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.

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

Jamming transitions in amorphous packings of frictionless spheres occur over a continuous range of volume fractions

We numerically produce fully amorphous assemblies of frictionless spheres in three dimensions and study the jamming transition these packings undergo at large volume fractions. We specify four protocols yielding a critical value for the jamming volume fraction which is sharply defined in the limit of large system size, but is different for each protocol. Thus, we directly establish the existence of a continuous range of volume fraction where nonequilibrium jamming transitions occur. However, these jamming transitions share the same critical behaviour. Our results suggest that, even in the absence of partial crystalline ordering, a unique location of a random close packing does not exist, and that volume fraction alone is not sufficient to describe the properties of jammed states.Comment: 5 pages, 3 fig

On the liquid-glass transition line in monatomic Lennard-Jones fluids

A thermodynamic approach to derive the liquid-glass transition line in the reduced temperature vs reduced density plane for a monatomic Lennard-Jones fluid is presented. The approach makes use of a recent reformulation of the classical perturbation theory of liquids [M. Robles and M. L\'opez de Haro, Phys. Chem. Chem. Phys. {\bf 3}, 5528 (2001)] which is at grips with a rational function approximation for the Laplace transform of the radial distribution function of the hard-sphere fluid. The only input required is an equation of state for the hard-sphere system. Within the Mansoori-Canfield/Rasaiah-Stell variational perturbation theory, two choices for such an equation of state, leading to a glass transition for the hard-sphere fluid, are considered. Good agreement with the liquid-glass transition line derived from recent molecular dynamic simulations [Di Leonardo et al., Phys. Rev. Lett. {\bf 84}, 6054(2000)] is obtained.Comment: 4 pages, 2 figure

Diffusion in simple fluids

Computed self diffusion coefficients for the Lennard-Jones and hard sphere fluids are related by Dej = DNs(aB) exp (--e/2kB T) where σB=σLJ(2/[1+ii(1+2kBT/ε)])1/6, the effective hard sphere diameter, is the (average) distance of closest approach in collisions between molecules which interact with the positive part of the LJ potential, and the Arrhenius term reflects the influence of the negative part. σLJ and ε are the size and well depth parameters. Measured diffusion coefficients of the halomethane liquids are reproduced by the equation over wide ranges of temperature and density and do not reveal any influence of the inelastic effects associated with molecular anisotropy

Physics of the liquid-liquid critical point

Within the inherent structure (IS) thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A {\bf 25}, 978 (1982)] we address the basic question of the physics of the liquid-liquid transition and of density maxima observed in some complex liquids such as water by identifying, for the first time, the statistical properties of the potential energy landscape (PEL) responsible for these anomalies. We also provide evidence of the connection between density anomalies and the liquid-liquid critical point. Within the simple (and physically transparent) model discussed, density anomalies do imply the existence of a liquid-liquid transition.Comment: Physical Review Letters, in publicatio

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

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

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