Prediction of entropy and dynamic properties of water below the homogeneous nucleation temperature

The behavior of thermodynamic and dynamic properties of liquid water at atmospheric pressure in the temperature range between the lower limit of supercooling (TH ≈ 235 K) and the onset of the glassy state at Tg has been the focus of much research, and many questions remain about the properties of water in this region. Since direct measurements on water in this temperature range remain largely infeasible, we use existing experimental measurements of the entropy, specific heat, and enthalpy outside this range to construct a possible form of the entropy in the “difficult-to-probe” region. Assuming that the entropy is well-defined in extreme metastable states, and that there is no intervening discontinuity at atmospheric pressure, we estimate the excess entropy Sex of the liquid over the crystal within relatively narrow limits. We find that our approximate form for Sex shows atypical behavior when compared with other liquids: using a thermodynamic categorization of “strong” and “fragile” liquids, water appears to be fragile on initial cooling below the melting temperature, and strong in the temperature region near the glass transition. This thermodynamic construction can be used, with appropriate reservations, to estimate the behavior of the dynamic properties of water by means of the Adam–Gibbs equation—which relates configurational entropy Sconf to dynamic behavior. Although the Adam–Gibbs equation uses Sconf rather than Sex as the control variable, the relation has been used successfully in a number of experimental studies with Sconf replaced by Sex. This is likely a result of a proportionality between Sconf and Sex, which we confirm for simulations of a model of water. Hence by using the constructed values of Sex, together with experimental data in the range where Sex is known, we estimate the temperature dependence of viscosity and diffusivity approaching the glass transition. Like the entropy plots, Arrhenius plots of viscosity or diffusion show an inflection, implying a crossover from fragile to strong liquid character below TH. The dynamics results also imply Tg ≈ 160 K, which is considerably above the expected value of 136 K from older experiments, but consistent with other recent evidence based on hyperquenched glass properties. We discuss the possibility of experimentally verifying our predictions, and briefly discuss other liquids that also may follow a strong-to-fragile pattern.