356 research outputs found
Wertheim perturbation theory: thermodynamics and structure of patchy colloids
We critically discuss the application of the Wertheim's theory to classes of
complex associating fluids that can be today engineered in the laboratory as
patchy colloids and to the prediction of their peculiar gas-liquid phase
diagrams. Our systematic study, stemming from perturbative version of the
theory, allows us to show that, even at the simplest level of approximation for
the inter-cluster correlations, the theory is still able to provide a
consistent and stable picture of the behavior of interesting models of
self-assembling colloidal suspension. We extend the analysis of a few cases of
patchy systems recently introduced in the literature. In particular, we discuss
for the first time in detail the consistency of the structural description
underlying the perturbative approach and we are able to prove a consistency
relationship between the valence as obtained from thermodynamics and from the
structure for the one-site case. A simple analytical expression for the
structure factor is proposed.Comment: 25 pages, 10 figure
The restricted primitive model of ionic fluids with nonadditive diameters
The restricted primitive model with nonadditive hard-sphere diameters is
shown to have interesting and peculiar clustering properties. We report
accurate calculations of the cluster concentrations. Implementing efficient and
ad hoc Monte Carlo algorithms we determine the effect of nonadditivity on both
the clustering and the gas-liquid binodal. For negative nonadditivity, tending
to the extreme case of completely overlapping unlike ions, the prevailing
clusters are made of an even number of particles having zero total charge. For
positive nonadditivity, the frustrated tendency to segregation of like
particles and the reduced space available to the ions favors percolating
clusters at high densities.Comment: 6 pages, 3 figure
Wertheim and Bjerrum-Tani-Henderson theories for associating fluids: a critical assessment
Two theories for associating fluids recently used to study clustering in
models for self-assembling patchy particles, Wertheim's and
Bjerrum-Tani-Henderson theories, are carefully compared. We show that, for a
fluid allowing only for dimerization, Wertheim theory is equivalent to the
Bjerrum-Tani-Henderson theory neglecting intercluster correlations.
Nonetheless, while the former theory is able to account for percolation and
condensation, the latter is not. For the Bjerrum-Tani-Henderson theory we also
rigorously prove the uniqueness of the solution for the cluster's
concentrations and the reduction of the system of equations to a single one for
a single unknown. We carry out Monte Carlo simulations of two simple models of
dimerizing fluids and compare quantitatively the predictions of the two
theories with the simulation data.Comment: 21 pages, 6 figure
Effective forces in square well and square shoulder fluids
We derive an analytical expression for the effective force between a pair of
macrospheres immersed in a sea of microspheres, in the case where the
interaction between the two unlike species is assumed to be a square well or a
square shoulder of given range and depth (or height). This formula extends a
similar one developed in the case of hard core interactions only. Qualitative
features of such effective force and the resulting phase diagram are then
analyzed in the limit of no interaction between the small particles.
Approximate force profiles are then obtained by means of integral equation
theories (PY and HNC) combined with the superposition approximation and
compared with exact ones from direct Monte Carlo simulations.Comment: 34 page
A numerical study of one-patch colloidal particles: from square-well to Janus
We perform numerical simulations of a simple model of one-patch colloidal
particles to investigate: (i) the behavior of the gas-liquid phase diagram on
moving from a spherical attractive potential to a Janus potential and (ii) the
collective structure of a system of Janus particles. We show that, for the case
where one of the two hemispheres is attractive and one is repulsive, the system
organizes into a dispersion of orientational ordered micelles and vesicles and,
at low , the system can be approximated as a fluid of such clusters,
interacting essentially via excluded volume. The stability of this cluster
phase generates a very peculiar shape of the gas and liquid coexisting
densities, with a gas coexistence density which increases on cooling,
approaching the liquid coexistence density at very low .Comment: 9 pages, 10 figures, Phys. Chem. Chem. Phys. in press (2010
Phase diagram of Janus Particles
We deeply investigate a simple model representative of the recently
synthesized Janus particles, i.e. colloidal spherical particles whose surface
is divided into two areas of different chemical composition. When the two
surfaces are solvophilic and solvophobic, these particles constitute the
simplest example of surfactants. The phase diagram includes a colloidal-poor
(gas) colloidal-rich (liquid) de-mixing region, which is progressively
suppressed by the insurgence of micelles, providing the first model where
micellization and phase-separation are simultaneously observed. The coexistence
curve is found to be negatively sloped in the temperature-pressure plane,
suggesting that Janus particles can provide a colloidal system with anomalous
thermodynamic behavior.Comment: 5 pages, 5 figures, Phys. Rev. Lett. in pres
Patchy sticky hard spheres: analytical study and Monte Carlo simulations
We consider a fluid of hard spheres bearing one or two uniform circular
adhesive patches, distributed so as not to overlap. Two spheres interact via a
``sticky'' Baxter potential if the line joining the centers of the two spheres
intersects a patch on each sphere, and via a hard sphere potential otherwise.
