arXiv subjects

Yu. A. Budkov

Publications and source records attributed to Yu. A. Budkov.

At least 19 recordsLinked to original sources

arXiv2025

Theory of Casimir Forces: A Unified Approach Using Finite-Temperature Field Theory

We present a quantum theory of Casimir forces between perfect electrical conductors, based on quantum electrodynamics and quantum statistical physics. This theory utilizes Kapusta's finite-temperature field theory, combined with the Faddeev-Popov ghost formalism. This approach allows us to calculate Casimir forces at finite temperatures, providing both previously known and new physical insights from a unified perspective. Furthermore, our method enables us to compute the stress tensor associated with Casimir forces, in accordance with the Helmholtz free energy of an equilibrium quantum electromagnetic field. Using this method, we calculate the tangential pressure in a slit-like pore due to the Casimir effect.

cond-mat.stat-mech↗

arXiv2025

First-principle theory of the Casimir screening effect

In this paper, we use the formalism of finite-temperature quantum field theory to investigate the Casimir force between flat, ideally conductive surfaces containing confined, but mobile ions. We demonstrate that, in the Gaussian approximation, the ionic fluctuations contribute separately from the electromagnetic fluctuations that are responsible for the standard Casimir effect. This is in line with the "separation hypothesis", has been previously applied on a purely intuitive basis. Our analysis demonstrates the significance of calculating the zero Matsubara frequency component in the electromagnetic contribution, using the formula developed by Schwinger et al., as opposed to the approach based on Lifshitz theory used by other researchers.

quant-ph↗

arXiv2024

Thermomechanical Approach to Calculating Mechanical Stresses in Inhomogeneous Fluids and Its Applications to Ionic Fluids

This extended article presents a thermomechanical approach for calculating the stress tensor from the thermodynamic potential of inhomogeneous fluids and some applications to ionic fluids. The technique, based on the invariance of the fluid's thermodynamic potential with respect to spatial transformations of translation and rotation, offers an alternative to the general covariant approach developed by two of the authors. We apply this technique to both pure mean-field theories of fluids in general and a theory that includes thermal fluctuations of the order parameter, using the example of ionic fluids. Additionally, we apply the thermomechanical approach to fluid models with vector order parameters, such as liquid dielectrics. For this case, we obtain a general expression for the stress tensor. Furthermore, we discuss specific issues related to the calculation of disjoining pressure in ionic fluids confined in nanoscale slit-like pores with metal or dielectric walls, using the Coulomb gas model. To test the robustness of the proposed approach, we reproduce a number of known results from the statistical theory of inhomogeneous fluids and obtain several new ones.

cond-mat.soft↗

arXiv2024

Modified Debye-Hückel-Onsager Theory for Electrical Conductivity in Aqueous Electrolyte Solutions. Account of Ionic Charge Nonlocality

The paper presents a mean field theory of electrolyte solutions, extending the classical Debye-Hückel-Onsager theory to provide a detailed description of the electrical conductivity in strong electrolyte solutions. The theory systematically incorporates the effects of ion specificity, such as steric interactions, hydration of ions, and their spatial charge distributions, into the mean-field framework. This allows for calculation of ion mobility and electrical conductivity, while accounting for relaxation and hydrodynamic phenomena. At low concentrations, the model reproduces the well-known Kohlrausch's limiting law. Using the exponential (Slater-type) charge distribution function for solvated ions, we demonstrate that experimental data on the electrical conductivity of aqueous 1:1, 2:1, and 3:1 electrolyte solutions can be approximated over a broad concentration range by adjusting a single free parameter representing the spatial scale of the nonlocal ion charge distribution. Using the fitted value of this parameter at 298.15 K, we obtain good agreement with available experimental data when calculating the electrical conductivity across different temperatures. We also analyze the effects of temperature and electrolyte concentration on the relaxation and electrophoretic contributions to total electrical conductivity, explaining the underlying physical mechanisms responsible for the observed behavior.

cond-mat.soft↗

arXiv2023

Statistical field theory of mechanical stresses in Coulomb fluids. Noether's theorem {\sl vs} General covariant approach

