Molecular Dynamics Simulation of Carbon Dioxide in Aqueous Electrolyte Solution
Total Page：16
File Type：pdf, Size：1020Kb
Molecular Dynamics Simulation of Carbon Dioxide in Aqueous Electrolyte Solution Tao Huang Dissertation Submitted in Fulfillment of the Requirements for the Degree of Doctor of Philosophy Faculty of Information and Communication Technologies Swinburne University of Technology 2012 Abstract The structural properties and diffusion coefficients of the H2O+NaCl+CO2 ternary system at various NaCl concentrations, temperatures and pressures are investigated using molecu- lar simulation. A CO2 potential model is selected for the simulation of CO2 diffusion coef- ficient in aqueous solution. As the most appropriate model, it produces simulation results which are in closest agreement with experimental data. The properties of the H2O+NaCl system are examined prior to the H2O+NaCl+CO2 system, including the radial distribu- tion functions, coordination numbers and diffusion coefficients at various temperatures and pressures. Three aspects of the ternary system are studied. First, the diffusion coefficients of the ternary system at different NaCl concentrations are observed. The NaCl concentra- tion is found to have a large impact on both the diffusion coefficients of the ternary system and also the cluster pattern of ions. Second, the diffusion coefficients of the system at dif- ferent temperatures are studied. Raising the temperature increases the diffusion coefficients and facilitates formation of ions pairs. Finally, the diffusion coefficients of the ternary sys- tem at different pressures are investigated. Pressure also has impact, but to a much lesser degree. At 278 K, the higher the pressure, the greater value of the diffusion coefficient. In contrast at a temperature of 298 K, a pressure increase leads to lower diffusion coefficient. Hydrogen bonds at low temperatures may be the reason for the unusual phenomenon. The diffusion data are compared to predictions of two models proposed by Ratcliff and Holdcroft (1963). The first approach is based on activation theory and results in both a linear and exponential relationship. They preferred a linear model over an exponential ii model due to the limiting experimental data. However, we demonstrate that the exponential model is more suitable for predicting diffusion coefficient with the help of simulation data. The other approach is based on the relation between diffusion coefficient and viscosity, whereby the diffusion coefficient of the gas in electrolyte solution is derived from a given viscosity. The diffusion coefficients obtained from molecular simulation agree with the results from the two equations, demonstrating the accuracy of the two prediction equations. iii Acknowledgement I would like to acknowledge and thank my supervisors Prof. Richard Sadus and Prof. Billy Todd for their positive direction and continuing support. In particular, I am very grateful to my principal supervisor Prof. Richard Sadus. I cannot thank him enough for his constructive guidance, innovative ideas and remarkable patience. During the past few years, I have learned from them the best attributes of a researcher and I believe these attributes will continue to be of great help to my career and life. I would also like to thank Prof. Feng Wang for her advice and encouragement. I would like to thank my wife, Jing, my mother and father, whose love continues to encourage me, as it has always done. I would not have completed this thesis without their encouragement and support. I gratefully acknowledge Dr. Zhongwu Zhou and Dr. Ming Liu for their encouragement and thoughtful discussions. I also thank Dr. Junfang Li, Dr. Jianhui Li, Dr. Jarek Bosko, Dr. Alex Bosowski, Dr. Liping Li for their generous help. I also like to acknowledge the support I have received from my fellow colleagues at CMS. My special thanks go to the staff of FICT and Swinburne Research for their contin- uing support with the highest professional standard possible. I am grateful to Swinburne University of Technology for providing me financial support through a Swinburne University Postgraduate Research Award (SUPRA). I also appreciate the Australian Partnership for Advanced Computing who generously provided an allocation of computing time to perform the simulation. iv Declaration I hereby declare that the thesis entitled “Molecular Dynamics Simulation of Carbon Diox- ide in Aqueous Electrolyte Solution” , and submitted in fulfillment of the requirements for the Degree of Doctor of Philosophy in the Faculty of Information and Communication Technologies of Swinburne University of Technology, is my own work and that it contains no material which has been accepted for the award to the candidate of any other degree or diploma, except where due reference is made in the text of the thesis. To the best of my knowledge and belief, it contains no material previously published or written by another person except where due reference is made in the text of the thesis. Tao Huang 2012 v Contents Abstract ii Acknowledgement iv Declaration v 1 Introduction 1 2 Diffusion Theories 4 2.1 Diffusion Theories . 