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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 analysis 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, have been reviewed.It was 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.