Double layer interaction energy of a concentrated system of charged parallel colloidal plates in aqueous electrolyte

Abstract

A concentrated system of charged plate-like colloidal particles, arranged in parallel layers at a common separation and immersed in a uni-univalent aqueous electrolyte is considered. The electric double layer free energy and force are derived under the assumptions that the plate charge is due to the adsorption or desorption of potential determining (p.d.) ions according to the Nernst equation and that the potential distribution in the diffuse layers satisfies the Poisson-Boltzmann (P.B.) equation. The simple case where the p.d. ion is one of the ion species of the 1–1 electrolyte is considered. In addition to exact expressions in terms of elliptic integrals, approximate formulae suitable at large separation and large potentials are obtained. Numerical results are given to illustrate the difference between this “concentrated sol” and the corresponding “dilute sol”, that is a pair of parallel plates in a large volume of electrolyte. The effective thickness of the double layers depends significantly on whether the p.d. ion is adsorbed or desorbed. In the case of adsorption, depletion of p.d. ions from the dispersion medium causes the double layer thickness and hence the double layer repulsion to be greater in the concentrated system, as compared with the dilute system. Comparison with some experiments of Barclay and Ottewill shows the same general trend. The opposite effect of a smaller double layer repulsion is obtained in the desorption case.