56 research outputs found
Tests of mode-coupling theory in two dimensions
We analyze the glassy dynamics of a binary mixtures of hard disks in two
dimensions. Predictions of the Mode-Coupling theory(MCT) are tested with
extensive Brownian dynamics simulations. Measuring the collective particle
density correlation functions in the vicinity of the glass transition we verify
four predicted mixing effects. For instance, for large size disparities, adding
a small amount of small particles at fixed packing fraction leads to a speed up
in the long time dynamics, while at small size disparity it leads to a slowing
down. Qualitative features of the non-ergodicity parameters and the
-relaxation which both depend in a non-trivial way on the mixing ratio
are found in the simulated correlators. Studying one system in detail we are
able to determine its ideal MCT glass transition point as and
test MCT predictions quantitatively.Comment: 12 pages, 18 figure
Comment on "Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition"
In the Letter [PRL 102, 085703 (2009)] Brambilla, et al. claimed to observe
activated dynamics in colloidal hard spheres above the critical packing
fraction of mode coupling theory (MCT). By performing microscopic MCT
calculations, we show that polydispersity in their system shifts the critical
packing fraction above the value determined by van Megen et al. for less
polydisperse samples, and that the data agree with theory except for, possibly,
the highest packing fraction.Comment: Comment in print in Phys. Rev. Lett.; for accompanying reply see
arXiv Brambilla et al. (Monday 18.10.2010
Hard discs under steady shear: comparison of Brownian dynamics simulations and mode coupling theory
Brownian dynamics simulations of bidisperse hard discs moving in two
dimensions in a given steady and homogeneous shear flow are presented close to
and above the glasstransition density. The stationary structure functions and
stresses of shear-melted glass are compared quantitatively to parameter-free
numerical calculations of monodisperse hard discs using mode coupling theory
within the integration through transients framework. Theory qualitatively
explains the properties of the yielding glass but quantitatively
overestimatesthe shear-driven stresses and structural anisotropies.Comment: 1. The original Phil. Trans. R. Soc. contains an error in the caption
of the y-axes of the upper left panel in figure 9: There's a factor
\dot{\gamma} missing in the denominato
Density Functional approach to Nonlinear Rheology
We present a density functional based closure of the pair Smoluchowski
equation for Brownian particles under shear flow. Given an equilibrium free
energy functional as input the theory provides first-principles predictions for
the flow-distorted pair correlation function and associated rheological
quantities over a wide range of volume fractions and flow rates. Taking
two-dimensional hard-disks under shear flow as an illustrative model we
calculate the pair correlation function, viscosity and normal stress difference
under both steady and start-up shear
Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation
We analyze the slow, glassy structural relaxation as measured through
collective and tagged-particle density correlation functions obtained from
Brownian dynamics simulations for a polydisperse system of quasi-hard spheres
in the framework of the mode-coupling theory of the glass transition (MCT).
Asymptotic analyses show good agreement for the collective dynamics when
polydispersity effects are taken into account in a multi-component calculation,
but qualitative disagreement at small when the system is treated as
effectively monodisperse. The origin of the different small- behaviour is
attributed to the interplay between interdiffusion processes and structural
relaxation. Numerical solutions of the MCT equations are obtained taking
properly binned partial static structure factors from the simulations as input.
Accounting for a shift in the critical density, the collective density
correlation functions are well described by the theory at all densities
investigated in the simulations, with quantitative agreement best around the
maxima of the static structure factor, and worst around its minima. A
parameter-free comparison of the tagged-particle dynamics however reveals large
quantiative errors for small wave numbers that are connected to the well-known
decoupling of self-diffusion from structural relaxation and to dynamical
heterogeneities. While deviations from MCT behaviour are clearly seen in the
tagged-particle quantities for densities close to and on the liquid side of the
MCT glass transition, no such deviations are seen in the collective dynamics.Comment: 23 pages, 26 figure
Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature and sampling time
The shear modulus G of two glass-forming colloidal model systems in d=3 and
d=2 dimensions is investigated by means of, respectively, molecular dynamics
and Monte Carlo simulations. Comparing ensembles where either the shear strain
gamma or the conjugated (mean) shear stress tau are imposed, we compute G from
the respective stress and strain fluctuations as a function of temperature T
while keeping a constant normal pressure P. The choice of the ensemble is seen
to be highly relevant for the shear stress fluctuations mu_F(T) which at
constant tau decay monotonously with T following the affine shear elasticity
mu_A(T), i.e. a simple two-point correlation function. At variance,
non-monotonous behavior with a maximum at the glass transition temperature T_g
is demonstrated for mu_F(T) at constant gamma. The increase of G below T_g is
reasonably fitted for both models by a continuous cusp singularity, G(T) is
proportional to (1-T/T_g)^(1/2), in qualitative agreement with some recent
replica calculations. It is argued, however, that longer sampling times may
lead to a sharper transition. The additive jump discontinuity predicted by
mode-coupling theory and other replica calculations thus cannot ultimately be
ruled out
Tagged-particle motion in glassy systems under shear: Comparison of mode coupling theory and Brownian Dynamics simulations
We study the dynamics of a tagged particle in a glassy system under shear.
The recently developed integration through transients approach based on mode
coupling theory, is continued to arrive at the equations for the tagged
particle correlators and the mean squared displacements. The equations are
solved numerically for a two dimensional system, including a nonlinear
stability analysis of the glass solution, the so called beta-analysis. We
perform Brownian Dynamics simulations in 2-D and compare with theory. After
switch on, transient glassy correlation functions show strong fingerprints of
the stress overshoot scenario, including, additionally to previously studied
superexponential decay, a shoulder-like slowing down after the overshoot. We
also find a new type of Taylor dispersion in glassy states which has intriguing
similarity to the known low density case. The theory qualitatively captures
most features of the simulations with quantitative deviations concerning the
shear induced timescales. We attribute these deviations to an underestimation
of the overshoot scenario in the theory.Comment: 22 pages, 28 figures, Eur. Phys. J. E (in print
Overshoots in stress strain curves: Colloid experiments and schematic mode coupling theory
The stress versus strain curves in dense colloidal dispersions under start-up
shear flow are investigated combining experiments on model core-shell
microgels, computer simulations of hard disk mixtures, and mode coupling
theory. In dense fluid and glassy states, the transient stresses exhibit first
a linear increase with the accumulated strain, then a maximum ('stress
overshoot') for strain values around 5%, before finally approaching the
stationary value, which makes up the flow curve. These phenomena arise in
well-equilibrated systems and for homogeneous flows, indicating that they are
generic phenomena of the shear-driven transient structural relaxation.
Microscopic mode coupling theory (generalized to flowing states by integration
through the transients) derives them from the transient stress correlations,
which first exhibit a plateau (corresponding to the solid-like elastic shear
modulus) at intermediate times, and then negative stress correlations during
the final decay. We introduce and validate a schematic model within mode
coupling theory which captures all of these phenomena and handily can be used
to jointly analyse linear and large-amplitude moduli, flow curves, and
stress-strain curves. This is done by introducing a new strain- and
time-dependent vertex into the relation between the the generalized shear
modulus and the transient density correlator.Comment: 21 pages, 13 figure
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