In this paper, we introduce a statistical field theory that describes the macroscopic mechanical forces in inhomogeneous Coulomb fluids. Our approach employs the generalization of Noether's first theorem for the case of fluctuating order parameter, 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 local stresses in a nonuniform Coulomb fluid. We also use previously formulated general covariant methodology [P.E. Brandyshev and Yu.A. Budkov, J. Chem. Phys. 158, 174114 (2023)] in conjunction with a functional Legendre transformation method and derive within it the same total stress tensor. We would like to emphasize that our general approaches are 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.

cond-mat.stat-mech↗

arXiv2023

Dielectric mismatch effects on polyelectrolyte solutions in electrified nanopores: Insights from mean-field theory

We utilize the self-consistent field theory to explore the mechanical and electrical properties of charged surfaces immersed in polyelectrolyte solutions that could be potentially useful for electrochemical applications. Our research focuses on how the dielectric heterogeneity of the solution could affect the disjoining pressure and differential capacitance of the electric double layer. Relying on the developed theoretical framework, based on the Noether's theorem, we calculate the stress tensor, containing the term, arising from the conformational entropy of the polymer chains. With its help we compute the disjoining pressure in polyelectrolyte solution confined between two parallel charged surfaces and analyze its behavior as a function of separation between the surfaces for different values of dielectric mismatch parameter. We also calculate the differential capacitance of the electric double layer and discuss how dielectric heterogeneity of the polyelectrolyte solution influences its values.

cond-mat.soft↗

arXiv2023

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

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.

cond-mat.stat-mech↗

arXiv2023

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

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{ü}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.

cond-mat.soft↗

arXiv2022

Modified Poisson-Boltzmann equations and macroscopic forces in inhomogeneous ionic fluids

We propose a field-theoretical approach based on the thermodynamic perturbation theory and within it derive a grand thermodynamic potential of the inhomogeneous ionic fluid as a functional of electrostatic potential for an arbitrary reference fluid system. We obtain a modified Poisson-Boltzmann equation as the Euler-Lagrange equation for the obtained functional. Applying Noether's theorem to this functional, we derive a general mean-field expression for the stress tensor consistent with the respective modified Poisson-Boltzmann equation. We derive a general expression for the macroscopic force acting on the dielectric or conductive body immersed in an ionic fluid. In particular, we derive a general mean-field expression for the disjoining pressure of an ionic fluid in a slit pore. We apply the developed formalism to describe three ionic fluid models of practical importance: nonpolarizable models (including the well-known Poisson-Boltzmann and Poisson-Fermi equations), polarizable models (ions carry nonzero permanent dipole or static polarizability), and models of ion-dipole mixtures (including the well-known Poisson-Boltzmann-Langevin equation). For these models, we obtain modified Poisson-Boltzmann equations and respective stress tensors, which could be valuable for different applications, where it is necessary to estimate the macroscopic forces acting on the dielectric or conductive bodies (electrodes, colloids, membranes, {\it etc}.) together with the local electrostatic potential (field) and ionic concentrations.

cond-mat.soft↗

arXiv2022

Electrosorption-induced deformation of a porous electrode with non-convex pore geometry in electrolyte solutions: a theoretical study

Porous carbon is well known as a good candidate for the development of electrochemical double-layer capacitors. Predominantly, many conventional carbons are microporous and often well described by the assumption of slit pore geometry. However, there is a class of carbons that is significantly different from the others, namely templated mesoporous carbons. In this work, we study electrosorption-induced deformation in CMK-3-like mesopores having nonconvex geometry applying a mean-field approach. The model is based on the modified Poisson-Boltzmann equation taking into account the excluded volume of the ions within the hard-sphere model in the Percus-Yevick approximation. We assume that the deformation is caused by two effects: ion osmotic pressure and electrostatic interactions of the electric double layers on charged rods. The latter were calculated via the Maxwell stress tensor agreeing with the modified Poisson-Boltzmann equation. We estimated the pore-load modulus of the CMK-3-like material and found an agreement with the previously obtained values by small-angle neutron scattering (SANS). Additionally, we studied the differential capacitance in the non-convex pore geometry and found that the behavior of the differential capacitance profiles was similar to that of the profiles obtained for flat electric double layers. Namely, we obtained the crowding regime at rather high voltages and more pronounced profile asymmetry with increasing differences in the ionic sizes.

