Primitive model of electrolytes

Camp P J and Patey G N 1999 Ion association and condensation in primitive models of electrolytes J. Chem. Phys. 

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

A possible reason that the problem of C < 0 did not receive much attention was the assertion [15] (BLH) that such an anomaly was forbidden. The proof was based on the statistical mechanical analysis of the primitive model of electrolytes between two oppositely charged planes, cr and —a. It was noticed in Ref. 10 that the BLH analysis missed a very simple contribution to the Hamiltonian, direct interaction between the charged walls, ItzLct (L is the distance between the walls). With proper choice of the Hamiltonian the condition on the capacitance would be C > 27re/L. It simply means that due to ionic shielding of the electric field, the capacitance exceeded its geometrical value corresponding to the electrolyte-free dielectric gap. 

Issue is taken here, not with the mathematical treatment of the Debye-Hiickel model but rather with the underlying assumptions on which it is based. Friedman (58) has been concerned with extending the primitive model of electrolytes, and recently Wu and Friedman (159) have shown that not only are there theoretical objections to the Debye-Hiickel theory, but present experimental evidence also points to shortcomings in the theory. Thus, Wu and Friedman emphasize that since the dielectric constant and relative temperature coefficient of the dielectric constant differ by only 0.4 and 0.8% respectively for D O and H20, the thermodynamic results based on the Debye-Hiickel theory should be similar for salt solutions in these two solvents. Experimentally, the excess entropies in D >0 are far greater than in ordinary water and indeed are approximately linearly proportional to the aquamolality of the salts. In this connection, see also Ref. 129. 

The sugars sucrose, fructose and glucose have also been found to affect bubble coalescence. On addition to water these sugars raise the surface tension and are desorbed from the air-water interface. Thus their effect on bubble coalescence equally cannot be described in terms of surfactant-like behaviour and certainly no charge effects are involved. Hence, even if an "explanation" could be found within the confines of the primitive model of electrolytes, that explanation could not accommodate this observation. The reduction in bubble coalescence achieved with increasing concentration is shown in Fig. 3.7. 

Caillol, J.M. A Monte Carlo study of the dielectric constant of the restricted primitive model of electrolytes on the vapor branch of the coexistence line. J. Chem. Phys., 1995, 102, p. 5471-5479. 

Kalyuzhnyi, Yu.V., and Stell, G. Solution of the polymer msa for the polymerizing primitive model of electrolytes. Chemical Physics Letters, 1995, 240, p. 157-164. 

This review discusses a newly proposed class of tempering Monte Carlo methods and their application to the study of complex fluids. The methods are based on a combination of the expanded grand canonical ensemble formalism (or simple tempering) and the multidimensional parallel tempering technique. We first introduce the method in the framework of a general ensemble. We then discuss a few implementations for specific systems, including primitive models of electrolytes, vapor-liquid and liquid-liquid phase behavior for homopolymers, copolymers, and blends of flexible and semiflexible... 

When applied to the primitive model of electrolyte solutions (i.e., charged hard spheres of arbitrary diameters in a dielectric continuum), the HNC equation is superior to the PY equation because it preserves the correct long-range behavior. On the other hand, in fluids with only short-range forces the PY equation can be successfully applied because some of the omitted terms cancel one another. 

The organization of the review is as follows, hi Sect. 2, the primitive model of electrolytes is introduced. A set of reduced parameters is discussed, and the connection to experimental systems is provided. Three different boundary conditions are presented, hi Sect. 3, some general simifiation aspects are given. The properties of four specific systems, representing different experimental cases, are provided in Sect. 4. Section 5 focuses on the calculation of the interaction between two macroions mediated by their counterions. Three numerical approaches will be examined and their relative merit compared, hi... 

The primitive model of electrolytes constitutes a Arm basis for statistical-mechanical description of solutions of charged colloids. This model will be adopted throughout, and it originates from the more general McMillan-Mayer solution theory [62,63]. 

Fig.1 Schematic illustration of the primitive model of electrolytes including spherical macroions with specified charge 2m and radius Ryi and spherical coimterions with charge Zi and radius Rj in a solution characterized by a relative permittivity...

The Metropolis MC method in the canonical ensemble is the most frequently used simulation approach to solve the primitive model of electrolytes. Averages of static properties are taken from a large set of Boltzmann-weighted configurations. Molecular dynamics and Brownian dynamics constitute two other methods to determine static and dynamic properties of molecular systems. Their implementations are, however, comphcated for systems possessing impulsive forces in combination with other forces. Hence, a soft-sphere repulsion is frequently used instead of the hard-sphere one when simulating such systems with these methods. 

More complex systems such as solutions containing macroions and short flexible coimterions have recently been simulated using the primitive model of electrolytes [112]. Solutions of macroions with simple coimterions at different amounts of oppositely charged polyelectrolyte have also been investigated, and the sequence complexation phase separation redissolution was observed [113]. Similar simulations where the macroion represented lysozyme have also been performed [114]. Finally, by using a related soft-sphere model, the dynamics and, in particular, the self-diffusion of the macroions and the counterions have been investigated by employing Brownian dynamics simulation [115]. 

In simulations of charged colloids using the primitive model of electrolytes, the small magnitude of the accumulated (total) macroion displacement constitutes a problem [103]. Therefore, an examination of the macroion root-mean-square (rms) displacement per MC pass, is particularly... 

Waisman E, Lebowitz JL (1970) Exact solution of an integral equation for structure of a primitive model of electrolytes. J Chem Phys 52 4307-4311... 

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