Copolymerization equation monomer reactivity ratio

Copolymerization Equation-Monomer Reactivity Ratios. During the copolymerization of two comonomers (A and B), the chain can grow by the occurence of the four following reactions that differ from one another by the nature of the free radical and the inserted monomer ... 

The distribution of the monomers between the initial charge and the feed was calculated by the copolymerization equation with reactivity ratios of 0.04 for acrylonitrile and 0.41 for styrene (8). 

Equation 6-12 is known as the copolymerization equation or the copolymer composition equation. The copolymer composition, d M /d Mi, is the molar ratio of the two monomer units in the copolymer. monomer reactivity ratios. Each r as defined above in Eq. 6-11 is the ratio of the rate constant for a reactive propagating species adding tis own type of monomer to the rate constant for its additon of the other monomer. The tendency of two monomers to copolymerize is noted by r values between zero and unity. An r value greater than unity means that Mf preferentially adds M2 instead of M2, while an r value less than unity means that Mf preferentially adds M2. An r value of zero would mean that M2 is incapable of undergoing homopolymerization. 

For any specific type of initiation (i.e., radical, cationic, or anionic) the monomer reactivity ratios and therefore the copolymer composition equation are independent of many reaction parameters. Since termination and initiation rate constants are not involved, the copolymer composition is independent of differences in the rates of initiation and termination or of the absence or presence of inhibitors or chain-transfer agents. Under a wide range of conditions the copolymer composition is independent of the degree of polymerization. The only limitation on this generalization is that the copolymer be a high polymer. Further, the particular initiation system used in a radical copolymerization has no effect on copolymer composition. The same copolymer composition is obtained irrespective of whether initiation occurs by the thermal homolysis of initiators such as AIBN or peroxides, redox, photolysis, or radiolysis. Solvent effects on copolymer composition are found in some radical copolymerizations (Sec. 6-3a). Ionic copolymerizations usually show significant effects of solvent as well as counterion on copolymer composition (Sec. 6-4). 

Fig. 5. Diagram of the composition of the copolymerization of CTCX with St. (O) refers to experimental values, ( ) values of the copolymerization of HCX with St, and (O) values of the copolymerization of TCX with St. Solid lines are obtained by means of the theoretical equation using the monomer reactivity ratios (r,(CTCX) = 12 and r2(St) = 0.03 for this system, r,(HCX) = 3.0 and r2(St) = 0.02 at 50 °C for the HCX-St system, and r,(TCX) = 85 and r2(St) = 0 at 22 °C for the TCX-St system...

In studies of the kinetics of copolymerization of cyclic compounds the Mayo—Lewis equations [150] for kinetics of copolymerization have been applied, often with deserved caution. Many monomer reactivity ratios have been derived in this way. A large number of them have been summarized previously [7, 151] and we will not repeat them here nor attempt to update the lists. Instead we shall concentrate on some of the factors that seem to be important in regulating the copolymerizations and on some of the newer approaches that have been suggested for dealing with the complicated kinetics and give only a few examples of individual rate studies. 

Graft copolymers were obtained by the ordinary copolymerization with suitable comonomers, and characterized mainly by GPC and NMR. The monomer reactivity ratios were estimated by Equation 1 under the condition [B] [A]. 

Equation (7.18) may be used to calculate the instantaneous composition of copolymer as a function of feed composition for various monomer reactivity ratios. A series of such curves are shown in Fig. 7.1 for ideal copolymerization, i.e., r r2 = 1. The term ideal copolymerization is used to show the analogy between the curves in Fig. 7.1 and Aose for vapor-liquid equilibria in ideal liquid mixtures. The vapor-liquid composition curves of ideal binary mixtures have no inflection points and neither do the polymer-composition curves for random copolymerization in which riV2 = 1. Such monomer systems are therefore called ideal. It does not in any sense imply an ideal type of copolymerization. 

The copolymerization data for the styrene(Mi)-fumaronitrile(M2) system indicate that there are also effects due to remote monomer units preceding the penultimate unit. The effect of remote units has been treated by further expansion of the copolymer composition equation by the use of greater number of monomer reactivity ratios for each monomer [34]. However, the utility of the resulting expression is limited due to the large number of variables involved. 

For the copolymerization of two monomers by an anionic mechanism, the copolymer composition equation (7.11) or (7.18), derived in Chapter 7 is applicable with the monomer reactivity ratios defined in the same way as the ratios of rate constants r = k /ki2 and T2 = /s22/ 2i> where k and /C22 are the rate constants for the homopropagation reactions ... 

In radical copolymerization the Alfrey-Price Q-e scheme has been proposed for systematizing a large amount of data and for correlating the reactivity of a monomer to its chemical structure. In this scheme the monomer reactivity ratios are given by the following equations ... 

