly which is shown in Figure 5.12. The viscosity dropped very quickly with a slight increase in temperature, for example the viscosity decreased by about 24% when the temperature was raised from 20°C to 25°C. The effect of temperature on selected vanadium(V) solutions is tabulated in Table 5.4. >* 40 -- U 30 -- TEMPERATURE (C) Figure 5.12. Effect of temperature on viscosity of 4.5M V(V) solution in 7M total sulfate/bisulfate. 133 Chapter 5______Stability of Supersaturated Vanadium(V) Solutions Table 5.4. Effect of temperature on viscosity of various vanadium (V) solutions. Solution ID Temp(C) Viscosity (cP) % Drop Remarks 3V6S 20 11.9 _ Solution kept 30 9.3 22 in closed bottle 40 6.8 43 4.5V7S 20 65.7 - Soln. Exposed 25 49.8 24 to atmosphere 30 39.0 41 40 25.6 61 5V7S 20 186 - Solution kept 22 150 19 in closed bottle Hatschek [1928] reported that at low temperatures the viscosity of sucrose solutions increases greatly with an increase in concentration, while at high concentration the decrease in viscosity with increasing temperature is extremely rapid. 53.3.2.3 Variation in Viscosity of V(V) Solutions with Time The viscosity of all vanadium(V) solutions under study was measured when they were initially prepared. The containers were closed tightly and again the viscosity was measured after about 1000 hours. The variations observed in the viscosity of these solutions are listed in Table 5.5. Viscosity decreased significantly in all the vanadium(V) solutions (2M - 5M V(V)) prepared in 5M total sulfates over a period of 45 days (approximately 1000 hours), whereas vanadium(V) solutions containing 7M total sulfates showed a minor drop in viscosity under identical conditions over the same period of time. The viscosity of 4.5M vanadium(V) solution in 7M total sulfate/bisulfate was monitored with time and it was observed that the viscosity decreased from 113 cP to 102 cP in 75 days, a drop of about 9.7%. This decrease in viscosity of vanadium solutions when kept in closed containers could be attributed to the settling of unreacted fine particles or possibly because of slight precipitation over such a long period. A thin yellow layer of solids was 134 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions observed at the bottom of the container. Because of high supersaturation, stratification also might have taken place making the lower layer more concentrated than the upper layers. The significant decrease in viscosity of the V(V) solutions in 5M total sulfates is probably partly due to settling of unreacted particles and stratification and also because of enhanced precipitation as compared to the more stable solutions in 6M and 7M total sulfates. Table 5.5. Viscosity variation of vanadium(V) solutions with time when stored in air tight containers. Soln. Description Initial Vise Final Vise % Decrease (0 days) (45 days) in Viscosity 2M V(V)-5M S04 6.7 6.5 2.99 3M V(V)-5M S04 12.1 11.6 4.13 4M V(V)-5M S04 21.7 20.2 6.91 5M V(V)-5M S04 41.2 33.9 17.72 2M V(V)-6M S04 6.9 6.9 0.00 3M V(V)-6M S04 12.9 12.5 3.10 4M V(V)-6M S04 32.9 31.8 3.34 5M V(V)-6M S04 114.8 108.7 5.31 2M V(V)-7M S04 10.5 10.5 0.00 3M V(V)-7M S04 23.5 23.5 0.00 4M V(V)-7M S04 51.3 49.5 3.51 5M V(V)-7M S04 186.0 179.0 3.76 5.3.3.2.4 Change in Viscosity of V(V) Solutions When Exposed to Atmosphere When the 4.5M V(V) solution in 7M total sulfur was exposed to atmosphere for 45 days the viscosity decreased from 103cP to 66cP, a drop of about 35% as compared to about 10% drop when stored in closed container for 75 days. A similar viscosity decrease was observed during preliminary evaluation of a 4.1 M V(V) solution in 5.5M total sulfates with corresponding increase in conductivity and the reason was probably the container was not closed tightly. 135 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The upper layer of the 4.5M V(V) solution in 7M total sulfur which was exposed to atmosphere appeared dark green when seen by tilting along the walls of the container. Small volumes of V(V) solution (about 5 ml) when placed in a beaker and kept open to atmosphere, the orange-red solution turned green after about 10 days. It was also observed that V(V) solution sticking to the walls of the beaker when left overnight becomes green. This green colour is normally observed when water is added to V(V) solutions during titrations and cleaning of the glassware. On the basis of all the above observations it is believed that the solution is absorbing moisture present in the atmosphere because of the hygroscopic nature of sulfuric acid. Thus, this significant drop in viscosity of vanadium solutions when exposed to atmosphere is probably due to a slight dilution and disturbance of the polyvanadic structure of supersaturated V(V) solution by absorbing moisture from the atmosphere. To develop a better understanding of the viscosity changes of the solutions when exposed to atmosphere, 1 vol/vol % distilled water was added to the above mentioned 4.5M V(V) solution, and after shaking it intermittently for about 2 hours the viscosity was measured and it was found to be 93 cP a drop of about 18%. This result is most surprising as the 1 vol/vol % water addition has a negligible effect on the vanadium or acid concentration. Again 1 vol/vol % 7M sulfuric acid was added to 5M V(V) solution in 7M total sulfur (5V7S), the viscosity dropped by about 9%. Although these observations are difficult to explain at this time, it is thought that the addition of water may be breaking the large size V(V) ions and sulfate/bisulfate complex species rendering more and more small size V02+ ions or molecules thus decreasing the viscosity significantly whereas addition of same amount of acid would not disturb the V(V)-sulfate complex and therefore decreases viscosity only slightly. Good [1966] from experiments confirms his earlier observations that ion-solvent interaction is the principal factor governing the fluid kinetics of electrolyte solutions. 136 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5.3.3.2.5 Electrochemical Studies of V(V) Solutions With and Without Water Addition The electrochemical behaviour of the solutions 5V7S and 5V7S with 1% distilled water (5V7S-DW) were studied by carrying out cyclic voltammetry. Figure 5.13 shows a typical cyclic voltammogram for 5M V(V) solution in 7M total sulfate. Starting from an initial potential of 1.45V and scanning in the negative direction, a cathodic peak appears at approximately 0.86V due to reduction of V(V) to V(IV). By sweeping the potential in the negative direction further, a second cathodic peak was observed at about -0.71V which is associated with the reduction of V(IV) to V(II). When the potential sweep was reversed at -0.85V, the oxidation of the V(II) to V(III) and the V(V) was observed at -0.49V and 1.05V respectively. The electrochemical activity of V(V) solution with distilled water (5V7S-DW) was thus found to be improved as shown in Figure 5.13 when compared to that of V(V) solution without distilled water (5V7S). The anodic peak current at 1.05V vs SCE for the 5V7S- DW solution was about 3.9 mA as compared with 2.9 mA in the case of 5V7S solution, an increase of about 34%. The cathodic peak current {for the reduction of V(V) to V(IV)} for the 5V7S-DW solution was -2.71 mA while that of 5V7S was -2.02 mA, again about 34% high. This is probably due to the decrease in viscosity of solution, allowing increased mobility of these ions. The peak separation potential of the V(IV)/V(V) redox couple in the solutions was found to be around 0.2 V in both cases. 5.3.3.2.6 51V NMR Studies of Vanadium (V) Solutions The 5V7S solution was analysed by recording 51V NMR spectra with a Bruker ACP 300 spectrometer to find out the effect of addition t)f water on the structure of V(V) solution and its speciation. The NMR spectra were obtained with a 10 mm broad-band probe tuned to observe 51V at 78.94 Mhz. Because of very high viscosity due to the high vanadium(V) concentration of the sample, the NMR did not show any peak and both the solutions (5V7S and 5V7S-DW) gave almost a flat spectrum as shown in Figure 5.14. 137 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Potential (V) vs SCE Figure 5.13. Cyclic voltammograms of 5M V(V) solution in 7M total sulfur (5V7S), and 5V7S solution with 1% distilled water at an scan rate of 0.02v/s. 5M V (V) -7MS 0.5V 7S - 4S 0.5V7S-7S -250 -350 -450 -550 -650 -750 -850 -950 (ppm) Figure 5.14. 51V NMR spectra of various V(V) solutions in different supporting electrolyte concentrations. 138 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Further 51V NMR investigations were carried out by analysing two dilute solutions (i) 2V7S solution diluted to 0.5M V(V) using 7M H2S04 labelled as 0.5V7S-7S (ii) 2V7S diluted to 0.5M V(V) using 4M H2S04 labelled as 0.5V7S- 4S in Figure 5.14. The peaks obtained from these solutions are quite broad, again probably due to the high viscosity of the solution which prevents a fast tumbling of the molecules. However, it can be observed from Figure 5.14 that the second solution having more water (resulting in a 0.5M V(V) in 4.8M H2S04) clearly indicates more free V(V) ions as compared with the first solution. Thus, it confirms that an increase in water content in the vanadium(V) solution breaks the large size vanadium-sulfate complex ions and generates small size free V(V) ions resulting in a significant drop in viscosity. It was also noticed that the first solution (0.5V7S-7S) when diluted with 7M H2S04 did not change its colour after dilution but the second solution became dark green after dilution with 4M H2S04. Both the solutions were analysed by potentiometric titration to determine the presence of any V(IV) species in the solution which may contribute to the green coloration. It was found that both the solutions were at the same state-of-charge but the first solution (0.5V7S-7S) has slightly higher starting potential than the second solution (0.5V7S-4S). The green coloration is probably due to the formation of some hydrolysed species at the slightly higher pH. 5.3.3.2.7 Verification of Moisture Absorption of V(V) Solutions When Exposed to Atmosphere As discussed above, the observation of a green coloration of the original orange-red vanadium(V) solution when exposed to atmosphere was believed to be due to moisture absorption from the atmosphere. This theory was further verified by conducting mass gain experiments by vanadium(V) solutions and sulfuric acid when exposed to atmosphere under enhanced conditions. About 4 ml of vanadium solution of different vanadium(V) concentrations (3M - 5M) in 6M total sulfate/bisulfate was placed in petri dishes of about 7.5 cm in diameter 139 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions so that a thin layer of solution was formed. After taking the initial weight on a high precision balance these petri dishes were exposed to atmosphere. It was observed that the weight of the sulfuric acid solutions as well as the vanadium(V) solutions in sulfuric acid started increasing in a matter of minutes. Surprisingly after five hours, the mass gain observed in 5M, 6M and 7M sulfuric acid was about 3.4%, 7.3% and 11.7% respectively. The monitoring was continued till equilibrium was reached and the equilibrium concentrations were measured. The percent mass gain in the three sulfuric acid solutions over a period of 10 days is plotted in Figure 5.15. The dynamic equilibrium between rate of absorption and rate of evaporation was reached in about 72 hours. A similar mass gain was observed in 3M V(V) solution in 5M, 6M and 7M sulfuric acid when exposed to atmosphere in the same size petri dishes as shown in Figure 5.16. 7M H2S04 6M H2S04 5M H2S04 TIME (hours) Figure 5.15. Mass gain comparison of 5M, 6M and 7M sulfuric acid. 140 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 3M V(V) - 7M S 3M V(V) - 6M S 3M V(V) - 5M S TIME (hours) Figure 5.16. Mass gain comparison of 3M V(V) solution in 5, 6, and 7M total sulfate/bisulfate. The percent mass gain after five hours was found to be 3.3%, 6.7% and 11.7% in 3V5S, 3V6S and 3V7S V(V) solutions respectively which is identical to the mass gain observed in sulfuric acid solutions of 5M, 6M and 7M alone indicating that vanadium ions are not contributing to the moisture absorption and that sulfate/bisulfate are mainly responsible for the moisture absorption of the solutions from atmosphere. The equilibrium concentrations of vanadium and total sulfur concentrations determined by ICP after 240 hours are listed in Table 5.6. The mass gain recorded for 2M, 3M, and 4M V(V) solutions in 6M total sulfate/bisulfate when exposed to atmosphere under identical conditions was found to be approximately same as shown in Figure 5.17. Another experiment was carried out by taking about 40 ml of 4.5M V(V) solution in 7M total sulfate/bisulfate concentration in a 100 ml beaker. The percent mass gain when exposed to atmosphere was about 12% over a period of 15 days. This lower value of mass gain in the beaker experiment was probably due to a smaller surface area and larger volume compared to the samples in the petri dishes. 141 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Table 5.6. Variation in concentration of H2S04 and vanadium(V) solutions in H2S04 when exposed to atmosphere for 240 hours. Solution Initial Conc.(M) Final Conc.(M) Drop in Cone (%) Description S V S V S V 5M H2S04 5.5 0 4.65 0 15.3 - 6M H2SO4 6.1 0 4.66 0 24.3 - 7M H2SO4 7.0 0 4.64 0 33.2 - 3V5S 5.18 3.19 4.28 2.71 17.4 15.1 3V6S 5.81 2.90 4.27 2.05 26.5 29.4 3V7S 6.89 2.92 4.33 1.73 33.2 40.7 2V6S 5.78 1.87 4.27 1.38 26.1 26.3 3V6S 5.81 2.90 4.27 2.05 26.5 29.4 4V6S 5.71 3.68 4.24 2.77 25.7 24.7 ♦—2V- 6S 3V- 6S ■A—4V- 6S TIME (hours) Figure 5.17. Mass gain comparison of 2M, 3M and 4M V(V) solution in 6M total sulfate/bisulfate. 142 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Thus it can be concluded that sulfuric acid (sulfate + bisulfate) is mainly responsible for moisture absorption from atmosphere. Significant water absorption may thus take place by vanadium(V) solutions in sulfuric acid supporting electrolyte if not stored in properly closed containers resulting in formation of different vanadium species and lowering of the viscosity and concentration over a period of time. 5.3.3.3 Effect of Supersaturation on Conductivity The electrical conductance of an aqueous solution can often be measured with high precision and thus affords a useful means of determining concentration. Robinson and Stokes [1970] has given a detailed account of the methods in this area, but most of the published work is concerned with dilute systems. In concentrated solutions, Mullin [1972] suggests that conductivity measurements are of limited use because of the poor reliability of measurement in near- saturated or supersaturated solutions. The temperature dependence of electrical conductivity usually demands a very high precision of temperature control. Conductivity measurements of supersaturated vanadium(V) solutions were thus made using Metrohm Model 660 conductometer at a constant temperature of 20°C. The conductivity was found to decrease with an increase in vanadium(V) concentration as shown in Figure 5.18. This is due to the fact that at constant total sulfate/bisulfate concentration, increasing V(V) concentration will lower the free H2S04 concentration and therefore decrease free H+ ions in the solution resulting in a lowering of the conductivity. Further experiments were carried out by measuring the conductivity of 5M, 6M and 7M sulfuric acid and it was found that the conductivity of sulfuric acid alone was also decreasing with increasing concentration in the range of 5M to 7M. 143 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5M Total S 500 - 4— 6M Total S ■*— 7M Total S 400 - 300 - 200 - 100 - V(V) CONCENTRATION (M) Figure 5.18. Conductivity of vanadium(V) solutions in sulfuric acid at 20°C. Gerzhberg et al [1969] reported the electrical conductivities of H2S04 solutions at temperatures 0 to -50°C in the concentration range 4 - 42% for accumulator industry applications. A plot of conductivity against concentration illustrates that the conductivities of H2S04 solutions passes through a maximum at about 28 wt.% H2S04 (corresponding to 5.1 M) as shown in Figure 5.19. Their interpretation of the maxima on the curve is due to the marked increase in viscosity of the solutions and apparently also to the decreasing role of the “estafette” mechanism of proton transfer through the solution and to the increase in interionic reactions in the concentrated solutions. A review of the literature was carried out to find a theoretical explanation for the decrease in conductivity of electrolytes with increasing concentrations. Ivanov and Valyashko [1976] pointed out that a maximum conductivity has been observed in aqueous solutions of LiCl, RbCl, CsCl, NaN03, KN03 and RbN03. They mentioned that these maxima show that a change takes place in the molecular structure of the solution when passing from dilute to concentrated solutions. 144 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions C! 0.30 Temp. = 0 °C Wt. %H2S04 Figure 5.19. Conductivity of FI2S04 solutions with concentration at 0°C [Gerzhberg et al, 1969]. In dilute solutions, the structure is determined by water-water and ion-water bonds, whereas in concentrated solutions the ion-water and ion-ion interactions are decisive. Typical isotherms of electrical conductance against concentration have been reported by many investigators [Bowen, 1943; Roughton, 1951; Saeger, 1960; Lukashov and Savenko, 1980]. A set of electrolytes exhibiting electrical conductivity maxima is presented in Figure 5.20. They discussed the conductivity maxima in the following manner. During the introduction of an electrolyte into water, the electrical conductance of the solution will increase. This is explained by the increase in the number of current carriers (ions), and the slopes of the isotherms indicate the magnitude of the increase. Similarly, when water is added to a liquid electrolyte the conductance of the system increases because of the dissociation of the molecules of the liquid electrolyte and the mobility of the ions formed also increases. The increase in electrical 145 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions conductance at the extreme parts of the isotherm indicates the presence of a maximum on the concentration-conductivity curve at some intermediate point. Vincent [1984] also observed a maximum conductance of lithium salt solutions in aprotic solvents. He mentioned that such a maxima can be interpreted on the basis of the opposing influence of an increasing number of charge carriers on the one hand (ion-ion interaction), and (a) increasing viscosity and (b) increasing ion association with the formation of non-conducting ion pairs, on the other. KOH (80 °C) NaOH (18 °C) Concentration of electrolyte (wt. %) Figure 5.20. Conductivity of aqueous electrolytes of various concentration of KOH and NaOH at constant temperature [Bowen, 1943]. 146 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions It can be seen from Figure 5.20 that an increase in temperature shifts the maximum conductance towards higher concentrations. This effect is explained by thermal dehydration, which disturbs the system of ionic linkages. Conversely, an increase in the charge and hydration of the ions causes the shift of the maximum towards lower concentrations. The electrical conductivities of aqueous solutions of electrolytes have been extensively studied and reviewed during the last 80 years, but most of the theoretical treatments and experimental investigations have been directed towards dilute aqueous solutions. Consequently the available estimation methods are valid only in the dilute solutions at moderate temperatures and pressures. The simplest but very crude equation often used for concentrated solutions is cube root law: Ac = A„-A c1/3 (5-10) where Ae is equivalent conductance of the solution, c is the concentration of the electrolyte, and A is a constant, independent of concentration and chemical nature of the electrolyte, but dependent on its valence type [Horvath, 1985]. The value of A becomes larger with increasing valence of the ions in the electrolyte. The equivalent conductivity at infinite dilution (AJ is usually calculated from the sum of the conductivity of each ion present in the solution (Kohlrausch’s principle). Miller [1956] proposed the following expression for aqueous solutions of NaSCN at concentrations upto 100 mol/1 for 0, 30, and 50°C. AeTlsoin^ A/TVsoin1/3 (5-11) where r|soln= viscosity of the solution, T = absolute temperature, K Vsoin= molar volume of the solution A = constant 147 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The Equation 5-11 has been derived on the assumptions that the conductance and the viscosity of an electrolyte may be considered as rate processes and that ionic migration in the solvent can be regarded as the motion of a sphere in an elastic medium [Lo Surdo and Wirth, 1979]. Also the mobility of an ion, and consequently the conductivity of an electrolyte therefore, depend on the resistance provided by the molecules of solvent to the passage of the ion through the solution (because of viscosity) and the interionic interactions. The conductivity is further reduced at higher concentrations because of ion association. It is clear from the above discussion that the decrease in conductivity of vanadium(V) solutions with increase in concentration is in accordance with the observations made by previous researchers for concentrated solutions. Furthermore, at constant total sulfate/bisulfate concentration, increasing V(V) concentration will hold more sulfate ions as described later in Equations 5-16 to 5-18 resulting in lowering of the free H2S04 concentration. This lower H2S04 concentration will consequently lower the free H+ ions which leads to a decrease in conductivity with increasing V(V) concentration. 5.3.4 Effect of the State-of-Charge on Stability The stability of vanadium(V) solutions is dependent on the state-of-charge (SOC) or oxidation state of the solution (i.e. V(V):V(IV) ratio) as discussed earlier in the literature review (Section 2.3.2). The effect of oxidation state was studied on 5M vanadium solution in 6M total sulfate/bisulfate. Two solutions were prepared having total vanadium [V(V)+V(IV)] concentration of 5M, one with oxidation state of 4.85 [Solution A, 85% V(V) +15% V(IV)] and the other with oxidation state of 4.95 [Solution B, 95% V(V) + 5% V(IV)]. The stability of these two solutions with different state-of-charge (SOC) was investigated at room temperature, and their concentration profiles with time are shown in Figure 5.21. 148 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions U 4 - — 5M V with oxid. state of 4.95 5M V with oxid. state of 4.85 TIME (hours) Figure 5.21. Variation in 5M V(V) solution in 6.0M H2S04 with different SOC at room temperature. It was observed that the solution with total vanadium [V(V)+V(IV)] concentration of 5M in 6.0M H2S04 with an oxidation state of 4.95 [Solution B, 95% V(V) + 5% V(IV) or 4.75M V(V) + 0.25 M V(IV)] decreased in concentration to 4.2M total vanadium (or 3.95M V(V) + 0.25M V(V)) after 1000 hours (42 days), a drop of 16%, while the one in 6.0M H2S04 with oxidation state of 4.85 [Solution A, 85% V(V) + 15% V(IV) or 4.25M V(V) + 0.75 M V(IV)] did not decrease its concentration over the same period of 1000 hours. Slightly lower oxidation state or the presence of low levels of V(IV) species improves the stability of V(V) solutions greatly even at total vanadium concentrations as high as 5M containing total sulfate/bisulfate concentration of 6M. This could be due to the interactions between the V(IV) and V(V) ions in the solution giving rise to enhanced stability of the V02+ species. 