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We investigate the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid-liquid critical point in (i) Two models of water, TIP 5P and ST2, which display a first order liquid-liquid phase tr ansition at low temperatures; (ii) the Jagla model, a spherically symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactio ns; and (iii) A Hamiltonian model of water where the idea of two length/energy scales is built in; this model also displays a first order liquid-liquid phase transition at low temperatures b esides the first order liquid-gas phase transition at high te mperatures. We find a correlation between the dynamic fragility crossove r and the locus of specific heat maxima Cmax P ("Widom line") emanating from the critical point. Our findings are consiste nt with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dy namics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connectio n between Cmax P and the dynamic crossover is not limited to the case of water, a hydrogen bonded network liquid, but is a more general feature of crossing the Widom line, an extension of the first-order coexistence line in the supercritical reg ion. We present evidence from experiments and computer simulations supporting the hypothesis that water displays polyamorphism, i.e., water separates into two distinct liquid phases. T his concept of a new liquid-liquid phase transition is finding applicati on to other liquids as well as water, such as silicon and silic a. We also discuss related puzzles, such as the mysterious behavior of confined water and the "skin" of hydration water near a biomolecule. Specifically, using molecular dynamics simu lations, we also investigate the relation between the dynamic transitions of biomolecules (lysozyme and DNA) and the dynamic and thermodynamic properties of hydration water. We find that the dynamic transition of the macromolecules, sometimes called a "protein glass transition", occurs at the temper ature of dynamic crossover in the diffusivity of hydration water, and also coincides with the maxima of the isobaric specific heat CP and the temperature derivative of the orientational order p arameter. We relate these findings to the hypothesis of a liqu id-liquid critical point in water. Our simulations are consistent wit h the possibility that the protein glass transition results from a change in the behavior of hydration water, specifically from crossi ng the Widom line.

Liquid Polyamorphism: Some Unsolved Puzzles of Water in Bulk, Nanoconfined, and Biological Environments