Terminal Model Monomer Reactivity Ratios

The instantaneous copolymer composition—the composition of the copolymer formed at very low conversions (about 5%)—is usually different from the composition of the comonomer feed from which the copolymer is produced, because different monomers have differing tendencies to undergo copolymerization. It was observed early that the relative copolymerization tendencies of monomers often bore little resemblance to their relative rates of homopolymerization [Staudinger and Schneiders, 1939]. Some monomers are more reactive in copolymerization than indicated by their rates of homopolymerization other monomers are less reactive. Further, and most dramatically, a few monomers, such as maleic 

Monomer Mi disappears by Reactions 6-2 and 6-4, while monomer M2 disappears by Reactions 6-3 and 6-5. The rates of disappearance of the two monomers, which are synonymous with their rates of entry into the copolymer, are given by 

Dividing Eq. 6-6 by Eq. 6-7 yields the ratio of the rates at which the two monomers enter the copolymer, that is, the copolymer composition, as 

In order to remove the concentration terms in Mf and M from Eq. 6-8, a steady-state concentration is assumed for each of the reactive species Mf and M separately. For the concentrations of Mf and Mf ro remain constant, their rates of interconversion must be equal. In other words, the rates of Reactions 6-3 and 6-4 must be equal  

Dividing the top and bottom of the right side of Eq. 6-10 by 21 [M ][Mi] and combining the result with the parameters r and r2, which are defined by 

---

While the terminal model and reactivity ratios provide a good description of copolymer composition, the kinetic studies summarized in this section indicate that additional parameters and penultimate radical fractions are required to represent k and k . (For a discussion of transfer to monomer in copolymer systems, see Ref 65.) These mechanistic complexities are often not considered when developing FRP models for polymer reaction engineering applications. It is expected that this situation will change as more data become available. 

The arrangement of monomer units in copolymer chains is determined by the monomer reactivity ratios which can be influenced by the reaction medium and various additives. The average sequence distribution to the triad level can often be measured by NMR (Section 7.3.3.2) and in special cases by other techniques.100 101 Longer sequences are usually difficult to determine experimentally, however, by assuming a model (terminal, penultimate, etc.) they can be predicted.7 102 Where sequence distributions can be accurately determined Lhey provide, in principle, a powerful method for determining monomer reactivity ratios. 

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. 

The implicit penultimate model was proposed for copolymerizations where the terminal model described the copolymer composition and monomer sequence distribution, but not the propagation rate and rate constant. There is no penultimate effect on the monomer reactivity ratios, which corresponds to... 

Copolymer composition curves in the copolymerization of MMA (Mi) and TrMA ( 2) with BuLi at -78°C are shown in Figure 1. From these curves the monomer reactivity ratios were determined to be ri=6.28 and 2 = 0.13 in toluene and ri = 0.62 and 2 0.62 in THF. In THF both the monomers showed similar reactivity. The compositional and configurational analyses of the copolymers indicated that the copolymerization approximately follows the terminal model in this solvent. 

We have previously reviewed ( 1, 2) the methods used to calculate structural features of copolymers and terpolymers from monomer reactivity ratios, monomer feed compositions and conversions, and have written a program for calculating structural features of copolymers from either terminal model or penultimate model reactivity ratios (3). This program has been distributed widely and is in general use. A listing of an instructive program for calculating structural features of instantaneous terpolymers from monomer feed compositions and terminal model reactivity ratios was appended to one of our earlier reviews (.1). 

There are two cases to consider when predicting flie effect of solvent polarity on copolymerization propagation kinetics (1) the solvent polarity is dominated by an added solvent and polarity is thus independent of the comonomer feed ratio, or (2) the solvent polarity does depend on the comonomer feed ratio, as it would in a bulk copolymerization. In the first case, the effect on copolymerization kinetics is simple. The monomer reactivity ratios (and additional reactivity ratios, depending on which copolymerization model is appropriate for that system) would vary fi om solvent to solvent, but, for a given copolymerization system they would be constant as a function of the monomer feed ratios. Assuming of course that there were no additional types of solvent effect present, fliese copolymerization systems could be described by their appropriate base model (such as the terminal model or the explicit or implicit penultimate models), depending on the chemical structure of the monomers. 

