50 research outputs found
A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model
The one-dimensional penetrable-square-well fluid is studied using both
analytical tools and specialized Monte Carlo simulations. The model consists of
a penetrable core characterized by a finite repulsive energy combined with a
short-range attractive well. This is a many-body one-dimensional problem,
lacking an exact analytical solution, for which the usual van Hove theorem on
the absence of phase transition does not apply. We determine a
high-penetrability approximation complementing a similar low-penetrability
approximation presented in previous work. This is shown to be equivalent to the
usual Debye-H\"{u}ckel theory for simple charged fluids for which the virial
and energy routes are identical. The internal thermodynamic consistency with
the compressibility route and the validity of the approximation in describing
the radial distribution function is assessed by a comparison against numerical
simulations. The Fisher-Widom line separating the oscillatory and monotonic
large-distance behavior of the radial distribution function is computed within
the high-penetrability approximation and compared with the opposite regime,
thus providing a strong indication of the location of the line in all possible
regimes. The high-penetrability approximation predicts the existence of a
critical point and a spinodal line, but this occurs outside the applicability
domain of the theory. We investigate the possibility of a fluid-fluid
transition by Gibbs ensemble Monte Carlo techniques, not finding any evidence
of such a transition. Additional analytical arguments are given to support this
claim. Finally, we find a clustering transition when Ruelle's stability
criterion is not fulfilled. The consequences of these findings on the
three-dimensional phase diagrams are also discussed.Comment: 17 pages, 12 figures; to be published in JC
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
Radial distribution function of penetrable sphere fluids to second order in density
The simplest bounded potential is that of penetrable spheres, which takes a
positive finite value if the two spheres are overlapped, being 0
otherwise. In this paper we derive the cavity function to second order in
density and the fourth virial coefficient as functions of (where is the Boltzmann constant and is the
temperature) for penetrable sphere fluids. The expressions are exact, except
for the function represented by an elementary diagram inside the core, which is
approximated by a polynomial form in excellent agreement with accurate results
obtained by Monte Carlo integration. Comparison with the hypernetted-chain
(HNC) and Percus-Yevick (PY) theories shows that the latter is better than the
former for only. However, even at zero temperature (hard sphere
limit), the PY solution is not accurate inside the overlapping region, where no
practical cancelation of the neglected diagrams takes place. The exact fourth
virial coefficient is positive for , reaches a minimum
negative value at , and then goes to zero from below as
for high temperatures. These features are captured qualitatively,
but not quantitatively, by the HNC and PY predictions. In addition, in both
theories the compressibility route is the best one for , while
the virial route is preferable if .Comment: 10 pages, 2 figures; v2: minor changes; to be published in PR
Phase diagram of the penetrable square well-model
We study a system formed by soft colloidal spheres attracting each other via
a square-well potential, using extensive Monte Carlo simulations of various
nature. The softness is implemented through a reduction of the infinite part of
the repulsive potential to a finite one. For sufficiently low values of the
penetrability parameter we find the system to be Ruelle stable with square-well
like behavior. For high values of the penetrability the system is
thermodynamically unstable and collapses into an isolated blob formed by a few
clusters each containing many overlapping particles. For intermediate values of
the penetrability the system has a rich phase diagram with a partial lack of
thermodynamic consistency.Comment: 6 pages and 5 figure
Structure of penetrable-rod fluids: Exact properties and comparison between Monte Carlo simulations and two analytic theories
Bounded potentials are good models to represent the effective two-body
interaction in some colloidal systems, such as dilute solutions of polymer
chains in good solvents. The simplest bounded potential is that of penetrable
spheres, which takes a positive finite value if the two spheres are overlapped,
being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model
is far from trivial, since interactions are not restricted to nearest neighbors
and so its exact solution is not known. In this paper we first derive the exact
correlation functions of penetrable-rod fluids to second order in density at
any temperature, as well as in the high-temperature and zero-temperature limits
at any density. Next, two simple analytic theories are constructed: a
high-temperature approximation based on the exact asymptotic behavior in the
limit and a low-temperature approximation inspired by the exact
result in the opposite limit . Finally, we perform Monte Carlo
simulations for a wide range of temperatures and densities to assess the
validity of both theories. It is found that they complement each other quite
well, exhibiting a good agreement with the simulation data within their
respective domains of applicability and becoming practically equivalent on the
borderline of those domains. A perspective on the extension of both approaches
to the more realistic three-dimensional case is provided.Comment: 19 pages, 11 figures, 4 tables: v2: minor changes; published final
versio
Density functional approach for inhomogeneous star polymers
We propose microscopic density functional theory for inhomogeneous star
polymers. Our approach is based on fundamental measure theory for hard spheres,
and on Wertheim's first- and second-order perturbation theory for the
interparticle connectivity. For simplicity we consider a model in which all the
arms are of the same length, but our approach can be easily extended to the
case of stars with arms of arbitrary lengths.Comment: 4 pages, 3 figures, submitte
Modelling the evaporation of nanoparticle suspensions from heterogeneous surfaces
We present a Monte Carlo (MC) grid-based model for the drying of drops of a
nanoparticle suspension upon a heterogeneous surface. The model consists of a
generalised lattice-gas in which the interaction parameters in the Hamiltonian
can be varied to model different properties of the materials involved. We show
how to choose correctly the interactions, to minimise the effects of the
underlying grid so that hemispherical droplets form. We also include the
effects of surface roughness to examine the effects of contact-line pinning on
the dynamics. When there is a `lid' above the system, which prevents
evaporation, equilibrium drops form on the surface, which we use to determine
the contact angle and how it varies as the parameters of the model are changed.
This enables us to relate the interaction parameters to the materials used in
applications. The model has also been applied to drying on heterogeneous
surfaces, in particular to the case where the suspension is deposited on a
surface consisting of a pair of hydrophilic conducting metal surfaces that are
either side of a band of hydrophobic insulating polymer. This situation occurs
when using inkjet printing to manufacture electrical connections between the
metallic parts of the surface. The process is not always without problems,
since the liquid can dewet from the hydrophobic part of the surface, breaking
the bridge before the drying process is complete. The MC model reproduces the
observed dewetting, allowing the parameters to be varied so that the conditions
for the best connection can be established. We show that if the hydrophobic
portion of the surface is located at a step below the height of the
neighbouring metal, the chance of dewetting of the liquid during the drying
process is significantly reduced.Comment: 14 pages, 14 figure
Breaking Cassie's Law for condensation in a nanopatterned slit
We study the phase transitions of a fluid confined in a capillary slit made from two adjacent walls, each of which are a periodic composite of stripes of two different materials. For wide slits the capillary condensation occurs at a pressure which is described accurately by a combination of the Kelvin equation and the Cassie law for an averaged contact angle. However, for narrow slits the condensation occurs in two steps involving an intermediate bridging phase, with the corresponding pressures described by two new Kelvin equations. These are characterised by different contact angles due to interfacial pinning, with one larger and one smaller than the Cassie angle. We determine the triple point and predict two types of dispersion force induced Derjaguin-like corrections due to mesoscopic volume reduction and the singular free-energy contribution from nanodroplets and bubbles. We test these predictions using a fully microscopic density functional model which confirms their validity even for molecularly narrow slits. Analogous mesoscopic corrections are also predicted for two-dimensional systems arising from thermally induced interfacial wandering
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