1,154 research outputs found
Equilibrium phase behavior of polydisperse hard spheres
We calculate the phase behavior of hard spheres with size polydispersity,
using accurate free energy expressions for the fluid and solid phases. Cloud
and shadow curves, which determine the onset of phase coexistence, are found
exactly by the moment free energy method, but we also compute the complete
phase diagram, taking full account of fractionation effects. In contrast to
earlier, simplified treatments we find no point of equal concentration between
fluid and solid or re-entrant melting at higher densities. Rather, the fluid
cloud curve continues to the largest polydispersity that we study (14%); from
the equilibrium phase behavior a terminal polydispersity can thus only be
defined for the solid, where we find it to be around 7%. At sufficiently large
polydispersity, fractionation into several solid phases can occur, consistent
with previous approximate calculations; we find in addition that coexistence of
several solids with a fluid phase is also possible
The short-time self-diffusion coefficient of a sphere in a suspension of rigid rods
The short--time self diffusion coefficient of a sphere in a suspension of
rigid rods is calculated in first order in the rod volume fraction. For low rod
concentrations the correction to the Einstein diffusion constant of the sphere
is a linear function of the rod volume fraction with the slope proportional to
the equilibrium averaged mobility diminution trace of the sphere interacting
with a single freely translating and rotating rod. The two--body hydrodynamic
interactions are calculated using the so--called bead model in which the rod is
replaced by a stiff linear chain of touching spheres. The interactions between
spheres are calculated numerically using the multipole method. Also an
analytical expression for the diffusion coefficient as a function of the rod
aspect ratio is derived in the limit of very long rods. We show that in this
limit the correction to the Einstein diffusion constant does not depend on the
size of the tracer sphere. The higher order corrections depending on the
applied model are computed numerically. An approximate expression is provided,
valid for a wide range of aspect ratios.Comment: 11 pages, 6 figure
Critical behaviors of sheared frictionless granular materials near jamming transition
Critical behaviors of sheared dense and frictionless granular materials in
the vicinity of the jamming transition are numerically investigated. From the
extensive molecular dynamics simulation, we verify the validity of the scaling
theory near the jamming transition proposed by Otsuki and Hayakawa (Prog.
Theor. Phys., 121, 647 (2009)). We also clarify the critical behaviors of the
shear viscosity and the pair correlation function based on both a phenomenology
and the simulation.Comment: 13pages, 26 figure
Stacking Entropy of Hard Sphere Crystals
Classical hard spheres crystallize at equilibrium at high enough density.
Crystals made up of stackings of 2-dimensional hexagonal close-packed layers
(e.g. fcc, hcp, etc.) differ in entropy by only about per sphere
(all configurations are degenerate in energy). To readily resolve and study
these small entropy differences, we have implemented two different
multicanonical Monte Carlo algorithms that allow direct equilibration between
crystals with different stacking sequences. Recent work had demonstrated that
the fcc stacking has higher entropy than the hcp stacking. We have studied
other stackings to demonstrate that the fcc stacking does indeed have the
highest entropy of ALL possible stackings. The entropic interactions we could
detect involve three, four and (although with less statistical certainty) five
consecutive layers of spheres. These interlayer entropic interactions fall off
in strength with increasing distance, as expected; this fall-off appears to be
much slower near the melting density than at the maximum (close-packing)
density. At maximum density the entropy difference between fcc and hcp
stackings is per sphere, which is roughly 30% higher
than the same quantity measured near the melting transition.Comment: 15 page
Self-diffusion coefficients of charged particles: Prediction of Nonlinear volume fraction dependence
We report on calculations of the translational and rotational short-time
self-diffusion coefficients and for suspensions of
charge-stabilized colloidal spheres. These diffusion coefficients are affected
by electrostatic forces and many-body hydrodynamic interactions (HI). Our
computations account for both two-body and three-body HI. For strongly charged
particles, we predict interesting nonlinear scaling relations and depending on volume fraction
, with essentially charge-independent parameters and . These
scaling relations are strikingly different from the corresponding results for
hard spheres. Our numerical results can be explained using a model of effective
hard spheres. Moreover, we perceptibly improve the known result for of
hard sphere suspensions.Comment: 8 pages, LaTeX, 3 Postscript figures included using eps
Fluid-fluid phase separation in hard spheres with a bimodal size distribution
The effect of polydispersity on the phase behaviour of hard spheres is
examined using a moment projection method. It is found that the
Boublik-Mansoori-Carnahan-Starling-Leland equation of state shows a spinodal
instability for a bimodal distribution if the large spheres are sufficiently
