Geometric modeling other considerations

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

More recent models include other considerations such as a condensation mechanism associated with the difference between the energies of different-sized particles as well as separate compressive and tensile geometric forces (e.g., Trujillo et al., 2003). Typically, these are considered in the context of particles that can vary in both size and density, some results of which we describe in Section 10.4.3. 

On the other hand, hi- or multi-metallic supported systems have been attracting considerable interest in research into heterogeneous catalysis as a possible way to modulate the catalytic properties of the individual monometalUc counterparts [12, 13]. These catalysts usually show new catalytic properties that are ascribed to geometric and/or electronic effects between the metalUc components. Of special interest is the preparation of supported bimetallic catalysts using metal carbonyls as precursors, since the milder conditions used, when compared with conventional methods, can render catalysts with homogeneous bimetallic entities of a size and composition not usually achieved when conventional salts are employed as precursors. The use of these catalysts as models can lead to elucidation of the relationships between the structure and catalytic behavior of bimetalUc catalysts. 

While this definition is arbitrary it is appropriate because it is based on chemical as well as geometric considerations and, like other definitions, it agrees with the conventional assignment in cases where there is no dispute. The definition can be justified for use with the bond valence model since any true bond that is excluded by this definition contributes at most only 4 per cent to the cation bond valence sum, and generally much less given that eqn (3.1) tends to overestimate the valence of weak bonds. 

This point may appear to be semantics to one interested primarily in the connection between stoichiometry and geometric structure however, for more detailed considerations the model used matters. For example, the two-center-two-electron bond model with a lone pair on P suggests electrophilic attack at a single P atom, e.g., protonation leading to a P-H terminal bond. On the other hand, in the delocalized MO model the degenerate e symmetry HOMOs of P4 are centered on the P-P edges. Frontier-orbital considerations, then, suggest electrophilic attack would... 

Reaction scheme 2 is proposed based on experimental results coming from the application of different experimental methods.The energy data was obtained by consideration of the total energy of each gas-phase species and also from each adsorbate interacting with a Cu22(14,8) cluster substrate used to model the perfect Cu(lll) surface. The geometric parameters of the transition state structures were taken from published data while details for the other structures considered, as well as the... 

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