Comparison of liquid-state anomalies in Stillinger-Weber models of water, silicon, and germanium

Abstract

We use molecular dynamics simulations to compare and contrast the liquid-state anomalies in the Stillinger-Weber models of monatomic water (mW), silicon (Si), and germanium (Ge) over a fairly wide range of temperatures and densities. The relationships between structure, entropy, and mobility, as well as the extent of the regions of anomalous behavior, are discussed as a function of the degree of tetrahedrality. We map out the cascade of density, structural, pair entropy, excess entropy, viscosity, and diffusivity anomalies for these three liquids. Among the three liquids studied here, only mW displays anomalies in the thermal conductivity, and this anomaly is evident only at very low temperatures. Diffusivity and viscosity, on the other hand, show pronounced anomalous regions for the three liquids. The temperature of maximum density of the three liquids shows re-entrant behavior consistent with either singularity-free or liquid-liquid critical point scenarios proposed to explain thermodynamic anomalies. The order-map, which shows the evolution of translational versus tetrahedral order in liquids, is different for Ge than for Si and mW. We find that although the monatomic water reproduces several thermodynamic and dynamic properties of rigid-body water models (e.g., SPC/E, TIP4P/2005), its sequence of anomalies follows, the same as Si and Ge, the silica-like hierarchy: the region of dynamic (diffusivity and viscosity) anomalies encloses the region of structural anomalies, which in turn encloses the region of density anomaly. The hierarchy of the anomalies based on excess entropy and Rosenfeld scaling, on the other hand, reverses the order of the structural and dynamic anomalies, i.e., predicts that the three Stillinger-Weber liquids follow a water-like hierarchy of anomalies. We investigate the scaling of diffusivity, viscosity, and thermal conductivity with the excess entropy of the liquid and find that for dynamical properties that present anomalies there is no universal scaling of the reduced property with excess entropy for the whole range of temperatures and densities. Instead, Rosenfeld's scaling holds for all the three liquids at high densities and high temperatures, although deviations from simple exponential dependence are observed for diffusivity and viscosity at lower temperatures and intermediate densities. The slope of the scaling of transport properties obtained for Ge is comparable to that obtained for simple liquids, suggesting that this low tetrahedrality liquid, although it stabilizes a diamond crystal, is already close to simple liquid behavior for certain properties.

Viscosity and self-diffusion of supercooled and stretched water from molecular dynamics simulations

“…At lower densities, where no experiment are available at present, our simulations yield a maximum in η versus ρ and a minimum in D versus ρ. The minimum in D has been previously observed in simulations 17,22,[24][25][26]36 . To our knowledge, the maximum in η is found here for the first time.…”

“…35 We are aware of only two simulation studies of viscosity in the supercooled region under pressure. The first by Dhabal et al 36 reported D and η for the coarse-grained mW model (monatomic water), and the density dependence gave a minimum and a maximum for D and a minimum for η. However, because it omits the reorientation of hydrogen atoms, mW gives D three times higher and η three times lower than experimental values for water at ambient conditions.…”

Two-structure thermodynamics for the TIP4P/2005 model of water covering supercooled and deeply stretched regions

“…50 Using a classical Stillinger-Weber (SW) potential, the cases of water, silicon, and germanium have been investigated: 40,51 as in TIP4P/2005 water, the TMD line does not touch the LVS, and the latter does not show a retracing behavior. In addition, for SW silicon, a line of compressibility maxima has also been reported.…”

Pattern of property extrema in supercooled and stretched water models and a new correlation for predicting the stability limit of the liquid state

“…For the systems that we consider, the loci of density, isothermal compressibility and isobaric heat capacity extrema, and the liquid-vapor spinodal exhibit a strikingly similar pattern. 23,50,51,57,62 The location of the critical points and the thermodynamic property extrema are clearly system-dependent, but the various extrema loci exhibit many common features imposed by thermodynamics. 23,62 In particular, the loci of response function maxima merge asymptotically at the LLCP.…”

“…Computer simulations, on the other hand, have shown that some molecular models of water exhibit liquid-liquid separation at deeply supercooled conditions. 22,[38][39][40][41][42][43][44][45][46][47][48] In tetrahedral systems, regardless of the existence or non-existence of the liquid-liquid separation (e.g., mW, [49][50][51] mTIP4P, 50 ST2, 52 The Journal of Chemical Physics ARTICLE scitation.org/journal/jcp TIP4P/2005, 53 TIP5P, 54 silicon, 30,31,55 silica, 32,33 and germanium 56 ), there is an underlying characteristic pattern of extrema lines for thermodynamic properties. The most wellknown is the line of density extrema, whose existence suggests a competition between low-density and high-density structures in the same liquid.…”