366 research outputs found
Phase behavior of polydisperse sticky hard spheres: analytical solutions and perturbation theory
We discuss phase coexistence of polydisperse colloidal suspensions in the
presence of adhesion forces. The combined effect of polydispersity and Baxter's
sticky-hard-sphere (SHS) potential, describing hard spheres interacting via
strong and very short-ranged attractive forces, give rise, within the
Percus-Yevick (PY) approximation, to a system of coupled quadratic equations
which, in general, cannot be solved either analytically or numerically. We
review and compare two recent alternative proposals, which we have attempted to
by-pass this difficulty. In the first one, truncating the density expansion of
the direct correlation functions, we have considered approximations simpler
than the PY one. These approximations can be systematically improved.
We have been able to provide a complete analytical description of polydisperse
SHS fluids by using the simplest two orders and , respectively.
Such a simplification comes at the price of a lower accuracy in the phase
diagram, but has the advantage of providing an analytical description of
various new phenomena associated with the onset of polydispersity in phase
equilibria (e.g. fractionation). The second approach is based on a perturbative
expansion of the polydisperse PY solution around its monodisperse counterpart.
This approach provides a sound approximation to the real phase behavior, at the
cost of considering only weak polydispersity. Although a final seattlement on
the soundness of the latter method would require numerical simulations for the
polydisperse Baxter model, we argue that this approach is expected to keep
correctly into account the effects of polydispersity, at least qualitatively.Comment: 12 pages, 4 figures, to appear in Molec. Phys. special issue Liblice
200
On the compressibility equation of state for multicomponent adhesive hard sphere fluids
The compressibility equation of state for a multicomponent fluid of particles
interacting via an infinitely narrow and deep potential, is considered within
the mean spherical approximation (MSA). It is shown that for a class of models
leading to a particular form of the Baxter functions containing
density-independent stickiness coefficient, the compressibility EOS does not
exist, unlike the one-component case. The reason for this is that a direct
integration of the compressibility at fixed composition, cannot be carried out
due to the lack of a reciprocity relation on the second order partial
derivatives of the pressure with respect to two different densities. This is,
in turn, related to the inadequacy of the MSA. A way out to this drawback is
presented in a particular example, leading to a consistent compressibility
pressure, and a possible generalization of this result is discussed.Comment: 13 pages, no figures, accepted for publication Molec. Physics (2002
Polydisperse fluid mixtures of adhesive colloidal particles
We investigate polydispersity effects on the average structure factor of
colloidal suspensions of neutral particles with surface adhesion. A sticky hard
sphere model alternative to Baxter's one is considered. The choice of
factorizable stickiness parameters in the potential allows a simple analytic
solution, within the ``mean spherical approximation'', for any number of
components and arbitrary stickiness distribution. Two particular cases are
discussed: i) all particles have different sizes but equal stickiness (Model
I), and ii) each particle has a stickiness proportional to its size (Model II).
The interplay between attraction and polydispersity yields a markedly different
behaviour for the two Models in regimes of strong coupling (i.e. strong
adhesive forces and low temperature) and large polydispersity. These results
are then exploited to reanalyze experimental scattering data on sterically
stabilized silica particles.Comment: 9 pages, 2 figures (included), Physica A (2001) to appea
Effect of Polydispersity and Anisotropy in Colloidal and Protein Solutions: an Integral Equation Approach
Application of integral equation theory to complex fluids is reviewed, with
particular emphasis to the effects of polydispersity and anisotropy on their
structural and thermodynamic properties. Both analytical and numerical
solutions of integral equations are discussed within the context of a set of
minimal potential models that have been widely used in the literature. While
other popular theoretical tools, such as numerical simulations and density
functional theory, are superior for quantitative and accurate predictions, we
argue that integral equation theory still provides, as in simple fluids, an
invaluable technique that is able to capture the main essential features of a
complex system, at a much lower computational cost. In addition, it can provide
a detailed description of the angular dependence in arbitrary frame, unlike
numerical simulations where this information is frequently hampered by
insufficient statistics. Applications to colloidal mixtures, globular proteins
and patchy colloids are discussed, within a unified framework.Comment: 17 pages, 7 figures, to appear in Interdiscip. Sci. Comput. Life Sci.
