Extended Soft Binding Mean Spherical- Contact Probability Approximation for Hard Ions

摘要

We propose a new analytical theory of electrolytes that extends the range of the Mean Spherical Approximation (MSA) to include extremely high charges [1, 2, 3, 4, 5]. In the MSA the thermodynamics and structure of the most general electrolyte are given in terms of a single screening parameter F, [1] which is obtained from the simple algebraic equation 4F2 47rABDa; (1) where zt— 11cr R2 Da = Epk4; Xi = AB= = 7.15 A; 1 + and /I is usually a small parameter that is zero for equal sizes ions [6]. Here zi is the charge of the ion i, the density is pi and cri is the diameter. When association occurs [7], /1 depends on the short ranged interactions, and on a, the degree of association which also determines E, the effective dielectric constant. The binding MSA (BIMSA) gives the correct high and low density limiting behavior of the contact pair distribution function and thermodynamics [8, 9]. It is very useful for practical applications[ 10, 11]. The BIMSA extends the range of the MSA substantially and is the only existing theory that gets the correct high and low density Debye-Hueckel limiting law including the associated ions and dipoles [12]. This term is crucial in obtaining the excellent agreement with computer simulations of Bresme et al [30] ( see figure 1, [13]). The correct behavior is obtained including nonlinear (exponential) terms in the closure of the Ornstein-Zernike equations. Many of the traditional exponential closures, such as the HNC and others (even those that include bridge functions [14]) are not adequate, since they do not get the full association limits correctly and the comparison to simulation is generally poor for charged systems. In our new theory we add an extra exponential term to the closure with the requirement that the contact pair correlation function be given by the exp approximation [15, 16], but treating the associating ions as an ion-dipole mixture [7, 12], gif (Cu] = gtJ-S (07 j)e t2e0 (3) In the case of the general polydisperse electrolyte this leads to a new analytical equation that we have solved explicitly in the one yukawa closure [17].