573 research outputs found
Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: Comparison of accurate simulation results with theory
We report a detailed study, using state-of-the-art simulation and theoretical
methods, of the depletion potential between a pair of big hard spheres immersed
in a reservoir of much smaller hard spheres, the size disparity being measured
by the ratio of diameters q=\sigma_s/\sigma_b. Small particles are treated
grand canonically, their influence being parameterized in terms of their
packing fraction in the reservoir, \eta_s^r. Two specialized Monte Carlo
simulation schemes --the geometrical cluster algorithm, and staged particle
insertion-- are deployed to obtain accurate depletion potentials for a number
of combinations of q\leq 0.1 and \eta_s^r. After applying corrections for
simulation finite-size effects, the depletion potentials are compared with the
prediction of new density functional theory (DFT) calculations based on the
insertion trick using the Rosenfeld functional and several subsequent
modifications. While agreement between the DFT and simulation is generally
good, significant discrepancies are evident at the largest reservoir packing
fraction accessible to our simulation methods, namely \eta_s^r=0.35. These
discrepancies are, however, small compared to those between simulation and the
much poorer predictions of the Derjaguin approximation at this \eta_s^r. The
recently proposed morphometric approximation performs better than Derjaguin but
is somewhat poorer than DFT for the size ratios and small sphere packing
fractions that we consider. The effective potentials from simulation, DFT and
the morphometric approximation were used to compute the second virial
coefficient B_2 as a function of \eta_s^r. Comparison of the results enables an
assessment of the extent to which DFT can be expected to correctly predict the
propensity towards fluid fluid phase separation in additive binary hard sphere
mixtures with q\leq 0.1.Comment: 16 pages, 9 figures, revised treatment of morphometric approximation
and reordered some materia
Four particle cluster approximation for the Maier-Saupe model of the isotropic-nematic phase transition
The cluster variation theory for the Maier-Saupe model of the isotropic-nematic phase transition is extended to the four-particle level. As in the case of the Heisenberg ferromagnet, the irregularities of the three-particle cluster approximation applied to cubic lattices, where there are no triangles of nearest neighbors, disappear. The extension from three- to four-particle clusters yields improved values of all quantities, characteristic for the phase transition
Gelation as arrested phase separation in short-ranged attractive colloid-polymer mixtures
We present further evidence that gelation is an arrested phase separation in
attractive colloid-polymer mixtures, based on a method combining confocal
microscopy experiments with numerical simulations recently established in {\bf
Nature 453, 499 (2008)}. Our results are independent of the form of the
interparticle attractive potential, and therefore should apply broadly to any
attractive particle system with short-ranged, isotropic attractions. We also
give additional characterization of the gel states in terms of their structure,
inhomogeneous character and local density.Comment: 6 figures, to be published in J. Phys. Condens. Matter, special issue
for EPS Liquids Conference 200
Waiting and Residence Times of Brownian Interface Fluctuations
We report on the residence times of capillary waves above a given height
and on the typical waiting time in between such fluctuations. The measurements
were made on phase separated colloid-polymer systems by laser scanning confocal
microscopy. Due to the Brownian character of the process, the stochastics vary
with the chosen measurement interval . In experiments, the discrete
scanning times are a practical cutoff and we are able to measure the waiting
time as a function of this cutoff. The measurement interval dependence of the
observed waiting and residence times turns out to be solely determined by the
time dependent height-height correlation function . We find excellent
agreement with the theory presented here along with the experiments.Comment: 5 figure
Critical behavior of colloid-polymer mixtures in random porous media
We show that the critical behavior of a colloid-polymer mixture inside a
random porous matrix of quenched hard spheres belongs to the universality class
of the random-field Ising model. We also demonstrate that random-field effects
in colloid-polymer mixtures are surprisingly strong. This makes these systems
attractive candidates to study random-field behavior experimentally.Comment: 4 pages, 3 figures, to appear in Phys. Rev. Let
Isotropic-nematic phase transition in suspensions of filamentous virus and the neutral polymer Dextran
We present an experimental study of the isotropic-nematic phase transition in
an aqueous mixture of charged semi-flexible rods (fd virus) and neutral polymer
(Dextran). A complete phase diagram is measured as a function of ionic strength
and polymer molecular weight. At high ionic strength we find that adding
polymer widens the isotropic-nematic coexistence region with polymers
preferentially partitioning into the isotropic phase, while at low ionic
strength the added polymer has no effect on the phase transition. The nematic
order parameter is determined from birefringence measurements and is found to
be independent of polymer concentration (or equivalently the strength of
attraction). The experimental results are compared with the existing
theoretical predictions for the isotropic-nematic transition in rods with
attractive interactions.Comment: 8 Figures. To be published in Phys. Rev. E. For more information see
http://www.elsie.brandeis.ed
On the calculation of the self-diffusion coefficient of interacting Brownian particles
We consider two ways to calculate the self-diffusion coefficient of interacting Brownian particles. The first approach is based on the calculation of the mean square displacement of a Brownian particle starting from the Smoluchowski equation. In the second approach the self-diffusion
coefficient is obtained as the product of the thermodynamic driving force and the mobility. The advantages and limitations of the two methods are discussed
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