Kinetic aspects of copolymer formation

The composition of copolymers obtained in a free radical polymerization can be predicted based on several kinetic parameters of copolymerization reaction. For a copolymer starting with two species of monomer P and P , it can be assumed that the rate of addition of the monomer to a growing free radical depends only on the nature of the end group. If the chain is indicated by X, this is equivalent with the assumption that the radical Ri will act equivalently with X-R, and the radical R will act equivalently with X-Ri . The following reactions will take place in the system  

In this case, the rate of disappearance of the monomers P and P is described by the expressions  

By defining rA = kAA/kAB and rB = ksB/ksA and combining rel. (2.3.19a) and (2.3.19b), it results that the composition of a copolymer formed at any instant is given by an expression known as copolymer equation, which has the form  

The parameters rA and rs are known as monomer reactivity ratios representing the ratio of rate constants for a radical to add to its own type polymer vs. rate constants for a radical to add to the other type polymer. When kAA = 0 and ksB = 0, it can be seen that rA = 0, re = 0, and each radical reacts exclusively with the other monomer. Rel. (2.3.20) is then reduced to d[P ]/d[P ] = 1, and the monomers alternate regularly along the chain of the copolymer, regardless of the composition of the monomer feed (an excess of one monomer may remain unreacted). This is an ideal case, but copolymers such as that made from (a) styrene and (b) diethyl fumarate (rA = 0.3, re = 0.07) can be close to the ideal case. The styrene/diethyl fumarate polymerization has the tendency to lead to an azeotropic copolymer with 57 mole percent styrene, regardless the feed composition. When the initial composition of the monomers is different from 57 mole percent, the alt-copolymer is formed until one of the materials is finished and the remaining monomer forms a homopolymer. 

20) allows the determination at any time during the reaction of the instantaneous composition of the feed and of the copolymer. Using the notation Fa for the mole fraction for monomer A in the polymer and Fb for the other monomer (Fb = 1 Fa), and the notation fA for monomer A in the feed and fs for the other monomer, (fs = 1 - fA), the following expressions can be written  

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