The Analytical Solutions of Poisson-Boltzmann Equation with two mixed electrolytes in Semi-infinite Planar Symmetry

Liu Guozhi; Luo Genxiang

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The Analytical Solutions of Poisson-Boltzmann Equation with two mixed electrolytes in Semi-infinite Planar Symmetry

Liu Guozhi 1 * #,Luo Genxiang 2

1.Department of Basic Courses,Yingkou Institute of Technology,115014,P.R.Chin

2.Department of Chemistry,School of Chemistry and Matherials Science,Liaoning Shiha University,113001,P.R.China

*Correspondence author

#Submitted by

Subject:

Funding: The work was financially supported by Liaoning Provincial Science and Technology Bureau （No.projerct no. 2009402004 and 2011402008）

Opened online:15 May 2015

Accepted by: none

Citation: Liu Guozhi,Luo Genxiang.The Analytical Solutions of Poisson-Boltzmann Equation with two mixed electrolytes in Semi-infinite Planar Symmetry[OL]. [15 May 2015] http://en.paper.edu.cn/en_releasepaper/content/4642579

In this paper,two analytical exact solutions and three analytical approximate solutions for the nonlinear Poisson-Boltzmann Equation in semi-infinite planar symmetry with two mixed electrolytes are reported. The two analytical exact solutions are applied to the mixtures of z-z with 2z-2z electrolytes, and the mixtures of z-2z with 2z-z electrolytes with identical concentration. The three analytical approximate solutions are applied to other mixed asymmetrical electrolytes with identical concentration (mixtures of 2-3 and 3-2 electrolytes or 1-3 and 3-1 electrolytes or 1-4 and 4-1 electrolytes). To evaluate the accuracy of the approximate solution, the solution was compared with the numerical results obtain from the MATLAB2009b. The error of the approximate solution for mixture of 2-3 and 3-2 electrolytes or 1-3 and 3-1 electrolytes or 1-4 and 4-1 electrolytes with identical concentration is not more than 1%. These new solutions can serve as a functional approximation for potential distribution of two interacting electric double layers when calculating electrostatic interaction energy if the superposition approximation is used.

Keywords:Poisson-Boltzmann equation; mixed electrolytes; potential distribution； Approximate analytical expression.

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