Surface tension of aqueous electrolyte solutions. A thermomechanical approach.

We determine the surface tension of aqueous electrolyte solutions in contact with non-polar dielectric media using a thermomechanical approach, which involves deriving the stress tensor from the thermodynamic potential of an inhomogeneous fluid. To obtain the surface tension, we calculate both the normal and tangential pressures using the components of the stress tensor, recently derived by us [Y. A. Budkov and P. E. Brandyshev, J. Chem. Phys. 159, 174103 (2023)] within the framework of Wang's variational field theory. Using this approach, we derive an analytical expression for the surface tension in the linear approximation. At low ionic concentrations, this expression represents the classical Onsager-Samaras limiting law. By utilizing only one fitting parameter, which is related to the affinity of anions to the dielectric boundary, we successfully approximated experimental data on the surface tension of several aqueous electrolyte solutions. This approximation applies to both the solution-air and solution-dodecane interfaces, covering a wide range of electrolyte concentrations.

Disjoining Pressure Decay Length in Room-Temperature Ionic Liquids: A Molecular Simulation Study.

We present all-atom molecular simulations to investigate the behavior of 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) in negatively charged carbon nanopores of different widths (h = 5÷15 nm) and lengths (l = 4÷10 nm). The goal of our study was to determine how the disjoining pressure varies as a function of the pore width at different lengths and to understand the influence of edge effects. Our results show that the edge effect decreases as the pore length increases. Using an exponential function, we can approximate the disjoining pressure at large pore widths and use this approximation to estimate the decay length that can correlate with the electrostatic screening length. The results agreed well with those of previous experimental studies.

Variational field theory of macroscopic forces in coulomb fluids.

Based on the variational field theory framework, we extend our previous mean-field formalism [Y. A. Budkov and A. L. Kolesnikov, JStatMech 2022, 053205.2022], taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that considers the electrostatic correlations of ions. This is accomplished through an additional term that depends on the autocorrelation function of the local electric field fluctuations. Utilizing the derived total stress tensor and applying the mechanical equilibrium condition, we establish a general expression for the disjoining pressure of the Coulomb fluids, confined in a pore with a slit-like geometry. Using this equation, we derive an asymptotic expression for the disjoining pressure in a slit-like pore with non-electrified conductive walls. Present theory is the basis for future modeling of the mechanical stresses that occur in electrode pores with conductive charged walls, immersed in liquid phase electrolytes beyond the mean-field theory.

Theory of electrolyte solutions in a slit charged pore: Effects of structural interactions and specific adsorption of ions.

In this paper, we present a continuation of our research on modeling electrolyte solutions within charged pores. We make use of the model developed by Blossey et al. [Phys. Rev. E 95, 060602 (2017)], which takes into account the structural interactions between ions through a bilinear form over the gradients of local ionic concentrations in the grand thermodynamic potential, as well as their steric interactions through the lattice gas model. The structural interactions may describe the effects of the molecular structure of ions at a phenomenological level. For example, these effects include steric effects due to non-spherical shapes of ions, their conformational lability, and solvent effects. In addition, we explore their specific interactions with the pore walls by incorporating external attractive potentials. Our primary focus is on observing the behavior of ionic concentration profiles and the disjoining pressure as the pore width changes. By starting with the local mechanical equilibrium condition, we derive a general expression for the disjoining pressure. Our findings indicate that considering the structural interactions of ions leads to a pronounced minimum on the disjoining pressure profiles at small pore widths. We attribute this minimum to the formation of electric double layers on the electrified surfaces of the pore. In addition, our results demonstrate that the inclusion of the attractive interactions of ions with the pore walls enhances this minimum and shifts it to smaller pore thicknesses. Our theoretical discoveries may be useful for those involved in supercapacitor electrochemical engineering, particularly when working with porous electrodes that have been infused with concentrated electrolyte solutions.

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.

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-Hückel 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.

Macroscopic forces in inhomogeneous polyelectrolyte solutions.

In this paper, we present a self-consistent field theory of macroscopic forces in spatially inhomogeneous flexible chain polyelectrolyte solutions. We derive an analytical expression for a stress tensor which consists of three terms: isotropic hydrostatic stress, electrostatic (Maxwell) stress, and stress rising from conformational entropy of polymer chains-conformational stress. We apply our theory to the description of polyelectrolyte solutions confined in a conductive slit nanopore and observe anomalous behavior of disjoining pressure and electric differential capacitance.

Influence of fluid flows on electric double layers in evaporating colloidal sessile droplets.

A model is developed for describing the transport of charged colloidal particles in an evaporating sessile droplet on the electrified metal substrate in the presence of a solvent flow. The model takes into account the electric charge of colloidal particles and small ions produced by electrolytic dissociation of the active groups on the colloidal particles and solvent molecules. We employ a system of self-consistent Poisson and Nernst-Planck equations for electric potential and average concentrations of colloidal particles and ions with the appropriate boundary conditions. The fluid dynamics, temperature distribution and evaporation process are described with the Navier-Stokes equations, equations of heat conduction and vapor diffusion in air, respectively. The developed model is used to carry out a first-principles numerical simulation of charged silica colloidal particle transport in an evaporating aqueous droplet. We find that electric double layers can be destroyed by a sufficiently strong fluid flow.

