Entropy, diffusivity, and structural order in liquids with waterlike anomalies

Abstract

The excess entropy, S e , defined as the difference between the entropies of the liquid and the ideal gas under identical density and temperature conditions, is shown to be the critical quantity connecting the structural, diffusional and density anomalies in water-like liquids. Based on simulations of silica and the two-scale ramp liquids, water-like density and diffusional anomalies can be seen as consequences of a characteristic non-monotonic density dependence of S e . The relationship between excess entropy, the order metrics and the structural anomaly can be understood using a pair correlation approximation to S e . 61.20.Qg,05.20.Jj The behaviour of water is anomalous when compared to simple liquids for which the structure and dynamics is dominated by strong, essentially isotropic, short-range repulsions [1,2].For example, over certain ranges of temperature and pressure,the density of water increases with temperature under isobaric conditions (density anomaly) while the self-diffusivity increases with density under isothermal conditions (diffusional anomaly). Experiments as well as simulations suggest that the anomalous thermodynamic and kinetic properties of water are due to the fluctuating, three-dimensional, locally tetrahedral hydrogen-bonded network. Water-like anomalies are seen in other tetrahedral network-forming liquids, such as silica, as well as in model liquids with isotropic core-softened or two-scale pair potentials [3,4,5,6,7,8,9,10,11].In the case of liquids such as water and silica, a quantitative connection between the structure of the tetrahedral network and the macroscopic density or temperature variables can be made by introducing order metrics to gauge the type as well as the extent of structural order [6,7]. The local tetrahedral order parameter, q tet , associated with an atom i (e.g. Si atom in SiO 2 ) is defined aswhere ψ jk is the angle between the bond vectors r ij and r ik where j and k label the four nearest neighbour atoms of the same type [6]. The translational order parameter, τ , measures the extent of pair correlations present in the system and is defined aswhere ξ = rρ 1/3 , r is the pair separation and ξ c is a suitably chosen cut-off distance [12].Since τ increases as the random close-packing limit is approached, it can be regarded as measuring the degree of density ordering. At a given temperature, q tet will show a maximum and τ will show a minimum as a function of density; the loci of these extrema in the order define a structurally anomalous region in the density-temperature (ρT ) plane. Within this structurally anomalous region, the tetrahedral and translational order parameters are found to be strongly correlated. The region of the density anomaly, where (∂ρ/∂T ) P > 0, is bounded by the structurally anomalous region. The diffusionally anomalous region ((∂D/∂ρ) T > 0) closely follows the boundaries of the structurally anomalous region, specially at low temperatures. In water, the structurally anomalous region encloses the region of anomalous diffusivit...

Phase diagram of Hertzian spheres

“…These multiple structural and dynamical anomalies, and their interrelation, has been seen before in bounded potentials, 29,30 in liquids with water-like anomalies 31 and colloids with short-ranged attractions. 32 This suggests that crystallization and fluid dynamics are inextricably connected, and that this connection is not independent of the underlying crystal structure.…”

Anomalies in a waterlike model confined between plates

“…Thermodynamic anomalies do not occur only in water, experiments for T e 40 , Ga, Bi, S 41,42 and Ge 15 T e 85 43 , liquid metals 44 and graphite 45 and simulations for silica [46][47][48] , silicon 49 and BeF 2 46 shown that these system also have thermodynamic anomalies. In addition, silica 48,50 and silicon 51 show diffusion anomalous behavior.…”

Self-Assembly and Water-like Anomalies in Janus Nanoparticles

“…In addition, silicon 33 and others material, as silica [34][35][36] shows thermodynamic anomalies 31 , while silicon 44 and silica 33,35,36,45 show a maximum in the diffusion coefficient at constant temperature. These systems and their density and diffusion anomalies can be described in an effective way by a two length scale core-softened potential.…”