2,404 research outputs found
Investigation of -dependent dynamical heterogeneity in a colloidal gel by x-ray photon correlation spectroscopy
We use time-resolved X-Photon Correlation Spectroscopy to investigate the
slow dynamics of colloidal gels made of moderately attractive carbon black
particles. We show that the slow dynamics is temporally heterogeneous and
quantify its fluctuations by measuring the variance of the instantaneous
intensity correlation function. The amplitude of dynamical fluctuations has a
non-monotonic dependence on scattering vector , in stark contrast with
recent experiments on strongly attractive colloidal gels [Duri and Cipelletti,
\textit{Europhys. Lett.} \textbf{76}, 972 (2006)]. We propose a simple scaling
argument for the -dependence of fluctuations in glassy systems that
rationalizes these findings.Comment: Final version published in PR
Nonlinear effects in charge stabilized colloidal suspensions
Molecular Dynamics simulations are used to study the effective interactions
in charged stabilized colloidal suspensions. For not too high macroion charges
and sufficiently large screening, the concept of the potential of mean force is
known to work well. In the present work, we focus on highly charged macroions
in the limit of low salt concentrations. Within this regime, nonlinear
corrections to the celebrated DLVO theory [B. Derjaguin and L. Landau, Acta
Physicochem. USSR {\bf 14}, 633 (1941); E.J.W. Verwey and J.T.G. Overbeck, {\em
Theory of the Stability of Lyotropic Colloids} (Elsevier, Amsterdam, 1948)]
have to be considered. For non--bulklike systems, such as isolated pairs or
triples of macroions, we show, that nonlinear effects can become relevant,
which cannot be described by the charge renormalization concept [S. Alexander
et al., J. Chem. Phys. {\bf 80}, 5776 (1984)]. For an isolated pair of
macroions, we find an almost perfect qualitative agreement between our
simulation data and the primitive model. However, on a quantitative level,
neither Debye-H\"uckel theory nor the charge renormalization concept can be
confirmed in detail. This seems mainly to be related to the fact, that for
small ion concentrations, microionic layers can strongly overlap, whereas,
simultaneously, excluded volume effects are less important. In the case of
isolated triples, where we compare between coaxial and triangular geometries,
we find attractive corrections to pairwise additivity in the limit of small
macroion separations and salt concentrations. These triplet interactions arise
if all three microionic layers around the macroions exhibit a significant
overlap. In contrast to the case of two isolated colloids, the charge
distribution around a macroion in a triple is found to be anisotropic.Comment: 10 pages, 9 figure
Direct Numerical Simulations of Electrophoresis of Charged Colloids
We propose a numerical method to simulate electrohydrodynamic phenomena in
charged colloidal dispersions. This method enables us to compute the time
evolutions of colloidal particles, ions, and host fluids simultaneously by
solving Newton, advection-diffusion, and Navier--Stokes equations so that the
electrohydrodynamic couplings can be fully taken into account. The
electrophoretic mobilities of charged spherical particles are calculated in
several situations. The comparisons with approximation theories show
quantitative agreements for dilute dispersions without any empirical
parameters, however, our simulation predicts notable deviations in the case of
dense dispersions.Comment: 4pages, 3figures, to appear in Phys. Rev. Let
Structure of a liquid crystalline fluid around a macroparticle: Density functional theory study
The structure of a molecular liquid, in both the nematic liquid crystalline
and isotropic phases, around a cylindrical macroparticle, is studied using
density functional theory. In the nematic phase the structure of the fluid is
highly anisotropic with respect to the director, in agreement with results from
simulation and phenomenological theories. On going into the isotropic phase the
structure becomes rotationally invariant around the macroparticle with an
oriented layer at the surface.Comment: 10 pages, 6 figues. Submitted to Phys. Rev.
An order parameter equation for the dynamic yield stress in dense colloidal suspensions
We study the dynamic yield stress in dense colloidal suspensions by analyzing
the time evolution of the pair distribution function for colloidal particles
interacting through a Lennard-Jones potential. We find that the equilibrium
pair distribution function is unstable with respect to a certain anisotropic
perturbation in the regime of low temperature and high density. By applying a
bifurcation analysis to a system near the critical state at which the stability
changes, we derive an amplitude equation for the critical mode. This equation
is analogous to order parameter equations used to describe phase transitions.
