Copolymerization prediction

The early kinetic models for copolymerization, Mayo s terminal mechanism (41) and Alfrey s penultimate model (42), did not adequately predict the behavior of SAN systems. Copolymerizations in DMF and toluene indicated that both penultimate and antepenultimate effects had to be considered (43,44). The resulting reactivity model is somewhat compHcated, since there are eight reactivity ratios to consider. 

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). 

An emulsion model that assumes the locus of reaction to be inside the particles and considers the partition of AN between the aqueous and oil phases has been developed (50). The model predicts copolymerization results very well when bulk reactivity ratios of 0.32 and 0.12 for styrene and acrylonitrile, respectively, ate used. 

Copolymer composition can be predicted for copolymerizations with two or more components, such as those employing acrylonitrile plus a neutral monomer and an ionic dye receptor. These equations are derived by assuming that the component reactions involve only the terminal monomer unit of the chain radical. The theory of multicomponent polymerization kinetics has been treated (35,36). 

Table 2 shows characteristic reactivity ratios for selected free-radical, ionic, and coordination copolymerizations. The reactivity ratios predict only tendencies some copolymerization, and hence some modification of physical properties, can occur even if and/or T2 are somewhat unfavorable. For example, despite their dissimilar reactivity ratios, ethylene and propylene can be copolymerized to a useful elastomeric product by adjusting the monomer feed or by usiag a catalyst that iacreases the reactivity of propylene relative to ethylene. 

Alfrey and Price proposed a means of predicting monomer reactivity in copolymerization from two parameters, (a measure of resonance) and e (a measure of polar effects) (8). These parameters have been related to the reactivity ratios by equations 15—17. 

Novel copolymerization and alloying technology were predicted to be the critical forces for shaping the devel-... 

Chain transfer is kinetically equivalent to copolymerization. The Q-e and Patterns of Reactivity schemes used to predict reactivity ratios in copolymerization (Section 7.3.4) can also be used to predict reactivities (chain transfer constants) in chain transfer and the same limitations apply. Tabulations of the appropriate parameters can be found in the Polymer Handbook 3 ... 

The various copolymerization models that appear in the literature (terminal, penultimate, complex dissociation, complex participation, etc.) should not be considered as alternative descriptions. They are approximations made through necessity to reduce complexity. They should, at best, be considered as a subset of some overall scheme for copolymerization. Any unified theory, if such is possible, would have to take into account all of the factors mentioned above. The models used to describe copolymerization reaction mechanisms arc normally chosen to be the simplest possible model capable of explaining a given set of experimental data. They do not necessarily provide, nor are they meant to be, a complete description of the mechanism. Much of the impetus for model development and drive for understanding of the mechanism of copolymerization conies from the need to predict composition and rates. Developments in models have followed the development and application of analytical techniques that demonstrate the inadequacy of an earlier model. 

Tire simplest model for describing binary copolyinerization of two monomers, Ma and Mr, is the terminal model. The model has been applied to a vast number of systems and, in most cases, appears to give an adequate description of the overall copolymer composition at least for low conversions. The limitations of the terminal model generally only become obvious when attempting to describe the monomer sequence distribution or the polymerization kinetics. Even though the terminal model does not always provide an accurate description of the copolymerization process, it remains useful for making qualitative predictions, as a starting point for parameter estimation and it is simple to apply. 

Rased on the above data, it would seem unusual if reactivity of the propagating species in copolymerization were insensitive to the nature of the last added monomer units. However, while there are ample experimental data to suggest that copolymerizations should be subject to penultimate unit effects that affect the rate and/or copolymer composition, the origin and magnitude of the effect is not always easily predictable. 

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. 

Azeotropic compositions are rare for terpolymerization and Ham 14 has shown that it follows from the simplified eqs. 38-40 that ternary azeotropes should not exist. Nonetheless, a few systems for which a ternary azeotrope exists have now been described (this is perhaps a proof of the limitations of the simplified equations) and equations for predicting whether an azeotropic composition will exist for copolymerizations of three or more monomers have been formulated.20113 This work also shows that a ternary azeotrope can, in principle, exist even in circumstances where there is no azeotropic composition for any of the three possible binary copolymerizations of tire monomers involved. 