5.3.5 Effect of Stirring on Stability The stability of supersaturated solutions is very often affected by mechanical factors such as filtration, stirring, ultrasound etc. It was observed before that V(IV) solutions are very sensitive to stirring and precipitate quickly. To find out the effect of stirring on the stability of V(V) solutions, a 4.0M V(V) solution 149 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions in 6.0M H2S04 was kept stirring at a speed of 200, 300 and 400 rpm at room temperature (about 20°C). No sign of precipitation was observed for three days and it was found that the concentration of these solutions also remained constant. Another solution of concentration 3M V(V) in 5M total sulfate/bisulfate was studied at about 200 rpm and 30°C. It was found that 3V5S solution did not show any sign of enhanced precipitation due to stirring and the induction time was about 6 days which is close to the observation made during unstirred experiments at 30°C. Thus, it can be concluded that, stirring has no effect on the induction time in the precipitation of V(V) solutions. 5.3.6 Electrochemical Behaviour of Vanadium(V) Solutions The electrochemical behaviour of supersaturated vanadium(V) solutions was studied using cyclic voltammetry as this is an effective electro-analytical technique for determining the variations in the positions of the V(V)/V(IV) redox couple peaks at different V(V) concentrations in various total sulfate/bisulfate levels. Information about reversibility of the V(V)/V(IV) system was obtained. The effect of various parameters such as V(V) concentration, total sulfate/bisulfate concentration, and elapsed time on the electrochemical activity of V(V) solutions was investigated. 5.3.6.1 Effect of Elapsed Time The electrochemical behaviour of vanadium(V) solutions with time was studied using cyclic voltammetry. The cyclic voltammogram (CV) of all V(V) solutions in different concentrations of total sulfate/bisulfate was obtained to investigate the effect of elapsed time on peak current and peak potential separation. The cyclic voltammogram of 3M V(V) solution in 5M total sulfate/bisulfate is shown in Figure 5.22. The solid line (curve 1) shows the CV of the V(V) solution when prepared initially, the dotted line (curve 2) is the CV of same solution after 1000 hours and the dashed line (curve 3) is the CV scanned for solution after 1000 hours between 1.45V and 0.2V. 150 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions -1.20 -0.80 -0.40 0.00 0.40 0.80 1.20 1.60 Potential (V) vs SCE. Figure 5.22. Cyclic voltammogram of 3M V(V) solution in 5M total sulfate/bisulfate at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C (Initial potential: 1.45 V; Electrode Area: 0.1cm2). The scan of curve 1 was started at an initial potential of 1.45V and as the potential was scanned in the negative direction, a cathodic peak was observed at a potential of 0.83 V corresponding to the reduction of V(V) to V(IV). By sweeping the potential in the negative direction further, a second cathodic peak was observed at about -0.67V which is associated with the reduction of V(IV) to V(II). Reversing the potential sweep at -0.85 leads to the oxidation of the V(II) to V(III) and the V(V) at -0.46V and 1.02V, respectively. The broad anodic peak appearing between 0.4 and 0.7V vs SCE is probably indicating the presence of some intermediate species formed during the cathodic scan. To confirm this explanation, another scan (curve 3) was performed by limiting the final potential to 0.2V and reversing the scan in the positive direction, so that V(V) was reduced to V(IV) and then reoxidised to V(V) by reversing potential 151 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions at 0.2V. The broad peak present in curves 1 and 2 between 0.4 and 0.7V disappeared in curve 3, because only V(IV) was reducing to V(V) during the anodic scan and any intermediate arising from V(II) and V(III) was absent. The anodic peak current at 1.01 Volts in curves 1 and 2 was found to be 4.65 and 4.63 mA respectively, and this remained practically the same over a period of 1000 hours. The cathodic peak current measured at 0.836 and 0.824 Volts in curve 1 and curve 2 was 4.41 and 4.55 mA respectively, again a small difference (~3% ) was observed after 1000 hours. The peak potential separation of the V(V)/V(IV) redox couple for curve 1 and curve 2 exhibited a similar level of irreversibility as the observed peak potential separation was 0.187V and 0.185V respectively. It appears that at 20°C, the 3M V(V) solution in 5M total sulfate/bisulfate is stable over a period of 1000 hours without changing its electrochemical behaviour significantly. The electrochemical behaviour of 4M V(V) solution in 6M total sulfate/bisulfate monitored initially (curve a), after 500 hours (curve b) and after 1000 hours (curve c) by obtaining cyclic voltammogram is shown in Figure 5.23. It can be observed that the scans are very similar, showing good stability of the 4M V(V) solution in 6M total sulfate/bisulfate for about 1000 hours. It also indicates that the three cyclic voltammogram obtained at different times are reproducible and the electrode surface preparation does not influence the voltammetric analysis. 152 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 6.0 Curve a Fresh V (V) Solution. Curve b After 500 Hours 4.0 Curve c After 1000 Hours. < 2.0 ? 0.0 c -6.0 -1.20 -0.80 -0.40 0.00 0.40 0.80 1.20 1.60 Potential (V) vs SCE Figure 5.23. Cyclic voltammogram of 4M V(V) solution in 6M total sulfate/bisulfate as a function of time at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C. The cyclic voltammogram of all the V(V) solutions was obtained initially when these solutions were prepared and after elapse of 1000 hours. No significant difference was observed in the peak potential separation (AEP) of all the V(V) solutions (2M - 5M V(V) in 5, 6 and 7 M H2S04) over a period of 1000 hours and the AEP values were found to be greater than 0.056V indicating that the system is quasi-reversible or irreversible. However, the V(V)/V(IV) redox couple can be considered quasi-reversible for the V(V) concentrations between 2 - 3M with a AEp of about 0.12V - 0.15V, and the system shows more irreversibility by increasing V(V) concentrations in the range of 4 - 5M reaching a AEp value of about 0.2 - 0.3V. 153 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions No appreciable difference was found in the peak current of all the V(V) solutions initially and after 1000 hours, as observed above in the case of 4M V(V) solution in 6M total sulfate/bisulfate(Figure 5.23). In general it can be stated that the aging of 2 -5M V(V) solutions in 5-7M total sulfate/bisulfate for a period of 1000 hours did not affected the electrochemical behaviour significantly. 5.3.6.2 Effect of V(V) Concentration This subsection deals with the study of the effect of increasing V(V) concentration on the electrochemical behaviour of the V(V)/V(IV) redox couple. The CV of 2, 3, 3.5, 4 and 5M V(V) solution in 6M total sulfate/bisulfate obtained using a glassy carbon electrode at a scan rate of 0.02 V/s is shown in Figure 5.24. To discuss the effect of V(V) concentration, the anodic and cathodic peak currents for the V(V)/V(IV) couple obtained from Figure 5.24 were plotted as a function of V(V) concentration in Figure 5.25. The magnitude of peak current increases linearly as V(V) concentration was increased from 2M to 3.5M, however, a further increase in V(V) concentration above 3.5M decreases the peak heights. The decrease in peak currents with increasing V(V) concentration above 3.5M may be due to the sharp increase in viscosity as discussed earlier in Figure 5.10. This sharp increase in viscosity results in a decrease in diffusion coefficient (see Section 5.3.6.5) of the vanadium ions which in turn leads to a decrease in peak currents. Furthermore, changes in the interfacial tension properties of the more concentrated solution may reduce the wettability of the glassy carbon electrode in the solution, thereby reducing the effective surface area and decreasing peak currents [Skyllas-Kazacos, Menictas and Kazacos, 1996]. 154 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions /Curve 1 3.5M V(V) Solution.V v Curve 2 3.0M V(V) Solution. i / Curve 3 2.0M V(V) Solution. vV Curve 4 4.0M V(V) Solution. \27 Curve 5 5.0M V(V) Solution. Potential (V) vs SCE Figure 5.24. Cyclic voltammogram of 2 - 5M V(V) solution in 6M total sulfate/bisulfate at a scan rate of 0.02V/S using glassy carbon electrode against SCE at 20°C. The peak potential separation (AEp) with increasing V(V) concentration is shown in Figure 5.26. The value of AEp increases with increasing V(V) concentration indicating increasing irreversibility of the system. The peak currents of 2 -5M V(V) solutions in 5, 6 and 7M total sulfate/bisulfate is shown in Figure 5.27 which has reproduced similar behaviour as that of V(V) solutions in 6M total sulfate/bisulfate. The optimum V(V) concentration to obtain highest peak current with a peak potential separation of about 0.15V is therefore, about 3 - 3.5M and the system may be considered as quasi-reversible. 155 Chapter Figure PEAK CURRENT (A) -0.005 -0.004 -0.003 - - 0.002 0.001 0.001 0.003 0.002 0.004 5 5.25. ------0.02V/s Effect (Solution: using of V(V) glassy 2-5M V(V) concentration carbon V(V) CONCENTRATION in 156 electrode 6M Stability total on of sulfate/bisulfate). peak Supersaturated against (M) currents SCE Vanadium(V) at at 20°C. an scan Solutions rate of Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 0.3 -- 0.1 - INITIAL V(V) CONC (M) Figure 5.26. Effect of V(V) concentration on peak potential separation at an scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C (Solution: 2-5M V(V) in 6M total sulfate/bisulfate). 5.3.6.3 Effect of Total Sulfates/Bisulfate Concentration The effect of total sulfate/bisulfate concentration was investigated by taking the CV of V(V) solutions at constant V(V) concentration and varying total sulfate/bisulfate concentration. A typical CV obtained for 4M V(V) solution in 5, 6 and 7M total sulfates using a glassy carbon electrode at a scan rate of 0.02 V/s is shown in Figure 5.28. Similar CV’s were obtained for 2, 3, and 5 M V(V) in 5, 6 and 7M total sulfates. Increasing the concentration of total sulfate/bisulfate decreases the magnitude of peak current as illustrated in Figure 5.29. Increasing the total sulfate/bisulfate concentration is believed to increase the formation of electrochemically inactive vanadium-sulfate complexes and polyvanadic species and in turn increases viscosity. The combined effect of formation of electrochemically inactive species and increase in viscosity, therefore, is to decrease the peak current heights for the V(V) solutions. It can 157 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions also be observed that the effect is more pronounced at 5M V(V) concentration in 7M total sulfate/bisulfate. 5M Total S 6M Total S 0.004 -- Ipa 7M Total S 0.002 -- -0.002 -- -0.004 - -0.006 V(V) CONCENTRATION (M) Figure 5.27. Effect of V(V) concentration on peak currents at a scan rate of 0.02V/S using glassy carbon electrode against SCE at 20°C. 158 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Curve 1 4M V (V) in 5M Total Sulfate. Curve 2 4M V (V) in 6M Total Sulfate. Curve 3 4M V(V) in 7M Total Sulfate. Potential (V) vs SCE Figure 5.28. Cyclic voltammogram of 4M V(V) solution in 5, 6 and 7 M total sulfate/bisulfate at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C. Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 0.004 - 3M V(V) 0.003 - 4M V(V) 2M V(V) 0.002 - 5M V(V) 0.001 - -0.001 -- -0.002 - -0.003 -- -0.004 - -0.005 TOTAL S ULFATF/B K ULFATE CONC (M) Figure 5.29. Effect of total sulfate/bisulfate concentration on peak currents at a scan rate of 0.02V/s using glassy carbon electrode against SCE at 20°C. 160 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions From the analysis of the effect of both V(V) concentration and total sulfate/bisulfate concentration, it can be suggested that the highest concentrations of vanadium(V) and total sulfate/bisulafte may be 3M and 6M respectively to be able to achieve maximum electrochemical activity, in the vanadium redox battery. 5.3.6.4 Calculation of Diffusion Coefficients and Rate Constants The series of cyclic voltammogram obtained at different scan rates (v) using a glassy carbon electrode for 2, 3 and 4M V(V) solution in 6M total sulfate/bisulfate are illustrated in Figure 5.30, 5.31 and 5.32 respectively. In all the three cases, the peak heights increases with increasing scan rate and the peak potential separation also increases with increasing scan rate showing the electrochemical irreversibility of the V(V)/V(IV) redox couple reactions. To determine the diffusion coefficient, the anodic and cathodic peak currents of V(V)/V(IV) redox couple were plotted against vl/2 as shown in Figures 5.33 and 5.34 for 3M V(V) solution in 6M total sulfate/bisulfate. Similar plots were drawn for the 2M and 4M V(V) solutions in 6M total sulfate/bisulfate and the diffusion coefficients were calculated according to the procedure described in Section 3.3.2 using the following equation for irreversible reactions. ip = (3.01 x 105) ne«xna)1/2Ae D0l/2C„v1/2 (5-12) where ip is the peak current (A) a is the transfer coefficient v is the scan rate (V/s) Ae is the surface area of electrode (cm2) D0 is the diffusion coefficient (cm /s) C0 is the bulk concentration (mol/cm3) ne = number of electrons na = number of electrons in the rate determining step 161 Chapter Current x10 (A) Figure Scan carbon 5 -1.20 rate 5=0.18V/s. 5.30. for curve electrode Cyclic -0.80 Initial l=0.02V/s, voltammogram for potential -0.40 2M curve V(V) 1.45V Potential 2=0.06V/s, solution 162 0.00 and obtained Stability initial (V) curve in of scan 0.40 Supersaturated for 6M vs 3=0.1 the direction total SCE V/s, first sulfate/bisulfate. 0 curve 80 cycle was Vanadium(V) 4=0.14V/s negative. at 1.20 the Solutions glassy curve 1.60 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions < fNI o X c OJ =3 L-J Potential (V) vs SCE. Figure 5.31. Cyclic voltammogram obtained for the first cycle at the glassy carbon electrode for 3M V(V) solution in 6M total sulfate/bisulfate. Scan rate for curve l=0.02V/s, curve 2=0.06V/s, curve 3=0.1V/s, curve 4=0.14V/s curve 5=0.18V/s. Initial potential 1.45V and initial scan direction was negative. 163 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 1.60 1.20 0.80 < 0.40 7 0.00 o * -0.40 £ -0.80 (_ 5 -1.20 -1.60 -2.00 -1.20 -0.80 -0.40 0.00 0.40 0.80 1.20 1.60 Potential (V) vs SCE Figure 5.32. Cyclic voltammogram obtained for the first cycle at the glassy carbon electrode for 4M V(V) solution in 6M total sulfate/bisulfate. Scan rate for curve l=0.02V/s, curve 2=0.06V/s, curve 3=0.1 V/s, curve 4=0.14V/s curve 5=0.18V/s. Initial potential 1.45V and initial scan direction was negative. 164 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 0.012 - cg 0.008 ■ ■ 0.500 SQRT(r) (V/s)1 Figure 5.33. Anodic peak currents versus scan rate of V(V)/V(IV) couple at the glassy carbon electrode for 3M V(V) solution in 6M total sulfate/bisulfate. 0.000 0.100 0.200 0.300 0.400 0.500 -0.004 - -0.008 - -0.012 Sqrt(r) (V/s)1 Figure 5.34. Cathodic peak currents versus scan rate of V(V)/V(IV) couple at the glassy carbon electrode for 3M V(V) solution in 6M total sulfate/bisulfate. 165 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Although the above equation is derived for systems with a large excess of supporting electrolyte so that ion migration effects can be eliminated, it is of interest to carry out an indicative analysis for the present vanadium solutions. The diffusion coefficients obtained from the slope of Figures 5.33 and 5.34 and Equation 5-12 are thus listed in Table 5.7. It is noticed that increasing V(V) concentration decreases the apparent diffusion coefficient probably due to the increase in viscosity of the concentrated V(V) solutions. The diffusion coefficient estimated using 0.1M V(V) solution in 6M H2SO4 was 2.26E-6 cmV which is of the same order of magnitude as that of published value of 5.7E-6 cmV1 for 0.055M V(V) solution in 1.8M H2S04 [Sum and Skyllas- Kazacos, 1985] thus confirming that the lower diffusion coefficients obtained for 2-4M V(V) solutions is due to the effect of higher viscosities. Table 5.7. Diffusion coefficient for V(V)/V(IV) redox couple obtained from cyclic voltammogram at glassy carbon electrode at different scan rates using various V(V) concentrations in 6M total sulfate/bisulfate. V(V)cone Diffusion Coefficient(cm2/s) (mol/1) Anodic Cathodic 0.1 2.26E-6 1.49E-6 2 9.87E-7 2.27E-7 3 3.45E-7 9.33E-8 4 1.98E-7 4.52E-8 The reaction rate constants for the above V(V)/V(IV) redox couple can be evaluated from the following equation: ip = 0.227nFACok°exp [ -(otnaF/ RT)(EP - E0’) ] (5-13) where k° is the heterogeneous rate constant E0’ is the formal potential, (E° = [ X (Epa + Epc)/2 ] / nc) Epa is the anodic peak potential Epc is the cathodic peak potential nc is the number of cycles 166 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions A plot of ln(ip) versus (Ep - E°) if straight line gives the intercept equal to ln(0.227nFAC°k°), thus providing a value for the rate constant (k°). A system is considered irreversible if the peak potential Ep is dependent on the scan rate v. The ln(ip) vs (Ep - E°) plot of 3M V(V) solution in 6M total sulfate/bisulfate for anodic and cathodic peaks of the V(V)/V(IV) couple are shown in Figure 5.35 and 5.36 respectively and the rate constants are tabulated in Table 5.8. The calculations are based on uncorrected Ep values, so some error in the calculated rate constants would be expected. 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 (Epa - Eo) (V) Figure 5.35. Anodic peak currents versus (Epa - E°) for V(V)/V(IV) couple at the glassy carbon electrode using 3M V(V) solution in 6M total sulfate/bisulfate. It appears that within experimental error the rate constants are fairly constant with increasing V(V) concentration. The published value of rate constant for 0.055M V(V) in 1.8M H2S04 [Sum and Skyllas-Kazacos, 1985] is 7.5E-4 cms'1 which is close to anodic rate constants obtained in this study. However, the cathodic rate constants were found to be lower than the anodic probably due to the oxygen transfer involved according to the following reaction at V(V)/V(IV) couple. 167 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions V02+ + 2H+ + e ^----- V02+ + H20 (5-14) It suggests that the lower value of k° for forward cathode reaction may be due to the difficulty in breaking the V-0 bond in the V02+ ion. -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 Figure 5.36. Cathodic peak currents versus (Epa - E°) for V(V)/V(IV) couple at the glassy carbon electrode for 3M V(V) solution in 6M total sulfate/bisulfate. Table 5.8. Rate constants for V(V)/V(IV) redox couple obtained from cyclic voltammogram at glassy carbon electrode at different scan rates using V(V) solution of various V(V) concentrations in 6M total sulfate/bisulfate. V(V)cone Rate Constant (ems1) (mol/1) Anodic Cathodic 2 3.93E-4 9.95E-5 3 3.11E-4 9.36E-5 4 3.60E-4 6.13E-5 168 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5.3.7 Desupersaturation Experiments of Vanadium(V) Solution The main purpose of this study was to investigate the optimum conditions for a stable vanadium(V)-sulfate/bisulfate system to achieve maximum energy density for the battery. A comprehensive stability evaluation program was undertaken by preparing 2, 3, 4, and 5M vanadium(V) solutions in H2S04 supporting electrolyte containing 5, 6 and 7M total sulfate/bisulfate. The detailed description of these solutions was given in Section 5.3.2. Each solution was evaluated at 20, 30, 40 and 50 °C to establish the stability region, determine the induction time and then study the kinetics of precipitation. These vanadium(V) solution stability evaluation experiments can be divided into three main groups. Group I consists of vanadium(V) solutions in 5M total sulfate/bisulfate, Group II deals with vanadium(V) solutions in 6M total sulfate/bisulfate and Group III vanadium(V) solutions are those prepared in 7M total sulfate/bisulfate. The variation in the vanadium(V) concentration with time for Group I solutions [V(V)-5M Total S] is shown in Figures 5.37 to 5.40. The concentration profiles of Group II solutions [V(V)-6M Total S] is presented in Figures 5.41 to 5.44 and those of Group III solutions [V(V)-7M Total S] are illustrated in Figures 5.45 to 5.48. The supersaturation level of all the vanadium(V) solutions prepared by electrolytic oxidation of V(IV) solution was very high based on the solubility data of V2O5 generated in this study. The supersaturated vanadium(V) solutions at equilibrium did not reach the saturation concentration close to that obtained from solubility experiments of V2O5 in H2S04 of similar conditions. The higher equilibrium V(V) concentration is due to the presence of 2-3% V(IV) species in the supersaturated V(V) solution. This phenomenon of increased equilibrium V(V) concentration at lower SOC was discussed in Section 5.3.4 (Figure 5-20) and also observed earlier by Kazacos et al. [1990]. The measured equilibrium concentration of V(V) species from desupersaturation experiments after 1000 hours is referred to in this thesis as the Apparent Equilibrium Concentration. 169 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 4.0 - 2M V(V) - 5M Total S 3.0 - 20C, 30 C 1.0 - TIME (hours) Figure 5.37. Variation in concentration of 2M vanadium(V) solution in 5M total sulfate/bisulfate at different temperatures. 4.00 - 3M V(V) - 5M Total S 3.00 «H • • • 2.00 - 1.00 - TIME (hours) Figure 5.38. Variation in concentration of 3M vanadium(V) solution in 5M total sulfate/bisulfate at different temperatures. 170 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 4M V(V) - 5M Total S 4.0 It 3.0 2.0 - 1.0 - TIME (hours) Figure 5.39. Variation in concentration of 4M vanadium(V) solution in 5M total sulfate/bisulfate at different temperatures. 4.00 - 3.00 - 2.00 - 5M V(V) - 5M Total S 1.00 - 0.00 4 TIME (hours) Figure 5.40. Variation in concentration of 5M vanadium(V) solution in 5M total sulfate/bisulfate at different temperatures. 171 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5.00 0.00 100 200 300 400 500 600 700 800 900 1000 TIME (hours) Figure 5.41. Variation in concentration of 2M vanadium(V) solution in 6M total sulfate/bisulfate at different temperatures. 3M V(V) - 6M Total S 4.00 - 20C, 30 C 2.00 - 1.00 - TIME (hours) Figure 5.42. Variation in concentration of 3M vanadium(V) solution in 6M total sulfate/bisulfate at different temperatures. 172 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 4M V(V) - 6M Total S 3.00 - 2.00 - 1.00 - TIME (hours) Figure 5.43. Variation in concentration of 4M vanadium(V) solution in 6M total sulfate/bisulfate at different temperatures. 5M V(V) - 6M Total S 3.00 - 2.00 - 1.00 - TIME (hours) Figure 5.44. Variation in concentration of 5M vanadium(V) solution in 6M total sulfate/bisulfate at different temperatures. 173 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 6.0 “I------ 5 0- 2M V(V) - 7M Total S Z o H 4.0 - 2 H wZ 3.0 - u z 20, 30,40, 50 C o u 2.0 in—■------*------■------•------■------* g/—V > 1.0 - 0.0 -I------1------1------1------1------1------H1------1------b1------1------0 100 200 300 400 500 600 700 800 900 1000 TIME (hours) Figure 5.45. Variation in concentration of 2M vanadium(V) solution in 7M total sulfate/bisulfate at different temperatures. 6.00 -1------ w 5 00 .. 3M V(V) - 7M Total S O H ^ 4.00- H WZ Z, 3.00 II« ■------■-----»------■------_ I 0 50C50 C 1 2.00- 1.00 -I------1------1------H1------b1------1------1------1------H1------b1------0 100 200 300 400 500 600 700 800 900 1000 TIME (hours) Figure 5.46. Variation in concentration of 3M vanadium(V) solution in 7M total sulfate/bisulfate at different temperatures. 174 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5.00 -- 4M V(V) - 7M Total S 4.00 n 3.00 - 2.00 - TIME (hours) Figure 5.47. Variation in concentration of 4M vanadium(V) solution in 7M total sulfate/bisulfate at different temperatures. 5M V(V) - 7M Total S 4.00 - 3.00 - 2.00 - 1.00 - TIME (hours) Figure 5.48. Variation in concentration of 5M vanadium(V) solution in 7M total sulfate/bisulfate at different temperatures. 