76,766 research outputs found
Low-temperature and high-temperature approximations for penetrable-sphere fluids. Comparison with Monte Carlo simulations and integral equation theories
The two-body interaction in dilute solutions of polymer chains in good
solvents can be modeled by means of effective bounded potentials, the simplest
of which being that of penetrable spheres (PSs). In this paper we construct two
simple analytical theories for the structural properties of PS fluids: a
low-temperature (LT) approximation, that can be seen as an extension to PSs of
the well-known solution of the Percus-Yevick (PY) equation for hard spheres,
and a high-temperature (HT) approximation based on the exact asymptotic
behavior in the limit of infinite temperature. Monte Carlo simulations for a
wide range of temperatures and densities are performed to assess the validity
of both theories. It is found that, despite their simplicity, the HT and LT
approximations exhibit a fair agreement with the simulation data within their
respective domains of applicability, so that they complement each other. A
comparison with numerical solutions of the PY and the hypernetted-chain
approximations is also carried out, the latter showing a very good performance,
except inside the core at low temperatures.Comment: 14 pages, 8 figures; v2: some figures redone; small change
Test of a universality ansatz for the contact values of the radial distribution functions of hard-sphere mixtures near a hard wall
Recent Monte Carlo simulation results for the contact values of polydisperse
hard-sphere mixtures at a hard planar wall are considered in the light of a
universality assumption made in approximate theoretical approaches. It is found
that the data seem to fulfill the universality ansatz reasonably well, thus
opening up the possibility of inferring properties of complicated systems from
the study of simpler onesComment: 9 pages, 2 figures; v2: minor changes; to be published in the special
issue of Molecular Physics dedicated to the Seventh Liblice Conference on the
Statistical Mechanics of Liquids (Lednice, Czech Republic, June 11-16, 2006
Communication: Inferring the equation of state of a metastable hard-sphere fluid from the equation of state of a hard-sphere mixture at high densities
A possible approximate route to obtain the equation of state of the
monodisperse hard-sphere system in the metastable fluid region from the
knowledge of the equation of state of a hard-sphere mixture at high densities
is discussed. The proposal is illustrated by using recent Monte Carlo
simulation data for the pressure of a binary mixture. It is further shown to
exhibit high internal consistency.Comment: 4 pages, 2 figures; v2: Simulation data for one-component hard
spheres included in Fig.
How `sticky' are short-range square-well fluids?
The aim of this work is to investigate to what extent the structural
properties of a short-range square-well (SW) fluid of range at a
given packing fraction and reduced temperature can be represented by those of a
sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective
stickiness parameter . Such an equivalence cannot hold for the radial
distribution function since this function has a delta singularity at contact in
the SHS case, while it has a jump discontinuity at in the SW case.
Therefore, the equivalence is explored with the cavity function .
Optimization of the agreement between y_{\sw} and y_{\shs} to first order
in density suggests the choice for . We have performed Monte Carlo (MC)
simulations of the SW fluid for , 1.02, and 1.01 at several
densities and temperatures such that , 0.2, and 0.5. The
resulting cavity functions have been compared with MC data of SHS fluids
obtained by Miller and Frenkel [J. Phys: Cond. Matter 16, S4901 (2004)].
Although, at given values of and , some local discrepancies
between y_{\sw} and y_{\shs} exist (especially for ), the SW
data converge smoothly toward the SHS values as decreases. The
approximate mapping y_{\sw}\to y_{\shs} is exploited to estimate the internal
energy and structure factor of the SW fluid from those of the SHS fluid. Taking
for y_{\shs} the solution of the Percus--Yevick equation as well as the
rational-function approximation, the radial distribution function of the
SW fluid is theoretically estimated and a good agreement with our MC
simulations is found. Finally, a similar study is carried out for short-range
SW fluid mixtures.Comment: 14 pages, including 3 tables and 14 figures; v2: typo in Eq. (5.1)
corrected, Fig. 14 redone, to be published in JC
Properties of the reaction front in a reaction-subdiffusion process
We study the reaction front for the process in which the reagents
move subdiffusively. We propose a fractional reaction-subdiffusion equation in
which both the motion and the reaction terms are affected by the subdiffusive
character of the process. Scaling solutions to these equations are presented
and compared with those of a direct numerical integration of the equations. We
find that for reactants whose mean square displacement varies sublinearly with
time as , the scaling behaviors of the reaction front can
be recovered from those of the corresponding diffusive problem with the
substitution Comment: Errata corrected, one reference update
Contact values of the particle-particle and wall-particle correlation functions in a hard-sphere polydisperse fluid
The contact values of the radial distribution functions
of a fluid of (additive) hard spheres with a given size distribution
are considered. A ``universality'' assumption is introduced,
according to which, at a given packing fraction ,
, where is a common function
independent of the number of components (either finite or infinite) and
is a
dimensionless parameter, being the -th moment of the diameter
distribution. A cubic form proposal for the -dependence of is made and
known exact consistency conditions for the point particle and equal size
limits, as well as between two different routes to compute the pressure of the
system in the presence of a hard wall, are used to express in terms of
the radial distribution at contact of the one-component system. For
polydisperse systems we compare the contact values of the wall-particle
correlation function and the compressibility factor with those obtained from
recent Monte Carlo simulations.Comment: 9 pages, 7 figure
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