Critique of Primitive Model Electrolyte Theories

TL;DR

This paper critically evaluates various primitive model electrolyte theories, comparing their adherence to theoretical bounds and stability criteria, revealing limitations of common approaches and the importance of ion pairing and depletion effects.

Contribution

It provides a comprehensive comparison of Debye-Hückel and MSA-based theories against bounds, highlighting the impact of ion pairing and depletion on their validity.

Findings

DH-based theories satisfy Totsuji's bound at low temperatures.

MSA violates Totsuji's bound in some regions.

All theories violate Gillan's bound near criticality without ion pairing.

Abstract

Approximate theories for the restricted primitive model electrolyte are compared in the light of Totsuji's lower bound for the energy (an improvement over Onsager's), Gillan's upper bound for the free energy, and thermal stability requirements. Theories based on the Debye-Hueckel (DH) approach and the mean spherical approximation (MSA), including extensions due to Bjerrum, Ebeling, Fisher and Levin, and Stell, Zhou, and Yeh (PMSA1,2,3) are tested. In the range T* = (k_B T)Da/q^2 \lesssim 10 T*_c \simeq 0.5, all DH-based theories satisfy Totsuji's bound, while the MSA possesses a significant region of violation. Both DH and MSA theories violate Gillan's bound in the critical region and below unless ion pairing and the consequent free-ion depletion are incorporated. However, the PMSA theories, which recognize pairing but not depletion, fail to meet the bound. The inclusion of excluded-volume terms has only small effects in this respect. Finally, all the pairing theories exhibit negative constant-volume specific heats when T* \gtrsim 2T*_c \simeq 0.1; this is attributable to the treatment of the association constant.