Kinetic requirements for

The kinetic requirements for a successful application of this concept are readily understandable. The primary issue is the rate at which the electroactive species can reach the matrix/reactant interfaces. The critical parameter is the chemical diffusion coefficient of the electroactive species in the matrix phase. This can be determined by various techniques, as discussed above. 

The bottom of individual pores is always curved, varying from a shallowly curved semicircle to an elongated conical depending on the formation conditions. As will be discussed later the curvature of pore bottom plays a critical role in the reaction kinetics required for formation of PS and its morphology. 

The kinetic requirements for this to be the case are k or lz i must be large... 

Herzfeld and Langmuir-Hinshelwood-Hougen-Watson cycles, could be formulated and solved in terms of analytical rate expressions (19,53). These rate expressions, which were derived from mechanistic cycles, are phrased, however, in terms of the formation and destruction of molecular species without the need for computing the composition of reactive intermediates. Thus, these expressions are the relevant kinetics required for molecular models and are rooted to the mechanistic cycles only implicitly by the mechanistic rate constants. The molecular model, in turn, transforms a vector of reactant molecules into a vector of product molecules, either of which is susceptible to thermodynamic analysis. This thermodynamic analysis helps to organize these components into relevant boiling point or solubility product classes. Thus the sequence of mechanistic to molecular to global models is intact. 

The detection of binuclear intermediates is important since it provides evidence for inner-sphere mechanisms conversely, outer-sphere mechanisms preclude their formation. It is significant that formally identical reaction sets do not necessarily all display binuclear intermediates. Not only might this be caused by a lack of the proper kinetic requirements for detectability but also by a lack of occurrence. This can be rationalized by pointing out that it is not necessary for these reaction sets to occur all by inner-sphere or all by outer-sphere mechanisms. In fact, examples of single reactions which apparently occur simultaneously by both mechanisms are Np( VI)-Cr(II) (89, 90), Pu( VI)-Fe(II) (56), and V(IV)-V(II) (57). 

Poly (methyl methacrylate) is the only polymer so far which approximates the kinetic requirements for the existence of this phenomenon however, it has not been demonstrated experimentally, presumably because Equation 8 was not obeyed. Again, the polymerization kinetics for this system should favor the validity of Equation 8. 

The transformation of the crystalline into the glassy state by solid-state reactions is extensively reviewed in its theoretical and experimental aspects. First, we give some historical background and describe the thermodynamics of metastable phase formations, adding as well the kinetic requirements for the amorphization process. Then we discuss the different experimental routes into the amorphous state hydriding, thin diffusion couples, and other driven systems. In the discussion and the summary, we close the gap between the melting phenomena and the amorphization and provide a tentative outlook. 

The success of an enzyme-catalyzed kinetic resolution is limited by the maximum chemical yield of 50% for each enantiomer. However, this drawback can be overcome by a process called dynamic kinetic resolution. The key idea of this principle is to racemize the slow reacting enantiomer continuously reproducing the faster one. In an ideal case at the end of the conversion one enantiomer is formed in 100% yield with 100% of enantiomeric excess[13S 1371. The kinetic requirements for a dynamic kinetic resolution are shown in Scheme 11.1-16[8bl. 

No adequate compilation of those solutions of the diffusion equation applicable to the diffusion of matter has as yet been made. The author has become aware of the difficulty of obtaining suitable solutions in a number of studies of diffusion, and it is hoped that this chapter will provide a source of reference for such solutions. Equations of chemical kinetics can be used readily in differential or integral form, but the equations of diffusion kinetics require for their treatment a special and often laborious technique. Many of the cases which can arise have not yet been solved rigorously, though the field is a rich one both from the mathematical and the experimental viewpoints. The present chapter aims at giving some solutions of the diffusion equation in a form in which they may be applied, together with cases of diffusion systems in which the boundary conditions are those of the diffusion equation solved ... 

M. R. Betancourt and D. Thirumalai, Exploring the kinetic requirements for enhaneement of protein folding rates in the GroEL cavity. J. Mol. Biol. 287, 627-644 (1999). 

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