Electrostatic calculations on colloids with planar and spherical charge distributions

A model of the electrical double layer has been derived by assuming that a fraction of double layer counter-ions remains associated with the charged surface (Nature 1984 310: 396). The magnitude of this fraction, i.e. the degree of counter-ion association, can be derived from experimental data. E.g. the electrostatic repulsions in clay gels can be quantitatively explained with the degree of counter-ion association that is independent of plate separation. The dependence of the degree of counter-ion association on bulk ionic strength is obtained from Lubetkin'set al data (Philos Trans R Soc London (1984) A311133), which permits the derivation of a new limiting law that predicts large and ionic strength independent repulsive forces at close surface separations. Such forces have been usually attributed to hydration forces. Within the DLVO framework the theory perdicts reasonable values of the equilibrium separations of swelling clays with divalent counter-ions. The Stern potentials of clays are also consistently accounted for. New calculations for spherical surfaces predict that Stern potentials can have maxima at certain ionic strengths. These maxima, which are often observed in the case of polymer latices, disappear in the limit of infinite radius.