157 research outputs found
The density functional theory of classical fluids revisited
We reconsider the density functional theory of nonuniform classical fluids
from the point of view of convex analysis. From the observation that the
logarithm of the grand-partition function is a convex
functional of the external potential it is shown that the Kohn-Sham free
energy is a convex functional of the density . and constitute a pair of Legendre transforms and each
of these functionals can therefore be obtained as the solution of a variational
principle. The convexity ensures the unicity of the solution in both cases. The
variational principle which gives as the maximum of a
functional of is precisely that considered in the density functional
theory while the dual principle, which gives as the maximum of
a functional of seems to be a new result.Comment: 10 page
Equilibrium solvation in quadrupolar solvents
We present a microscopic theory of equilibrium solvation in solvents with
zero dipole moment and non-zero quadrupole moment (quadrupolar solvents). The
theory is formulated in terms of autocorrelation functions of the quadrupolar
polarization (structure factors). It can be therefore applied to an arbitrary
dense quadrupolar solvent for which the structure factors are defined. We
formulate a simple analytical perturbation treatment for the structure factors.
The solute is described by coordinates, radii, and partial charges of
constituent atoms. The theory is tested on Monte Carlo simulations of solvation
in model quadrupolar solvents. It is also applied to the calculation of the
activation barrier of electron transfer reactions in a cleft-shaped
donor-acceptor complex dissolved in benzene with the structure factors of
quadrupolar polarization obtained from Molecular Dynamics simulations.Comment: Submitted to J. Chem. Phys., 20 pages and 13 figure
Field theory for size- and charge asymmetric primitive model of electrolytes. Mean-field stability analysis and pretransitional effects
The primitive model of ionic systems is investigated within a field-theoretic
description for the whole range of size-, \lambda, and charge, Z, ratios of the
two ionic species. Two order parameters (OP) are identified, and their
relations to physically relevant quantities are described for various values of
\lambda and Z. Instabilities of the disordered phase associated with the two
OP's are determined in the mean-field approximation.
A gas-liquid separation occurs for any Z and \lambda different from 1. In
addition, an instability with respect to various types of periodic ordering of
the two kinds of ions is found
Field-theoretic description of ionic crystallization in the restricted primitive model
Effects of charge-density fluctuations on a phase behavior of the restricted
primitive model (RPM) are studied within a field-theoretic formalism. We focus
on a -line of continuous transitions between charge-ordered and
charge-disordered phases that is observed in several mean-field (MF) theories,
but is absent in simulation results. In our study the RPM is reduced to a
theory, and a fluctuation contribution to a grand thermodynamic
potential is obtained by generalizing the Brazovskii approach. We find that in
a presence of fluctuations the -line disappears. Instead, a
fluctuation-induced first-order transition to a charge-ordered phase appears in
the same region of a phase diagram, where the liquid -- ionic-crystal
transition is obtained in simulations. Our results indicate that the
charge-ordered phase should be identified with an ionic crystal.Comment: 31 pages, 10 figure
Theory of solvation in polar nematics
We develop a linear response theory of solvation of ionic and dipolar solutes
in anisotropic, axially symmetric polar solvents. The theory is applied to
solvation in polar nematic liquid crystals. The formal theory constructs the
solvation response function from projections of the solvent dipolar
susceptibility on rotational invariants. These projections are obtained from
Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist
both in the isotropic and nematic phase. Based on the properties of the solvent
susceptibility from simulations and the formal solution, we have obtained a
formula for the solvation free energy which incorporates experimentally
available properties of nematics and the length of correlation between the
dipoles in the liquid crystal. Illustrative calculations are presented for the
Stokes shift and Stokes shift correlation function of coumarin-153 in
4-n-pentyl-4'-cyanobiphenyl (5CB) and 4,4-n-heptyl-cyanopiphenyl (7CB) solvents
as a function of temperature in both the nematic and isotropic phase.Comment: 19 pages, 9 figure
Phase Coexistence of a Stockmayer Fluid in an Applied Field
We examine two aspects of Stockmayer fluids which consists of point dipoles
that additionally interact via an attractive Lennard-Jones potential. We
perform Monte Carlo simulations to examine the effect of an applied field on
the liquid-gas phase coexistence and show that a magnetic fluid phase does
exist in the absence of an applied field. As part of the search for the
magnetic fluid phase, we perform Gibbs ensemble simulations to determine phase
