Clathrate modeling

Ashbaugh, H. S. Asthagiri, D. Pratt, L. R. Rempe, S. B., Hydration of krypton and consideration of clathrate models of hydrophobic effects from the perspective of quasichemical theory, Biophys. Chem. 2003,105, 323-338... 

We have discussed some examples which indicate the existence of thermal anomalies at discrete temperatures in the properties of water and aqueous solutions. From these and earlier studies at least four thermal anomalies seem to occur between the melting and boiling points of water —namely, approximately near 15°, 30°, 45°, and 60°C. Current theories of water structure can be divided into two major groups—namely, the uniformist, average type of structure and the mixture models. Most of the available experimental evidence points to the correctness of the mixture models. Among these the clathrate models and/or the cluster models seem to be the most probable. Most likely, the size of these cages or clusters range from, say 20 to 100 molecules at room tempera-... 

Bakker RJ, Dubessy J, Cathelineau M (1996) Improvements in clathrate modelling I. The H2O-CO2 system with various salts. Geochim Cos-mochim Acta 60 1657-1681... 

While the clathrate model is attractive, it is not correct to assume that the water is organized in some long-lived structure the observation that the self-diffusion coefficient for co-sphere water is larger than that for the solute rules this out. However, the rotational correlation time is shorter for ethanol and t-butyl alcohol in water (in the clathrate cage ) than in the pure liquid (Goldammer and Hertz, 1970 Goldammer and Zeidler, 1969). Nmr experiments show that in water the solvent dipole moments point away from the apolar groups (Hertz and Radle, 1973). 

Several cluster models have been tested to account for patterns of small clusters (p = 1 or 2 bar in Fig. 18). First, clathrate models have been examined. The most popular of these consists of a regular dodedecahedron with one H2O molecule at each of the 20 vertices and possibly one additional molecule at the center. In this model, HjO molecules form regular pentagons with a molecular angle HOH of 108°, which is intermediate between 104.5°, the value for the free molecule, and 109.5°, that for tetrahedral bonding in the diamond cubic structure. Such a clathrate model, stabilized by an additional proton, accounts well for mass spectrometry results, but is found to be far too symmetrical to account for the structure of neutral clusters. An amorphous model,derived from Polk s random dense packing, has been tested. This... 

The thermodynamic properties of clathrates can be derived from a simple model which corresponds to the three-dimensional generalization of ideal localized adsorption. In ref. 52 the deriva-... 

The pair of Eqs. 12, 13 epitomizes the relation between the equilibrium vapor pressure, composition, and chemical potential of the solvent in a clathrate obeying the present model. These expressions were used in the calculation of the thermodynamic properties of gas hydrates30 and have also been formulated by Barrer and Stuart 4 for a clathrate with a single type of cavity and one occluded component they reduce to the equations of ref. 52. 

The fact that both heats of formation and equilibrium pressures of the hydrates of spherical molecules correctly follow from one model must mean that the L-J-D theory gives a good account of the entropy associated with the motions of these solutes in the cavities of a clathrate. That the heat of formation of ethane hydrate is predicted correctly, whereas the theoretical value of its vapor pressure is too low, is a further indication that the latter discrepancy must be ascribed to hindered rotation of the ethane molecules in their cavities. 

Spin orbitals, 258, 277, 279 Square well potential, in calculation of thermodynamic quantities of clathrates, 33 Stability of clathrates, 18 Stark effect, 378 Stark patterns, 377 Statistical mechanics base, clathrates, 5 Statistical model of solutions, 134 Statistical theory for clathrates, 10 Steam + quartz system, 99 Stereoregular polymers, 165 Stereospecificity, 166, 169 Steric hindrance, 376, 391 Steric repulsion, 75, 389, 390 Styrene methyl methacrylate polymer, 150... 

Spatial accommodation of the guest evidently allows disordering of the guest molecule, another characteristic feature of true clathrates. This structure may serve as a general model for other possible inclusion compounds of 1 with apolar guests and also, in lack of the structure of the free host 1 (cf. Sect. 4.1), it may help to imagine a probable steric arrangement for that case... 

An important advantage of the inclusion complexes of the cyclodextrins over those of other host compounds, particularly in regard to their use as models of enzyme-substrate complexes, is their ability to be formed in aqueous solution. In the case of clathrates, gas hydrates, and the inclusion complexes of such hosts as urea and deoxycholic acid, the cavity in which the guest molecule is situated is formed by the crystal lattice of the host. Thus, these inclusion complexes disintegrate when the crystal is dissolved. The cavity of the cyclodextrins, however, is a property of the size and shape of the molecule and hence it persists in solution. In fact, there is evidence that suggests that the ability of the cyclodextrins to form inclusion complexes is dependent on the presence of water. Once an inclusion complex has formed in solution, it can be crystallized however, in the solid state, additional cavities appear in the lattice, as in the case of the hosts previously mentioned, which enable the inclusion of further guest molecules. ... 

For clarity and because of space limitations, we will consider only examples of complexes in which the guest interacts with the host from above (or/and below) the cavity, and the structure has been confirmed by X-ray analysis. These complexes serve as models for the interaction of neutral molecules which are nearly concave/ convex complementary in their. spatial interaction. Although complementary in shape, some guest molecules simply fill spatial voids in the host lattice. These clathrate-like structures will not be considered. 

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.

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... 

Clathrate-Cage Model. The final water model which is of major interest is based on clathrate hydrate cage structures. It was originally proposed by Pauling (116), who noted the existence of clathrate hydrates of many inert gases and suggested, by analogy to the chlorine hydrate,... 

Before proceeding, it is important to recall the significant feature which appears to distinguish the cluster model from the two other prominent mixture models—i.e., the broken-down ice lattice and the clathrate hydrate cage structures. The latter two theories allow for the existence of discrete sites in water, owing to the cavities present either in the ice... 

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