Copolymerization reactivity ratio significance

However, this does not preclude mini emulsion copolymerization in a CSTR for extremely water-insoluble comonomers. In spite of the fact that the copolymer composition in the continuous miniemulsion is less than that predicted using the homogeneous copolymerization reactivity ratios, the miniemulsion copolymer might be more uniform than the macroemulsion copolymer, where the possibility of significant droplet nucleation could lead to two separate homopolymers or, at the very best, copolymers of various composition. Therefore, it is very important to use CSTR data to scale up a continuous miniemulsion copolymerization product to take into account the different particle growth kinetics for batch and continuous reactors. 

As mentioned previously, the Alfrey Priee Q and e values for vinyl acetate are 0.026 and —0.22, respectively [226]. Thus vinyl acetate is rather sluggish in its free-radical copolymerization, with most monomers, particularly olefinic monomers, bearing electron-donating subtitutents. The copolymerization reactivity ratios reflect the reluctance of vinyl acetate to enter into copolymerization with other monomers [270]. Nevertheless, vinyl acetate copolymers with a great many electron-rich as well as electron-poor olefins have been prepared. Especially significant from a commercial point of view are copolymers with ethylene, vinyl chloride, acrylates, methacrylates, fumarates, and maleates. Often, mixtures of three and more comonomers are used in these copolymerizations. 

GopolymeriZation Initiators. The copolymerization of styrene and dienes in hydrocarbon solution with alkyUithium initiators produces a tapered block copolymer stmcture because of the large differences in monomer reactivity ratios for styrene (r < 0.1) and dienes (r > 10) (1,33,34). In order to obtain random copolymers of styrene and dienes, it is necessary to either add small amounts of a Lewis base such as tetrahydrofuran or an alkaU metal alkoxide (MtOR, where Mt = Na, K, Rb, or Cs). In contrast to Lewis bases which promote formation of undesirable vinyl microstmcture in diene polymerizations (57), the addition of small amounts of an alkaU metal alkoxide such as potassium amyloxide ([ROK]/[Li] = 0.08) is sufficient to promote random copolymerization of styrene and diene without producing significant increases in the amount of vinyl microstmcture (58,59). 

VEs do not readily enter into copolymerization by simple cationic polymerization techniques instead, they can be mixed randomly or in blocks with the aid of living polymerization methods. This is on account of the differences in reactivity, resulting in significant rate differentials. Consequendy, reactivity ratios must be taken into account if random copolymers, instead of mixtures of homopolymers, are to be obtained by standard cationic polymeriza tion (50,51). Table 5 illustrates this situation for butyl vinyl ether (BVE) copolymerized with other VEs. The rate constants of polymerization (kp) can differ by one or two orders of magnitude, resulting in homopolymerization of each monomer or incorporation of the faster monomer, followed by the slower (assuming no chain transfer). 

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... 

Methods for evaluation of reactivity ratios comprise a significant proportion of the literature on copolymerization. There are two basic types of information that can be analyzed to yield reactivity ratios. These are (a) copolymer composition/convcrsion data (Section 7.3.3.1) and (b) the monomer sequence distribution (Section 7.3.3.2). The methods used to analyze these data are summarized in the following sections. 

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. 

For copolymerizations between non protie monomers solvent effects are less marked. Indeed, early work concluded that the reactivity ratios in copolymerizations involving only non-protic monomers (eg. S, MMA, AN, VAe, etc.) should show no solvent dependence.100101 More recent studies on these and other systems (e.g. AN-S,102-105 E-VAc,106 MAN-S,107 MMA-S,10s "° MMA-VAc1" ) indicate small yet significant solvent effects (some recent data for AN-S copolymerization are shown in Table 8.5). However, the origin of the solvent effect in these cases is not clear. There have been various attempts to rationalize solvent effects on copolymerization by establishing correlations between radical reactivity and various solvent and monomer properties.71,72 97 99 None has been entirely successful. 

Studies on the reactions of small model radicals with monomers provide indirect support but do not prove the bootstrap effect.111 Krstina et ahL i showed that the reactivities of MMA and MAN model radicals towards MMA, S and VAc were independent of solvent. However, small but significant solvent effects on reactivity ratios are reported for MMA/VAc111 and MMA S 7 copolymerizations. For the model systems, where there is no polymer coil to solvate, there should be no bootstrap effect and reactivities are determined by the global monomer ratio [Ma0]/[Mb0].1j1... 

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). 

The effect of temperature on r is not large, since activation energies for radical propagation are relatively small and, more significantly, fall in a narrow range such that En Eu is less than 10 kJ mol-1 for most pairs of monomers. However, temperature does have an effect, since E 2 — E is not zero. An increase in temperature results in a less selective copolymerization as the two monomer reactivity ratios of a comonomer pair each tend toward unity with decreasing preference of either radical for either monomer. Temperature has the greatest... 

In copolymerization butadiene reacts preferentially, however, significant concentration of isoprene units are also incorporated in a random manner during the early stage of reaction. Butadiene has higher reactivity ratio than isoprene. 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

Comparing the reactivity ratios of the DADMAC/AAM copolymerization with results of the copolymerization of other cationic monomers with AAM, significant differences can be identified. The differences between rx and r2 are much lower, and the cationic monomer even reacts preferentially during the copolymerization. As an example, for cationic methacrylic esters and methacrylamid derivatives, 1 nonideal copolymerization preferring the cationic component. For the cationic analogs of acrylic acid and acrylamide, 0.34azeotropic copolymerization, preferring the cationic monomer only at low content in the comonomer mixture. 

The thorough treatment of the experimental data does allow one to obtain reliable values of the reactivity ratios. The results of such a treatment are presented in Table 6.3 for some concrete system let us form a notion about an accuracy of the reactivity ratios estimations. The detailed analysis of such a significant problem in the case of the well-studied copolymerization of styrene with methyl methacrylate is reported in Ref. [227]. Important results on the comparison of the precision of rj, r2 estimates by means of different methods are presented by O Driscoll et al. [228]. Such a comparison of six well-known linear least-squares procedures [215-218,222,223] with the statistically correct non-linear least-squares method leads to the conclusion that some of them [216, 217, 222] can provide rather precise rls r2 estimates when the experiment is properly planned. 

Numerous reports are available [19,229-248] on the development and analysis of the different procedures of estimating the reactivity ratio from the experimental data obtained over a wide range of conversions. These procedures employ different modifications of the integrated form of the copolymerization equation. For example, intersection [19,229,231,235], (KT) [236,240], (YBR) [235], and other [242] linear least-squares procedures have been developed for the treatment of initial polymer composition data. Naturally, the application of the non-linear procedures allows one to obtain more accurate estimates of the reactivity ratios. However, majority of the calculation procedures suffers from the fact that the measurement errors of the independent variable (the monomer feed composition) are not considered. This simplification can lead in certain cases to significant errors in the estimated kinetic parameters [239]. Special methods [238, 239, 241, 247] were developed to avoid these difficulties. One of them called error-in-variables method (EVM) [239, 241, 247] seems to be the best. EVM implies a statistical approach to the general problem of estimating parameters in mathematical models when the errors in all measured variables are taken into account. Though this method requires more information than do ordinary non-linear least-squares procedures, it provides more reliable estimates of rt and r2 as well as their confidence limits. 

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