Expanding core model

An unusual variation of the shrinking core model is the expanding core model in which the reaction starts at the center (see Doraiswamy and Gokarn, 1988). The product— ash core instead of the reactant core in normal behavior— moves outward till it completely envelops the particle. The controlling mechanisms described for the shrinking core model apply equally here, but the equations are different. We shall discuss this at some length later in this section while describing a model for the disproportionation of potassium terephthalate. 

As explained thoroughly in the original report, by careful comparison of the frequencies of these core-size markers with a series of structurally well-defined model compounds, the authors concluded that the photoproduct has a slightly expanded core relative to the deoxy structure and inferred that the probable cause for this expansion is restriction of the out-of-plane displacement of the iron brought about by protein restraint on the proximal histidine. Given this interpretation, it should be expected that significant differences in the iron-histidine stretching frequency are likely to be observed, and, as will be seen, it is indeed this feature which exhibits the most substantial shifts for these intermediate species. 

Figure 15.8 The expanding core or rotting apple (because the apple rots from the center) model for fluid-solid reactions.

The quality of quantum-chemical calculations depends not only on the chosen n-electron model but also critically on the flexibility of the one-electron basis set in terms of which the MOs are expanded. Obviously, it is possible to choose basis sets in many different ways. For highly accurate, systematic studies of molecular systems, it becomes important to have a well-defined procedure for generating a sequence of basis sets of increasing flexibility. A popular hierarchy of basis functions are the correlation-consistent basis sets of Dunning and coworkers [15-17], We shall use two varieties of these sets the cc-pVXZ (correlation-consistent polarized-valence X-tuple-zeta) and cc-pCVXZ (correlation-consistent polarized core-valence X-tuple-zeta) basis sets see Table 1.1. 

Both the Menger-Portnoy model and the model by Berezin were effectively derived on the assumption that micellar solutions contain two pseudophases, namely the micellar pseudophase and bulk water. However, both models can be expanded to take more than one micellar pseudophase into account. For example, this could be done when the micellar pseudophase is seen to consist of two separate pseudophases (zones) itself, namely a pseudophase corresponding to the hydrophobic core and a pseudophase corresponding to the micellar Stern region. " If one then assumes a reaction to occur with a rate constant k in the Stern region while the reaction does not occur in the micellar core, the expression for k includes the distribution of the reactant over different zones [Equation (6)]. " ... 

This simplification was used by Ottewill and Walker (7) in their study of the adsorption of a nonionic surfactant onto polystyrene latex in aqueous sodium chloride. In the case of carboxylated emulsion polymers, evidence from conductometric titrations suggests that the carboxyl groups are generally concentrated near the particle surface. The resultant model of an expanded particle is that of a hydrated acid-rich shell surrounding a compact polymer core. The hydrated shell may be viewed as a dilute polymer solution where the density is close to that of water, i.e., Pe= P0. With this assumption, Equation 1 reduces to the form ... 

A drawing of a two-dimensional, electron-domain model of a conventional Lewis lone pair is shown in Fig. 23. The lone pair and bonding pairs are structurally equivalent they have identical van der Waals envelopes. Such seems to be nearly the case for lone pairs in the valence-shells of small-core, non-octet-expanding atoms (carbon, nitrogen, oxygen and fluorine). 

Ellmarfs group expanded the scope of the difunctionalized ketone core, in that not only 1,3 diaminoketones were prepared combinatorially, but also 1-amino-propanones with acyloxy and alkylated mercapto substituents in the 3-posihon (Figure 1.17) [95], In this model study, no biological data on target proteases were reported [95],... 

Fig. 4. Thermodynamic models of membrane protein folding. (A) In the two-step model of folding, the TM helices fold and insert into the membrane and subsequently move laterally to associate (Popot and Engelman, 1990). (B) White and co-workers constructed an expanded model, which includes the protein residing in water (states 1-3), the interfacial region (states 4 and 5), and the membrane core (states 6 and 7) (White and Wimley, 1999).

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