Abstract
The statistical mechanics of a mixture of hard-core ions and dipoles in one dimension, namely, the one-dimensional version of the so-called nonprimitive model of an electrolyte, is considered by stressing the effect of the charge-dipole interactions and the hard-core repulsions on the thermodynamics and, especially, on the many-body functions of the systems. The adaptation of Baxter's generating function technique to this model lets us express the thermodynamic and structural functions in terms of a non-Hermitian generalized Hill-type Hamiltonian. The eigenvalues and eigenfunctions of this differential operator yield, in closed form, then-body correlation functions in the bulk and near the container's walls. We also comment on the screening of the electric fields by the system ions and study the Donnan equilibrium when one of the ionic species in the mixture cannot diffuse through a semipermeable membrane.
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Vericat, F., Blum, L. Many-body functions of nonprimitive electrolytes in one dimension. J Stat Phys 61, 1161–1185 (1990). https://doi.org/10.1007/BF01014370
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DOI: https://doi.org/10.1007/BF01014370