Evaluation of Monomer Reactivity Ratios

The method of Fineman and Ross represents a considerable improvement in the direction of straightforward analysis of copolymerization data. In their method Eq. (8) is rearranged to the linear form 

Styrene Styrene Styrene Vinyl acetate Vinyl acetate Maleic anhydride Methyl acrylate 

Butadiene p-Methoxystyrene Vinyl acetate Vinyl chloride Diethyl maleate Isopropenyl acetate Vinyl chloride 

For the remaining three systems, styrene-vinyl acetate, vinyl acetate-vinyl chloride, and methyl acrylate-vinyl chloride, one reactivity ratio is greater than unity and the other is less than unity. They are therefore nonazeotropic. Furthermore, since both ri and 1/7 2 are either greater than or less than unity, both radicals prefer the same monomer. In other words, the same monomer—styrene, vinyl chloride, and methyl acrylate in the three systems, respectively—is more reactive than the other with respect to either radical. This preference is extreme in the styrene-vinyl acetate system where styrene is about fifty times as reactive as vinyl acetate toward the styrene radical the vinyl acetate radical prefers to add the styrene monomer by a factor of about one hundred as compared with addition of vinyl acetate. Hence polymerization of a mixture of similar amounts of styrene and vinyl acetate yields an initial product which is almost pure polystyrene. Only after most of the styrene has polymerized is a copolymer formed 

The effect of temperature on the monomer reactivity ratio is fairly small. In those few cases examined with sufficient accuracy,the ratio nearly always changes toward unity as the temperature increases —a clear indication that a difference in activation energy is responsible, in part at least, for the difference in rate of the competing reactions. In fact, the difference in energy of activation seems to be the dominant factor in these reactions differences in entropy of activation usually are small, which suggests that steric effects ordinarily are of minor importance only. 

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.  

This method is also known as the method of intersections. First described by Mayo and Lewis (1944), the method has been widely used for computing reactivity ratios by fitting experimental data to the differential copolymer equation.- In this procedure, Eq. (7.11) is rearranged to the form (Ghosh, 1990)  

A plot of the term on the left side of Eq. (7.27) or (7.28) against the coef cient of ri should thus yield a straight line with slope r and intercept ri. 

Problem 7.7 The initial concentrations of styrene (Mi) and acrylonitrile (M2) employed in a series of low conversion free-radical copolymerizations are given below together with the nitrogen contents (% N by wt.) of the corresponding copolymer samples produced  

Determine ri and r2 for the monomer pair by the Fineman-Ross method. 

Various methods have been used to obtain monomer reactivity ratios from the copolymer composition data. Several procedures for extracting reactivity ratios from the differential copolymer equation [Eq. (7.11) or 

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High-resolution nuclear magnetic resonance spectroscopy, especially 13C NMR, is a powerful tool for analysis of copolymer microstructure [Bailey and Henrichs, 1978 Bovey, 1972 Cheng, 1995, 1997a Randall, 1977, 1989 Randall and Ruff, 1988], The predicted sequence length distributions have been verihed in a number of comonomer systems. Copolymer microstructure also gives an alternate method for evaluation of monomer reactivity ratios [Randall, 1977]. The method follows that described in Sec. 8-16 for stereochemical microstructure. For example, for the terminal model, the mathematical equations from Sec. 8-16a-2 apply except that Pmm, Pmr, Pm and Prr are replaced by p, pi2, p2j, and p22. 

Another troublesome aspect of the reactivity ratios is the fact that they must be determined and reported as a pair. It would clearly simplify things if it were possible to specify one or two general parameters for each monomer which would correctly represent its contribution to all reactivity ratios. Combined with the analogous parameters for its comonomer, the values rj and t2 could then be evaluated. This situation parallels the standard potential of electrochemical cells which we are able to describe as the sum of potential contributions from each of the electrodes that comprise the cell. With x possible electrodes, there are x(x - l)/2 possible electrode combinations. If x = 50, there are 1225 possible cells, but these can be described by only 50 electrode potentials. A dramatic data reduction is accomplished by this device. Precisely the same proliferation of combinations exists for monomer combinations. It would simplify things if a method were available for data reduction such as that used in electrochemistry. 

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... 

Fineman, M. Ross, S.D. Linear method for determining monomer reactivity ratios in copolymerization. J. Polym. Sci. 1950, 5, 259-262. Tiidos, F. Kelen, T. Foldes-Berezsnich, T. Turcsanyi, A. Evaluation of high conversion... 

The copolymers produced possessed high molecular weights and narrow molecular weight distribution with high Tg values irrespective of the Ti complex used. The activities of norbomene-propene copolymerization were too high to evaluate monomer reactivity ratios. Thus, the copolymerization abilities of each Ti complex were investigated with norbomene-l-octene copolymerization by changing the monomer feed ratio. 

The monomer reactivity ratios of the TO-S copolymer were evaluated by a graphic solution of the copolymer equation (20). The equation was rearranged, giving ... 

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. 

In the literature one can find extensive compilations of reactivity ratios for numerous monomer pairs. For evaluation of the copolymerization experiments and for calculating the reactivity ratios, there is now extensive software available. 

The reactivity ratios may be evaluated by performing a series of low-conversion copolymerizations at different, monomer-feed ratios, isolating the copolymer, and determining its composition. A number of mathematical analyses have been proposed in order to provide, from the experimental data, correct values for the two unknown reactivity ratios. There is some difference of opinion as to the best method for obtaining values having quantifiable errors.84,64" However, several of... 

Copolymerization has been used for evaluating the reactivity of the monomeric, anhydro sugar derivatives, and also to prepare stereoregular polysaccharides of structures more complex than those of those prepared from a single monomer.98-104,107 The procedure adopted has been first to determine the reactivity ratios of the monomers, and then to perform preparative experiments under conditions that provide polysaccharides having the desired, copolymer composition. 

Mechanistic Aspects of Cationic Copolymerizations The relative reactivities of monomers can be estimated from copolymerization reactivity ratios using the same reference active center. However, because the position of the equilibria between active and dormant species depends on solvent, temperature, activator, and structure of the active species, the reactivity ratios obtained from carbocationic copolymerizations are not very reproducible [280]. In general, it is much more difficult to randomly copolymerize a variety of monomers by an ionic mechanism than by a radical. This is because of the very strong substituent effects on the stability of carbanions and carbenium ions, and therefore on the reactivities of monomers substituents have little effect on the reactivities of relatively nonpolar propagating radicals and their corresponding monomers. The theoretical fundamentals of random carbocationic copolymerizations are discussed in detail and the available data are critically evaluated in Ref. 280. This review and additional references [281,282] indicate that only a few of the over 600 reactivity ratios reported are reliable. 

This study was undertaken to see if improved tire cord adhesive systems could be developed using poly (DHA-co-4VP) and/or poly(DHA-co-NVP) materials. Since these copolymer systems were new and since previously published Q and e values for DHA (8), 4VP (9), and NVP (10) suggested poor copolymerizability between the monomer sets, a detailed copolymerization study of these monomer pairs was needed. In summary, this study was initiated to determine copolymerization characteristics, i.e. reactivity ratios, of DHA-co-4VP and DHA-co-NVP, to characterize briefly some of the physical and chemical properties of the resultant materials, and to evaluate select copolymers in tire cord adhesive systems. 

The Q-e scheme allows the reactivity ratios of unknown monomer pairs to be evaluated on the basis of experimentally determined values, and allows an assessment to be made of the copolymerization capacity of these monomers. In such an evaluation, it follows that ... 

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