709 research outputs found

### Simulation studies of fluid critical behaviour

We review and discuss recent advances in the simulation of bulk critical
phenomena in model fluids. In particular we emphasise the extensions to
finite-size scaling theory needed to cope with the lack of symmetry between
coexisting fluid phases. The consequences of this asymmetry for simulation
measurements of quantities such as the particle density and the heat capacity
are pointed out and the relationship to experiment is discussed. A general
simulation strategy based on the finite-size scaling theory is described and
its utility illustrated via Monte-Carlo studies of the Lennard-Jones fluid and
a two-dimensional spin fluid model. Recent applications to critical polymer
blends and solutions are also briefly reviewed. Finally we consider the outlook
for future simulation work in the field.Comment: 35 pages Revtex, 11 eps figures. Review article to appear in J.
Phys.: Condens. Matte

### A non-equilibrium Monte Carlo approach to potential refinement in inverse problems

The inverse problem for a disordered system involves determining the
interparticle interaction parameters consistent with a given set of
experimental data. Recently, Rutledge has shown (Phys. Rev. E63, 021111 (2001))
that such problems can be generally expressed in terms of a grand canonical
ensemble of polydisperse particles. Within this framework, one identifies a
polydisperse attribute (`pseudo-species') $\sigma$ corresponding to some
appropriate generalized coordinate of the system to hand. Associated with this
attribute is a composition distribution $\bar\rho(\sigma)$ measuring the number
of particles of each species. Its form is controlled by a conjugate chemical
potential distribution $\mu(\sigma)$ which plays the role of the requisite
interparticle interaction potential. Simulation approaches to the inverse
problem involve determining the form of $\mu(\sigma)$ for which
$\bar\rho(\sigma)$ matches the available experimental data. The difficulty in
doing so is that $\mu(\sigma)$ is (in general) an unknown {\em functional} of
$\bar\rho(\sigma)$ and must therefore be found by iteration. At high particle
densities and for high degrees of polydispersity, strong cross coupling between
$\mu(\sigma)$ and $\bar\rho(\sigma)$ renders this process computationally
problematic and laborious. Here we describe an efficient and robust {\em
non-equilibrium} simulation scheme for finding the equilibrium form of
$\mu[\bar\rho(\sigma)]$. The utility of the method is demonstrated by
calculating the chemical potential distribution conjugate to a specific
log-normal distribution of particle sizes in a polydisperse fluid.Comment: 6 pages, 3 figure

### Errors in Monte Carlo simulations using shift register random number generators

We report large systematic errors in Monte Carlo simulations of the
tricritical Blume-Capel model using single spin Metropolis updating. The error,
manifest as a $20\%$ asymmetry in the magnetisation distribution, is traced to
the interplay between strong triplet correlations in the shift register random
number generator and the large tricritical clusters. The effect of these
correlations is visible only when the system volume is a multiple of the random
number generator lag parameter. No such effects are observed in related models.Comment: 7 pages Revtex, 4 ps figures (uuencoded). Paper also available from:
http://moses.physik.uni-mainz.de/~wilding/home_wilding.htm

### Concentration and energy fluctuations in a critical polymer mixture

A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with
the bond fluctuation model to investigate the critical properties of an
asymmetric binary (AB) polymer mixture. By applying the equal peak-weight
criterion to the concentration distribution, the coexistence curve separating
the A-rich and B-rich phases is identified as a function of temperature and
chemical potential. To locate the critical point of the model, the cumulant
intersection method is used. The accuracy of this approach for determining the
critical parameters of fluids is assessed. Attention is then focused on the
joint distribution function of the critical concentration and energy, which is
analysed using a mixed-field finite-size-scaling theory that takes due account
of the lack of symmetry between the coexisting phases. The essential Ising
character of the binary polymer critical point is confirmed by mapping the
critical scaling operator distributions onto independently known forms
appropriate to the 3D Ising universality class. In the process, estimates are
obtained for the field mixing parameters of the model which are compared both
with those yielded by a previous method, and with the predictions of a mean
field calculation.Comment: 17 pages Latex, 9 figures appended as uuencoded .gz tar fil

