Reply to Soper et al.: Fluctuations in water around a bimodal distribution of local hydrogen-bonded structural motifs

Soper et al. (1) propose that the rise in the structure factor S(Q) at low Q in the small-angle x-ray scattering (SAXS) data reported in ref. 2 is caused by stochastic number fluctuations present in all liquids and that these fluctuations are not qualitatively different for water. Water, however, exhibits enhanced number density fluctuations both at higher and lower temperatures. Clearly, the driving force cannot be the same in both temperature regimes. In ref. 2, we suggest that the balance between minimizing enthalpy (tetrahedral regions) and entropy (disordered regions) provides the driving force dominating at low temperatures and that cooperatively enhanced H bonds associated with lower-density, tetrahedral regions may play an important role.

Eq. 2 of ref. 1 applies to two-component systems with sharp boundaries and a bimodal density distribution. This view is not advocated in ref. 2; the LDL/HDL (low-/high-density liquid) nomenclature refers to our interpretation of XAS and XES spectra in terms of two distinct H-bond structural motifs, proposed in ref. 2 to be correlated with the density (number) fluctuations observed in SAXS. The dynamic balance between LDL (higher volume, lower entropy) and HDL (lower volume, higher entropy) can be further understood from the increasing anticorrelation between fluctuations in local volume and in entropy on cooling the liquid.

A recent pressure-dependent SAXS study of water (3) showed the rise at small Q to vanish with increasing pressure, fully consistent with the picture in ref. 2 of LDL tetrahedral motifs, which, with increasing pressure, decrease in number in favor of the HDL disordered motifs undergoing normal stochastic thermally induced fluctuations, with a reduction in small-angle scattering as a consequence.

There is a recent water simulation model that allows for including approximately one million water molecules (4), which displays nanometer-scale heterogeneities between four-coordinated (assigned in ref. 4 as low-temperature motifs) and more disordered (high-temperature) motifs, albeit without SAXS intensity enhancement. The structural heterogeneity is seen even at 300 K, nearly 100 K above the extrapolated liquid-liquid transformation temperature in the simulation; structural fluctuations can thus persist in simulations far from a critical region. The specific model studied in ref. 4, however, lacks treatment of cooperatively enhanced H bonds, which we suggest in ref. 2 to additionally favor forming strongly bonded low-density regions.

The bimodality of the experimentally observed structural heterogeneity is derived from x-ray spectroscopic data (2). The x-ray spectroscopy data are qualitatively different from the broad and featureless IR and Raman OH stretch data in that well-resolved spectral features are seen that eliminate the need to discuss isosbestic points. In particular, the XES spectra show two well-resolved peaks in the lone-pair region with relative intensity depending on temperature; no broadening is observed with increased temperature nor is there any apparent spectral intensity between the two peaks showing that the redistribution of spectral intensity is not continuous in energy. Our interpretation of these experimental data, presented in ref. 2, is the proposed bimodal distribution of local structures associated with the density heterogeneity observed in SAXS. Finally, we note that this picture is fully consistent with wide-angle x-ray and neutron diffraction data (see ref. 5 and reference 32 in ref. 2).