Ice-I, structure

An X-ray liquid diffraction experiment on a solution corresponding to the stoichiometry of the trimethylamine decahydrate [807], 4(CH3)3N 40H2O, provided the radial distribution function shown in Fig. 21.14, which could be fitted equally well with models based on the hydrate crystal structure or on the ice I structure with interstitial amine molecules. This result clearly illustrates the insensibility of X-ray liquid diffraction data alone for distinguishing between competing models for aqueous solutions which have similar first- and second-order coordinations. 

The tetrahedral hydrogen-bonding structure for a central water molecule linked to its four nearest neighbors is shown in Figure 9. (Strictly speaking, this refers to the ice I structure since for bulk water at 20°C there are on average 4.5 water molecules coordinated to any one central water molecule.) As a result of these structural links, any one water molecule can-... 

The iceberg theory of ionic solutions (17) and of hydration of proteins (18) is closely related to the hydrate microcrystal theory of anesthesia the only change suggested for these theories is that the ordered arrangement of water molecules about the solute ions and protein, side chains has one or another of the dathrate structures rather than the more compact ice-I structure. 

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. 

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. 

Before considering the details of the structure of liquid water, it is important to define precisely what is meant by the term structure as applied to this liquid. If we start from ice I, in which molecules are vibrating about mean positions in a lattice, and apply heat, the molecules vibrate with greater energy. Gradually they become free to move from their original... 

Let us now turn our attention to liquid water. Just as in ice I, molecular motions may be divided into rapid vibrations and slower diffusional motions. In the liquid, however, vibrations are not centred on essentially fixed lattice sites, but around temporary equilibrium positions that are themselves subject to movement. Water at any instant may thus be considered to have an I-structure. An instant later, this I-structure will be modified as a result of vibrations, but not by any additional displacements of the molecules. This, together with the first I-structure, is one of the structures that may be averaged to allow for vibration, thereby contributing to the V-structure. Lastly, if we consider the structure around an individual water molecule over a long time-period, and realize that there is always some order in the arrangement of adjacent molecules in a liquid even over a reasonable duration, then we have the diffusionally averaged D-structure. 

An important phenomenon when considering the differences between ice I and liquid water is that water achieves its maximum density not in the solid state, but at 4 °C, i.e. in the liquid state. The reasons for this were first discussed by Bernal Fowler (1933). They noted that the separation of molecules in ice I is about 0-28 nm, corresponding to an effective molecular radius of 014 nm. Close packing of molecules of such radius would yield a substance of density 1-84 g cm" . To account for the observed density of 10 g cm" , it was necessary to postulate that the arrangement of molecules was very open compared with the disordered, close-packed structures of simple liquids such as argon and neon. 

In its solid state, however, the basic structural features of ordinary hexagonal ice (ice I) are well established. In this structure (Figure 1.2), each water molecule is hydrogen bonded to four others in nearly perfect tetrahedral coordination. This arrangement leads to an open lattice in which intermolecular cohesion is large. 

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 ice I model used to describe the structure of H20(as) 77 K/77 K does not predict any oxygen-oxygen distances in the region 2.76 A <7 <4.5 A and is hence not capable of explaining the observed distance spectrum and density of HoO(as) 10 K/10 K. We defer to a later section the discussion of an appropriate model for this high density H20(as). 

Note added in proof. Earlier in the text it was mentioned that the model used to describe the structure function of low density H20(as) does not describe that of high density H20(as). However, Narten, Venkatesh and Rice 27) do show than an ice I-like network with a near neighbor distance of 2.76 A has the density and distance spectrum of high density H20(as) if one permits 45% of the cavities characteristic of this structure to be occupied by water molecules. These are not ordinary unbonded interstitials. If the cavity molecules are located on the c axis at a distance of 2.76 A from the nearest network molecule each cavity molecule would have second neighbor network molecules at a distance of 3.25 A. Moreover, since occupancy of 45% of the cavities implies that 81% of the water molecules are part of the tetrahedral network and 19% in cavity positions, the average coordination number of nearest neighbors in this model is 4.3, as is found for H20(as) 10 K/10 K. Structure functions calculated for this interstitial variant of a randomized ice I model (the randomization is effected as in the simple ice I... 

Following the same line of thought, we are led to propose that high temperature H iO as) has a simple random network structure derived from an ice I type lattice [i.e. like Ge(as) and Si(as)]. 

This is an appropriate point to remark on some of the thermodynamic aspects of the complicated random network structure envisaged for the liquid. Now, the thermodynamic properties of ices II and III are very similar 1h The ice II ice III transition (249 K, 3.4 kbar) involves only a very small change in volume, namely 0.26 cm3/mole, 1.6% of the molar volume), a small change in entropy 1.22 cal/° mole, and a small change in enthalpy, 304 cal/mole. Similarly, the ice I ice II,... 

Mixture Models Broken-Down Ice Structures. Historically, the mixture models have received considerably more attention than the uniformist, average models. Somewhat arbitrarily, we divide these as follows (1) broken-down ice lattice models (i.e., ice-like structural units in equilibrium with monomers) (2) cluster models (clusters in equilibrium with monomers) (3) models based on clathrate-like cages (again in equilibrium with monomers). In each case, it is understood that at least two species of water exist—namely, a bulky species representing some... 

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