From the Cp measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties. The Cp maximum is at a similar tem- perature as the maxima of the isothermal compressibility and cor- relation length. We observed a sharp increase in Cp, from 88 J/mol/K at 244 K to about 218 J/mol/K at 229 K where a maximum is seen. Evaporative cooling of ∼15-μm diameter droplets in vacuum enabled us to reach a temperature down to ∼228 K with a small fraction of the droplets remaining unfrozen. Here, we have utilized a meth- odology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infra- red laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. The challenge is that the relevant temperature range falls in the region where ice crystallization becomes rapid, which has previously excluded experiments. If a maximum in Cp exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid–liquid critical point model that can ex- plain the anomalous increase in thermodynamic response func- tions. Knowledge of the temperature dependence of the isobaric specific heat (Cp) upon deep supercooling can give insights regarding the anomalous properties of water. From the Cp measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties decrease rapidly below 235 K. The Cp maximum is at a similar temperature as the maxima of the isothermal compressibility and correlation length. Evaporative cooling of ∼15-µm diameter droplets in vacuum enabled us to reach a temperature down to ∼228 K with a small fraction of the droplets remaining unfrozen. Here, we have utilized a methodology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infrared laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. If a maximum in Cp exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid–liquid critical point model that can explain the anomalous increase in thermodynamic response functions. The reported values of Tc for D2O and, particularly, H2O suggest that improved water models are needed for the study of supercooled water. Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water, Pc=203±4 MPa, Tc=175☒ K, and ρc=1.03☐.01 g/cm3).
Isotope substitution effects are important the LLCP location in q-TIP4P/F D2O is estimated to be Pc=176±4 MPa, Tc=177☒ K, and ρc=1.13☐.01 g/cm3. Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H2O, from PIMD simulations, is located at Pc=167☙ MPa, Tc=159☖ K, and ρc=1.02☐.01 g/cm3. The data from PIMD/MD for H2O and D2O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS).
Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H2O and D2O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The density ρ(T), isothermal compressibility κT(T), and self-diffusion coefficients D(T) of H2O and D2O are in excellent agreement with available experimental data the isobaric heat capacity CP(T) obtained from PIMD and MD simulations agree qualitatively well with the experiments. We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H2O and D2O using the q-TIP4P/F water model over a wide range of temperatures and pressures.
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