Several theoretical treatments of cyclocopolymerization have been reported previously (8-11). These relate the compositions of cyclocopolymers to monomer feed concentrations and appropriate rate constant ratios. To our knowledge, procedures for calculating sequence distributions for either cyclocopolymers or for copolymers derived from them have not been developed previously. In this paper we show that procedures for calculating sequence distributions of terpolymers can be used for this purpose. Most previous studies on styrene-methacrylic anhydride copolymerizations (10,12,13) have shown that a high proportion of the methacrylic anhydride units are cyclized in these polymers. Cyclization constants were determined from monomer feed concentrations and the content of uncyclized methacrylic anhydride units in the copolymers. These studies invoked simplifying assumptions that enabled the conventional copolymer equation to be used in determinations of monomer reactivity ratios for this copolymerization system. 

The monomer reactivity ratios r and r2 can be determined from the experimental conversion-composition data of binary copolymerization using both the instantaneous and integrated binary copolymer composition equations, described previously. However, in the former case, it is essential to restrict the conversion to low values (ca. < 5%) in order to ensure that the feed composition remains essentially unchanged. Various methods have been used to obtain monomer reactivity ratios from the instantaneous copolymer composition data. Several procedures for extracting reactivity ratios from the differential copolymer equation [Eq. (7.11) or (7.17)] are mentioned in the following paragraphs. Two of the simpler methods involve plotting of r versus r2 or F versus f. ... 

If both monomer reactivity ratios ri and f2 will become in the limit 0, then alternating copolymerization is indicated. Clearly, the ratio of both sequence lengths will give the expression for the copolymerization equation. 

These equations show that the composition of the copolymer formed from a specific comonomer mixture is controlled by the monomer reactivity ratios for the copolymerization. Additionally, they control the sequence distribution of the different repeat units in the copolymer. If ta > 1 then "> A prefers to add monomer A (i.e., it prefers to homopropagate) and extended sequences of A-type repeat units are introduced, whereas if ta < 1 A prefers to add monomer B, i.e., to cross-propagate. In a similar way, ra describes the behaviour of monomer B. The effects of some specific combinations of ta and re values upon copolymer composition and repeat unit sequence distribution are considered in the next section. 

In the second case, the effect of the solvent on copolymerization kinetics is much more complicated. Since the polarity of the reacting medium would vary as a function of the comonomer feed ratios, the monomer reactivity ratios would no longer be constant for a given copolymerization system. To model such behavior, it would be first necessary to select an appropriate base model for the copolymerization, depending on the chemical structure of the monomers. It would then be necessary to replace the constant reactivity ratios in this model by functions of the composition of the comonomer mixture. These functions would need to relate the reactivity ratios to the solvent polarity, and then the solvent polarity to the comonomer feed composition. The overall copolymerization kinetics would therefore be very complicated, and it is difficult to suggest a general kinetic model to describe these systems. However, it is obvious that such solvent effects would cause deviations fi om the behavior predicted by their appropriate base model and might therefore account for the deviation of some copolymerization systems from the terminal model composition equation. 

With Q-e values (20), the reactivity ratios of comonomers, rj and r, can be estimated using Equations 2 and 3. Monomer reactivity ratios can also be determined empirically by carrying out a series of copolymerizations and determining the polymer composition at low conversions. (20b) The reactivity ratios can be used to predict the nature of the copolymer type from a polymerization. For example, when the product of q and r has a value of zero, an alternating copolymer is likely to result from the copolymerization. On the other hand, when the product is near the value of one, the copolymer is likely to be a random copolymer. In a copolymerization process, if one of the comonomers does not homopolymerize, such as in the copolymerization of styrene (rj=0.019) and maleic anhydride (rj=0.0) at 50 °C (20,21), the polymer produced would be an alternating copolymer (Reaction 4). 

The apparent reactivity ratios that govern the copolymerization in the solvents were determined and are significantly different. Nevertheless, the triad distribution as a funrtion of copolymer composition shows that within experimental error, one set of curves describes all three situations. This again is clear evidence that solvents do not affect the tme monomer reactivity ratios, but only the monomer partitioning. In the derivations by Klumperman and O Driscoll it is clearly shown that these partitioning effects cancel from the sequence distribution versus copolymer composition equations. 

Note I The parameters may be the monomer reactivity ratios for the separate copolymerizations of the monomers concerned, namely, I and 2, with a nonpolar monomer, e.g., styrene (S), and a polar monomer, e.g., acrylonitrile (A). The equations for the desired monomer reactivity ratios, r 2 and r2, are then as follows ... 

Empirical equations expressing the monomer reactivity ratios in a binary radical copolymerization, C 2 and rj, in terms of the empirical parameters Q and e for the two monomers, namely, Qj, Q, Cp and C2, with... 

Monomer reactivity ratios are important quantities since for a given instantaneous comonomer composition, they control the overall composition of the copolymer formed at that instant and also the sequence distribution of the different repeat units in the copolymer. From Equation (2.86), they are the ratios of the homopropagation to the cross-propagation rate constants for the active centres derived from each respective monomer. Thus if a> 1 then prefers to add monomer A (i.e. it prefers to homopolymerize), whereas if rA[Pg.120]

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