Deviations from Terminal Copolymerization Model

The derivation of the terminal (or hrst-order Markov) copolymer composition equation (Eq. 6-12 or 6-15) rests on two important assumptions—one of a kinetic nature and the other of a thermodynamic nature. The Erst is that the reactivity of the propagating species is independent of the identity of the monomer unit, which precedes the terminal unit. The second is the irreversibility of the various propagation reactions. Deviations from the quantitative behavior predicted by the copolymer composition equation under certain reaction conditions have been ascribed to the failure of one or the other of these two assumptions or the presence of a comonomer complex which undergoes propagation. 

---

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). 

In contrast to the kinetic approach, deviations from the terminal model have also been treated from a thermodynamic viewpoint [Kruger et al., 1987 Lowry, 1960 Palmer et al., 2000, 2001]. Altered copolymer compositions in certain copolymerizations are accounted for in this treatment in terms of the tendency of one of the monomers (M2) to depropagate. An essential difference between the kinetic and thermodynamic treatments is that the latter implies that the copolymer composition can vary with the concentrations of the monomers. If the concentration of monomer M2 falls below its equilibrium value [M]c at the particular reaction temperature, terminal M2 units will be prone to depropagate. The result would be a... 

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. 

It was reported by Barb in 1953 that solvents can affect the rates of copolymerization and the composition of the copolymer in copolymerizations of styrene with maleic anhydride [145]. Later, Klumperman also observed similar solvent effects [145]. This was reviewed by Coote and coworkers [145]. A number of complexation models were proposed to describe copolymerizations of styrene and maleic anhydride and styrene with acrylonitrile. There were explanations offered for deviation from the terminal model that assumes that radical reactivity only depends on the terminal unit of the growing chain. Thus, Harwood proposed the bootstrap model based upon the study of styrene copolymerized with MAA, acrylic acid, and acrylamide [146]. It was hypothesized that solvent does not modify the inherent reactivity of the growing radical, but affects the monomer partitioning such that the concentrations of the two monomers at the reactive site (and thus their ratio) differ from that in bulk. 

Klumperman and coworkers [259] observed that while it is lately quite common to treat living radical copolymerization as being completely analogous to its radical counterpart, small deviatiOTis in the copolymerization behavior do occur. They interpret the deviations on the basis of the reactions being specific to controlled/living radical polymerization, such as activation—deactivation equilibrium in ATRP. They observed that reactivity ratios obtained from atom transfer radical copolymerization data, interpreted according to the conventional terminal model deviate from the true reactivity ratios of the propagating radicals. 

Many analytical techniques have been utilized to analyze the SAN microstructure including LALLS [38], CNMR [19,31,39-44], infrared spectroscopy [45-49], ultraviolet spectroscopy [50-52], pyrolysis GC [8,27,53], pyrolysis mass spectroscopy [54,55], fluorescence [20,56], GPC-IR [57,58], and GPC-UV [52]. Since the terminal model allows the calculation of sequence distribution, the calculated and measured sequence distributions can be compared. This comparison generally shows deviation of the measured sequence distribution vs that predicted using the terminal model. Ham [59] was the first to notice the deviation and explained the deviation based upon penultimate effects. Since that time several other researchers have also notic deviation of their data from the terminal model and have applied more elaborate copolymerization models (Scheme 4) to explain the mechanism of SAN copolymerization. The penultimate [60,61] and complex participation models [33,62,63] have both been evaluated and give a better fit to the SAN system than the terminal model. 

There have been many studies of the copolymerization of styrene (S) and acrylonitrile (AN), both in bulk and in solution. Frequently the terminal model has been used to describe the polymerization, for example studies conducted by Pichot and Pham (3), and Arita et al. (4). However, other workers have reported deviations from the terminal model, and these have been explained in terms of the penultimate model, for example Ham (5) and Guyot and Guillot (6), or the complex model, Sandner et al. (7) or Kucher et al. (8). 

When solvent effects on the propagation step occnr in free-radical copolymerization reactions, they result not only in deviations from the expected overall propagation rate, but also in deviations from the ejqiected copolymer composition and microstracture. This may be trae even in bulk copolymerization, if either of the monomers exerts a direct effect or if strong cosolvency behavior causes preferential solvation. A number of models have been proposed to describe the effect of solvents on the composition, microstmcture and propagation rate of copolymerization. In deriving each of these models, an appropriate base model for copolymerization kinetics is selected (such as the terminal model or the implicit or explicit penultimate models), and a mechanism by which the solvent influences the propagation step is assumed. The main mechanisms by which the solvent (which may be one or both of the comonomers) can affect the propagation kinetics of free-radical copolymerization reactions are as follows ... 

Equation (7.52) can also be derived from Eq. (7.43) by eliminating radical concentrations with the help of two steady-state assumptions written as Eqs. (7.44) and (7.47) and then using the definitions of ri and r2- Equation (7.52) represents a one-parameter model for the copolymerization rate (Melville et al., 1947) containing the parameter 0. Statistically, ip is expected to equal unity. However, the values of ip obtained in practice by inserting experimental copolymerization rates into Eq. (7.52) are frequently greater than unity. (For styrene-methyl methacrylate, for example, (p is 15, while for styrene-butyl acrylate ip is 150.) These deviations are ascribed to polar effects that favor cross-termination over homotennination. 

---