36 research outputs found
Phase diagram of symmetric binary mixtures at equimolar and non-equimolar concentrations: a systematic investigation
We consider symmetric binary mixtures consisting of spherical particles with
equal diameters interacting via a hard-core plus attractive tail potential with
strengths epsilon_{ij}, i,j=1,2, such that epsilon_{11} = epsilon_{22} >
epsilon_{12}. The phase diagram of the system at all densities and
concentrations is investigated as a function of the unlike-to-like interaction
ratio delta = epsilon_{12}/epsilon_{11} by means of the hierarchical reference
theory (HRT). The results are related to those of previous investigations
performed at equimolar concentration, as well as to the topology of the
mean-field critical lines. As delta is increased in the interval 0 < delta < 1,
we find first a regime where the phase diagram at equal species concentration
displays a tricritical point, then one where both a tricritical and a
liquid-vapor critical point are present. We did not find any clear evidence of
the critical endpoint topology predicted by mean-field theory as delta
approaches 1, at least up to delta=0.8, which is the largest value of delta
investigated here. Particular attention was paid to the description of the
critical-plus-tricritical point regime in the whole density-concentration
plane. In this situation, the phase diagram shows, in a certain temperature
interval, a coexistence region that encloses an island of homogeneous,
one-phase fluid.Comment: 27 pages + 20 figure
Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group
The Hierarchical Reference Theory (HRT) of fluids is a general framework for
the description of phase transitions in microscopic models of classical and
quantum statistical physics. The foundations of HRT are briefly reviewed in a
self-consistent formulation which includes both the original sharp cut-off
procedure and the smooth cut-off implementation, which has been recently
investigated. The critical properties of HRT are summarized, together with the
behavior of the theory at first order phase transitions. However, the emphasis
of this presentation is on the close relationship between HRT and non
perturbative renormalization group methods, as well as on recent
generalizations of HRT to microscopic models of interest in soft matter and
quantum many body physics.Comment: 17 pages, 5 figures. Review paper to appear in Molecular Physic
Phase transitions in simple and not so simple binary fluids
Compared to pure fluids, binary mixtures display a very diverse phase
behavior, which depends sensitively on the parameters of the microscopic
potential. Here we investigate the phase diagrams of simple model mixtures by
use of a microscopic implementation of the renormalization group technique.
First, we consider a symmetric mixture with attractive interactions, possibly
relevant for describing fluids of molecules with internal degrees of freedom.
Despite the simplicity of the model, slightly tuning the strength of the
interactions between unlike species drastically changes the topology of the
phase boundary, forcing or inhibiting demixing, and brings about several
interesting features such as double critical points, tricritical points, and
coexistence domains enclosing `islands' of homogeneous, mixed fluid.
Homogeneous phase separation in mixtures can be driven also by purely repulsive
interactions. As an example, we consider a model of soft particles which has
been adopted to describe binary polymer solutions. This is shown to display
demixing (fluid-fluid) transition at sufficiently high density. The nature and
the physical properties of the corresponding phase transition are investigated.Comment: 6 pages + 3 figures, presented at the 5th EPS Liquid Matter
Conference, Konstanz, 14-18 September 200
Implementation of the Hierarchical Reference Theory for simple one-component fluids
Combining renormalization group theoretical ideas with the integral equation
approach to fluid structure and thermodynamics, the Hierarchical Reference
Theory is known to be successful even in the vicinity of the critical point and
for sub-critical temperatures. We here present a software package independent
of earlier programs for the application of this theory to simple fluids
composed of particles interacting via spherically symmetrical pair potentials,
restricting ourselves to hard sphere reference systems. Using the hard-core
Yukawa potential with z=1.8/sigma for illustration, we discuss our
implementation and the results it yields, paying special attention to the core
condition and emphasizing the decoupling assumption's role.Comment: RevTeX, 16 pages, 2 figures. Minor changes, published versio
Nonuniversal route to universality: Critical phenomena in colloidal dispersions
We investigate critical phenomena in colloids by means of the
renormalization-group based hierarchical reference theory of fluids (HRT). We
focus on three experimentally relevant model systems: namely, the
