Fractional kinetic orders, degree

A good example of this kinetic behavior was found in the study of the n-butyllithium-styrene system in benzene, in which a kinetic order dependency on n-butyllithium concentration was observed, consistent with the predominantly hexameric degree of association of n-butyllithium (Worsfold and By water, 1960). However, this expected correspondence between the degree of association of the alkyllithium compound and the fractional kinetic order dependence of the initiation reaction on alkyllithium concentration was not always observed (Young et al., 1984). One source of this discrepancy is the assumption that only the unassociated alkyllithium molecule can initiate polymerization. With certain reactive initiators, such as 5 c-butyllithium in hexane solution, the initial rate of initiation exhibits approximately a first-order dependence on alkyllithium concentration, suggesting that the aggregate can react directly with monomer to initiate polymerization (Bywater and Worsfold, 1967a). A further... 

The kinetics of the addition of poly(2,4-hexadienyl)lithium to 1,1-diphenylethylene has been investigated by two groups. Fetters et al. [99] observed that the rate of addition exhibited a first-order dependence on the concentration of poly(2,4-hexadienyl)lithium, but the apparent first-order rate constant for addition was inversely proportional to the initial concentration of poly(2,4-hex-adienyl)lithium chain ends. However, in contrast to the dimeric degree of association of poly(styryl)lithium, it was determined by concentrated solution viscometry studies that 35-40% of the poly(2,4-hexadienyl)lithium chain ends were not associated. Thus, it was concluded therein and elsewhere [100, 101] that there is no necessary relationship between the degree of association of the chain ends and the fractional kinetic orders observed. 

Thus kp for lithium counterion is 1/300 of kp for potassium counterion. The low reactivity and association of lithium alkoxide was reported in the anionic polymerization of epoxides.We have found that two fold increase of the lithium initiator concentration has led to a decrease of the kp nearly to one half. This indicates that the kinetic order with respect to the initiator would be near to zero, suggesting a very high degree of association of the active species. Thus the propagation reaction appears to proceed in practice through a very minor fraction of monomeric active species in case of lithium catalyst. 

The propagation reaction in hydrocarbon media has been found by most authors to be very much affected by association phenomena. In the three monomers considered here the propagating species are ion pairs to stabilize themselves in nonpolar solvents, they are forced to form aggregates. It appears that the small concentrations of free ion pairs in equilibrium with the aggregates are the active moieties, and the propagation reactions are fractional order in active chain ends because of this. The degree of association is in some dispute for isoprene and butadiene but not for styrene. In the latter case dimerization of the active centers was postulated from kinetic evidence (27) and inde-... 

The isothermal pyrolysis in the presence of air proceeds at a much faster rate and higher weight losses are obtained as compared to vacuum pyrolysis at the same temperature. The first order rate constant obtained is linearly related to the expression [%LOR + o-(% crystallinity)]//o with a degree of correlation r = 0.923, where a is the accessible surface fraction of the crystalline regions according to Tyler and Wooding [501], and / is the orientation factor. No correlation could be found with DP due to very rapid depolymerization. The fact that the rate is inversely proportional to the orientation and that it decreases with the increase in the thickness of the fibers indicates that the rate of the diffusion of the oxygen into the fibers controls the kinetics and that oxidation is the predominant process in air pyrolysis. 

In contrast to the case for gases, where an advanced kinetic theory to explain molecular motion is available, theories of the structure of liquids and their transport characteristics are still inadequate to allow a rigorous treatment. Liquid diffusion coefficients are several orders of magnitude smaller than gas diffiisivities, and depend on concentration due to the changes in viscosity with concentration and changes in the degree of ideality of the solution. As the mole fraction of either component in a binary mixture approaches unity, the thermodynamic factor T approaches unity and the Fick diffusivity and the MS diffusivity are equal. The diffusion coefficients obtained under these conditions are the infinite dilution diffusion coefficients and are given the symbol TP. 

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