cond-mat.soft↗

arXiv2021

Theory of ionic liquids with polarizable ions on a charged electrode

We formulate a general mean-field theory of a flat electric double layer in ionic liquids and electrolyte solutions with ions possessing static polarizability and a permanent dipole moment on a charged electrode. We establish a new analytical expression for electric double layer differential capacitance determining it as an absolute value of the ratio of the local ionic charge density to the local electric field on an electrode surface. We demonstrate that this expression generalizes the analytical expressions previously reported by Kornyshev and Maggs and Podgornik. Using the obtained analytical expression, we explore new features of the differential capacitance behavior with an increase in the static polarizability and permanent dipole moment of cations. We relate these features to the behavior of ionic concentrations on the electrode. In particular, we elucidate the role of the competition between the dielectrophoretic attraction and Coulomb repulsion forces acting on polarizable or polar cations in the electric double layer in the behavior of the differential capacitance. The developed theoretical model and obtained theoretical findings could be relevant for different electrochemical applications, e.g. batteries, supercapacitors, catalysis, electrodeposition, etc.

cond-mat.stat-mech↗

arXiv2021

On gyration radius distributions of star-like macromolecules

Using the path integral approach, we obtain the characteristic functions of the gyration radius distributions for Gaussian star and Gaussian rosette macromolecules. We derive the analytical expressions for cumulants of the both distributions. Applying the steepest descent method, we estimate the probability distribution functions of the gyration radius in the limit of a large number of star and rosette arms in two limiting regimes: for strongly expanded and strongly collapsed macromolecules. We show that in both cases, in the regime of a large gyration radius relative to its mean-square value, the probability distribution functions can be described by the Gaussian functions. In the shrunk macromolecule regime, both distribution functions tend to zero faster than any power of the gyration radius. Based on the asymptotic behavior of the distribution functions and the behavior of statistical dispersions, we demonstrate that the probability distribution function for the rosette is more densely localized near its maximum than that for the star polymer. We construct the interpolation formula for the gyration radius distribution for the Gaussian star macromolecule which can help to take into account the conformational entropy of the flexible star macromolecules within the Flory-type mean-field theories

cond-mat.soft↗

arXiv2020

Two-component electrolyte solutions with dipolar cations on a charged electrode: Theory and computer simulations

The development of advanced electrochemical devices for energy conversion and storage requires fine tuning of electrode reactions, which can be accomplished by altering the electrode/solution interface structure. Particularly, in case of an alkali-salt electrolyte the electric double layer (EDL) composition can be managed by introducing organic cations (e.g. room temperature ionic liquid cations) that may possess polar fragments. To explore this approach, we develop a theoretical model predicting the efficient replacement of simple (alkali) cations with dipolar (organic) ones within the EDL. For the typical values of the molecular dipole moment ($2-4~D$) the effect manifests itself at the surface charge densities higher than 30 $μC/cm^2$. We show that the predicted behavior of the system is in qualitative agreement with the molecular dynamics simulation results.

cond-mat.soft↗

arXiv2020

Statistical field theory of ion-molecular solutions

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.

cond-mat.soft↗

arXiv2020

Nonlocal density functional theory of water taking into account many-body dipole correlations: Binodal and surface tension of 'liquid-vapour' interface

In this paper we formulate a nonlocal density functional theory of inhomogeneous water. We model a water molecule as a couple of oppositely charged sites. The negatively charged sites interact with each other through the Lennard-Jones potential (steric and dispersion interactions), square-well potential (short-range specific interactions due to electron charge transfer), and Coulomb potential, whereas the positively charged sites interact with all types of sites by applying the Coulomb potential only. Taking into account the nonlocal packing effects via the fundamental measure theory (FMT), dispersion and specific interactions in the mean-field approximation, and electrostatic interactions at the many-body level through the random phase approximation, we describe the liquid-vapour interface. We demonstrate that our model without explicit account of the association of water molecules due to hydrogen bonding and with explicit account of the many-body electrostatic interactions at the many-body level is able to describe the liquid-vapour coexistence curve and the surface tension at the ambient pressures and temperatures. We obtain very good agreement with available in the literature MD simulation results for density profile of liquid-vapour interface at ambient state parameters. The formulated theory can be used as a theoretical background for describing of the capillary phenomena, occurring in micro- and mesoporous materials.