175 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Although the concentration of 4M V(V) solution in 6M total sulfate/bisulfate at 30°C (Figure 5.43) and 3M V(V) solution in 7M total sulfate/bisulfate at 40°C and 50°C (Figure 5.46) appears to be still decreasing after 1000 hours, when further measured one month later, they did not show any significant drop. The V(V) concentrations at 1000 hours for these solutions can thus be considered as the apparent equilibrium concentration. The apparent equilibrium concentrations of V(V) solution along with the solubility data of V2O5 are presented in graphical form in Figures 5.49 - 5.51 where the thick solid line represents the saturation curve and the fine solid lines represent the apparent equilibrium concentration for vanadium(V) solutions with different initial vanadium(V) concentration. Some of the solutions showed no precipitation at 20°C (and 30°C) after 1000 hours. These are represented by a dashed line in the figures. It should be noted here that the saturated V(V) solutions of the solubility experiments contained 100% V(V) species generated from the dissolution of V205 in sulfuric acid whereas supersaturated V(V) solutions obtained from the electrolytic oxidation of supersaturated V(IV) solution contained 2-3% of V(IV) species. The presence of a small amount of V(IV) species in the supersaturated V(V) solutions may be responsible for the higher equilibrium concentrations observed in Figures 5.49-5.51. It was also observed that the higher the initial vanadium(V) concentration, the higher the final equilibrium concentration measured after 1000 hours at each temperature. This is probably due to the higher viscosity of the more concentrated solutions which may slow down the precipitation reaction. It may, however, also suggest the presence of a more stable V(V) species in the more concentrated solutions. The apparent equilibrium concentration of V(V) solutions at a particular temperature reaches lower values in 5M total sulfate/bisulfate (Figure 5.49) compared to that in 7M total sulfate/bisulfate (Figure 5.51). This behaviour is possibly because of the increased stability of 176 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Solb. curve P 3 - TEMPERATURE (C) Figure 5.49. Apparent equilibrium concentration of vanadium(V) solutions in 5M total sulfate/bi sulfate at different temperatures after 1000 hours. Solb curve 2V6S X. . 3V6S 4V6S 5V6S O 3 - TEMPERATURE (C) Figure 5.50. Apparent equilibrium concentration of vanadium(V) solutions in 6M total sulfate/bisulfate at different temperatures after 1000 hours. 177 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions • So lb curve ------2V7S - - -A- - - 3V7S —X—4V7S p 3 - —e—5V7S TEMPERATURE (C) Figure 5.51. Apparent equilibrium concentration of vanadium(V) solutions in 7M total sulfate/bisulfate at different temperatures after 1000 hours. the V(V) solutions due to V(V)-sulfate complex formation at higher total sulfate/bisulfate concentration. The new apparent equilibrium concentration of the vanadium(V) solutions will serve as a basis for calculating the degree of supersaturation and kinetic parameters. The induction times exhibited by the solutions in these three groups at different temperatures are discussed in the following section. The effect of temperature and sulfuric acid concentration (total sulfate/bisulfate) on the stability of vanadium(V) solutions and the kinetics of thermal precipitation is also presented. 5.3.8 Induction time One of the main objectives of this study was to determine the induction times of various supersaturated vanadium(V) solutions at different temperatures. Due to the intense colour of the highly supersaturated V(V) solutions, the start of precipitation was difficult to observe visually. In this study therefore, the time 178 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions required to reduce the concentration of vanadium(V) solutions by 2% (considered as a significant change) was taken as the induction time. The observed induction times of all the vanadium(V) solutions under study are listed in Table 5.9. The effects of total sulfate/bisulfate concentration and temperature on induction times of vanadium(V) solutions are illustrated in graphical form in Figure 5.52, 5.53 and 5.54. It should be noted that in each of these graphs the solutions which are shown to have an induction time of 42 days, did not in fact precipitate at all during the 42 day test period. These are represented by dashed lines in the Figures 5.53 and 5.54. Table 5.9. Induction times of vanadium(V) solutions at various temperatures. Induction Timetdavsl Solution 20°C 30°C 40°C 50°C Description 2V5S >42 >42 6 1 3V5S 15 8 1 <1 4V5S 12 6 1 <1 5V5S 4 2 <1 <1 2V6S >42 >42 18 6 3V6S >42 42 8 1 4V6S >42 28 3 <1 5V6S 5 1.5 <1 <1 2V7S >42 >42 >42 >42 3V7S >42 >42 26 21 4V7S >42 30 9 3 5V7S 10 3.5 1 <1 179 Chapter Figure 5 INDUCTION TIME (day;) n> INDUCTION TIME (day;) 5.53. — Induction Induction ------* — 50 C 30 20C C times times different different INITIAL of of INITIAL V(V) V(V) 180 V(V) temperatures. temperatures. Stability solutions V(V) solutions CONC CONC of (M) Supersaturated in in (M) 5M 6M total total Vanadium(V) sulfate/bisulfate sulfate/bisulfate Solutions at at Chapter 5 Stability of Supersaturated Vanadium(V) Solutions ------20 C -- 30 C INITIAL V(V) CONC (M) Figure 5.54. Induction times of V(V) solutions in 7M total sulfate/bisulfate at different temperatures. From the analysis of the induction time data, it can be stated that while V(V) solutions in 7M total sulfates were the most stable, the V(V) solutions containing 5M total sulfates were found to be least stable. When the V(V) solution in the positive half-cell of the vanadium redox battery transforms to the discharged state, the vanadium solution exist as V(IV) species whose instability increases with increasing total sulfates. Keeping both the V(IV) and V(V) solution precipitation tendency in mind therefore, one should optimise the total sulfate concentration to obtain a stable vanadium solution of maximum concentration to be able to achieve the higher energy density. 5.3.9 Effect of Temperature on Stability The literature review of the stability of V(V) solutions indicated that it suffers from thermal precipitation at higher temperatures. Desupersaturation experiments were conducted to evaluate the effect of temperature on the stability of V(V) solutions over an extended period of time. 181 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The effect of temperature on the stability of V(V) solutions is shown in Figure 5.49, 5.50 and 5.51 for V(V) solutions in 5M, 6M and 7M total sulfate/bisulfate respectively. Increasing temperature decreases the stability of V(V) solutions generally because of the endothermic nature of precipitating reaction of V(V) ions, but it was noticed that V(V) solutions in the range of 2M-4M in 6M and 7M total sulfate/bisulfate were found to be more stable up to 30°C. For example, the 4M V(V) solutions in 6M and 7M total sulfate/bisulfate at 30°C dropped in concentration by only 5% and 3% respectively after 1000 hours, whereas 4M V(V) solution in 5M total sulfate/bisulfate decreased in concentration by 17% over the same period of 1000 hours. While vanadium(V) solutions in 5M and 6M total sulfate/bisulfate showed significantly increased precipitation above 30°C, the V(V) solution in 7M total sulfate/bisulfate was found to be stable up to 50°C. At 40°C, 4M V(V) solution in 5M and 6M total sulfate/bisulfate dropped in concentration by 47% and 34% respectively and in 7M total sulfate/bisulfate the V(V) concentration decreased by only 6%. An acceptable total sulfate/bisulfate concentration required for reasonable stability of V(V) solutions up to 40°C may thus be 6M. 5.3.10 Effect of Sulfuric Acid Concentration on Stability Sulfuric acid concentration plays a very important role in stabilising the supersaturated vanadium(V) solutions. Changes in H2S04 concentration basically changes the concentration of H+, HS04' and S042 ions which has direct interaction with the precipitation phenomena of V(V) species. Since the analysis of the samples was carried out by ICP which gives total sulfates and bisulfate, the results are discussed in terms of total sulfate/bisulfate present in the system. The desupersaturation experiments were designed to study the effect of sulfuric acid concentrations of 5M, 6M and 7M total sulfate/bisulfate on the stability of V(V) solutions. The stability of V(V) solutions increased with increasing total sulfate/bisulfate concentration. The effect of total sulfate/bisulfate concentration on 3M and 4M V(V) solution after 1000 hours is 182 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions shown in Figure 5.55 and Figure 5.56 respectively and it is obvious that the solutions are most stable in 7M total sulfate/bisulfate. At 40°C, the drop in concentration of 3M V(V) solution in 5M total sulfate/bisulfate after 1000 hours was found to be 46% as compared to 8% in 6M total sulfate/bisulfate and 5% in 7M total sulfate/bisulfate. The 4M V(V) solution at 40°C and after 1000 hours showed 47% decrease in V(V) concentration in 5M total sulfate/bisulfate, 34% in 6M total sulfate/bisulfate and 6% in 7M total sulfate/bisulfate. The increased stability at higher H2S04 concentration is due to the presence of more H+ ions (increased ratio of H+ ions to V(V) ions) which favours the following reaction in the forward direction [Kazacos et al 1990; Baes and Mesmer, 1976]. V205 (c) + 2H+ 2 V02+ + H20 (5-15) The stability might also be improved because of excess HS04 /S042 ions (increased ratio of S to V(V) ions) available at higher H2S04 concentration which could prevent precipitation of V02+ ions to V205 by forming sulfate complexes with V02+ ions according to the following reactions [Kazacos et al, 1990; Ivakin, 1966]: vo2+ + hso4‘ V02S04' + H+ (5-16) vo2+ + so42‘ , - V02 S04- (5-17) vo2+ + vo2 so4------(vo2)2so4 (5-18) 183 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 3M V(V) initial cone TOTAL S ULFATF7B IS ULFATE (M) Figure 5.55. Effect of total sulfate/bisulfate concentration on stability of 3M V(V) solution after 1000 hours at different temperatures. 4M V(V) initial cone TOTAL S ULFATFVB IS ULFATE (M) Figure 5.56. Effect of total sulfate/bisulfate concentration on stability of 4M V(V) solution after 1000 hours at different temperatures. 184 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Further, increase in stability could be attributed to the formation of a dimer proposed by Madie et al [1984] for V(V) ions in sulfuric acid media represented by the following reactions: 2V02+ V2042+ (5-19) 2V02+ + H+ .------V2034+ + H20 (5-20) They obtained the evidence for V(V) dimerisation by UV-visible, Raman and NMR spectroscopy, X-ray scattering, and cyclic voltammetry. Although increasing sulfuric acid concentration increases the stability of V(V) solution, the main limitation on sulfuric acid concentration arises from the stability of V(IV) species. It appears from the overall evaluation of the desupersaturation experiments that 3M V(V) solution in 5M to 6M total sulfate/bisulfate may be recommended for use in high energy density vanadium redox battery. 5.3.10.1 51V NMR Studies of Vanadium (V) Solutions with Different Total Sulfate/bisulfate The V(V) solution was further analysed by obtaining 51V NMR spectra of 2M V(V) solution in different total sulfate/bisulfate concentration using a Bruker ACP-300 spectrophotometer with a 10 mm broad-band probe tuned to observe 51V at 78.94 Mhz. Samples of approximately 3ml were measured at 300 K, without lock and are referenced externally to VOCl3 (0 ppm). Figure 5.57 shows the 51V NMR spectra recorded for 2M V(V) solutions in 5, 6 and 7M total sulfate/bisulfate at room temperature. The NMR spectra showed a peak at around -560 ppm, with increasing broadening at higher total sulfate/bisulfate concentrations. This may be due to the high viscosity of the medium. 185 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The peak areas or intensities can not be regarded as accurately proportional to the concentration of 51V present, however, the 51V NMR spectra of 2M V(V) solution indicated the presence of more V02+ species in 5M total sulfate/bisulfate as compared to that in 6M and 7M total sulfate/bisulfate. Again, these results suggest that a different V(V) species may be formed at higher sulfate levels, which is consistent with the results from the cyclic voltammetric studies. 100 0 -100 -300 -500 -700 -900 -1100 (ppm) Figure 5.57. 5INMR spectra of 2M V(V) solution in 5, 6 and 7M total sulfate/bisulfate at room temperature. 186 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5.3.11 Kinetics of Thermal Precipitation of Vanadium(V) Solutions 5.3.11.1 Kinetics of Crystal Growth A knowledge of precipitation kinetics of vanadium(V) species is of considerable interest in predicting the performance of high energy density vanadium redox batteries. The precipitation of supersaturated vanadium(V) ions can be represented by the following simplified reaction. 2V02+(aq) + H20(aq) V205(c) + 2H+(aq) (5-21) In an earlier study of the thermal precipitation of V205 from 2M V(V) solutions over the temperature range of 30°C - 60°C, Cheng [1991] assumed the first order reversible reaction and represented the rate of precipitation as follows: -dCv /dt = kf Cv - kb CH (5-22) where kf and kb are the forward and backward rate constants, Cv and CH are the V(V) and H+ ion concentrations respectively at any time t. At t—0, Ch — CHo and Cy = Cy0 Using mass balance, at any time t, CH - CHo = CVo - Cv When the reaction reaches equilibrium, CH = CHe, Cv = Cve and kf Cve — kbCffe The following equation was derived after substituting for CH in Equation 5-22 -dCy/dt = (kf +kb)(Cv -CVe) (5-23) which on integration produced log(Cy - Cve) = “(kf + kb) t + log(Cy0 - Cve) (5-24) 187 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions From the plots of log(Cv - Cve) vs t and using values of the equilibrium constant determined separately, the average values of kf and kb obtained at 30°C were 0.00288 hr'1 and 0.00055 hr'1 respectively. Cheng’s results thus showed that kf is considerably greater than kb over the temperature range of 30°C - 60°C. On the basis of above discussion it is seen that for the present study of V205 thermal precipitation, it should be possible to use the general form of the rate equation suggested by Nancollas and Purdie [1964], Mullin [1980] and Yeboah et al [1994] discussed earlier in Section 3.2.3. -dC/dt = kg (C - Ceq)g (5-25) where kg is the overall rate constant based on the concentration driving force, and ‘g’ is the order of reaction. 5.3.11.2 Evaluation of Rate Constants Growth curves representing the variation in concentration of supersaturated vanadium(V) solution with time are shown in the previous Section (Figures 5.37-5.48). To evaluate the rate constants Equation 5-25 can be rewritten as -log(-dC/dt) = -logkg - g log(C - Ceq) (5-26) Thus, a plot of -log(-dC/dt) versus -log(C - Ceq), if linear, gives a slope of ‘g’ as the order of reaction, and the intercept at -log(C - Ceq)=0 determines the effective rate constants kg. Figure 5.58 shows the plot of -log(-dC/dt) versus -log(C - Ceq) for 4M V(V) solution in 5M total sulfate/bisulfate (4V5S) at 40°C. In this figure, the y-axis shows the decrease of the crystal growth from bottom to top, and the x-axis shows the decrease in relative supersaturation from left to right. 188 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 5.0 4.0 S' 3.0 D 1.0 0.0 -0.50 0.00 0.50 1.00 1.50 2.00 -log(C-Ceq) Figure 5.58. Plot of growth rate of 4M V(V) solution in 5M total sulfates against relative supersaturation at 40°C (see Figure 5.39 for Cone vs time). It can be observed from Figure 5.58 that there is a short transition period in the beginning where the rate does not obey the rate equation (Equation 5-25). During this period, probably only primary nucleation is occurring. When the primary nucleation is completed, the number of growth sites becomes constant and the crystal growth occurs predominantly on these sites. The growth rate is then expected to follow the standard rate equation [Lee et. al, 1988]. Figure 5.58 shows that after the transition period, a linear region is observed in the plot, with change in slope at a value of -log(C-Ceq) of approximately 1.40, which corresponds to a time of 528 hours and V(V) concentration of 2.17M. Under certain experimental conditions therefore, the growth rate appears to obey a second order reaction model for some time during the main crystal growth period due to high supersaturation and then changes to first order kinetics when the supersaturation drops to lower levels. The growth rates beyond the transition period are plotted in Figure 5.59 for 4V5S solution at various temperatures during the main growth period. 189 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions 4.0 -- 2.0 -- 1.0 -- -log(C - Ceq), mol/1 Figure 5.59. Plot of growth rate of 4M V(V) solution in 5M total sulfates against relative supersaturation at different temperatures. Although the initial concentration was the same for all the three plots, different temperatures exhibited different equilibrium concentrations and different slopes. At 30°C, the supersaturation ratio (Co/Ceq) was 1.2 and the slope (reaction order, g’) was found to be 1.5, at 40°C the supersaturation ratio was found to be 1.9 and the slope obtained was 1.8, and at 50°C the supersaturation ratio was 2.5 and the corresponding slope was 1.8. The differential form of the equation (Equation 5-26) was used initially to evaluate the reaction order and rate constants of all the solutions. Plots similar to Figure 5.59 were drawn for all the desupersaturation experiments of vanadium(V) solutions in 5M and 6M total sulfate/bisulfate, the slopes (g’) and corresponding rate constants calculated from the intercept (kg’) are tabulated in Table 5.10 and actual plots with regression coefficients are illustrated in Appendix G. Integrated form of rate equation (5-25) with appropriate reaction order (1 or 2) was then used to re-evaluate the rate constants. In all the cases where the slope was found to be 1.5 or more the reaction order was assumed as 2, and their respective rate constants were evaluated using the integrated form of the second order rate equation: 1/(C - Ceq ) - l/( C0 - Ceq ) = kt (5-27) 190 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions where C is the concentration at any time t, Ceq the equilibrium concentration, C0 the initial concentration and k the effective rate constant. It should be noted that the effective rate constant k is actually (ks) where s is the surface area as discussed earlier in Section 3.2.3. Davies and Nancollas [1955] reported that in crystallisation experiments, the area s available for reaction could be taken as constant. However, a surface area correction factor is necessary in the case of dissolution since a considerable amount of seed is dissolved during the experiments. Nancollas and Purdie [1964] also mentioned that in many systems the effective growth area of the crystals becomes constant at a certain stage in the process even though the crystal increase in size. In this study therefore, it was assumed that after the transition period (observed in Figure 5.59) the surface area remains constant and thus effective rate constant (ks) or k were evaluated. In some cases when the supersaturations were low and the reaction order was found to be less than 1.5 (using Equation 5-25) during the main crystal growth period then, first order reaction kinetics was assumed and the rate constants were calculated by the following equation: log[(C0 - Ceq ) / ( C - Ceq )] =kt (5-28) The reaction order (g) and rate constants (kg or kd) were re-evaluated using the appropriate integrated rate equations (5-27 or 5-28) and the kinetic data are listed in Table 5.11. The analysis of the kinetic data presented in Table 5.11 reveals that the reaction order is dependent on the supersaturation of the V(V) solutions. It appears that the growth rate obeys first order reaction kinetics for all the solutions at lower temperatures below 30°C exhibiting low supersaturations with crystal growth controlled either by diffusion or surface reaction. At high supersaturations second order precipitation rate was observed. The rate of V2O5 precipitation increases with increase in temperature however, the increased temperature leads to increased supersaturations caused by the decrease in the solubility of V2O5. 191 Chapter Table 5.10. Sum m ary of V(V) de-supersaturation rate data: slope(g’) and kg’ calculated from intercept of log(-dC/dt) vs log(C-Ceq) plots 5 oo oo oo Q •n oo oo oo oo oo oo s c <0 o P cn in > 00 poop — — OO ^ no d ON co NO - oo oo — in ^ O £ wo O OO (N ON d 8 CO Ol oo O ö o o oo d o n > (N — Tf n ' n ■ p — t"; r4 O >n in > oo d ON Tt. 2° d o o co ; 1 of p p p ~ odd o O CNOt"; T 00 — Supersaturated NO co 00 > d o (N co in I I I f ’ p — O P p oo p — r- in NO © > 00 CN o o NO Vanadium(V) • U ^ co U W T3 T3 w / u rj 5 .. U r ~ 2 w U O 03 «3 a, 2 cd S Tr c3 »■H O C C/3 ^ 3 It I h F T3 U 'S. iU - -a u 2 3 t U u 'S JD ifa " 2 -tf 60 o 5 cx c/3 (D > o Ö o ° 03 od S c D o CX o W) > C/3 o &0 II öo o O II I 3 ■ 8 M “ -z: U 3 ^ W ^ -b .2 i s- > < W rj n W s O — — = cd o a O" cx cx c3 ’ Chapter Table 5.11. Summary of V(V) de-supersaturation kinetic data with corresponding reaction order and rate constants from integrated rate equations. 