Saddles in the energy landscape: extensivity and thermodynamic formalism

We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system size, as well as several approximations for the properties of low-order saddles (i.e., those with only a few unstable directions). We then cast the canonical partition function in a saddle-explicit form and develop, for the first time, a rigorous energy landscape approach capable of reproducing trends observed in simulations, in particular the temperature dependence of the energy and fractional order of sampled saddles.Comment: 4 pages, 1 figur

Variation of the glass transition temperature with rigidity and chemical composition

The effects of flexibility and chemical composition in the variation of the glass transition temperature are obtained by using the Lindemann criteria, that relates melting temperature with atomic vibrations. Using this criteria and that floppy modes at low frequencies enhance in a considerable way the average cuadratic displacement, we show that the consequence is a modified glass transition temperature. This approach allows to obtain in a simple way the empirically modified Gibbs-DiMarzio law, which has been widely used in chalcogenide glasses to fit the changes in the glass transition temperature with the chemical composition . The method predicts that the constant that appears in the law depends upon the ratio of two characteristic frequencies (or temperatures). Then, the constant for the Se-Ge-As glass is estimated by using the experimental density of vibrational states, and the result shows a very good agreement with the experimental fit from glass transition temperature variation

Scaling properties of critical bubble of homogeneous nucleation in stretched fluid of square-gradient density-functional model with triple-parabolic free energy

The square-gradient density-functional model with triple-parabolic free energy is used to study homogeneous bubble nucleation in a stretched liquid to check the scaling rule for the work of formation of the critical bubble as a function of scaled undersaturation $\Delta\mu/\Delta\mu_{\rm spin}$, the difference in chemical potential $\Delta\mu$ between the bulk undersaturated and saturated liquid divided by $\Delta\mu_{\rm spin}$ between the liquid spinodal and saturated liquid. In contrast to our study, a similar density-functional study for a Lennard-Jones liquid by Shen and Debenedetti [J. Chem. Phys. {\bf 114}, 4149 (2001)] found that not only the work of formation but other various quantities related to the critical bubble show the scaling rule, however, we found virtually no scaling relationships in our model near the coexistence. Although some quantities show almost perfect scaling relations near the spinodal, the work of formation divided by the value deduced from the classical nucleation theory shows no scaling in this model even though it correctly vanishes at the spinodal. Furthermore, the critical bubble does not show any anomaly near the spinodal as predicted many years ago. In particular, our model does not show diverging interfacial width at the spinodal, which is due to the fact that compressibility remains finite until the spinodal is reached in our parabolic models.Comment: 10 pages, 10 figures, Journal of Chemical Physics accepted for publicatio

Cooperative Origin of Low-Density Domains in Liquid Water

We study the size of clusters formed by water molecules possessing large enough tetrahedrality with respect to their nearest neighbors. Using Monte Carlo simulation of the SPC/E model of water, together with a geometric analysis based on Voronoi tessellation, we find that regions of lower density than the bulk are formed by accretion of molecules into clusters exceeding a minimum size. Clusters are predominantly linear objects and become less compact as they grow until they reach a size beyond which further accretion is not accompanied by a density decrease. The results suggest that the formation of "ice-like" regions in liquid water is cooperative.Comment: 16 pages, 6 figure

Energy landscape and rigidity

The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this effect. The model predicts a deviation from the Debye law at low temperatures. Then, the connection between the topography of the energy landscape, the topology of the phase space and the rigidity of a glass is explored. As a result, we relate the number of constraints and floppy modes with the statistics of the landscape. We apply these ideas to a simple model for which we provide an approximate expression for the number of energy basins as a function of the rigidity. This allows to understand certains features of the glass transition, like the jump in the specific heat or the reversible window observed in chalcogenide glasses.Comment: 1 text+3 eps 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

A closer look at arrested spinodal decomposition in protein solutions

Concentrated aqueous solutions of the protein lysozyme undergo a liquid solid transition upon a temperature quench into the unstable spinodal region below a characteristic arrest temperature of Tf=15C. We use video microscopy and ultra-small angle light scattering in order to investigate the arrested structures as a function of initial concentration, quench temperature and rate of the temperature quench. We find that the solid-like samples show all the features of a bicontinuous network that is formed through an arrested spinodal decomposition process. We determine the correlation length Xi and demonstrate that Xi exhibits a temperature dependence that closely follows the critical scaling expected for density fluctuations during the early stages of spinodal decomposition. These findings are in agreement with an arrest scenario based on a state diagram where the arrest or gel line extends far into the unstable region below the spinodal line. Arrest then occurs when during the early stage of spinodal decomposition the volume fraction phi2 of the dense phase intersects the dynamical arrest threshold phi2Glass, upon which phase separation gets pinned into a space-spanning gel network with a characteristic length Xi

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

Crystallization Mechanism of Hard Sphere Glasses

In supercooled liquids, vitrification generally suppresses crystallization. Yet some glasses can still crystallize despite the arrest of diffusive motion. This ill-understood process may limit the stability of glasses, but its microscopic mechanism is not yet known. Here we present extensive computer simulations addressing the crystallization of monodisperse hard-sphere glasses at constant volume (as in a colloid experiment). Multiple crystalline patches appear without particles having to diffuse more than one diameter. As these patches grow, the mobility in neighbouring areas is enhanced, creating dynamic heterogeneity with positive feedback. The future crystallization pattern cannot be predicted from the coordinates alone: crystallization proceeds by a sequence of stochastic micro-nucleation events, correlated in space by emergent dynamic heterogeneity.Comment: 4 pages 4 figures Accepted for publication in Phys. Rev. Lett., April 201

Thermodynamic behaviour and structural properties of an aqueous sodium chloride solution upon supercooling

We present the results of a molecular dynamics simulation study of thermodynamic and structural properties upon supercooling of a low concentration sodium chloride solution in TIP4P water and the comparison with the corresponding bulk quantities. We study the isotherms and the isochores for both the aqueous solution and bulk water. The comparison of the phase diagrams shows that thermodynamic properties of the solution are not merely shifted with respect to the bulk. Moreover, from the analysis of the thermodynamic curves, both the spinodal line and the temperatures of maximum density curve can be calculated. The spinodal line appears not to be influenced by the presence of ions at the chosen concentration, while the temperatures of maximum density curve displays both a mild shift in temperature and a shape modification with respect to bulk. Signatures of the presence of a liquid-liquid critical point are found in the aqueous solution. By analysing the water-ion radial distribution functions of the aqueous solution we observe that upon changing density, structural modifications appear close to the spinodal. For low temperatures additional modifications appear also for densities close to that corresponding to a low density configurational energy minimum.Comment: 10 pages, 13 figures, 2 tables. To be published in J. Chem. Phy