Surface Polaron Effect on the Ion Transfer across the Interface of Two Immiscible Electrolytes

An ion disposed near the interface of two immiscible liquids creates a protrusion of one solvent into the other, subject to hydrophobic or hydrophilic interaction with these solvents. Due to a finite relaxation time the protrusion may not be able to spontaneously follow the ion when it moves across the interface. This, as well as any improper thermal fluctuation of the protrusion, will cause slowdown of the ion transfer. Here we present the results of theoretical analysis in which the stochastic motions of the ion and protrusion are coupled and considered on the same footing. We show that if the equilibrium electrochemical potential for the ion has no barrier, the ion transport is purely diffusional with D_eff = k_BT/{6[r + (4/3)(h_max/)²L]} being the effective diffusion coefficient. Here, is the average viscosity of the liquids, r is the Stokes radius of an ion, L and h_max are the average lateral size and the maximal height of the protrusion, and is the half-width of the function h_eq(z) which characterizes the equilibrium ion-interface coupling [h_eq(z) is the height of the protrusion for a given distance of the ion to the unperturbed interface, if the ion had been infinitely slowly moving]. This function could be obtained from model calculations or molecular dynamic simulations. The second term in the denominator is the one that causes the slowdown of ion transfer across the interface. This expression can easily rationalize an order of magnitude slowdown, but hardly much more than that. This is not inconsistent with recent more careful claims on the true scale of the observed effect. Otherwise, one should invoke models that rest on the existence of the barrier in the electrochemical potential.