12 research outputs found
On extrapolation of virial coefficients of hard spheres
Several methods of extrapolating the virial coefficients, including those
proposed in this work, are discussed. The methods are demonstrated on
predicting higher virial coefficients of one-component hard spheres. Estimated
values of the eleventh to fifteenth virial coefficients are suggested. It has
been speculated that the virial coefficients, B_n, beyond B_{14} may decrease
with increasing n, and may reach negative values at large n. The extrapolation
techniques may be utilized in other fields of science where the art of
extrapolation plays a role.Comment: 8 pages, 1 figur
Structure of ternary additive hard-sphere fluid mixtures
Monte Carlo simulations on the structural properties of ternary fluid
mixtures of additive hard spheres are reported. The results are compared with
those obtained from a recent analytical approximation [S. B. Yuste, A. Santos,
and M. Lopez de Haro, J. Chem. Phys. 108, 3683 (1998)] to the radial
distribution functions of hard-sphere mixtures and with the results derived
from the solution of the Ornstein-Zernike integral equation with both the
Martynov-Sarkisov and the Percus-Yevick closures. Very good agreement between
the results of the first two approaches and simulation is observed, with a
noticeable improvement over the Percus-Yevick predictions especially near
contact.Comment: 11 pages, including 8 figures; A minor change; accepted for
publication in PR
Self-assembly mechanism in colloids: perspectives from Statistical Physics
Motivated by recent experimental findings in chemical synthesis of colloidal
particles, we draw an analogy between self-assembly processes occurring in
biological systems (e.g. protein folding) and a new exciting possibility in the
field of material science. We consider a self-assembly process whose elementary
building blocks are decorated patchy colloids of various types, that
spontaneously drive the system toward a unique and predetermined targeted
macroscopic structure.
To this aim, we discuss a simple theoretical model -- the Kern-Frenkel model
-- describing a fluid of colloidal spherical particles with a pre-defined
number and distribution of solvophobic and solvophilic regions on their
surface. The solvophobic and solvophilic regions are described via a
short-range square-well and a hard-sphere potentials, respectively.
Integral equation and perturbation theories are presented to discuss
structural and thermodynamical properties, with particular emphasis on the
computation of the fluid-fluid (or gas-liquid) transition in the
temperature-density plane.
The model allows the description of both one and two attractive caps, as a
function of the fraction of covered attractive surface, thus interpolating
between a square-well and a hard-sphere fluid, upon changing the coverage.
By comparison with Monte Carlo simulations, we assess the pros and the cons
of both integral equation and perturbation theories in the present context of
patchy colloids, where the computational effort for numerical simulations is
rather demanding.Comment: 14 pages, 7 figures, Special issue for the SigmaPhi2011 conferenc
Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
We evaluate the virial coefficients B_k for k<=10 for hard spheres in
dimensions D=2,...,8. Virial coefficients with k even are found to be negative
when D>=5. This provides strong evidence that the leading singularity for the
virial series lies away from the positive real axis when D>=5. Further analysis
provides evidence that negative virial coefficients will be seen for some k>10
for D=4, and there is a distinct possibility that negative virial coefficients
will also eventually occur for D=3.Comment: 33 pages, 12 figure
Integral equation study of additive two-component mixtures of hard spheres
The Ornstein-Zernike equation for additive hard sphere mixtures is solved numerically by using the Martynov- Sarkisov (MS) closure and a recent modification of the Verlet (MV) closure. A comparison of the predictions for the equation of state and, to a lesser extent, the contact values of the radial distribution function, shows both theories to give similar, reasonably accurate, results in most situations. However, an examination of the pair cavity functions for zero separation shows the two closures to give quite different results, and the MV closure results are believed to be better. More attention should be given to the cavity function at zero separation. In addition, the MV closure satisfies known asymptotic relations for a small concentration of exceedingly large spheres, whereas the MS and Percus-Yevick closures do not satisfy these relations.link_to_subscribed_fulltex