Analytical solution of Poisson-Boltzmann equation for interacting plates of arbitrary potentials and same sign

JOURNAL OF COLLOID AND INTERFACE SCIENCE

卷:341

Article

Polat, M.¹  Polat, H.² 

[1] Izmir Inst Technol, Dept Chem Engn, Gulbahce Urla Izmir, Turkey

[2] Izmir Inst Technol, Dept Chem, Gulbahce Urla Izmir, Turkey

关键词: Poisson-Boltzmann;    Colloidal;    Electrostatic interaction;    Analytical solution;   

DOI  :  10.1016/j.jcis.2009.09.008

来源: Elsevier

【 摘 要 】

Efficient calculation of electrostatic interactions in colloidal systems is becoming more important with the advent of such probing techniques as atomic force Microscopy. Such practice requires solving the nonlinear Poisson-Boltzmann equation (PBE). Unfortunately, explicit analytical solutions are available only for the weakly charged surfaces. Analysis of arbitrarily charged surfaces is possible only through cumbersome numerical computations. A compact analytical solution of the one-dimensional PBE is presented for two plates interacting in symmetrical electrolytes. The plates can have arbitrary Surface potentials at infinite separation as long they have the same sign. Such a condition covers a majority of the colloidal systems encountered. The solution leads to a simple relationship which permits determination Of Surface potentials, surface charge densities, and electrostatic pressures as a function of plate separation H for different charging scenarios. An analytical expression is also presented for the potential profile between the plates for a given separation. Comparison of these potential profiles with those obtained by numerical analysis shows the validity of the proposed Solution. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free