Investigation of the relation between local diffusivity and local inherent structures in the Kob-Andersen Lennard-Jones model

We analyze one thousand independent equilibrium trajectories of a system of 155 Lennard Jones particles to separate in a model-free approach the role of temperature and the role of the explored potential energy landscape basin depth in the particle dynamics. We show that the diffusion coefficient $D$ can be estimated as a sum over over contributions of the sampled basins, establishing a connection between thermodynamics and dynamics in the potential energy landscape framework. We provide evidence that the observed non-linearity in the relation between local diffusion and basin depth is responsible for the peculiar dynamic behavior observed in supercooled states and provide an interpretation for the presence of dynamic heterogeneities.Comment: minor text changes, references adde

Noro-Frenkel scaling in short-range square well: A Potential Energy Landscape study

We study the statistical properties of the potential energy landscape of a system of particles interacting via a very short-range square-well potential (of depth $-u_0$), as a function of the range of attraction $\Delta$ to provide thermodynamic insights of the Noro and Frenkel [ M.G. Noro and D. Frenkel, J.Chem.Phys. {\bf 113}, 2941 (2000)] scaling. We exactly evaluate the basin free energy and show that it can be separated into a {\it vibrational} ($\Delta$-dependent) and a {\it floppy} ($\Delta$-independent) component. We also show that the partition function is a function of $\Delta e^{\beta u_o}$, explaining the equivalence of the thermodynamics for systems characterized by the same second virial coefficient. An outcome of our approach is the possibility of counting the number of floppy modes (and their entropy).Comment: 4 pages, 4 figures accepted for publication on PR

Mode-Coupling Theory of Colloids with Short-range Attractions

Within the framework of the mode-coupling theory of super-cooled liquids, we investigate new phenomena in colloidal systems on approach to their glass transitions. When the inter-particle potential contains an attractive part, besides the usual repulsive hard core, two intersecting liquid-glass transition lines appear, one of which extends to low densities, while the other one, at high densities, shows a re-entrant behaviour. In the glassy region a new type of transition appears between two different types of glasses. The complex phenomenology can be described in terms of higher order glass transition singularities. The various glass phases are characterised by means of their viscoelastic properties. The glass driven by attractions has been associated to particle gels, and the other glass is the well known repulsive colloidal glass. These correspondences, in associations with the new predictions of glassy behaviour mean that such phenomena may be expected in colloidal systems with, for example, strong depletion or other short-ranged attractive potentials.Comment: 17 pages, 8 figure

Free energy surface of ST2 water near the liquid-liquid phase transition

We carry out umbrella sampling Monte Carlo simulations to evaluate the free energy surface of the ST2 model of water as a function two order parameters, the density and a bond-orientational order parameter. We approximate the long-range electrostatic interactions of the ST2 model using the reaction-field method. We focus on state points in the vicinity of the liquid-liquid critical point proposed for this model in earlier work. At temperatures below the predicted critical temperature we find two basins in the free energy surface, both of which have liquid-like bond orientational order, but differing in density. The pressure and temperature dependence of the shape of the free energy surface is consistent with the assignment of these two basins to the distinct low density and high density liquid phases previously predicted to occur in ST2 water.Comment: 8 pages, 9 figure

"Swarm relaxation": Equilibrating a large ensemble of computer simulations

It is common practice in molecular dynamics and Monte Carlo computer simulations to run multiple, separately-initialized simulations in order to improve the sampling of independent microstates. Here we examine the utility of an extreme case of this strategy, in which we run a large ensemble of $M$ independent simulations (a "swarm"), each of which is relaxed to equilibrium. We show that if $M$ is of order $10^3$, we can monitor the swarm's relaxation to equilibrium, and confirm its attainment, within $\sim 10\bar\tau$, where $\bar\tau$ is the equilibrium relaxation time. As soon as a swarm of this size attains equilibrium, the ensemble of $M$ final microstates from each run is sufficient for the evaluation of most equilibrium properties without further sampling. This approach dramatically reduces the wall-clock time required, compared to a single long simulation, by a factor of several hundred, at the cost of an increase in the total computational effort by a small factor. It is also well-suited to modern computing systems having thousands of processors, and is a viable strategy for simulation studies that need to produce high-precision results in a minimum of wall-clock time. We present results obtained by applying this approach to several test cases.Comment: 12 pages. To appear in Eur. Phy. J. E, 201

