Statistical field theory of ion-molecular solutions

TL;DR

This paper develops a statistical field theory framework for salt solutions containing zwitterionic and multipolar molecules, deriving generalized electrostatic equations, potentials, and free energies, extending classical models like Poisson-Boltzmann and Debye-Hückel.

Contribution

It introduces a unified theoretical approach for complex salt solutions, generalizing classical electrostatic models to include multipolar and zwitterionic molecules with analytical and RPA-based results.

Findings

Derived generalized Poisson-Boltzmann equations.

Obtained analytical potentials for test ions in complex solutions.

Analyzed oscillating electrostatic behavior in multipolar solutions.

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. 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. 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.