On adsorption at the oil/water interface and the calculation of electrical potentials in the aqueous surface phase. II. The effects of ionic size

Abstract

An equation is derived similar to the Gouy equation for a flat diffuse double layer but which takes into acount the finite sizes of the adsorbed and counter ions. The corresponding equation giving the variation of potential with the distance from the plane of charge is derived for systems where the potential exceeds ca . 50 mV. A relation between specific surface charge and surface pressure (equation of state) is deduced on this basis for completely ionized adsorbed films. These equations are tested for films of sodium alkyl sulphates and dodecyltrimethylammonium bromide adsorbed at the petroleum-ether/water interface, allowance being made for the presence of counter-ions above the plane of the film ions. The modified equations predict the electrical potentials in the region of the interface much more completely than the simple Gouy equation. An estimate of the number of counter ions present in the region above the head groups is given and the possible effects of their presence there on surface viscosity and electrophoretic phenomena briefly considered. Other possible corrections to simple diffuse double-layer theory are discussed; it is concluded (in agreement with other recent authors) that electrical polarization and dielectric saturation effects tend to cancel out over the experimental range of electric field strengths. Fluctuation phenomena (‘self atmosphere * effects) may become important at high values of kx and in this region may cancel out the ionic size effect, so that the potential-distance relation derived from the standard Gouy-Chapman treatment should be obeyed in the outer regions of the diffuse double layer. Deviations occur from the modified Gouy equation for the shorter chain surface active agents in absence of any added electrolyte. The causes suggested are: (1) the inadequacy of the simple geometrical model used for determining the film ion size correction; (2) the inapplicability of the expression used to calculate bulk phase activity coefficients for detergents at high concentrations.