Penultimate polymerization model

By jove, I think we ve done it We have related the observed structure to the type of polymerization mechanism and devised a method to determine the fundamental parameters, at least for the terminal model. Admittedly, a number of assumptions have been made including isothermal conditions, reactivities independent of chain length, and instantaneous conditions (no conversion) but it has demonstrated the approach we are taking. However, before we become enraptured with our success, let us examine a polymerization model, which is slightly more complicated, that is, the penultimate polymerization model. 

Reactivity ratios rj are defined by r, = ka/kij, the ratio of homopropagation, ka, to cross-propagation, rate coefficients, where fcy refers to the addition of monomer j to a free-radical chain-end terminating in species i. Under ideal polymerization conditions the mole fraction of monomer units i contained in the copolymer Fj is given by eq (4.6-14), which holds for both the terminal and the implicit penultimate unit models (see Section 4.6.4.3) [45]. 

It has been known since 1980 that the terminal model for free-radical copolymerization sometimes fails, due to the penultimate unit effect. Direct detection of the penultimate unit effect by ESR has been unsuccessfully attempted many times. In this section, direct detection of the penultimate unit effect using dimeric model radicals generated from dimeric model radical precursors prepared by ATRA is discussed (Fig. 19). The structures of the dimeric model radicals studied are summarized in Fig. 20. For a detailed discussion of the penultimate unit effect, dimeric, monomeric, and polymeric model radicals were examined. The radicals were generated by three methods homolytic cleavage of carbon-bromine bonds of alkyl bromides with hexabutyldistannane, photodecomposition of an azo-initiator, and radical polymerization performed directly in a sample cell in a cavity. 

The polymerization model most commonly adopted for olefin copolymerization is the terminal model, particularly for studies of polymerization kinetics. In the terminal model, only the last monomer molecule added to the chain end influences polymerization and transfer rates. Besides the fact that it is logically expected, there is also significant experimental evidence supporting the terminal model for olefin polymerization. Since monomer propagation and chain-transfer reactions take place by insertion between the chemical bond formed by the metal in the active site and the polymer chain end, it is certainly reasonable to assume that both the nature of the active site and the type of monomer last added to the chain will affect these reactions. On the other hand, higher-order models such as the penultimate and pen-penultimate models have not found widespread use in coordination polymerization. 

The average difference is 0.050 that indicates agreement between the experimental and predicted triad fractions and establishes that the model copolymer is made by a terminal mechanism rather than a penultimate mechanism. We cannot determine the parameters of the polymerization models, i.e. ta and re, since we only have one polymer system to examine rather than a number of polymers prepared by systematically varying x. 

The first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

For many systems, the copolymer composition appears to be adequately described by the terminal model yet the polymerization kinetics demand application of the penultimate model. These systems where rAAB=rliAR and aha bba hut sAfsB are said to show an implicit penultimate effect. The most famous system of this class is MMA-S copolymerization (Section 7.3.1.2.3). 

The Chemistry of Radical Polymerization Table 7.5. Implicit Penultimate Model Reactivity Ratios... 

More recent work has shown that the observed variation in propagation rate constants with composition is not sufficient to define the polymerization rates.5" 161,1152 There remains some dependence of the termination rate constant on the composition of the propagating chain. Thus, the chemical control (Section 7.4.1) and the various diffusion control models (Section 7.4.2) have seen new life and have been adapted by substituting the terminal model propagation rate constants (ApXv) with implicit penultimate model propagation rate constants (kpKY -Section 7.3.1.2.2). 

The first-order markov model describes a polymerization where the penultimate unit is important in determining subsequent stereochemistry. Meso and racemic dyads can each react in two ways ... 

In the early 1940s when the polymerization theory was developed, tiie ideal, terminal, and penultimate models for fhe copolymerization were established also the possible distribution laws for the monomer sequence along the copolymer chains were defined Bemoullian, firsf- and second-order Markoffian. ... 

With some classical polymerization reactions, e.g., styrene with methyl metacrylate, deviations were observed, e.g., by Fukuda et and O Driscoll and Reilly, whereby a penultimate unit effect was discussed and corrections introduced. This is expected on the basis of the Markov chain model because in this model only the last added unit controls the next step. As the correction method of O Driscoll also took errors in the variables into account, it is called the error in variables method (EVM). ... 

A slightly similar model was suggested by Bawn and Ledwith." It is based on the probability that a growing polymeric alkyllithium should have some enolic character, with the lithium coordinating to the carbonyl oxygen of the penultimate unit ... 

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