Assessing thermodynamic-dynamic relationships for waterlike liquids.

Here we investigate a family of isotropic waterlike glass-forming liquids, in which each thermodynamic state point corresponds to a different potential energy surface which is prescribed to reproduce the g(OO)(r;T,rho) of the reference TIP4P-Ew water model potential. Although each isotropic potential is simulated separately, together the family of isotropic potentials displays anomalous dynamics with density and fragile diffusivity with temperature. By removing a common energy landscape, and therefore expected thermodynamic trends with temperature within a single potential, we can more rigorously evaluate whether various entropic measures used in popular phenomenological thermodynamic theories can quantitatively predict the diffusivity or viscosity. We find that the Adam-Gibbs relation between diffusion (or viscosity) and the temperature scaled configurational entropy, S(c), is a poor predictor of fragility trends and density anomalies when necessary anharmonic corrections are added. By contrast the Dzugutov scaling relationship that uses the pair correlation approximation to S(excess) approximately S(2) provides excellent agreement for diffusion anomalies and for fragile dynamics for weakly supercooled states for the family of isotropic potentials, within a single isotropic potential, and for the TIP4P-Ew model, but deviates strongly in all three cases at more deeply supercooled temperatures. By studying the microscopic dynamics at these low temperatures, we find an increased heterogeneity in the mobility of particle populations reflected in a highly non-Gaussian distribution of particle displacements, even at very long time scales. We conclude that after the onset of dynamical heterogeneity, new consideration of higher structural correlations and/or more complex connectivity paths between basins through barriers appear to be critical for the formulation of a predictive theory for dynamics.