Copolymerization penultimate effect

Methyl-2-furaldehyde gave a similar overall behaviour, but a penultimate effect was observed in its copolymerization with isopropenylbenzene whereby two molecules of the aldehyde could add together if the penultimate unit in the growing chain was from the olefin. This was borne out by the copolymers composition and spectra. The values of the reactivity ratios showed this interesting behaviour rx = 1.0 0.1, r2 = 0.0 0.1. An apparent paradox occurred the aldehyde, which could not homo-polymerize, had equal probability of homo- and copolymerization and the olefin, which homopolymerized readily, could only alternate. The structure arising from this situation was close to a regular sequence of the type ... 

Cases have been reported where the application of the penultimate model provides a significantly better fit to experimental composition or monomer sequence distribution data. In these copolymerizations raab "bab and/or C BA rBBA- These include many copolymerizations of AN, 4 26 B,"7 MAH28" 5 and VC.30 In these cases, there is no doubt that the penultimate model (or some scheme other than the terminal model) is required. These systems arc said to show an explicit penultimate effect. In binary copolynierizations where the explicit penultimate model applies there may be between zero and three azeotropic compositions depending on the values of the reactivity ratios.31... 

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). 

More complex schemes have been proposed, such as second-order Markov chains with four independent parameters (corresponding to a copolymerization with penultimate effect, that is, an effect of the penultimate member of the growing chain), the nonsymmetric Bernoulli or Markov chains, or even non-Maikov models a few of these will be examined in a later section. Verification of these models calls for the knowledge of the distribution of sequences that become longer, the more complex the proposed mechanism. Considering only Bernoulli and Markov processes it may be said that at the dyad level all models fit the experimental data and hence none can be verified at the triad level the Bernoulli process can be verified or rejected, while all Markov processes fit at the tetrad level the validity of a first-order Markov chain can be confirmed, at the pentad level that of a second-order Maikov chain, and so on (10). 

The original mathematical treatment of the penultimate effect was presented by Merz and coworkers [Barb, 1953 Ham, 1964 Merz et al., 1946], Fukuda and coworkers developed a more extensive treatment, which distinguished between two penultimate models of copolymerization behavior—the explicit penultimate and implicit penultimate models [Coote and Davis, 1999, 2000 Davis, 2001 Fukuda et al., 1985, 1987, 1992, 2002 Ma et al., 2001], The explicit penultimate model for copolymerization involves the use of eight propagation reactions... 

The implicit penultimate model was proposed for copolymerizations where the terminal model described the copolymer composition and monomer sequence distribution, but not the propagation rate and rate constant. There is no penultimate effect on the monomer reactivity ratios, which corresponds to... 

Penultimate effects have been observed for many comonomer pairs. Among these are the radical copolymerizations of styrene-fumaronitrile, styrene-diethyl fumarate, ethyl methacrylate-styrene, methyl methacrylate l-vinylpyridine, methyl acrylate-1,3-butadiene, methyl methacrylate-methyl acrylate, styrene-dimethyl itaconate, hexafluoroisobutylene-vinyl acetate, 2,4-dicyano-l-butene-isoprene, and other comonomer pairs [Barb, 1953 Brown and Fujimori, 1987 Buback et al., 2001 Burke et al., 1994a,b, 1995 Cowie et al., 1990 Davis et al., 1990 Fordyce and Ham, 1951 Fukuda et al., 2002 Guyot and Guillot, 1967 Hecht and Ojha, 1969 Hill et al., 1982, 1985 Ma et al., 2001 Motoc et al., 1978 Natansohn et al., 1978 Prementine and Tirrell, 1987 Rounsefell and Pittman, 1979 Van Der Meer et al., 1979 Wu et al., 1990 Yee et al., 2001 Zetterlund et al., 2002]. Although ionic copolymerizations have not been as extensively studied, penultimate effects have been found in some cases. Thus in the anionic polymerization of styrene t-vinylpyri-dine, 4-vinylpyridine adds faster to chains ending in 4-vinylpyridine if the penultimate unit is styrene [Lee et al., 1963]. 

