59 research outputs found
Glassy behavior of molecular crystals: A comparison between results from MD-simulation and mode coupling theory
We have investigated the glassy behavior of a molecular crystal built up with
chloroadamantane molecules. For a simple model of this molecule and a rigid fcc
lattice a MD simulation was performed from which we obtained the dynamical
orientational correlators and the ``self''
correlators , with ,
. Our investigations are for the diagonal correlators
. Since the lattice constant decreases with decreasing
temperature which leads to an increase of the steric hindrance of the
molecules, we find a strong slowing down of the relaxation. It has a high
sensitivity on , . For most , there is a two-step
relaxation process, but practically not for , ,
and . Our results are consistent with the -relaxation
scaling laws predicted by mode coupling theory from which we deduce the glass
transition temperature . From a first principle solution
of the mode coupling equations we find . Furthermore mode
coupling theory reproduces the absence of a two-step relaxation process for
, , and , but underestimates the critical
nonergodicity parameters by about 50 per cent for all other . It is
suggested that this underestimation originates from the anisotropic crystal
field which is not accounted for by mode coupling theory. Our results also
imply that phonons have no essential influence on the long time relaxation
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 Structures, Configurational Entropy and Slow Glassy Dynamics
We give a short introduction to the inherent structure approach, with
particular emphasis on the Stillinger and Weber decomposition, of glassy
systems. We present some of the results obtained in the framework of spin-glass
models and Lennard-Jones glasses. We discuss how to generalize the standard
Stillinger and Weber approach by including the entropy of inherent structures.
Finally we discuss why this approach is probably insufficient to describe the
behavior of some kinetically constrained models.Comment: 16 pages, 8 figures, Contribution to the ESF SPHINX meeting `Glassy
behaviour of kinetically constrained models' (Barcelona, March 22-25, 2001
Static and Dynamic Anomalies in a Repulsive Spherical Ramp Liquid: Theory and Simulation
We compare theoretical and simulation results for static and dynamic
properties for a model of particles interacting via a spherically symmetric
repulsive ramp potential. The model displays anomalies similar to those found
in liquid water, namely, expansion upon cooling and an increase of diffusivity
upon compression. In particular, we calculate the phase diagram from the
simulation and successfully compare it with the phase diagram obtained using
the Rogers-Young (RY) closure for the Ornstein-Zernike equation. Both the
theoretical and the numerical calculations confirm the presence of a line of
isobaric density maxima, and lines of compressibility minima and maxima.
Indirect evidence of a liquid-liquid critical point is found. Dynamic
properties also show anomalies. Along constant temperature paths, as the
density increases, the dynamics alternates several times between slowing down
and speeding up, and we associate this behavior with the progressive
structuring and de-structuring of the liquid. Finally we confirm that mode
coupling theory successfully predicts the non-monotonic behavior of dynamics
and the presence of multiple glass phases, providing strong evidence that
structure (the only input of mode coupling theory) controls dynamics.Comment: Static and Dynamic Anomalies in a Repulsive Spherical Ramp Liquid:
Theory and Simulatio
How does the relaxation of a supercooled liquid depend on its microscopic dynamics?
Using molecular dynamics computer simulations we investigate how the
relaxation dynamics of a simple supercooled liquid with Newtonian dynamics
differs from the one with a stochastic dynamics. We find that, apart from the
early beta-relaxation regime, the two dynamics give rise to the same relaxation
behavior. The increase of the relaxation times of the system upon cooling, the
details of the alpha-relaxation, as well as the wave vector dependence of the
Edwards-Anderson-parameters are independent of the microscopic dynamics.Comment: 6 pages of Latex, 4 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
Dynamics of supercooled liquids: density fluctuations and Mode Coupling Theory
We write equations of motion for density variables that are equivalent to
Newtons equations. We then propose a set of trial equations parameterised by
two unknown functions to describe the exact equations. These are chosen to best
fit the exact Newtonian equations. Following established ideas, we choose to
separate these trial functions into a set representing integrable motions of
density waves, and a set containing all effects of non-integrability. It
transpires that the static structure factor is fixed by this minimum condition
to be the solution of the Yvon-Born-Green (YBG) equation. The residual
interactions between density waves are explicitly isolated in their Newtonian
representation and expanded by choosing the dominant objects in the phase space
of the system, that can be represented by a dissipative term with memory and a
random noise. This provides a mapping between deterministic and stochastic
dynamics. Imposing the Fluctuation-Dissipation Theorem (FDT) allows us to
calculate the memory kernel. We write exactly the expression for it, following
two different routes, i.e. using explicitly Newtons equations, or instead,
their implicit form, that must be projected onto density pairs, as in the
development of the well-established Mode Coupling Theory (MCT). We compare
these two ways of proceeding, showing the necessity to enforce a new equation
of constraint for the two schemes to be consistent. Thus, while in the first
`Newtonian' representation a simple gaussian approximation for the random
process leads easily to the Mean Spherical Approximation (MSA) for the statics
and to MCT for the dynamics of the system, in the second case higher levels of
approximation are required to have a fully consistent theory
Fast relaxation in a fragile liquid under pressure
The incoherent dynamic structure factor of ortho-terphenyl has been measured
by neutron time-of-flight and backscattering technique in the pressure range
from 0.1 MPa to 240 MPa for temperatures between 301 K and 335 K.
Tagged-particle correlations in the compressed liquid decay in two steps. The
alpha-relaxation lineshape is independent of pressure, and the relaxation time
proportional to viscosity. A kink in the amplitude f_Q(P) reveals the onset of
beta relaxation. The beta-relaxation regime can be described by the
mode-coupling scaling function; amplitudes and time scales allow a consistent
determination of the critical pressure P_c(T). alpha and beta relaxation depend
in the same way on the thermodynamic state; close to the mode-coupling
cross-over, this dependence can be parametrised by an effective coupling Gamma
~ n*T**{-1/4}.Comment: 4 Pages of RevTeX, 4 figures (submitted to Physical Review Letters
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
Dynamical heterogeneities close to a colloidal gel
Dynamical heterogeneities in a colloidal fluid close to gelation are studied
by means of computer simulations. A clear distinction between some fast
particles and the rest, slow ones, is observed, yielding a picture of the gel
composed by two populations with different mobilities. Analyzing the statics
and dynamics of both sets of particles, it is shown that the slow particles
form a network of stuck particles, whereas the fast ones are able to move over
long distances. Correlation functions show that the environment of the fast
particles relaxes much faster than that of the slow ones, but at short times
the bonds between fast particles are longer lived due to the flexibility of
their structure. No string-like motion is observed for the fast particles, but
they occupy preferential sites in the surface of the structure formed by the
slow ones
- âŠ