94 research outputs found
Test of mode coupling theory for a supercooled liquid of diatomic molecules. II. q-dependent orientational correlators
Using molecular dynamics computer simulations we study the dynamics of a
molecular liquid by means of a general class of time-dependent correlators
S_{ll'}^m(q,t) which explicitly involve translational (TDOF) and orientational
degrees of freedom (ODOF). The system is composed of rigid, linear molecules
with Lennard- Jones interactions. The q-dependence of the static correlators
S_{ll'}^m(q) strongly depend on l, l' and m. The time dependent correlators are
calculated for l=l'. A thorough test of the predictions of mode coupling theory
(MCT) is performed for S_{ll}^m(q,t) and its self part S_{ll}^{(s)m}(q,t), for
l=1,..,6. We find a clear signature for the existence of a single temperature
T_c, at which the dynamics changes significantly. The first scaling law of MCT,
which involves the critical correlator G(t), holds for l>=2, but no critical
law is observed. Since this is true for the same exponent parameter lambda as
obtained for the TDOF, we obtain a consistent description of both, the TDOF and
ODOF, with the exception of l=1. This different behavior for l \ne 1 and l=1
can also be seen from the corresponding susceptibilities
(chi'')_{ll}^m(q,omega) which exhibit a minimum at about the same frequency
omega_{min} for all q and all l \ne 1, in contrast to (chi'')_{11}^m(q,omega)
for which omega'_{min} approx 10 omega_{min} . The asymptotic regime, for which
the first scaling law holds, shrinks with increasing l. The second scaling law
of MCT (time-temperature superposition principle) is reasonably fulfilled for l
\ne 1 but not for l=1. Furthermore we show that the q- and (l,m)-dependence of
the self part approximately factorizes, i.e. S_{ll}^{(s)m}(q,t) \cong
C_l^{(s)}(t) F_s(q,t) for all m.Comment: 11 pages of RevTex, 16 figure
Structural relaxation in a system of dumbbell molecules
The interaction-site-density-fluctuation correlators, the dipole-relaxation
functions, and the mean-squared displacements of a system of symmetric
dumbbells of fused hard spheres are calculated for two representative
elongations of the molecules within the mode-coupling theory for the evolution
of glassy dynamics. For large elongations, universal relaxation laws for states
near the glass transition are valid for parameters and time intervals similar
to the ones found for the hard-sphere system. Rotation-translation coupling
leads to an enlarged crossover interval for the mean-squared displacement of
the constituent atoms between the end of the von Schweidler regime and the
beginning of the diffusion process. For small elongations, the superposition
principle for the reorientational -process is violated for parameters
and time intervals of interest for data analysis, and there is a strong
breaking of the coupling of the -relaxation scale for the diffusion
process with that for representative density fluctuations and for dipole
reorientations.Comment: 15 pages, 14 figures, Phys. Rev. E in pres
Test of mode coupling theory for a supercooled liquid of diatomic molecules.I. Translational degrees of freedom
A molecular dynamics simulation is performed for a supercooled liquid of
rigid diatomic molecules. The time-dependent self and collective density
correlators of the molecular centers of mass are determined and compared with
the predictions of the ideal mode coupling theory (MCT) for simple liquids.
This is done in real as well as in momentum space. One of the main results is
the existence of a unique transition temperature T_c, where the dynamics
crosses over from an ergodic to a quasi-nonergodic behavior. The value for T_c
agrees with that found earlier for the orientational dynamics within the error
bars. In the beta- regime of MCT the factorization of space- and time
dependence is satisfactorily fulfilled for both types of correlations. The
first scaling law of ideal MCT holds in the von Schweidler regime, only, since
the validity of the critical law can not be confirmed, due to a strong
interference with the microscopic dynamics. In this first scaling regime a
consistent description within ideal MCT emerges only, if the next order
correction to the asymptotic law is taken into account. This correction is
almost negligible for q=q_max, the position of the main peak in the static
structure factor S(q), but becomes important for q=q_min, the position of its
first minimum. The second scaling law, i.e. the time-temperature superposition
principle, holds reasonably well for the self and collective density
correlators and different values for q. The alpha-relaxation times tau_q^(s)
and tau_q follow a power law in T-T_c over 2 -- 3 decades. The corresponding
exponent gamma is weakly q-dependent and is around 2.55. This value is in
agreement with the one predicted by MCT from the value of the von Schweidler
exponent but at variance with the corresponding exponent gammaComment: 14 pages of RevTex, 19 figure
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.
