The distribution of ions under a charged monolayer, and a surface equation of state for charged films

Abstract

The potential at a charged interface between water and oil or between water and air is a function of the ionic strength of the aqueous phase. This potential has been determined in four different ways, which include measurements of rates of desorption of surface films and of the area occupied by 'gaseous' films of long-chain detergents. Comparison of the rates of desorption of lauric acid laurate ions shows that the Gouy equations for the electrical potential at a surface may be applied to ionized mono-layers on solutions of ionic strengths as high as 2n. The Gouy equations are also verified by studying ionized films on solutions of very low ionic strength. At high ionic strengths the finite sizes of the counter-ions become important and, from the deviations from ideal behaviour, the distributions of these is deduced. Elimination of the electrical potential term from the four independent equations in which it occurs leads to six new relationships applying to ionized monolayers. One of these is the surface equation of state for charged films. According to this equation of state for monolayers of long-chain ions, on very dilute solutions and at moderate areas per ion, a charged 'gaseous' film should obey the equation II( A ─ A 0 ) ═ 3 kT . Experimental support of this presented from the force-area relationships of films of C 26 H 53 N(CH 3 ) + 3 at the oil-water interface. The effect of added electrolyte and equations of previous investigators are discussed, together with some consequences of possible biological interest.