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Statistical field theory of ion–molecular solutions

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Abstract

In this article, I summarize my theoretical developments in the statistical field theory of salt solutions of zwitterionic and multipolar molecules. Based on the Hubbard–Stratonovich integral transformation, I represent configuration integrals of dilute salt solutions of zwitterionic and multipolar molecules in the form of functional integrals over the space-dependent fluctuating electrostatic potential. In the mean-field approximation, for both cases, I derive integro-differential self-consistent field equations for the electrostatic potential, generated by the external charges in solutions media, which generalize the classical Poisson–Boltzmann equation. Using the obtained equations, in the linear approximation, I derive for the both cases a general expression for the electrostatic potential of a point-like test ion, expressed through certain screening functions. I derive an analytical expression for the electrostatic potential of the point-like test ion in a salt zwitterionic solution, generalizing the well known Debye–Hueckel potential. In the salt-free solution case, I obtain analytical expressions for the local dielectric permittivity around the point-like test ion and its effective solvation radius. For the case of salt solutions of multipolar molecules, I find a new oscillating behavior of the electrostatic field potential of the point-like test ion at long distances, which is caused by the nonzero quadrupole moments of the multipolar molecules. I obtain a general expression for the average quadrupolar length of a multipolar solute. Using the random phase approximation (RPA), I derive general expressions for the excess free energy of bulk salt solutions of zwitterionic and multipolar molecules and analyze the limiting regimes resulting from them. I generalize the salt zwitterionic solution theory for the case when several kinds of zwitterions are dissolved in the solution. In this case, within the RPA, I obtain a general expression for the solvation energy of the test zwitterion. Finally, I demonstrate how to take a systematic account of the excluded volume correlations between multipolar molecules in addition to their electrostatic correlations. I believe that the formulated findings could be useful for the future theoretical models of the real ion–molecular solutions, such as salt solutions of micellar aggregates, metal–organic complexes, proteins, betaines, etc.

Graphical abstract: Statistical field theory of ion–molecular solutions

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Article information


Submitted
05 May 2020
Accepted
10 Jun 2020
First published
10 Jun 2020

Phys. Chem. Chem. Phys., 2020, Advance Article
Article type
Paper

Statistical field theory of ion–molecular solutions

Y. A. Budkov, Phys. Chem. Chem. Phys., 2020, Advance Article , DOI: 10.1039/D0CP02432E

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