Shape selectivity lattice model

Micellar structure has been a subject of much discussion [104]. Early proposals for spherical [159] and lamellar [160] micelles may both have merit. A schematic of a spherical micelle and a unilamellar vesicle is shown in Fig. Xni-11. In addition to the most common spherical micelles, scattering and microscopy experiments have shown the existence of rodlike [161, 162], disklike [163], threadlike [132] and even quadmple-helix [164] structures. Lattice models (see Fig. XIII-12) by Leermakers and Scheutjens have confirmed and characterized the properties of spherical and membrane like micelles [165]. Similar analyses exist for micelles formed by diblock copolymers in a selective solvent [166]. Other shapes proposed include ellipsoidal [167] and a sphere-to-cylinder transition [168]. Fluorescence depolarization and NMR studies both point to a rather fluid micellar core consistent with the disorder implied by Fig. Xm-12. 

If stationary phase interactions are negligible the lattice statistical thermodynamic model and the solvophobic model predict similar results. The strength of the lattice statistical thermodynamic model is that it can explain the shape selectivity observed for certain stationary phases and can accommodate silanophllic interactions. 

The authors [13] also proposed a multiphase mass transport model for toluene nitration, the details of, which are given in Fig. 2.4. It is based on the formation of a thin aqueous film aroimd the hydrophilic catalyst particles, which are dispersed in toluene medium. The model also accounted for the existence of vapor phase over the liquid-liquid-solid reaction medium. The major mass transfer resistances are offered by the liquid film around the catalyst particles and in the catalyst pores. The aqueous film and the liquid in the pores constitute the micro environment necessary to facilitate the desired level of lattice transformation in the catalyst particles. Figure 2.4 also shows the concept of the microenvironment within and around the catalyst particle. These studies have demonstrated that shape selectively effect of zeolite Beta catalyst is significantly enhanced by the specific microenvironment created within and around the catalyst particles. This has significantly enhanced the para-selectivity from 0.7 to 1.5. The microenvironment has also improved the accessibility of reactant molecules to the catalyst active sites. 

In models of proteins, complete cubic lattices of fewer than 100 points have been utilized for selecting favorable sequences, for investigating the temperatures of folding, and for a wide variety of other folding simulations. Usually these have been performed on highly symmetric forms such as cubes. There is some advantage in considering spaces with less dense surface shells. The combinations of such shapes with cores and less dense surface shells has been considered. " ... 

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