The effect of ion size on the pressure between two surfaces in liquid

Abstract

The pressure between two parallel planar surfaces at equal electric potentials is calculated using both the classical Poisson–Boltzmann (PB) equation and the modified PB (MPB) equation of Borukhov et al. (2000) to account for finite ion size. Results are presented for a z:z symmetric electrolyte. The pressures predicted by the two models differ more as the bulk ion concentration, surface potential, and ion size increase. For a bulk ion concentration of 0.001 M and a surface potential of 25 mV, the two models predict almost identical pressures. However, for a bulk ion concentration of 1 M and a surface potential of 100 mV, the MPB model predicted a pressure that is 60 and 400 percent higher than the PB model for an ion size of 0.6 nm and 0.9 nm, respectively. The ratio of the pressures predicted by the two models is relatively independent of the distance of separation between the two plates.