(2011), special issue dedicated to Prof. Lesser Blu
The Psychodynamic Diagnostic Manual – 2nd edition (PDM-2)
For decades many clinicians, especially psychodynamic and humanistic therapists, have resisted thinking about their patients in terms of categorical diagnoses. In the current era, they find themselves having to choose between reluctantly “accepting” the DSM diagnostic labels, “denying” them, or developing alternatives more consistent with the dimensional, inferential, contextual, biopsychosocial diagnostic formulations characteristic of psychoanalytic and humanistic approaches. The Psychodynamic Diagnostic Manual (PDM) reflects an effort to articulate a psychodynamically oriented diagnosis that bridges the gap between clinical complexity and the need for empirical and methodological validity. In this paper the authors (the steering committee of the PDM-2) describe the process of construction of the PDM-1 and discuss changes proposed for implementation in PDM-2
Stability boundaries, percolation threshold, and two phase coexistence for polydisperse fluids of adhesive colloidal particles
We study the polydisperse Baxter model of sticky hard spheres (SHS) in the
modified Mean Spherical Approximation (mMSA). This closure is known to be the
zero-order approximation (C0) of the Percus-Yevick (PY) closure in a density
expansion. The simplicity of the closure allows a full analytical study of the
model. In particular we study stability boundaries, the percolation threshold,
and the gas-liquid coexistence curves. Various possible sub-cases of the model
are treated in details. Although the detailed behavior depends upon the
particularly chosen case, we find that, in general, polydispersity inhibits
instabilities, increases the extent of the non percolating phase, and
diminishes the size of the gas-liquid coexistence region. We also consider the
first-order improvement of the mMSA (C0) closure (C1) and compare the
percolation and gas-liquid boundaries for the one-component system with recent
Monte Carlo simulations. Our results provide a qualitative understanding of the
effect of polydispersity on SHS models and are expected to shed new light on
the applicability of SHS models for colloidal mixtures.Comment: 37 pages, 7 figures, 1 tabl
Probing the existence of phase transitions in one-dimensional fluids of penetrable particles
Phase transitions in one-dimensional classical fluids are usually ruled out
by making appeal to van Hove's theorem. A way to circumvent the conclusions of
the theorem is to consider an interparticle potential that is everywhere
bounded. Such is the case of, {\it e.g.}, the generalized exponential model of
index 4 (GEM-4 potential), which in three dimensions gives a reasonable
description of the effective repulsion between flexible dendrimers in a
solution. An extensive Monte Carlo simulation of the one-dimensional GEM-4
model [S. Prestipino, {\em Phys. Rev. E} {\bf 90}, 042306 (2014)] has recently
provided evidence of an infinite sequence of low-temperature cluster phases,
however also suggesting that upon pushing the simulation forward what seemed a
true transition may eventually prove to be only a sharp crossover. We hereby
investigate this problem theoretically, by three different and increasingly
sophisticated approaches ({\it i.e.}, a mean-field theory, the transfer matrix
of a lattice model of clusters, and the exact treatment of a system of point
clusters in the continuum), to conclude that the alleged transitions of the
one-dimensional GEM4 system are likely just crossovers.Comment: 18 pages, 9 figure
Small Angle Scattering data analysis for dense polydisperse systems: the FLAC program
FLAC is a program to calculate the small-angle neutron scattering intensity
of highly packed polydisperse systems of neutral or charged hard spheres within
the Percus-Yevick and the Mean Spherical Approximation closures, respectively.
The polydisperse system is defined by a size distribution function and the
macro-particles have hard sphere radii which may differ from the size of their
scattering cores. With FLAC, one can either simulate scattering intensities or
fit experimental small angle neutron scattering data. In output scattering
intensities, structure factors and pair correlation functions are provided.
Smearing effects due to instrumental resolution, vertical slit, primary beam
width and multiple scattering effects are also included on the basis of the
existing theories. Possible form factors are those of filled or two-shell
spheres.Comment: 18 pages, 1 figure, uses elsart.st
Structure factors for the simplest solvable model of polydisperse colloidal fluids with surface adhesion
Closed analytical expressions for scattering intensity and other global
structure factors are derived for a new solvable model of polydisperse sticky
hard spheres. The starting point is the exact solution of the ``mean spherical
approximation'' for hard core plus Yukawa potentials, in the limit of infinite
amplitude and vanishing range of the attractive tail, with their product
remaining constant. The choice of factorizable coupling (stickiness) parameters
in the Yukawa term yields a simpler ``dyadic structure'' in the Fourier
transform of the Baxter factor correlation function , with a
remarkable simplification in all structure functions with respect to previous
works. The effect of size and stickiness polydispersity is analyzed and
numerical results are presented for two particular versions of the model: i)
when all polydisperse particles have a single, size-independent, stickiness
parameter, and ii) when the stickiness parameters are proportional to the
diameters. The existence of two different regimes for the average structure
factor, respectively above and below a generalized Boyle temperature which
depends on size polydispersity, is recognized and discussed. Because of its
analycity and simplicity, the model may be useful in the interpretation of
small-angle scattering experimental data for polydisperse colloidal fluids of
neutral particles with surface adhesion.Comment: 32 pages, 7 figures, RevTex style, to appear in J. Chem. Phys. 1
December 200
Pathologies in the sticky limit of hard-sphere-Yukawa models for colloidal fluids. A possible correction
A known `sticky-hard-sphere' model, defined starting from a
hard-sphere-Yukawa potential and taking the limit of infinite amplitude and
vanishing range with their product remaining constant, is shown to be
ill-defined. This is because its Hamiltonian (which we call SHS2) leads to an
{\it exact}second virial coefficient which {\it diverges}, unlike that of
Baxter's original model (SHS1). This deficiency has never been observed so far,
since the linearization implicit in the `mean spherical approximation' (MSA),
within which the model is analytically solvable, partly {\it masks} such a
pathology. To overcome this drawback and retain some useful features of SHS2,
we propose both a new model (SHS3) and a new closure (`modified MSA'), whose
combination yields an analytic solution formally identical with the SHS2-MSA
one. This mapping allows to recover many results derived from SHS2, after a
re-interpretation within a correct framework. Possible developments are finally
indicated.Comment: 21 pages, 1 figure, accepted in Molecular Physics (2003
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