Erratum: “Relationship between thermodynamics and dynamics of supercooled liquids” [J. Chem. Phys. 125, 076102 (2006)]

Water and water-like liquids: relationships between structure, entropy and mobility

Liquids with very diverse underlying interactions share the thermodynamic and transport anomalies of water, including metalloids, ionic melts and mesoscopic fluids. The generic feature that characterises such water-like liquids is a density-driven shift in the nature of local order in the condensed phases. The key semiquantitative relationships between structural order, thermodynamics and transport that are necessary in order to map out the consequences of this common qualitative feature for liquid-state properties and phase transformations of such systems are reviewed here. The application of these ideas to understand and model tetrahedral liquids, especially water, is discussed and possible extensions to other complex fluids are considered.

Structural correlations and cooperative dynamics in supercooled liquids

The relationships between diffusivity and the excess, pair and residual multiparticle contributions to the entropy are examined for Lennard-Jones liquids and binary glassformers, in the context of approximate inverse power law mappings of simple liquids. In the dense liquid where diffusivities are controlled by collisions and cage relaxations, Rosenfeld-type excess entropy scaling of diffusivities is found to hold for both crystallizing as well as vitrifying liquids. The crucial differences between the two categories of liquids emerge only when local cooperative effects in the dynamics result in significant caging effects in the time-dependent behaviour of the single-particle mean square displacement. In the case of glassformers, onset of such local cooperativity coincides with onset of deviations from Rosenfeld-type excess entropy scaling of diffusivities and increasing spatiotemporal heterogeneity. In contrast, for two- and three-dimensional liquids with a propensity to crystallise, the onset of local cooperative dynamics is sufficient to trigger crystallization provided that the liquid is sufficiently supercooled that the free energy barrier to nucleation of the solid phase is negligible. The state points corresponding to onset of transient caging effects can be associated with typical values, within reasonable bounds, of the excess, pair, and residual multiparticle entropy as a consequence of the isomorph-invariant character of the excess entropy, diffusivity and related static and dynamic correlation functions.

Thermodynamic, diffusional, and structural anomalies in rigid-body water models

Structural, density, entropy, and diffusivity anomalies of the TIP4P/2005 model of water are mapped out over a wide range of densities and temperatures. The locus of temperatures of maximum density (TMD) for this model is very close to the experimental TMD locus for temperatures between 250 and 275 K. Four different water models (mTIP3P, TIP4P, TIP5P, and SPC/E) are compared with the TIP4P/2005 model in terms of their anomalous behavior. For all the water models, the density regimes for anomalous behavior are bounded by a low-density limit at around 0.85-0.90 g cm(-3) and a high-density limit at about 1.10-1.15 g cm(-3). The onset temperatures of the density anomaly in the various models show a much greater variation, ranging from 202 K for mTIP3P to 289 K for TIP5P. The order maps for the various water models are qualitatively very similar with the structurally anomalous regions almost superimposable in the q(tet)-τ plane. Comparison of the phase diagrams of water models with the region of liquid-state anomalies shows that the crystalline phases are much more sensitive to the choice of water models than the liquid state anomalies; for example, SPC/E and TIP4P/2005 show qualitatively similar liquid state anomalies but very different phase diagrams. The anomalies in the liquid in all the models occur at much lower pressures than those at which the melting line changes from negative to positive slope. The results in this study demonstrate several aspects of structure-entropy-diffusivity relationships of water models that can be compared with experiment and used to develop better atomistic and coarse-grained models for water.

Excess entropy scaling of dynamic quantities for fluids of dumbbell-shaped particles

We use molecular simulation to study the ability of entropy scaling relationships to describe the kinetic properties of two Lennard-Jones dumbbell models. We begin by examining the excess entropy, the key quantity used to correlate dynamic properties within entropy scaling strategies. We compute the thermodynamic excess entropy as well as contributions to the two-body excess entropy stemming from translational and orientational intermolecular correlations. Our results indicate that the total two-body contribution accounts for more than 70% of the thermodynamic excess entropy at all state conditions explored. For the two dumbbell models studied here, the orientational component of the two-body excess entropy dominates at moderate and high fluid densities. We next investigate the relationships between kinetic properties and various contributions to the excess entropy. Four dynamic properties are considered: translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediate-scattering function. We find that the thermodynamic excess entropy provides the best metric for describing kinetic properties. For each of the dynamic properties considered, reduced data collapse onto a common curve when expressed as a function of the thermodynamic excess entropy. The likelihood of a two-body contribution to the excess entropy serving as a reliable scaling variable is linked to the extent to which it correlates with the thermodynamic excess entropy. The total two-body term contributes significantly to the excess entropy, and therefore this quantity generally serves as a suitable scaling variable.