5 on 11 '§ o e on on on on on on on .B* C/3 Q 'S. c ö o © CM d o O co m poop cm > m on r- Ö o o eo S CM d o o d o O 3" vO OO d o co r- CM © o SO tj — oo 3" m > on - 2 .4 o in CM d o oo d o CO o Os d o in vO m CM CM 3" o m on M" > 2 .5 195 so o d o o CM 3; d O O CM p d o m in > m on oo CM cm CM d o oo 10.2 Stability p SO © cm > on d o O oo cm 1 © O d o O CM oo d o co CM CM r- — sO on > of Supersaturated © p d >n CM O CM CM as d o CM C" CM SO on > 2 .0 so d o o r- CM d as m so o O O CM CM in CM o co CM d as > on o co oo 2 .0 Vanadium(V) • TD • -o O-i T u T » W u u u O Cd c oo on S w s s »jH c/3 0 *§ £ £ ^ v 7 P M a 0 rs 3 3 O o C 3 Ho U 3 p ^ -X P M r ’ U U :> > S ^ B O or «2 2 3 C_> 3 O 3 “ ° C S 3 II 11 ll ? > Solutions U = I W < u O o £ ’ Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The increased supersaturations at higher initial V(V) concentrations and higher temperatures leads to the enhanced diffusion rates so that the precipitation becomes reaction controlled, thus shifting the reaction to the second order dependence. The reaction order and rate constants determined in the present study at low supersaturations are comparable with those of Cheng [1991]. Although Cheng has considered both the forward and the backward reactions, the rate equation obtained [ log(Cvo - Ceq ) / ( C - Ceq )] = (kf + kb)t ] was similar to that of Equation 5-28 where the effective rate constant k is equal to kf + kb. Under conditions where the reaction order in the present study was one, the effective rate constants estimated in the present work are close to the forward rate constants reported by Cheng [1991] for 2M V(V) solutions. As mentioned previously, the backward rate constants obtained by Cheng were very low, indicating negligible backward reaction rates. At high supersaturations the reaction order with respect to V(V) ion was found to be 2. Considering a reversible reaction therefore, and assuming second order reaction with respect to V(V) ion and first order with respect to H+ ion, the following rate equation is obtained -dCy/dt = kfCv2-kbCH (5-29) where kf and kb are the forward and backward rate constants, Cv and CH are the V(V) and H+ ion concentrations respectively at any time t, and Ceq the equilibrium V(V) ion concentration. Using mass balance and equilibrium condition CH can be eliminated and Equation 5-29 transforms to the following form: -dCv/dt = kfCv2+ kbCv - (kf Ceq 2 + kbCeq) (5-30) 194 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Integration of Equation 5-30 yields [log(-Cv + Ceq) - log( kf Cv + kf Ceq + kb) ]/[2 kf Ceq + kb] “ [l°g(-CVo + Ceq ) " log(kf Ceq + kf Cvo +kb) ]/[2 kf Ceq + kb] = -t (5-31) Evaluation of kf and kb was difficult from Equation 5-31 because of its complicated form therefore, the constants kf and kb were evaluated by regression analysis using Equation 5-30 and experimental data -dCv /dt, Cv and Ceq. The experimental data does not fit Equation 5-30 very well and the predicted values of -dCv/dt showed high deviations from the experimental data. When a second order reversible model is assumed, the rate equation obtained is as follows -dCv /dt = kf Cv2 - kbCH2 (5-32) using mass balance and equilibrium expression Equation 5-32 reduces to -dCv/dt = kf Cv2 - ktU^kf / kb))Ceq + Ceq - Cv))2 (5-33) The integrated form of the above differential equation (Equation 5-33) will be much more complicated than that of Equation 5-31 and highly non-linear to perform regression analysis. Therefore, Equation 5-33 was used to perform regression analysis to evaluate the constants kf and kb. Again high deviations was observed between predicted values of -dCv /dt and the experimental data. Davies and Jones [1949] and Nielsen [1979] also noticed bad data fitting with the use of rate equation considering reversible reactions and they recommended the use of rate equation similar to that of Equation 5-25, which gave better representation of their kinetic data for the precipitation experiments. In this study also excellent agreement between the proposed second order rate law (Equation 5-25) and the experimental data is illustrated in Figure 5.59. The kinetics of precipitation of 3M V(V) solution in 5M total sulfate/ bisulfate 195 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions was also studied at 30°C with stirring of the solution at about 200 rpm. It was noticed that the stirring did not influence the induction time but the precipitation rate was higher as observed by the lower equilibrium concentration of 2.35M compared to 2.58M for unstirred experiments after about 500 hours, thus confirming diffusion controlled crystal growth at conditions of low supersaturations. Concentration profiles for the desupersaturation experiments of 3M V(V) solution in 5M total sulfate/bisulfate with and without stirring is shown in Figure 5.60. Unstirred Stirred TIME (hours) Figure 5.60. Concentration profiles of 3M V(V) solution in 5M total sulfate/bisulfate with and without stirring at 30°C. Another experiment was conducted similarly with stirring using 4M V(V) solution in 5M total sulfate/bisulfate at 30°C. The absence of any appreciable effect of mixing observed during this study supports the surface reaction control mechanism at high supersaturations. The first order diffusion controlled growth rates at lower V(V) supersaturation and second order surface-reaction-controlled growth at higher supersaturation 196 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions were further confirmed by calculating the activation energies as presented in the following Section. 5.3.11.3 Dependence of Rate Constants on Temperature The rate constants calculated from the experimental data were used to estimate the activation energy by the following relationship: kg = Ag exp(- Ea/RT) (5-34) where kg is the growth rate constant, Ag preexponential factor, Ea activation energy, R gas constant and T is temperature in K. The kinetic data obtained from the vanadium(V) solutions in 5M total sulfate/bisulfate were found to be more useful as precipitation was observed at all the four temperatures. The Arrhenius plot using second order rate constants from precipitation of V(V) solutions in 5M total sulfate/bisulfate at high supersaturation levels is shown in Figure 5.61 and the activation energy was found to be 77.2 kJmol1. 1000/T (K) Figure 5.61. Arrhenius plot for the precipitation of V(V) solution using second order rate constants in 5M total sulfate/bisulfate. 197 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The activation energy calculated similarly from the first order reaction rate constants at low supersaturation levels was 9.0 kJmol'1. The second order dependence of the rate and high activation energy of 77.2 kJmol"1 suggest that the precipitation of V(V) solution in the high supersaturation region (SR > 1.4) is surface-reaction-controlled and at lower supersaturations crystal growth kinetics shifts to first order with small activation energy (9.0 kJmol'1), indicating diffusion controlled growth. The preexponential factor (A) for V(V) precipitation was estimated to be 5.77xl0n (mol/l)'1!!*1 in the above Equation 5-26 during second order crystal growth. This small value compared to 3.6xl015 (mol/1)' V for the standard collision frequency of a bimolecular reaction [Yeboah et al, 1994] indicates that the V(V) precipitation to V205 is a slow reaction. 5.4 SUMMARY OF RESULTS Supersaturated vanadium(V) solution preparation, its properties and stability evaluation experiments were carried out covering the V(V) concentration range of 2M to 5M in initial sulfuric acid concentrations of 5M to 7M at temperatures ranging from 20°C to 50°C. The results of this study are summarised in the following paragraphs. 1. It is recommended to prepare supersaturated vanadium(V) solution by electrolytic oxidation of supersaturated V(IV) solution obtained by the reaction of stoichiometric quantities of V203 and V205 powders in the desired concentration of sulfuric acid solution. 2. Supersaturated V(IV) solution preparation by reacting V205 and V203 in sulfuric acid solution required about 15% excess V203 to obtain the blue colour V(IV) solution with V(IV) species greater than 95%. The 15% extra V203 over stoichiometric amount is needed because of some percentage of X^O/VOSCU present in the industrial grade V203 evident 198 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions from the blue colour of V(IV) species in the initial stages of V203 dissolution in H2S04. Since the supersaturated V(IV) solutions are very sensitive to agitation, they readily precipitate in the electrolysis cell due to nitrogen bubbling during preparation of V(V) solution. Therefore, the stability of V(IV) solution needs to be improved by preheating for an hour at its boiling point of about 115°C and filtering the V(IV) solution twice by Whatmann ashless filter paper. 3. The density of supersaturated vanadium(V) solutions vary from 1.5 gm/cc to 1.8 gm/cc for 2M V(V) solution in 5M total sulfate/bisulfate and 5M V(V) in 7M total sulfate/bisulfate respectively. A correlation has been developed to predict the density of supersaturated vanadium(V) electrolyte as a function of vanadium(V) and sulfuric acid concentration at room temperature. 4. The viscosity of supersaturated V(V) solutions containing total sulfate/bisulfate between 5M and 7M increases gradually with increasing V(V) concentration in the range of 2M to 3.5M, but a further increase in V(V) concentration to 5M increases viscosity exponentially and the effect is more sharper at higher total sulfate/bisulfate concentration. This behaviour indicates that the supersaturated V(V) solutions remain in the hydraulic type flow region at V(V) concentrations below 3.5M and transform to the plastic flow region with further increase in vanadium(V) concentration. The increase in viscosity is due to the formation of large size extended chain polyvanadic molecules and V(V)-sulfate complex formation at higher total sulfate/bisulfate concentration. Also at such high supersaturations, ion distribution attains a degree of order resembling crystallinity and the influence of ion-ion interaction on viscosity increases significantly. 199 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Increasing temperature significantly decreases the viscosity of V(V) solutions. The viscosity of V(V) solutions decreases slightly (3-7%) with time and the effect is more pronounced at lower total sulfate/bisulfate concentrations because of precipitation. A significant drop in viscosity due to moisture absorption was observed when V(V) solutions were exposed to atmosphere. This significant drop in viscosity of vanadium solutions when exposed to atmosphere is probably due to a slight dilution and disturbance of the polyvanadic structure of the supersaturated V(V) solution by absorbing moisture from the atmosphere. Cyclic voltammetry and 51V NMR studies also confirmed that an increase in water content in the vanadium(V) solution breaks the large size vanadium-sulfate complex ions and generates small size free V(V) ions resulting in a significant drop in viscosity and increase in conductivity. 5. It was discovered during the course of the study that supersaturated V(V) solutions absorb significant moisture when exposed to atmosphere. Therefore, the supersaturated V(V) solutions should be stored in closed containers, otherwise they will absorb moisture from the atmosphere, lowering the vanadium and sulfate/bisulfate concentrations. It was found that the sulfuric acid is responsible for moisture absorption from the atmosphere. 6. It was observed that the conductivity of supersaturated V(V) solutions decreases with increasing V(V) concentration for constant total sulfate/bisulfate concentration. The main reason for the decrease in conductivity with increasing V(V) concentration is due to the increased consumption of sulfuric acid during the conversion from V(IV) to V(V) (i.e. V02+ + 2H+ 200 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions conductivity of an electrolyte, depend on the resistance provided by the molecules of solvent to the passage of the ion through the solution (because of viscosity) and the interionic interactions. The conductivity is further reduced at higher concentrations because of ion association. 7. The cyclic voltammogram of the supersaturated vanadium(V) solutions revealed that in the concentration range of 2 - 3.5 M the peak height increases with increasing V(V) concentration, while further increasing V(V) concentration decreases the peak currents. This decrease in peak current with increasing V(V) concentration may be attributed to the following reasons. Firstly, increasing the V(V) concentration increases viscosity gradually in the concentration range 2 - 3.5M V(V), but as the concentration increases above 3.5M, the viscosity rises sharply thus restricting the mobility of the V(V) ions. This sharp increase in viscosity was found to decrease diffusion coefficient of the vanadium ions which in turn leads to a decrease in peak currents. Secondly, changes in the interfacial tension properties of the more concentrated solutions may reduce the wettability of the glassy carbon electrode in the solution thereby reducing the effective surface area and decreasing the peak currents. A significant change in the wetting properties of the V(V) solutions in the glass sample tubes was observed with increasing V(V) concentration above 3.5 M. The effect of total sulfate/bisulfate concentration on the peak heights indicated that at constant V(V) concentration, increasing total sulfate/bisulfate concentration decreases the peak heights due to the formation of electrochemically inactive vanadium-sulfate complex species and polyvanadic species. The effect is more pronounced at higher vanadium concentration. 201 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The aging of the V(V) solutions was studied by taking cyclic voltammograms of the V(V) solutions initially and after about 1000 hours. The cyclic voltammogram exhibited similar peak heights and peak potential separation and did not showed any significant difference. The diffusion coefficient was determined using 2, 3, and 4M V(V) solution in 6M total sulfate/bisulfate at a glassy carbon electrode at different scan rates. The diffusion coefficient was found to decrease with increasing V(V) concentration. The heterogeneous rate constants for the V(IV)/V(V) couple were also observed to decrease with increase in V(V) concentration. From the overall evaluation of the electrochemical behaviour of vanadium supersaturated solutions, it can be concluded that the maximum vanadium(V) concentration should not exceed 3.5M containing not more than 6M of total sulfate/bisulfate to achieve good reversibility and peak currents. It may be stated that the V(V) solutions in the concentration range of 3-3.5M in total sulfate concentrations of 5- 6M are quasi-reversible. 8. Induction times recorded during the desupersaturation experiments of V(V) solutions suggest that increasing total sulfate/bisulfate concentration increases induction time. The induction time drops sharply above 30°C and the effect is more pronounced in V(V) solutions containing 5M total sulfate/bisulfate. However, the state-of-charge (SOC) of the V(V) solution has a significant effect on the stability. A slightly lower state-of-charge of the V(V) solutions (i.e. presence of low levels of V(IV) ions) increases induction time significantly. This is due to interactions between the V(V) and the V(IV) ions in the solution giving rise to enhanced stability of the V02+ species. 202 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions The increase in induction time (or stability) with increasing sulfuric acid concentration is believed to be due to the presence of more H+ ions (increased ratio of H+ ions to V(V) ions) which shifts the V205 precipitation equilibrium towards the formation of V02+. The stability might also be improved because of excess S04 " ions (increased ratio of S to V(V) ions) available at higher H2S04 concentration which can prevent precipitation of V02+ ions to V205 by forming sulfate complexes with V02+. Further, the increase in stability could be attributed to the dimerisation of V02+ ions to V2042+ and V2034+ species. Stirring of the V(V) solutions showed no sign of enhanced precipitation and the induction time was practically the same with and without stirring. 9. The kinetic study of thermal precipitation of V(V) solutions indicated that the growth rate follows first order reaction kinetics under the conditions of low supersaturations with an activation energy of about 9.0 kJmof1, indicating diffusion controlled growth. At high supersaturations the V(V) precipitation obeys a second order rate equation. The high activation energy of 77.2 kJmol'1 during second order crystal growth suggests that the precipitation of V(V) solution in the high supersaturation region is surface-reaction-controlled. 10. From the overall evaluation of the desupersaturation experiments, viscosity, conductivity measurements and electrochemical behaviour of V(V) solutions, it appears that a suitable composition of V(V) electrolyte for the high energy density vanadium redox battery may be 3M V(V) solution in 6M total sulfate/bisulfate up to a temperature of about 30°C. 203 Chapter 5 Stability of Supersaturated Vanadium(V) Solutions Use of additives might extend the V(V) concentration range above 3M, decrease sulfuric acid concentration below 6M and allow temperatures over 30°C. The evaluation of additives to stabilise supersaturated V(V) solutions is reported in Section 6. 204 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation CHAPTER 6 EVALUATION OF ADDITIVES TO INHIBIT VANADIUM(V) PRECIPITATION 6.1 INTRODUCTION One of the main objectives of this study was to stabilise supersaturated V(V) solutions so as to increase the energy density of the vanadium redox battery. Precipitation rates in vanadium solutions with concentrations above 3M V(V) were found to be significantly fast as presented in the previous section. Stabilising V(V) solutions at concentrations above 3M would be of interest for mobile applications. A detailed investigation was undertaken to stabilise V(V) solutions of concentration 3M and above by using various chemical scale inhibitors. The study focused on increasing the induction times of V(V) solution in different total sulfate/bisulfate concentrations and at various temperatures using antisealants. In all areas where solids are formed by crystallisation or precipitation, the influence of impurities upon various features of such processes is increasingly recognised. Next to it is the addition of chemicals to retard the formation of scale in a variety of applications such as desalination, oil recovery, biomineralisation etc. Currently acceptable methods of preventing scale formation utilise chemicals, which are generically known as threshold agents. It was found that the addition of less than stoichiometric quantities of certain polyphosphates to supersaturated solutions of various salts, would prevent precipitation for substantial periods of time [Rice and Partridge, 1939; Buehrer and Reitemeier, 1940]. The specific mechanism of threshold activity is not clearly understood but it is believed that a common feature of threshold agents is sequestration or the capability of forming stable complexes with polyvalent cations. Threshold 205 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation treated solutions are evidently stabilised in some manner involving alteration in crystal morphology at the time of nucleation and subsequent inhibition in growth rate [Spiegler and Laird, 1980]. According to Logan and Walker [1982] additives may act to stifle scale formation by one of several possible routes. They may change the precipitating salt’s chemical potential by affecting complex formation and adsorption, additives may adsorb onto the precipitating ions, thus inhibiting scale nucleation or they may adsorb onto growing crystals, thus distorting and/or inhibiting further crystal formation. It is likely that effective inhibitors function through more than one of the above routes. But it is well established that once supersaturation has occurred in any real system, precipitation is inevitable, regardless of the merits of any known or conceivable threshold inhibitor. To increase the energy density of vanadium battery, the induction times of supersaturated vanadium solution can be improved by use of appropriate additives, which inhibit precipitation. In this study evaluation of various additives were undertaken to retard the precipitation of V(V) species from supersaturated V(V) solutions in sulfuric acid. A threshold inhibitor can retard precipitation for a sufficiently long period of time so that the supersaturated V(V) ions transforms to V(IV) ions during battery operation before the retardation time is exceeded. Even though the main purpose of this study was to focus on prevention of V(V) thermal precipitation, since the V(V) solutions during charge and discharge cycling undergo changes from V(V) to V(IV), it was felt necessary to evaluate selected additives against precipitation of V(IV) electrolytes also. 206 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation 6.2 EXPERIMENTAL PROCEDURE The evaluation of additives was carried out by the experimental procedure similar to that used for stability evaluation as explained in Section 5.2.3. Vanadium(V) solution of about 10 gm was taken in a sample glass bottle of capacity 40 ml with a teflon stopper and placed in a constant temperature water bath at the desired temperature. The temperatures selected for additive evaluation of V(V) solutions were 30, 40 and 50°C. Each additive was added to the V(V) solution on the weight percent (wt%) basis at various dose levels. The additive was mixed thoroughly by shaking the bottle for about 5 minutes. After taking the initial sample the bottles were placed in the water bath of desired temperature. Liquid samples were taken periodically using a 0.45 pm Millipore filter and diluted as discussed earlier for the stability evaluation experiments. The vanadium concentration was analysed by atomic absorption. Although it was difficult to visually see the onset of precipitation because of the dark brownish red colour of the supersaturated V(V) solutions, the solutions were monitored daily to note down the time elapsed for the appearance of any precipitate. The true indication of precipitation was however, determined by the drop in concentration of V(V) solution measured by periodic sampling. For evaluating the additives to prevent precipitation of supersaturated V(IV) solutions, a similar procedure as described above (for V(V) solutions) was adopted, except the evaluation was carried out at a temperature of 20°C. 6.3 RESULTS AND DISCUSSION The initial screening of the additives to prevent thermal precipitation of supersaturated V(V) solution was carried out at 50°C using 4.7M V(V) solution in 6M total sulfate/bisulfate as this solution without additive precipitated within a day. Because the V(V) solution in its discharged condition transforms to the 207 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation V(IV) oxidation state, the additives whose performance was found to be good to inhibit V(V) precipitation were again tested to evaluate the effectiveness against precipitation of V(IV) solution. Then formulations were developed by blending two or more additives that showed promising results for both V(V) and V(IV) solutions to see if they could make any improvement over individual additives. The newly developed formulations were evaluated using 4M V(V) solution in 6M total sulfate/bisulfate at 40°C. The successful formulation was further studied at different dose levels to identify the optimum dosage and its performance was evaluated on the long term basis to inhibit V(V) precipitation at various temperatures, V(V) concentrations and total sulfate/bisulfate concentration. Finally some selected formulations were tested to evaluate their effectiveness in preventing the precipitation of supersaturated V(II), V(III) and V(IV) solutions. 6.3.1 Preliminary Screening of Additives A large number of scale inhibitors which are generally used to prevent precipitation of carbonate and sulfate scales in desalination plants, cooling towers and oil wells at high temperatures were screened to inhibit thermal precipitation of supersaturated V(V) solutions at 50°C. Some promising additives tested earlier by Skyllas-Kazacos and Kazacos [1994, 1996] were also included in the initial screening under identical conditions. These additives contains charged or neutral but polar functional groups mainly responsible for inhibiting the precipitating ions. It has been reported that structural matching between the functional groups of the additives and the cations at the crystal surface plays an important role in determining the effectiveness of the additives [Davey, 1982; Amjad, 1988]. The molecular structures of some antisealants evaluated in this study are shown in Figure 6.1. 208 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation H H r -I 1 1 H COOH ---C------c—- | | II —c------c o ffi- -n- 1 1 i OH COOH H . n - (a) Polyacrylic acid (b) Polymaleic acid H H I I C C H-c- C—H I I I H H c=o I nh2 OH n (c) Carboxylic acid (d) Polyacrylamide (Propionic acid) H O O I II 0 o NaO —P O— P-40Na 1 II O-H P — c—p; O H-Ox O—H Na ch3 (e) Polyphosphate (f) HEDP Figure 6.1 Structural characteristics of antisealants [Source: Amjad, 1985; Drew, 1994; Shanefield, 1996] 209 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation The performance of various additives evaluated, along with their dose level are listed in Table 6.1. It can be observed that sodium hexametaphosphate (SHMP), Briquest 3010-25K of Albright and Wilson, pHreedom of Calgon showed good performance compared to the rest of the chemicals listed in Table 6.1. Both pHreedom and Briquest 3010-25K increased induction time from 8 hours to 48 hours, whereas SHMP increased the induction time to 96 hours. The Calgon antisealant, pHreedom, is a liquid formulation of polymeric dispersants and a patented organic inhibitor [1-hydroxyethylene 1,1- diphosphonic acid, (HEDP) based] specifically designed to prevent calcium sulfate scale in mining processes and it functions both in acidic and alkaline environments without losing effectiveness. The Phosphonic acid group (CP03H2) exhibits a high degree of anionic functionality, which makes it particularly useful as a cation sequestring agent. The carbon-to-phosphorous-to- oxygen bonding arrangement in these molecules is more resistant to hydrolysis [Drew, 1994] and is more stable against oxidation by V(V) than the organic additives containing -OH or -OOH groups. Briquest 3010-25K is a potassium nitrilotri(methylenephosphonate)-N-oxide based additive. Flocon-100, a polyacrylate, is an antisealant for inhibiting carbonate and sulfate scales in reverse osmosis desalination plants [Reitz, 1984]. Ethylene diamine tetra(methylene phosphonic acid), EDTMP was reported by Gill and Varsanik [1986] to show very good inhibition against calcium sulfate scaling. It is reported that the anionic functional groups such as -COOH present in polyacrylic acid, polymaleic acid and polycarboxylic acid ionise in aqueous system to release negatively charged species [Drew, 1994]. The electrostatic attraction between these negatively charged functional groups and positively charged V(V) ions was believed to influence the precipitation behaviour. All organic compounds showed poor performance in the V(V) solution however, due to the oxidising effect of V(V) ions. 210 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Table 6.1. List of additives studied for preventing V(V) precipitation in 4.7 M V(V) solution in 6.0M H2S04at 50°C. Expt# Name Dosage Initial appearance Degree of of precipitation precipitation (wt/vol)% (days) (%) ADO Blank 0.0 <8 hours 100 ADI Ammonium Carbonate 0.5 <1 100 AD2 Polyacrylic acid 0.5 <1 50 AD3 Polyacrylamide 0.5 <2 30 AD24 Polymaleic acid 0.5 <2 30 AD4 Alanine 0.5 <1 100 AD5 Glycine 0.5 <1 100 AD6 SodiumPolyPhos. 