Propagation kinetic order

The observations discussed above suggest that the kinetic order of lithium poly-isoprene propagation should vary with the living polymer concentration. The effect is imperceptible in aliphatic hydrocarbons, but is observed in benzene solutions. The apparent propagation constants of lithium polyisoprene (MW 2 2 10 ) were determined in benzene and the results are displayed in Fig. 16 in the form of a plot of log kapp vs log c, c denoting the total living polymer concentration. 

It is unfortunate that many workers have not appreciated how essential a clue to the kinetics can be provided by the kinetic order of the whole reaction curve. The use of initial rates was carried over from the practice of radical polymerisation, and it can be very misleading. This was in fact shown by Gwyn Williams in the first kinetic study of a cationic polymerization, in which he found the reaction orders deduced from initial rates and from analysis of the whole reaction curves to be signfficantly different [111]. Since then several other instances have been recorded. The reason for such discrepancies may be that the initiation is neither much faster, nor much slower than the propagation, but of such a rate that it is virtually complete by the time that a small, but appreciable fraction of the monomer, say 5 to 20%, has been consumed. Under such conditions the overall order of the reaction will fall from the initial value determined by the consumption of monomer by simultaneous initiation and propagation, and of catalyst by initiation, to a lower value characteristic of the reaction when the initiation reaction has ceased. 

It also follows from this discussion that for the range of conditions indicated, which are those most frequently used for kinetic studies, the propagating species which are likely to be significant participants in second-order propagation are P+n, P+nA", and P+nP, but the last of these, for the reasons given, is included with P+n. 

The polymerization of styrene by trichloroacetic acid without solvent and in 1,2-dichloro-ethane and nitroethane solutions illustrates the situation where the initiator solvates ionic propagating species [Brown and Mathieson, 1958]. The kinetic order in the concentration of trichloroacetic acid increases from 1 in the highly polar nitroethane to 2 in the less polar 1,2-dichloroethane to 3 in neat styrene. 

The situation is similar qualitatively but differs quantitatively for isoprene and 1,3-buta-diene. The dependence of Rp on initiator varies from g- to -order depending on the specific reaction system. The reaction orders for all monomers are affected hy the relative as well as absolute concentrations of initiator and monomer. Thus the dependence of Rp on initiator for the n-butyllithium polymerization of isoprene in benzene at 30°C is -order at initiator concentrations above 10-4 M but -order at initiator concentrations below 10 4 M [Van Beylen et al., 1988]. Higher initiator concentrations yield higher degrees of aggregation and lower kinetic orders. The excess of monomer over initiator is also important. Higher kinetic orders are often observed as the monomer initiator ratio increases, apparently as a result of breakup of initiator and propagating ion-pair associations by monomer. 

The above mechanism served as a prototype accounting for other similar polymerizations. However, the kinetics of propagation of lithium polydienes revealed a dependence on the polymer concentration lower than 1/2, apparently 1/4 or less order. This prompted the assumption that the lithium polydienyls form higher aggregates than dimers. 

The influence of diphenyl ether and anisole on the association of the polystyryllithium and 1,1-di-phenylmethyllithium active centers has been measured. Severe disaggregation of the polystyryllithium dimers, present in pure benzene, was found to occur at levels of ether addition at which several reliable kinetic studies reported in the literature unequivocally demonstrate a 1/2 order dependence upon polystyryllithium. These results indicate that a necessary connection between the degree of aggregation of organo1ithium polymers and the observed kinetic order of the propagation reaction need not exist. 

Several studies have appeared (12,13,14) in which the propagation reactions involving styryllithium were examined in mixed solvent systems comprising benzene or toluene and ethers. The kinetics were examined under conditions where the ether concentration was held constant and the active center concentration varied. In most cases, the kinetic orders of the reactions were identical to those observed in the absence of the ether. Thus, in part, the conclusion was reached (13,14) that the ethers did not alter the dimeric association state of polystyryllithium. The ethers used were tetrahydrofuran, diphenyl ether, anisole, and the ortho and para isomers of ethylanisole. 