polydisperse, and if there is sufficient disparity in mean size between the
small and large spheres. The spinodal instability direction points to the
appearance of a very dense phase of large spheres.Comment: 7 pages, 3 figures, moderately REVISED following referees' comments
(original was 4 pages, 3 postscript figures
Fish, Flows, Isotopes and Food Webs: the Importance of Connectivity in Northern Australian Rivers
Northern Australia contains a rich freshwater biodiversity due largely to low levels of human impact. Most rivers remain unimpacted and free-flowing. The latter characteristic is important as it ensures that natural levels of connectivity throughout the riverine landscape exist and organisms and, importantly,carbon and nutrients, can be shifted between ecosystems and different parts of the landscape. This high degree of connectivity differs between rivers according to their flow regime however; most rivers of northern Australia are highly seasonal and flow intermittently. The present paper details the importance ofmaintaining connectivity within the river and between the river and its floodplain for the maintenance of species diversity and the structure of aquatic food webs. It draws upon large datasets concerning fish biodiversity and several foodweb studies using stable isotopes assembled or conducted with the TropicalRivers and Coastal Knowledge program to illustrate the importance of connectivit
Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies
The asymptotic frequency , dependence of the dynamic viscosity of
neutral hard sphere colloidal suspensions is shown to be of the form , where has been determined as a
function of the volume fraction , for all concentrations in the fluid
range, is the solvent viscosity and the P\'{e}clet time. For
a soft potential it is shown that, to leading order steepness, the asymptotic
behavior is the same as that for the hard sphere potential and a condition for
the cross-over behavior to is given. Our result for the hard
sphere potential generalizes a result of Cichocki and Felderhof obtained at low
concentrations and agrees well with the experiments of van der Werff et al, if
the usual Stokes-Einstein diffusion coefficient in the Smoluchowski
operator is consistently replaced by the short-time self diffusion coefficient
for non-dilute colloidal suspensions.Comment: 18 pages LaTeX, 1 postscript figur
Mixtures of Charged Colloid and Neutral Polymer: Influence of Electrostatic Interactions on Demixing and Interfacial Tension
The equilibrium phase behavior of a binary mixture of charged colloids and
neutral, non-adsorbing polymers is studied within free-volume theory. A model
mixture of charged hard-sphere macroions and ideal, coarse-grained,
effective-sphere polymers is mapped first onto a binary hard-sphere mixture
with non-additive diameters and then onto an effective Asakura-Oosawa model [S.
Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is
defined by a single dimensionless parameter -- the ratio of the polymer
diameter to the effective colloid diameter. For high salt-to-counterion
concentration ratios, a free-volume approximation for the free energy is used
to compute the fluid phase diagram, which describes demixing into colloid-rich
(liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic
interactions shifts the demixing binodal toward higher polymer concentration,
stabilizing the mixture. The enhanced stability is attributed to a weakening of
polymer depletion-induced attraction between electrostatically repelling
macroions. Comparison with predictions of density-functional theory reveals a
corresponding increase in the liquid-vapor interfacial tension. The predicted
trends in phase stability are consistent with observed behavior of
protein-polysaccharide mixtures in food colloids.Comment: 16 pages, 5 figure
Phase Separation in Charge-Stabilized Colloidal Suspensions: Influence of Nonlinear Screening
The phase behavior of charge-stabilized colloidal suspensions is modeled by a
combination of response theory for electrostatic interparticle interactions and
variational theory for free energies. Integrating out degrees of freedom of the
microions (counterions, salt ions), the macroion-microion mixture is mapped
onto a one-component system governed by effective macroion interactions. Linear
response of microions to the electrostatic potential of the macroions results
in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume
energy, while nonlinear response modifies the effective interactions [A. R.
Denton, \PR E {\bf 70}, 031404 (2004)]. The volume energy and effective pair
potential are taken as input to a variational free energy, based on
thermodynamic perturbation theory. For both linear and first-order nonlinear
effective interactions, a coexistence analysis applied to aqueous suspensions
of highly charged macroions and monovalent microions yields bulk separation of
macroion-rich and macroion-poor phases below a critical salt concentration, in
qualitative agreement with predictions of related linearized theories [R. van
Roij, M. Dijkstra, and J.-P. Hansen, \PR E {\bf 59}, 2010 (1999); P. B. Warren,
\JCP {\bf 112}, 4683 (2000)]. It is concluded that nonlinear screening can
modify phase behavior but does not necessarily suppress bulk phase separation
of deionized suspensions.Comment: 14 pages of text + 9 figure
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