Closed-form solution of mid-potential between two parallel charged plates with more extensive application Project supported by the National Key Basic Research Program of China (Grant No. 2012CB026103), the National Natural Science Foundation of China (Grant No. 51009136), and the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2011212)

• Published in: Chinese physics B 2015-10, Vol.24 (10)
• Main Authors: Shang, Xiang-Yu, Yang, Chen, Zhou, Guo-Qing
• Format: Article
• Language: English
• Subjects: charged plate; empirical closed-formed solution; mid-plane potential; semi-analytical solution
• ISSN: 1674-1056
• DOI: 10.1088/1674-1056/24/10/108203

Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or particle scale mechanical analyses of these systems. The electrostatic repulsive force depends on the mid-plane potential between two charged particles. Previous analytical solutions of the mid-plane potential, including those based on simplified assumptions and modern mathematic methods, are reviewed. It is shown that none of these solutions applies to wide ranges of inter-particle distance from 0 to 10 and surface potential from 1 to 10. Three previous analytical solutions are chosen to develop a semi-analytical solution which is proven to have more extensive applications. Furthermore, an empirical closed-form expression of mid-plane potential is proposed based on plenty of numerical solutions. This empirical solution has extensive applications, as well as high computational efficiency.