1.0 <1 60 AD7 Sod.TriPolyPhos 1.0 <1 60 AD 14 Ammonium Sulfate 2.0 <1 80 AD 15 Potassium Sulfate 2.0 <1 60 AD 19 Poly Styrene S. Acid 2.0 <1 50 AD20 Teric PE61, ICI 2.0 <1 70 AD21 Teric BL8, ICI 2.0 <1 60 AD9 Flocon-100 2.0 1 20 AD 17 Calgon EL-5600 2.0 2 40 AD 13 Briquest 3010-25K 2.0 2 20 AD18 pHreedom 2.0 2 10 AD 8 SHMP 1.0 2 30 AD 16 SHMP 2.0 4 10 211 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation In order to see if polymeric antisealant without charged group would have any effect on the rate of V(V) precipitation, an experiment was conducted using polyacrylamide ( -CONH2), but again this additive also failed to prevent V(V) precipitation. However, SHMP (a stable six-membered ring structure) was found to demonstrate better performance over long chain molecules of organic compounds. Sodium hexametaphosphate is most commonly used in reverse osmosis systems because of its low cost and good performance in waters of high calcium sulfate content. According to Reddy et al. [1973], SHMP provided maximum gypsum scale inhibition compared with seven other commercial organic additives they evaluated. Since V(V) species transforms to the V(IV) oxidation state during the discharge cycle of the battery and precipitates as sulfate scale (VOSO4), it was decided to evaluate these additives (effective in preventing sulfate scales) against V(IV) solution precipitation before conducting any further screening for V(V) solutions. Skyllas-Kazacos and Peng [1996] in a separate study indicated that potassium sulfate (K2S04) showed better performance in preventing supersaturated V(IV) solution precipitation. But the performance of K2S04 was found to be very poor for inhibiting V(V) precipitation, which is one of the main objectives of this study. To develop a comprehensive additive, which can stabilise both V(V) and V(IV) species in the positive half cell of the battery K3P04 and KHS04 were selected as possible compounds to study the effect on their precipitation. Absence of sulfate ions in K3P04 was expected to give better performance for V(IV) inhibition and presence of phosphate was found to provide inhibition effect for V(V) solution. Table 6.2 shows the performance of selected chemicals against the precipitation of 4M V(IV) solution in 6M total sulfate/bisulfate at 20°C. 212 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Table 6.2. Effectiveness of additives studied for preventing precipitation of 4 M V(IV) solution in 6.0M H2S04at 20°C. Expt# Name Dosage Initial appearance Degree of of precipitation precipitation (wt/vol)% (days) (%) AD4-0 Blank 0.0 2 30 AD4-1 k2so4 1.0 60 few crystals AD4-2 K3PO4 1.0 68 few crystals AD4-3 KHSO4 1.0 2 10 AD4-4 pHreedom 1.0 6 20 AD4-5 Flocon-100 1.0 5 10 AD4-6 Calgon EL-5600 1.0 6 10 AD4-7 Briquest 3010-25K 1.0 2 20 AD4-8 EDTMP 1.0 3 30 AD4-9 SHMP 1.0 34 10 AD4-10 CL-4000 1.0 6 10 EDTMP = Ethylene diamine tetramethylene phosphonic acid CL-4000 = Antisealant by Calgon Surprisingly the performance of K3PO4 was found to be the best among all the additives tested against precipitation of V(IV) solution and increased the induction time by 34 times. The performance of K2S04 was also about the same as that of K3P04, and SHMP increased the induction time of V(IV) solution by about 16 times. It was thus concluded that K2S04, K3P04 and SHMP appears to prevent precipitation of supersaturated V(IV) solution significantly. These three compounds were finally evaluated using 4M V(V) solution in 6M total sulfate at 50°C to see their effectiveness against thermal precipitation of supersaturated V(V) solution and the results are presented in Table 6.3. 213 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Table 6.3. Performance of various additives studied for preventing precipitation of 4.0 M V(V) solution in 6.0M H2S04 at 50°C. Formulation Name Dosage Initial appearance Degree of of precipitation precipitation (days) (%) Blank 0.0 1 10 K2S04 1.0 mole % 1 15 EDTMP 1.0 mole % 8 5 K3PO4 1.0 mole % 9 5 SHMP 1.0 mole % 12 5 It is obvious from Table 6.3 that K2S04 failed to inhibit the precipitation of V(V) solution at 50°C whereas tripotassium phosphate and SHMP showed better performance at a dose level of 1 mole % and increased the induction period by about 10 times. The additive EDTMP showed good performance against V(V) precipitation (see Table 6.3) but showed poor performance against V(IV) precipitation (see Table 6.2). The performance of SHMP is slightly better than K3P04 for V(V) solution but the problem with SHMP is that it is not easily soluble in vanadium solution while K3P04 dissolves quickly. In the case of V(IV) solution on the other hand, the performance of SHMP was found to be relatively inferior to K3P04 The additives, SHMP and K3P04 were thus found to stabilise both supersaturated V(V) and V(IV) solutions reasonably well. Therefore, further investigations were carried out by mixing these together in different proportions to develop a suitable blend for the stabilisation of both V(IV) and V(V) supersaturated solutions. Different formulations were developed by combining these two additives in various ratios and also with very small amounts of a dispersant like polystyrene sulfonic acid (PSA). The details of the formulations and their effectiveness are discussed in the following sub-section. 214 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation 6.3.2 Development of Additive Formulations After evaluating these additives individually, several formulations were developed by mixing SHMP, K3PO4 and PSA to establish whether they can make any improvement. The composition of various formulations prepared in this study to inhibit V(V)/V(IV) precipitation are given in Table 6.4. In the formulations SP-S, KP-S and KSP-S the dispersant polystyrene sulfonic acid (PSA) was added by preparing a 10 wt% solution whereas, SHMP and K3P04 were added as solid material to the vanadium solution. During the additive evaluation experiment it was observed that SHMP can not dissolve easily in vanadium solution and that although K3P04 dissolves fully in vanadium solution, it sometimes sticks to the walls of the container and poses precipitation problems. So, after conducting some initial experiments, it was decided to prepare 50 wt% solution of SHMP and K3P04 separately in 1M H2S04 and the additives were added to vanadium solution in the desired amount using these 50 wt% SHMP and 50 wt% K3P04 solutions. Distilled water was not used to prepare the additive solutions as addition of small amounts of water to V(V) solution has been found to change the structure and speciation of the V(V) species as discussed earlier in Section 5.3.3. These additive solutions were prepared carefully by first taking 1M H2S04 in the beaker and while stirring the sulfuric acid solution, SHMP or K3P04 was added in small portions until the desired amount of SHMP was dissolved fully. To add 1 wt% SHMP, 0.2 gm of 50 wt% SHMP solution was added to 10 gm of V(V) solution. To quickly dissolve the SHMP, the temperature should not be increased. Because at high temperature metaphosphate reversion to orthophosphate occurs which reduces the effectiveness of the additive [Ostroff, 1979]. Details of the performance of these formulations and dosages of each additive (SHMP, K3P04) used are given in the next sub-section. 215 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Table 6.4. List of various formulations prepared for the prevention of V(IV)/V(V) precipitation. Formulation SHMP k3po4 PSA EDTMP 1 M H2S04 ID SP-S X - X - - KP-S - X X - - KSP-S X X X - - SP-L X - X - X KP-L - X X - X KSP-L X X X - X KS-L X X - - X SHMP: sodium hexametaphosphate; PSA: dispersant, polystyrene sulfonic acid ETDMP: ethylene diamine tetramethylene phosphonic acid; DW: distilled water 1. In formulation SP-S, KP-S, KSP-S the additive SHMP and K3P04 was added as solid and PSA was added as 10% liquid in distilled water. 2. In formulation SP-L, KP-L, KSP-L, KS-L the additives both SHMP and K3P04 were added by preparing 50 wt.% solution in 1M H2S04. 6.3.3 Evaluation of Different Additive Formulations The effectiveness of the formulations developed were investigated using 4M V(V) solution in 6M total sulfate/bisulfate at 50°C and 4M V(IV) solution in 6M total sulfate/bisulfate at 20°C. The details of their performance and dosage levels used are given in Table 6.5 and 6.6 respectively. Table 6.5. Performance of Various formulations studied for inhibiting precipitation of 4.0 M V(V) solution in 6.0M H2S04 at 50°C. Formulation Dosage Initial appearance Degree of Name of precipitation precipitation (days) (%) Blank 0.0 1 10 SP-S 2.3wt% SHMP + 0.1 wt% PSA 16 slight ppt KP-S 2.0wt% K3P04+ 0.1 wt% PSA 12 slight ppt KSP-S 1.3wt% K3P04+ 0.7wt% SHMP 16 slight ppt + 0.1 wt% PSA 216 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Table 6.6. Effectiveness of various formulations to inhibit precipitation of 4 M V(IV) solution in 6.0M H2S04 at 20°C. Formulation Dosage Initial appearance Degree of Name of precipitation precipitation (days) (%) Blank 0.0 1 few crystals SP-S 2.3wt% SHMP + 0.1 wt% PSA 21 few crystals KP-S 2.0wt% K3PO4+ 0.1 wt% PSA 31 few crystals KSP-S 1.3wt% K3PO4+ 0.7wt% SHMP 29 few crystals + 0.1 wt% PSA The blank V(V) solution precipitated within one day at 50°C and similarly blank V(IV) solution also precipitated within one day at 20°C. From the analysis of the results in Table 6.5 and 6.6 it can be stated that addition of the dispersant PSA improves the stability of V(V) solution. In the case of the precipitation of V(IV) solution however, the addition of PSA decreases the induction time from 68 days with K3P04 (Table 6.2) to 31 days for the combination of K3P04 + PSA. For both V(V) and V(IV) solutions however, the additives provide a dramatic increase in induction time compared with the blanks. Systematic additive trials were conducted according to the experimental procedure described before by measuring the concentration of vanadium with time. Liquid formulations of SHMP (50 wt% solution) and K3P04 (50 wt% solution) prepared in 1M sulfuric acid solution were used instead of adding solid additive to the V(V) solution. Figure 6.2 shows the concentration profiles of V(V) solution without additive and with 2 wt% SHMP, formulation SP-L, 2 wt% K3P04 and formulation KP-L at 40°C. 217 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation s 4.00 it* Z 2.00 - Blank SHMP SP-L > 1.00 - K3P04 KP-L TIME (hours) Figure 6.2. Precipitation behaviour of 4M V(V) solution in 6M total sulfate/bisulfate with and without inhibitor at 40°C. SHMP = 2 wt%; SP-L = 2 wt% SHMP + 0.02% PSA K3PO4 = 2 wt%; KP-L = 2 wt% K3P04 + 0.02% PSA The addition of SHMP increased the induction time from 3 days for blank V(V) solution to about 30 days whereas the formulation SP-L demonstrated the best performance by increasing the induction time to 40 days, thus indicating that a small amount of the dispersant PSA improves the stability of the V(V) solution compared with SHMP alone. The performance of K3PO4 and KP-L was found to be inferior to SHMP against V(V) precipitation, but it is more effective in inhibiting the precipitation of V(IV) solutions. It was also observed that the efficiency of K3PO4 was found to be reduced by addition of PSA to retard the precipitation of V(V) solution. The relative performance of the additives in inhibiting V(V) precipitation can thus be rated as SP-L > SHMP > K3PO4 > KP- L. Since K3P04 is more effective for V(IV) solution and SHMP is better for controlling V(V) precipitation, mixtures of these two additives were tested at 40°C with and without dispersant and EDTMP. The effectiveness of these formulations is plotted in Figure 6.3. 218 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Blank SP-L KS KSP KSPE TIME (hours) Figure 6.3. Effect of different formulations on precipitation of V(V) solution at 40°C. SP-L = 2 wt% SHMP + 0.02% PSA; KS = 2 wt% SHMP + 2 wt% K3P04 KSP = 2 wt% SHMP + 2 wt% K3P04 + 0.02% PSA KSPE = 2 wt% SHMP + 2 wt% K3P04 + 0.5% EDTMP + 0.02% PSA The performance of KS (2 wt% SHMP + 2 wt% K3PO4) and SP-L (2 wt% SHMP + 0.02% PSA) was found to be equally good without any drop in V(V) concentration for 1000 hours and an increase in the induction time from 3 days to 40 days. The second formulation in the order of merit was KSPE (2 wt% SHMP + 2 wt% K3PO4 + 0.5% EDTMP + 0.02% PSA) which increased the induction time of V(V) solution to 16 days with a V(V) concentration of 3.6M after 1000 hours. The formulation KSP (2 wt% SHMP + 2 wt% K3PO4 + 0.02% PSA) extended the induction time to about 15 days but the final V(V) concentration dropped to 3.1M after 1000 hours. Although KS and SP-L were found to be equally good, the presence of K3P04 in the formulation KS was found to enhance the inhibition of V(IV) precipitation and has definite benefit over SP-L. Therefore, formulation KS (SHMP + K3P04) was considered as the best among all the formulations developed in this study to prevent precipitation of supersaturated V(V) solutions. 219 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation The influence of additives upon V2O5 precipitation reaction rates can be explained in this study in terms of the following two effects, (i) direct chelation with the crystal lattice ions in the solution, and (ii) adsorption of the additive onto to the precipitating ion, thus inhibiting scale nucleation, or adsorption onto the growing crystals, thus distorting and/or inhibiting further crystal formation. The phosphates [SHMP (NaP03)6 and K3P04], present in the formulation KS for the control of V02+ ions precipitation may be forming stable chelate complexes like (V02)3P04 as reported by Silva and Ogasawara [1993]. To prevent precipitation, it is not necessary to complex all the scale forming cations (V02+), but only enough to reduce the concentration so that the solubility limit is not exceeded [Ostroff, 1979]. Another possible mechanism for the inhibition of V(V) precipitation may be due to the adsorption of inhibitors on the crystal surface. Inorganic phosphates, commonly known as polyphosphates work on the principle of the threshold- effect treatment. Substoichiometric levels of the phosphates are normally required and as the crystals begin to grow, the phosphate ions cling to the nuclei of these developing crystals and inhibit against further growth. Thus, it is possible for a small amount of phosphate to tie up a large amount of scale forming material. The most active threshold agent in this group is SHMP [Liu and Nancollas, 1973; Gevecker, 1976; Spiegler and Laird, 1980]. Since the formulation KS contains a smaller concentration of phosphate than that of the V02+ ion, an adsorption process appears to offer a more feasible explanation. It is however likely that the formulation KS functions through both of the above mentioned routes. The phosphate ions (P043 ) released from K3P04 may be forming a stable complex with the V02+ ions such as (V02)3P04 and P03' from SHMP (NaP03)6 block crystal growth by surface adsorption onto the active sites. While the above mechanisms could be used to explain observed experimental trends with different additives, it is interesting to note that it is still 220 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation difficult to predict how a particular compound might behave as a precipitation inhibitor, and as pointed out by Gill and Varsanik [1986] and Myerson [1990] , scale inhibitors are still actually tested individually on a trial and error basis for their application. Other formulations KSP and KSPE developed in this study did not perform very well. The formulation KSP was developed by adding a minute amount of PSA in order to keep any precipitation if initiated, in the dispersed form and prevent or delay further growth [Porteous, 1983]. But the experimental data revealed that the performance of KSP deteriorated against precipitation of V(V) solutions with the addition of dispersant probably because of interaction of V(IV) ions (present in small quantities in V(V) solution, about 3-4%) with PSA. It is well known that phosphonates (organic phosphates) exhibit a high degree of anionic functionality and stability which makes them particularly useful for sequestring cations in the desalination industry [Drew, 1994]. It was thought that addition of a small amount of EDTMP to KS might improve the performance against V(V) precipitation, however the performance did not improve. The reason for poor performance may be the oxidation of EDTMP by V(V) ions thus reducing its ability to inhibit precipitation. Similar oxidation of organic compounds like hydroxycarboxylic acids, D-galacturonic acid and carbohydrates by V(V) ions has been reported by Micera et. al [1986]. The formulation KS was further evaluated at different dose levels of SHMP and K3PO4 to optimise the amounts of each additive. The effectiveness of formulation KS was later investigated against the precipitation of V(IV) species, which is the discharged state of the vanadium ions in the positive half-cell. The formulation KS was also evaluated against precipitation of V(II) and V(III) electrolyte in the negative half-cell of the vanadium redox battery with a view to find whether it can act as a comprehensive additive for both the positive as well as the negative half cell of the battery. 221 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation If the formulation KS can inhibit the precipitation of all the four species of vanadium, it will be convenient to mix the additives in the beginning to a vanadium solution of 50% V(III) + 50% V(IV) (i.e. V3 5+) and start the battery. 6.3.4 Dosage Optimization of Formulation KS The formulation KS was studied by mixing SHMP and K3P04 in different ratios to achieve the maximum induction time for the V(V) solutions. The details of various blends of formulation KS investigated using 4M V(V) solution in 6M total sulfate/bisulfate are given in Table 6.7 and the performance of these blends is illustrated in Figure 6.4. It can be observed from Figure 6.4 that increasing the concentration of SHMP and K3P04 improved the performance of additive blend KS till it reaches 1 wt% K3P04 and lwt% SHMP (blend KS11). Further increase in the amount of SHMP and K3P04 (blends KS12, KS13, etc) however, dropped the performance. While at low additive concentrations retardation of V(V) precipitation occurs through additive adsorption onto nuclei and crystals, the precipitation process may just be stimulated at higher additive levels when the additive acts as a template for nucleation. Such a behaviour was observed in practical situations where the cations of the mineral salts in solution can sometimes form insoluble tiny particles with the inhibitor molecules above a certain dosage level. This level is not fixed, but is largely dependent on the salt, the additives, the presence of other components like complexing agents in solution and their respective concentrations [Van der Leeden and Van Rosmalen, 1987]. Logan and Kimura [1985] while discussing the control of gypsum scale on reverse osmosis membranes indicated that lower SHMP dosage resulted in better control than the higher dosage. Amjad et al.[ 1995] reported that in desalination plants polyphosphates are considered as good antisealants, but suffer from the disadvantage of being susceptible to hydrolysis under certain conditions. The resultant phosphate ion can then react with calcium to form calcium phosphate. 222 Chapter 6______Evaluation of Additives to Inhibit Vanadium(V) Precipitation Table 6.7. Details of different mixtures of SHMP and K3PO4 investigated to develop optimum blend of formulation KS at 40°C. Blend Ratio Induction V(V) Conc(M) Name Time(days) after 1000 hours Blank 3 2.65 KS55 0.5 wt% K3PO4 + 0.5 wt% SHMP 32 3.24 KS11 1.0 wt% K3PO4 + 1.0 wt% SHMP 40 3.93 KS12 1.0 wt% K3P04 + 2.0 wt% SHMP 30 3.83 KS13 1.0 wt% K3PO4 + 3.0 wt% SHMP 21 3.64 KS21 2.0 wt% K3PO4 + 1.0 wt% SHMP 16 2.94 KS1515 1.5 wt% K3PO4 + 1.5 wt% SHMP 25 3.50 oZ H £ H wZ u Blank z KS55 o u KS11 KS12 KS13 KS1515 KS21 TIME (hours) Figure 6.4. Effect of different blends of formulation KS on precipitation of V(V) solution at 40°C. KS55 = 0.5wt% K3PO4+ 0.5wt% SHMP; KS11 = 1 wt% K3P04 + lwt% SHMP KS12 = lwt% K3PO4+ 2wt% SHMP; KS13 = 1 wt% K3PO4 + 3wt% SHMP KS21 =2wt% K3PO4+ lwt% SHMP; KS1515 = 1.5 wt% K3PO4 + 1.5wt% SHMP 223 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation From Figure 6.4 and Table 6.7 it can be suggested that the blend KS11 which consists of 1 wt% K3P04 and lwt% SHMP showed the best performance over all other combinations with only a 2% decrease in V(V) concentration after 40 days. The blend KS55 and KS12 also demonstrated better performance, while KS13, KS1515 and KS21 dropped induction time significantly. Therefore, formulation KS11 was considered as optimum and it was finally selected for the long term evaluation against V(V) thermal precipitation at 40°C and to study the effect of various parameters like initial V(V) concentration, temperature and total sulfate/bisulfate concentration. 6.3.5 Performance Evaluation of KS11 6.3.5.1 Long Term Performance Evaluation of KS 11 The effectiveness of the formulation KS 11 was further evaluated on a long term basis for about 2400 hours using 4M V(V) solution in 6M total sulfate/bisulfate as shown in Figure 6.5. The 4 M V(V) solution prepared earlier for the precipitation study was used for the evaluation of KS11. The blank solution started precipitating after 3 days and reached an equilibrium concentration of about 2.5M, whereas addition of KS11 to the V(V) solution increased the induction time to about 40 days with final V(V) concentration of 3.2M after about 100 days. The stability of 4M V(V) solution in 6M total sulfate/bisulfate was thus increased by about 13 times with the additive KS11 and the final V(V) concentration dropped by about 20% compared to 38% for blank V(V) solution. If the V(V) solution in the vanadium redox battery is discharged within a period of one month therefore, the formulation KS 11 may be used safely to prevent the precipitation of 4M V(V) solution in 6M total sulfate/bisulfate. Although the precipitation with additive KS 11 will begin after 40 days, the concentration of V(V) will reach 3.2M after 60 days thus indicating an increase in the solubility of V(V) species. 224 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Z, 2 -- Blank (4M V(V) - 6M S04) ■*— 4M V(V)-6M S04 + KS11 TIME (hours) Figure 6.5. Effect of KS11 on the precipitation of 4M V(V) solution in 6M total sulfate/bisulfate at 40°C. KS11 = 1 wt% K3PO4 + lwt% SHMP It can be observed from Figure 6.5 that a small addition of formulation KS 11 has markedly decreased the precipitation rate. The inhibition can be attributed to the combination of both stable complex formation of phosphate ions with V02+ ions and adsorption of additive on the crystal surface. The analysis of the liquid samples using ICP was carried out to detect the amounts of additives present in the solution at the start of the additive experiment and after 1000 hours. About 60% active additive ( P and K ) was found in the solution after 1000 hours the loss of large amount of the original additive in the solution indicates that it has probably adsorbed onto the crystal surface or complexed with V02+ ions [Reddy and Nancollas, 1973]. On the basis of long term evaluation it can be concluded that the addition of additive KS11 to 4M V(V) solution in 6M total sulfate/bisulfate at 40°C increases the induction time by about 13 times and decreases the precipitation rates significantly. 