90 research outputs found
A mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid
Generalizing the mode-coupling theory for ideal liquid-glass transitions,
equations of motion are derived for the correlation functions describing the
glassy dynamics of a diatomic probe molecule immersed in a simple glass-forming
system. The molecule is described in the interaction-site representation and
the equations are solved for a dumbbell molecule consisting of two fused hard
spheres in a hard-sphere system. The results for the molecule's arrested
position in the glass state and the reorientational correlators for
angular-momentum index and near the glass transition are
compared with those obtained previously within a theory based on a
tensor-density description of the molecule in order to demonstrate that the two
approaches yield equivalent results. For strongly hindered reorientational
motion, the dipole-relaxation spectra for the -process can be mapped on
the dielectric-loss spectra of glycerol if a rescaling is performed according
to a suggestion by Dixon et al. [Phys. Rev. Lett. {\bf 65}, 1108 (1990)]. It is
demonstrated that the glassy dynamics is independent of the molecule's inertia
parameters.Comment: 19 pages, 10 figures, Phys. Rev. E, in prin
The Debye-Waller factor of liquid silica: Theory and simulation
We show that the prediction of mode-coupling theory for a model of a
network-forming strong glass-former correctly describes the wave-vector
dependence of the Debye-Waller factor. To obtain a good description it is
important to take into account the triplet correlation function c_3, which we
evaluate from a computer simulation. Our results support the possibility that
this theory is able to accurately describe the non-ergodicity parameters of
simple as well as of network-forming liquids.Comment: 5 pages of Latex, 3 figure
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
Computer Simulations of Supercooled Liquids and Glasses
After a brief introduction to the dynamics of supercooled liquids, we discuss
some of the advantages and drawbacks of computer simulations of such systems.
Subsequently we present the results of computer simulations in which the
dynamics of a fragile glass former, a binary Lennard-Jones system, is compared
to the one of a strong glass former, SiO_2. This comparison gives evidence that
the reason for the different temperature dependence of these two types of glass
formers lies in the transport mechanism for the particles in the vicinity of
T_c, the critical temperature of mode-coupling theory. Whereas the one of the
fragile glass former is described very well by the ideal version of
mode-coupling theory, the one for the strong glass former is dominated by
activated processes. In the last part of the article we review some simulations
of glass formers in which the dynamics below the glass transition temperature
was investigated. We show that such simulations might help to establish a
connection between systems with self generated disorder (e.g. structural
glasses) and quenched disorder (e.g. spin glasses).Comment: 37 pages of Latex, 11 figures, to appear as a Topical Review article
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
Conformational and Structural Relaxations of Poly(ethylene oxide) and Poly(propylene oxide) Melts: Molecular Dynamics Study of Spatial Heterogeneity, Cooperativity, and Correlated Forward-Backward Motion
Performing molecular dynamics simulations for all-atom models, we
characterize the conformational and structural relaxations of poly(ethylene
oxide) and poly(propylene oxide) melts. The temperature dependence of these
relaxation processes deviates from an Arrhenius law for both polymers. We
demonstrate that mode-coupling theory captures some aspects of the glassy
slowdown, but it does not enable a complete explanation of the dynamical
behavior. When the temperature is decreased, spatially heterogeneous and
cooperative translational dynamics are found to become more important for the
structural relaxation. Moreover, the transitions between the conformational
states cease to obey Poisson statistics. In particular, we show that, at
sufficiently low temperatures, correlated forward-backward motion is an
important aspect of the conformational relaxation, leading to strongly
nonexponential distributions for the waiting times of the dihedrals in the
various conformational statesComment: 13 pages, 13 figure
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
Glass transition in systems without static correlations: a microscopic theory
We present a first step toward a microscopic theory for the glass transition
in systems with trivial static correlations. As an example we have chosen N
infinitely thin hard rods with length L, fixed with their centers on a periodic
lattice with lattice constant a. Starting from the N-rod Smoluchowski equation
we derive a coupled set of equations for fluctuations of reduced k-rod
densities. We approximate the influence of the surrounding rods onto the
dynamics of a pair of rods by introduction of an effective rotational diffusion
tensor D and in this way we obtain a self-consistent equation for D. This
equation exhibits a feedback mechanism leading to a slowing down of the
relaxation. It involves as an input the Laplace transform v_0(l/r) at z=0,
l=L/a, of a torque-torque correlator of an isolated pair of rods with distance
R=ar. Our equation predicts the existence of a continuous ergodicity-breaking
transition at a critical length l_c=L_c/a. To estimate the critical length we
perform an approximate analytical calculation of v_0(l/r) based on a
variational approach and obtain l_c^{var}=5.68, 4.84 and 3.96 for an sc, bcc
and fcc lattice. We also evaluate v_0(l/r) numerically exactly from a two-rod
simulation. The latter calculation leads to l_c^{num}=3.45, 2.78 and 2.20 for
the corresponding lattices. Close to l_c the rotational diffusion constant
decreases as D(l) ~ (l_c - l)^\gamma with \gamma=1 and a diverging time scale
t_\epsilon ~ |l_c - l|^{-\delta}, \delta=2, appears. On this time scale the t-
and l-dependence of the 1-rod density is determined by a master function
depending only on t/t_\epsilon. In contrast to present microscopic theories our
approach predicts a glass transition despite the absence of any static
correlations.Comment: 22 pages, 7 figures (minor revisions in the text, corrected figures
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