4 research outputs found

    Statistical field theory of mechanical stresses in Coulomb fluids: beyond mean-field theory

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    In this paper, we introduce a statistical field theory that describes the macroscopic forces in inhomogeneous Coulomb fluids. Our approach employs a general covariant methodology, in conjunction with a functional Legendre transformation method, to calculate the stress tensor for Coulomb fluids. This tensor encompasses the mean-field stress tensor and the fluctuation corrections derived through the one-loop approximation. The correction for fluctuations includes a term that accounts for the thermal fluctuations of the local electrostatic potential and field in the vicinity of the mean-field configuration. This correlation stress tensor determines how electrostatic correlation affects the local stresses in a non-uniform Coulomb fluid. We would like to emphasize that our general approach is applicable not only to Coulomb fluids, but also to nonionic simple or complex fluids, for which the field-theoretic Hamiltonian is known as a functional of the relevant scalar order parameters

    Noether's second theorem and covariant field theory of mechanical stresses in inhomogeneous ionic liquids

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    In this paper, we present a covariant approach that utilizes Noether's second theorem to derive a symmetric stress tensor from the grand thermodynamic potential functional. We focus on the practical case where the density of the grand thermodynamic potential is dependent on the first and second coordinate derivatives of the scalar order parameters. Our approach is applied to several models of inhomogeneous ionic liquids that consider electrostatic correlations of ions or short-range correlations related to packing effects. Specifically, we derive analytical expressions for the symmetric stress tensors of the Cahn-Hilliard-like model, Bazant-Storey-Kornyshev model, and Maggs-Podgornik-Blossey model. All of these expressions are found to be consistent with respective self-consistent field equations.Comment: Submitted to Journal of Chemical Physic

    Theory of self-coacervation in semi-dilute and concentrated zwitterionic polymer solutions

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    Based on the random phase approximation, we develop a molecular theory of self-coacervation in zwitterionic polymer solutions. We show that the interplay between the volume interactions of the monomeric units and electrostatic correlations of charged groups on a polymer backbone can result in liquid-liquid phase separation (self-coacervation). We analyse the behavior of the coacervate phase polymer concentration depending on the electrostatic interaction strength -- the ratio of the Bjerrum length to the bond length of the chain. We establish that in a wide range of polymer concentration values -- from a semi-dilute to a rather concentrated solution -- the chain connectivity and excluded volume interaction of the monomeric units have an extremely weak effect on the contribution of the electrostatic interactions of the dipolar monomeric units to the total free energy. We show that for rather weak electrostatic interactions, the electrostatic correlations manifest themselves as Keesom interactions of point-like freely rotating dipoles (Keesom regime), while in the region of strong electrostatic interactions the electrostatic free energy is described by the Debye-H{\"u}ckel limiting law (Debye regime). We show that for real zwitterionic coacervates the Keesom regime is realized only for sufficiently small polymer concentrations of the coacervate phase, while the Debye regime is approximately realized for rather dense coacervates. Using the mean-field variant of the density functional theory, we calculate the surface tension (surface free energy) of the ""coacervate-solvent"" interface as a function of the bulk polymer concentration. Obtained results can be used to estimate the parameters of the polymer chains needed for practical applications such as drug encapsulation and delivery, as well as the design of adhesive materials.Comment: Submitted to Soft Matte