476 research outputs found
Structural Relaxation and Mode Coupling in a Simple Liquid: Depolarized Light Scattering in Benzene
We have measured depolarized light scattering in liquid benzene over the
whole accessible temperature range and over four decades in frequency. Between
40 and 180 GHz we find a susceptibility peak due to structural relaxation. This
peak shows stretching and time-temperature scaling as known from
relaxation in glass-forming materials. A simple mode-coupling model provides
consistent fits of the entire data set. We conclude that structural relaxation
in simple liquids and relaxation in glass-forming materials are
physically the same. A deeper understanding of simple liquids is reached by
applying concepts that were originally developed in the context of
glass-transition research.Comment: submitted to New J. Phy
Critical Decay at Higher-Order Glass-Transition Singularities
Within the mode-coupling theory for the evolution of structural relaxation in
glass-forming systems, it is shown that the correlation functions for density
fluctuations for states at A_3- and A_4-glass-transition singularities can be
presented as an asymptotic series in increasing inverse powers of the logarithm
of the time t: , where
with p_n denoting some polynomial and x=ln (t/t_0). The results are
demonstrated for schematic models describing the system by solely one or two
correlators and also for a colloid model with a square-well-interaction
potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in
Colloidal Systems with Short-Range Attractions", Messina, Italy, December
2003 (submitted
Universal and non-universal features of glassy relaxation in propylene carbonate
It is demonstrated that the susceptibility spectra of supercooled propylene
carbonate as measured by depolarized-light-scattering, dielectric-loss, and
incoherent quasi-elastic neutron-scattering spectroscopy within the GHz window
are simultaneously described by the solutions of a two-component schematic
model of the mode-coupling theory (MCT) for the evolution of glassy dynamics.
It is shown that the universal beta-relaxation-scaling laws, dealing with the
asymptotic behavior of the MCT solutions, describe the qualitative features of
the calculated spectra. But the non-universal corrections to the scaling laws
render it impossible to achieve a complete quantitative description using only
the leading-order-asymptotic results.Comment: 37 pages, 16 figures, to be published in Phys. Rev.
A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system
Using a molecular dynamics computer simulation we determine the temperature
dependence of the partial structure factors for a binary Lennard-Jones system.
These structure factors are used as input data to solve numerically the
wave-vector dependent mode-coupling equations in the long time limit. Using the
so determined solutions, we compare the predictions of mode-coupling theory
(MCT) with the results of a previously done molecular dynamics computer
simulation [Phys. Rev. E 51, 4626 (1995), ibid. 52, 4134 (1995)]. From this
comparison we conclude that MCT gives a fair estimate of the critical coupling
constant, a good estimate of the exponent parameter, predicts the wave-vector
dependence of the various nonergodicity parameters very well, except for very
large wave-vectors, and gives also a very good description of the space
dependence of the various critical amplitudes. In an attempt to correct for
some of the remaining discrepancies between the theory and the results of the
simulation, we investigate two small (ad hoc) modifications of the theory. We
find that one modification gives a worse agreement between theory and
simulation, whereas the second one leads to an improved agreement.Comment: Figures available from W. Ko
Cooperativity Beyond Caging: Generalized Mode Coupling Theory
The validity of mode coupling theory (MCT) is restricted by an uncontrolled
factorization approximation of density correlations. The factorization can be
delayed and ultimately avoided, however, by explicitly including higher order
correlations. We explore this approach within a microscopically motivated
schematic model. Analytic tractability allows us to discuss in great detail the
impact of factorization at arbitrary order, including the limit of avoided
factorization. Our results indicate a coherent picture for the capabilities as
well as limitations of MCT. Moreover, including higher order correlations
systematically defers the transition and ultimately restores ergodicity.
Power-law divergence of the relaxation time is then replaced by continuous but
exponential growth.Comment: 4 pages, 2 figure
Multiple-scattering effects on incoherent neutron scattering in glasses and viscous liquids
Incoherent neutron scattering experiments are simulated for simple dynamic
models: a glass (with a smooth distribution of harmonic vibrations) and a
viscous liquid (described by schematic mode-coupling equations). In most
situations multiple scattering has little influence upon spectral
distributions, but it completely distorts the wavenumber-dependent amplitudes.
This explains an anomaly observed in recent experiments
Role of structural relaxations and vibrational excitations in the high-frequency dynamics of liquids and glasses
We present theoretical investigation on the high-frequency collective
dynamics in liquids and glasses at microscopic length scales and terahertz
frequency region based on the mode-coupling theory for ideal liquid-glass
transition. We focus on recently investigated issues from
inelastic-X-ray-scattering and computer-simulation studies for dynamic
structure factors and longitudinal and transversal current spectra: the
anomalous dispersion of the high-frequency sound velocity and the nature of the
low-frequency excitation called the boson peak. It will be discussed how the
sound mode interferes with other low-lying modes present in the system.
Thereby, we provide a systematic explanation of the anomalous sound-velocity
dispersion in systems -- ranging from high temperature liquid down to deep
inside the glass state -- in terms of the contributions from the
structural-relaxation processes and from vibrational excitations called the
anomalous-oscillation peak (AOP). A possibility of observing negative
dispersion -- the {\em decrease} of the sound velocity upon increase of the
wave number -- is argued when the sound-velocity dispersion is dominated by the
contribution from the vibrational dynamics. We also show that the low-frequency
excitation, observable in both of the glass-state longitudinal and transversal
current spectra at the same resonance frequency, is the manifestation of the
AOP. As a consequence of the presence of the AOP in the transversal current
spectra, it is predicted that the transversal sound velocity also exhibits the
anomalous dispersion. These results of the theory are demonstrated for a model
of the Lennard-Jones system.Comment: 25 pages, 22 figure
Spatial correlations in sheared isothermal liquids : From elastic particles to granular particles
Spatial correlations for sheared isothermal elastic liquids and granular
liquids are theoretically investigated. Using the generalized fluctuating
hydrodynamics, correlation functions for both the microscopic scale and the
macroscopic scale are obtained. The existence of the long-range correlation
functions obeying power laws has been confirmed. The validity of our
theoretical predictions have been verified from the molecular dynamics
simulation.Comment: 34 pages, 12 figure
Colloidal gelation and non-ergodicity transitions
Within the framework of the mode coupling theory (MCT) of structural
relaxation, mechanisms and properties of non-ergodicity transitions in rather
dilute suspensions of colloidal particles characterized by strong short-ranged
attractions are studied. Results building on the virial expansion for particles
with hard cores and interacting via an attractive square well potential are
presented, and their relevance to colloidal gelation is discussed.Comment: 10 pages, 4 figures; Talk at the Conference: "Unifying Concepts in
Glass Physics" ICTP Trieste, September 1999; to be published in J. Phys.:
Condens. Matte
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
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