Correction: Electrochemistry meets polymer physics: polymerized ionic liquids on an electrified electrode.

Correction for 'Electrochemistry meets polymer physics: polymerized ionic liquids on an electrified electrode' by Yury A. Budkov et al., Phys. Chem. Chem. Phys., 2022, DOI: 10.1039/d1cp04221a.

Electrochemistry meets polymer physics: polymerized ionic liquids on an electrified electrode.

Polymeric ionic liquids are emerging polyelectrolyte materials for modern electrochemical applications. In this paper, we propose a self-consistent field theory of a polymeric ionic liquid on a charged conductive electrode. Taking into account the conformational entropy of rather long polymerized cations within the Lifshitz theory and electrostatic and excluded volume interactions of ionic species within the mean-field approximation, we obtain a system of self-consistent field equations for the local electrostatic potential and average concentrations of monomeric units and counterions. We solve these equations in the linear approximation for the cases of a point-like charge and a flat infinite uniformly charged electrode immersed in a polymeric ionic liquid and derive analytical expressions for local ionic concentrations and electrostatic potential, and derive an analytical expression for the linear differential capacitance of the electric double layer. We also find a numerical solution to the self-consistent field equations for two types of boundary conditions for the local polymer concentration on the electrode, corresponding to the cases of the specific adsorption absence (indifferent surface) and strong short-range repulsion of the monomeric units near the charged surface (hard wall case). For both cases, we investigate the behavior of differential capacitance as a function of applied voltage for a pure polymeric ionic liquid and a polymeric ionic liquid dissolved in a polar organic solvent. We observe that the differential capacitance profile shape is strongly sensitive to the adopted boundary condition for the local polymer concentration on the electrode.

Molecular theory of the electrostatic collapse of dipolar polymer gels.

We develop a new quantitative molecular theory of liquid-phase dipolar polymer gels. We model monomer units of the polymer network as a couple of charged sites separated by a fluctuating distance. For the first time, within the random phase approximation, we have obtained an analytical expression for the electrostatic free energy of the dipolar gel. Depending on the coupling parameter of dipole-dipole interactions and the ratio of the dipole length to the subchain Kuhn length, we describe the gel collapse induced by electrostatic interactions in the good solvent regime as a first-order phase transition. This transition can be realized at reasonable physical parameters of the system (temperature, solvent dielectric constant, and dipole moment of monomer units). The obtained results could be potentially used in modern applications of stimuli-responsive polymer gels and microgels, such as drug delivery, nanoreactors, molecular uptake, coatings, superabsorbents, etc.

Impregnation of Poly(methyl methacrylate) with Carbamazepine in Supercritical Carbon Dioxide: Molecular Dynamics Simulation.

Fully atomistic molecular dynamics simulations are employed to study impregnation of the poly(methyl methacrylate) (PMMA) matrix with carbamazepine (CBZ) in supercritical carbon dioxide. The simulation box consists of 108 macromolecules of the polymer sample with the polymerization degree of 100, 57 molecules of CBZ, and 242,522 CO2 molecules. The simulation is performed at 333 K and 20 MPa. It is found that by the end of the simulation, the CBZ uptake reaches 1.09 wt % and 50 molecules are sorbed by PMMA. The main type of interaction between PMMA and CBZ is hydrogen bonding between the carbonyl oxygen of PMMA and the hydrogen atoms of the CBZ NH2-group. At the polymer surface, CBZ exists not only in the molecular form, as inside the polymer and in the bulk solution, but also in the form of dimers and trimers. The energy of formation of the hydrogen-bonded complexes is estimated within ab initio calculations.

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. 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.

Molecular fields and statistical field theory of fluids: Application to interface phenomena.

Using the integral transformation, the field-theoretical Hamiltonian of the statistical field theory of fluids is obtained along with the microscopic expressions for the coefficients of the Hamiltonian. Applying this approach to the liquid-vapor interface, we derive an explicit analytical expression for the surface tension in terms of temperature, density, and parameters of the intermolecular potential. We also demonstrate that a clear physical interpretation may be given to the formal statistical field arising in the integral transformation-it may be associated with the one-body local microscopic potential. The results of the theory, lacking any ad hoc or fitting parameters are in good agreement with available simulation data.

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.

Nonlocal statistical field theory of dipolar particles in electrolyte solutions.

We present a nonlocal statistical field theory of a dilute electrolyte solution with a 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, resulting in two limiting regimes. Finally, we analyze the limiting laws, following from the general relation for the electrostatic free energy of solution in presence of both the ions and the dipolar particles for the case of Yukawa-type PDF.