Abstract
Analytic methods for the Percus-Yevick hard sphere correlation functions
Highlights
The hard sphere (HS) fluid is a simple representative fluid that, through perturbation theory [1, 2], is the basis of a simple and successsful theory of liquids
The reason why the HS fluid is so useful is that accurate analytic expressions can be obtained from the Percus-Yevick (PY) theory [3]
Since the mean spherical approximation (MSA) is more widely used, perhaps the PY results for hard spheres should be called the MSA results
Summary
The hard sphere (HS) fluid is a simple representative fluid that, through perturbation theory [1, 2], is the basis of a simple and successsful theory of liquids. The PY theory for the HS fluid is obtained by combining the OZ equation together with both the exact. This equation, which we may call the PY zero separation equation, is valid only for the PY theory for hard spheres It is obtained from the OZ equation, equation (2), in the limit R12 = 0, together with equations (3) and (4). It is interesting to note that there is an exact zero separation theorem, y(0) = exp(β∆μ), where ∆μ is the chemical potential of the hard sphere fluid in excess of that of an ideal gas. Analytic methods for the Percus-Yevick hard sphere correlation functions close to satisfying the exact zero separation theorem. Because the PY theory is approximate, the pressure that results from the (p) and (c) equations will be inconsistent and slightly different. The author has decided to publish these lecture notes, as a review, so that they might be more widely available
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