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1 Bulletin of the Polish Academy of Sciences. Chemistry

1 2001

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Electrostatic interactions of colloid particles in mixed electrolytes

Warszyński P., Adamczyk Z.

Bulletin of the Polish Academy of Sciences. Chemistry

2001

Vol. 49, No. 1

101-114

Electrostatic interactions of two spherical particles immersed in an electrolyte mixture were analyzed theoretically. A numerical scheme was developed for solving the governing Poisson-Boltzmann equation expressed in the bispherical co-ordinate system. The method was based on the alternating direction over-relaxation procedure using the Newton-Raphson iteration. The novelty of the algorithm consists in using the grid transforming functions enabling a more uniform distribution of mesh points in regions characterized by strong electric field. Using the numerical method, electric potential distribution (within and outside the sphere) was calculated which allowed one to determine the effective surface potential of a spherical particle immersed in a mixture of electrolytes. The interaction energy of particles as a function of their separation was also determined numerically for various amounts of a 2:1 electrolyte added to a 1:1 electrolyte. These energy profiles were compared with analytical approximations derived using the linear superposition approach (LSA) exploiting the effective potential determined previously. It was demonstrated that the LSA can be used as a good estimate of the potential distribution and interaction energy for distances between particles exceeding the double-layer thickness. It was also shown that a small addition of the 2:1 electrolyte decreased significantly the interaction energy between particles, which has implications for colloid stability.