Asakura-Oosawa model of a colloidal dispersion under the influence of
polymer-induced attractive depletion forces; fluids with competing short-range
attractive and longer-range repulsive interactions; solutions of star-polymers
whose pair potential presents both an attractive well and an ultrasoft
repulsion at shorter distance. Our results show that the ability to tune the
effective interactions between colloidal particles allows one to generate a
variety of crossovers to the asymptotic critical behavior, which are not
observed in atomic fluids.Comment: 4 pages, 3 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
Integral equations for simple fluids in a general reference functional approach
The integral equations for the correlation functions of an inhomogeneous
fluid mixture are derived using a functional Taylor expansion of the free
energy around an inhomogeneous equilibrium distribution. The system of
equations is closed by the introduction of a reference functional for the
correlations beyond second order in the density difference from the equilibrium
distribution. Explicit expressions are obtained for energies required to insert
particles of the fluid mixture into the inhomogeneous system. The approach is
illustrated by the determination of the equation of state of a simple,
truncated Lennard--Jones fluid and the analysis of the behavior of this fluid
near a hard wall. The wall--fluid integral equation exhibits complete drying
and the corresponding coexisting densities are in good agreement with those
obtained from the standard (Maxwell) construction applied to the bulk fluid.
Self--consistency of the approach is examined by analyzing the
virial/compressibility routes to the equation of state and the Gibbs--Duhem
relation for the bulk fluid, and the contact density sum rule and the Gibbs
adsorption equation for the hard wall problem. For the bulk fluid, we find good
self--consistency for stable states outside the critical region. For the hard
wall problem, the Gibbs adsorption equation is fulfilled very well near phase
coexistence where the adsorption is large.For the contact density sum rule, we
find some deviationsnear coexistence due to a slight disagreement between the
coexisting density for the gas phase obtained from the Maxwell construction and
from complete drying at the hard wall.Comment: 29 page
Continuous demixing at liquid-vapor coexistence in a symmetrical binary fluid mixture
We report a Monte Carlo finite-size scaling study of the demixing transition
of a symmetrical Lennard-Jones binary fluid mixture. For equal concentration of
species, and for a choice of the unlike-to-like interaction ratio delta=0.7,
this transition is found to be continuous at liquid-vapor coexistence. The
associated critical end point exhibits Ising-like universality. These findings
confirm those of earlier smaller scale simulation studies of the same model,
but contradict the findings of recent integral equation and hierarchical
reference theory investigations.Comment: 7 pages, 6 figure
Liquid-vapour transition in screened Coulomb binary mixtures
The smooth cut-off hierarchical reference theory (HRT) is applied to a simple model of charged colloid mixture: an equimolar binary fluid of hard-core particles with a Yukawa potential which is repulsive between particles of the same species, and attractive between particles of different species. The critical behaviour of this Yukawa restricted primitive model (YRPM) is determined, and shown to belong to the Ising universality class for every value of the inverse Yukawa screening length z. This remains true even in the limit z -> 0 of unscreened Coulomb potential, when the YRPM reduces to the restrictive primitive model (RPM) of ionic fluids, thereby providing a microscopic justification to the occurrence of Ising-like criticality in the RPM. A simple closure for the pair correlations based on the generalized mean spherical approximation (GMSA) is adopted. Within such an approximation scheme, the fluid-fluid phase diagram and critical point are obtained for two representative values of the inverse screening length: z = 2 and z = 0.1
The asymptotic critical regime in binary mixtures: Can it be experimentally observed?
The lack of direct experimental evidence of the detection of the asymptotic critical behaviour in binary mixtures has led to the conjecture that the extent of the critical regime is exceedingly small in these systems. We address this problem from the theoretical side and find that: (i) the strong crossovers which affect the critical phenomena in mixtures are due to the competition between two different renormalization group fixed points; (ii) the crossover temperature is governed by a characteristic parameter which depends on the range of interactions as well as on purely thermodynamic quantities; and (iii) the extent of the asymptotic region is not necessarily small: specific systems and regimes allowing for the experimental observation of the true critical exponents are identified