Reaction kinetics cage effects

For near and supercritical conditions, combustion gas-phase data are often used as the point of reference to assess solvent effects. The gas-phase values of kig, available for temperatures 800-2500 K, show the activation energy 90 kJ mol In condensed phase, stabilization of H2O molecules via H-bonding may increase the activation barrier, but on the other hand the reaction can be promoted by the solvent cage effect. Diffusion-kinetic modelling and stochastic simulation of chemical reactions in radiation tracks have shown that the occurrence of reaction (15.19) is consistent with the anomalous increase in H2 yield observed in water radiolysis at temperatures above 523 K, if kig is of the order of 1-2x10 s (4-8x10 s ) at 573 K. Considering the two... 

In this case of uncharged, nonpolar reactions, there is little interaction between the reactants and the solvent. As a result, the solvent does not play an important role in the kinetics per se, except through its role in determining the solubility of reactive species and cage effects. The rate constants for such reactions therefore tend to be similar to those for the same reactions occurring in the gas phase. Thus, as we saw earlier, diffusion-controlled reactions in the gas phase have rate constants of 10-ll) cm3 molecule-1 s-1, which in units of L mol-1 s-1 corresponds to 6 X 1010 L mol-1 s-1, about equal to (usually slightly greater than) that for diffusion-controlled reactions in solution. 

Previous studies of the reactions of guaiacol (orthomethoxy-phenol) (3 ), dibenzyl ether (4 ), and benzyl phenyl amine (5) in dense water elucidated parallel hydrolysis and pyrolysis pathways, the selectivity to the latter increasing with water density. Reactant decomposition kinetics were interestingly nonlinear in water density and consistent with two mechanistic interpretations. The first involved "cage" effects, as described for reactions in liquid solutions (6 ). The second led to parallel pyrolysis and solvolysis reaction pathways wherein associated rate constants were dependent upon pressure. These two schemes are probed herein through the reactions of benzyl phenyl amine (BPA) in water and methanol. 

Practical free-radical polymerizations often deviate from Eq. (6.126) because the assumptions made in the ideal kinetic scheme are not fuUy satisfied by the actual reaction conditions or because some of these assumptions are not valid. For example, according to the ideal kinetic scheme that leads to Eq. (6.126), the initiation rate (Rf) and initiator efficiency (/) are independent of monomer concentration in the reaction mixture and primary radicals (i.e., radicals derived directly from the initiator) do not terminate kinetic chains, thoughrifi reality R may depend on [M], as in the case of cage effect (see Problem 6.7) and, at high initiation rates, some of the primary radicals may terminate kinetic chains (see Problem 6.25). Moreover, whereas in the ideal kinetic scheme, both kp and kt are assumed to be independent of the size of the growing chain radical, in reahty k[ may be size-dependent and diffusion-controlled, as discussed later. 

This discussion was intended to provide some insight into the dynamic events that are incorporated into the kinetic theory expression for the rate kernel. These include all the events that are normally associated with qualitative ideas concerning caging effects on reaction dynamics. We next indicate how such kinetic theory results might be analyzed further, and how they are related to the diffusion equation results discussed earlier. 

When water-soluble initiators are used, most of the authors concluded that acrylamide polymerization proceeds within the monomer droplets, irrespective of the nature of the organic phase (aromatic or aliphatic) [28,30-34], Both monomer and initiator reside in the dispersed droplets and each particle acts as a small batch reactor. The process is essentially a suspension polymerization and therefore the kinetics resemble those for solution polymerization. Note that a prefix micro has been added in some cases to this type of polymerization (microsuspension) to emphasize the smallness of the reactor (d 1 pm) and the possibility of interfacial reactions [33]. A square root dependence of the polymerization rate, / p, on initiator concentration, [I] was often observed, in good accord with solution polymerization [28,32-34]. Higher orders were also found which were attributed to chain transfer to the emulsifier [30]. The reaction order with respect to monomer was found to vary from 1 [2832] to 1.7 [3031]> Orders higher than 1 are common for acrylamide polymerization in homogeneous aqueous solution and are explained by the occurrence of a cage effect [35]. 

ABSTRACT. The amount of published work on molecular shape-selective catalysis with zeolites is vast. In this paper, a brief overview of the general principles involved in molecular shape-selectivity is provided. The recently proposed distinction between primary and secondary shape-selectivity is discussed. Whereas primary shape-selectivity is the result of the interaction of a reactant with a micropore system, secondary shape-selectivity is caused by mutual interactions of reactant molecules in micropores. The potential of diffusion/reaction kinetic analysis and molecular graphics for rationalizing molecular shape-selectivity is illustrated, and an alternative explanation for the cage and window effect in cracking and hydrocracking is proposed. Pore mouth catalysis is a speculative mechanism advanced for some systems (a combination of a specific zeolite and a reactant), which exhibit peculiar selectivities and for which the intracrystalline diffusion rates of reactants are very low. 

The stereochemical situation however, is appreciably more complex in incomplete corrins, such as cob(II)ester (24) and base-off forms of complete corrins. The axial ligand at the corrin-boimd Co(II) center is expected to direct the formation of the Co - C bond. In this way kinetic control can lead with high efficiency to the rare Q -alkyl-Co(III)-corrins [84,128[. In such radical recombination reactions the axial ligand at the a- or -side of the metal center will not only steer the diastereoselectivity of the alkylation but also may contribute to significant altering of the cage effects [122,123[. 

The polymerization rate is directly proportional to the monomer concentration for ideal free radical polymerization kinetics. Deviations from this first-order kinetics can be caused by a whole series of effects which must be checked by separate kinetic experiments. These effects include cage effects during initiator free radical formation, solvation of or complex formation by the initiator free radicals, termination of the kinetic chain by primary free radicals, diffusion controlled termination reactions, and transfer reactions with reduction in the degree of polymerization. Deviations from the square root dependence on initiator concentration are to be primarily expected for termination by primary free radicals and for transfer reactions with reduction in the degree of polymerization. 

An authoritative account of diffusional limitation in homogeneous reactions b treated by R. M. Noyes in Progress in Chemical Kinetics, Vol. I, G. Porter, ed. Pergamon Press, Inc., Long Island City, N.Y., 1961. The illustration of the cage effect by photolysis of azomethane is due to R. K. Lyon and D. H. Levy, J. Am. Chem. Soc., 83, 4290 (1961). Many aspects of these questions are covered in E. F, Caldin s Fast Reactions in Solutions, John Wiley and Sons, Inc., New York, 1964. 

---