Equilibrium in copolymerization

The overall equilibrium in copolymerization requires attaining in the system the equilibrium composition and microstmcture of a copolymer and the equilibrium concentrations of comonomers and all linear and cyclic oligomers and polymers. When the rate constants of all reactions operating in... 

The term equilibrium copolymerization was introduced by Alfrey and Tobolsky in 1959, who stated that, mathematically, the equilibrium in copolymerization is identical with the Ising problem in ferromagnetism, which leads to the same solution. Consequently, the authors formulated the most important... 

Most of the equations, derived by O Driscoll and co-workers with the assumption of infinite chains, appeared to be valid also for the equilibrium systems with low (number-average degree of polymerization), which was shown by Szymanski ° in his analysis of equilibrium in copolymerization systems. 

Reversibility of propagation is often observed in RO polymerization systems, including copolymerization. Although attaining equilibrium is rather infrequently the aim of copolymerization, it can be used as a tool not only for obtaining copolymers of thermodynamically defined properties but also for other purposes. The term equilibrium copolymerization means not only the equilibrium in copolymerization but also copolymerization in which one or more of homo- or... 

Polymerization equilibria frequently observed in the polymerization of cyclic monomers may become important in copolymerization systems. The four propagation reactions assumed to be irreversible in the derivation of the Mayo-Lewis equation must be modified to include reversible processes. Lowry114,11S first derived a copolymer composition equation for the case in which some of the propagation reactions are reversible and it was applied to ring-opening copalymerization systems1 16, m. In the case of equilibrium copolymerization with complete reversibility, the following reactions must be considered. 

Some monomers with no tendency toward homopolymerization are found to have some (not high) activity in copolymerization. This behavior is found in cationic copolymerizations of tetrahydropyran, 1,3-dioxane, and 1,4-dioxane with 3,3-bis(chloromethyl)oxetane [Dreyfuss and Dreyfuss, 1969]. These monomers are formally similar in their unusual copolymerization behavior to the radical copolymerization behavior of sterically hindered monomers such as maleic anhydride, stilbene, and diethyl fumarate (Sec. 6-3b-3), but not for the same reason. The copolymerizability of these otherwise unreactive monomers is probably a consequence of the unstable nature of their propagating centers. Consider the copolymerization in which M2 is the cyclic monomer with no tendency to homopolymerize. In homopolymerization, the propagation-depropagation equilibrium for M2 is completely toward... 

In the homopolymerization of dioxolane below 30°C. tertiary oxonium ions exist exclusively (2, 5). Otherwise hydride transfer would occur (carbonium ions abstract hydride from monomeric cyclic formats) (II, 16). In trioxane polymerization, however, at least some of the active chain ends are carbonium ions they cause hydride transfer and elimination of formaldehyde (9, II, 13). Thus, in copolymerization we must expect two different kinds of structures for cationic chains with terminal trioxane unit. Oxonium ions (I) and carbonium ions (II) may have different reactivity ratios in the copolymerization, but hopefully this does not cause severe disturbance since I and II seem to be in a fast kinetic equilibrium with each other (3). Hence, we expect [I]/[II] to be constant under similar reaction conditions. 

CH3)3CO— is an initiator residue]. With copolymerization of free monomers, they should have observed an increasing A/B ratio according to the method used with complex propagation, A/B should remain constant. The authors observed both cases. They concluded that maleic anhydride with a monomeric donor, like styrene, yields a DA complex by a reversible reaction, with an equilibrium constant of 10-1 to 10-2 dm3 mol-1. The initiating radical is formed from the complex, and the copolymerization is in fact a terpolymerization involving the two free monomers and their complex. These authors have applied the same technique in a study of the type of radicals formed in copolymerization of maleic anhydride with vinyl sulphides. Even in this case they provided evidence of the existence of a complex. 

When donor—acceptor complexes are formed from the monomers, they can take part in copolymerization. When the equilibrium constants of complex formation are not extremely high, both complexes and monomers coexist and compete with active centres in the reaction. In addition, the reverse case may occur when one part of the active centres forms complexes with some component of the medium, the reactivity of the complexed centers is, of course, different from that of the free centres. The situation is formally similar to that of the preceding paragraph. 

