Polymer, Vol.35, No.8, 1714-1721, 1994
On the Validity of the Steady-State Approximations in High Conversion Diffusion-Controlled Free-Radical Copolymerization Reactions
Chain addition polymerization reactions involve active intermediates (i.e. free radicals) whose total concentration at all times is very small. In copolymerization, in contrast to homopolymerization, one can identify two radical populations, ’P’ and ’Q’, ending in an M1 or in an M2 monomer unit, respectively. As a result, two distinct quasi-steady-state approximations (QSSAs) can be made. The first QSSA is applied to the total radical concentration and implies that the total rate of radical initiation is approximately equal to the total rate of radical termination. The second QSSA is applied to the separate radical populations P and Q and states that the rate of reaction of a P-type radical with an M2 monomer is equal to the rate of reaction of a Q radical with an M1 monomer. However, whether or not both approximations are applicable to a given copolymerization system is a point of concern. In the present study, the validity of the two QSSAs is examined. The conditions under which both approximations can be applied to a given copolymerization system are identified, through the application of the method of moments to several experimentally investigated free-radical copolymerization systems leading to linear and branched copolymers. It is shown that the validity of the QSSAs in free-radical copolymerization depends on the polymerization conditions, namely, the polymerization process (e.g. bulk versus solution) and the importance of diffusion-controlled reactions at high monomer conversions. However, the effect of both approximations on the final molecular properties is, in general, not significant.