Wertheim association theory for ion pairing in electrolytes: effect of neutral clusters

Abstract

We address the problem of the vapor-liquid phase transition in the restricted primitive model (RPM) using Wertheim's statistical associating fluid theory to capture the effects of ion pairing which dominate the low-temperature vapor phase. For this we employ a reference system in which ion-pairing is suppressed by a judicious modification of the interaction between unlike charges from 1/r to erf(kappa r)/r, where kappa is a state-dependent parameter chosen so that the Helmholtz free energy A is at a null point (dA/d(kappa) = 0). Unlike the original RPM, this reference fluid admits real solutions to the hypernetted-chain (HNC) closure of the Ornstein-Zernike equations over a wide range of densities and temperatures. In the present study, we go beyond previous work [M. Li, Ph.D. thesis, University of Manchester (2011)] to allow for isodesmic assembly of ion pairs into neutral clusters. We find this has the potential to improve significantly the agreement with the Monte-Carlo results for the RPM vapor phase boundary. We can also match recent results on anomalous underscreening in the RPM [H\"artel et al., Phys. Rev. Lett. 130, 108202 (2023)] assuming that only the free ions contribute to the screening length.