225 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation 6.3.5.2 Effect of Vanadium(V) concentration The precipitation behaviour of V(V) solutions was studied by varying the V(V) concentration using formulation KS11 at 40°C. Different concentrations of V(V) solutions (3, 4 and 5M ) in 6M total sulfate/bisulfate were investigated to study the performance of KS11. Figure 6.6 shows the V(V) concentrations after 1000 hours for the blank solution and for the corresponding V(V) solution with KS11, as a function of initial V(V) concentration. < 2 - Blank V(V) soluton V(V) Soln + KS11 INITIAL V(V) CONC (M) Figure 6.6. Effect of initial V(V) concentration on performance of KS11 to prevent precipitation of different V(V) solutions in 6M total sulfate/bisulfate at 40°C. KS 11 = 1 wt% K3PO4 + lwt% SHMP The additive formulation KS11 maintained the V(V) concentration in the 3M and 4M V(V) solutions in 6M total sulfate/bisulfate, but failed to stop the precipitation of 5M V(V) solution in 6M total sulfate/bisulfate at 40°C, reaching a V(V) concentration of 3.72M after 1000 hours making the curve flat between the concentration 4M and 5M. This increased precipitation is due to higher supersaturations when the initial V(V) concentration was raised to 5M. 226 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Although 5M V(V) solution concentration dropped to 4.83M after 9 days, no precipitation was observed visually in 5M V(V) solution for about 15 days at 40°C. In the case of blank V(V) solutions at 40°C, the 4M and 5M V(V) solutions thermally precipitated significantly due to high level of supersaturation and their concentrations measured after 1000 hours were 2.65M and 3.3M respectively. The induction times of different V(V) solutions with initial concentrations 3M, 4M and 5M are tabulated in Table 6.8. The concentration of blank V(V) solutions and with additive KS11 measured after 1000 hours are also reported. 6.3.5.3 Effect of Temperature The improvement in the stability of 4M V(V) solution in 6M total sulfate/bisulfate with KS11 was studied at different temperatures of 30, 40 and 50°C. The final V(V) concentrations after 1000 hours at these temperatures are plotted in Figure 6.7. The effectiveness of KS11 at 30 and 40°C was very good and V(V) concentration was almost constant for 1000 hours. Increasing the temperature further to 50°C decreased the V(V) concentration from 4M to about 2.32 M after 1000 hours, a drop of about 42 %. Figure 6.8 shows the effect of temperature on 3M V(V) solution in 6M total sulfate/bisulfate. Again the additive KS11 was able to maintain the V(V) solution concentration constant at 3M till 40°C and at 50°C the V(V) concentration after 1000 hours decreased to 2.10 M, a drop of 30 %. 227 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Table 6.8. Summary of induction times and final V(V) concentration of V(V) solutions without additive and with additive KS11 in various total sulfate/bisulfate concentrations at different temperatures. Temperature V(V) solutions in V(V) solutions in 5M total sulfur 6M total sulfur 3V5S 4V5S 5V5S 3V6S 4V6S 5V6S 30°C Induction Time(days) Blank V(V) soln. 8 6 2 42 28 1.5 V(V) soln.+ KS11 >42 42 >42 >42 Cone after 1000 hrs(M) Blank V(V) soln. 2.46 3.33 3.5 3 3.81 4.05 V(V) soln.+ KS11 3 3.91 3 4 40° C Induction Time(days) Blank V(V) soln. 1 1 <1 8 3 <1 V(V) soln. + KS11 10 7 1 >42 40 8 Cone after 1000 hrs(M) Blank V(V) soln. 1.62 2.13 2.45 2.76 2.65 3.3 V(V) soln.+ KS11 1.98 2.79 3.41* 3 3.95 3.72 50°C Induction Time(days) Blank V(V) soln. <1 <1 <1 1 <1 <1 V(V) soln. + KS11 2 1 9 4 Cone after 1000 hrs(M) Blank V(V) soln. 1.24 1.56 0.49 1.76 2 2.5 V(V) soln.+ KS11 1.78 2.15* 2.1 2.32 V(V) concentration after 500 hours indicates that no experiments were conducted at those conditions 228 Chapter Figure V(V) CONC AFTER 1000 HOURS (M ) 3 V(V) CONC AFTER 1000 HOURS (M ) 6 6.8. Effect Effect 4M 3M Blank 3M of V(V) V(V) 4M Blank of V(V)in temperature temperature V(V) 3M KSl KS 4M solution solution V(V) in 11 6 V(V)- 1 M 6 = = M - S Evaluation 1 1 6 6 S + wt% wt% M M + TEMPERATURE KS11 TEMPERATURE in in S KS1 S04 on on K3PO4 K 229 6M 6M 3 1 PO performance performance of 4 total total Additives + + lwt% 1 wt% sulfate/bisulfate. sulfate/bisulfate. (C) (C) SHMP SHMP to Inhibit of of formulation formulation Vanadium(V) KS1 KS Precipitation 11 1 using using Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Because of lower supersaturation in the case of 3M V(V) solution, the additive KS11 was able to hold the precipitation to an extent that the equilibrium concentration dropped by 21% as compared to 27% in case of 4M V(V) solution. It can be concluded that the additive KS11 was very effective up to a temperature of about 40°C but a further increase in temperature to 50°C deteriorates its performance significantly. The induction times observed and V(V) concentrations measured for blank solutions and with additive KS11 at different temperatures are tabulated in Table 6.8. 6.3.5.4 Effect of total Sulfate/bisulfate Concentration It was found earlier during stability evaluation of supersaturated V(V) solutions that increasing the total sulfate/bisulfate concentration increases the stability of V(V) solutions. The effect of KS11 when added to different V(V) solutions was studied in total sulfate/bisulfate concentrations of 5M and 6M. The induction times measured for blank solutions and with additive KS 11 in total sulfate/bisulfate concentrations 5M and 6M are listed in Table 6.8. The effect of increasing sulfuric acid concentration for a given V(V) solution with KS11 increases induction time significantly. The induction time of 3M and 4M V(V) solution in 5M total sulfate/bisulfate was found to be 10 days and 7 days respectively whereas 3M and 4M V(V) solution in 6M total sulfate/bisulfate exhibited induction times of >42 days and 40 days respectively, an improvement of about five times. This increased stability is probably due to the formation of sulfate complexes with V02+ ions and dimerisation of V02+ ions to V2042+ or V2034+ at higher sulfuric acid concentrations as discussed earlier in Section 5.3.10. Apart from increasing the induction time, addition of KS11 and increasing sulfuric acid concentration increases the apparent equilibrium concentration. For example, the apparent equilibrium concentration of the initially 4M V(V) solution in 5M total sulfate/bisulfate at 40°C was increased from 2.13M to 230 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation 2.79M with addition of additive KS11, an improvement of 36%. By increasing total sulfate/bisulfate concentration to 6M, the apparent equilibrium concentration of 4M V(V) solution was raised from 2.65 to 3.95, an increase of about 50 %. In addition to the dimerisation and sulfate/bisulfate complex formation, the excess H+ ions available at higher sulfuric acid concentrations are responsible for shifting the V2O5 precipitation equilibrium towards the formation of V02+ ions thus increasing the apparent equilibrium V(V) concentration. Therefore, it can be recommended that a 4M V(V) solution in 6M total sulfate/bisulfate with addition of KS11 (1 wt% K3PO4 + lwt% SHMP ) can be used in the vanadium redox battery up to a temperature of 40°C without precipitation for about 40 days. However, a slightly lower total sulfate concentration will enhance the stability of the V(IV) species, which exists in the discharged state in the positive half cell of the battery. Therefore, the stability of a 3.5M V(V) solution in 5.7M total sulfate/bisulfate was investigated with and without additive KS11 at 40°C. The precipitation behaviour of blank solution and with additive is shown in Figure 6.9. An induction time of 25 days was observed with the blank solution and addition of KS11 increased the induction time to about 60 days. The addition of KS11 also increased the apparent equilibrium concentration of V(V) solution to 3.21M as compared to blank V(V) solution equilibrium concentration of 2.72M. Decreasing V(V) concentration to 3.5M allowed a slight decrease in total sulfate/bisulfate concentration to 5.7M with a reasonable induction time of 25 days. Addition of KS11 makes this composition (3.5V-5.7S) more attractive with an induction time of about 60 days and an apparent equilibrium V(V) concentration of 3.21M. 231 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation Z 2.00 - w 1.00 - -A— Blank (3.5M V(V) - 5.7M S04) (3.5M V(V) - 5.7M S04) + KS11 TIME (hours) Figure 6.9. Stability of 3.5M V(V) solution in 5.7M total sulfate/bisulfate with additive formulation KS11 at 40°C. KS11 = 1 wt% K3PO4 + lwt% SHMP 6.3.6 Effect of Additive Addition on Electrochemical Behaviour The stability of supersaturated V(V) solution is improved by adding formulated additives to prevent thermal precipitation at higher temperatures of about 40- 50°C. The effect of the addition of the additive on the electrochemical activity of V(V) solutions was evaluated by cyclic voltammetry. The formulation KS11 developed in this study, which showed good performance in inhibiting precipitation of V(V) solution was added to 4M V(V) solution containing 5M total sulfate/bisulfate. The additive dosage was about 1 wt./wt.% and hand shaking of the solution was done periodically over approximately 100 hours. The cyclic voltammograms obtained before KS11 addition to this V(V) solution (curve 1) and after addition (curve 2), at a scan rate of 0.02V/S at a glassy carbon electrode are shown in Figure 6.10. It can be observed that the two voltammograms with and without additive are very similar, and the additive addition did not affected the electrochemical behaviour of the V(V) solution. 232 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation — Without" Additive _ With Additive c -0.40 Potential (V) vs SCE Figure 6.10. Cyclic voltammogram of 4M V(V) solution in 5M total sulfate/bisulfate with and without additive. 233 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation 6.3.7 Evaluation of the Stability of V(II), V(III) and V(IV) Solutions using KS11 The V(V) species in the positive half-cell is transformed to V(IV) species during discharge of the vanadium batteries. Until it is charged back to the V(V) state it will remain as V(IV) species and thus has to be stable under the discharged condition of the battery. The initial screening of additives for the V(IV) solution was discussed earlier (Table 6.2), and the long term evaluation (2400 hours) of 4M V(IV) solution in 6M total sulfate/bisulfate is presented here. Figure 6.11 illustrates the effectiveness of KS11 against the precipitation of 4M V(IV) solution in 6M total sulfate/bi sulfate at 20°C. The additive KS11 thus shows very good performance with an induction time of about 56 days and an apparent equilibrium V(IV) concentration of 3.23M. -er- Blank, 4M V(IV) - 6M S04 «— (4M V(TV) - 6M S04) + KS11 TIME (hours) Figure 6.11. Performance of KS11 to inhibit precipitation of 4M V(IV) solution in 6M total sulfate/bisulfate at 20°C. Thus additive formulation KS11 can prevent precipitation of both 4M V(V) and V(IV) species in 6M total sulfate/bisulfate for a minimum period of about 40 days without any decrease in vanadium concentration. The negative half-cell of 234 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation the vanadium redox battery contains V(II) and V(III) species in its charged and discharged state respectively. The stability of these two solutions is also equally important at similar vanadium concentrations to be able to operate the battery at high energy density. A V(III) solution of 4M concentration was prepared in 6M total sulfate/bi sulfate. Additive formulations KS11 and SP-L at a dose level of 2 wt% were evaluated using 4M V(III) solution in 6M total sulfate/bisulfate at 20°C. The sample in which SP-L was added started to precipitate immediately. This quick precipitation was probably due to some reaction with the PSA present in the formulation SP-L. However, the blank V(III) solution and the V(III) solution with KS11 did not precipitated for six days. Both the samples were moved from the 20°C water bath to a refrigerator maintained at about 3°C. In the beginning both samples were monitored on a daily basis to visually observe the start of any V(III) precipitation. No precipitation was observed for about 1000 hours, in both the blank solution as well as in V(III) solution with KS11 at 3°C. The solutions were left in the refrigerator for a longer time with periodic monitoring . Surprisingly it was noted that both V(III) solution and V(III) solution + KS11 did not show any sign of precipitation for about three months at 3°C. Since the blank V(III) solution of concentration 4M in 6M total sulfate/bisulfate did not precipitate at 3°C for about three months, it was therefore difficult to evaluate the effect of additive formulation KS11 on the precipitation of V(III) solution. Thus, it can be stated that 4M V(III) solution in 6M total sulfate/bisulfate was found to be stable for three months without any additive at a temperature of about 3°C. Preliminary evaluation of KS11 was carried out by Skyllas-Kazacos and Asem [1997] to prevent precipitation of V(II) species. Encouraging results were obtained when a 2M V(II) solution in 5M total sulfate/bisulfate was evaluated using KS11 at 3°C. The blank V(II) solution started precipitation after five days whereas V(II) solution containing formulation KS11 was able to hold the 235 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation precipitation for 27 days, an increase in induction time by a factor of five. The evaluation of KS11 in the system V(II)/V(III) was carried out at 3°C because, V(II)/V(III) are less stable at low temperatures. Also by evaluating at 3°C, it is possible to compare the effectiveness of KS11 with other additives tested previously at similar temperature (5°C). It appears therefore, that the formulation KS11 developed in this study has a significant potential to stabilize the supersaturated vanadium solutions of V(II), V(III), V(IV) and V(V) species at a vanadium concentration of 3.5M in 5.7M total sulfate/bisulfate for a period of about one month at operating temperatures between 5°C and 40°C. The evaluation of KS11 for preventing precipitation of supersaturated V(V) solution was carried out systematically by studying the effect of all the relevant parameters. However a detailed investigation of the effectiveness of KS11 against precipitation of supersaturated V(II), V(III) and V(IV) solutions at lower temperatures (5°C - 20°C), vanadium concentration (3M - 3.5M) and total sulfate/bisulfate concentration (5M-6M) on a long term basis is recommended. 6.4 SUMMARY OF RESULTS This study focused on the evaluation of various antisealants to inhibit the thermal precipitation of supersaturated V(V) solutions by varying the V(V) concentration, total sulfate/bisulfate concentration and temperature. Because V(V) species in the positive half-cell electrolyte transforms to the V(IV) oxidation state in its discharged condition, the successful formulation developed for stabilising supersaturated V(V) solutions was also investigated against V(IV) precipitation. Since the negative half-cell of the vanadium redox battery contains supersaturated V(II)/V(III) solution, a preliminary evaluation of the developed formulation was also carried out to see if it can prevent V(II)/V(III) precipitation. The main findings of the additive evaluation for the prevention of supersaturated vanadium solutions are summarised as follows. 236 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation 1. Preliminary screening of various additives was carried out using 4.7M V(V) solution in 6M total sulfate/bisulfate at 50°C. It was found that the precipitation of supersaturated V(V) solutions can be prevented significantly by SHMP, K3P04, pHreedom of Calgon, and Briquest 3010- 25K of Albright and Wilson at a dose level of 2 wt%/vol%. The precipitation of 4.0M V(IV) solution in 6M total sulfate/bisulfate was found to be controlled by K2S04 and K3P04 at a dose level of 1 wt%/vol% for about 60 days, and 1 wt%/vol% of SHMP was found to inhibit the V(IV) precipitation for 30 days. The performance of K2S04, K3P04, SHMP and EDTMP was evaluated using 4.0M V(V) and 4M V(IV) solutions in 6M total sulfate/bisulfate at a dose level of 1 mole %. Although K2S04 showed an induction time of 60 days for 4.0M V(IV) solution at 20°C, it failed to inhibit the precipitation of 4M V(V) solution at 50°C. The performance of SHMP was found to be the best for the V(V) solution at 50°C by extending the induction time to about 12 days and K3P04 and EDTMP exhibited equally good performance with an induction time of 8 days. The additives SHMP, EDTMP and K3P04 were thus found to stabilise V(V) and V(IV) supersaturated solutions significantly at a temperature of 50°C and 20°C respectively. The additives SHMP and EDTMP showed a better inhibiting effect against precipitation of V(V) solution while K3P04 showed better effectiveness against V(IV) precipitation. A number of formulations were thus developed by mixing these three additives (SHMP, EDTMP and K3P04) in different ratios and also by adding a small amount of dispersant such as polystyrene sulfonic acid in 1M sulfuric acid solution. 2. A comprehensive evaluation of various formulations developed in this study was carried out to prevent thermal precipitation of supersaturated 237 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation V(V) solutions. Formulation KS (SHMP + K3P04) showed better performance than all other formulations evaluated using 4M V(V) solution in 6M total sulfate/bisulfate at 40°C for 1000 hours. The influence of these inhibitors on the nucleation rates and crystal growth may be due to (i) direct chelation of phosphate ion with V02+ ions to form stable complex (V02)3P04 and (ii) adsorption of the additive onto the precipitating ion, thus inhibiting scale nucleation, or adsorption onto the growing crystals, thus distorting and/or inhibiting further precipitation. Structural matching between the functional groups of the additives and the cations at the crystal surface plays an important role in determining the effectiveness of the additives. 3. Dosage optimization studies of formulation KS (SHMP + K3P04) indicated that lwt% SHMP + lwt% K3P04 exhibited superior performance over other additive blends. The induction time of 4M V(V) solution in 6M total sulfate/bisulfate at 40°C was extended from 3 days for the blank solution to 40 days with formulation KS11, an improvement of about 13 times. 4. Long term evaluation of formulation KS11 indicated that the apparent equilibrium concentration of 4M V(V) solution in 6M total sulfate/bisulfate reached a level of 3.2M while the apparent equilibrium concentration without formulation KS11 was found to be 2.5M after 100 days. The formulation KS11 has thus shown an increased solubility effect by increasing the apparent equilibrium concentration from 2.5M to 3.2M. The analysis of the additive conducted at the beginning of the experiment and after 1000 hours indicated that about 60% of active additive was available in the solution while the remaining additive (phosphates) probably adsorbed on the surface of the crystal nuclei or complexed with V02+ ions and prevents precipitation. It is not necessary 238 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation to complex all the V02+ ions, but only enough to reduce the concentration so that solubility limit is not exceeded. This effect of adsorption/complexation reduced the precipitation rates and probably resulted in the increased equilibrium concentration. 5. The effect of increasing V(V) concentration on the performance of KS11 indicated that at 40°C, formulation KS11 was able to hold the precipitation of 3M and 4M V(V) solution in 6M total sulfate/bisulfate for >42 days and 40 days respectively, but failed to prevent the precipitation of 5M V(V) solution in 6M total sulfate/bisulfate after 8 days. The final V(V) concentrations observed after 1000 hours (42 days) were 3, 3.95 and 3.72M for initial V(V) concentrations of 3, 4 and 5M respectively. The significant drop in equilibrium concentration of 5M V(V) solution is due to the higher supersaturation levels and subsequent increase in precipitation rates. 6. The variation in temperature has a significant effect on the effectiveness of the formulation KS11. The formulation KS11 can prevent the precipitation of 3V6S and 4V6S solution up to 40°C for 1000 hours. Further increase in temperature to 50°C starts the precipitation of 3V6S and 4V6S solution after 9 days and 4 days with final concentrations of 2.1 and 2.32 M respectively after 1000 hours. 7. Increasing the total sulfate/bisulfate concentration increases the stability of V(V) solutions. The effect of increasing sulfuric acid concentration for a given V(V) solution with addition of KS11 further enhances induction time significantly. The induction time of 3V5S and 4V5S solution with formulation KS11 at a temperature of 40°C was found to be 10 days and 7 days, whereas an increase in total sulfate/bisulfate concentration to 6M extends the induction times of 3V6S and 4V6S solution to >42 days and 40 days respectively. Further increase in 239 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation induction time is probably due to the dimerisation of V(V) ions and formation of V(V) and sulfate/bisulfate complexes. At 40°C, the apparent equilibrium V(V) concentration of 3V5S and 4V5S solution with formulation KS11 was 1.98M and 2.79M respectively after 1000 hours. Increasing the total sulfate/bisulfate concentration to 6M increases the apparent equilibrium V(V) concentration of 4V6S solution with additive KS11 to about 3.95M. This increase in apparent equilibrium V(V) concentration from 2.79M to 3.95M may be again attributed to the increased dimerisation and sulfate complex formation of V02+ ions and shifting of V205 precipitation equilibrium towards the formation of V02+ at higher sulfuric acid concentrations. Also higher viscosity of the more concentrated solutions may slow down the precipitation reaction resulting in higher equilibrium concentration. Since a slightly lower total sulfate/bisulfate concentration would allow more stability to the V(IV) species which exists in the discharged condition in the positive half-cell, the stability of 3.5M V(V) solution in 5.7M total sulfate/bisulfate was investigated with and without additive. The blank solution exhibited an induction time of 25 days while addition of KS11 extended the induction time to about 60 days. The final concentration of V(V) solution was increased from 2.72M for blank solution to 3.21 M with addition of additive KS11. 8. A solution of composition 3.5M V(V) in total sulfate/bisulfate concentration of 5.7M with additive formulation KS11 appears to be very attractive for a high energy density vanadium redox battery up to a temperature of 40°C. If 3.5M V(V) solution in 5.7M total sulfate/bisulfate is kept fully charged before it being discharged in the vanadium redox battery, then the 240 Chapter 6 Evaluation of Additives to Inhibit Vanadium(V) Precipitation formulation KS11 may be used safely to hold the precipitation for about two months. The transformation of V(V) species to V(IV) during the discharge cycle of the battery will further enhance the stability of V(V) solution due to the lowering of the state-of-charge. 9. The effect of additive addition does not influence the electrochemical behaviour of the V(V) solutions, which exhibited very similar cyclic voltammograms with additive, and without additive. 