The mean activity coefficients of 2:2 electrolyte solutions: an integral equation study of the restricted primitive...

We apply the closure theory ZSEP (self-consistent zero-separation based closures) developed earlier to the restricted primitive model (RPM) of 2:2 electrolytes in order to (i) obtain the activity coefficient information via the direct formula for chemical potentials [L. L. Lee, J. Chem. Phys. 97, 8606 (1992)] and (ii) test the performance of this flexible ZSEP closure at high-coupling strengths (i.e., high valency and low temperatures) for cases of 2:2 electrolytes where other closure schemes have encountered difficulties [e.g., the hypernetted chain (HNC) equation]. In particular, we shall remedy the shortcomings of the HNC theory at low concentrations (from 0.001M to 0.2M). The ZSEP closure is found to perform well at coupling strengths beta(') = absolute value(z(1)z(2))e(2)/(epsilon(m)kTd) approaching approximately 10 where some other closure theories cease to give good results. In addition, by applying the direct chemical potential formula, we demonstrate numerically that, in the RPM cases examined, the logarithm of the mean activity coefficients of electrolytes are closely approximated by the electrostatic internal energy, an easily accessible quantity, a fact that shall afford ready access to the chemical potentials for phase equilibrium and electrochemical calculations on electrolytic systems.