56 research outputs found
Adsorption of hard spheres: structure and effective density according to the potential distribution theorem
We propose a new type of effective densities via the potential distribution
theorem. These densities are for the sake of enabling the mapping of the free
energy of a uniform fluid onto that of a nonuniform fluid. The potential
distribution theorem gives the work required to insert a test particle into the
bath molecules under the action of the external (wall) potential. This
insertion work W_ins can be obtained from Monte Carlo (MC) simulation (e.g.
from Widom's test particle technique) or from an analytical theory. The
pseudo-densities are constructed thusly so that when their values are
substituted into a uniform-fluid equation of state (e.g. the Carnahan-Starling
equation for the hard-sphere chemical potentials), the MC nonuniform insertion
work is reproduced. We characterize the pseudo-density behavior for the hard
spheres/hard wall system at moderate to high densities (from \rho^*= 0.5745 to
0.9135). We adopt the MC data of Groot et al. for this purpose. The
pseudo-densities show oscillatory behavior out of phase (opposite) to that of
the singlet densities. We also construct a new closure-based density functional
theory (the star-function based density functional theory) that can give
accurate description of the MC density profiles and insertion works. A viable
theory is established for several cases in hard sphere adsorption.Comment: 15 pages, 10 figure
Thermodynamic stability of fluid-fluid phase separation in binary athermal mixtures: The role of nonadditivity
We study the thermodynamic stability of fluid-fluid phase separation in
binary nonadditive mixtures of hard-spheres for moderate size ratios. We are
interested in elucidating the role played by small amounts of nonadditivity in
determining the stability of fluid-fluid phase separation with respect to the
fluid-solid phase transition. The demixing curves are built in the framework of
the modified-hypernetted chain and of the Rogers-Young integral equation
theories through the calculation of the Gibbs free energy. We also evaluate
fluid-fluid phase equilibria within a first-order thermodynamic perturbation
theory applied to an effective one-component potential obtained by integrating
out the degrees of freedom of the small spheres. A qualitative agreement
emerges between the two different approaches. We also address the determination
of the freezing line by applying the first-order thermodynamic perturbation
theory to the effective interaction between large spheres. Our results suggest
that for intermediate size ratios a modest amount of nonadditivity, smaller
than earlier thought, can be sufficient to drive the fluid-fluid critical point
into the thermodinamically stable region of the phase diagram. These findings
could be significant for rare-gas mixtures in extreme pressure and temperature
conditions, where nonadditivity is expected to be rather small.Comment: 17 pages, 7 figures, to appear in J. Phys. Chem.
Free energy determination of phase coexistence in model C60: A comprehensive Monte Carlo study
The free energy of the solid and fluid phases of the Girifalco C60 model are
determined through extensive Monte Carlo simulations. In this model the
molecules interact through a spherical pair potential, characterized by a
narrow and attractive well, adjacent to a harshly repulsive core. We have used
the Widom test particle method and a mapping from an Einstein crystal, in order
to estimate the absolute free energy in the fluid and solid phases,
respectively; we have then determined the free energy along several isotherms,
and the whole phase diagram, by means of standard thermodynamic integrations.
We highlight how the interplay between the liquid-vapor and the liquid-solid
coexistence conditions determines the existence of a narrow liquid pocket in
the phase diagram, whose stability is assessed and confirmed in agreement with
previous studies. In particular, the critical temperature follows closely an
extended corresponding-states rule recently outlined by Noro and Frenkel [J.
Chem. Phys. 113:2941 (2000)].
We discuss the emerging "energetic" properties of the system, which drive the
phase behavior in systems interacting through short-range forces [A. A. Louis,
Phil. Trans. R. Soc. A 359:939 (2001)], in order to explain the discrepancy
between the predictions of several structural indicators and the results of
full free energy calculations, to locate the fluid phase boundaries.
