Aggregation fractional kinetic orders

Fractional kinetic orders of homogenous reactions in solution may point to association of a particular reagent. The kinetics of the initiation step of styrene polymerization in the presence of n-BuLi (equation 33) is in accordance with the assumption that this organolithium compound in a nonbonding solvent forms aggregates of six molecules on the average" . 

Since n-butyllithium is aggregated predominantly into hexamers in hydrocarbon solution [44], the fractional kinetic order dependency of the initiation process on the total concentration of initiator has been rationalized on the basis that unassociated n-butyllithium is the initiating species and that it is formed by the equilibrium dissociation of the hexamer as shown in Scheme 7.8. 

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... 

An alternative interpretation of these fractional kinetic orders in alkyl-lithium concentration as proposed by Wakefield [19] is that the rate-determining step involves coordination of a DPE molecule to one face of the polyhedral organolithium aggregate. As suggested previously [8], incomplete or stepwise dissociation equilibria such as those shown in Scheme 3 would be expected to require less energy as predicted by theoretical calculations [32]. It is important to note that Brown and coworkers [34, 35] have reported that dissociation energies for tetramer-dimer equilibria are 46.1 kj/mol and lOOkJ/mol for methyl-lithium in ether [34] and ferf-butyllithium in cyclopentane [35], respectively. 

The enolate has a direct impact on the polymerization kinetics. Indeed, the kinetics order with respect to [P ] is 1 when /sTda[P ] < 1 (equation 17) and fractional order with respect to [P ] is the rule when 7sTda[P ] 1 (equation 18). A fractional order in initiator is thus the signature of aggregation. 

In fact, kinetic experiments of polymerization of MMA with lithium counterion in THF at -65 °C showed that the reaction order changes from 0.58 to 0.75 in the concentration range from 2.5 to 0.12 mM, allowing for the determination of k , and Ka and proving that the aggregation is an important factor in the polymerization of alkyl (meth)acrylates in polar solvent. Further, the fractional reaction order was confirmed by Baskaran who obtained a reaaion order of 0.53 for the polymerization of MMA using DPHLi as initiator in THF at 20 C. 

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 value of fcprop of the associated species is at least two orders of magnitude lower than fcprop of the nonassodated ion parrs . Consistently, nonassodated ion pairs can be considered as dormant and can be omitted in kinetic equations. Table 4 compares the values of various equilibrium and kinetic parameters for the polymerization of MMA, tBuMA and tBuA. Association is less important for tBMA than for MMA, more likely as a result of the buUdness of the ester groups. In the same line, aggregation is less extensive in the polymerization of tBuMA than tBuA, because of the steric hindrance of the a-methyl subsituent . Values of kf and ko in Table 4 were calculated according to equations 15 and 27, where a denotes the fraction of nonassociated ion pairs. 

Kinetically, these reagents become more basic as aggregate size diminishes more reactive species are obtained in ethers, e.g., in Et20 or THF, than in hydrocarbons or on addition of a donor molecule, e.g., TMED triethylenediamine (DABCO), hexamethyl-phosphorictriamide (HMPA) or dimethylsulfoxide (DMSO). Kinetic studies of metalla-tions by RLi in hydrocarbons or ethers reveal fractional orders in RLi. These arise from dissociation of the larger oligomers, (tetramers and hexamers) to smaller and more reactive species (monomers and dimers) in pre-rate-determining steps. Increasing basicity of the solvent should also help to stabilize the transition state. 

L2Fe(OCHC6H5)2 (L stands for A7, A7 -bis(trimethylsilyl)benzamidinate) (Fig. 15) is also an effective initiator. The polydispersity of poly(e-CL) and poly(LA) is however rather high (1.5 < M IM < 1.9), and the order in iron alkoxide is fractional (0.5), which points to an aggregation phenomenon. In this case, the bulky ligand makes the kinetics more complex and 50 times slower (86). 

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