Thermodynamic and structural aspects of the potential energy surface of simulated water

Relations between the thermodynamics and dynamics of supercooled liquids approaching a glass transition have been proposed over many years. The potential energy surface of model liquids has been increasingly studied since it provides a connection between the configurational component of the partition function on one hand, and the system dynamics on the other. This connection is most obvious at low temperatures, where the motion of the system can be partitioned into vibrations within a basin of attraction and infrequent inter-basin transitions. In this work, we present a description of the potential energy surface properties of supercooled liquid water. The dynamics of this model has been studied in great details in the last years. Specifically, we locate the minima sampled by the liquid by ``quenches'' from equilibrium configurations generated via molecular dynamics simulations. We calculate the temperature and density dependence of the basin energy, degeneracy, and shape. The temperature dependence of the energy of the minima is qualitatively similar to simple liquids, but has anomalous density dependence. The unusual density dependence is also reflected in the configurational entropy, the thermodynamic measure of degeneracy. Finally, we study the structure of simulated water at the minima, which provides insight on the progressive tetrahedral ordering of the liquid on cooling

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

Transitions between Inherent Structures in Water

The energy landscape approach has been useful to help understand the dynamic properties of supercooled liquids and the connection between these properties and thermodynamics. The analysis in numerical models of the inherent structure (IS) trajectories -- the set of local minima visited by the liquid -- offers the possibility of filtering out the vibrational component of the motion of the system on the potential energy surface and thereby resolving the slow structural component more efficiently. Here we report an analysis of an IS trajectory for a widely-studied water model, focusing on the changes in hydrogen bond connectivity that give rise to many IS separated by relatively small energy barriers. We find that while the system \emph{travels} through these IS, the structure of the bond network continuously modifies, exchanging linear bonds for bifurcated bonds and usually reversing the exchange to return to nearly the same initial configuration. For the 216 molecule system we investigate, the time scale of these transitions is as small as the simulation time scale ($\approx 1$ fs). Hence for water, the transitions between each of these IS is relatively small and eventual relaxation of the system occurs only by many of these transitions. We find that during IS changes, the molecules with the greatest displacements move in small ``clusters'' of 1-10 molecules with displacements of $\approx 0.02-0.2$ nm, not unlike simpler liquids. However, for water these clusters appear to be somewhat more branched than the linear ``string-like'' clusters formed in a supercooled Lennar d-Jones system found by Glotzer and her collaborators.Comment: accepted in PR

Dynamics in a supercooled molecular liquid: Theory and Simulations

We report extensive simulations of liquid supercooled states for a simple three-sites molecular model, introduced by Lewis and Wahnstr"om [L. J. Lewis and G. Wahnstr"om, Phys. Rev. E 50, 3865 (1994)] to mimic the behavior of ortho-terphenyl. The large system size and the long simulation length allow to calculate very precisely --- in a large q-vector range --- self and collective correlation functions, providing a clean and simple reference model for theoretical descriptions of molecular liquids in supercooled states. The time and wavevector dependence of the site-site correlation functions are compared with detailed predictions based on ideal mode-coupling theory, neglecting the molecular constraints. Except for the wavevector region where the dynamics is controlled by the center of mass (around 9 nm-1), the theoretical predictions compare very well with the simulation data.

Numerical study of the glass-glass transition in short-ranged attractive colloids

We report extensive numerical simulations in the {\it glass} region for a simple model of short-ranged attractive colloids, the square well model. We investigate the behavior of the density autocorrelation function and of the static structure factor in the region of temperatures and packing fractions where a glass-glass transition is expected according to theoretical predictions. We strengthen our observations by studying both waiting time and history dependence of the numerical results. We provide evidence supporting the possibility that activated bond-breaking processes destabilize the attractive glass, preventing the full observation of a sharp glass-glass kinetic transition.Comment: 15 pages, 9 figures; Proceedings of "Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions", Messina, Italy, December 2003 (submitted to J. Phys.: Condens. Matt.