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Exact analytical formulas for the distribution functions of charged hard spheres in the mean spherical approximation

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Abstract

Exact analytical expressions are derived for the electrostatic part of the mean spherical approximation (MSA) radial distribution functions (RDFs) for a system of charged hard spheres. These expressions are valid for all distances. In addition, it is shown that these same expressions arise in the MSA description of the charge profile of charged hard spheres near a charged hard wall. We also derive analytical expressions for the nonelectrostatic part of the profile in this case, valid forz ⩽ 5σ, and discuss a numerical method for obtaining results forz > 5σ. Some simple approximate expressions are also considered.

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Author notes

  1. William R. Smith

    Present address: Departments of Mathematics and of Physiology and Biophysics, Dalhousie University, Halifax, Nova Scotia, Canada

Authors and Affiliations

  1. IBM Research Laboratory, San Jose, California

    Douglas Henderson & William R. Smith

Authors
  1. Douglas Henderson
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  2. William R. Smith
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Additional information

Partially supported by an IBM World Trade Corp. fellowship to WRS during his stay in San Jose.

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Henderson, D., Smith, W.R. Exact analytical formulas for the distribution functions of charged hard spheres in the mean spherical approximation. J Stat Phys 19, 191–200 (1978). https://doi.org/10.1007/BF01012511

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  • DOI: https://doi.org/10.1007/BF01012511

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