High-frequency longitudinal and transverse dynamics in water

Abstract

High-resolution, inelastic x-ray scattering measurements of the dynamic structure factor S(Q, ω) of liquid water have been performed for wave vectors Q between 4 and 30 nm −1 in distinctly different thermodynamic conditions (T= 263 -420 K ; at, or close to, ambient pressure and at P = 2 kbar). In agreement with previous inelastic x-ray and neutron studies, the presence of two inelastic contributions (one dispersing with Q and the other almost non-dispersive) is confirmed.The study of their temperature-and Q-dependence provides strong support for a dynamics of liquid water controlled by the structural relaxation process. A viscoelastic analysis of the Q-dispersing mode, associated with the longitudinal dynamics, reveals that the sound velocity undergoes the complete transition from the adiabatic sound velocity (c 0 ) (viscous limit) to the infinite frequency sound velocity (c ∞ ) (elastic limit). On decreasing Q, as the transition regime is approached from the elastic side, we observe a decrease of the intensity of the second, weakly dispersing feature, which completely disappears when the viscous regime is reached. These findings unambiguously identify the second excitation to be a signature of the transverse dynamics with a longitudinal symmetry component, which becomes visible in the S(Q, ω) as soon as the purely viscous regime is left.

High-frequency dynamics of liquid and supercritical nitrogen

“…As already observed in other experiments performed in this Qrange [6][7][8][9][20][21][22], we found that the value of τ α (Q) decreases with increasing Q at a given temperature. As an example we report the Q-dependence of such a parameter for two selected temperatures in the inset of fig.3.…”

“…As a consequence the corresponding term in the memory function can be approximated by a δ(t)-function [7,8]. The second exponential term in eq.2 accounts for the visco-elastic transition responsible for the positive sound dispersion.…”

“…In the intermediate (visco-elastic) regime the acoustic propagation is strongly coupled with the active relaxation. The sound velocity strongly depends on the frequency of the probed acoustic wave, reflected in an upwards bending of the sound dispersion relation with respect to the linear behaviour characteristic of the viscous regime (positive sound dispersion) [4][5][6][7][8][9].…”

Collective modes and thermodynamics of the liquid state

“…[77,78]), transverse modes have been later studied in low-viscous liquids on the basis of positive dispersion [64][65][66]68] (recall our previous discussion that the presence of high-frequency transverse modes increases sound velocity from the hydrodynamic to the solid-like value). These studies included water [79], where it was found that the onset of transverse excitations coincides with the inverse of liquid relaxation time [80], as predicted by (11). More recently, transverse modes in liquids were directly measured in the form of distinct dispersion branches and verified on the basis of computer modeling [69][70][71][72][73].…”

The history of the "fast sound" in liquid water

“…Correspondingly, there exists a frequency Ω o = 1/τ that marks the transition between a liquid-like behavior (ω < Ω o ) and a solid-like one (ω > Ω o ). In the latter regime, the system has an increased sound velocity ("fast sound") and supports transverse excitations (dispersionless branch) [23]. Both the fast sound and the existence of a second branch, therefore, got their ultimate origin from the existence of a structural relaxation process.…”