Figures 6-12 and 6-13 shows plots of copolymer composition and propagation rate constant, respectively, versus comonomer feed composition for styrene-diethyl fumarate copolymerization at 40°C with AIBN [Ma et al., 2001]. The system follows well the implicit penultimate model. The copolymer composition data follow the terminal model within experimental error, which is less than 2% in this system. The propagation rate constant shows a penultimate effect, and the results conform well to the implicit penultimate model with si = 0.055, S2 — 0.32.

The ability to determine which copolymerization model best describes the behavior of a particular comonomer pair depends on the quality of the experimental data. There are many reports in the literature where different workers conclude that a different model describes the same comonomer pair. This occurs when the accuracy and precision of the composition data are insufficient to easily discriminate between the different models or composition data are not obtained over a wide range of experimental conditions (feed composition, monomer concentration, temperature). There are comonomer pairs where the behavior is not sufficiently extreme in terms of depropagation or complex participation or penultimate effect such that even with the best composition data it may not be possible to conclude that only one model fits the composition data [Hill et al., 1985 Moad et al., 1989]. 

In some cases, the reactivity of the growing chain end depends on the nature of the last but one monomer unit. So, eight propagation constants have to be considered. This so-called penultimate effect can be the reason why the binary copolymerization cannot be described precisely enough by Eq. 3.18. 

In the copolymerization of ethene with 4-methyl-l-pentene, a penultimate effect has been observed (8). The 4-methyl-l-pentene unit in the penultimate position causes a remarkable decrease of the ethene reactivity. For this reason, isolated units of ethene are decreased in the copolymer. Actually, just the reverse would be expected from the concept of steric hindrance. However, the particular microstructure is produced by highly isospecific catalytic sites. 

The copolymerization equation is valid if all propagation steps are irreversible. If reversibility occurs, a more complex equation can be derived. If the equilibrium constants depend on the length of the monomer sequence (penultimate effect), further changes must be introduced into the equations. Where the polymerization is subjected to an equilibrium, a-methylstyrene was chosen as monomer. The polymerization was carried out by radical initiation. With methyl methacrylate as comonomer the equilibrium constants are found to be independent of the sequence length. Between 100° and 150°C the reversibilities of the homopolymerization step of methyl methacrylate and of the alternating steps are taken into account. With acrylonitrile as comonomer the dependence of equilibrium constants on the length of sequence must be considered. 

Some quantitative data (r1 r2, Q, e values) for the copolymerization of captodative olefins are available, mainly for the copolymerization with styrene. They are compiled in Tables 11-14. In Tables 11 and 12, the data for the copolymerization of captodative olefins with styrene are given for comparison together with the values for other 1,1-disubstituted olefins. However, these data have to be considered with caution because of the possibility that some propagation steps could be reversible and because of possible penultimate effects [95]. 

For the above reactions, it is assumed that the reactivity of the propagating radical is dependent only on its terminal radical unit. However, the rate of addition of a monomer to the growing radical depends on the type of monomer in the penultimate position. The importance of the penultimate effects has not been widely investigated. As a result, it is assumed that the simple copolymerization equations given above are valid. 

Another series of papers [296-298] should be mentioned, where low-molecular model compounds are used to prove the correctness of the penultimate model of copolymerization. Japanese scientists by means of the ESP-method [297-298] managed to observe a noticeable penultimate effect for the acrylate radical reactivity. 

This is the case, for example, in the copolymerization of carbon monoxide and ethylene where the CO will not add to itself but does copolymerize with the olefin monomer. General theoretical treatments have been developed for such cases, taking into account temperature and penultimate effects. Again, the superiority of these more complicated theories over the simpler copolymer model is not proved for all systems to which they have been applied. 

The effect of the penultimate unit in binary copolymerization has been studi i extensivety 33,34,33). The analogous probkm in the ca of teipolymerization is rather complex 26) owing to the existence of twenty seven possible propagation reactions, compared with eight in the case of binary copolymerization. If for a certain terminal monomer imit in the growing chain a penultimate effect exists, the reactivity ratios in the Alfrey-Goldfinger terpolymerization eqs. (7) may be replaced as follows ... 

