355 research outputs found
Landscapes, dynamic heterogeneity and kinetic facilitation in a simple off-lattice model
We present a simple off-lattice hard-disc model that exhibits glassy
dynamics. The inherent structures are enumerated exactly, transitions between
metabasins are well understood, and the particle configurations that act to
facilitate dynamics are easily identified. The model readily maps to a coarse
grained dynamic facilitation description.Comment: 5 pages, 5 figures, submitted to PR
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
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
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
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
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
Freezing by Monte Carlo Phase-Switch
We describe a Monte Carlo procedure which allows sampling of the disjoint
configuration spaces associated with crystalline and fluid phases, within a
single simulation. The method utilises biased sampling techniques to enhance
the probabilities of gateway states (in each phase) which are such that a
global switch (to the other phase) can be implemented. Equilibrium
freezing-point parameters can be determined directly; statistical uncertainties
prescribed transparently; and finite-size effects quantified systematically.
The method is potentially quite general; we apply it to the freezing of hard
spheres.Comment: 5 pages, 2 figure
Stacking Entropy of Hard Sphere Crystals
Classical hard spheres crystallize at equilibrium at high enough density.
Crystals made up of stackings of 2-dimensional hexagonal close-packed layers
(e.g. fcc, hcp, etc.) differ in entropy by only about per sphere
(all configurations are degenerate in energy). To readily resolve and study
these small entropy differences, we have implemented two different
multicanonical Monte Carlo algorithms that allow direct equilibration between
crystals with different stacking sequences. Recent work had demonstrated that
the fcc stacking has higher entropy than the hcp stacking. We have studied
other stackings to demonstrate that the fcc stacking does indeed have the
highest entropy of ALL possible stackings. The entropic interactions we could
detect involve three, four and (although with less statistical certainty) five
consecutive layers of spheres. These interlayer entropic interactions fall off
in strength with increasing distance, as expected; this fall-off appears to be
much slower near the melting density than at the maximum (close-packing)
density. At maximum density the entropy difference between fcc and hcp
stackings is per sphere, which is roughly 30% higher
than the same quantity measured near the melting transition.Comment: 15 page
Properties of a continuous-random-network model for amorphous systems
We use a Monte Carlo bond-switching method to study systematically the
thermodynamic properties of a "continuous random network" model, the canonical
model for such amorphous systems as a-Si and a-SiO. Simulations show
first-order "melting" into an amorphous state, and clear evidence for a glass
transition in the supercooled liquid. The random-network model is also extended
to study heterogeneous structures, such as the interface between amorphous and
crystalline Si.Comment: Revtex file with 4 figure
Random Packings of Frictionless Particles
We study random packings of frictionless particles at T=0.
The packing fraction where the pressure becomes nonzero is the same as the
jamming threshold, where the static shear modulus becomes nonzero. The
distribution of threshold packing fractions narrows and its peak approaches
random close-packing as the system size increases. For packing fractions within
the peak, there is no self-averaging, leading to exponential decay of the
interparticle force distribution.Comment: 4 pages, 3 figure
- …