Static and Dynamic Properties of a Viscous Silica Melt Molecular Dynamics Computer Simulations
We present the results of a large scale molecular dynamics computer
simulation in which we investigated the static and dynamic properties of a
silica melt in the temperature range in which the viscosity of the system
changes from O(10^-2) Poise to O(10^2) Poise. We show that even at temperatures
as high as 4000 K the structure of this system is very similar to the random
tetrahedral network found in silica at lower temperatures. The temperature
dependence of the concentration of the defects in this network shows an
Arrhenius law. From the partial structure factors we calculate the neutron
scattering function and find that it agrees very well with experimental neutron
scattering data. At low temperatures the temperature dependence of the
diffusion constants shows an Arrhenius law with activation energies which
are in very good agreement with the experimental values. With increasing
temperature we find that this dependence shows a cross-over to one which can be
described well by a power-law, D\propto (T-T_c)^gamma. The critical temperature
T_c is 3330 K and the exponent gamma is close to 2.1. Since we find a similar
cross-over in the viscosity we have evidence that the relaxation dynamics of
the system changes from a flow-like motion of the particles, as described by
the ideal version of mode-coupling theory, to a hopping like motion. We show
that such a change of the transport mechanism is also observed in the product
of the diffusion constant and the life time of a Si-O bond, or the space and
time dependence of the van Hove correlation functions.Comment: 30 pages of Latex, 14 figure
Dynamics of the rotational degrees of freedom in a supercooled liquid of diatomic molecules
Using molecular dynamics computer simulations, we investigate the dynamics of
the rotational degrees of freedom in a supercooled system composed of rigid,
diatomic molecules. The interaction between the molecules is given by the sum
of interaction-site potentials of the Lennard-Jones type. In agreement with
mode-coupling theory (MCT), we find that the relaxation times of the
orientational time correlation functions C_1^(s), C_2^(s) and C_1 show at low
temperatures a power-law with the same critical temperature T_c, and which is
also identical to the critical temperature for the translational degrees of
freedom. In contrast to MCT we find, however, that for these correlators the
time-temperature superposition principle does not hold well and that also the
critical exponent gamma depends on the correlator. We also study the
temperature dependence of the rotational diffusion constant D_r and demonstrate
that at high temperatures D_r is proportional to the translational diffusion
constant D and that when the system starts to become supercooled the former
shows an Arrhenius behavior whereas the latter exhibits a power-law dependence.
We discuss the origin for the difference in the temperature dependence of D (or
the relaxation times of C_l^(s) and D_r. Finally we present results which show
that at low temperatures 180 degree flips of the molecule are an important
component of the relaxation dynamics for the orientational degrees of freedom.Comment: 17 pages of RevTex, 12 figure
Molecular mode-coupling theory applied to a liquid of diatomic molecules
We study the molecular mode coupling theory for a liquid of diatomic
molecules. The equations for the critical tensorial nonergodicity parameters
and the critical amplitudes of the - relaxation
are solved up to a cut off = 2 without any
further approximations.
Here are indices of spherical harmonics. Contrary to previous studies,
where additional approximations were applied, we find in agreement with
simulations, that all molecular degrees of freedom vitrify at a single
temperature . The theoretical results for the non ergodicity parameters
and the critical amplitudes are compared with those from simulations. The
qualitative agreement is good for all molecular degrees of freedom. To study
the influence of the cut off on the non ergodicity parameter, we also calculate
the non ergodicity parameters for an upper cut off . In addition we
also propose a new method for the calculation of the critical nonergodicity
parameterComment: 27 pages, 17 figure
Propylene Carbonate Reexamined: Mode-Coupling Scaling without Factorisation ?
The dynamic susceptibility of propylene carbonate in the moderately viscous
regime above is reinvestigated by incoherent neutron and
depolarised light scattering, and compared to dielectric loss and solvation
response. Depending on the strength of relaxation, a more or less
extended scaling regime is found. Mode-coupling fits yield consistently
and K, although different positions of the
susceptibility minimum indicate that not all observables have reached the
universal asymptotics
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
A semi-schematic model for the center of mass dynamics in supercooled molecular liquids
We introduce a semi-schematic mode-coupling model to describe the slow
dynamics in molecular liquids, retaining explicitly only the description of the
center of mass degrees of freedom. Angular degrees of freedom are condensed in
a q-vector independent coupling parameter. We compare the time and q-dependence
of the density fluctuation correlators with numerical data from a 250 ns long
molecular dynamics simulation. Notwithstanding the choice of a network-forming
liquid as a model for comparing theory and simulation, the model describes the
main static and dynamic features of the relaxation in a broad q-vector range.Comment: Revtex, 2 figure
- …