IMPROVED MSA THEORY FOR CONCENTRATED ELECTROLYTE SOLUTIONS BASED ON MONTE CARLO SIMULATION AT HIGH IONIC STRENGTHS

摘要

Current search for valid ionic solution properties correlations at high concentrations has focused on the mean spherical approximation (MSA) because of its ability to treat ion size effects. We propose a fundamentally sound modification of the MSA based on comparisons with new Monte Carlo simulations for aqueous salt solutions. The osmotic coefficient phi=P-osm/rho k(B)T in this study is decomposed into three parts in line with the primitive-model pair potentials. The more familiar long-range (Coulombic), and the contact hard-core parts are well reproduced by most approximate ionic theories. The short-range electrostatic (SRE) contribution is the part that poses as a challenge to many theoretical efforts. In order to characterize the SRE behavior, Monte Carlo simulation with Ewald sum is carried out for 1-1 electrolytes up to 15 molar. The short-range electrostatic phi'(SRE), is a non-negligible quantity that can reach 30 of the value of the long-range phi'(LR). Any ionic solution theory that ignores phi'(SRE) will incur inaccuracies. An interesting behavior of the SRE phi is a unimodal maximum as the molarity M varies from 0 to 15. This takes place an similar to 10 M for aqueous LiCl solutions, well beyond the ranges investigated by most existing simulation data. The new MC data cover 1.01, 2.2, 3.4, 4.3, 5.3 and 6.4 molar for NaCl, and in addition, 7.5, 10, 12.5 and 15 molar for LiCl solutions. The diameter ratio sigma(--)/sigma(++) ranges from 1 to 3. To interpret this behavior, we examine a number of prevailing theories including the mean spherical approximation (MSA), hypernetted-chain (HNC) equation, hypervertex equations, and a number of modified MSA equations (such as LIN, LIN+SQ and EXP). In addition to 1-1 electrolytes, comparisons are also made with molten salt (at Bjerrum lengths similar to 30) and 2-2 electrolyte data. Some of our observations are consistent with previous studies on primitive model systems based on less extensive simulation data sets. However, none of the analytical theories (HNC presently excluded) are able to reproduce MC results for wide ranges. We propose two analytical formulations: MIXL and MIXQ based on the MSA solutions from Blum and Hoye for this purpose. These have been tested: MIXQ is good for concentrated electrolyte solutions (up to 15 M), and MIXL is valid for high Bjerrum length molten salts. References: 71