111 research outputs found
The role of localization in glasses and supercooled liquids
This is the publisher's version, also available electronically from http://scitation.aip.org/content/aip/journal/jcp/104/13/10.1063/1.471147.Localized excitations (tunneling modes, soft harmonic vibrations) are believed to play a dominant role in the thermodynamics and transport properties of glasses at low temperature. Using instantaneous normalâmode (INM) analysis, we explore the role that such localization plays in determining the behavior of such systems in the vicinity of the glass transition. Building on our previous study [Phys. Rev. Lett. 74, 936 (1995)] we present evidence that the glass transition in two simple model systems is associated with a transition temperature below which all unâ stable INMâs become localized. This localization transition is a possible mechanism for the change in diffusion mechanism from continuous flow to localized hopping that is believed to occur in fragile glass formers at a temperature just above T g
Entropy, Dynamics and Instantaneous Normal Modes in a Random Energy Model
It is shown that the fraction f of imaginary frequency instantaneous normal
modes (INM) may be defined and calculated in a random energy model(REM) of
liquids. The configurational entropy S and the averaged hopping rate among the
states R are also obtained and related to f, with the results R~f and
S=a+b*ln(f). The proportionality between R and f is the basis of existing INM
theories of diffusion, so the REM further confirms their validity. A link to S
opens new avenues for introducing INM into dynamical theories. Liquid 'states'
are usually defined by assigning a configuration to the minimum to which it
will drain, but the REM naturally treats saddle-barriers on the same footing as
minima, which may be a better mapping of the continuum of configurations to
discrete states. Requirements of a detailed REM description of liquids are
discussed
Saddles in the energy landscape probed by supercooled liquids
We numerically investigate the supercooled dynamics of two simple model
liquids exploiting the partition of the multi-dimension configuration space in
basins of attraction of the stationary points (inherent saddles) of the
potential energy surface. We find that the inherent saddles order and potential
energy are well defined functions of the temperature T. Moreover, decreasing T,
the saddle order vanishes at the same temperature (T_MCT) where the inverse
diffusivity appears to diverge as a power law. This allows a topological
interpretation of T_MCT: it marks the transition from a dynamics between basins
of saddles (T>T_MCT) to a dynamics between basins of minima (T<T_MCT).Comment: 4 pages, 3 figures, to be published on PR
Energy landscape of a Lennard-Jones liquid: Statistics of stationary points
Molecular dynamics simulations are used to generate an ensemble of saddles of
the potential energy of a Lennard-Jones liquid. Classifying all extrema by
their potential energy u and number of unstable directions k, a well defined
relation k(u) is revealed. The degree of instability of typical stationary
points vanishes at a threshold potential energy, which lies above the energy of
the lowest glassy minima of the system. The energies of the inherent states, as
obtained by the Stillinger-Weber method, approach the threshold energy at a
temperature close to the mode-coupling transition temperature Tc.Comment: 4 RevTeX pages, 6 eps figures. Revised versio
Mean-atom-trajectory model for the velocity autocorrelation function of monatomic liquids
We present a model for the motion of an average atom in a liquid or
supercooled liquid state and apply it to calculations of the velocity
autocorrelation function and diffusion coefficient . The model
trajectory consists of oscillations at a distribution of frequencies
characteristic of the normal modes of a single potential valley, interspersed
with position- and velocity-conserving transits to similar adjacent valleys.
The resulting predictions for and agree remarkably well with MD
simulations of Na at up to almost three times its melting temperature. Two
independent processes in the model relax velocity autocorrelations: (a)
dephasing due to the presence of many frequency components, which operates at
all temperatures but which produces no diffusion, and (b) the transit process,
which increases with increasing temperature and which produces diffusion.
Because the model provides a single-atom trajectory in real space and time,
including transits, it may be used to calculate all single-atom correlation
functions.Comment: LaTeX, 8 figs. This is an updated version of cond-mat/0002057 and
cond-mat/0002058 combined Minor changes made to coincide with published
versio
Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"
We consider a system of coupled classical harmonic oscillators with spatially
fluctuating nearest-neighbor force constants on a simple cubic lattice. The
model is solved both by numerically diagonalizing the Hamiltonian and by
applying the single-bond coherent potential approximation. The results for the
density of states are in excellent agreement with each other. As
the degree of disorder is increased the system becomes unstable due to the
presence of negative force constants. If the system is near the borderline of
stability a low-frequency peak appears in the reduced density of states
as a precursor of the instability. We argue that this peak
is the analogon of the "boson peak", observed in structural glasses. By means
of the level distance statistics we show that the peak is not associated with
localized states
Molecular structural order and anomalies in liquid silica
The present investigation examines the relationship between structural order,
diffusivity anomalies, and density anomalies in liquid silica by means of
molecular dynamics simulations. We use previously defined orientational and
translational order parameters to quantify local structural order in atomic
configurations. Extensive simulations are performed at different state points
to measure structural order, diffusivity, and thermodynamic properties. It is
found that silica shares many trends recently reported for water [J. R.
Errington and P. G. Debenedetti, Nature 409, 318 (2001)]. At intermediate
densities, the distribution of local orientational order is bimodal. At fixed
temperature, order parameter extrema occur upon compression: a maximum in
orientational order followed by a minimum in translational order. Unlike water,
however, silica's translational order parameter minimum is broad, and there is
no range of thermodynamic conditions where both parameters are strictly
coupled. Furthermore, the temperature-density regime where both structural
order parameters decrease upon isothermal compression (the structurally
anomalous regime) does not encompass the region of diffusivity anomalies, as
was the case for water.Comment: 30 pages, 8 figure
String-like Clusters and Cooperative Motion in a Model Glass-Forming Liquid
A large-scale molecular dynamics simulation is performed on a glass-forming
Lennard-Jones mixture to determine the nature of dynamical heterogeneities
which arise in this model fragile liquid. We observe that the most mobile
particles exhibit a cooperative motion in the form of string-like paths
(``strings'') whose mean length and radius of gyration increase as the liquid
is cooled. The length distribution of the strings is found to be similar to
that expected for the equilibrium polymerization of linear polymer chains.Comment: 6 pages of RevTex, 6 postscript figures, uses epsf.st
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