Comment to “Dynamics of supercooled confined water measured by deep inelastic neutron scattering”

Abstract

We comment on the findings of “Dynamics of supercooled confined water measured by deep inelastic neutron scattering”, by V. De Michele, G. Romanelli, and A. Cupane [Front. Phys. 13, 138205 (2018)]. We show that the current sensitivity of the deep inelastic neutron scattering (DINS) method, cannot detect with confidence small differences in the proton kinetic energy, Ke(H), involved in a liquid-liquid transition in supercooled water confined in nanoporous silica. We also critisize the calculation of Ke(H) carried out in Front. Phys. 13, 138205 (2018).

Graphical abstract

Keywords

supercooled water / liquid–liquid transition / deep inelastic neutron scattering / libration / vibrational density of states / proton kinetic energy

An attempt to capture the liquid liquid transition (LLT) in H₂O was recently reported by a deep inelastic netron scattering (DINS) study [1]. In that paper, the proton kinetic energy was measured, using a sample of deeply supercooled water (SCW) nanoconfined in silica Xerogel of ~20 Å effective pore dimension (hereby denoted as SCW@SX). The results were [1]: \text{K}\text{e}(\text{H})=(157\pm 3) meV at 210K and (156±2) meV at 250K. This small and statistically insignificant 1±1.8 meV difference in Ke(H), complemented with a quantum harmonic semi empirical (SE) calculation of the temperature effect on Ke(H) in SCW@SX, was suggested in Ref. [1] to indicate the occurrence of a liquid–liquid transition (LLT). The reasoning behind this suggestion relied on the assumption that the seemingly higher Ke(H) value at 210 K, compared to that at 250 K, indicates that at 210 K the water protons experience a stiffer intermolecular potential than at 250 K, in contradiction to the expectation that water at 210 K and 250 K should be mainly in high and low density liquid states respectively. This conclusion seems however to be doubtful because the current level of sensitivity of the DINS technique [2] cannot detect with confidence the Ke(H) differences at 210 K and 250 K related to variations in the density of the liquid.

In addition, the general known trend of variation of Ke(H) in water between 200 K and 260 K, covering the above T range is a slowly increasing one [3, 4], as also supported in a very recent report on the same system [5].

In this commentary, we examined the calculated T-effect made in Ref. [1], revealing some difficulties which seem to invalidate its conclusions.

The Ke(H) value in condensed H₂O phases may be calculated using the well-established SE method [3]; it may be expressed as

\begin{array}{}\text{(1)}& \text{K}\text{e}(\text{H})={\displaystyle \sum _i}{S}_i\text{K}\text{e}{(\text{H})}_i\mathrm{,}\end{array}

where the indices i={\text{T}}_{\text{r}}, L, B, SS, AS respectively refer to translation ({\text{T}}_{\text{r}}) and libration (L) of the whole H₂O molecule, and to its internal modes: HOH bending (B), and symmetric (SS) and asymmetric (AS) OH stretching. The S_i coefficients in Eq. (1) correspond to the kinetic energy fractions repectively shared by the proton in the above modes of motion; the details of calculation may be found elsewhere [6].

In Ref. [1] the T-effect of Ke(H) in SCW@SX was calculated by adopting the measured internal modes of liquid H₂O of Ref. [7], together with their corresponding SE calculated kinetic energy fractions. To account for the contribution of the external (lattice) modes of the confined H₂O, the normalized integral of the vibrational density of states (VDOS), measured by inelastic neutron scattering (INS) for the same system [1] (of 20 Å pore diameter and a 0.4 hydration level - gr H₂O/gr SiO₂) [8], was utilized. The results of Ref. [1] are reproduced in Fig. 1 (blue curve). The measured [1] DINS values are shown as green data points in Fig. 1.

Note that the calculated blue curve of Ke(H) vs. T of Ref. [1] (Fig. 1) suffered from two drawbacks [9]: First, only the translational contribution to Ke(H) was accounted for while ignoring that of libration occurring at ~200 to 1250 cm^-1. As a result, the kinetic energy fraction S_{{\text{T}}_{\text{r}}} (shared by the H₂O protons in translation) used to calculate Ke(H) came out wrong.

Table 1 lists the frequencies of the five modes of motion of the H₂O molecules together with the calculated energy fractions of the protons used in Ref. [1] and in the present work. A check for the correctness of the energy fractions is usually made by calculating the sum rule which should add up to unity. This sum rule may be written as [3]

\begin{array}{}\text{(2)}& S_{{\text{T}}_{\text{r}}}+S_{\text{L}}+\frac{1}{3}{\displaystyle \sum _{i=1}^3}{S}_i=1.\end{array}

It is fulfilled for the present calculation but not for that of Ref. [1] where the sum of the energy fractions is 1.47 (see Table 1).

Altogether, the calculated T-effect of the Ke(H) values of Ref. [1] was severely underestimated in particular at low T, and gradually increases with T (see blue curve in Fig. 1).

To correct for the missing librational mode, we accounted for the INS measured librational frequency of a closely related system of nanoconfined water, namely H₂O nanoconfined in 14 Å single wall carbon nanotubes (SWCNTs) [10]. In addition, the corrected values of S_{{\text{T}}_{\text{r}}} and S_{\text{L}} were used to account for the kinetic energy fraction of the proton in the translational and librational motions. The result of these two corrections on the calculated value of Ke(H) vs. T is shown as the dash red curve in Fig. 1 (see also Ref. [9]).

Note the huge deviation between the T-effect originally calculated in Ref. [1] (solid blue curve in Fig. 1) and that of its corrected version (dash red curve in Fig. 1). Note also the excellent agreement between the calculation of Ref. [9] and that of ordinary H₂O (dot-dash purple curve) [7], as well as the good agreement with the measured DINS values of Ref. [1] (shown as green data points in Fig. 1).

The fact that the T-effect of ordinary H₂O practically coincides with that of SCW@SX, strongly questions the conclusion made in Ref. [1] regarding the LLT.

Finally it is very interesting to note that in a very recent paper by the authors of Ref. [1], the values of Ke(H) were measured in a wider T range 170–325 K and an excellent agreement with the calculations of Ref. [9] was obtained [5]. This again confirms our present conclusion regarding the LLT. It should be noted however that differently from Ke(H), the kinetic energy of the electrons in water is indeed sensitive to temperature variations between 256 K and 293 K, showing a strong increase upon supercooling from 277 K to 256 K [11].

References

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[5] V. De Michele, G. Romanelli, and A. Cupane, Kinetic energy and radial momentum distribution of hydrogen and oxygen atoms of water confined in silica hydrogel in the temperature interval 170–325 K, Sci. China Phys. Mech. & Astron. 62, 107012 (2019)

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[9] Y. Finkelstein and R. Moreh, On H-dynamics of supercooled water confined in nanoporous silica, Chem. Phys. 523, 83 (2019)

[10] A. I. Kolesnikov, J. M. Zanotti, C. K. Loong, P. Thiyagarajan, A. P. Moravsky, R. O. Loutfy, and C. J. Burnham, Anomalously soft dynamics of water in a nanotube: A revelation of nanoscale confinement, Phys. Rev. Lett. 93(3), 035503 (2004)

[11] F. Lehmkühler, Y. Forov, T. Büning, C. J. Sahle, I. Steinke, K. Julius, T. Buslaps, M. Tolan, M. Hakala, and C. Sternemann, Intramolecular structure and energetics in supercooled water down to 255 K, Phys. Chem. Chem. Phys. 18(9), 6925 (2016)

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