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. 

The initiating radicals derived from AIBN, AZE and APE can be regarded as models for the growing radicals of MAN, MMA and STY, respectively in each case, the model radical has a hydrogen atom in place of a polymer chain. In the absence of effects of non-terminal groups, it would be expected that the ratio of the rate constants (k >/kM")foT the reactions of two monomers with, say, the Me2C(CN) radical, would be close to that for their reactions with the polyMAN radical, as deduced from studies of copolymerizations and values of monomer reactivity ratios. 

The penultimate imit effect is thus assumed to be absent from the monomer reactivity ratios, which are equivalent to their terminal model forms, and only to... 

Thus the adjusted monomer reactivity ratios of the penultimate model are replaced simply by their corresponding terminal model values. However, since the penultimate imit effect can remain in the radical reactivity ratios (ie, through values of Si 1), equation 4 does not collapse to its equivalent terminal model form (ie, kii kiii). Since the composition and triad/pentad fraction equations contain only n terms, they collapse to the corresponding terminal model equations. However, since it contains both ft and ku terms, the propagation rate equation, though simpler than that of the explicit penultimate model, continues to differ from that of the terminal model. There is thus an implicit penultimate unit effect— that is, a penultimate unit effect on the propagation rate but not the composition or sequence distribution. 

Brar and Sunita [58] described a method for the analysis of acrylonitrile-butyl acrylate (A/B) copolymers of different monomer compositions. Copolymer compositions were determined by elemental analyses and comonomers reactivity ratios were determined using a non-linear least squares errors-in-variables model. Terminal and penultimate reactivity ratios were calculated using the observed distribution determined from C( H)-NMR spectra. The triad sequence distribution was used to calculate diad concentrations, conditional probability parameters, number-average sequence lengths and block character of the copolymers. The observed triad sequence concentrations determined from C( H)-NMR spectra agreed well with those calculated from reactivity ratios. 

In eqn (3], Fi is the instantaneous copolymer composition referred to monomer 1, and rj and r2 are the monomer reactivity ratios for monomer 1 and 2 (terminal model), respectively. During intervals I and II, the concentration of the monomers in the polymer partides are governed by the partitioning of the monomers among monomer droplets, polymer particles, and aqueous phase. In interval III, there are no droplets and the monomer is mostly located in the polymer particles. The concentration of the monomers in the polymer partides depends on the relative values of mass transfer and polymerization rates. Except for poorly emulsified, highly water-insoluble systems, mass transfer is much faster than polymerization rate, and hence the concentration of monomers in the different phases is given by the thermodynamic equilibrium. 

Four independent conditional probabilities can be written, with four monomer reactivity ratios, in a manner similar to the terminal model ... 

Fig. 1.4. Number distribution of monomer sequences calculated from terminal and penultimate models. The reactivity ratios for both models were the same as in Fig. 1.3. (Reproduced with permission from Ref. [9]. 1964 John Wiley and Sons, Inc.)...

Table 7.1 Terminal Model Reactivity Ratios for Some Common Monomer Pairs9...

Thus, the terminal model allows the copolymer composition for a given monomer feed to be predicted from just two parameters the reactivity ratios rAB and rBA- Some values of terminal model reactivity ratios for common monomer pairs are given in Table 7.1. Values for other monomers can be found in data... 

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... 

Terminal model reactivity ratios may be estimated from the initial monomer feed composition and the dyad concentrations in low conversion polymers using the following relationships (eqs. 45, 46). 

Harwood112 proposed that the solvent need not directly affect monomer reactivity, rather it may influence the way the polymer chain is solvated. Evidence for the proposal was the finding for certain copolymerizations, while the terminal model reactivity ratios appear solvent dependent, copolymers of the same overall composition had the same monomer sequence distribution. This was explained in... 

The apparent terminal model reactivity ratios are then r => aK and c =rR, K It follows that rABVBf = rABrBA - const. The bootstrap effect does not require the terminal model and other models (penultimate, complex participation) in combination with the bootstrap effect have been explored.103,1 4215 Variants on the theory have also appeared where the local monomer concentration is a function of the monomer feed composition.11[Pg.431]

---