Coherent structural relaxation of water from meso- to intermolecular scales measured using neutron spectroscopy with polarization analysis

By means of the recent implementation of neutron polarization analysis on a wide-angle time-of-flight spectrometer, we have been able to separately measure coherent and incoherent dynamic structure factors of heavy water with sub-meV resolution in a wide scattering vector $\left(Q\right)$ range. The observed decorrelation of collective fluctuations at mesoscales hardly depends on $Q$. In the crossover towards intermolecular scales, the coherent dynamics is nicely described by the convolution of a $Q$-independent mode and diffusion, in addition to collective excitations.

Figure 1

(a) The ratio between coherent and incoherent differential cross sections ${(\partial \sigma /\partial \mathrm{\Omega })}_{\text{coh}}/{(\partial \sigma /\partial \mathrm{\Omega })}_{\text{inc}}$ of ${\mathrm{D}}_2\mathrm{O}$ at 298 K (hollow dots) as a function of $Q$ obtained by diffraction with PA (D7 at the Institute Laue Langevin, Grenoble, France) [9], and calculated from MD simulations (solid line, see SM [19]). The figure also includes the additional $y$-axis scale (right) corresponding to $S\left(Q\right)={(\partial \sigma /\partial \mathrm{\Omega })}_{\text{coh}}/[{\sigma }_{\text{coh}}/\left(4\pi \right)]$ where ${\sigma }_{\text{coh}}/\left(4\pi \right)={lim}_{Q\to \infty }{(\partial \sigma /\partial \mathrm{\Omega })}_{\text{coh}}$. Squares represent the QENS amplitudes (rescaled to match the D7 data) obtained from the application of the model to the LET results (filled, $E_i=3.84$ meV; empty, $E_i=1.81$ meV). (b) and (c) Comparison of the coherent and incoherent dynamical structure factors measured by LET on ${\mathrm{D}}_2\mathrm{O}$ at 295 K at the $Q$ values indicated, and the total spectra (coherent $+$ incoherent). Vertical dotted lines represent the resolution FWHM.

Figure 2

Imaginary part of the dynamical susceptibility corresponding to the coherent dynamical structure factor of water at 295 K at the $Q$ values indicated. Results in (a) have been obtained with $E_i=1.81$ meV and in (b) with $E_i=3.84$ meV. For $Q=0.44{\AA }^{-1}$, the description in terms of a single Lorentzian up to 100 GHz is shown by the solid line (extrapolated to higher frequencies by the dotted line). For the rest of the data, solid lines are fits with the proposed model. For $Q=1.05{\AA }^{-1}$, the dashed, dashed-dotted, and dotted lines in (b) display the diffusive, effective $Q^o$-mode and vibrational contributions, respectively.

Figure 3

(a) Relative contributions of the diffusive $\left[C\right(Q\left)A\right(Q)$, circles], effective $Q^o$ mode $\left[C\right(Q\left)\right[1-A\left(Q\right)]$, squares] and vibrational $[1-C(Q)$, diamonds] processes to ${\chi }_{\text{coh}}^{″}/S\left(Q\right)$ at $T=295$ K (filled symbols, $E_i=3.84$ meV; empty symbols, $E_i=1.81$ meV). MD-simulation results are also included $(\times$, vibrational; $⊞$, structural contributions). (b) $Q$ dependence of the characteristic relaxation times: ${\tau }_d$ (circles) and ${\tau }_c$ (squares). The ${\tau }_d$ values have been obtained from incoherent scattering $\left({\tau }_d^{\text{inc}}\right)$ with $E_i=1.81$ meV $(\circ )$ and $E_i=1.05$ meV $(\odot )$, and from the fit of the coherent scattering results to the model $(•)$, all at 295 K. Solid line: fit of $D^{-1}{Q}^{-2}$ to ${\tau }_d^{\text{inc}}$, with $D=0.200\pm 0.016{\AA }^2$/ps in agreement with [24]. The ${\tau }_c$ values correspond to $E_i=1.81$ meV $(\square )$, $E_i=3.84$ meV $\left(\blacksquare \right)$, and $E_i=1.05$ meV $(⊠)$ obtained at $T=295$ (green), 280 (blue), and 350 K (magenta) and simulations $(⊞)$. ${\tau }_c$ and $\langle \tau \rangle$ values calculated with the model at 295 K are shown by the dashed and dashed-dotted lines, respectively. Inset: Arrhenius plot of ${\tau }_c^o\left(\blacksquare \right)$, the structural time from IXS $(\circ )$ [4], Brillouin light scattering $(▿)$ [25] and Brillouin UV scattering $\left(▵\right)$[26], $\langle \tau \left(Q_{\text{max}}\right)\rangle$ (crosses), and the laws describing the Arrhenius fit of ${\tau }_c^o$ (dashed line), the viscosity dependence $\eta /T$ (solid line), and the NMR rotational time for ${\mathrm{D}}_2\mathrm{O}$ [27] (dotted line).