5 2.1.1 Hydrodynamic Theory . 5 2.1.2 Activated State Theory . 7 2.1.3 Free Volume Theory . 9 2.1.4 Kinetic Theory . 10 2.2 Diffusion Theories of Electrolyte Solutions . 11 2.2.1 Basic Equations of Diffusion in Solution . 14 2.2.2 Diffusion for Single Electrolyte —Nernst-Hartley Equation . 15 2.2.3 Electrophoretic Effect in Diffusion—Onsager-Fuoss Equation . 17 2.2.4 Diffusion for Partly Ionized Electrolytes . 19 2.2.5 Self-Diffusion in Electrolyte Solutions—Onsager Limiting Law . 19 vi 2.2.6 Self-Diffusion in Multicomponent Aqueous Electrolyte Systems in Wide Concentration Ranges . 20 2.3 Summary . 24 3 Molecular Simulation 26 3.1 Introduction . 26 3.2 Molecular Dynamics . 28 3.2.1 Force Field . 29 3.2.2 Lennard-Jones Reduced Units . 31 3.2.3 Periodic Boundary Conditions . 32 3.2.4 Equation of Motion . 32 3.2.5 Time Integration Algorithm . 34 3.2.6 Constant Temperature . 36 3.2.7 Electrostatic Force . 37 3.3 The Applications of Molecular Dynamics . 41 3.3.1 Trajectory Analysis . 41 3.3.2 Radial Distribution Function . 42 3.3.3 Correlation Function . 44 3.3.4 Mean Square Displacement . 44 4 Diffusion Coefficients of Carbon Dioxide in Water using Different CO2 Models 47 4.1 Introduction . 47 4.2 Intermolecular Potential between Water and Carbon Dioxide . 49 4.2.1 Water Models . 49 4.2.2 Carbon Dioxide Models . 53 4.3 Diffusivities of CO2 in Water under Different Potential Models . 57 4.3.1 Simulation Details . 57 4.3.2 Results and Discussion . 58 vii 5 Structural Properties and Diffusion Coefficients of NaCl Aqueous Solutions 63 5.1 Introduction . 63 5.2 Intermolecular Potential between Water and NaCl . 65 5.3 Simulation Details . 65 5.4 Structural Properties of Binary System . 68 5.4.1 Temperature Dependence . 68 5.4.2 Pressure Dependence . 75 5.5 Dynamic Properties . 82 6 Structural Properties and Diffusion Coefficients of Carbon Dioxide in Aqueous Solutions 87 6.1 Introduction . 87 6.2 Simulation Systems . 88 6.3 Structural Properties of Ternary System . 91 6.3.1 Effects of Different NaCl Concentrations . 91 6.3.1.1 Ion-Ion distribution functions . 91 6.3.1.2 Solvent atom distribution functions . 94 6.3.1.3 Ion-Water, CO2 –Water and Ion-CO2 distribution functions 98 6.3.2 Effects of Temperatures on the Ternary System . 106 6.3.3 Effects of Pressures on the Ternary System . 112 6.4 Diffusion in the Ternary System . 123 7 Prediction of Diffusion Coefficient of CO2 in Electrolyte Solutions 129 7.1 Introduction . 129 7.2 Prediction Equation of Diffusion Coefficient Modified From Activation Theory and Perturbation Model . 132 7.2.1 Theory . 132 7.2.2 Results and Discussion . 135 viii 7.3 Predicting Diffusion Coefficient via Viscosity . 139 7.3.1 Theory . 139 7.3.2 Results and Discussion . 141 7.3.2.1 The value of k . 141 7.3.2.2 Comparison of different relationships between diffusion and viscosity via experimental diffusion data . 145 7.3.2.3 Comparison of different relationships between diffusion and viscosity via molecular dynamics diffusion data . 148 8 Conclusions and Recommendations 152 Bibliography 156 ix List of Tables 4.1 Summary of the parameters of various water models (Chaplin, 2011) . 53 4.2 Potential function parameters of different CO2 models . 55 4.3 Diffusivities of H2O under different models and ensembles (Mahoney and Jorgensen, 2001) . 58 4.4 Comparison of diffusivities of CO2 of experimental and different CO2 mod- els. The values for the diffusion constants are given in 10−5cm2=s. 62 5.1 Temperature dependence in NaCl solutions . 67 5.2 Pressure dependence in NaCl solutions . 67 5.3 Potential parameter used in NaCl solutions . 67 5.4 Peak heights and coordination numbers of ion-ion at different temperatures in the NaCl solutions . 71 5.5 Peak heights and coordination numbers of ion-water in different tempera- tures in the NaCl solutions . 72 5.6 Peak heights and coordination numbers between ions for different pres- sures in the NaCl solutions. 77 5.7 Peak heights and coordination numbers of ions-water for different pres- sures in the NaCl solutions . 79 6.1 Concentration dependence settings . 90 6.2 Temperature dependence settings . 90 x 6.3 Pressure dependence settings . 90 6.4 Structure features of ions-ions at different NaCl concentrations . 92 6.5 Parameters used to model Lennard-Jones interactions of anions and cations. 94 6.6 Structure features of Figure 6.4 and Figure 6.5. 102 6.7 Structure features of Figure 6.7 and Figure 6.8. 105 6.8 Structure features of Figure 6.12. 109 6.9 Structure features of Figure 6.15 and Figure 6.16 . 115 6.10 Structure features of Figure 6.20 and Figure 6.21 . 121 ◦ 7.1 Diffusion coefficient of CO2 in NaCl solutions at 25 C and 1atm (Ratcliff and Holdcroft 1963) .