712 research outputs found
Rescaled density expansions and demixing in hard-sphere binary mixtures
The demixing transition of a binary fluid mixture of additive hard spheres is
analyzed for different size asymmetries by starting from the exact low-density
expansion of the pressure. Already within the second virial approximation the
fluid separates into two phases of different composition with a lower consolute
critical point. By successively incorporating the third, fourth, and fifth
virial coefficients, the critical consolute point moves to higher values of the
pressure and to lower values of the partial number fraction of the large
spheres. When the exact low-density expansion of the pressure is rescaled to
higher densities as in the Percus-Yevick theory, by adding more exact virial
coefficients a different qualitative movement of the critical consolute point
in the phase diagram is found. It is argued that the Percus-Yevick factor
appearing in many empirical equations of state for the mixture has a deep
influence on the location of the critical consolute point, so that the
resulting phase diagram for a prescribed equation has to be taken with caution.Comment: 5 pages, 1 figure; to be published in The Journal of Chemical Physic
Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations
Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution
to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is
explicitly found. This allows the derivation of the equation of state for the
fluid taking both the virial and the compressibility routes. An analysis of the
virial coefficients and the determination of the radius of convergence of the
virial series are carried out. Molecular dynamics simulations of the same
system are also performed and a comparison between the simulation results for
the compressibility factor and theoretical expressions for the same quantity is
presented.Comment: 12 pages, 4 figures; v3: Equation (A.19) corrected (see
http://dx.doi.org/10.1063/1.2390712
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
On the radial distribution function of a hard-sphere fluid
Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem.
Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B.
Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of
analytical forms of the radial distribution function of a fluid of hard spheres
are compared. While they share similar starting philosophy, the first one
involves the determination of eleven parameters while the second is a simple
extension of the solution of the Percus-Yevick equation. It is found that the
{second} approach has a better global accuracy and the further asset of
counting already with a successful generalization to mixtures of hard spheres
and other related systems.Comment: 3 pages, 1 figure; v2: slightly shortened, figure changed, to be
published in JC
Nagel scaling and relaxation in the kinetic Ising model on a n-isotopic chain
The kinetic Ising model on a n-isotopic chain is considered in the framework
of Glauber dynamics. The chain is composed of N segments with n sites, each one
occupied by a different isotope. Due to the isotopic mass difference, the n
spins in each segment have different relaxation times in the absence of the
interactions, and consequently the dynamics of the system is governed by
multiple relaxation mechanisms. The solution is obtained in closed form for
arbitrary n, by reducing the problem to a set of n coupled equations, and it is
shown rigorously that the critical exponent z is equal to 2. Explicit results
are obtained numerically for any temperature and it is also shown that the
dynamic susceptibility satisfies the new scaling (Nagel scaling) proposed for
glass-forming liquids. This is in agreement with our recent results (L. L.
Goncalves, M. Lopez de Haro, J. Taguena-Martinez and R. B. Stinchcombe, Phys.
Rev. Lett. 84, 1507 (2000)), which relate this new scaling function to multiple
relaxation processes.Comment: 4 pages, 2 figures, presented at Ising Centennial Colloquium, to be
published in the Proceedings (Brazilian Journal of Physics.
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