Statistical theory of fluids with a complex electric structure: Application to solutions of soft-core dipolar particles

Based on the thermodynamic perturbation theory (TPT) and the Random phase approximation (RPA), we present a statistical theory of solutions of electrically neutral soft molecules, every of which is modelled as a set of sites that interact with each other through the potentials, presented as the sum of the Coulomb potential and arbitrary soft-core potential. As an application of our formalism, we formulate a general statistical theory of solution of the soft-core dipolar particles. For the latter, we obtain a new analytical relation for the screening function. As a special case, we apply this theory to describing the phase behavior of a solution of the dipolar particles interacting with each other in addition to the electrostatic potential through the repulsive Gaussian potential -- Gaussian core dipolar model (GCDM). Using the obtained analytic expression for the total free energy of the GCDM, we obtain the liquid-liquid phase separation with an upper critical point. The developed formalism could be used as a general framework for the coarse-grained description of thermodynamic properties of solutions of macromolecules, such as proteins, betaines, polypeptides, etc.Comment: Mansuscript has been accepted in Fluid Phase Equilibri

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.Comment: Published in Journal of Molecular Liquid

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.Comment: Published in Journal of Physics Condensed Matte

Statistical description of co-nonsolvency suppression at high pressures

We present an application of Flory-type self-consistent field theory of the flexible polymer chain dissolved in the binary mixture of solvents to theoretical description of co-nonsolvency. We show that our theoretical predictions are in good quantitative agreement with the recently published MD simulation results for the conformational behavior of a Lennard-Jones flexible chain in a binary mixture of the Lennard-Jones fluids. We show that our theory is able to describe co-nonsolvency suppression through pressure enhancement to extremely high values recently discovered in experiment and reproduced by full atomistic MD simulations. Analysing a co-solvent concentration in internal polymer volume at different pressure values, we speculate that this phenomenon is caused by the suppression of the co-solvent preferential solvation of the polymer backbone at rather high pressure imposed. We show that when the co-solvent-induced coil-globule transition takes place, the entropy and the enthalpy contributions to the solvation free energy abruptly decrease, while the solvation free energy remains continuous

On a new application of the path integrals in polymer statistical physics

We propose a new approach based on the path integral formalism to the calculation of the probability distribution functions of quadratic quantities of the Gaussian polymer chain in d-dimensional space, such as the radius of gyration and potential energy in the parabolic well. In both cases we obtain the exact relations for the characteristic function and cumulants. Using the standard steepest-descent method, we evaluate the probability distribution functions in two limiting cases of the large and small values of corresponding variables.Comment: This manuscript has been accepted for publication in Journal of Statistical Mechanics: Theory and experimen

Field-regulated force by grafted polyelectrolytes

Generation of mechanical force regulated by external electric field is studied both theoretically and by molecular dynamics (MD) simulations. The force arises in deformable bodies linked to the free end of a grafted polyelectrolyte chain which is exposed to electric field that favours its adsorption. We consider a few target bodies with different force-deformation relations including (i) linear and (ii) cubic dependences as well as (iii) Hertzian-like force. Such force-deformation relations mimic the behaviour of (i) coiled and (ii) stretched polymer chains, respectively, or (iii) that of a squeezed colloidal particle. The magnitude of the arising force varies over a wide interval although the electric field alters within a relatively narrow range only. The predictions of our theory agree quantitatively well with the results of numerical simulations. Both cases of zero and finite electrical current are investigated and we do not obtain substantial differences in the force generated. The phenomenon studied could possibly be utilised to design, e.g., vice-like devices to fix nano-sized objects

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.Comment: Revised version submitted to Journal of Physics: Condensed Matter 15 September 201

Polarizable polymer chain under external electric field in a dilute polymer solution

We study the conformational behavior of polarizable polymer chain under an external homogeneous electric field within the Flory type self-consistent field theory. We consider the influence of electric field on the polymer coil as well as on the polymer globule. We show that when the polymer chain conformation is a coil, application of external electric field leads to its additional swelling. However, when the polymer conformation is a globule, a sufficiently strong field can induce a globule-coil transition. We show that such $"$field-induced$"$ globule-coil transition at the sufficiently small monomer polarizabilities goes quite smoothly. On the contrary, when the monomer polarizability exceeds a certain threshold value, the globule-coil transition occurs as a dramatic expansion in the regime of first-order phase transition. The developed theoretical model can be applied to predicting polymer globule density change under external electric field in order to provide more efficient processes of polymer functionalization, such as sorption, dyeing, chemical modification, etc

The Equation of State for Solution of Semiflexible Polymer Chains

We formulate a self-consistent procedure for calculation of thermodynamic and structural properties of polymer solutions based on the Gaussian equivalent representation method (GER) for functional integrals calculation beyond the mean-field approximaton. We show that an equation of state, potential of mean force of interaction monomer-monomer, and persistent length should be defined self-consistently by solving of some system of coupled equation

On the theory of electric double layer with explicit account of a polarizable co-solvent

We present a continuation of our theoretical research into the influence of co-solvent polarizability on a differential capacitance of the electric double layer [EPL 111, 28002 (2015)]. We formulate a modified Poisson-Boltzmann theory, using the formalism of density functional approach on the level of local density approximation taking into account the electrostatic interactions of ions and co-solvent molecules as well as their excluded volume. We derive the modified Poisson-Boltzmann equation, considering the three-component symmetric lattice gas model as a reference system and minimizing the grand thermodynamic potential with respect to the electrostatic potential. We apply present modified Poisson-Boltzmann equation to the electric double layer theory