More generally, we aim to provide extended reference data for calculations of
the free energy of the C60 fullerite in the low temperature regime, as for the
determination of the phase diagram of higher order fullerenes and other
fullerene-related materials, whose description is based on the same model
adopted in this work.Comment: RevTeX, 11 pages, 9 figure
Equilibrium cluster phases and low-density arrested disordered states: The role of short-range attraction and long-range repulsion
We study a model in which particles interact with short-ranged attractive and
long-ranged repulsive interactions, in an attempt to model the equilibrium
cluster phase recently discovered in sterically stabilized colloidal systems in
the presence of depletion interactions. At low packing fraction particles form
stable equilibrium clusters which act as building blocks of a cluster fluid. We
study the possibility that cluster fluids generate a low-density disordered
arrested phase, a gel, via a glass transition driven by the repulsive
interaction. In this model the gel formation is formally described with the
same physics of the glass formation.Comment: RevTeX4, 4 pages, 4 eps figure
Theory and simulation of short-range models of globular protein solutions
We report theoretical and simulation studies of phase coexistence in model
globular protein solutions, based on short-range, central, pair potential
representations of the interaction among macro-particles. After reviewing our
previous investigations of hard-core Yukawa and generalised Lennard-Jones
potentials, we report more recent results obtained within a DLVO-like
description of lysozyme solutions in water and added salt. We show that a
one-parameter fit of this model based on Static Light Scattering and
Self-Interaction Chromatography data in the dilute protein regime, yields
demixing and crystallization curves in good agreement with experimental
protein-rich/protein-poor and solubility envelopes. The dependence of cloud and
solubility points temperature of the model on the ionic strength is also
investigated. Our findings highlight the minimal assumptions on the properties
of the microscopic interaction sufficient for a satisfactory reproduction of
the phase diagram topology of globular protein solutions.Comment: 17 pages, 8 figures, Proc. of Conference "Structural Arrest
Transitions in Colloidal Systems with Short-Range Attractions", Messina
(ITALY) 17-20 December 200
Population inversion of a NAHS mixture adsorbed into a cylindrical pore
A cylindrical nanopore immersed in a non-additive hard sphere binary fluid is
studied by means of integral equation theories and Monte Carlo simulations. It
is found that at low and intermediate values of the bulk total number density
the more concentrated bulk species is preferentially absorbed by the pore, as
expected. However, further increments of the bulk number density lead to an
abrupt population inversion in the confined fluid and an entropy driven
prewetting transition at the outside wall of the pore. These phenomena are a
function of the pore size, the non-additivity parameter, the bulk number
density, and particles relative number fraction. We discuss our results in
relation to the phase separation in the bulk.Comment: 7 pages, 8 Figure
Effective pair potentials for spherical nanoparticles
An effective description for spherical nanoparticles in a fluid of point
particles is presented. The points inside the nanoparticles and the point
particles are assumed to interact via spherically symmetric additive pair
potentials, while the distribution of points inside the nanoparticles is taken
to be spherically symmetric and smooth. The resulting effective pair
interactions between a nanoparticle and a point particle, as well as between
two nanoparticles, are then given by spherically symmetric potentials. If
overlap between particles is allowed, the effective potential generally has
non-analytic points, but for each effective potential the expressions for
different overlapping cases can be written in terms of one analytic auxiliary
potential. Effective potentials for hollow nanoparticles (appropriate e.g. for
buckyballs) are also considered, and shown to be related to those for solid
nanoparticles. Finally, explicit expressions are given for the effective
potentials derived from basic pair potentials of power law and exponential
form, as well as from the commonly used London-Van der Waals, Morse,
Buckingham, and Lennard-Jones potential. The applicability of the latter is
demonstrated by comparison with an atomic description of nanoparticles with an
internal face centered cubic structure.Comment: 27 pages, 12 figures. Unified description of overlapping and
nonoverlapping particles added, as well as a comparison with an idealized
atomic descriptio
Simple Fluids with Complex Phase Behavior
We find that a system of particles interacting through a simple isotropic
potential with a softened core is able to exhibit a rich phase behavior
including: a liquid-liquid phase transition in the supercooled phase, as has
been suggested for water; a gas-liquid-liquid triple point; a freezing line
with anomalous reentrant behavior. The essential ingredient leading to these
features resides in that the potential investigated gives origin to two
effective core radii.Comment: 7 pages including 3 eps figures + 1 jpeg figur
Theoretical description of phase coexistence in model C60
We have investigated the phase diagram of the Girifalco model of C60
fullerene in the framework provided by the MHNC and the SCOZA liquid state
theories, and by a Perturbation Theory (PT), for the free energy of the solid
phase. We present an extended assessment of such theories as set against a
recent Monte Carlo study of the same model [D. Costa et al, J. Chem. Phys.
118:304 (2003)]. We have compared the theoretical predictions with the
corresponding simulation results for several thermodynamic properties. Then we
have determined the phase diagram of the model, by using either the SCOZA, or
the MHNC, or the PT predictions for one of the coexisting phases, and the
simulation data for the other phase, in order to separately ascertain the
accuracy of each theory. It turns out that the overall appearance of the phase
portrait is reproduced fairly well by all theories, with remarkable accuracy as
for the melting line and the solid-vapor equilibrium. The MHNC and SCOZA
results for the liquid-vapor coexistence, as well as for the corresponding
critical points, are quite accurate. All results are discussed in terms of the
basic assumptions underlying each theory. We have selected the MHNC for the
fluid and the first-order PT for the solid phase, as the most accurate tools to
investigate the phase behavior of the model in terms of purely theoretical
approaches. The overall results appear as a robust benchmark for further
theoretical investigations on higher order C(n>60) fullerenes, as well as on
other fullerene-related materials, whose description can be based on a
modelization similar to that adopted in this work.Comment: RevTeX4, 15 pages, 7 figures; submitted to Phys. Rev.
- …