Forces between dissimilar colloidal plates for various surface conditions: I. General method

Abstract

A method is developed for considering the double-layer interaction between parallel colloidal plates with general surface conditions which may be different for the two plates. The general solution of the Poisson-Boltzmann equation is graphed as a set of isodynamic slope curves where the rate of change with distance of the diffuse-layer potential is plotted against the potential itself for a given value of the double-layer force between the plates. The charge-potential isotherms for the two plates (either experimentally or theoretically derived) are then superimposed on the isodynamic slope curves. The range of values taken by the force, as the plate separation is reduced from infinity to zero, together with the existence of maxima or minima in the force, can be seen from the graph. For a given value of the force the potentials of the plates can be read off and any extreme value of the potentials of the plates can be found. The force-separation curve can then be calculated. This method is applicable for any electrolyte type or any mixture of electrolytes. As illustration, the interaction of plates with constant but unequal charges of various signs is considered, and also the case with one plate at constant potential and the other at constant charge.