It is found that this amplitude equation describes the appearance of the
dynamic yield stress, and it gives a value of 2/3 for the shear thinning
exponent. This value is related to the mean field value of the critical
exponent in the Ising model.Comment: 8 pages, 2 figure
Electric-field-induced displacement of a charged spherical colloid embedded in an elastic Brinkman medium
When an electric field is applied to an electrolyte-saturated polymer gel
embedded with charged colloidal particles, the force that must be exerted by
the hydrogel on each particle reflects a delicate balance of electrical,
hydrodynamic and elastic stresses. This paper examines the displacement of a
single charged spherical inclusion embedded in an uncharged hydrogel. We
present numerically exact solutions of coupled electrokinetic transport and
elastic-deformation equations, where the gel is treated as an incompressible,
elastic Brinkman medium. This model problem demonstrates how the displacement
depends on the particle size and charge, the electrolyte ionic strength, and
Young's modulus of the polymer skeleton. The numerics are verified, in part,
with an analytical (boundary-layer) theory valid when the Debye length is much
smaller than the particle radius. Further, we identify a close connection
between the displacement when a colloid is immobilized in a gel and its
velocity when dispersed in a Newtonian electrolyte. Finally, we describe an
experiment where nanometer-scale displacements might be accurately measured
using back-focal-plane interferometry. The purpose of such an experiment is to
probe physicochemical and rheological characteristics of hydrogel composites,
possibly during gelation
The Electric Double Layer Structure Around Charged Spherical Interfaces
We derive a formally simple approximate analytical solution to the
Poisson-Boltzmann equation for the spherical system via a geometric mapping.
Its regime of applicability in the parameter space of the spherical radius and
the surface potential is determined, and its superiority over the linearized
solution is demonstrated.Comment: 7 pages, 5 figure
Influence of polydispersity on the critical parameters of an effective potential model for asymmetric hard sphere mixtures
We report a Monte Carlo simulation study of the properties of highly
asymmetric binary hard sphere mixtures. This system is treated within an
effective fluid approximation in which the large particles interact through a
depletion potential (R. Roth {\em et al}, Phys. Rev. E{\bf 62} 5360 (2000))
designed to capture the effects of a virtual sea of small particles. We
generalize this depletion potential to include the effects of explicit size
dispersity in the large particles and consider the case in which the particle
diameters are distributed according to a Schulz form having degree of
polydispersity 14%. The resulting alteration (with respect to the monodisperse
limit) of the metastable fluid-fluid critical point parameters is determined
for two values of the ratio of the diameters of the small and large particles:
and . We find that inclusion of
polydispersity moves the critical point to lower reservoir volume fractions of
the small particles and high volume fractions of the large ones. The estimated
critical point parameters are found to be in good agreement with those
predicted by a generalized corresponding states argument which provides a link
to the known critical adhesion parameter of the adhesive hard sphere model.
Finite-size scaling estimates of the cluster percolation line in the one phase
fluid region indicate that inclusion of polydispersity moves the critical point
deeper into the percolating regime. This suggests that phase separation is more
likely to be preempted by dynamical arrest in polydisperse systems.Comment: 11 pages, 10 figure
Simple and Robust Solver for the Poisson-Boltzmann Equation
A variational approach is used to develop a robust numerical procedure for
solving the nonlinear Poisson-Boltzmann equation. Following Maggs et al., we
construct an appropriate constrained free energy functional, such that its
Euler-Lagrange equations are equivalent to the Poisson-Boltzmann equation. We
then develop, implement, and test an algorithm for its numerical minimization,
which is quite simple and unconditionally stable. The analytic solution for
planar geometry is used for validation. Furthermore, some results are presented
for a charged colloidal sphere surrounded by counterions.Comment: 11 pages, 5 figures, 2 table
Scattering series in mobility problem for suspensions
The mobility problem for suspension of spherical particles immersed in an
arbitrary flow of a viscous, incompressible fluid is considered in the regime
of low Reynolds numbers. The scattering series which appears in the mobility
problem is simplified. The simplification relies on the reduction of the number
of types of single-particle scattering operators appearing in the scattering
series. In our formulation there is only one type of single-particle scattering
operator.Comment: 11 page
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