88 research outputs found
Reorientational relaxation of a linear probe molecule in a simple glassy liquid
Within the mode-coupling theory (MCT) for the evolution of structural
relaxation in glass-forming liquids, correlation functions and susceptibility
spectra are calculated characterizing the rotational dynamics of a top-down
symmetric dumbbell molecule, consisting of two fused hard spheres immersed in a
hard-sphere system. It is found that for sufficiently large dumbbell
elongations, the dynamics of the probe molecule follows the same universal
glass-transition scenario as known from the MCT results of simple liquids. The
-relaxation process of the angular-index-j=1 response is stronger,
slower and less stretched than the one for j=2, in qualitative agreement with
results found by dielectric-loss and depolarized-light-scattering spectroscopy
for some supercooled liquids. For sufficiently small elongations, the
reorientational relaxation occurs via large-angle flips, and the standard
scenario for the glass-transition dynamics is modified for odd-j responses due
to precursor phenomena of a nearby type-A MCT transition. In this case, a major
part of the relaxation outside the transient regime is described qualitatively
by the -relaxation scaling laws, while the -relaxation scaling
law is strongly disturbed.Comment: 40 pages. 10 figures as GIF-files, to be published in Phys. Rev.
Inherent Structure Entropy of Supercooled Liquids
We present a quantitative description of the thermodynamics in a supercooled
binary Lennard Jones liquid via the evaluation of the degeneracy of the
inherent structures, i.e. of the number of potential energy basins in
configuration space. We find that for supercooled states, the contribution of
the inherent structures to the free energy of the liquid almost completely
decouples from the vibrational contribution. An important byproduct of the
presented analysis is the determination of the Kauzmann temperature for the
studied system. The resulting quantitative picture of the thermodynamics of the
inherent structures offers new suggestions for the description of equilibrium
and out-of-equilibrium slow-dynamics in liquids below the Mode-Coupling
temperature.Comment: 11 pages of Latex, 3 figure
Simulation study of Non-ergodicity Transitions: Gelation in Colloidal Systems with Short Range Attractions
Computer simulations were used to study the gel transition occurring in
colloidal systems with short range attractions. A colloid-polymer mixture was
modelled and the results were compared with mode coupling theory expectations
and with the results for other systems (hard spheres and Lennard Jones). The
self-intermediate scattering function and the mean squared displacement were
used as the main dynamical quantities. Two different colloid packing fractions
have been studied. For the lower packing fraction, -scaling holds and
the wave-vector analysis of the correlation function shows that gelation is a
regular non-ergodicity transition within MCT. The leading mechanism for this
novel non-ergodicity transition is identified as bond formation caused by the
short range attraction. The time scale and diffusion coefficient also show
qualitatively the expected behaviour, although different exponents are found
for the power-law divergences of these two quantities. The non-Gaussian
parameter was also studied and very large correction to Gaussian behaviour
found. The system with higher colloid packing fraction shows indications of a
nearby high-order singularity, causing -scaling to fail, but the
general expectations for non-ergodicity transitions still hold.Comment: 13 pages, 15 figure
Equilibration times in numerical simulation of structural glasses: Comparing parallel tempering and conventional molecular dynamics
Generation of equilibrium configurations is the major obstacle for numerical
investigation of the slow dynamics in supercooled liquid states. The parallel
tempering (PT) technique, originally proposed for the numerical equilibration
of discrete spin-glass model configurations, has recently been applied in the
study of supercooled structural glasses. We present an investigation of the
ability of parallel tempering to properly sample the liquid configuration space
at different temperatures, by mapping the PT dynamics into the dynamics of the
closest local potential energy minima (inherent structures). Comparing the PT
equilibration process with the standard molecular dynamics equilibration
process we find that the PT does not increase the speed of equilibration of the
(slow) configurational degrees of freedom.Comment: 5 pages, 3 figure
The mean-squared displacement of a molecule moving in a glassy system
The mean-squared displacement (MSD) of a hard sphere and of a dumbbell
molecule consisting of two fused hard spheres immersed in a dense hard-sphere
system is calculated within the mode-coupling theory for ideal liquid-glass
transitions. It is proven that the velocity correlator, which is the second
time derivative of the MSD, is the negative of a completely monotone function
for times within the structural-relaxation regime. The MSD is found to exhibit
a large time interval for structural relaxation prior to the onset of the
-process which cannot be described by the asymptotic formulas for the
mode-coupling-theory-bifurcation dynamics. The -process for molecules
with a large elongation is shown to exhibit an anomalously wide cross-over
interval between the end of the von-Schweidler decay and the beginning of
normal diffusion. The diffusivity of the molecule is predicted to vary
non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin
Multiple glass transitions in star polymer mixtures: Insights from theory and simulations
The glass transition in binary mixtures of star polymers is studied by mode
coupling theory and extensive molecular dynamics computer simulations. In
particular, we have explored vitrification in the parameter space of size
asymmetry and concentration of the small star polymers at
fixed concentration of the large ones. Depending on the choice of parameters,
three different glassy states are identified: a single glass of big polymers at
low and low , a double glass at high and low
, and a novel double glass at high and high which is
characterized by a strong localization of the small particles. At low
and high there is a competition between vitrification and phase
separation. Centered in the -plane, a liquid lake shows up
revealing reentrant glass formation. We compare the behavior of the dynamical
density correlators with the predictions of the theory and find remarkable
agreement between the two.Comment: 15 figures, to be published in Macromolecule
Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
This review reports on the research done during the past years on violations
of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused
on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy
systems and the currently supporting knowledge gained from numerical simulation
studies. It covers a broad range of non-stationary aging and stationary driven
systems such as structural-glasses, spin-glasses, coarsening systems,
ferromagnetic models at criticality, trap models, models with entropy barriers,
kinetically constrained models, sheared systems and granular media. The review
is divided into four main parts: 1) An introductory section explaining basic
notions related to the existence of the FDT in equilibrium and its possible
extension to the glassy regime (QFDT), 2) A description of the basic analytical
tools and results derived in the framework of some exactly solvable models, 3)
A detailed report of the current evidence in favour of the QFDT and 4) A brief
digression on the experimental evidence in its favour. This review is intended
for inexpert readers who want to learn about the basic notions and concepts
related to the existence of the QFDT as well as for the more expert readers who
may be interested in more specific results.Comment: 120 pages, 37 figures. Topical review paper . Several typos and
misprints corrected, new references included and others updated. to be
published in J. Phys. A (Math. Gen.
Aspects of the dynamics of colloidal suspensions: Further results of the mode-coupling theory of structural relaxation
Results of the idealized mode-coupling theory for the structural relaxation
in suspensions of hard-sphere colloidal particles are presented and discussed
with regard to recent light scattering experiments. The structural relaxation
becomes non-diffusive for long times, contrary to the expectation based on the
de Gennes narrowing concept. A semi-quantitative connection of the wave vector
dependences of the relaxation times and amplitudes of the final
-relaxation explains the approximate scaling observed by Segr{\`e} and
Pusey [Phys. Rev. Lett. {\bf 77}, 771 (1996)]. Asymptotic expansions lead to a
qualitative understanding of density dependences in generalized Stokes-Einstein
relations. This relation is also generalized to non-zero frequencies thereby
yielding support for a reasoning by Mason and Weitz [Phys. Rev. Lett {\bf 74},
1250 (1995)]. The dynamics transient to the structural relaxation is discussed
with models incorporating short-time diffusion and hydrodynamic interactions
for short times.Comment: 11 pages, 9 figures; to be published in Phys. Rev.
Technical Report on the Design, Construction, Commissioning and Operation of the Super-FRS of FAIR
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