Experimental observation of mesoscopic fluctuations to identify origin of thermodynamic anomalies of ambient liquid water

We report an experimental observation of mesoscopic fluctuations underlying the thermodynamic anomalies of ambient liquid water. The combination of two sound-velocity-measurement methods with largely different frequencies, namely inelastic x-ray scattering (IXS) in the terahertz band and ultrasonic (US) in the megahertz band, allows us to investigate a relaxation phenomenon that has a characteristic frequency between the two aforementioned frequencies. We performed IXS measurements to obtain the IXS sound velocity of liquid water from the ambient conditions to the supercritical region of liquid–gas phase transition (LGT) and compared the results with the US sound velocity reported in the literature. We found that the ratio of the sound velocities, S_{f}, which corresponds to the relaxation strength, obtained using these two methods exhibits a simple but significant change. Two distinct rises were observed in the high- and low-temperature regions, implying that two relaxation phenomena exist. In the high-temperature region, a peak was observed near the LGT critical ridge line, which was linked to changes in the magnitude of density fluctuation and isochoric and isobaric-specific heat capacities. This result indicates that the high-temperature relaxation originates from the LGT critical fluctuation, proving that this method is effective for observing such mesoscopic fluctuations. Meanwhile, in the low-temperature region, S_{f} increased from 550 K toward the low-temperature region and reached a high value, attaining the “fast sound” state under ambient conditions. This result indicates that another mechanism of relaxation exists, which causes the sound velocity anomaly, including the “fast sound” phenomenon of liquid water under ambient conditions. The change in S_{f} in the low-temperature region is linked to the change in the isochoric heat capacity, which identified that this relaxation causes the well-known heat capacity anomaly of liquid water. This low-temperature relaxation corresponds to the critical fluctuation of the liquid–liquid phase transition (LLT) that is speculated to exist in the supercooled region. In this study, both LGT and LLT critical fluctuations were observed, and the relationship between thermodynamics and the critical fluctuations was comprehensively discussed by analyzing the similarities and differences between the two phase transitions.