Statistical mechanics of a Coulomb gas with finite size particles: A lattice field theory approach

A recently proposed lattice field theory approach to the statistical mechanics of a classical Coulomb gas [J. Chem. Phys. 97, 5653 (1992)] is generalized to treat gas particles of finite size. To do this, a repulsive Yukawa interaction between all pairs of gas particles is added to the usual pairwise Coulombic interactions of the gas particles with each other and also with an arbitrary collection of immobile charges. Such a model is directly relevant for understanding the energetics of systems composed of macroions in electrolytic solutions when the simple ions that comprise the electrolyte are sufficiently large. A field theoretic representation of the grand partition function for the modified Coulomb gas is derived. Two coupled three‐dimensional scalar fields are involved. Physically, one is related to the electrostatic potential and the other to the Yukawa potential. The field theory expression, once discretized onto an appropriate lattice, can be evaluated via saddle point expansion. The zeroth order ...

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