### A liquid state theory that remains successful in the critical region

A thermodynamically self-consistent Ornstein-Zernike approximation (SCOZA) is
applied to a fluid of spherical particles with a pair potential given by a
hard-core repulsion and a Yukawa attractive tail $w(r)=-\exp [-z(r-1)]/r$. This
potential allows one to take advantage of the known analytical properties of
the solution to the Ornstein-Zernike equation for the case in which the direct
correlation function outside the repulsive core is given by a linear
combination of two Yukawa tails and the radial distribution function $g(r)$
satisfies the exact core condition $g(r)=0$ for $r<1$. The predictions for the
thermodynamics, the critical point, and the coexistence curve are compared here
to other theories and to simulation results. In order to unambiguously assess
the ability of the SCOZA to locate the critical point and the phase boundary of
the system, a new set of simulations has also been performed. The method
adopted combines Monte Carlo and finite-size scaling techniques and is
especially adapted to deal with critical fluctuations and phase separation. It
is found that the version of the SCOZA considered here provides very good
overall thermodynamics and a remarkably accurate critical point and coexistence
curve. For the interaction range considered here, given by $z=1.8$, the
critical density and temperature predicted by the theory agree with the
simulation results to about 0.6%.Comment: Prepared for the John Barker festschrift issue of Molecular Physics.
22 pages Latex, 6 ps figure

### Liquid-gas phase behaviour of an argon-like fluid modelled by the hard-core two-Yukawa potential

We study a model for an argon-like fluid parameterised in terms of a
hard-core repulsion and a two-Yukawa potential. The liquid-gas phase behaviour
of the model is obtained from the thermodynamically self-consistent
Ornstein-Zernike approximation (SCOZA) of Hoye and Stell, the solution of which
lends itself particularly well to a pair potential of this form. The
predictions for the critical point and the coexistence curve are compared to
new high resolution simulation data and to other liquid-state theories,
including the hierarchical reference theory (HRT) of Parola and Reatto. Both
SCOZA and HRT deliver results that are considerably more accurate than standard
integral-equation approaches. Among the versions of SCOZA considered, the one
yielding the best agreement with simulation successfully predicts the critical
point parameters to within 1%.Comment: 10 pages 6 figure

### Effects of Confinement on Critical Adsorption: Absence of Critical Depletion for Fluids in Slit Pores

The adsorption of a near-critical fluid confined in a slit pore is
investigated by means of density functional theory and by Monte Carlo
simulation for a Lennard-Jones fluid. Our work was stimulated by recent
experiments for SF_6 adsorbed in a mesoporous glass which showed the striking
phenomenon of critical depletion, i.e. the adsorption excess "Gamma" first
increases but then decreases very rapidly to negative values as the bulk
critical temperature T_c is approached from above along near-critical
isochores. By contrast, our density functional and simulation results, for a
range of strongly attractive wall-fluid potentials, show Gamma monotonically
increasing and eventually saturating as the temperature is lowered towards T_c
along both the critical (rho=rho_c) and sub-critical isochores (rho<\rho_c).
Such behaviour results from the increasingly slow decay of the density profile
away from the walls, into the middle of the slit, as T->T_c. For rho < rho_c we
find that in the fluid the effective bulk field, which is negative and which
favours desorption, is insufficient to dominate the effects of the surface
fields which favour adsorption. We compare this situation with earlier results
for the lattice gas model with a constant (negative) bulk field where critical
depletion was found. Qualitatively different behaviour of the density profiles
and adsorption is found in simulations for intermediate and weakly attractive
wall-fluid potentials but in no case do we observe the critical depletion found
in experiments. We conclude that the latter cannot be accounted for by a single
pore model.Comment: 21 pages Revtex. Submitted to Phys. Rev.

- …