One final point should be made. The observation of significant solvent effects on kp in homopolymerization and on reactivity ratios in copolymerization (Section 8.3.1) calls into question the methods for reactivity ratio measurement which rely on evaluation of the polymer composition for various monomer feed ratios (Section 7.3.2). If solvent effects arc significant, it would seem to follow that reactivity ratios in bulk copolymerization should be a function of the feed composition.138 Moreover, since the reaction medium alters with conversion, the reactivity ratios may also vary with conversion. Thus the two most common sources of data used in reactivity ratio determination (i.e. low conversion composition measurements and composition conversion measurements) are potentially flawed. A corollary of this statement also provides one explanation for any failure of reactivity ratios to predict copolymer composition at high conversion. The effect of solvents on radical copolymerization remains an area in need of further research. 

The rate of copolymerization often shows a strong dependence on the monomer feed composition. Many theories have been developed to predict the rate of copolymerization based on the terminal model for chain propagation (Section 7.3.1.1), This usually requires an overall rate constant for termination in copolymerization that is substantially different from that observed in homopolymerization of any of the component monomers. 

Indeed, cumyl carbocations are known to be effective initiators of IB polymerization, while the p-substituted benzyl cation is expected to react effectively with IB (p-methylstyrene and IB form a nearly ideal copolymerization system ). Severe disparity between the reactivities of the vinyl and cumyl ether groups of the inimer would result in either linear polymers or branched polymers with much lower MW than predicted for an in/mcr-mediated living polymerization. Styrene was subsequently blocked from the tert-chloride chain ends of high-MW DIB, activated by excess TiCU (Scheme 7.2). 

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. 

Prediction of Copolymerization Conversion from Reactor Head-Space Vapor Composition... 

Using copolymerization theory and well known phase equilibrium laws a mathematical model is reported for predicting conversions in an emulsion polymerization reactor. The model is demonstrated to accurately predict conversions from the head space vapor compositions during copolymerization reactions for two commercial products. However, it appears that for products with compositions lower than the azeotropic compositions the model becomes semi-empirical. 

Data of Nomura and Funita (12). The predictive capabilities of EPM for copolymerizations are shown in Figures 8-9. Nomura has published a very extensive set of seeded experimental data for the system styrene-MMA. Figures 8 and 9 summarize the EPM calculations for two of these runs which were carried out in a batch reactor at 50 °C at an initiator concentration of 1.25 g dm 3 water. The concentration of the seeded particles was 6x10 dm 3 and the total mass of monomer was 200 g dm 3. The ratio of the mass of MMA to the total monomer was 0.5 and 0.1 in Figures 8 and 9 respectively. The agreement between the measured and predicted values of the total monomer conversion, the copolymer composition, and the concentration of the two monomers in the latex particles is excellent. The transition from Interval II to Interval III is predicted satisfactorily. In accordance with the experimental observations, EPM predicted no new particle formation under the conditions of this run. 

From these approaches, DBnmr=0.42 and DBtheo=0-49 can be obtained at y=l.l (h=0.62), respectively. Note that these values represent a rough estimate, as they are calculated based on the assumption of equal rate constants for copolymerization. For low y values (y=0.5),the DB (DBnmr=0-48) even exceeds the value for poly(inimer 1) (DBnmr=0-43) obtained by a homo-SCVP. This is an accordance with theoretical prediction that a maximum of DB=0.5 is reached at y=0.6 [73]. The effect can be explained by the addition of monomer molecules to in-chain active centers (i.e., in linear segments), leading to very short branches. For 2.5>y>0.5, DBnmr decreases with y, as predicted by calculations. 

Hence by assigning two parameters, a Q and an c, to each of a set of monomers, it should be possible according to this scheme to compute reactivity ratios ri and V2 for any pair. In consideration of the number of monomer pairs which may be selected from n monomers—about n /2—the advantages of such a scheme over copolymerization experiments on each pair are obvious. Price has assigned approximate values to Q and e for 31 monomers, based on copolymerization of 64 pairs. The latitude of uncertainty is unfortunately large assignment of more accurate values is hampered by lack of better experimental data. Approximate agreement between observed and predicted reactivity ratios is indicated, however. 

Determination of Compositional Sequences. In the copolymerization of MMA and MAA or TBTM, compositional dyads and triads are generated. These sequences are determined by the relative concentration of monomers as well as by their relative reactivity. These compositional sequences characterize the material and allow predictions of activity based on structure by comparison with field tested polymers. 

To our knowledge, this is the first time that an emulsion copolymerization model has been developed based on a population balance approach. The resulting differential equations are more involved and complex than those of the homopolymer case. Lack of experimental literature data for the specific system VCM/VAc made it impossible to directly check the model s predictive powers, however, successful simulation of extreme cases and reasonable trends obtained in the model s predictions are convincing enough about the validity and usefulness of the mathematical model per se. 

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