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

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(κr)/r, where the state-point-dependent parameter κ is chosen so that the Helmholtz free energy A is at a null point (∂A/∂κ = 0). Unlike the original RPM, this reference fluid admits real solutions to the hypernetted-chain 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 ion pairs to assemble into neutral clusters. We find that 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 [A. Härtel et al., Phys. Rev. Lett. 130, 108202 (2023)], assuming that only the free ions contribute to the screening length.