Primitive model electrolytes. A comparison of the HNC approximation for the activity coefficient with Monte Carlo data

Abstract

Accuracy of the mean activity coefficient expression (Hansen-Vieillefosse-Belloni equation), valid within the hypernetted chain (HNC) approximation, was tested in a wide concentration range against new Monte Carlo (MC) data for +1:−1 and +2:−2 primitive model electrolytes. The expression has an advantage that the excess chemical potential can be obtained directly, without invoking the time consuming Gibbs-Duhem calculation. We found the HNC results for the mean activity coefficient to be in good agreement with the machine calculations performed for the same model. In addition, the thermodynamic consistency of the HNC approximation was tested. The mean activity coefficients, calculated via the Gibbs-Duhem equation, seem to follow the MC data slightly better than the Hansen-Vieillefosse-Belloni expression. For completeness of the calculation, the HNC excess internal energies and osmotic coefficients are also presented. These results are compared with the calculations based on other theories commonly used to describe electrolyte solutions, such as the mean spherical approximation, Pitzer's extension of the Debye-Hückel theory, and the Debye-Hückel limiting law.

A multiple decay-length extension of the Debye–Hückel theory: to achieve high accuracy also for concentrated solutions and explain under-screening in dilute symmetric electrolytes

“…Many nonlinear approximations for electrolytes have been used to obtain pair distributions and thermodynamical quantities. They include the HNC approximation [51][52][53][54][55] and other integral equation theories. 54,[56][57][58][59][60][61] There are also improved versions of the PB approximation that correct for the neglect of correlations in the ion cloud around each ion, like the Modified PB approximation by Outhwaite et al 16,[62][63][64] and the correlation-enhanced PB theory by Su and coworkers.…”

“…Pair distributions and thermodynamical quantities for bulk electrolytes have, of course, been calculated also by simulations. 11,12,[17][18][19][20]55,59,61,[71][72][73][74][75][76][77][78][79][80] The nonlinear theories do not in general provide any explicit equation for the decay parameter like the linear ones above do, but from these theories and from computer simulations, the values of k, k 0 etc. have been extracted numerically for various electrolytes.…”

An analytical longitudinal dielectric function of primitive electrolyte solutions and its application in predicting thermodynamic properties

“…Note that the analytical constraints of k l mentioned in this study depends only on k D , while HNC theory shows that k l depends on both k D and the reduced inverse temperature β [36], one can expect that a more sophisticated theoretical constraint of k 1,2 will lead to a better dielectric description of electrolyte solutions.…”

“…The HNC theory is known to be very accurate in a wide range of the parameter space [36], and is used as a benchmark in this study. The correlation function h ij (r) of the solvent species from HNC calculation is used to evaluate S zz (k) and the response function χ(k).…”

Extended Debye–Hückel Theory for Studying the Electrostatic Solvation Energy

“…To test the validity of the MDH theory and the ESDH theory, we considered the solvation of a charged hard sphere in a 1:−1 primitive solvent with diameter σ s =1 and charge q s =1. The hyper‐netted‐chain (HNC) integral equation method37 was used to compute the electrostatic solvation energy βU e , which is known to be almost as accurate as Monte Carlo simulations over a wide concentration range for primitive models 38. The dielectric constant was ε s =1, the reduced inverse temperature was β =1/( k B T )=9, and the total particle number density was ρ =0.4, from which the conventional Debye parameter was evaluated to be ${k_{\rm{D}} \sigma = \sqrt {{{4\pi \beta q_{\rm{s}}^{\rm{2}} \rho } \over {\varepsilon _{\rm{s}} }}} \sigma = 6.726}$ .…”