10. Preliminary evaluation of formulation KS11 to inhibit precipitation of supersaturated V(II), V(III) and V(IV) solution was carried out. The induction time of 4M V(IV) solution in 6M total sulfate/bisulfate at 20°C was increased from 2 days for the blank solution to 56 days with the addition of KS 11. The performance of KS11 against V(III) solution was evaluated at 3°C in the refrigerator. The blank V(III) solution of concentration 4M in 6M total sulfate/bisulfate as well as a sample with KS 11 surprisingly did not show any sign of precipitation for about 3 months. The induction time of 2M V(II) solution in 5M total sulfate/bisulfate however, was found to be about 5 days and addition of KS 11 increased the induction time to about 27 days at 3°C. 11. It appears that formulation KS 11 may act as a comprehensive additive if it shows promising results after further investigations against the precipitation of V(II), V(III) and V(IV) solutions at temperatures of about 5°C - 40°C, higher vanadium concentrations of 3.5M and total sulfate/bisulfate concentrations up to 6M. 241 Chapter 7 Conclusions CHAPTER 7 CONCLUSIONS Demand for new energy storage systems is increasing for applications such as remote area power systems, wind turbine generators, load levelling at electric power stations, as well as emergency back-up applications. Longer lifetime and higher energy density batteries are needed for mobile applications to meet the new requirements for zero-emission vehicles. This research was undertaken to increase the energy density of the vanadium redox battery so as to reduce the weight and volume required for mobile applications. The main emphasis of the study was on determining the optimum conditions for stabilising vanadium(V) electrolyte used in the positive half-cell of the vanadium redox battery. Solubility data of vanadium compounds in sulfuric acid were systematically generated. Comprehensive studies were conducted to investigate the properties, stability, electrochemical behaviour and kinetics of precipitation of supersaturated vanadium(V) solutions. The performance of various antisealants and formulations developed during this research was also evaluated to increase the stability of supersaturated vanadium(V) electrolytes. The main findings of this research are summarised in the following paragraphs. 1. The solubility of V2O5 was determined in sulfuric acid concentrations between 0 - 9M and at temperatures ranging from 10°C - 50°C. It was found that increasing the sulfuric acid concentration increases the solubility of V2O5 due to several factors such as the increase in H+ ions, formation of vanadium and sulfate/bisulfate complexes, and dimerisation/polymerisation of V02+ ions. 242 Chapter 7 Conclusions The solubility of V2O5 was found to decrease with increasing temperature because of the endothermic nature of the precipitation of V02+ ions to V205. The effect is more pronounced at higher sulfuric acid concentrations, probably due to the sharply decreasing second dissociation constant of H2S04 with rising temperature resulting in a reduction of S042 ions. This will lead to a decrease in formation of V02+ and S042 complexes with subsequent decrease in solubility of V205 A solubility correlation was developed to predict the solubility of V205 in sulfuric acid concentrations ranging from 3M to 9M over the temperature range of 10°C - 50°C with an overall average absolute deviation of about 9%. 2. The solubility data for vanadyl sulfate was generated in sulfuric acid concentrations ranging from 0 to 9 M and over the temperature range 10°C to 50°C. It was found that the solubility of vanadyl sulfate decreases with increasing sulfuric acid concentration and decreasing temperature. The variation in solubility is due to the common ion effect and is strongly linked with the second dissociation constant of H2S04 at different temperatures and sulfuric acid concentrations. The solubility data and saturation ionic product (KSip) data of vanadyl sulfate was correlated using the Extended Debye-Huckel functional form for above mentioned sulfuric acid concentration and temperature range with an average absolute deviation of less than 4.5%. 3. An attempt was made to determine the solubility of V203 in sulfuric acid concentrations ranging from OM to 7M over the temperature range of 20°C - 50°C. It was observed that the dark blackish blue coloured solids of V203 transformed to the bright blue colour of V0S04 after 2-3 weeks during the solubility experiment resulting in a phase change. Hence the 243 Chapter 7 Conclusions saturation concentrations of vanadium may not represent the solubility of V203 and therefore, this should be referred to as saturation concentration of vanadium obtained from V203 and not as the solubility of V203 in sulfuric acid. However, the saturation concentration of V203 was maximum at H2S04 concentrations around 5M and it increases with increasing temperature. A fairly high saturation concentration of about 2M total vanadium(III) was achieved using reagent grade V203 as compared with the very low value of about 0.22M total V(V) from V205 in 5M H2S04 concentration at 20°C. 4. The equilibrium calculations for the system V205 - H2S04 - H20 revealed that increasing the H2S04 concentration increases the V02+ concentration, confirming the observations made in the solubility experiments for V205 in H2S04 solutions. 5. It is recommended to prepare supersaturated vanadium(V) solution by electrolytic oxidation of supersaturated V(IV) solution obtained by reacting V205 and V203 in sulfuric acid solution with about 15% excess V203. The 15% extra V203 over stoichiometric amount is needed because of some percentage of V204A^0S04 present in the industrial grade V203. The supersaturated V(IV) solutions are very sensitive to agitation. To avoid precipitation in the electrolysis cell due to nitrogen bubbling, the stability of V(IV) solution needs to be improved by preheating for an hour at its boiling point. 6. The density of supersaturated vanadium(V) solutions varies from 1.5 gm/cc to 1.8 gm/cc for 2M V(V) solution in 5M total sulfate/bisulfate and 5M V(V) in 7M total sulfate/bisulfate respectively. 7. The viscosity of supersaturated V(V) solutions containing total sulfate/bisulfate between 5M and 7M increases gradually with increasing 244 Chapter 7 Conclusions V(V) concentration in the range of 2M to 3.5M, but a further increase in V(V) concentration to 5M increases viscosity exponentially and the effect is more sharp at higher total sulfate/bisulfate concentration. This behaviour indicates that the supersaturated V(V) solutions remain in the hydraulic type flow region at V(V) concentrations below 3.5M and transform to the plastic flow region with further increase in vanadium(V) concentration. Increasing temperature significantly decreases the viscosity of V(V) solutions. The viscosity of V(V) solutions decreases slightly (3- 7%) with time and the effect is more pronounced at lower total sulfate/bisulfate concentrations because of precipitation. 8. A significant drop in viscosity and corresponding increase in conductivity due to moisture absorption was observed when V(V) solutions were exposed to the atmosphere. This significant drop in viscosity is probably due to a slight dilution and disturbance of the polyvanadic structure of the supersaturated V(V) solution by absorbing moisture. It was found that the sulfuric acid is responsible for moisture absorption from the atmosphere. 9. The conductivity of supersaturated V(V) solutions decreases with increasing V(V) concentration at constant total sulfate/bisulfate concentration. The main reason for the decrease in conductivity with increasing V(V) concentration is due to the reduced sulfuric acid concentration resulting in a lowering of free H+ ions in the solution. The conductivity is further reduced at higher concentrations because of ion association and interionic interactions. 10. The cyclic voltammogram of the supersaturated vanadium(V) solutions revealed that in the concentration range of 2 - 3.5 M the peak height increases with increasing V(V) concentration but further increasing V(V) concentration decreases the peak currents. This decrease in peak current with increase in V(V) concentration above 3.5M may be attributed to the 245 Chapter 7 Conclusions sharp increase in viscosity leading to a decrease in diffusion coefficient Also changes in the interfacial tension properties of the more concentrated solutions may reduce the wettability of the glassy carbon electrode in the solution thereby reducing the effective surface area and decreasing the peak currents. Increasing total sulfate/bisulfate concentration decreases the peak heights due to increased viscosity and perhaps due to the formation of electrochemically inactive vanadium-sulfate complex species or polyvanadic species. The cyclic voltammogram of the V(V) solutions prepared initially and after 1000 hours exhibited similar peak heights and peak potential separation and did not show any significant difference because of aging. The heterogeneous rate constants for the V(IV)/V(V) couple and diffusion coefficients determined at a glassy carbon electrode at different scan rates were found to decrease with increasing V(V) concentration (2-4M). From the overall evaluation of the electrochemical behaviour of vanadium(V) supersaturated solutions, it can be concluded that the maximum vanadium(V) concentration should not exceed 3.5M containing not more than 6M of total sulfate/bisulfate to achieve good reversibility and peak currents. 11. Stirring of the V(V) solutions at high supersaturations showed no sign of enhanced precipitation and the induction time was practically the same with and without stirring suggesting that the V(V) thermal precipitation reaction is not diffusion controlled. 12. Increasing total sulfate/bisulfate concentration increases induction time probably due to the presence of more H+ ions which shifts the V205 precipitation equilibrium towards the formation of V02+. The stability 246 Chapter 7 Conclusions might also be improved because of the dimerisation and formation of sulfate/bisulfate complexes with V02+. However, a slightly lower state of the charge of V(V) solutions increases induction time significantly. This is due to the decrease in the V(V) concentration in the partially reduced solution, but could also be due to interactions between the V(V) and the V(IV) ions in the solution giving rise to enhanced stability of the V02+ species. 13. The kinetic study of thermal precipitation of V(V) solutions indicated that the growth rate follows first order reaction kinetics under the conditions of low supersaturations with an activation energy of about 9.0 kJmol', indicating diffusion controlled growth. At high supersaturations the V(V) precipitation obeys a second order rate equation. The high activation energy of 77.2 kJmof1 during second order crystal growth suggests that the precipitation of V(V) solution in the high supersaturation region is surface reaction controlled. 14. Preliminary screening of various additives indicated that the additives SHMP, EDTMP and K3P04 can stabilise V(V) and V(IV) supersaturated solutions significantly at temperatures of 50°C and 20°C respectively. A number of formulations were thus developed by mixing these three additives (SHMP, EDTMP and K3P04) in different ratios. Formulation KS (SHMP + K3P04) showed better performance than all other formulations evaluated using 4M V(V) solution in 6M total sulfate/bisulfate at 40°C for 1000 hours. The formulation KS increased the induction times and decreased the precipitation rates significantly. Dosage optimization studies of formulation KS (SHMP + K3P04) indicated that lwt% SHMP + lwt% K3P04 exhibited superior performance over other additive blends. 247 Chapter 7 Conclusions The influence of these inhibitors on the nucleation rates and crystal growth may be due to (i) direct chelation of phosphate ion with V02+ ions to form stable complex (V02)3P04 and (ii) adsorption of the additive onto the precipitating ion, thus inhibiting scale nucleation, or adsorption onto the growing crystals, thus distorting and/or inhibiting further precipitation. Structural matching between the functional groups of the additives and the cations at the crystal surface plays an important role in determining the effectiveness of the additives. 15. Long term evaluation of formulation KS11 indicated that the apparent equilibrium concentration of 4M V(V) solution in 6M total sulfate/bisulfate reached a level of 3.2M while the apparent equilibrium concentration without formulation KS11 was found to be 2.5M after 100 days. This increase in apparent equilibrium concentration may be attributed to the reduced precipitation rates due to additive KS11 and also probably due to the higher viscosity of the more concentrated solutions, which may slow down the precipitation reaction. 16. The effect of increasing V(V) concentration on the performance of KS11 indicated that at 40°C, formulation KS11 was able to hold the precipitation of 3M and 4M V(V) solution in 6M total sulfate/bisulfate for about 40 days, but failed to prevent the precipitation of 5M V(V) solution in 6M total sulfate/bisulfate after 8 days due to high supersaturations. The increase in temperature above 50°C reduces the effectiveness of the formulation KS11 significantly. The induction time of V(V) solutions with additive KS11 can be further enhanced by increasing the total sulfate/bisulfate concentration because of dimerisation and sulfate/bisulfate complex formation. The stability of 3.5M V(V) solution in 5.7M total sulfate/bisulfate when investigated with and without additive at 40°C indicated that the blank 248 Chapter 7 Conclusions solution has an induction time of 25 days while addition of KS11 extended the induction time to about 60 days. 17. The effect of additive addition does not influence the electrochemical behaviour of the V(V) solutions, which exhibited very similar voltammograms of the V(V) solutions with additive, and without additive. 18. Preliminary evaluation of formulation KS11 to inhibit precipitation of supersaturated V(II), V(III) and V(IV) solution was carried out. The induction time of 4M V(IV) solution in 6M total sulfate/bisulfate at 20°C was increased from 2 days for the blank solution to 56 days with the addition of KS11. The blank V(III) solution of concentration 4M in 6M total sulfate/bisulfate as well as a sample with KS 11 surprisingly did not show any sign of precipitation for about 3 months at 3°C. The induction time of 2M V(II) solution in 5M total sulfate/bisulfate however, was found to be about 5 days and addition of KS 11 increased the induction time to about 27 days at 3°C. 19. 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Power Sources, 36, p. 29. 267 APPENDICES 268 APPENDIX A CALIBRATION CURVE FOR ICP ANALYSIS AND SAMPLE CALCULATION 1. Calibration Curve To analyze the solubility samples for total vanadium and total sulfur, a calibration curve was developed by preparing standard solutions of different total vanadium and total sulfur concentration using 1000 mg/1 standards of V(V) species in 0.1M HC1. Because the samples for the V2O5 solubility experiments were diluted using 0.02M HC1 to avoid precipitation of V(V) ions, the samples contains Cl' ions in addition to sulfate/bisulfate ions and vanadium ions. The matrix of the standard solutions in terms of V, S and Cl were therefore, kept similar to that of the unknown samples obtained from solubility experiments. The calibration curve obtained from standard vanadium solutions of concentration 50 mg/1, 150 mg/1 and 250 mg/1 in 0.02M HC1 is shown in Figure A.l along with its equation. 200 - ■w 150 -- E 100" Vanadium Cone, ICP (mg/1) Figure A.l. Calibration curve: total vanadium concentration measured by ICP, versus actual vanadium concentration from standard vanadium solution A-l 350 300 - 250 - 200 - 150 - 100 - y = 1.0308x R2 = 1 Total Sulfur Cone, 1CP (mg/1) Figure A.2. Calibration curve: total sulfur concentration measured by ICP, versus actual sulfur concentration from standard solutions. The calibration curve of total sulfur obtained from standard solutions of concentration 38 mg/1, 100 mg/1 and 334 mg/1 in 0.02M HC1 is shown in Figure A.2. 2. Sample Solubility Calculation A sample calculation is presented here for the solubility of V2O5 in 1M sulfuric acid at 20°C. The average reading obtained from ICP for vanadium in the diluted sample was 183 mg/1 and for total sulfur was 333 mg/1. The details of the calculations to obtain the saturation concentration of vanadium and sulfur in the actual sample are presented below. A-2 Vanadium concentration Total Vanadium from ICP : 183 (mg/1) Dilution Factor : 92.6 Correction Factor from calibration curve (Figure A.l): 0.98 Actual Vanadium Concentration: 183*92.6*0.98 16607 (mg/1) Actual V205 Concentration: 16607/(1000*2*50.94) 0.163 (M) Sulfur concentration Total Sulfur from ICP: 333 (mg/1) Dilution Factor : 92.6 Correction Factor from calibration curve (Figure A.2): 1.031 Actual Sulfur Concentration: 333*92.6*1.031 31792 (mg/1) Actual Sulfur Concentration: 31792/(1000*32.06) 0.9916 (M) APPENDIX B CALCULATION OF ACTIVITY COEFFICIENT USING BROMLEY CORRELATION Bromley [1973] correlated the mean activity coefficients of strong aqueous electrolytes by the following equation. -A\z+z_\4Tm | (0.06 + 0.6sJz+Z_ |/. logy± = + BJ. B-l 1 + ai-*7r \2 1 + |Z+Z ,, where A is Debye Huckel parameter (0.511 at 25 °C) aj is temperature independent constant The value of a, varies according to the type of electrolyte. For electrolytes of type 1:1, 1:2, 2:1 and 2:2, the value of aj is 1 ± 0.2. Z+, Z. are the ionic charges Bm is the Bromley parameters Im is the ionic strength of the system at equilibrium Sample Calculation of y± for HS04' ion System: 2m V(V) solution in 6m H2S04 at 25 °C The system consists of reaction described in Equation 4-23 to 4-25 and the ionic strength of the system at equilibrium (Im) = 6.67 molal A = 0.511 HS04' dissociates into H+ and S04 Z+ = 1 Z. - -2 B-l Bm — Bh+ + B so42 + [Öh+][Öso42] {from Bromley, 1973} = 0.0875 + 0.00 [0.103] *[-0.4] = 0.0463 Substituting the values for all the variables A, ai, Z+, Z-, Im and Bm in Equation B-l gives the value of y± for HS04' = 0.1805. B-2 APPENDIX C COMPUTER PROGRAM IN FORTRAN TO CALCULATE EQUILIBRIUM COMPOSITION OF VARIOUS SPECIES FOR THE SYSTEM: V205-H2S04-H20 c==—=—==—======C MAIN PROGRAM C======$debug DIMENSION A0( 10),AJINV(5,5),W(250),AA( 10 DIMENSION SK( 10),A( 10),C( 10),G( 10),T( 10),XM( 10),WM( 10),T0( 10) COMMON/AR 1 / SK,T,XM,AI OPEN( 1 ,FILE='V5EQ 1 .INP’,STATUS=’OLD’) OPEN(4,FILE='V5EQ 1 .OUT',STATUS=’NEW') OPEN(2,FILE='V411 A.OUT’,STATUS='NEW') TM=298.15 P=l. WM(1)=87.62 WM(2)=66.9 WM(3)=96.0616 WM(4)=22.9898 WM(5)=35.453 WM(6)=24.312 WM(7)=61.02 WM(8)=137.34 STEP=.01 ACC=0.000001 MAXFUN=100 DMAX=10. KW=4 READ(1,*) M READ(1,*) N READ(1,*) (SK(J),J=1,N) READ( 1 ,*) ITMAX,IPRINT,EPS 1 ,EPS2,(A0(K),K=1 ,M) MM1=M-I M4=M+4 CALL FONT(KW,l) WRITE(KW,2) 2 FORMAT(/,20X,'EQUILIBRIUM CONCENTRATIONS CALCULATION’,/) CALL FONT(KW,3) WRITE(KW,4) 4 FORMAT(13X,’System & Dissociation Constants (Input):’) CALL FONT(KW,0) WRITE(KW,5) (SK(J),J=1,N) 5 FORMAT( &10X/H2O —> H+ + OH- ==> K1 =’,E12.5,/, &1 OX,‘Dummy (c) —> Dm++ + S04- ==> K2 =’,E12.5,/, &10X,’V205(c)+H+—> V02+ + H20 => K3 =’,E12.5,/, &10X,’HSO4- (aq)—> H+ + S04- ==> K4 =’,E12.5,/,) READ(1,*) (T0(K),K=1,M4) TT=(T0(4)/WM(4)+T0(2)/WM(2)+T0(6)/WM(6))/100. C DENS=DNACL(TM,P,T0(4),'MGL’) C-l DENS=1.2 DO 3 K=1,M4 3 T(K)=T0(K)/(WM(K)*1000.*(DENS-T0(K)/1.E6)) READ( 1 ,*) MAXFN1 ,MAXFN2,PSTEP,ACC,DMAX,EPS3 CALL FONT(KW,3) WRITE(KW,6) 6 FORMAT(/,13X,'Total Concentrations (Input):') CALL FONT(KW,0) WRITE(KW,7) (T0(KL),T(KL),KL=2,MM 1) 7 FORMAT(10X,'Species',09X,'(Mg/1)',09X,'(Molal)',//, &10X,'VO2+ ',5X,F7.0,8X,F8.6,/, &10X,'SO4— ',5X,F7.0,8X,F8.6,/) C &10X/DM++ ',5X,F7.0,8X,F8.6,/, CALL FONT(KW,3) WRITE(KW,13) DENS 13 FORMAT(13X,'Density of System ( based on NaCl only) ',F7.4, &' gm/cc',/) DO 48 K=1,M 48 A(K)=A0(K) DO 58 J=1,N 58 XM(J)=1. C( 1 )=SK(2)/A(3)*( 1 ./XM(2)) C(2)=SK(3)*A(4)/XM(3) C(3)=A(4)*A(3)/SK(4)*(XM(4)) C(4)=S K( 1 )/A(4)*( 1 ./XM( 1)) CALL IONSTR(A,C,T,AIO) WRITE(2,19) AIO MAXFUN=MAXFN 1 DO 300 LK=1,ITMAX DO 290 LJ=1,M 290 AA(LJ)=ABS(A(LJ)) STEP=PSTEP* AMIN 1 (AA( 1), AA(2), AA(3), AA(4)) CALL NSO1 A(M,A,G,AJINV,STEP,DMAX,ACC,MAXFUN,IPRINT,W) MAXFUN=MAXFN2 C( 1 )=SK(2)/A(3)*( 1 ./XM(2)) C(2)=SK(3)*A(4)/XM(3) C C(2)=SK(3)/A(3)*( 1 ./XM(3)) C(3)=A(4)*A(3)/SK(4)*(XM(4)) C(4)=S K( 1 )/A(4)*( 1 ,/XM( 1)) CALL IONSTR(A,C,T,AI) WRITE(2,19) AI 19 FORMAT(/'IONICSTR.= ',F10.5) IF(ABS((AI-AI0)/AI0).LE.EPS3) THEN CALL FONT(KW,3) WRITE(KW,11) 11 FORMAT(13X,'Molal Concentrations Of Various Species ', & 'At Equilibrium (Output):',/) CALL FONT(KW,0) WRITE(KW, 12) C( 1 ),C(2),A(3),A(4),C(4),C(3),A( 1 ),A(2) 12 FORMAT( &1 OX,‘Dummy Ion Dm++ (aq) = ',E 12.5,/, &10X,'Vanadium(V) Ion V02+ (aq) = ’.E12.5,/, &1 OX,'Sulfate Ion S04- (aq) =',E12.5,/, &1 OX,'Hydrogen Ion H+ (aq) =',E12.5,/, &1 OX,'Hydroxide Ion OH- (aq) = ’.E12.5,/, &1 OX,'Bisulfate Ion HS04- (aq) =',E12.5,/, &10X,'Dummy Dummy (c) = ',E 12.5,/, &1 OX,'Vanadium Sulfate V205 (c) =’,E12.5,/,) CALL FONT(KW,3) C-2 WRITE(KW,16) 16 FORMAT(13X,'Non-Ideality Factors (F) for Various Reactions', &' (Bromley):') CALL FONT(KW,0) WRITE(KW,51) (XM(J),J=1,N) 51 FORMAT(/, &10X,'H2O —> H+ + OH- ==> FI =',E12.5,/, &10X,'Dummy (c) —> Dm++ + S04- ==> F2 =’,E12.5,/, & 10X,'V2O5(c)+H+—> V02+ + H20 ==> F3 =',E12.5,/, &10X/HSO4- (aq)—> H+ + S04- ==> F4 =',E12.5,/,) CALL FONT(KW,3) WRITE(KW,17) AI 17 FORMAT(13X,'Ionic Strength of System @ Equilibrium = ',F7.4, &' Molal’) CALL FONT(KW,0) GO TO 500 ELSE CALL BROM(AI,T,XM) AI0=AI ENDIF 300 CONTINUE WRITER,400) ITMAX WRITE(KW,400) ITMAX 400 FORMAT(13X,'No Convergence After '13,' Iterations') 500 STOP END C*’******************************************************************************** C SUBROUTINES C======SUBROUTINE BROM(AI,T,XM) DIMENSION XM( 10),B(10),Z( 10),V( 10),U( 10),T( 10) B(l)=0.0605 B(2)=-.0195 B(3)=-.0102 B(4)=0.0463 Z(l)=l. Z(2)=4. Z(3)=4. Z(4)=2. V(l)=2. V(2)=2. V(3)=2. V(4)=2. U(l)=l. U(2)=l. U(3)=l. U(4)=0.65 A=l. AB=0.5108 AP=0.5091 SI=SQRT(AI) D=1.+A*SI DO 5 1=1,4 T1=-AB*Z(I)*SI/D T2=(.06+.6*B(I))*Z(I)*AI/(1.+L5*AI/Z(I))**2 T3=B(I)*AI G AM A= 10. * *(T 1+T2+T3) XM(I)=(GAMA**V(I))/U(I) 5 CONTINUE C-3 C...... -...... C F=-4.*AP/(3.*2.3026) C TPl=SI/( 1 .+1,2*SI)+ALOG( 1.+1,2*SI)/0.6 C TP=F*TP1+.1599*T(4)-.5172*AI**( 1 ,/3.) C XM(2)=(10.**TP)**2 C...... -...... CALL GSRS04(AI,T,G) XM(2)=G**2 C-...... CALL GCAS04(AI,G) XM(3)=G**2 XM(3)=.5 C------C AL=70. C E=.005 C B(3)=.1000 C T1=-AB*Z(3)*SI/D C T2=(.06+.6*B(3))*Z(3)*AI/(1.+ 1.5*AI/Z(3))**2 C T3=B(3)*AI C T4=-E*AL*SI*(1.-EXP(-AL*SI)) C G AM A= 10. **(T 1+T2+T3+T4) C XM(3)=(GAMA**V(3))/U(3) RETURN END C======SUBROUTINE IONSTR(A,C,T,AI) DIMENSION A( 10),C( 10),T( 10) CONST=T(4)+T(5)+4.*T(6)+T(7)+4.*T(8) AI=.5*(A(4)+C(4)+4.*C(l)+4.*A(3)+4.*C(2)+C(3)+CONST) RETURN END C===—=—======SUBROUTINE CALFUN(M,A,G) DIMENSION A(1),G(1) DIMENSION SK( 10),C( 10),T( 10),XM( 10) COMMON/AR1/ SK,T,XM,AI C( 1 )=SK(2)/A(3)*( 1 ./XM(2)) C(2)=SK(3)*A(4)/XM(3) C C(2)=SK(3)/A(3)*(1./XM(3)) C(3)=A(4)*A(3)/SK(4)*(XM(4)) C(4)=SK( 1 )/A(4)*( 1 ./XM( 1)) CC=T(4)-T(5)+2.*T(6)-T(7)+2.*T(8) G( 1 )=C( 1)+A( 1 )-T( 1) G(2)=C(2)+A(2)-T(2) G(3)=A( 1 )+A(3)+C(3)-T(3) G(4)=A(4)-2*A(3)+2.*C( 1)+ C(2)-C(3)+C(4) C CALL IONSTR(A,C,T,AI) C CALL B ROM(AI,T,XM) RETURN END C======SUBROUTINE GCAS04(AI,G) SI=AI**.5 ASP=1.50 S=0.5091 B=-.60E-3 C=16.4E-3 G1=-4.*S*SI/(1.+ASP*SI)-.5*B*AI+.5*C*AI**2 G=10.**G1 C-4 RETURN END SUBROUTINE GSRS04(AI,T,G) DIMENSION T(10) REAL MNA,MMG,MCA MNA=T(4) MCA=T(2) MMG=T(6) Bl=.1599 Cl=-.5172 B2=.7445 C2=-.6456 B3=.9937 C3=-.7980 VI =2. V2=3. V3=3. V=4. S1=MNA S2=3.0*MMG S3=3.0*MCA ST=AI**0.5 SlT=Sl**(l./3.) S2T=S2**(l./3.) S3T=S3**(l./3.) SV=AI IF(SV.NE.O.) THEN P1=S1/SV P2=S2/SV P3=S3/SV ELSE P1=0. P2=0. P3=0. ENDIF S V=MNA*V 1 +MMG*V2+MCA*V3 IF(SV.NE.O.) THEN Q1=MNA*V1/SV Q2=MMG*V2/SV Q3=MC A* V 3/S V ELSE Q1=0. Q2=0. Q3=0. ENDIF A=0.5091 R=4.*A/(3.*2.3026) G1 =-R*(ST/( 1 .+1.2*ST)+(2./l .2)*ALOG( 1 .