Neutron-scattering measurements of wave-vector-dependent hydrogen density of states in liquid water

On the temperature dependence of the density of states of liquids at low energies

We report neutron-scattering measurements of the density of states (DOS) of water and liquid Fomblin in a wide range of temperatures. In the liquid phase, we confirm the presence of a universal low-energy linear scaling of the experimental DOS as a function of the frequency, g ( ω ) = a ( T ) ω , which persists at all temperatures. The low-frequency scaling of the DOS exhibits a sharp jump at the melting point of water, below which the standard Debye's law, g ( ω ) ∝ ω 2 , is recovered. On the contrary, in Fomblin, we observe a continuous transition between the two exponents reflecting its glassy dynamics, which is confirmed by structure measurements. More importantly, in both systems, we find that the slope a(T) grows with temperature following an exponential Arrhenius-like form, a ( T ) ∝ exp ( - ⟨ E ⟩ / T ) . We confirm this experimental trend using molecular dynamics simulations and show that the prediction of instantaneous normal mode (INM) theory for a(T) is in qualitative agreement with the experimental data.

Experimental Confirmation of the Universal Law for the Vibrational Density of States of Liquids

An analytical model describing the vibrational density of states (VDOS) of liquids has long been elusive, owing to the complexities of liquid dynamics. Nevertheless, Zaccone and Baggioli have recently developed such a model which was proposed to be the universal law for the vibrational density of states of liquids. Distinct from the Debye law, g(ω) ∝ ω², for solids, the universal law for liquids reveals a linear relationship, g(ω) ∝ ω, in the low-energy region. We have confirmed this universal law with experimental VDOS measured by inelastic neutron scattering on real liquid systems including water, liquid metal, and polymer liquids, and have applied this model to extract the effective relaxation rate for the short time dynamics for each liquid. The model has also been further evaluated in the prediction of the specific heat with comparison to existing experimental data as well as with values obtained by different approaches.

Temperature-dependent dynamic structure factors for liquid water inferred from inelastic neutron scattering measurements

Temperature-dependent dynamic structure factors S(Q, ω) for liquid water have been calculated using a composite model, which is based on the decoupling approximation of the mean square displacement of the water molecules into diffusion and solid-like vibrational parts. The solid-like vibrational part S_vib(Q, ω) is calculated with the phonon expansion method established in the framework of the incoherent Gaussian approximation. The diffusion part S_diff(Q, ω) relies on the Egelstaff-Schofield translational diffusion model corrected for jump diffusions and rotational diffusions with the Singwi-Sjölander random model and Sears expansion, respectively. Systematics of the model parameters as a function of temperature were deduced from quasi-elastic neutron scattering data analysis reported in the literature and from molecular dynamics (MD) simulations relying on the TIP4P/2005f model. The resulting S(Q, ω) values are confronted by means of Monte Carlo simulations to inelastic neutron scattering data measured with IN4, IN5, and IN6 time-of-flight spectrometers of the Institut Laue-Langevin (ILL) (Grenoble, France). A modest range of temperatures (283-494 K) has been investigated with neutron wavelengths corresponding to incident neutron energies ranging from 0.57 to 67.6 meV. The neutron-weighted multiphonon spectra deduced from the ILL data indicate a slight overestimation by the MD simulations of the frequency shift and broadening of the librational band. The descriptive power of the composite model was suited for improving the comparison to experiments via Bayesian updating of prior model parameters inferred from MD simulations. The reported posterior temperature-dependent densities of state of hydrogen in H₂O would represent valuable insights for studying the collective coupling interactions in the water molecule between the inter- and intramolecular degrees of freedom.

Free-film small-angle neutron scattering: a novel container-free in situ sample environment with minimized H/D exchange

The development of a container-free sample environment which is particularly well suited for in situ reaction studies of liquid samples by small-angle neutron scattering and related techniques is reported. Hydrogen exchange with the humidity from air is reduced by an encapsulating setup in a bag filled with an inert gas such as He. The effectiveness of this measure is quantitatively accessed by infrared absorption and gravimetry, and further correlated with neutron scattering.

Density of states from mode expansion of the self-dynamic structure factor of a liquid metal

We show that by exploiting multi-Lorentzian fits of the self-dynamic structure factor at various wave vectors it is possible to carefully perform the Q→0 extrapolation required to determine the spectrum Z(ω) of the velocity autocorrelation function of a liquid. The smooth Q dependence of the fit parameters makes their extrapolation to Q=0 a simple procedure from which Z(ω) becomes computable, with the great advantage of solving the problems related to resolution broadening of either experimental or simulated self-spectra. Determination of a single-particle property like the spectrum of the velocity autocorrelation function turns out to be crucial to understanding the whole dynamics of the liquid. In fact, we demonstrate a clear link between the collective mode frequencies and the shape of the frequency distribution Z(ω). In the specific case considered in this work, i.e., liquid Au, analysis of Z(ω) revealed the presence, along with propagating sound waves, of lower frequency modes that were not observed before by means of dynamic structure factor measurements. By exploiting ab initio simulations for this liquid metal we could also calculate the transverse current-current correlation spectra and clearly identify the transverse nature of the above mentioned less energetic modes. Evidence of propagating transverse excitations has actually been reported in various works in the recent literature. However, in some cases, like the present one, these modes are difficult to detect in density fluctuation spectra. We show here that the analysis of the single-particle dynamics is able to unveil their presence in a very effective way. The properties here shown to characterize Z(ω), and the information in it contained therefore allow us to identify it with the density of states (DoS) of the liquid. We demonstrate that only nonhydrodynamic modes contribute to the DoS, thus establishing its purely microscopic origin. Finally, as a by-product of this work, we provide our estimate of the self-diffusion coefficient of liquid gold just above melting.

Tetrahedral order in homologous disaccharide-water mixtures

The present work aims at evidencing the "kosmotrope" nature of trehalose through the analysis of inelastic neutron scattering measurements on trehalose and sucrose water solutions at different temperatures. Neutron spectra were collected by using the spectrometer MARI at the ISIS pulsed neutron source of the Rutherford Appleton Laboratory (Chilton, UK). To study the structural modifications induced on the tetrahedral hydrogen-bond network of water by homologous disaccharides, as a first step, the vibrational properties of pure water at different temperatures have been investigated. In particular, the temperature behavior of the intramolecular OH stretching mode has been analyzed. Successively, the vibrational properties for pure water have been compared with those of the sugar water solutions focusing the attention on the tetrahedral network-forming tendency. Finally, the obtained findings have been compared with previous Raman scattering evidences, and the results interpreted in the frame of recent molecular dynamics simulation works.