Generalized mean spherical approximation

Beyond the MSA Cluster Series Expansion and Generalized Mean Spherical Approximations... 

J. S. H0ye, J. L. Lebowitz, and G. Stell, Generalized mean spherical approximations for polar and ionic fluids, J. Chem. Phys. 61, 3253-3260 (1974). 

G. Stell and S. F. Sun, Generalized mean spherical approximation for charged hard spheres, J. Chem. Phys. 63, 5333 (1975). 

Continuum dielectric models of solvation can be generalized to include some aspects of the solvent molecularity. This has lead to the dynamic mean spherical approximation which improves the agreement between these kind of theories and experimental observations."... 

We start with a model of polar molecules in which the effects of polarizability are neglected. More precisely, we assume that in the absence of external fields, the potential energy associated with N particles is a sum of pair potentials < >( /), each of which depends on the positions r, and tj and orientations S2, and itj of particles / and j. Thus the particles are regarded as rigid, with no internal coordinates, and we assume for simplicity that they are all identical. Extensions of the results of Section II to mixtures are for the most part straightforward, as discussed by Hoye and StelP and in references they cite. Pertinent references to the mean spherical approximation generalized to mixtures are also given at an appropriate point in this chapter. 

FH = Flory-Huggins GF = generalized Flory GFD = generalized Flory dimer HNC = hypemetted chain HTA = high temperature approximation IFJC = ideal freely joined chain ISM = interaction site model LCT = lattice cluster theory MS = Martynov-Sarkisov PMMA = polymethyl methacrylate PRISM = polymer reference interaction site model PVME = polyvinylmethylether PS = polystyrene PY = Percus-Yevick RMMSA = reference molecule mean spherical approximation RMPY = reference molecular Percus-Yevick SANS = small angle neutron scattering SFC = semiflexible chain TPT = thermodynamic perturbation theory. 

Percus-Yevick, and the mean spherical approximations. The last of these assumes that the solvent consists of hard spheres with a long-range attractive force. It is widely applied to the modeling of solvent effects. Generalizations to multi-component fluids are straightforward. ... 

The starting point for such analytical efforts is linear response theory. Different approaches include the dynamical mean spherical approximation (MSA), " generalized transport equations, and ad hoc models for the frequency and wavevector dependence of the dielectric response function e(k,w). These linear response theories are very valuable in providing fundamental understanding. However, they carmot explore the limits of validity of the imderlying hnear response models. Numerical simulations can probe nonlinear effects. They are very useful in the direct visualization and examination of the interplay between solvent and solute properties and the different relaxation times associated... 

While Onsager s formula has been widely used, there have also been numerous efforts to improve and generalize it. An obvious matter for concern is the cavity. The results are very sensitive to its size, since Eqs. (33) and (35) contain the radius raised to the third power. Within the spherical approximation, the radius can be obtained from the molar volume, as determined by some empirical means, for example from the density, the molar refraction, polarizability, gas viscosity, etc.90 However the volumes obtained by such methods can differ considerably. The shape of the cavity is also an important issue. Ideally, it should be that of the molecule, and the latter should completely fill the cavity. Even if the second condition is not satisfied, as by a point dipole, at least the shape of the cavity should be more realistic most molecules are not well represented by spheres. There was accordingly, already some time ago, considerable interest in progressing to more suitable cavities, such as spheroids91 92 and ellipsoids,93 using appropriate coordinate systems. Such shapes... 

The Mean-Spherical Equal Arm Stretching Approximation General Formalism... 

It owes that name to a study of sphericalized lattice gases by Lebowitz and Percus/ who generalized the mean spherical model of Lewis and Wannier to a cli of mean spherical models with extended hard cores, and pointed out that the lattice-gas analog of (47) holds for the whole family. Although important in its own right, that work does not seem to shed much light on the status of the approximation (17) for fluid Hamiltonians. 

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