The structures of ice

In this section, rather than give a detailed account of theories of the liquid state, a more qualitative approach is adopted. What follows includes first a description of the structure of ice then from that starting-point, ideas concerning the structure of liquid water are explained. 

The arrangement of oxygen atoms in ice I is isomorphous with the wurtzite form of zinc sulphide, and also with the silicon atoms in the tridymite form of silicon dioxide. Hence, ice I is sometimes referred to as the wurtzite or tridymite form of ice (Eisenberg Kauzmann, 1969). 

Location of the hydrogen atoms in ice I has caused more problems. This is because hydrogen is less effective at scattering X-rays or electrons than oxygen. For a long time, arguments about the position of hydrogen were based on indirect evidence, such as vibrational spectra or estimates of 

Ice I is one of at least nine polymorphic forms of ice. Ices II to VII are crystalline modifications of various types, formed at high pressures ice VIII is a low-temperature modification of ice VII. Many of these polymorphs exist metastably at liquid nitrogen temperature and atmospheric pressure, and hence it has been possible to study their structures without undue difficulty. In addition to these crystalline polymorphs, so-called vitreous ice has been found within the low-temperature field of ice I. It is not a polymorph, however, since it is a glass, i.e. a highly supercooled liquid. It is formed when water vapour condenses on surfaces cooled to below — 160°C. 

It is not appropriate in this chapter to give a detailed review of the solid-state behaviour of water in its various crystalline modifications. However, there are some general structures which are relevant and worth highlighting. Firstly, water molecules in these various solids have dimensions and bond angles which do not differ much from those of an isolated water molecule. Secondly, the number of nearest neighbours to which each individual molecule is hydrogen-bonded remains four, regardless of the ice polymorph. 

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Complete and Incomplete Ionic Dissociation. Brownian Motion in Liquids. The Mechanism of Electrical Conduction. Electrolytic Conduction. The Structure of Ice and Water. The Mutual Potential Energy of Dipoles. Substitutional and Interstitial Solutions. Diffusion in Liquids. 

The Structure of Ice and Water. It has not yet been necessary to consider in detail the properties of particular solvents. In Table 1 we gave a list of values for the dielectric constants of various solvents but apart from this we have not yet paid attention to the observed properties of solvents or of the ions which are commonly dissolved in them. Before continuing the discussion which was in progress in Sec. 23, it will be useful to review in some detail the state of our knowledge of the liquids which are used as solvents, and of the species of ions which are most often studied in solution. Although non-aqueous solutions are of great interest for the sake of comparison, nevertheless aqueous solutions are still of paramount importance, and we shall pay most of our attention to H20 and D20 and to ions dissolved in these liquids. 

Fig. 20. The structure of ice Molecules numbered 8, 7, 6 are in contact with 5, while molecules 5, 4, 3, 2 arc in contact with 1. Molecules 2, 3, 4 are among the next-nearest neighbors of 5, while molecules 0, 7, 8 are among the next-nearest neighbors of 1. [Diagram taken from E. J. W. Verivey, Rec. trav. chim. 60, 893 (1941).]...

The theory of the structure of ice and water, proposed by Bernal and Fowler, has already been mentioned. They also discussed the solvation of atomic ions, comparing theoretical values of the heats of solvation with the observed values. As a result of these studies they came to the conclusion that at room temperature the situation of any alkali ion or any halide ion in water was very similar to that of a water molecule itself— namely, that the number of water molecules in contact with such an ion was usually four. At any rate the observed energies were consistent with this conclusion. This would mean that each atomic ion in solution occupies a position which, in pure water, would be occupied by a water moldfcule. In other words, each solute particle occupies a position normally occupied by a solvent particle as already mentioned, a solution of this kind is said to be formed by the process of one-for-one substitution (see also Sec. 39). 

The structure of ice. In ice, the water molecules are arrenged in an open pattern that gives ice its low density Each oxygen atom (red) is bonded covalently to two hydrogen atoms (gray) and forms hydrogen bonds with two other hydrogen atoms. 

Self-Test 7.10B Suggest a reason why the entropy of ice is nonzero at T = 0 think about how the structure of ice is affected by the hydrogen bonds. 

FIGURE 8.5 The structure of ice notice how the hydrogen bonds hold the water molecules apart from one another in a hexagonal array. The two gray spheres between the oxygen atoms indicate the two possible locations of the hydrogen atom in that region of the structure. Only one of the positions is occupied. 

Let us now make the following assumptions (to be supported later by a discussion of the entropy) regarding the structure of ice. 

