216 research outputs found
Self Consistent Molecular Field Theory for Packing in Classical Liquids
Building on a quasi-chemical formulation of solution theory, this paper
proposes a self consistent molecular field theory for packing problems in
classical liquids, and tests the theoretical predictions for the excess
chemical potential of the hard sphere fluid. Results are given for the self
consistent molecular fields obtained, and for the probabilities of occupancy of
a molecular observation volume. For this system, the excess chemical potential
predicted is as accurate as the most accurate prior theories, particularly the
scaled particle (Percus-Yevick compressibility) theory. It is argued that the
present approach is particularly simple, and should provide a basis for a
molecular-scale description of more complex solutions.Comment: 6 pages and 5 figure
Equilibrium phase behavior of polydisperse hard spheres
We calculate the phase behavior of hard spheres with size polydispersity,
using accurate free energy expressions for the fluid and solid phases. Cloud
and shadow curves, which determine the onset of phase coexistence, are found
exactly by the moment free energy method, but we also compute the complete
phase diagram, taking full account of fractionation effects. In contrast to
earlier, simplified treatments we find no point of equal concentration between
fluid and solid or re-entrant melting at higher densities. Rather, the fluid
cloud curve continues to the largest polydispersity that we study (14%); from
the equilibrium phase behavior a terminal polydispersity can thus only be
defined for the solid, where we find it to be around 7%. At sufficiently large
polydispersity, fractionation into several solid phases can occur, consistent
with previous approximate calculations; we find in addition that coexistence of
several solids with a fluid phase is also possible
Segregation by thermal diffusion of an intruder in a moderately dense granular fluid
A solution of the inelastic Enskog equation that goes beyond the weak
dissipation limit and applies for moderate densities is used to determine the
thermal diffusion factor of an intruder immersed in a dense granular gas under
gravity. This factor provides a segregation criterion that shows the transition
between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by
varying the parameters of the system (masses, sizes, density and coefficients
of restitution). The form of the phase-diagrams for the BNE/RBNE transition
depends sensitively on the value of gravity relative to the thermal gradient,
so that it is possible to switch between both states for given values of the
parameters of the system. Two specific limits are considered with detail: (i)
absence of gravity, and (ii) homogeneous temperature. In the latter case, after
some approximations, our results are consistent with previous theoretical
results derived from the Enskog equation. Our results also indicate that the
influence of dissipation on thermal diffusion is more important in the absence
of gravity than in the opposite limit. The present analysis extends previous
theoretical results derived in the dilute limit case [V. Garz\'o, Europhys.
Lett. {\bf 75}, 521 (2006)] and is consistent with the findings of some recent
experimental results.Comment: 10 figure
Influence of hydrodynamics on many-particle diffusion in 2D colloidal suspensions
We study many-particle diffusion in 2D colloidal suspensions with full
hydrodynamic interactions through a novel mesoscopic simulation technique. We
focus on the behaviour of the effective scaled tracer and collective diffusion
coefficients and , where is the
single-particle diffusion coefficient, as a function of the density of the
colloids . At low Schmidt numbers , we find that
hydrodynamics has essentially no effect on the behaviour of . At
larger , is enhanced at all densities, although the
differences compared to the case without hydrodynamics are minor. The
collective diffusion coefficient, on the other hand, is much more strongly
coupled to hydrodynamical conservation laws and is distinctly different from
the purely dissipative case
Simple geometrical interpretation of the linear character for the Zeno-line and the rectilinear diameter
The unified geometrical interpretation of the linear character of the
Zeno-line (unit compressibility line Z=1) and the rectilinear diameter is
proposed. We show that recent findings about the properties of the Zeno-line
and striking correlation with the rectilinear diameter line as well as other
empirical relations can be naturally considered as the consequences of the
projective isomorphism between the real molecular fluids and the lattice gas
(Ising) model.Comment: 7 pages, 2 figure
Predicting phase equilibria in polydisperse systems
Many materials containing colloids or polymers are polydisperse: They
comprise particles with properties (such as particle diameter, charge, or
polymer chain length) that depend continuously on one or several parameters.
This review focusses on the theoretical prediction of phase equilibria in
polydisperse systems; the presence of an effectively infinite number of
distinguishable particle species makes this a highly nontrivial task. I first
describe qualitatively some of the novel features of polydisperse phase
behaviour, and outline a theoretical framework within which they can be
explored. Current techniques for predicting polydisperse phase equilibria are
then reviewed. I also discuss applications to some simple model systems
including homopolymers and random copolymers, spherical colloids and
colloid-polymer mixtures, and liquid crystals formed from rod- and plate-like
colloidal particles; the results surveyed give an idea of the rich
phenomenology of polydisperse phase behaviour. Extensions to the study of
polydispersity effects on interfacial behaviour and phase separation kinetics
are outlined briefly.Comment: 48 pages, invited topical review for Journal of Physics: Condensed
Matter; uses Institute of Physics style file iopart.cls (included
Diffusion of impurities in a granular gas
Diffusion of impurities in a granular gas undergoing homogeneous cooling
state is studied. The results are obtained by solving the Boltzmann--Lorentz
equation by means of the Chapman--Enskog method. In the first order in the
density gradient of impurities, the diffusion coefficient is determined as
the solution of a linear integral equation which is approximately solved by
making an expansion in Sonine polynomials. In this paper, we evaluate up to
the second order in the Sonine expansion and get explicit expressions for
in terms of the restitution coefficients for the impurity--gas and gas--gas
collisions as well as the ratios of mass and particle sizes. To check the
reliability of the Sonine polynomial solution, analytical results are compared
with those obtained from numerical solutions of the Boltzmann equation by means
of the direct simulation Monte Carlo (DSMC) method. In the simulations, the
diffusion coefficient is measured via the mean square displacement of
impurities. The comparison between theory and simulation shows in general an
excellent agreement, except for the cases in which the gas particles are much
heavier and/or much larger than impurities. In theses cases, the second Sonine
approximation to improves significantly the qualitative predictions made
from the first Sonine approximation. A discussion on the convergence of the
Sonine polynomial expansion is also carried out.Comment: 9 figures. to appear in Phys. Rev.
Superdipole Liquid Scenario for the Dielectric Primary Relaxation in Supercooled Polar liquids
We propose a dynamic structure of coupled dynamic molecular strings for
supercooled small polar molecule liquids and accordingly we obtain the
Hamiltonian of the rotational degrees of freedom of the system. From the
Hamiltonian, the strongly correlated supercooled polar liquid state is
renormalized to a normal superdipole (SD) liquid state. This scenario describes
the following main features of the primary or a-relaxation dynamics in
supercooled polar liquids: (1) the average relaxation time evolves from a high
temperature Arrhenius to a low temperature non-Arrhenius or super-Arrhenius
behavior; (2) the relaxation function crosses over from the high temperature
exponential to low temperature non-exponential form; and (3) the temperature
dependence of the relaxation strength shows non-Curie features. According to
the present model, the crossover phenomena of the first two characteristics
arise from the transition between the superdipole gas and the superdipole
liquid. The model predictions are quantitatively compared with the experimental
results of glycerol, a typical glass-former.Comment: 40 pages, 3 figure
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