The equilibrium concentrations in copolymerization according to Eq. 2-50 are expressed through the proportions of the chain ends and equilibrium constants ... 

The equilibrium constants Kn and K22 are reciprocals of the monomer equilibrium concentrations in homopropagations. Therefore, as a and p are less than unity, the equilibrium concentration of monomers, Mi and M2 is reduced in copolymerization ([M]e < [M]e (homo)) ... 

Monomer equilibrium concentrations in copolymerization will be discussed in more detail in the next section, which is devoted to the polymerization of 1,3,5-trioxepane. 

The polymerization of 3,3-bis(chloromethyl)oxetane (BCMO) initiated with living polytetrahydrofuran (polyTHF) was studied by Saegusa 117). In this system, due to the high equilibrium concentration of THF, some monomer remains in equilibrium with the polymer after the first stage is completed (i.e. at the polyTHF THF equilibrium). After addition of the second monomer, the remaining THF may participate in copolymerization with added BCMO (cf. Sect. 15.2.2.1., copolymerization above T0), leading to random copolymer. Only after the complete consumption of THF the second monomer may form the required homoblock. Thus, the two homoblocks are separated by a third random BCMO/THF copolymer block ... 

The Tobolsky-Eisenberg polymerization theory was considered potentially useful for predicting molecular structure in vitreous materials. In principle, the copolymerization form of the theory described by Tobolsky and Owen (3) provides a way to calculate the concentrations of the various species present in equilibrium in the liquid phase. As a first approximation, the molecular constitution of the liquid phase at the M.P. is the structure retained in the vitreous phase upon rapid quenching to room temperature. A slight modification of the Tobolsky-Owen theory... 

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. 

The validity of scaling laws has been tested on several swollen network systems (Table 29.9). Munch et al. [99] studied the concentration dependence of the shear modulus for polystyrene model networks synthesized by copolymerization of styrene and divinylbenzene and swollen to equilibrium in benzene (good solvent for polystyrene). It was found that the modulus obeys a scaling law with equilibrium concentration, similar to that obtained for semidilute polymer solutions. The best fit to the equation G = Brpi yields... 

The most interesting finding, however, was the fact that in copolymerization experiments, the apparent reactivity ratios (rj and r2) are directly related (Fig. 27) to the respective equilibrium formation constants of the corresponding complexes (kf of the monomer—iron complex, as determined independently). In simple words, the monomer which is more strongly bonded to the Mj is incorporated preferentially, even if its rate of insertion is not the higher one. That situation can be summarized as shown in the Scheme. 

Equation [24] (after rearrangement) can be used for computing the maaocyclization equilibrium constants in copolymerization on the basis of the determined equilibrium concentrations of macrocydes and linear copolymer miaostmcture. 

When the cydization equilibrium constants in copolymerization are known, the same eqn [24] can be used to predict the equilibrium concentrations of macrocydes provided the equilibrium composition and microstmcture of linear copolymer is known. When the properties of the equilibrium linear copolymer cannot be determined, but the equilibrium constants of macrocydization and copolymerization are known, the prediction of the equilibrium concentrations of macrocydes can still be accomplished, but only by formulation and solving the set of equations, taking into accormt besides eqn [23] the mass balance equations for comonomer units in linear and cydic fractions. 

The general equation for determination of the equilibrium cyclization constants for the composed cyclics is in fact the one shown previously in Section 4.04.2 (eqn [24]), because the equilibrium in polymerizations of such monomers is the same as in copolymerization of corresponding simpler monomers (e.g., 1,3,5-trioxepane polymerization versus 1 1 copolymerization of 1,3-dioxolane and formaldehyde). 

Equilibrium in 1,3,5-trioxepane polymerization regarded as an example of the equilibrium copolymerization 62... 

Concentrations of comonomers at the copolymerization equilibrium are lower than those in homopolymerizations, provided no specific interaaions/solvation play important roles in distinguishing these systems qualitatively or quantitatively. The decrease in the monomer equilibrium concentration in copolymerization stems from the decrease in the proportion of homosequences. For instance, for the dyad model of copo-lymerization, when we assume the same value for the equilibrium constant of homopropagation (no specific interactions) as in homopolymetization (cf. Scheme 2), the following equation for the equilibrium concentration of monomer A can be formulated, independently if homo- or copolymerization is considered ... 

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