Relation Between the Widom Line and the Dynamic Crossover in Bulk Water and in Protein Hydration Water

We investigate, for two water models displaying a liquid-liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid-liquid critical point. We find a correlation between the dynamic fragility transition and the locus of specific heat maxima Cmax P (“Widom line”) emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between Cmax P and 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. Specifically, we also study the Jagla potential, 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 interactions. Using molecular dynamics simulations, 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 temperature 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 parameter. We relate these findings to the hypothesis of a liquid-liquid critical point in water. Our simulations are consistent with the possibility that the protein glass transition results from a change in the behavior of hydration water, specifically from crossing the Widom line. INTRODUCTION: THE WIDOM LINE By definition, in a first order phase transitions, thermodynamic state functions such as density ρ and enthalpy H discontinuously change as we cool the system along a path crossing the equilibrium coexistence line [Figure 1(a), path β]. In a real experiment, this discontinuous change may not occur at the coexistence line since a substance can remain in a supercooled metastable phase until a limit of stability (a spinodal) is reached [1] [Figure 1(b), path β]. If the system is cooled isobarically along a path above the liquid-gas critical pressure Pc [Figure 1(b), path α], the state functions continuously change from the values characteristic of a high temperature phase (gas) to those characteristic of a low temperature phase (liquid). The thermodynamic response functions which are the derivatives of the state functions with respect to temperature [e.g., isobaric heat capacity CP ≡ (∂H/∂T )P ] have maxima at temperatures denoted by Tmax(P ). Remarkably these maxima are still prominent far above the critical pressure [5–9], and the values of the response functions at Tmax(P ) (e.g., Cmax P ) diverge as the critical point is approached. The lines of the maxima for different response functions asymptotically approach one another as the