2,828 research outputs found
Simplified Onsager theory for isotropic-nematic phase equilibria of length polydisperse hard rods
Polydispersity is believed to have important effects on the formation of
liquid crystal phases in suspensions of rod-like particles. To understand such
effects, we analyse the phase behaviour of thin hard rods with length
polydispersity. Our treatment is based on a simplified Onsager theory, obtained
by truncating the series expansion of the angular dependence of the excluded
volume. We describe the model and give the full phase equilibrium equations;
these are then solved numerically using the moment free energy method which
reduces the problem from one with an infinite number of conserved densities to
one with a finite number of effective densities that are moments of the full
density distribution. The method yields exactly the onset of nematic ordering.
Beyond this, results are approximate but we show that they can be made
essentially arbitrarily precise by adding adaptively chosen extra moments,
while still avoiding the numerical complications of a direct solution of the
full phase equilibrium conditions.
We investigate in detail the phase behaviour of systems with three different
length distributions: a (unimodal) Schulz distribution, a bidisperse
distribution and a bimodal mixture of two Schulz distributions which
interpolates between these two cases. A three-phase isotropic-nematic-nematic
coexistence region is shown to exist for the bimodal and bidisperse length
distributions if the ratio of long and short rod lengths is sufficiently large,
but not for the unimodal one. We systematically explore the topology of the
phase diagram as a function of the width of the length distribution and of the
rod length ratio in the bidisperse and bimodal cases.Comment: 18 pages, 16 figure
Short-time diffusion in concentrated bidisperse hard-sphere suspensions
Diffusion in bidisperse Brownian hard-sphere suspensions is studied by
Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical
scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method
[Physica 120A, 388 (1983) & 126A, 349 (1984)]. Two species of hard spheres are
suspended in an overdamped viscous solvent that mediates the salient
hydrodynamic interactions among all particles. In a comprehensive parameter
scan that covers various packing fractions and suspension compositions, we
employ numerically accurate SD simulations to compute the initial diffusive
relaxation of density modulations at the Brownian time scale, quantified by the
partial hydrodynamic functions. A revised version of Beenakker and Mazur's
-scheme for monodisperse suspensions is found to exhibit
surprisingly good accuracy, when simple rescaling laws are invoked in its
application to mixtures. The so-modified scheme predicts
hydrodynamic functions in very good agreement with our SD simulation results,
for all densities from the very dilute limit up to packing fractions as high as
.Comment: 12 pages, 6 figure
Shearing behavior of polydisperse media
We study the shearing of polydisperse and bidisperse media with a size ratio
of 10. Simulations are performed with a the two dimensional shear cell using
contact dynamics. With a truncated power law for the polydisperse media we find
that they show a stronger dilatancy and greater resistance to shearing than
bidisperse mixtures. Motivated by the practical problem of reducing the energy
needed to shear granular media, we introduce "point-like particles"
representing charged particles in the distribution. Even though changing the
kinematic behavior very little, they reduce the force necessary to maintain a
fixed shearing velocity.Comment: 17 pages, 15 figure
Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
We have studied how 2- and 3- dimensional systems made up of particles
interacting with finite range, repulsive potentials jam (i.e., develop a yield
stress in a disordered state) at zero temperature and applied stress. For each
configuration, there is a unique jamming threshold, , at which
particles can no longer avoid each other and the bulk and shear moduli
simultaneously become non-zero. The distribution of values becomes
narrower as the system size increases, so that essentially all configurations
jam at the same in the thermodynamic limit. This packing fraction
corresponds to the previously measured value for random close-packing. In fact,
our results provide a well-defined meaning for "random close-packing" in terms
of the fraction of all phase space with inherent structures that jam. The
jamming threshold, Point J, occurring at zero temperature and applied stress
and at the random close-packing density, has properties reminiscent of an
ordinary critical point. As Point J is approached from higher packing
fractions, power-law scaling is found for many quantities. Moreover, near Point
J, certain quantities no longer self-average, suggesting the existence of a
length scale that diverges at J. However, Point J also differs from an ordinary
critical point: the scaling exponents do not depend on dimension but do depend
on the interparticle potential. Finally, as Point J is approached from high
packing fractions, the density of vibrational states develops a large excess of
low-frequency modes. All of these results suggest that Point J may control
behavior in its vicinity-perhaps even at the glass transition.Comment: 21 pages, 20 figure
Tuning Jammed Frictionless Disk Packings from Isostatic to Hyperstatic
We perform extensive computational studies of two-dimensional static
bidisperse disk packings using two distinct packing-generation protocols. The
first involves thermally quenching equilibrated liquid configurations to zero
temperature over a range of thermal quench rates and initial packing
fractions followed by compression and decompression in small steps to reach
packing fractions at jamming onset. For the second, we seed the system
with initial configurations that promote micro- and macrophase-separated
packings followed by compression and decompression to . We find that
amorphous, isostatic packings exist over a finite range of packing fractions
from in the large-system limit,
with . In agreement with previous calculations,
we obtain for , where is the rate
above which is insensitive to rate. We further compare the structural
and mechanical properties of isostatic versus hyperstatic packings. The
structural characterizations include the contact number, bond orientational
order, and mixing ratios of the large and small particles. We find that the
isostatic packings are positionally and compositionally disordered, whereas
bond-orientational and compositional order increase with contact number for
hyperstatic packings. In addition, we calculate the static shear modulus and
normal mode frequencies of the static packings to understand the extent to
which the mechanical properties of amorphous, isostatic packings are different
from partially ordered packings. We find that the mechanical properties of the
packings change continuously as the contact number increases from isostatic to
hyperstatic.Comment: 11 pages, 15 figure
Disordering Transitions and Peak Effect in Polydisperse Particle Systems
We show numerically that in a binary system of Yukawa particles, a dispersity
driven disordering transition occurs. In the presence of quenched disorder this
disordering transition coincides with a marked increase in the depinning
threshold, known as a peak effect. We find that the addition of poorly pinned
particles can increase the overall pinning in the sample by increasing the
amount of topological disorder present. If the quenched disorder is strong
enough to create a significant amount of topological disorder in the
monodisperse system, addition of a poorly pinned species generates further
disorder but does not produce a peak in the depinning force. Our results
indicate that for binary mixtures, optimal pinning occurs for topological
defect fraction densities of 0.2 to 0.25. For defect densities below this
range, the system retains orientational order. We determine the effect of the
pinning density, strength, and radius on the depinning peak and find that the
peak effect is more pronounced in weakly pinning systems.Comment: 8 pages, 8 postscript figures. Version to appear in PR
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