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 dependence of the propagation rate on the concentration of growing chains is illustrated in Figures 6 and 7, and is listed in Table II. The first-order rate constant from Table II are plotted as a function of the initiator concentration. Although the kinetics of organolithium polymerization in nonpolar solvents have been subjected for intensive studies, the results were still somewhat controversial. In view of the strong experimental evidence for association between the organolithium species, the kinetic order ascribed to this phenomenon was postulated (30,31) as shown in Equations (5) and (6). 

A similar kinetic order in respect to monomer for propagation and termination, since the molecular weight of the formed polymer... 

The mechanisms and resulting kinetic equations are shown in Figure 4. Other mechanisms are possible as well as modifications of these—e.g., disproportion termination of chain reactions, and condensation between unlike monomers. The left sides of the equations represent the reactor operator (note that all resulting differential equations are nonlinear because of the second-order propagation and termination reactions). To this is added the complexity of considering separate equations for the thousands of separate species frequently required to define completely commercially useful polymers. Solution by direct application of classical techniques is impractical or impossible in most cases even direct numerical solution is often difficult. Simplifying assumptions or special mathematical techniques must be used (described below in the calculations of MWD). 

Both decay processes are due to minor side reactions of some of the same carbenium ions as those propagating the "fhiitful" reactions of cracking and isomerization. Their effects combine to yield an equation for the kinetics of catalyst decay which can be anywhere from first to second order in site concentration. In practice, small molecules of the type studied as model compounds generally exhibit almost pure second-order decay in site concentration, while the large molecules found in gas oils tend to show a lower kinetic order, often approaching first-order decay. 

The CH3-radicals are p radicals since they undergo second-order propagation steps, so that termination is pp. It can easily be verified by a steady-state treatment that this scheme of reactions (which is an oversimplified version of the true mechanism) does lead to 3/2-order kinetics. 

Propagation is the irreversible repetitive first order addition of monomer to the growing chain [1, 43], The kinetics of propagation have been treated in detail [1]. According to our model, propagation includes species of different ionicities in the absence or presence of electron donor. 

Propagation The anionic propagation kinetics for styrene (S) polymerization with lithium as counterion is relatively unambiguous. The reaction in monomer concentration is first order, as it is for polymerization of all styrene and diene monomers in heptane, cyclohexane, benzene, and toluene [3, 55, 56], The reaction order dependence on total chain-end concentration, [PSLi]o, is one-half as shown in Equation 7.15. The observed one-half kinetic order dependence on chain-end concentration is consistent with the fact that poly(styryl)lithium is predominantly associated into dimers in hydrocarbon solution [85, 86], If the unassociated poly(styryl)lithium is the reactive entity for... 

Elucidation of the mechanism of propagation for iso-prene and butadiene in hydrocarbon solution with lithium as counterion in the past has been complicated by disagreement in the literature regarding both the kinetic order dependence on chain-end concentration and the degree of association of the chain ends, as well as by apparent changes in kinetic reaction orders with chain-end concentration [3, 56], Eor butadiene and isoprene propagation, reported reaction order dependencies on the concentration of poly(dienyl)lithium chain ends include 0.5, 0.33, 0.25, and 0.167. Kinetic smdies of isoprene propagation with lithium as counterion in hydrocarbon solvents showed... 

The kinetic order dependence on the active chain-end concentration is approximately 0.25 for diene propagation, while the kinetic order dependence on the active chain end concentration is approximately 1.0 for cis-trans isomerization of the chains ends [3, 56]. Thus, while the unassociated chain ends add monomer, isomerization of the chain ends occurs in the aggregated state. Since aggregation is favored by increasing chain-end concentrations, high 1,2-microstructure is observed (47% for butadiene) for high chain-end concentrations ([PBDLi] = circa 0.1 M) and high CM-1,4 microstructure (86% for butadiene) is obtained at low chain-end concentrations (circa 10 M Table 7.4). 

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