ELECTROSTATIC INTERACTIONS OF COLLOID PARTICLES IN SYMMETRICAL ELECTROLYTES

Electrostatic interactions between two spherical particles and between a particle and a planar interface in a symmetric electrolyte have bee n quantitatively described. A numerical scheme has been developed for solving the nonlinear Poisson-Boltzmann equation expressed in the bisp herical coordinate system. The method is based on the alternating dire ction over-relaxation procedure using the Newton-Raphson iteration. Th e novelty of the algorithm is the application of the grid transforming functions, enabling a more uniform distribution of mesh points in reg ions characterized by strong electric field. Using the numerical metho d, electric potential distribution (within and outside the sphere) hav e been calculated as well as the energy of interaction as a function o f the particle interface separation. The boundary conditions in the fo rm of the constant-potential, constant charge and the mixed case have been applied in these calculations. The energy profiles calculated for various screening lengths were compared with analytical approximation s derived using the Hogg-Healy-Fuerstenau method and the Linear superp osition approach (LSA). It was demonstrated that the LSA can be used a s a good estimate of the potential distribution and interaction energy for a broad range of kappa a including kappa a < 1.