On the Influence of Ion Excluded Volume (Steric) Effects on the Double-Layer Polarization of a Nonconducting Spherical Particle in an AC Field

The dipole moment of a charged, dielectric, spherical particle under the influence of a uniform alternating electric field is computed by solving the modified Poisson-Nernst-Planck (PNP) equations (Bikerman's mean-field model) (Philos. Mag. 1942, 33, 384-397) accounting for excluded volume effects of the finite ion size as a function of the double-layer thickness, the electric field frequency, the particle's surface charge, and the volume fraction of the ions in the bulk characterizing the excluded volume repulsion. In the limit of thin electric double layers, we carry out an asymptotic analysis to develop simple models calculating dipole moments which are in favorable agreement with the modified PNP model. Our results reveal that excluded volume effects, imposing a maximum on the counterion concentration, reduce the dipole moment at high frequencies and possibly enhance the dipole moment at low frequencies, assuming that the particle bears the same zeta potential. Excluded volume effects often become significant in highly concentrated salt solutions or near highly charged surfaces. The modified PNP model considering the ion size generally improves the theoretical predictions in comparison to experimental data, and a possible explanation for such improvement is suggested.