Dielectric Susceptibility of Liquid Water: Microscopic Insights from Coherent and Incoherent Neutron Scattering

The analysis of neutron scattering results on H dynamics (${\mathrm{H}}_2\mathrm{O}$) and the dynamic structure factor (${\mathrm{D}}_2\mathrm{O}$) around the intermolecular peak and at intermediate length scales in terms of the susceptibilities reveals three processes (diffusive, local relaxational and vibrational) at frequencies below 3 THz, to which the contributions commonly invoked in dielectric studies can be directly mapped. We achieve a unified description of the results from both techniques, clarifying the nature of the molecular motions involved in the dielectric spectra and their impact on the structural relaxation.

Figure 1

Imaginary part of water susceptibility at 298 K. (a) DS (closed [5] and open [2] circles), Raman [6] (diamonds) and LS [7] (squares; $T=293\mathrm{K}$) results. Lines are fitting curves of DS results from Ref. [5] and respective components: dashed-dotted lines correspond to the fit proposed in Ref. [5] with processes 1 (main Debye), 2, and 3; solid line to the fit obtained in this work with process $d$ for $Q^{\star }=0.7{\AA }^{-1}$ and processes $\ell d$ and $V$ (dashed lines). Inset: difference between the DS results and our fit, and model resonance given in Ref. [3] (line). (b) Incoherent NS results. (c) Coherent NS results. In (b) and (c), black solid lines are fits with the three components (red, diffusive; green, effective local; blue, vibrational) to the data at $Q=0.7{\AA }^{-1}$ (circles, dashed lines) and $2.0{\AA }^{-1}\approx Q_{\max }$ (squares, dotted lines).

Figure 2

$Q$ dependence of the parameters characterizing ${\chi }_{\mathrm{Q},\text{inc}}^{\prime \prime }$ (open symbols) and ${\chi }_{\mathrm{Q},\text{coh}}^{\prime \prime }$ (closed symbols). (a) Amplitudes $C(Q)$ (squares) and $A(Q)$ (circles). Lines: DWF-like fits. (b): Characteristic times corresponding to the diffusive (circles), vibrational (squares), effective local (diamonds), and local (dashed line) processes. Solid line: fit of the low-$Q$ incoherent times to ${\tau }_d\propto Q^{-2}$. D7 results for ${\mathrm{D}}_2\mathrm{O}$ are shown for comparison (dots) in both panels [in arb. units in (a)].

Figure 3

(a) MSD experimentally obtained for H atoms (different symbols for different $Q$ values in the range $0.19\le Q\le 2.0{\AA }^{-1}$) and calculated from the simulations for H (solid line) and O atoms (dashed-dotted line). The computed ${\alpha }_2(t)$ are shown as dashed (H atoms) and dotted (O atoms) lines. (b) Effective power exponent $y$ for H (solid line) and O atoms (dashed-dotted line) and mean displacement of O atoms ${\xi }^{\mathrm{O}}$ (dashed line) as functions of the mean displacement of H atoms ${\xi }^{\mathrm{H}}$. Gray dotted line: ${\xi }^{\mathrm{O}}={\xi }^{\mathrm{H}}$-law.