154 research outputs found
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
Dynamic glass transition: bridging the gap between mode-coupling theory and the replica approach
We clarify the relation between the ergodicity breaking transition predicted
by mode-coupling theory and the so-called dynamic transition predicted by the
static replica approach. Following Franz and Parisi [Phys. Rev. Lett. 79, 2486
(1997)], we consider a system of particles in a metastable state characterized
by non-trivial correlations with a quenched configuration. We show that the
assumption that in a metastable state particle currents vanish leads to an
expression for the replica off-diagonal direct correlation function in terms of
a replica off-diagonal static four-point correlation function. A factorization
approximation for this function results in an approximate closure for the
replica off-diagonal direct correlation function. The replica off-diagonal
Ornstein-Zernicke equation combined with this closure coincides with the
equation for the non-ergodicity parameter derived using the mode-coupling
theory.Comment: revised version; to be published in EP
Profile blunting and flow blockage in a yield stress fluid: A molecular dynamics study
The flow of a simple glass forming system (a 80:20 binary Lennard-Jones
mixture) through a planar channel is studied via molecular dynamics
simulations. The flow is driven by an external body force similar to gravity.
Previous studies show that the model exhibits both a static [Varnik et al. J.
Chem. Phys. 120, 2788 (2004)] and a dynamic [F. Varnik and O. Henrich Phys.
Rev. B 73, 174209 (2006)] yield stress in the glassy phase. \blue{These
observations are corroborated by the present work, where we investigate how the
presence of a yield stress may affect the system behavior in a Poiseuille-type
flow geometry.} In particular, we observe a blunted velocity profile across the
channel: A relatively wide region in the channel center flows with a constant
velocity (zero shear rate) followed by a non linear change of the shear rate as
the walls are approached. The observed velocity gradients are compared to those
obtained from the knowledge of the shear stress across the channel and the
flow-curves (stress versus shear rate), the latter being determined in our
previous simulations of homogeneous shear flow. Furthermore, using the value of
the (dynamic) yield stress known from previous simulations, we estimate the
threshold body force for a complete arrest of the flow. Indeed, a blockage is
observed as the imposed force falls below this threshold value. Small but
finite shear rates are observed at stresses above the dynamic but below the
static yield stress. We discuss the possible role of the \blue{stick-slip like
motion} for this observation.Comment: 22 pages, 8 figure
Scaling behavior in the dynamics of a supercooled Lennard-Jones mixture
We present the results of a large scale molecular dynamics computer
simulation of a binary, supercooled Lennard-Jones fluid. At low temperatures
and intermediate times the time dependence of the intermediate scattering
function is well described by a von Schweidler law. The von Schweidler exponent
is independent of temperature and depends only weakly on the type of
correlator. For long times the correlation functions show a Kohlrausch behavior
with an exponent that is independent of temperature. This dynamical
behavior is in accordance with the mode-coupling theory of supercooled liquids.Comment: 6 pages, RevTex, three postscript figures available on request,
MZ-Physics-10
Microscopic theory for the glass transition in a system without static correlations
We study the orientational dynamics of infinitely thin hard rods of length L,
with the centers-of-mass fixed on a simple cubic lattice with lattice constant
a.We approximate the influence of the surrounding rods onto dynamics of a pair
of rods by introducing an effective rotational diffusion constant D(l),l=L/a.
We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a
time-dependent torque-torque correlator of an isolated pair of rods. A glass
transition occurs at l_c, if v(l_c)=1. We present a variational and a
numerically exact evaluation of v(l).Close to l_c the diffusion constant
decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a
glass transition in the absence of any static correlations, in contrast to
present form of mode coupling theory.Comment: 6 pages, 3 figure
Are there localized saddles behind the heterogeneous dynamics of supercooled liquids?
We numerically study the interplay between heterogeneous dynamics and
properties of negatively curved regions of the potential energy surface in a
model glassy system. We find that the unstable modes of saddles and
quasi-saddles undergo a localization transition close to the Mode-Coupling
critical temperature. We also find evidence of a positive spatial correlation
between clusters of particles having large displacements in the unstable modes
and dynamical heterogeneities.Comment: 7 pages, 3 figures, submitted to Europhys. Let
Atomic motions in the -region of glass-forming polymers: Molecular versus Mode Coupling Theory approach
We present fully atomistic Molecular Dynamics simulation results on a
main-chain polymer, 1,4-Polybutadiene, in the merging region of the -
and -relaxations. A real space analysis reveals the occurrence of
localized motions (``-like'') in addition to the diffusive structural
relaxation. A molecular approach provides a direct connection between the local
conformational changes reflected in the atomic motions and the secondary
relaxations in this polymer. Such local processes occur just in the time window
where the -process of the Mode Coupling Theory is expected. We show that
the application of this theory is still possible, and yields an unusually large
value of the exponent parameter. This result might originate from the
competition between two mechanisms for dynamic arrest: intermolecular packing
and intramolecular barriers for local conformational changes
(``-like'').Comment: 10 pages, 6 figure
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
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
Aging in a simple glassformer
Using molecular dynamics computer simulations we investigate the
out-of-equilibrium dynamics of a Lennard-Jones system after a quench from a
high temperature to one below the glass transition temperature. By studying the
radial distribution function we give evidence that during the aging the system
is very close to the critical surface of mode-coupling theory. Furthermore we
show that two-time correlation functions show a strong dependence on the
waiting time since the quench and that their shape is very different from the
one in equilibrium. By investigating the temperature and time dependence of the
frequency distribution of the normal modes we show that the energy of the
inherent structures can be used to define an effective (time dependent)
temperature of the aging system.Comment: Talk presented at ``Unifying Concepts in Glass Physics'', ICTP,
Trieste 15 - 18 September 1999; 12 pages of Late
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