cond-mat.soft↗

arXiv2019

A statistical field theory of salt solutions of 'hairy' dielectric particles

In this paper, we formulate a field-theoretical model of dilute salt solutions of electrically neutral spherical colloid particles. Each colloid particle consists of a 'central' charge that is situated at the center and compensating peripheral charges (grafted to it) that are fixed or fluctuating relative to the central charge. In the framework of the random phase approximation, we obtain a general expression for electrostatic free energy of solution and analyze it for different limiting cases. In the limit of infinite number of peripheral charges, when they can be modelled as a continual charged cloud, we obtain an asymptotic behavior of the electrostatic potential of a point-like test charge in a salt colloid solution at long distances, demonstrating the crossover from its monotonic decrease to damped oscillations with a certain wavelength. We show that the obtained crossover is determined by certain Fisher-Widom line. For the same limiting case, we obtain an analytical expression for the electrostatic free energy of a salt-free solution. In the case of nonzero salt concentration, we obtain analytical relations for the electrostatic free energy in two limiting regimes. Namely, when the ionic concentration is much higher than the colloid concentration and the effective size of charge cloud is much bigger than the screening lengths that are attributed to the salt ions and the central charges of colloid particles. The proposed theory could be useful for theoretical description of the phase behavior of salt solutions of metal-organic complexes and polymeric stars.

cond-mat.soft↗

arXiv2019

Nonlocal statistical field theory of dipolar particles forming chain-like clusters

We present a nonlocal statistical field theory of a diluted solution of dipolar particles which are capable of forming chain-like clusters in accordance with the 'head-to-tail' mechanism. As in our previous study [Yu.A. Budkov 2018 J. Phys.: Condens. Matter 30 344001], we model dipolar particles as dimers comprised of oppositely charged point-like groups, separated by fluctuating distance. For the special case of the Yukawa-type distribution function of distance between the charged groups of dipolar particles we obtain an analytical expression for the electrostatic free energy of solution within the random phase approximation. We show that an increase in the association constant leads to a decrease in the absolute value of the electrostatic free energy of solution, preventing its phase separation which is in agreement with the former computer simulations and theoretical results. We obtain a non-linear integro-differential equation for the self-consistent field potential created by the fixed external charges in a solution medium, taking into account the association of dipolar particles. As a consequence of the derived self-consistent field equation, in regime of weak electrostatic interactions, we obtain an analytical expression for the electrostatic potential of the point-like test ion, surrounded by the chain-like clusters of the dipolar particles. We show that in the mean-field approximation the association does not change the bulk dielectric permittivity of the solution, but increases the solvation radius of the point-like charge, relative to the theory of non-associating dipolar particles.

cond-mat.soft↗

arXiv2019

Nonlocal statistical field theory of dipolar particles in electrolyte solutions

We present a nonlocal statistical field theory of a dilute electrolyte solution with small additive of dipolar particles. We postulate that every dipolar particle is associated with an arbitrary probability distribution function (PDF) of distance between its charge centers. Using the standard Hubbard-Stratonovich transformation, we represent the configuration integral of the system in the functional integral form. We show that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson-Boltzmann-Langevin (PBL) functional. In the mean-field approximation we obtain a non-linear integro-differential equation with respect to the mean-field electrostatic potential, generalizing the PBL equation for the point-like dipoles obtained first by Abrashkin et al. We apply the obtained equation in its linearized form to derivation of the expressions for the mean-field electrostatic potential of the point-like test ion and its solvation free energy in salt-free solution, as well as in solution with salt ions. For the 'Yukawa'-type PDF we obtain analytic relations for both the electrostatic potential and the solvation free energy of the point-like test ion. We obtain a general expression for the bulk electrostatic free energy of the solution within the random phase approximation (RPA). For the salt-free solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic relation for the electrostatic free energy.

cond-mat.soft↗