+1.2*ST)) 1+(B 1 *MNA*Q 1 +B2*MMG*Q2+B3 *MCA*Q3) 1 +(C 1 *S 1 T*P 1 +C2*S2T*P2+C3*S3T*P3) G=10.**G1 RETURN END C======SUBROUTINE FONT(KW,N) IF(N.EQ.O) THEN WRITE(KW,10) 10 FORMAT('_(8U_(sOp') C-5 ELSEIF(N.EQ.l) THEN WRITE(KW,20) 20 FORMAT(’_(0U_(s 1 p_(s 14.4V_(s7B') ELSEIF(N.EQ.2) THEN WRITE(KW,30) 30 FORM AT('_(0U_(s 1 p_(s 10V_(s0B_(s0S') ELSEIF(N.EQ.3) THEN WRITE(KW,40) 40 FORMAT('_(OU_(slp_(slOV_(s7B_(sOS') ELSEIF(N.EQ.4) THEN WRITE(KW,50) 50 FORMAT('_(0U_(s 1 p_(s 10V_(s0B_(s 1 S') ELSEIF(N.EQ.5) THEN WRITE(KW,60) 60 FORMAT('_(OU_(slp_(s8V_(s-7B') ENDIF RETURN END SUBROUTINE NS01 A(N,X,F,AJINV,DSTEP,DMAX,ACC,MAXFUN,IPRINT,W) DIMENSION X( 1 ),F( 1),AJINV(N,N),'W( 1 ),QX( 10) MAXC=0 NT=N+4 NTEST=NT DTEST=FLOAT(N+N)-0.5 NX=N*N NF=NX+N NW=NF+N MW=NW+N NDC=MW+N ND=NDC+N FMIN=0. DD=0. DSS=DSTEP*DSTEP DM=DMAX*DMAX DMM=4.*DM IS=5 TINC=1. IF(IPRINT) 1,1,85 85 WRITE(2,86) 86 FORMAT(") 1 M AXC=M AXC+1 CALL CALFUN(N,X,F) FSQ=0. DO 2 1=1,N FSQ=FSQ+F(I)*F(I) 2 CONTINUE IF(FSQ-ACC) 3,3,4 3 IF(IPRINT) 5,5,6 6 WRITE(2,7) MAXC 7 FORMAT(///5X,'FINAL SOLUTION BY NS01A REQURIED',15, «fe'FUNCTION CALLS’) WRITE(2,8) (I,X(I),F(I),I=1,N) 8 FORMAT(//4X,T,7X,'X(I)',12X,'F(I)'//(I5,2E17.8)) WRITE(2,9) FSQ 9 FORMAT(/5X,’THE SUM OF SQUARES IS',E17.8) 5 RETURN zz 4 GO TO (10,11,11,10,11),IS C-6 10 IF(FSQ-FMIN) 15,20,20 20 IF(DD-DSS) 12,12,11 12 NTEST=NTEST-1 IF(NTEST) 13,14,11 14 WRITE(2,16) NT 16 FORMAT(///5X,’ERROR RETURN FROM NS01A BECAUSE',15, &' CALLS OF CALFUN FAILED TO IMPROVE THE RESIDUALS’) 17 DO 18 1=1,N NXI=NX+I NFI=NF+I X(I)=W(NXI) F(I)=W(NFI) 18 CONTINUE FSQ=FMIN GO TO 3 13 WRITE(2,19) 19 FORMAT(///5X,'ERROR RETURN FROM NS01A BECAUSE F(X)', &'FAILED TO DECREASE USING A NEW JACOBIAN') GOTO 17 15 NTEST=NT 11 IF(MAXFUN-MAXC) 21,21,22 21 WRITE(2,23) MAXC 23 FORMAT(///5X,'ERROR RETURN FROM NS01A BECAUSE ’ &,'THERE HAVE BEEN',15,'CALLS OF CALFUN') IF(FSQ-FMIN) 3,17,17 22 IF(IPRINT) 24,24,25 25 WRITE(2,26) MAXC 26 FORMAT(///5X,'AT THE ',I5,'TH CALL OF CALFUN WE HAVE') WRITE(2,8) (I,X(I),F(I),I=1,N) WRITE(2,9) FSQ 24 GO TO (27,28,29,87,30),IS 30 FMIN=FSQ DO 31 1=1,N NXI=NX+I NFI=NF+I W(NXI)=X(I) W(NFI)=F(I) 31 CONTINUE 32 IC=0 IS=3 33 IC=IC+1 X(IC)=X(IC)+DSTEP GO TO 1 29 K=IC DO 34 1=1,N NFI=NF+I W(K)=(F(I)-W(NFI))/DSTEP K=K+N 34 CONTINUE NXIC=NX+IC X(IC)=W (NXIC) IF(IC-N) 33,35,35 35 K=0 DO 36 1=1,N DO 37 J=1,N K=K+1 AJINV(I,J)=W(K) NDK=ND+K W(NDK)=0. C-7 37 CONTINUE NDCKI=NDC+K+I W(NDCKI)=1. NDCI=NDC+I W(NDCI)= 1 .+FLOAT(N-I) 36 CONTINUE C CALL MB01B(AJINV,N,N) EPS=1.0E-20 DET=SIMUL(N,AJINV,QX,EPS,-1,10) 38 DS=0. DN=0. SP=0. DO 39 1=1,N X(I)=0. F(I)=0. K=I DO 40 J=1,N NFJ=NF+J X(I)=X(I)-W (K) * W (NFJ) F(I)=F(I)-AJINV (I, J)*W (NFJ) K=K+N 40 CONTINUE DS=DS+X(I)*X(I) DN=DN+F(I)*F(I) SP=SP+X(I)*F(I) 39 CONTINUE IF(FMIN*FMIN-DMM*DS) 41,41,42 42 GO TO (43,43,44),IS 44 WRITE(2,45) 45 FORMAT(///5X,’ERROR RETURN FROM NS01A BECAUSE A' &'NEARBY STATIONARY POINT OF F(X) IS PREDICTED') GO TO 17 43 NTEST=0 DO 46 1=1,N NXI=NX+I X(I)=W(NXI) 46 CONTINUE GO TO 32 41 IS=2 IF(DN-DD) 47,47,48 47 DD=AM AX 1 (DN,DSS) DS=0.25*DN TINC=1. IF(DN-DSS) 49,58,58 49 IS=4 GO TO 80 48 K=0 DMULT=0. DO 51 1=1,N DW=0. DO 52 J=1,N K=K+1 DW=DW+W(K)*X(J) 52 CONTINUE DMULT=DMULT+DW*DW 51 CONTINUE DMULT=DS/DMULT DS=DS *DMULT*DMULT IF(DS-DD) 53,54,54 C-8 54 IF(DD) 55,55,56 55 DD=AMAX 1 (DSS,AMIN 1 (DM,DS)) DS=DS/(DMULT*DMULT) GO TO 41 56 ANMULT=0. DMULT=DMULT*SQRT(DD/DS) GO TO 98 53 SP=SP*DMULT ANMULT=(DD-DS)/((SP-DS)+SQRT((SP-DD)**2+(DN-DD) &*(DD-DS))) DMULT=DMULT*( 1 ,-ANMULT) 98 DN=0. SP=0. DO 57 1=1,N NDI=ND+I F(I)=DMULT*X(I)+ANMULT*F(I) DN=DN+F(I)*F(I) SP=SP+F(I)*W(NDI) 57 CONTINUE DS=0.25*DN NDC1=NDC+1 IF(W(NDC 1 )-DTEST) 58,58,59 59 IF(SP*SP-DS) 60,58,58 50 IS=2 60 DO 61 1=1,N NXI=NX+I NDI=ND+I NDCI=NDC+I NDCI1 =NDC+I+1 X(I)=W(NXI)+DSTEP*W(NDI) W(NDCI)=W(NDCI 1)+1. 61 CONTINUE W(ND)=1. DO 62 1=1,N K=ND+I SP=W(K) DO 63 J=2,N KN=K+N W(K)=W(KN) K=K+N 63 CONTINUE W(K)=SP 62 CONTINUE GOTO 1 58 SP=0. K=ND DO 64 1=1,N NDCI=NDC+I NDCI 1 =NDC+I+1 X(I)=DW DW=0. DO 65 J=1,N K=K+1 DW=DW+F(J)*W(K) 65 CONTINUE GO TO (68,66),IS 66 W(NDCI)=W(NDCI)+1. SP=SP+DW*DW IF(SP-DS) 64,64,67 C-9 67 IS=1 KK=I X(1)=DW GO TO 69 68 X(I)=DW 69 W(NDCI)=W(NDCI 1)+1. 64 CONTINUE W(ND)=1. IF(KK-1)70,70,71 71 KS=NDC+KK*N DO 72 1=1,N KMN=K-N K=KS+I SP=W(K) DO 73 J=2,KK W(K)=W(KMN) K=K-N 73 CONTINUE W(K)=SP 72 CONTINUE 70 DO 74 1=1,N NWI=NW+I W(NWI)=0. 74 CONTINUE SP=X(1)*X(1) K=ND DO 75 1=2,N DS=SQRT(SP*(SP+X(I)*X(I))) DW=SP/DS DS=X(I)/DS SP=SP+X(I)*X(I) DO 76 J=1,N K=K+1 KN=K+N NWJ=NW+J IM 1=1-1 W(NWJ)=W(NWJ)+X(IM 1 )*W(K) W(K)=DW*W(KN)-DS*W(NWJ) 76 CONTINUE 75 CONTINUE SP= 1 ./SQRT(DN) DO 77 1=1,N K=K+1 W(K)=SP*F(I) 77 CONTINUE 80 FNP=0. K=0 DO 78 1=1,N NXI=NX+I NWI=NW+I NFI=NF+I X(I)=W(NXI)+F(I) W(NWI)=W(NFI) DO 79 J=1,N K=K+1 W(NWI)=W(NWI)+W(K)*F(J) 79 CONTINUE FNP=FNP+W(NWI)**2 78 CONTINUE C-10 GO TO 1 27 DMULT=.9*FMIN+. 1 *FNP-FSQ IF(DMULT) 82,81,81 82 DD=AMAX1(DSS,.25*DD) TINC=1. IF(FSQ-FMIN) 83,28,28 81 SP=0. SS=0. DO 84 1=1,N NWI=NW+I SP=SP+ABS(F(I)*(F(I)-W(NWI))) SS=SS+(F(I)-W(NWI))**2 84 CONTINUE PJ= 1 ,+DMULT/(SP+SQRT(SP*SP+DMULT*SS)) SP=AMIN1(4.,TINC,PJ) TINC=PJ/SP DD=AMIN 1 (DM,SP*DD) GO TO 83 87 IF(FSQ-FMIN) 83,50,50 83 FMIN=FSQ DO 88 1=1,N SP=X(I) NXI=NX+I NFI=NF+I NWI=NW+I X(I)=W(NXI) W(NXI)=SP SP=F(I) F(I)=W(NFI) W(NFI)=SP W (NWI)=-W (NWI) 88 CONTINUE IF(IS-l) 28,28,50 28 DO 89 1=1,N NXI=NX+I NFI=NF+I X(I)=X(I)-W(NXI) F(I)=F(I)-W (NFI) 89 CONTINUE K=0 DO 90 1=1,N MWFMW+I NWI=NW+I W(MWI)=X(I) W(NWI)=F(I) DO 91 J=1,N W (MWI)=W (MWI)-AJINV (I, J)*F(J) K=K+1 W (NWI)=W (NWI)-W(K) *X( J) 91 CONTINUE 90 CONTINUE SP=0. SS=0. DO 92 1=1,N DS=0. DO 93 J=1,N DS=DS+AJINV(J,I)*X(J) 93 CONTINUE SP=SP+DS*F(I) C-ll SS=SS+X(I)*X(I) F(I)=DS 92 CONTINUE DMULT=1. IF(ABS(SP)-0.1 *SS) 94,95,95 94 DMULT=0.8 95 PJ=DMULT/SS PA=DMULT/(DMULT*SP+( 1 ,-DMULT)*SS) K=0 DO 96 1=1,N NWI=NW+I MWI=MW+I SP=PJ*W(NWI) SS=PA*W(MWI) DO 97 J=1,N K=K+1 W(K)=W(K)+SP*X(J) AJINV(I,J)=AJINV(I,J)+SS*F(J) 97 CONTINUE 96 CONTINUE GO TO 38 END SUBROUTINE TEST(NN) WRITER,3) NN WRITE(3,3) NN 3 FORMATC TEST’,12) RETURN END C======FUNCTION DNACL(T,P,Y,Q) C IMPLICIT REAL*8 (A-H,0-Z) CHARACTER*3 Q A(T)=5.916365-0.01035794*T+0.9270048E-5 *T**2 &-1127.522/T+100674.1/T**2 B(T)=0.5204914E-2-. 10482101 E-4*T+.8328532E-8*T**2 &-1.1702939/T+102.2783/T**2 C(T)=0.118547E-7-.6599143E-10*T D(T)=-2.5166+.0111766*T-0.170552E-4*T**2 E(T)=2.84851-.0154305 *T+0.223982E-4*T**2 F(T)=-.0014814+.82969E-5 *T-0.12469E-7*T**2 G(T)=0.0027141 -. 15 391 E-4*T+0.22655E-7 *T**2 H(T)=0.62158E-6-.40075E-8*T+0.65972E-l 1*T**2 IF(Q.EQ.’MGL'.OR.Q.EQ.'G/L'.OR.Q.EQ.'MLR') THEN IF(Q.EQ.'G/L') THEN X=Y/1000. ELSEIF(Q.EQ.'MGL') THEN X=Y/1000000. ELSEIF(Q.EQ.'MLR') THEN X=Y*58.44/1000. WRITE(*,*) X ENDIF P=1.03323*P A0=X**2*(E(T)-P*G(T)) B0=X*(D(T)-P*F(T)-.5*P**2*H(T))-1. C0=A(T)-P*B(T)-P**2*C(T) V=(-B0-SQRT(B0**2-4.*A0*C0))/(2.*A0) C-12 DNACL=1./V ELSEIF(Q.EQ.'WTP'.OR.Q.EQ.'WTF'.OR.Q.EQ.’MOL') THEN IF(Q.EQ.'WTP') THEN X=Y/100. ELSEIF(Q.EQ.'MOL') THEN X=Y*58.44/(X*58.44+1000.) ENDIF V=A(T)-P*B(T)-P**2*C(T)+X*D(T)+X**2*E(T)-X*P*F(T) &-X**2*P*G(T)-.5*X*P**2*H(T) DNACL= 1 ./V ENDIF RETURN END FUNCTION SIMUL(N,A,X,EPS,INDIC,NRC) C IMPLICIT REAL*8 (A-H, O-Z) C IMPLICIT REAL*8(A-H, O-Z) C REAL*8 A,X,EPS,SIMUL DIMENSION IROW(50),JCOL(50),JORD(50),Y(50),A(NRC,NRC),X(N) C MAX=N IF(INDIC.GE.O) MAX=N+1 IF(N.LE.50) GO TO 5 WRITE(*,200) WRITE(2,200) SIMUL=0. RETURN 5 DETER=1. DO 18 K=1,N KM1=K-1 PIVOT=0. DO 11 1=1,N DO 11 J=1,N IF(K.EQ.l) GO TO 9 DO 8 ISCAN=1,KM1 DO 8 JSCAN=1,KM1 IF(I.EQ.IROW(ISCAN)) GO TO 11 IF(J.EQ.JCOL(JSCAN)) GO TO 11 8 CONTINUE C 9 IF(DABS(A(I,J)).LE.DABS(PIVOT)) GO TO 11 9 IF(ABS(A(I,J)).LE.ABS(PIVOT)) GO TO 11 PIVOT=A(I,J) IROW(K)=I JCOL(K)=J 11 CONTINUE C IF(DABS(PIVOT).GT.EPS) GO TO 13 IF(ABS(PIVOT).GT.EPS) GO TO 13 SIMUL=0. RETURN 13 IROWK=IROW(K) JCOLK=JCOL(K) DETER=DETER*PI V OT DO 14 J= 1,MAX 14 A(IROWK,J)=A(IROWK,J)/PIVOT A(IROWK,JCOLK)=l ./PIVOT DO 18 1=1,N AIJCK=A(I,JCOLK) IF(I.EQ.IROWK) GO TO 18 A(I,JCOLK)=-AIJCK/PIVOT C-13 DO 17 J=1,MAX 17 IF(J.NE.JCOLK) A(I,J)=A(I,J)-AIJCK*A(IROWK,J) 18 CONTINUE C DO 20 1=1,N IROWI=IROW(I) JCOLI=JCOL(I) JORD(IROWI)=JCOLI 20 IF(INDIC.GE.O) X(JCOLI)=A(IROWI,MAX) C INTCH=0. NM 1 =N-1 DO 22 1=1,NM1 IP1=I+1 DO 22 J=IP1,N IF(JORD(J).GE.JORD(I)) GO TO 22 JTEMP=JORD(J) JORD(J)=JORD(I) JORD(I)=JTEMP INTCH=INTCH+1 22 CONTINUE IF(INTCH/2*2.NE.INTCH) DETER=-DETER C IF(INDIC.LE.O) GO TO 26 SIMUL=DETER RETURN C 26 DO 28 J=1,N DO 27 1=1,N IRO WI=IRO W (I) JCOLI=JCOL(I) 27 Y(JCOLI)=A(IROWI,J) DO 28 1=1,N 28 A(I,J)=Y(I) DO 30 1=1,N DO 29 J=1,N IROWJ=IROW(J) JCOLJ=JCOL(J) 29 Y(IROWJ)=A(I,JCOLJ) C DO 30 J=1,N 30 A(I,J)=Y(J) C SIMUL=DETER RETURN 200 FORMAT(lX,'TOO BIG') END C====== C-14 APPENDIX D PROCEDURE TO ADJUST TOTAL VANADIUM AND TOTAL SULFUR CONCENTRATION OF A GIVEN V(V) SOLUTION IN SULFURIC ACID Supersaturated vanadium(V) solution in sulfuric acid can be prepared by the electrolytic oxidation of supersaturated V(IV) solution according to the procedure described in Section 5.2.1.1. It is difficult to prepare a V(IV) solution of a particular vanadium and sulfur concentration accurately. So, if the V(V) solution after ICP analysis was found to be 3.7M V(V) in 5.8M total sulfate/bisulfate, then to prepare for example, 3.5M V(V) solution in 6M total sulfate/bisulafte, the following procedure was adopted. Initial composition of the V(V) solution: 3.7M V(V) - 5.8 M total sulfate Suppose it is desired to prepare 200ml of 3.5M V(V) solution in 6M total sulfate Vanadium Concentration Balance 3.7M*Vvi ml = 3.5M*200 ml => Vvi= 189 ml This means 189 ml of 3.7M V(V) + 11 ml of sulfuric acid will give 3.5M V(V) solution. But the concentration of 11 ml of sulfuric acid is unknown to obtain 6M total sulfates in the resulting 200 ml solution. To adjust the total sulfur concentration it is necessary to carry out sulfur concentration balance. Sulfur Concentration Balance 5.8 M*189 ml + Cs*l 1 ml = 6.0 M*200 ml => Cs = 9.44M D-l Therefore, 189 ml of 3.7M V(V) + 11 ml of 9.44M sulfuric acid will give 3.5M V(V) solution in 6.0M total sulfur. It is recommended to prepare initial solution having slightly higher V(V) concentration and slightly lower total sulfur concentration than the desired value. D-2 APPENDIX E CALIBRATION CURVE FOR ATOMIC ABSORPTION ANALYSIS AND SAMPLE CALCULATION The concentration of supersaturated vanadium solutions of stability evaluation and kinetic experiments were analysed by atomic absorption Model Varian AA2 Plus. Standards of concentration 50 mg/1, 100 mg/1 and 200 mg/1 vanadium were prepared using 1000 mg/1 vanadium standard solution. To avoid the matrix effects of the unknown samples, the standards were prepared in 0.02 M HC1 and sulfuric acid was also added to it to keep the total sulfates and chlorides in similar amounts that was expected in the unknown samples. The calibration curve developed using standards is shown in Figure E.l along with its equation. The unknown sample of supersaturated vanadium(V) solutions were diluted taking 0.2 ml of unknown sample in 500 ml 0.02M HC1, a dilution factor of 2500. The AAS was set to measure two readings of each unknown sample and provide a mean reading. The instrument was calibrated before and after analyzing each set of samples to avoid any drift in the instrument and the vanadium concentration of unknown samples were obtained using the calibration curve shown in Figure E-l. Sample calculations are given below for 3M V(V) solution. 0,25 y = 0,0016x R2 =0,9995 Concentration (mg/1) Figure E.l Calibration Curve: total vanadium concentration versus absorbance Sample Calculation A sample calculation is presented here for a fresh solution of about 3M V(V) solution in 6M total sulfate/bisulfate. The mean absorbance obtained from AAS for diluted sample of 3M V(V) solution was 0.099. Using calibration curve shown in Figure E.l, the concentration of vanadium in the actual sample was calculated according to the following procedure. Absorbance obtained for unknown sample: 0.099 Concentration of V(V) in the unknown sample: 0.099/0.0016 (mg/1) (From calibration curve: Figure E.l) Dilution Factor: 2500 Actual vanadium concentration: (0.099/0.0016)*2500 154687 (mg/1) Actual vanadium concentration: 154687/(1000*50.94) 3.04 (M) E-2 APPENDIX F FORTRAN PROGRAM TO CALCULATE DENSITY OF SULFURIC ACID SOLUTIONS AS A FUNCTION OF TEMPERATURE AND CONCENTRATION c C MAIN PROG TO PREDICT DENSITIES OF MIXED ELECTROLYTES SOLUTIONS OR DENSITY OF SULFURIC ACID SOLUTIONS C...... C:SULFURIC ACID CONC. RANGE: 0 -70%; TEMP RANGE: 0 - 100°C C: C Binary Density Correlations from C Novotny and O. Sohnel, “Densities of Binary Aqueous C Solutions of 306 Inorganic Substances”, J. Chem. Eng. Data, 33, No.l, 49-55, 1988. C Mixing Rule from Potter, R. W. and Hass J. L. Jr., "Models for Calculating Density and Vapor C Pressure of Geothermal Brines", Jour. Research U.S. Geol. Survey, Vol. 6, No. 2, pp. 247-257 Mar. C Apr. 1978 C------c IMPLICIT REAL*8 (A-H.O-Z) CHARACTER CH CHARACTERS Q CHARACTERS RANGE CHARACTERS NM(99) DIMENSION CONCG(20),DEN(20),CONCX(20) COMMON/AR1/ A,B,C,D,E,F,WM COMMON/AR2/ RANGE CH=CHAR(27) SUM=0. WRITE(*,'(1X,2A\)') CH,'[2J' WRITE(*,51) 51 FORMAT(//22X,'MIXTURE DENSITY OF MULTICOMPONENT SOLUTION'//) WRITE/*,53) 53 FORMAT(12X,'AVAILABLE CONCENTRATION UNITS ARE:'//, &12X,'MGL -> mg/1 ; GML -> gm/1 '/, &12X,'WTP -> WT. % ; WTF -> WT. FRACTION'/, &12X,'MLR-> MOLARITY; MOL-> MOLALITY ’//) WRITE/*,55) 55 FORMAT/12X,'SPECIFY CONC. UNITS : \) READ/*,57) Q 57 FORMAT/A3) WRITE/*,59) 59 FORMAT/12X,’No. OF COMPONENTS : \) READ(*,61) NC 61 FORMAT/I2) WRITE/*,63) 63 FORMAT/12X,'TEMPERATURE (C) : \) READ/*,65) TEMP 65 FORMAT/F8.2) DO 3 1=1,NC WRITE/*,67) I 67 FORMAT//12X,'FORMULA OF COMPONENT No.',12,': \) READ/*,69) NM/I) 69 FORMAT/A8) CALL CDATA/NM/I)) WRITE/*,72) RANGE F-l 72 FORMAT(12X,'VALIDITY RANGE -> ’A25) WRITE(*,71) 71 FORMAT( 12X,'CONCENTRATION : ’,\) READ(*,73) CONCG(I) 73 FORMAT(F12.5) IFCQ.EQ.’WTP'.OR.Q.EQ.’WTF) THEN SUM=SUM+CONCG(I) ENDIF 3 CONTINUE DO 5 1=1,NC CALL CDATA(NM(I)) C IFCQ.EQ.’MGL'.OR.Q.EQ.'G/L'.OR.Q.EQ.'MLR’) THEN IF(Q.EQ.'G/L') THEN CONCX(I)=CONCG(I)/WM ELSEIF(Q.EQ.'MGL') THEN CONCX(I)=CONCG(I)/( 1000. *WM) ELSEIF(Q.EQ.’MLR') THEN CONCX(I)=CONCG(I) ENDIF LF=1 ELSEIFCQ.EQ.'WTP'.OR.Q.EQ.’WTF.OR.Q.EQ.'MOL') THEN IF(Q.EQ.'WTP') THEN CONCX(I)= 1000.*CONCG(I)/(WM*( 100.-SUM)) ELSEIF(Q.EQ.’WTF) THEN CONCX(I)= 1000.*CONCG(I)/(WM*( 1 .-SUM)) ELSEIF(Q.EQ.'MOL') THEN CONCX(I)=CONCG(I) ENDIF LF=2 ENDIF C 5 CONTINUE IF(LF.EQ. 1) THEN Q='MLR' ELSEIF(LF.EQ.2) THEN Q='MOL' ENDIF TMOL=0. DO 10 J=1,NC 10 TMOL=TMOL+CONCX(J) C C CALCULATE BINARY-DENSITIES C DO 20 J=1,NC 20 DEN(J)=DENS(NM(J),TEMP,TMOL,Q) c C DETERMINE THE MINIMUM BINARY-DENSITY C DMIN=10. DO 30 K=1,NC IF(DEN(K).LT.DMIN) THEN DMIN=DEN(K) NK=K ENDIF 30 CONTINUE DS=DEN(NK) DO 40 L=1,NC IF(L.NE.NK) THEN F-2 DEL=DEN(L)-DEN(NK) F=CONCX(L)/TMOL DS=DS+F*DEL ENDIF 40 CONTINUE WRITE(*,77) DS 77 FORMAT(//12X,'MIXTURE DENSITY : \F8.5,' gm/cc7//) C WRITE(*,*) DS STOP END C SUBROUTINES C======C FUNCTION PROG TO CALC BINARY DENSITY C FUNCTION DENS(NAME,TEMP,CONC,UNIT) IMPLICIT REAL*8 (A-H,0-Z) COMMON/AR1/ A,B,C,D,E,F,WM CHARACTER*3 UNIT,Q CHARACTER *8 NAME CALL CDATA(NAME) Q=UNIT Y=CONC T=TEMP IFCQ.EQ.'MGL'.OR.Q.EQ.'G/L'.OR.Q.EQ.'MLR') THEN IF(Q.EQ.'G/L') THEN X=YAVM ELSEIF(Q.EQ.'MGL') THEN X=Y/(1000. *WM) ELSEIF(Q.EQ.'MLR') THEN X=Y ENDIF DENS=DMLR(T,X)/1000. RETURN ELSEIFCQ.EQ.'WTP'.OR.Q.EQ.'WTF'.OR.Q.EQ.'MOL') THEN IF(Q.EQ.'WTP') THEN X=Y/100. ELSEIF(Q.EQ.’WTF') THEN X=Y ELSEIF(Q.EQ.MOL') THEN X=Y * WM/( Y * WM+1000.) ENDIF DENS=DWTF(T,X)/1000. ENDIF RETURN END C======C FUNCTION PROG TO CALC BINARY DENSITY WHEN INPUT CONC. Mass/Vol. Units C FUNCTION DMLR(T,W) IMPLICIT REAL*8 (A-H,0-Z) COMMON/AR1/ A,B,C,D,E,F,WM A0=999.65+.20438*T-.061744*T**(3./2.) U=W**(3./2.) DMLR=A0+A*W+B*T*W+C*W*T**2+D*U+E*U*T+F*U*T**2 RETURN END C======C FUNCTION PROG TO CALC BINARY DENSITY WHEN INPUT CONC. Mass/Mass Units F-3 c FUNCTION DWTF(T,W) IMPLICIT REAL*8 (A-H.O-Z) COMMON/ AR1/ A,B,C,D,E,F,WM CALL PQR(T,W,P,Q,R) X=1000. DO 5 11=1,500 CALL XFUNC(P,Q,R,X,FF,DF) IF(DABS(FF).LE. 1.0D-02) THEN DWTF=X RETURN ENDIF X=X-FF/DF 5 CONTINUE DWTF=0. RETURN END C======C SUBROUTINE PROG TO READ BINARY CONSTANTS AND VALIDITY RANGE C SUBROUTINE CDATA(NAME) IMPLICIT REAL*8 (A-H,0-Z) DIMENSION CF(10,7) CHARACTERS RNG(99),RANGE CHARACTER*8 NAME,NM(99) COMMON/AR1/ A,B,C,D,E,F,WM COMMON/AR2/ RANGE OPEN( 1 ,FILE='CDATA.INP',STATUS='OLD') READ(1,*) N DO 3 1=1,N 3 READ(1,*) NM(I),(CF(I,J) ,J=1,7),RNG(I) DO 5 1=1,N IF(NAME.EQ.NM(I)) THEN K=I GO TO 8 ENDIF 5 CONTINUE 8 A=CF(K,1) B=CF(K,2) C=CF(K,3) D=CF(K,4) E=CF(K,5) F=CF(K,6) WM=CF(K,7) RANGE=RNG(K) RETURN END C======C SUBROUTINE PROG TO EVALUATE P, Q, R TO SOLVE CUBIC EQ. C SUBROUTINE PQR(T,W,P,Q,R) IMPLICIT REAL*8 (A-H.O-Z) COMMON/AR1/ A,B,C,D,E,F,WM WF=W A0=999.65+.20438*T-.061744*T**(3./2.) X=WF/WM Y=X**(3./2.) A1=A*X B 1=B*T*X F-4 C1=C*X*T**2. D1=D*Y E1=E*Y*T F1=F*Y*T**2 T1=D1+E1+F1 Sl=l.-Al-B 1-C1 G=S1/T1 H=A0/T1 P=-1.*G*G Q=2.*G*H R=-1.*H*H RETURN END C======™======C SUBROUTINE PROG TO EVALUATE DF,FF TO SOLVE CUBIC EQ. C SUBROUTINE XFUNC(P,Q,R,V,FF,DF) IMPLICIT REAL*8 (A-H,0-Z) FF=V**3+P*V**2+Q*V+R DF=3.*V**2+2.*P*V+Q RETURN END C======INPUT FILE: CDATA.INP c=====™======10 Number of data points in the input file 'NACL' ,4.4850D01 ,-9.634D-2,6.136D-4,-2.7120D0,1.009D-2,0.00000D0,58.4430,'TEMP(C):0-100; Cmax=satd' 'CACL2' , 1.0120D02,-6.156D-2,1,028D-3,-9.7490D0,9.694D-3,-3.165D-4,110.981 ,TEMP(C):0-100; Cmax=satd' MGCL2’ ,8.0990D011.887D-1,2.315D-3,-6.0290D0,7.449D-2,-8.305D-4,95.2110,TEMP(C):0-100; Cmax=satd' 'KCL' ,4.9710D01,-7.150D-2,6.506D-4,-2.3760D0,000.0D02,0.00000D0,74.5510,TEMP(C):0-100; Cmax=satd' 'NA2S04' , 1.4120D02,-4.535D-1.3.766D-3,-1.7510D1,2.111D-1,-1.773D-3,142.037,TEMP(C):0-100; Cmax=satd' 'MGS04' , 1,4370D02,-6.531D-1,5.263D-3,-23.280D0,39.11 D-2,-27.83D-4,120.363,TEMP(C):0-100; Cmax=satd' 'HCL' ,0.2046D02,-.9435D-1,1.090D-3.-1.2270D0,1.269D-2,-1.980D-4,036.461 ,’TEMP(C):0-80 ; Cmax=36 %' 'H2S04' ,0.7060D02,-2.367D-l,1.676D-3,-4.9030D0,5.698D-2,-3.985D-4,098.073,TEMP(C):0-100; Cmax=70 %’ 'SR(N03)2', 1,8000D02,-4.794D-1,3.631D-3,-12.140D0,18.35D-2,- 14.25D-4,211,630,'TEMP(C):0-100; Cmax=satd' 'SRCL2 ’,1.5360D02,-4.157D-l,3.586D-3,-14.630D0,23.11D-2.-18.94D-4,158.526,TEMP(C):0-100; Cmax=satd' 'FORMULA', A ,B ,C,D,E,F ,Mw ,’TEMP(C):0-100; Cmax=satd’ F-5 APPENDIX G PLOTS OF GROWTH RATE OF V(V) SOLUTIONS IN 5M AND 6M TOTAL SULFATE/BISULFATE AT 20,30, 40 AND 50 °C 2V5S at 40 C 4.0 - 3.5 -- n =0.96 Kg' = 0.0042 5 3.0 -- 2.5 -- U 2.0 - y =0.9591x +2.3754 ec 1.5 -- R2 =0.9301 1.0 0.5 -- -log(C-Ceq), mol/1 Figure G-l. Plot of growth rate of 2 M V(V) solution in 5 M total sulfates against relative supersaturation at 40°C 4.0 -- 2V5S at 50 C n = 1.1 3.5 -- Kg' = 0.0102 s 3-0 -- 2.5 -- U 2.0 -- y = 1.0972x + 1.9893 R2 =0.9734 “ 1.5 -- 1.0 -- 0.5 -log(C-Ceq), mol/1 Figure G-2. Plot of growth rate of 2 M V(V) solution in 5 M total sulfates against relative supersaturation at 50°C G-l 4.0 -- 3.5 -- 3V5S at 20 C n =0.9 «5 3.0 -- Kg'= 0.0036 1 2-5 5 2.0 U •v y =0.9131x + 2.4406 i* 1.5 _o R2 = 0.8139 1.0 0.5 + 0.0 —I— 0.0 0.5 1.0 1.5 2.0 -log(C-Ceq), mol/1 Figure G-3. Plot of growth rate of 3 M V(V) solution in 5 M total sulfates against relative supersaturation at 20°C 3.5 -- 3V5S at 30 C n =0.9 3.0 -- Kg' = 0.0050 2 2.5 -- 2.0 -- y =0.8661x +2.2982 £ 1.5 - R2 =0.8859 • 1.0 -- 0.5 -- -log(C-Ceq), mol/1 Figure G-4. Plot of growth rate of 3 M V(V) solution in 5 M total sulfates against relative supersaturation at 30°C G-2 4.0 3.5-- 3V5S at 40 C n = 1.6 3.0 -- Kg'= 0.0314 2 2.5 -- 2.0 -- V 1.5 -- y = 1.6433x + 1.5032 R2 =0.9977 T 1.0 -- 0.5 -- 0.0 -I------1------1------1------1------1------1------0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 -log(C-Ceq), mol/1 Figure G-5. Plot of growth rate of 3 M V(V) solution in 5 M total sulfates against relative supersaturation at 40°C 4.0 -- 3V5S at 50 C 3.5 -- n = 1.8 Kg'= 0.0653 ^ 3.0 -- 2.5 -- U 2.0 -- y = 1.8323x + 1.185 R2 = 0.9828 » 1.5 -- 1.0 -- 0.5 -- -log(C-Ceq), mol/1 Figure G-6. Plot of growth rate of 3 M V(V) solution in 5 M total sulfates against relative supersaturation at 50°C G-3 4.5 4V5S at 20 C n = 1.0 <5 Kg’= 0.0058 "3 E 5 U «o '5b y =0.9783x + 2.234 o R2 = 0.9404 0.5 0.0 + 0.0 0.5 1.0 1.5 2.0 -log(C-Ceq), mol/1 Figure G-7. Plot of growth rate of 4 M V(V) solution in 5 M total sulfates against relative supersaturation at 20°C 4V5S at 30 C n = 1.5 Kg’ = 0.0093 o 2.5 y = 1.4925x +2.031 R2 = 0.9784 -log(C-Ceq), mol/1 Figure G-8. Plot of growth rate of 4 M V(V) solution in 5 M total sulfates against relative supersaturation at 30°C G-4 4.0 -- 4V5S at 40 C 3.5 -- n = 1.8 5 3.0 -- Kg'= 0.0521 2.5 -- ü 2.0 -- y = 1.8326x + 1.2835 ge 1.5 -- R2 = 0.9956 1.0 -- 0.5 -- -log(C-Ceq), mol/1 Figure G-9. Plot of growth rate of 4 M V(V) solution in 5 M total sulfates against relative supersaturation at 40°C 3.5 -- 4V5S at 50 C 3.0 -- n = 1.8 Kg'=0.0910 o 2.5 -- 2.0 - 1.5 -- y = 1.7796X + 1.0355 R2 =0.9883 1.0 -- 0.5 -- -log(C-Ceq), mol/1 Figure G-10. Plot of growth rate of 4 M V(V) solution in 5 M total sulfates against relative supersaturation at 50°C G-5 3.5 -- 5V5S at 20 C 3.0 -- n =0.9 Kg' = 0.0047 © 2.5 -- 2.0 -- 1.5 -- ' 1.0 -- y = 0.8504x + 2.3235 R2 = 0.9641 0.5 -- -log(C-Ceq), mol/1 Figure G-l 1. Plot of growth rate of 5 M V(V) solution in 5 M total sulfates against relative supersaturation at 20°C 5V5S at 30 C 3.0 - n = 1.7 Kg'= 0.0103 «c 2.5 -- £ 2.0 -- y = 1.7154x + 1.9857 R2 = 0.9754 T 1.0 -- 0.5 -- -log(C-Ceq), mol/1 Figure G-l2. Plot of growth rate of 5 M V(V) solution in 5 M total sulfates against relative supersaturation at 30°C G-6 3.5 5V5S at 40 C 3.0 -- n = 2 Kg' = 0.0267 2.5 -- S 2.0 -- y = 1.9923x + 1.5732 R2 =0.9958 " 1.0 -- 0.5 -- 0.0 -I------1------1------1------1------0.0 0.2 0.4 0.6 0.8 1.0 -log(C-Ceq), mol/1 Figure G-13. Plot of growth rate of 5 M V(V) solution in 5 M total sulfates against relative supersaturation at 40°C 5V5S at 50 C n = 1.9 Kg' = 0.0996 y = 1.8497x + 1.0019 R2 =0.9812 -log(C-Ceq), mol/1 Figure G-14. Plot of growth rate of 5 M V(V) solution in 5 M total sulfates against relative supersaturation at 50°C G-7 4.0 -- 2V6S at 50 C n =0.7 3.5 - Kg'= 0.0014 5 3.0 -- 2.5 -- U 2.0 -- 1.5 -- y =0.6812x +2.8437 R2 =0.7216 1.0 - 0.5 -- -log(C-Ceq), mol/1 Figure G-15. Plot of growth rate of 2 M V(V) solution in 6 M total sulfates against relative supersaturation at 50°C 3.5 -- 3V6S at 40 C n = 1.2 3.0 -- Kg' = 0.0044 o 2.5 -- 2.0 - y = 1.1645x +2.3563 1.5 -- R2 =0.9324 1.0 -- 0.5 -- -log(C-Ceq), mol/1 Figure G-16. Plot of growth rate of 3 M V(V) solution in 6 M total sulfates against relative supersaturation at 40°C G-8 3V6S at 50 C 3.5 -- n= 1.8 3.0 Kg'=0.0235 o 2.5 -- 2.0 -- 1.5 -- y = 1.759x + 1.6286 R2 = 0.9757 1.0 -- 0.5 -- -log(C-Ceq), mol/1 Figure G-17. Plot of growth rate of 3 M V(V) solution in 6 M total sulfates against relative supersaturation at 50°C 3.5 - 4V6S at 40 C n =2.0 Kg'=0.0386 © 2.5 -- 2.0 y = 2.0959x + 1.4137 1.5 - R2 =0.984 ’ 1.0 0.5 -- -log(C-Ceq), mol/1 Figure G-18. Plot of growth rate of 4 M V(V) solution in 6 M total sulfates against relative supersaturation at 40°C G-9 4.0 -- 4V6S at 50 C 3.5 -- n = 1.9 Kg' = 0.0923 2.5 -- U 2.0 -- y = 1.9218x + 1.035 R2 =0.9591 “ 1.5 -- 1.0 -- 0.5 -- -log(C-Ceq), mol/1 Figure G-19. Plot of growth rate of 4 M V(V) solution in 6 M total sulfates against relative supersaturation at 50°C 4.0 -- 5V6S at 20 C 3.5 -- n = 1.1 Kg' =0.0106 2 3.0 -- 2.5 -- U 2.0 -- » 1.5 -- y = 1.1039x + 1.9749 R2 =0.9848 1.0 -- 0.5 -- -log(C-Ceq), mol/1 Figure G-20. Plot of growth rate of 5 M V(V) solution in 6 M total sulfates against relative supersaturation at 20°C G-10 3.5 -- 5V6S at 30 C n = 1.2 3.0 - Kg'= 0.0149 Ö 2.5 -- 2.0 -- 1.5 -- y = 1.381 lx+ 1.8257 R2 = 0.9742 ' 1.0 - 0.5 -- -log(C-Ceq), mol/1 Figure G-21. Plot of growth rate of 5 M V(V) solution in 6 M total sulfates against relative supersaturation at 30°C 3.0 -- 5V6S at 40 C n = 1.7 S 2.0 -- y = 1.6759x + 1.7407 T 1.0 -- R2 =0.9918 0.5 -- -log(C-Ceq), mol/1 Figure G-22. Plot of growth rate of 5 M V(V) solution in 6 M total sulfates against relative supersaturation at 40°C G-i l 3.0 -- 5V6S at 50 C n = 1.7 «c 2.5 -- Kg’=0.0332 E 2.0 -- y = 1.6587x + 1.479 ■7 1.0 - R2 =0.997 0.5 -- -log(C-Ceq), mol/1 Figure G-23. Plot of growth rate of 5 M V(V) solution in 6 M total sulfates against relative supersaturation at 50°C G-12