Anomalous Behavior of Proton Zero Point Motion in Water Confined in Carbon Nanotubes

The momentum distribution of the protons in ice $I_h$, ice VI, high density amorphous ice, and water in carbon nanotubes has been measured using deep inelastic neutron scattering. We find that at 5 K the kinetic energy of the protons is 35 meV less than that in ice $I_h$ at the same temperature, and the high momentum tail of the distribution, characteristic of the molecular covalent bond, is not present. We observe a phase transition between 230 and 268 K to a phase that does resemble ice $I_h$. Although there is yet no model for water that explains the low temperature momentum distribution, our data reveal that the protons in the hydrogen bonds are coherently delocalized and that the low temperature phase is a qualitatively new phase of ice.

Figure 1

The experimental neutron Compton profile $J(y)$ at 5 and 268 K, constructed by binning the time of flight data for each of the 28 detectors in $\Delta y$ bins assuming that the data satisfies $y$ scaling [Eq. (1)]. The solid and dashed curves are fits to the entire data set and include the instrumental resolution and final state effects.

Figure 2

The momentum distribution of the protons in nanotube ice compared with that in three forms of bulk ice. The dotted lines are 1 standard deviation error limits. The inset shows the effect of varying the parameters in an anisotropic harmonic model of the proton momentum distribution in the hydrogen bond, with the momentum width along the bond fixed and the transverse widths varied [2.8 (dotted-dashed curve), 3.2 (dashed curve), and $3.6{\AA }^{-1}$ (solid curve)], keeping the width along the bond of $6{\AA }^{-1}$. The lowest value of the transverse width gives a kinetic energy comparable to that observed in the nanotubes at 5 K; the highest value corresponds to the fit to the ice $I_h$ data [12]. The HDA ice and ice VI data are displaced vertically for clarity.

Figure 3

Comparison of the momentum distributions for nanotube ice at 268 K, bulk ice $I_h$ at 269 K, and the low temperature phase of nanotube ice, represented by the data at 5 K. The circles are a fit to a model in which the proton is delocalized along the bond in a double well potential. The potential (solid curve) and the wave function (dashed curve) corresponding to the fit to the momentum distribution data along the bond direction are shown in the inset.