Semi-analytical method of calculating the electrostatic interaction of colloidal solutions

doi:10.1088/1674-1056/26/1/017801

Abstract We present a semi-analytical method of calculating the electrostatic interaction of colloid solutions for confined and unconfined systems. We expand the electrostatic potential of the system in terms of some basis functions such as spherical harmonic function and cylinder function. The expansion coefficients can be obtained by solving the equations of the boundary conditions, combining an analytical translation transform of the coordinates and a numerical multipoint collection method. The precise electrostatic potential and the interaction energy are then obtained automatically. The method is available not only for the uniformly charged colloids but also for nonuniformly charged ones. We have successfully applied it to unconfined diluted colloid system and some confined systems such as the long cylinder wall confinement, the air-water interfacial confinement and porous membrane confinement. The consistence checks of our calculations with some known analytical cases have been made for all our applications. In theory, the method is applicable to any dilute colloid solutions with an arbitrary distribution of the surface charge on the colloidal particle under a regular solid confinement, such as spherical cavity confinement and lamellar confinement.

Keywords: Poisson-Boltzmann equation like-charged attraction basis function expansion multipoint collection method

Received: 24 July 2016
Revised: 31 October 2016
Accepted manuscript online:

PACS:	78.20.Bh	(Theory, models, and numerical simulation)
	02.70.-c	(Computational techniques; simulations)
	05.10.-a	(Computational methods in statistical physics and nonlinear dynamics)
	78.67.Bf	(Nanocrystals, nanoparticles, and nanoclusters)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11304169), the Natural Science Foundation of Ningbo City, China (Grant No. 2012A610178), the Open Foundation of the Most Important Subjects of Zhejiang Province, China (Grant No. xkzwl1505), and K. C. Wong Magna Fund in Ningbo University of China.

Corresponding Authors: Zengju Lian
E-mail: lianzengju@nbu.edu.cn

Cite this article:

Hongqing Tian(田洪庆), Zengju Lian(连增菊) Semi-analytical method of calculating the electrostatic interaction of colloidal solutions 2017 Chin. Phys. B 26 017801

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Semi-analytical method of calculating the electrostatic interaction of colloidal solutions

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