Observation of Fractional Stokes-Einstein Behavior in the Simplest Hydrogen-Bonded Liquid

Quasielastic neutron scattering has been used to investigate the single-particle dynamics of hydrogen fluoride across its entire liquid range at ambient pressure. For $T>230\mathrm{K}$, translational diffusion obeys the celebrated Stokes-Einstein relation, in agreement with nuclear magnetic resonance studies. At lower temperatures, we find significant deviations from the above behavior in the form of a power law with exponent $\xi =-0.71\pm 0.05$. More striking than the above is a complete breakdown of the Debye-Stokes-Einstein relation for rotational diffusion. Our findings provide the first experimental verification of fractional Stokes-Einstein behavior in a hydrogen-bonded liquid, in agreement with recent computer simulations [S. R. Becker et al., Phys. Rev. Lett. 97, 055901 (2006)].

Figure 1

QENS spectra at $T=195\mathrm{K}$ measured on IRIS-ISIS. Fits are shown in red (or gray) and individual Lorentzian components in dashed blue (or dark gray). In all cases, the instrumental resolution has been folded into our Lorentzian model for the purposes of fitting.

Figure 2

(a) Inverse QENS energy widths for the translational mode as a function of momentum transfer (IRIS-ISIS); (b) temperature dependence of the translational self-diffusion coefficient and comparison with PFG-NMR results.

Figure 3

QENS form factor ($T=195\mathrm{K}$). The inset shows the temperature dependence of $D_R$ (see text for details).

Figure 4

Log-log plots of QENS diffusion coefficients vs $\eta /T$ (data in black circles; open: rotational; solid: translational). SE and DSE behavior is characterized by a power-law exponent $\xi =-1$. For the purposes of comparison, diffusion coefficients have been normalized by their corresponding high-temperature values ($T=290\mathrm{K}$). Red (or gray) and blue (or dark gray) lines show ${\tau }_{\mathrm{free}}^{-1}$ for freely rotating HF in two and three dimensions.