A Theory of the Structure of Ice

Linus Pauling, December 1935.

By 1935 – 75 years ago this year – Linus Pauling was in the thick of his scientific career. He had been at Caltech for over a decade, and had already conducted an impressive amount of important research on crystal structures and the chemical bond. During this year, Pauling also postulated a theory of the structure and entropy of ice, one of his lesser-known, yet still very significant, contributions.

Pauling’s work on this subject was encapsulated in a paper titled “The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement,” which appeared in the Journal of the American Chemical Society in December 1935.

In order to better understand Pauling’s theory, it is necessary to discuss what was already known about water and ice at this time. First, as stated in Pauling’s paper, “it has been generally recognized since the discovery of the hydrogen bond that the unusual properties of water and ice (high melting and boiling points, low density, association, etc.) owe their existence to hydrogen bonds between water molecules.”

Second, the precise arrangement of the oxygen atoms – but not of the hydrogen atoms – in ice crystals was already known. Each single oxygen atom is tetrahedrally surrounded by four other oxygen atoms.  It was also generally understood that there is only one hydrogen atom located between each oxygen atom.

From this base of knowledge Pauling pondered “whether a given hydrogen atom is midway between the two oxygen atoms it connects or closer to one than to the other.”  In evaluating the experimental evidence, Pauling decided in his paper that the hydrogen atom is, in fact, closer to one oxygen that to the other.

At this point, Pauling made four assumptions, all of which he supported later in the paper. These assumptions are as follows:

1. In ice each oxygen atom has attached to it two hydrogen atoms affixed at distances of about 0.95 Å.  These atoms form a water molecule, with the H-O-H angle measured at about 105º, as in the gas molecule.
2. Each water molecule is oriented such that its two hydrogen atoms are directed approximately toward two of the four oxygen atoms which surround it tetrahedrally, forming hydrogen bonds.
3. The orientations of adjacent water molecules are arranged such that only one hydrogen atom lies approximately along each oxygen-oxygen axis.
4. Under ordinary conditions the interaction of non-adjacent molecules would not appreciably stabilize any one of the many configurations satisfying the preceding conditions with reference to the others.

Adhering to these assumptions, Pauling theorized that the water molecules in ice crystals can orient themselves in a number of different ways, and that the crystal can likewise change from one orientation to another, provided that it adheres to the four assumptions.

Pauling used his theory to calculate the number of possible configurations available to the crystal (as allowed by his theory), and in turn used this number to calculate the residual entropy of ice. He found this value to be in very good agreement with the experimentally observed entropy value.

Pauling felt good about his data, concluding that “the observed entropy of ice at low temperatures provides strong support for a particular structure of ice, and thus gives an answer to the question which has been extensively discussed during the past few years.”

Historians of science now concur with Pauling’s assessment. Writing on the matter in his Pauling biography Force of Nature, Thomas Hager notes

[I]n 1935, Pauling had a flash of insight that led to paper on ‘orientational disorder’ – a theory concerning water molecules that explained the residual entropy of ice at absolute zero. It was purely theoretical work, harkening back to his days with [Richard C.] Tolman. Thirty years later, when sophisticated computers were finally able to run the numbers thoroughly, Pauling’s theory was proven right. Now called ‘proton disorder,’ the idea became, as one student of the field say, ‘the most important American contribution to the modern crystallography of water.’