Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Integral equation

# A Study on Ornstein-Zernike Equation Theory for Electrolytes Based on First-Order Mean Spherical Approximation

Author XuQinZhi
Tutor WuKaiZuo
School Beijing University of Chemical Technology
Course Applied Mathematics
Keywords Electrolytes OZ integral equation An order mean spherical approximation Radial distribution function Total correlation function
CLC O175.5
Type Master's thesis
Year 2008
Downloads 36
Quotes 1
• Abstract
• Contents

Ornstein-Zernike (0Z) integral equation of the radial distribution function and total correlation function in the field of chemical engineering and materials theory has a very important role. This departure from statistical mechanics , by establishing and solving integral equations based electrolytes OZ obtained radial distribution functions between ions and total analytical expression for the correlation function , the main tasks include: 1 , in order to improve the hard-sphere and electrostatic potential energy function model , the introduction of Yukawa potential function, create a new hard-sphere and electrostatic directly related to the function model to solve hard ball soft ball and a long-range electrostatic effects of non- convergence problems , making the electrolyte solution on the original model OZ integral equation solver closer to the actual situation . 2 , by introducing entropy correction to improve the system energy calculation accuracy , making the system radial distribution function in the vicinity of the point of contact ion pairs calculation conditions greatly improved. 3, based on the modified hard sphere model and electrostatic direct correlation function by means of Fourier transform , Hilbert transform and Laplace transform math skills in the basic thermodynamic consistency within the framework of the establishment of an electrolyte original model order mean spherical approximation solution method . The mathematical analysis and statistical mechanics theory combined study of the electrolyte solution structure and thermodynamic properties . 4, the analytical solution obtained directly related to the function of the four parameters , the index reflects the electrolyte solution electrostatic shield strength, coefficient reflects the original MSA in the vicinity of the point of contact ion pairs deviation , which has a clear physical meaning . 5 , for the analysis of first-order mean spherical approximation for solving the resulting analytical accuracy, calculated from the dilute solution to molten salt , from low to high and then to the critical state of the whole process , the global temperature range of the radial distribution electrolyte system functions and part of the total correlation function . Compared with the MSA , calculated RDF values ??near the point of contact has been significantly improved. And GMSA compared to solving this method is simple, more accurate , and without the introduction of molecular simulation parameters to ensure the internal consistency of the theory .

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