Binary Copolymer Composition - Terminal Model

Simultaneous polymerization of two monomers by chain initiation usually results in a copolymer whose composition is different from that of the feed. This shows that different monomers have different tendencies to undergo copolymerization. These tendencies often have little or no resemblance to their behavior in homopolymerization. For example, vinyl acetate polymerizes about twenty times as fast as styrene in a free-radical reaction, but the product obtained by free-radical polymerization of a mixture of vinyl acetate and styrene is found to be almost pure polystyrene with hardly any content of vinyl acetate. By contrast, maleic anhydride, which has very little or no tendency to imdergo homopolymerization with radical initiation, readily copolymerizes with styrene forming one-to-one copolymers. The composition of a copolymer thus caimot be predicted simply from a knowledge of the polymerization rates of the different monomers individually. The simple copolymer model described below accoimts for the copolymerization behavior of monomer pairs. It enables one to calculate the distribution of sequences of each monomer in the macromolecule and the drift of copolymer composition with the extent of conversion of monomers to polymer. 

The ratio of these two rates, namely t/[Mi]/J[M2], thus gives the relative rates of incorporation of the two monomeric units in the copolymer (Rudin, 1982)  

To remove the concentration terms [M ] and [Mj] from this expression, a steady state is assumed for each chain radical type M and MJ in the reaction mixture. This assumption requires that the rate of conversion of M to Mj must equal that of MJ to M, or in mathematical terms. 

By de ning two parameters (called monomer reactivity ratios), r and r2, as 

This is the so-called copolymer equation or the copolymer composition equation. The ratio d M ld M2] representing the ratio of the rates at which the two monomers Mi and M2 enter the copolymer gives the molar ratio of the two monomer units in the copolymer (being formed at a given instant), and hence is referred to as the copolymer composition. According to Eq. (7.11), the copolymer composition depends on the concentrations of the two types of monomers in the feed, namely, [Mi] and [M2], and on the kinetic parameters ri and 2, known as the monomer reactivity ratios (ratios of propagation rate constants). Since initiation and termination rate constants are not involved in Eq. (7.11), the copolymer composition should be independent of the initiator used and of the absence or presence of inhibitors/retarders or chain transfer agents. 

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Tire simplest model for describing binary copolyinerization of two monomers, Ma and Mr, is the terminal model. The model has been applied to a vast number of systems and, in most cases, appears to give an adequate description of the overall copolymer composition at least for low conversions. The limitations of the terminal model generally only become obvious when attempting to describe the monomer sequence distribution or the polymerization kinetics. Even though the terminal model does not always provide an accurate description of the copolymerization process, it remains useful for making qualitative predictions, as a starting point for parameter estimation and it is simple to apply. 

The simple copolymer model, with two reactivity ratios for a binary comonomer reaction, explains copolymer composition data for many systems. It appears to be inadequate, however, for prediction of copolymerization rates. (The details of various models that have been advanced for this purpose are omitted here, in view of their limited success.) Copolymerization rates have been rationalized as a function of feed composition by invoking more complicated models in which the reactivity of a macroradical is assumed to depend not Just on the terminal monmomer unit but on the two last monomers in the radical-ended chain. This is the penultimate model, which is mentioned in the next Section. 

The simple copolymer model is a first-order Markov chain in which the probability of reaction of a given monomer and a macroradical depends only on the terminal unit in the radical. This involves consideration of four propagation rate constants in binary copolymerizations, Eqs. (7-2)-(7-4). The mechanism can be extended by including a penultimate unit effect in the macroradical. This involves eight rate constants. A third-order case includes antepenultimate units and 16 rate coefficients. A true test of this model is not provided by fitting experimental and predicted copolymer compositions, since a match must be obtained sooner or later if the number of data points is not saturated by the adjustable reactivity ratios. 

According to the terminal model, the composition of binary copolymers is determined by the reactivity ratios r and by the composition of the monomer mixture via Eq. (4) [33] ... 

The simplest copolymerization model is the terminal model, according to which the reactivity of the growing chain is determined by the last (terminal) monomer imit. In this case two reactivity ratios (ri and T2) are sufficient to describe the instantaneous composition of a binary copolymer ... 

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