We analyze the location of the fluid-fluid transition and of the percolation
line as a function of the size of the patch (the fractional coverage of the
sphere's surface) and of the number of patches within a virial expansion up to
third order and within the first two terms (C0 and C1) of a class of closures
Cn hinging on a density expansion of the direct correlation function. We find
that the locations of the two lines depend sensitively on both the total
adhesive coverage and its distribution. The treatment is almost fully
analytical within the chosen approximate theory. We test our findings by means
of specialized Monte Carlo (MC) simulations and find the main qualitative
features of the critical behaviour to be well captured in spite of the low
density perturbative nature of the closure. The introduction of anisotropic
attractions into a model suspension of spherical particles is a first step
towards a more realistic description of globular proteins in solution.Comment: 47 pages, 18 figures, to appear on J. Chem. Phy
Coexistence of low and high overlap phases in a supercooled liquid: An integral equation investigation
The pair structure, free energy, and configurational overlap order parameter Q of an annealed system of two weakly coupled replicas of a supercooled \u201csoft sphere\u201d fluid are determined by solving the hypernetted-chain (HNC) and self-consistent Rogers-Young (RY) integral equations over a wide range of thermodynamic conditions \u3c1 (number-density), T (temperature), and inter-replicas couplings \u3b512. Analysis of the resulting effective (or Landau) potential W(\u3c1,T; Q) and of its derivative with respect to Q confirms the existence of a \u201cprecursor transition\u201d between weak and strong overlap phases below a critical temperature Tc well above the temperature To of the \u201cideal glass\u201d transition observed in the limit \u3b512\u21920. The precursor transition is signalled by a loss of convexity of the potential W(Q) and by a concomitant discontinuity of the order parameter Q just below Tc, which crosses over to a mean-field-like van der Waals loop at lower temperatures. The HNC and RY equations lead to the same phase transition scenario, with quantitative differences in the predicted temperatures Tc and To
Liquid-vapor coexistence in square-well fluids: an RHNC study
We investigate the ability of the reference hypernetted-chain integral
equation to describe the phase diagram of square-well fluids with four
different ranges of attraction. Comparison of our results with simulation data
shows that the theory is able to reproduce with fairly good accuracy a
significant part of the coexistence curve, provided an extrapolation procedure
is used to circumvent the well-known pathologies of the pseudo-spinodal line,
which are more severe at reduced width of the attractive well. The method
provides a useful approach for a quick assessment of the location of the
liquid-vapor coexistence curve in this kind of fluid and serves as a check for
the more complex problem of anisotropic "patchy" square-well molecules
Phase diagram and structural properties of a simple model for one-patch particles
We study the thermodynamic and structural properties of a simple, one-patch
fluid model using the reference hypernetted-chain (RHNC) integral equation and
specialized Monte Carlo simulations. In this model, the interacting particles
are hard spheres, each of which carries a single identical,
arbitrarily-oriented, attractive circular patch on its surface; two spheres
attract via a simple square-well potential only if the two patches on the
spheres face each other within a specific angular range dictated by the size of
the patch. For a ratio of attractive to repulsive surface of 0.8, we construct
the RHNC fluid-fluid separation curve and compare with that obtained by Gibbs
ensemble and grand canonical Monte Carlo simulations. We find that RHNC
provides a quick and highly reliable estimate for the position of the
fluid-fluid critical line. In addition, it gives a detailed (though
approximate) description of all structural properties and their dependence on
patch size.Comment: 27 pages, 10 figures, J. Chem. Phys. in pres
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