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Studies of Property and Interaction of Electric Double Layer with Functional Theory

Author: XuZuMin
Tutor: ZhangGeXin
School: Jiangnan University
Course: Analytical Chemistry
Keywords: electric double layer (EDL) interaction force and energy thickness functional theory
CLC: O646.1
Type: Master's thesis
Year: 2008
Downloads: 124
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Abstract

By introducing the functional theory into the calculation of electric double layer (EDL) interaction, the interaction energies of two identical parallel plates , two identical charged spherical particles having both equal radii( a 1 = a2 = a) and equal potential (ψ1 =ψ2=ψor the dimensionless potentialφ1 =φ2=φ) are calculated respectively at high, moderate and low potentials. Compared with what from the Debye-Hückel (DH), the Langmuir and the numerical methods respectively, Simple forms of the interaction force and energy at are valid for general potentials are obtained. And the correlation among the electric double layer(EDL) thickness, the radius and the surface potential of the spherical reverse micelles has been estimated.The main contents of the dissertation were as follows:By introducing the functional theory into the calculation of electric double layer (EDL) interaction, the interaction energies of two identical parallel plates are calculated respectively at high (128 /mv), moderate (77 /mv) and low (25.7 /mv) potentials. Compared with what from the Debye-Hückel (DH), the Langmuir and the numerical methods respectively, the results show that DH’and the Langmuir’methods are applicable just for the critical potentials, but the functional approach with quite accurate and simple analytic expression holds true at any potential.The interaction energies of two identical parallel plates are calculated respectively at low, moderate and high potentials with the functional theory. Compared with what from the Debye-Hüchel (DH) approximation and the numerical method at low potential, what from the Langmuir method and the numerical method at high potential, and also what from the DH approximation, the Langmuir method and the numerical method at moderate potential, the results show that DH approximation and Langmuir method are applicable at low and high potentials respectively, but the functional approach holds true at any potential.Investigate Functional-theary by using the function form changing of the iterative solutions of Poisson-Boltzmann Equation(PBE) we have been derived previously and integral method of the Linear-Superposition-Approximation(L.S.A), of finding the formulas of electrical-double-layer(EDL) interaction force and free-energy for two identical charged spherical particles having both equal radii( a 1 = a2 = a) and equal potential (ψ1 =ψ2=ψor the dimensionless potentialφ1 =φ2=φ). Numerical values of interaction free energy and force are compared with our method. The method can be applied to high surface potentials (evenΨ= 0.2056V i.e. the dimensionless potentialΦ= 8),outside the Debye-Huckel range. Two simple forms of the interaction force and energy at large separations (κR≥3 where R is the distance between the two spherical centers ) are valid for general potentials are obtained.Based on the equivalent condenser model with the same center of the particle, the correlation among the electric double layer(EDL) thickness, the radius and the surface potential of the spherical reverse micelles has been estimated. We obtained the real solution of the thickness equation of spherical reverse micelles from the correlation between the radius and the surface potential which was based on the second iterative solution of the Poisson-Boltzmann (PB) equation of spherical reverse micelles in functional analysis and expressed it by graphical format. The relation of the spherical reverse micelles thickness with the parameters: the concentration of ions c, the dielectric constantε, the system temperature T and the charge number of ion z has been shown in the corresponding figures and the fitted curves between the electric double layer thickness of a spherical reverse micelles and the above mentioned parameters c,ε, T and z have also been exhibited. One of the interesting results in our study is the EDL thickness of the spherical reverse micelles was enlarged other than decreased ,as the increasing of z, which was contrary to the positive micelle.

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