The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: an integral equation study

Abstract

The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation is obtained and solved numerically for a totally asymmetric primitive model electrolyte around a spherical macroparticle. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential vs charge relationship, radial distribution functions, mean electrostatic potential and cumulative reduced charge for representative cases of 1:1 and 2:2 salts with a size asymmetry ratio of 2. Our results are collated with those of the Modified Gouy-Chapman (MGC) and unequal radius Modified Gouy-Chapman (URMGC) theories and with those of HNC/MSA in the restricted primitive model (RPM) to assess the importance of size asymmetry effects. One of the most striking characteristics found is that,\textit{contrary to the general belief}, away from the point of zero charge the properties of an asymmetric electrical double layer (EDL) are not those corresponding to a symmetric electrolyte with the size and charge of the counterion, i.e. \textit{counterions do not always dominate}. This behavior suggests the existence of a new phenomenology in the EDL that genuinely belongs to a more realistic size-asymmetric model where steric correlations are taken into account consistently. Such novel features can not be described by traditional mean field theories like MGC, URMGC or even by enhanced formalisms, like HNC/MSA, if they are based on the RPM.