Year: 1997
Type: article
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-H\"uckel (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 ${T}^{*}{=k}_{B}{TDa/q}^{2}\ensuremath{\lesssim}{10T}_{c}^{*}\ensuremath{\simeq}0.5,$ 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 ${T}^{*}\ensuremath{\gtrsim}{2T}_{c}^{*}\ensuremath{\simeq}0.1;$ this is attributable to the treatment of the association constant.
Authors: Daniel Zuckerman, Michael Fisher, Benjamin Lee
Institution: University of Maryland, College Park
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2163131458