49 research outputs found

### 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

### 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

### 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.Comment: Paper is accepted for publication in Physical Chemistry Chemical
Physic

### 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