The structure of ice is seen to be of a type intermediate between that of carbon monoxide and nitrous oxide, in which each molecule can assume either one of two orientations essentially independently of the orientations of the other molecules in the crystal, and that of a perfect molecular crystal, in which the position and orientation of each molecule are uniquely determined by the other molecules. In ice the orientation of a given molecule is dependent on the orientations of its four immediate neighbors, but not directly on the orientations of the more distant molecules. 

The structure of ice. (a) Each oxygen atom is at the center of a distorted tetrahedron of hydrogen atoms. The tetrahedron is composed of two short covalent O—H bonds and two long H—O hydrogen bonds, (b) Water molecules are held in a network of these tetrahedra. 

There are various theories on the structure of these species and their size. Some authors have assumed the presence of monomers and oligomers up to pentamers, with the open structure of ice I, while others deny the presence of monomers. Other authors assume the presence of the structure of ice I with loosely arranged six-membered rings and of structures similar to that of ice III with tightly packed rings. Most often, it is assumed that the structure... 

The structure of ice is shown in the diagram. The crystal structure of ice is essentially tetrahedral. When water melts, the hydrogen bonds are progressively broken. The molecules pack closer together and so an initial reduction in volume of the liquid occurs before the usual expansion effect from raising the temperature is observed. Water, therefore, has its maximum density at 4°C. 

To proceed further we require some information about the structures of ices Ih, II and III, and how these structures can be converted, one to the other. In the following we draw heavily upon an excellent discussion published by von Hippel and Farrell 74>. 

At this stage in the literature, there is no method available by which one can directly determine the orientation of molecules of liquids at interfaces. Molecules are situated at interfaces (e.g., air-liquid, liquid-liquid, and solid-liquid) under asymmetric forces. Recent studies have been carried out to obtain information about molecular orientation from surface tension studies of fluids (Birdi, 1997). It has been concluded that interfacial water molecules, in the presence of charged amphiphiles, are in a tetrahedral arrangement similar to the structure of ice. Extensive studies of alkanes... 

The structure of ice cream has been studied in detail using electron microscopy. Trapped air bubbles are found to be separated by only few micrometer-thick layers of the continuous phase. 

Figure 1.4 The structure of ice-lh (he hydrogen atoms are I placed symmetrically between the 0- 0 pairs lor simplicity...

Does thermal motion make a difference for this aspect of the structure of ice Figure lb shows a snapshot from a simulation at finite temperature, prior to melting. While the perfect molecular alignments of the ideal lattice have been lost, the picture still shows discernible channels molecules in solids do move, but this motion does not affect the overall symmetry. 

The peculiar properties of water, which have been so important in the development of life on Earth, are largely attributable to hydrogen bonding. The structure of a liquid is much harder to understand than that of a solid. We shall therefore approach the peculiarities of water through the structure of ice. 

In this section, the structures of ice, water, and the hydrogen bond are based on the classical works of Bernal and Fowler (1933), Pauling (1935), and Bjerrum (1952), as well as the reviews of Frank (1970), and Stillinger (1980). These subjects are treated in comprehensive detail in the seven volume series edited by Franks (1972-1982), to which any student of water compounds will wish to refer. A second series of monographs on water, also edited by Franks (1985-1990), was published to update the earlier monograph series. Discussion on computer simulation studies of the structure and dynamics of water is largely based on the work of Debenedetti (1996, 2003). 

Computational studies have advanced the study of the solid phase of water and of the interfacial region where the phase transition occurs [1-5]. As water exhibits very unusual properties in the liquid phase, it also exhibits peculiar properties in the solid phase as well. Much about the structure of ice is known from x-ray diffraction experiments or computational studies. Some experiments have been performed on the interfacial region between the liquid and solid phase of water to understand the freezing process, but additional studies are still needed to characterize the... 

Figure 1. The structure of ice I (reproduced from ref 16). Each site is connected by hydrogen bonding with three sites from the same layer and one site from either one or the other of the neighboring layers. Copyright 1962 by the American Institute of Physics.

Figure 12.2. The structure of ice cream mix and ice cream. (A). Fat globules (F) in mix with crystalline fat within the globule and adsorbed casein micelles (C), as viewed by thin section transmission electron microscopy. (B). Close-up of an air bubble (A) with adsorbed fat, as viewed by low temperature scanning electron microscopy. (C). Air bubble (A) with adsorbed fat cluster (FC) that extends into the unfrozen phase, as viewed by thin section transmission electron microscopy with freeze substitution and low temperature embedding.

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