Highly asymmetric electrolyte: Comparison between one- and two-component models at different levels of approximations

Abstract

An accurate structure of a two-component asymmetric (charge asymmetry 1:20) electrolyte is used to investigate the mean spherical approximation (MSA), the hypernetted-chain (HNC), and the Rogers–Young (RY) equations. It is demonstrated that the inherent approximations of the MSA and HNC theories cause the micellar charge currently extracted from small-angle neutron scattering experiments to be smaller than the nominal one. Thus, the extracted micellar charge should be viewed as a purely fitting parameter and a value smaller than the nominal one does not necessarily imply an incomplete ionization of the counterions from the micelle, as previously suggested. The HNC theory gives a considerable improvement over the MSA theory, but is still not sufficiently accurate for providing quantitative correct results (15% error). The accurate structure is also used to assess the usefulness of using a simpler one-component model with an effective macroion potential, either with simulation or with liquid-state theories. It was found that the screened Coulomb potential is an excellent approximation and moreover the optimal prefactor and screening length fulfill the DLVO relation provided that the micellar charge is regarded as a fitting parameter. However, when one of the liquid-state theories is employed, the DLVO relation is not fulfilled. The RY approximation gave an improved structure as compared to the HNC and the MSA equations.