1,185 research outputs found
Fractionation effects in phase equilibria of polydisperse hard sphere colloids
The equilibrium phase behaviour of hard spheres with size polydispersity is
studied theoretically. We solve numerically the exact phase equilibrium
equations that result from accurate free energy expressions for the fluid and
solid phases, while accounting fully for size fractionation between coexisting
phases. Fluids up to the largest polydispersities that we can study (around
14%) can phase separate by splitting off a solid with a much narrower size
distribution. This shows that experimentally observed terminal polydispersities
above which phase separation no longer occurs must be due to non-equilibrium
effects. We find no evidence of re-entrant melting; instead, sufficiently
compressed solids phase separate into two or more solid phases. Under
appropriate conditions, coexistence of multiple solids with a fluid phase is
also predicted. The solids have smaller polydispersities than the parent phase
as expected, while the reverse is true for the fluid phase, which contains
predominantly smaller particles but also residual amounts of the larger ones.
The properties of the coexisting phases are studied in detail; mean diameter,
polydispersity and volume fraction of the phases all reveal marked
fractionation. We also propose a method for constructing quantities that
optimally distinguish between the coexisting phases, using Principal Component
Analysis in the space of density distributions. We conclude by comparing our
predictions to perturbative theories for near-monodisperse systems and to Monte
Carlo simulations at imposed chemical potential distribution, and find
excellent agreement.Comment: 21 pages, 23 figures, 2 table
Phase separation in mixtures of colloids and long ideal polymer coils
Colloidal suspensions with free polymer coils which are larger than the
colloidal particles are considered. The polymer-colloid interaction is modeled
by an extension of the Asakura-Oosawa model. Phase separation occurs into
dilute and dense fluid phases of colloidal particles when polymer is added. The
critical density of this transition tends to zero as the size of the polymer
coils diverges.Comment: 5 pages, 3 figure
Density Functional for Anisotropic Fluids
We propose a density functional for anisotropic fluids of hard body
particles. It interpolates between the well-established geometrically based
Rosenfeld functional for hard spheres and the Onsager functional for elongated
rods. We test the new approach by calculating the location of the the
nematic-isotropic transition in systems of hard spherocylinders and hard
ellipsoids. The results are compared with existing simulation data. Our
functional predicts the location of the transition much more accurately than
the Onsager functional, and almost as good as the theory by Parsons and Lee. We
argue that it might be suited to study inhomogeneous systems.Comment: To appear in J. Physics: Condensed Matte
Phase behaviour of a model of colloidal particles with a fluctuating internal state
Colloidal particles are not simple rigid particles, in general an isolated
particle is a system with many degrees of freedom in its own right, e.g., the
counterions around a charged colloidal particle.The behaviour of model
colloidal particles, with a simple phenomenological model to account for these
degrees of freedom, is studied. It is found that the interaction between the
particles is not pairwise additive. It is even possible that the interaction
between a triplet of particles is attractive while the pair interaction is
repulsive. When this is so the liquid phase is either stable only in a small
region of the phase diagram or absent altogether.Comment: 12 pages including 4 figure
The global burden attributable to low bone mineral density
Introduction: The Global Burden of Disease Study 2010 estimated the worldwide health burden of 291 diseases and injuries and 67 risk factors by calculating disability-adjusted life years (DALYs). Osteoporosis was not considered as a disease, and bone mineral density (BMD) was analysed as a risk factor for fractures, which formed part of the health burden due to falls. Objectives: To calculate (1) the global distribution of BMD, (2) its population attributable fraction (PAF) for fractures and subsequently for falls, and (3) the number of DALYs due to BMD. Methods: A systematic review was performed seeking population-based studies in which BMD was measured by dual-energy X-ray absorptiometry at the femoral neck in people aged 50 years and over. Age- and sex-specific mean ± SD BMD values (g/cm2) were extracted from eligible studies. Comparative risk assessment methodology was used to calculate PAFs of BMD for fractures. The theoretical minimum risk exposure distribution was estimated as the age- and sex-specific 90th centile from the Third National Health and Nutrition Examination Survey (NHANES III). Relative risks of fractures were obtained from a previous meta-analysis. Hospital data were used to calculate the fraction of the health burden of falls that was due to fractures. Results: Global deaths and DALYs attributable to low BMD increased from 103 000 and 3 125 000 in 1990 to 188 000 and 5 216 000 in 2010, respectively. The percentage of low BMD in the total global burden almost doubled from 1990 (0.12%) to 2010 (0.21%). Around one-third of falls-related deaths were attributable to low BMD. Conclusions: Low BMD is responsible for a growing global health burden, only partially representative of the real burden of osteoporosis
Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
We evaluate the virial coefficients B_k for k<=10 for hard spheres in
dimensions D=2,...,8. Virial coefficients with k even are found to be negative
when D>=5. This provides strong evidence that the leading singularity for the
virial series lies away from the positive real axis when D>=5. Further analysis
provides evidence that negative virial coefficients will be seen for some k>10
for D=4, and there is a distinct possibility that negative virial coefficients
will also eventually occur for D=3.Comment: 33 pages, 12 figure
Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems
The theoretical framework for higher-order correlation functions involving
multiple times and multiple points in a classical, many-body system developed
by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to
include tagged particle densities. Such densities have found an intriguing
application as proposed measures of dynamical heterogeneities in structural
glasses. The theoretical formalism is based upon projection operator techniques
which are used to isolate the slow time evolution of dynamical variables by
expanding the slowly-evolving component of arbitrary variables in an infinite
basis composed of the products of slow variables of the system. The resulting
formally exact mode-coupling expressions for multiple-point and multiple-time
correlation functions are made tractable by applying the so-called N-ordering
method. This theory is used to derive for moderate densities the leading mode
coupling expressions for indicators of relaxation type and domain relaxation,
which use dynamical filters that lead to multiple-time correlations of a tagged
particle density. The mode coupling expressions for higher order correlation
functions are also succesfully tested against simulations of a hard sphere
fluid at relatively low density.Comment: 15 pages, 2 figure
Pressure Dependence of Born Effective Charges, Dielectric Constant and Lattice Dynamics in SiC
The pressure dependence of the Born effective charge, dielectric constant and
zone-center LO and TO phonons have been determined for -SiC by a linear
response method based on the linearized augmented plane wave calculations
within the local density approximation. The Born effective charges are found to
increase nearly linearly with decreasing volume down to the smallest volume
studied, , corresponding to a pressure of about 0.8 Mbar. This
seems to be in contradiction with the conclusion of the turnover behavior
recently reported by Liu and Vohra [Phys.\ Rev.\ Lett.\ {\bf 72}, 4105 (1994)]
for -SiC. Reanalyzing their procedure to extract the pressure dependence of
the Born effective charges, we suggest that the turnover behavior they obtained
is due to approximations in the assumed pressure dependence of the dielectric
constant , the use of a singular set of experimental data
for the equation of state, and the uncertainty in measured phonon frequencies,
especially at high pressure.Comment: 25 pages, revtex, 5 postscript figures appended, to be published in
Phys. Rev.
Phase equilibria and glass transition in colloidal systems with short-ranged attractive interactions. Application to protein crystallization
We have studied a model of a complex fluid consisting of particles
interacting through a hard core and a short range attractive potential of both
Yukawa and square-well form. Using a hybrid method, including a self-consistent
and quite accurate approximation for the liquid integral equation in the case
of the Yukawa fluid, perturbation theory to evaluate the crystal free energies,
and mode-coupling theory of the glass transition, we determine both the
equilibrium phase diagram of the system and the lines of equilibrium between
the supercooled fluid and the glass phases. For these potentials, we study the
phase diagrams for different values of the potential range, the ratio of the
range of the interaction to the diameter of the repulsive core being the main
control parameter. Our arguments are relevant to a variety of systems, from
dense colloidal systems with depletion forces, through particle gels,
nano-particle aggregation, and globular protein crystallization.Comment: 20 pages, 10 figure
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