Critique of primitive model electrolyte theories

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-Hückel ~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*5kBTDa/q &10Tc *.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**2Tc *.0.1; this is attributable to the treatment of the association constant. @S1063-651X~97!03212-1#