Viscoelastic behavior of water in the terahertz-frequency range: An inelastic x-ray scattering study

High-resolution, inelastic x-ray scattering measurements of the dynamic structure factor $S(q,\omega )$ of liquid water in the THz frequency range have been performed as a function of wave vector q (1–7 ${\mathrm{nm}}^{-1})$ and temperature T (273–473 K), using pressure (0–1.5 kbar) to keep the density at $\rho \approx 1\hspace{0.5em}{\mathrm{g}/\mathrm{c}\mathrm{m}}^3.$ We show that, for $q<~2\hspace{0.5em}{\mathrm{nm}}^{-1},$ the $S(q,\omega )$ spectra can be consistently explained in terms of a hydrodynamic formalism which includes a viscoelastic, q-independent contribution to the memory function for the density fluctuations. This allows us to extract values for the infinite frequency sound velocity and for the structural relaxation time which are found to compare favorably with those obtained using techniques which probe a lower-frequency range. As a consequence, the atomic dynamics in water is shown to have a homogeneous character down to a length scale of $\approx 3$ nm. At $q>\mathrm{}2\mathrm{}\hspace{0.5em}{\mathrm{nm}}^{-1},$ we find that the viscoelastic contribution to the memory function becomes q dependent. Thus this work provides a view on the evolution of the collective dynamics of water across the q region where the continuum approximation inherent in the hydrodynamic formulation begins to fail. The physical consequences of such a result are discussed in some detail.