388 research outputs found
Evaluation of configurational entropy of a model liquid from computer simulations
Computer simulations have been employed in recent years to evaluate the
configurational entropy changes in model glass-forming liquids. We consider two
methods, both of which involve the calculation of the `intra-basin' entropy as
a means for obtaining the configurational entropy. The first method involves
the evaluation of the intra-basin entropy from the vibrational frequencies of
inherent structures, by making a harmonic approximation of the local potential
energy topography. The second method employs simulations that confine the
liquid within a localized region of configuration space by the imposition of
constraints; apart from the choice of the constraints, no further assumptions
are made. We compare the configurational entropies estimated for a model liquid
(binary mixture of particles interacting {\it via} the Lennard-Jones potential)
for a range of temperatures, at fixed density.Comment: 10 pages, 5 figures, Proceedings of "Unifying Concepts in Glass
Physics" Trieste 1999 (to appear in J. Phys. Cond. Mat.
The relationship between fragility, configurational entropy and the potential energy landscape of glass forming liquids
Glass is a microscopically disordered, solid form of matter that results when
a fluid is cooled or compressed in such a fashion that it does not crystallise.
Almost all types of materials are capable of glass formation -- polymers, metal
alloys, and molten salts, to name a few. Given such diversity, organising
principles which systematise data concerning glass formation are invaluable.
One such principle is the classification of glass formers according to their
fragility\cite{fragility}. Fragility measures the rapidity with which a
liquid's properties such as viscosity change as the glassy state is approached.
Although the relationship between features of the energy landscape of a glass
former, its configurational entropy and fragility have been analysed previously
(e. g.,\cite{speedyfr}), an understanding of the origins of fragility in these
features is far from being well established. Results for a model liquid, whose
fragility depends on its bulk density, are presented in this letter. Analysis
of the relationship between fragility and quantitative measures of the energy
landscape (the complicated dependence of energy on configuration) reveal that
the fragility depends on changes in the vibrational properties of individual
energy basins, in addition to the total number of such basins present, and
their spread in energy. A thermodynamic expression for fragility is derived,
which is in quantitative agreement with {\it kinetic} fragilities obtained from
the liquid's diffusivity.Comment: 8 pages, 3 figure
Liquid Limits: The Glass Transition and Liquid-Gas Spinodal Boundaries of Metastable Liquids
The liquid-gas spinodal and the glass transition define ultimate boundaries
beyond which substances cannot exist as (stable or metastable) liquids. The
relation between these limits is analyzed {\it via} computer simulations of a
model liquid. The results obtained indicate that the liquid - gas spinodal and
the glass transition lines intersect at a finite temperature, implying a glass
- gas mechanical instability locus at low temperatures. The glass transition
lines obtained by thermodynamic and dynamic criteria agree very well with each
other.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let
Potential Energy Landscape Equation of State
Depth, number, and shape of the basins of the potential energy landscape are
the key ingredients of the inherent structure thermodynamic formalism
introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys.
Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only
on the volume dependence of these landscape properties is derived. Vibrational
and configurational contributions to pressure are sorted out in a transparent
way. Predictions are successfully compared with data from extensive molecular
dynamics simulations of a simple model for the fragile liquid orthoterphenyl.Comment: RevTeX4, 4 pages, 5 figure
Two-dimensional lattice-fluid model with water-like anomalies
We investigate a lattice-fluid model defined on a two-dimensional triangular
lattice, with the aim of reproducing qualitatively some anomalous properties of
water. Model molecules are of the "Mercedes Benz" type, i.e., they possess a D3
(equilateral triangle) symmetry, with three bonding arms. Bond formation
depends both on orientation and local density. We work out phase diagrams,
response functions, and stability limits for the liquid phase, making use of a
generalized first order approximation on a triangle cluster, whose accuracy is
verified, in some cases, by Monte Carlo simulations. The phase diagram displays
one ordered (solid) phase which is less dense than the liquid one. At fixed
pressure the liquid phase response functions show the typical anomalous
behavior observed in liquid water, while, in the supercooled region, a
reentrant spinodal is observed.Comment: 9 pages, 1 table, 7 figure
The Glass Transition and Liquid-Gas Spinodal Boundaries of Metastable Liquids
A liquid can exist under conditions of thermodynamic stability or
metastability within boundaries defined by the liquid-gas spinodal and the
glass transition line. The relationship between these boundaries has been
investigated previously using computer simulations, the energy landscape
formalism, and simplified model calculations. We calculate these stability
boundaries semi-analytically for a model glass forming liquid, employing
accurate liquid state theory and a first-principles approach to the glass
transition. These boundaries intersect at a finite temperature, consistent with
previous simulation-based studies.Comment: Minor text revisions. Fig.s 4, 5 update
Energy landscapes, ideal glasses, and their equation of state
Using the inherent structure formalism originally proposed by Stillinger and
Weber [Phys. Rev. A 25, 978 (1982)], we generalize the thermodynamics of an
energy landscape that has an ideal glass transition and derive the consequences
for its equation of state. In doing so, we identify a separation of
configurational and vibrational contributions to the pressure that corresponds
with simulation studies performed in the inherent structure formalism. We
develop an elementary model of landscapes appropriate to simple liquids which
is based on the scaling properties of the soft-sphere potential complemented
with a mean-field attraction. The resulting equation of state provides an
accurate representation of simulation data for the Lennard-Jones fluid,
suggesting the usefulness of a landscape-based formulation of supercooled
liquid thermodynamics. Finally, we consider the implications of both the
general theory and the model with respect to the so-called Sastry density and
the ideal glass transition. Our analysis shows that a quantitative connection
can be made between properties of the landscape and a simulation-determined
Sastry density, and it emphasizes the distinction between an ideal glass
transition and a Kauzmann equal-entropy condition.Comment: 11 pages, 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
A test of non-equilibrium thermodynamics in glassy systems: the soft-sphere case
The scaling properties of the soft-sphere potential allow the derivation of
an exact expression for the pressure of a frozen liquid, i.e., the pressure
corresponding to configurations which are local minima in its multidimensional
potential energy landscape. The existence of such a relation offers the unique
possibility for testing the recently proposed extension of the liquid free
energy to glassy out-of-equilibrium conditions and the associated expression
for the temperature of the configurational degrees of freedom. We demonstrate
that the non-equilibrium free energy provides an exact description of the
soft-sphere pressure in glass states
Enumeration of distinct mechanically stable disk packings in small systems
We create mechanically stable (MS) packings of bidisperse disks using an
algorithm in which we successively grow or shrink soft repulsive disks followed
by energy minimization until the overlaps are vanishingly small. We focus on
small systems because this enables us to enumerate nearly all distinct MS
packings. We measure the probability to obtain a MS packing at packing fraction
and find several notable results. First, the probability is highly
nonuniform. When averaged over narrow packing fraction intervals, the most
probable MS packing occurs at the highest and the probability decays
exponentially with decreasing . Even more striking, within each
packing-fraction interval, the probability can vary by many orders of
magnitude. By using two different packing-generation protocols, we show that
these results are robust and the packing frequencies do not change
qualitatively with different protocols.Comment: 4 pages, 3 figures, Conference Proceedings for X International
Workshop on Disordered System
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