coexistence curves at large dipole moments, . The critical temperature is
found to depend linearly on for intermediate values of beyond the
initial nonlinear behavior near and less than the where no
liquid-gas phase coexistence has been found. For phase coexistence in an
applied field, the critical temperatures as a function of the applied field for
two different are mapped onto a single curve. The critical densities
hardly change as a function of applied field. We also verify that in an applied
field the liquid droplets within the two phase coexistence region become
elongated in the direction of the field.Comment: 23 pages, ReVTeX, 7 figure
Ab initio study of the vapour-liquid critical point of a symmetrical binary fluid mixture
A microscopic approach to the investigation of the behaviour of a symmetrical
binary fluid mixture in the vicinity of the vapour-liquid critical point is
proposed. It is shown that the problem can be reduced to the calculation of the
partition function of a 3D Ising model in an external field. For a square-well
symmetrical binary mixture we calculate the parameters of the critical point as
functions of the microscopic parameter r measuring the relative strength of
interactions between the particles of dissimilar and similar species. The
calculations are performed at intermediate () and moderately long
() intermolecular potential ranges. The obtained results agree
well with the ones of computer simulations.Comment: 14 pages, Latex2e, 5 eps-figures included, submitted to
J.Phys:Cond.Ma
Universality class of the critical point in the restricted primitive model of ionic systems
A coarse-grained description of the restricted primitive model is considered
in terms of the local charge- and number-density fields. Exact reduction to a
one-field theory is derived, and exact expressions for the number-density
correlation functions in terms of higher-order correlation functions for the
charge-density are given. It is shown that in continuum space the singularity
of the charge-density correlation function associated with short-wavelength
charge-ordering disappears when charge-density fluctuations are included by
following the Brazovskii approach. The related singularity of the individual
Feynman diagrams contributing to the number-density correlation functions is
cured when all the diagrams are segregated ito disjoint sets according to their
topological structure. By performing a resummation of all diagrams belonging to
each set a regular expression represented by a secondary diagram is obtained.
The secondary diagrams are again segregated into disjoint sets, and the series
of all the secondary diagrams belonging to a given set is represented by a
hyperdiagram. A one-to-one correspondence between the hyperdiagrams
contributing to the number-density vertex functions, and diagrams contributing
to the order-parameter vertex functions in a certain model system belonging to
the Ising universality class is demonstrated. Corrections to scaling associated
with irrelevant operators that are present in the model-system Hamiltonian, and
other corrections specific to the RPM are also discussed
Modal Logics of Topological Relations
Logical formalisms for reasoning about relations between spatial regions play
a fundamental role in geographical information systems, spatial and constraint
databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's
modal logic of time intervals based on the Allen relations, we introduce a
family of modal logics equipped with eight modal operators that are interpreted
by the Egenhofer-Franzosa (or RCC8) relations between regions in topological
spaces such as the real plane. We investigate the expressive power and
computational complexity of logics obtained in this way. It turns out that our
modal logics have the same expressive power as the two-variable fragment of
first-order logic, but are exponentially less succinct. The complexity ranges
from (undecidable and) recursively enumerable to highly undecidable, where the
recursively enumerable logics are obtained by considering substructures of
structures induced by topological spaces. As our undecidability results also
capture logics based on the real line, they improve upon undecidability results
for interval temporal logics by Halpern and Shoham. We also analyze modal
logics based on the five RCC5 relations, with similar results regarding the
expressive power, but weaker results regarding the complexity
Ginzburg Criterion for Coulombic Criticality
To understand the range of close-to-classical critical behavior seen in
various electrolytes, generalized Debye-Hueckel theories (that yield density
correlation functions) are applied to the restricted primitive model of
equisized hard spheres. The results yield a Landau-Ginzburg free-energy
functional for which the Ginzburg criterion can be explicitly evaluated. The
predicted scale of crossover from classical to Ising character is found to be
similar in magnitude to that derived for simple fluids in comparable fashion.
The consequences in relation to experiments are discussed briefly.Comment: 4 pages, revtex, 2 tables (latex2.09 required due to revtex's
incompatibility with latex2e tables
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