43 research outputs found
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
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
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
Molecular mode-coupling theory for supercooled liquids: Application to water
We present mode-coupling equations for the description of the slow dynamics
observed in supercooled molecular liquids close to the glass transition. The
mode-coupling theory (MCT) originally formulated to study the slow relaxation
in simple atomic liquids, and then extended to the analysis of liquids composed
by linear molecules, is here generalized to systems of arbitrarily shaped,
rigid molecules. We compare the predictions of the theory for the -vector
dependence of the molecular nonergodicity parameters, calculated by solving
numerically the molecular MCT equations in two different approximation schemes,
with ``exact'' results calculated from a molecular dynamics simulation of
supercooled water. The agreement between theory and simulation data supports
the view that MCT succeeds in describing the dynamics of supercooled molecular
liquids, even for network forming ones.Comment: 22 pages 4 figures Late
Supercooled Water and the Kinetic Glass Transition II: Collective Dynamics
In this article we study in detail the Q-vector dependence of the collective
dynamics in simulated deeply supercooled SPC/E water. The evolution of the
system has been followed for 250 ns at low T, allowing a clear identification
of a two step relaxation process. We present evidence in favor of the use of
the mode coupling theory for supercooled liquid as framework for the
description of the slow alpha-relaxation dynamics in SPC/E water,
notwithstanding the fact that the cage formation in this system is controlled
by the formation of an open network of hydrogen bonds as opposed to packing
constraints, as in the case of simple liquids.Comment: rev-tex + 9 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
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
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
Model for Glass Transition in a Binary fluid from a Mode Coupling approach
We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary
fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a
proper choice of the slow variables corresponding to the conservation laws. The
resulting model equations are solved in the long time limit to locate the
dynamic transition. The transition point from our model is considerably higher
than predicted in existing MCT models for binary systems. This is in agreement
with what is seen in Computer Simulation of binary fluids. fluids.Comment: 9 Pages, 3 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