Clearly, this approach is straightforward only for ultimate group or terminal group copolymerization. If more than penultimate effects are required, the equations become unwieldy. Using the concepts and mathematics of Markovian processes, Ham (9) generalized an extended form of the selectivity equation. Later, Price (20, 21) formalized the theory of Markov chains as applied to... 

The mathematical treatment of the penultimate effect [33,34] in a binary copolymerization system involves the use of eight propagating reactions ... 

The experimental copolymer composition data for styrene(Mi)-fumaroni-trile(M2) give a good fit to Eq. (7.86) with rj = 0.072 and r[ = 1.0 [33], but deviate markedly from the behavior predicted by the st-order Markov model with ri = 0.23. Penultimate effects have been observed in a number of other systems. Among these are the radical copolymerizations of ethyl methacrylate-styrene, methyl methaciylate-4-vinyl pyridine, methyl acrylate-l,3-butadiene, and other monomer pairs. 

Recently, the Research Group on NMR, SPSJ, assessed reliability of copolymer analysis by NMR using three samples of radically prepared copolymers of MMA and acrylonitrile with different compositions. 1H and 13C NMR spectra of the copolymers were collected from 46 NMR spectrometers (90 500 MHz) and the composition and sequence distribution were determined.232 Table 14 summarizes the monomer reactivity ratios determined by 13C NMR analysis. The large difference between rxx and r2X indicates the presence of a penultimate effect in this radical copolymerization, as previously reported.233 The values of riy, especially rxx, depended on the comonomer feed ratio, suggesting higher order of neighbouring unit effect on the reactivity of chain-end radicals. 

On the other hand, for a reason why the intermolecular ht addition may be equilibrated, the electrostatic repulsion between the highly polar anhydride units may be considered similar to the well known case in the radical copolymerization of vinyl monomers carrying carbonyl(34) or nitrile group(35) in which the penultimate effect is involved. That is, the polymer(D) obtained via intramolecular hh and intermolecular tt additions in which five-membered anhydride units are separated by two methylene units is sterically and/or electrostatically favorable compared with the polymer(E) formed via intramolecular ht and intermolecular ht additions in which six-membered anhydride units are separated by only one methylene unit. 

Penultimate Model Some copolymerization systems in which the values for reactivity ratios measured at different compositions are inconsistent can be adequately represented by the penultimate model [86]. In this case, the reactivity of the propagating chain depends on the chemical nature of the last two monomeric units the one at the active end and the previous one (penultimate) [87, 88], This is common in systems in which the monomers contain bulky substituents such as the fumaronitrile-styrene copolymerization [89], In other systems, the penultimate effect has been reported to be limited [90], The penultimate model can be formulated as follows. Consider the reaction of a growing chain having a penultimate unit j and terminal unit i with a monomer n, M ... 

Anionic copolymerizations have been investigated by applying the classical Mayo-Lewis treatment which was originally developed for free-radical chain reaction polymerization [198]. The copolymerization of two monomers (Mj and M2) can be uniquely defined by the following the four elementary kinetic steps in Scheme 7.21, assuming that the reactivity of the chain end (Mj" or ) depends only on the last unit added to the chain end, that is, there are no penultimate effects. 

The influence of the penultimate member of the growing polymer chain (what is called the penultimate effect) has been often discussed as a cause of deviations from the simple copolymerization equation, especially in the case of strongly polar monomers. Very accurate experiments at very low monomer ratios must be carried out to establish such influences and to correspondingly modify the simple copolymerization equation. However, the penultimate chain end effect can often be better explained by the formation of CT complexes (see Figure 22-11). In this case, the CT complexes function as third monomer. 

The copolymerization equation was derived under the assumption that the probability for the addition of a monomer to the growing chain is determined only by the last monomeric unit. With highly polar monomeric units, however, the penultimate chain end may be expected to have an influence (penultimate effect). Consequently, instead of one equation for the rate, for example, of the process —MJ -h there are... 

Guillot, J. Penultimate Effects in Radical Copolymerization I - Kinetical Study. 

---