ELECTRICAL DOUBLE-LAYER INTERACTIONS FOR SPHERICAL CHARGE REGULATING COLLOIDAL PARTICLES

A new way of linearising the Poisson-Boltzmann equation is presented w hich is capable of producing accurate answers for moderately high surf ace charge and surface potentials. Unlike the Debye-Huckel approximati on, the linearisation is based on the fact that electric potential var iation, rather than the magnitude of the potential itself, remains sma ll between two charged plates at close separation. The method can be a pplied quite generally to any type of surface. The cases of constant s urface charge, the constant surface potential and charge regulating sy stems are considered as examples. The results for constant charge and potentials as high as 5 mu C/cm(2) and 200 mV are within 7% of the exa ct answers for plate separations of one Debye length or less. In contr ast, the Debye-Huckel approximation produces answers that are at least an order of magnitude too large, for the same problems. The applicati on of the method to the problem of calculating the electrostatic force s between charge regulated spherical particles is also addressed in so me detail.