27 research outputs found
The phase transition of the first order in the critical region of the gas-liquid system
This is a summarising investigation of the events of the phase transition of
the first order that occur in the critical region below the liquid-gas critical
point. The grand partition function has been completely integrated in the
phase-space of the collective variables. The basic density measure is the
quartic one. It has the form of the exponent function with the first, second,
third and fourth degree of the collective variables. The problem has been
reduced to the Ising model in an external field, the role of which is played by
the generalised chemical potential . The line , where
is the density, is the line of the phase transition. We consider the
isothermal compression of the gas till the point where the phase transition on
the line is reached. When the path of the pressing reaches the
line in the gas medium, a droplet of liquid springs up. The work for
its formation is obtained, the surface-tension energy is calculated. On the
line we have a two-phase system: the gas and the liquid (the
droplet) one. The equality of the gas and of the liquid chemical potentials is
proved. The process of pressing is going on. But the pressure inside the system
has stopped, two fixed densities have arisen: one for the gas-phase and the other for the liquid-phase (symmetrically to the rectlinear diameter), where
is the critical density. Starting from that moment the
external pressure works as a latent work of pressure. Its value is obtained. As
a result, the gas-phase disappears and the whole system turns into liquid. The
jump of the density is equal to , where . and are coefficients of the Hamiltonian in the last cell
connected with the renormalisation-group symmetry.Comment: 27 pages, 9 figure
A mesoscopic field theory of ionic systems versus a collective variable approach
We establish a link between the two functional approaches: a mesoscopic field
theory developed recently by A.Ciach and G.Stell [A. Ciach and G. Stell, J.
Mol. Liq. 87 (2000) 253] for the study of ionic models and an exact statistical
field theory based on the method of collective variables.Comment: 7 page
Liquid-gas phase transition at and below the critical point
This article is a continuation of our previous works (see Yukhnovskii I.R. et
al., J. Stat. Phys, 1995, 80, 405 and references therein), where we have
described the behavior of a simple system of interacting particles in the
region of temperatures at and about the critical point, T \geqslant T_{c}. Now
we present a description of the behavior of the system at the critical point
(T_{c}, \eta_{c}) and in the region below the critical point. The calculation
is carried out from the first principles. The expression for the grand
canonical partition function is brought to the functional integrals defined on
the set of collective variables. The Ising-like form is singled out. Below
T_{c}, when a gas-liquid system undergoes a phase transition of the first
order, i.e., boiling, a "jump" occurs from the "extreme" high probability gas
state to the "extreme" high probability liquid state, releasing or absorbing
the latent heat of the transition. The phase equilibria conditions are also
derived.Comment: 23 pages, 9 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
Gas-liquid critical point in ionic fluids
Based on the method of collective variables we develop the statistical field
theory for the study of a simple charge-asymmetric primitive model (SPM).
It is shown that the well-known approximations for the free energy, in
particular DHLL and ORPA, can be obtained within the framework of this theory.
In order to study the gas-liquid critical point of SPM we propose the method
for the calculation of chemical potential conjugate to the total number density
which allows us to take into account the higher order fluctuation effects. As a
result, the gas-liquid phase diagrams are calculated for . The results
demonstrate the qualitative agreement with MC simulation data: critical
temperature decreases when increases and critical density increases rapidly
with .Comment: 18 pages, 1 figur
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
Spatial inhomogeneities in ionic liquids, charged proteins and charge stabilized colloids from collective variables theory
Effects of size and charge asymmetry between oppositely charged ions or
particles on spatial inhomogeneities are studied for a large range of charge
and size ratios. We perform a stability analysis of the primitive model (PM) of
ionic systems with respect to periodic ordering using the collective variables
based theory. We extend previous studies [A. Ciach et al., Phys. Rev.E
\textbf{75}, 051505 (2007)] in several ways. First, we employ a non-local
approximation for the reference hard-sphere fluid which leads to the
Percus-Yevick pair direct correlation functions for the uniform case. Second,
we use the Weeks-Chandler-Anderson regularization scheme for the Coulomb
potential inside the hard core. We determine the relevant order parameter
connected with the periodic ordering and analyze the character of the dominant
fluctuations along the -lines. We show that the above-mentioned
modifications produce large quantitative and partly qualitative changes in the
phase diagrams obtained previously. We discuss possible scenarios of the
periodic ordering for the whole range of size- and charge ratios of the two
ionic species, covering electrolytes, ionic liquids, charged globular proteins
or nanoparticles in aqueous solutions and charge-stabilized colloids
A formally exact field theory for classical systems at equilibrium
We propose a formally exact statistical field theory for describing classical
fluids with ingredients similar to those introduced in quantum field theory. We
consider the following essential and related problems : i) how to find the
correct field functional (Hamiltonian) which determines the partition function,
ii) how to introduce in a field theory the equivalent of the indiscernibility
of particles, iii) how to test the validity of this approach. We can use a
simple Hamiltonian in which a local functional transposes, in terms of fields,
the equivalent of the indiscernibility of particles. The diagrammatic expansion
and the renormalization of this term is presented. This corresponds to a non
standard problem in Feynman expansion and requires a careful investigation.
Then a non-local term associated with an interaction pair potential is
introduced in the Hamiltonian. It has been shown that there exists a mapping
between this approach and the standard statistical mechanics given in terms of
Mayer function expansion. We show on three properties (the chemical potential,
the so-called contact theorem and the interfacial properties) that in the field
theory the correlations are shifted on non usual quantities. Some perspectives
of the theory are given.Comment: 20 pages, 8 figure
Thermodynamic characteristics of the classical n-vector magnetic model in three dimensions
The method of calculating the free energy and thermodynamic characteristics
of the classical n-vector three-dimensional (3D) magnetic model at the
microscopic level without any adjustable parameters is proposed. Mathematical
description is perfomed using the collective variables (CV) method in the
framework of the model approximation. The exponentially decreasing
function of the distance between the particles situated at the N sites of a
simple cubic lattice is used as the interaction potential. Explicit and
rigorous analytical expressions for entropy,internal energy, specific heat near
the phase transition point as functions of the temperature are obtained. The
dependence of the amplitudes of the thermodynamic characteristics of the system
for and on the microscopic parameters of the interaction
potential are studied for the cases and . The obtained
results provide the basis for accurate analysis of the critical behaviour in
three dimensions including the nonuniversal characteristics of the system.Comment: 25 pages, 5 figure