Copolymerization discrimination

It has been argued that for a majority of copolymerizations, composition data can be adequately predicted by the terminal model copolymer composition equation (eqs. 5-9). However, in that composition data are not particularly good for model discrimination, any conclusion regarding the widespread applicability of the implicit penultimate model on this basis is premature. 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

In their paper Hill and coworkers discriminate between alternative copolymerization models by fitting the models to composition data and then predicting sequence distributions based on the fitted models. Measured and fitted sequence distributions are then compared. A better approach taken here is to fit the models to the sequence distribution data directly. 

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]. 

The sequence distributions expected for the different models have been described [Hill et al., 1982, 1983 Howell et al., 1970 Tirrell, 1986] (Sec. 6-5a). Sequence distributions obtained by 13C NMR are sometimes more useful than composition data for discriminating between different copolymerization models. For example, while composition data for the radical copolymerization of styrene-acrylonitrile are consistent with either the penultimate or complex participation model, sequence distributions show the penultimate model to give the best fit. 

The termination rate constants and molecular weights for the different copolymerization models have also been studied for purposes of discriminating between different copolymerization models [Buback and Kowollik, 1999 Landry et al., 1999]. 

Counterion effects similar to those in ionic chain copolymerizations of alkenes (Secs. 6-4a-2, 6-4b-2) are present. Thus, copolymerizations of cyclopentene and norbomene with rhenium- and ruthenium-based initiators yield copolymers very rich in norbomene, while a more reactive (less discriminating) tungsten-based initiator yields a copolymer with comparable amounts of the two comonomers [Ivin, 1987]. Monomer reactivity ratios are also sensitive to solvent and temperature. Polymer conformational effects on reactivity have been observed in NCA copolymerizations where the particular polymer chain conformation, which is usually solvent-dependent, results in different interactions with each monomer [Imanishi, 1984]. 

Figure 6.13 Radical polymerization of a growing polymer chain in the presence of two distinct monomers (i.e., copolymerization conditions) can at every step incorporate one monomer or the other. How might one quantitatively go about estimating the intrinsic preference for one monomer over the other What other molecular properties expected to correlate with this discrimination might be subject to computation ...

The practical value of the quantitative theory of radical copolymerization depends to a great extent on the adequacy of the applied kinetic model to the real systems. Hence, in Sect. 6 we shall discuss the issues of model discrimination and also the problems of reliability and validity of the calculations of the model parameters with an account of the potentialities of the modern experimental techniques. 

Systems modified by hybrid P-N ligands (68-75) were also found to be active for the copolymerization of styrene. In contrast to the N-N hgand [8, 9], their productivity is increased by increasing the pressure of carbon monoxide. In the case of the phosphine-dihydrooxazole ligands (68-72) the geometry of the ligand is very important for the steric control. The presence of only one substituent on position 4 of the dihydrooxazole ring (e.g., 69) is essential to achieve isotactic copolymerization [98]. Chirality associated with the presence of two different substituents in that position (Scheme 8.14, 72) is not sufficient to cause efficient i-enantio-face discrimination [99]. On the basis of these results, the model for styrene coordination (76) reported in Scheme 8.15 was assumed. 

Hilker et al. [59] studied the Novozym 435-catalyzed copolymerization of racemic a,a -dimethyl-l,4-benzenedimethanol with secondary hydroxyl groups with dimethyl adipate. Due to CALB enantioselectivity, hydroxyl groups at (R) stereocenters preferably reacted to form ester bonds with liberation of methanol. The reactivity ratio was estimated as (R)/(S) = 1 x 106. In situ racemization of monomer stereocenters from (S) to (R) by ruthenium catalysis allowed the polymerization to proceed and reach high functional group conversations. Readers should also refer to Chapter 11 for more information on chiral discriminations by lipases. 

If the terminal model adequately explains the copolymer composition, as is often the case, the terminal model is usually assumed to apply. Even where statistical tests show that the penultimate model does not provide a significantly better fit to experimental data than the tenninal model, this should not be construed as evidence that penultimate unit effects are unimportant. It is necessary to test for model discrimination, rather than merely for fit to a given model. In this context, it is important to remember that composition data are of very low power when it comes to model discrimination. For MMA-S copolymerization, even though experimental precision is high, the penultimate model confidence intervals are quite large 0.4[Pg.348]

However, these observations are not proof of the role of a donor-acceptor complex in the copolymerization mechanism. Even with the availability of sequence information it is often not possible to discriminate between the complex model, the penultimate model (Seetion 7.3.1.2) and other, higher order, models. A further problem in analyzing the kinetics of these copolymerizations is that many donor-acceptor systems also give spontaneous initiation (Section 3.3.6.3). 

For all these reasons, careful assessment of the model adequacy, aided by statistical techniques, must be used to discriminate among competing models aimed at explaining copolymerization data. Statistical experimental design should also be used whenever possible. 

Regarding the question of alternative copolymerization kinetic models, as mentioned earlier, in the event of discriminating between competing models (e.g., terminal model kinetics vs penultimate model kinetics), a set of equidistant monomer feed compositions along the entire composition range can serve as an appropriate design of experiments. Once one has determined that an alternative model is operative, the same four questions noted for the terminal model above should be revisited. There are several examples of the estimation of penultimate unit kinetic parameters in the literature [125, 112]. 

Solvents affect free-radical polymerization reactions in a number of different ways. Solvent can influence any of the elementary steps in the chain reaction process either chemically or physically. Some of these solvent effects are substantial, for instance, the influence of solvents on the gel effect and on the polymerization of acidic or basic monomers. In the specific case of copolymerization then solvents can influence transfer and propagation reactions via a number of different mechanisms. For some systems, such as styrene-acrylonitrile or styrene-maleic anhydride, the selection of an appropriate copolymerization model is still a matter of contention and it is likely that complicated copolymerization models, incorporating a number of different phenomena, are required to explain all experimental data. In any case, it does not appear that a single solvent effects model is capable of explaining the effect of solvents in all copolymerization systems, and model discrimination should thus be performed on a case-by-case basis. 

It is clear that in the future, advanced experiments and high-accuracy analytical equipment will further increase the ability to carry out the model discrimination for radical copolymerization. 

Although the application of model discrimination methods should improve our ability to discriminate, there are still many questions to be answered. How much will the application of model discrimination methods improve copolymerization modeling Which model discrimination method is the most reliable and efficient Which of the available copolymerization measurements (copolymer composition, triad fraction or rate data) will provide the most information ... 

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