Abstract
We derive from statistical mechanics the Gibbs free energy of an elastic random-walk chain affected by the presence of an external electric field. Intrachain charge interactions are ignored. In addition, we find two approximations of the Helmholtz potential for this system analogous to the gaussian and Cohen-Padé approximations for an elastic strand without the presence of an electric field. Our expressions agree well with exact numerical calculations of the potential in a wide range of conditions. Our analog of the gaussian approximation exhibits distortion of the monomer density due to the presence of the electric field, and our analog of the Cohen-Padé approximation additionally includes finite chain extensibility effects. The Helmholtz potential may be used in modeling the dynamics of electrophoresis experiments.
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