Hard-sphere models Percus-Yevick approximation

The theoretical form of (3—x)/a was also calculated using interference functions derived from a hard-sphere alloy in the Percus-Yevick approximation (Ashcroft and Langreth, (1967), Enderby and North, (1968)). The results are given in curve (b) of Figure 7.27 and it is clear that the model fails to predict the sharp peak in the experimental data discussed above. The reason for this is that the hard sphere model predicts that should fall roughly midway between n-Sn Cu-Cu complementary effect of the concentration dependence of a. and cu-Sn which occurs in evaluation F(2kp) will be absent for hard spheres. 

We will describe integral equation approximations for the two-particle correlation fiinctions. There is no single approximation that is equally good for all interatomic potentials in the 3D world, but the solutions for a few important models can be obtained analytically. These include the Percus-Yevick (PY) approximation [27, 28] for hard spheres and the mean spherical (MS) approximation for charged hard spheres, for hard spheres with point dipoles and for atoms interacting with a Yukawa potential. Numerical solutions for other approximations, such as the hypemetted chain (EfNC) approximation for charged systems, are readily obtained by fast Fourier transfonn methods... 

When the smoothed or nonlocal density approximation (or NL-DFT model) is used, the weighting function is chosen so that the hard-sphere direct pair-correlation function is well described for the uniform fluid over a wide range of densities. One example of such a weighting function is the model proposed by Tarazona [69], which uses the Percus-Yevick theory for approximating the correlation function over a wide range of density. In this case, the weighting function is expanded as a power series of the smoothed density. The use of a smoothed density in NL-DFT provides an oscillating density profile expected of a fluid adjacent to a sohd surface, the existence of which is corroborated by molecular simulation results [17,18]. 

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 MSA was first introduced by Percus and Yevick [9] as an approximate way of introducing hard-core effects rm the distribution of charged particles. Then, Waisman and Lebowitz applied this approximation to electrolytes [10]. They obtained the solution to the Omstein-Zenuke equation [8] in the case of ions having the same diameter, in the primitive model of solutions in which ions are regarded as charged spheres immersed in a continuum (the solvent) of relative permittivity e. The treatment was later extended to the case of ions of different diameters by Blum [11] and Blum and Hpye [12]. 

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