Proton order in ices

Kamb Davis (1964) have proposed for Ice VII, and by implication for VIII also, the simple structure shown in fig. 3.7. As in the case of Ice VI, the structure consists of two interpenetrating frameworks of HgO molecules, each of which is completely hydrogen-bonded within itself and makes no bonds to the other. In the present case each framework is a diamond cubic Ice Ip structure with exact tetrahedral bonding and the interpenetration would give just twice the density of Ice Ip, were it not for the fact that there is repulsive contact between oxygen atoms in the alternative frameworks. This increases the 0-H... 0 distance to 2-86 A in Ice VII at 25 kbar compared with the distance 2-76 A in Ice I at I bar. The mode of proton ordering in Ice VIII is not yet known. 

This essential absence of longer-range proton order in tetrahedral H-bond networks is the origin of the famous zero-point entropy of ice L. Pauling, J. Am. Chem. Soc. 57 (1935), 2680 and L. Pauling, note 16, pp. 466-468. 

Figure 13.3 Proton ordering in hydrogen bonding, illustrating favorable (Grotthuss-like) ordering in a chain (above) or cyclic hexamer (a), contrasted with the unfavorable isomer (b), one of many similar that cannot survive thermodynamically. All clusters are ice rule-compliant (cf. Sidebar 5.18).

Kamb B, Hamilton WC, LaPlaca SJ, Prakash A (1971) Ordered proton configuration in ice II from single-crystal neutron diffraction. J Chem Phys 55 1934-1945... 

Calculate a statistical/spectroscopic value of Sg(p, T ), compare this with your thermodynamic value, and report the discrepancy. For most substances, these two Sg values agree and the third law is valid for the solid as Tapproaches 0 K. However, you should find that 5g(spectroscopic) > (thermodynamic) for H2O, which means that ice does not have the perfect order at 0 K required by the third law. The explanation for this in terms of the disorder in the proton configurations in ice was first given by Pauling and is well described by Davidson. ... 

H. Fukazawa, S Mae, S. Ikeda O. Watanabe (1998). Chem Phys Lett., 294, 554-558. Proton ordering in Antarctic ice observed by Raman and neutron scattering. 

Protonic diffusion in ice has been investigated by a spectroscopic method. This method is based on the isotope effect on molecular vibrations. The mass difference between hydrogen and deuteron results in a frequency difference by a factor of V2 for the stretch mode. The peak positions are well separated in the spectra and hence their heights are converted to the H(D) concentrations with good accuracy. The diffusion process is monitored by measuring the reflection spectra of an H2O/ D2O ice bilayer, for which the equation of diffusion is described in analytical form. The H/D mutual diffusion coefficient measured at 400 K shows a monotonic decrease by two orders of magnitude as the pressure increases from 8 to 63 GPa. 

Since it is known that Ice In has proton disorder at all temperatures, a study of the I-III transition entropy as a function of temperature should give information about the amount of ordering in Ice III. There will certainly be some contribution to this... 

Fig. 3.4. Oxygen positions in Ice III and its proton-ordered analogue Ice IX. The drawing is a projection along the c-axis with heights above the projection plane given in hundredths of the c-axis (c = 6-83 A). (Kamb, 1968.) (From Structural Chemistry and Molecular Biology, ed. Alexander Rich and Norman Davidson. San Francisco Freeman Co., copyright 1968.)...

As we have indicated, solids generally give very broad, featureless NMR spectra whilst liquids may give very sharp lines, some times narrower. This would be true, for example, for the proton resonance in ice and liquid water at 273 K. Why is this The answer can only be in the fact that in the liquid the nuclear spins are undergoing much faster and more developed relative motions, i.e., rotations, translations, etc., and this must clearly lead to an averaging away of the dipolar proton-proton local fields responsible for the broad line in the ice. This indeed is the reason and we should then ask ourselves how fast do the motions have to be and about what directions in space must they occur in order that averaging will take place. 

Many of the high-pressure forms of ice are also based on silica structures (Table 14.9) and in ice II, VIII and IX the protons are ordered, the last 2 being low-temperature forms of ice VII and III respectively in which the protons are disordered. Note also that the high-pressure polymorphs VI and VII can exist at temperatures as high as 80°C and that, as expected, the high-pressure forms have substantially greater densities than that for ice I. A vitreous form of ice can be obtained by condensing water vapour at temperatures of — 160°C or below. 

Figure 13.4 Low-level 18-cluster QCE model (RHF/3-21G level) of the water phase diagram, showing (above) the dominant W24 clathrate-type cluster of the ice-like solid phase, and (below) the overall phase diagram near the triple point (with a triangle marking the actual triple point). Note that numerous other clusters in the W2o-W26 range were included in the mixture, but only that shown (with optimal proton ordering) acquired a significant population.

There is some form of hydrogen disorder in nearly all polymorphs, just as in ice(Ih). However the rhombohedral ice(II) is an exception. Its protons are ordered. As was suggested by Whalley (1967), this may have profound significance. Were ice(II) proton-disordered, it would have a higher entropy. A possible consequence would be that this polymorph would become thermodynamically stable under conditions that might arise on Earth. As ice(II) has a density 1.2 g cm-3, it would then accumulate at the bottom of lakes or seas, so that Earth s waters would freeze from the depths upwards. Life, as we know it, could hardly have developed, or survived, in such circumstances. 

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