Effect of chain length on rates of diffusion-limited small molecule-polymer and polymer-polymer reactions: Phosphorescence quenching studies

Abstract

Model interactions have been studied by phosphorescence quenching to obtain a better understanding of the chain length dependence of interpolymeric chain end‐chain end reactions such as those involved in the termination step of free radical polymerization. For small molecule‐polymer interactions in dilute cyclohexane solution, quenching rate constant (kq) data agree with the Smoluchowski equation prediction that kq scales as polymer molecular weight (MW) to the ‐½ power, confirming self‐diffusion control. For polymer‐polymer interactions in dilute solution, the chain length dependence is weaker than that predicted by translational diffusion control, as described by the Smoluchowski equation, but is stronger than that predicted by renormalization group theory. For interactions between 70000 MW benzil‐end‐labeled polystyrene and varying MWs of anthracene‐end‐labeled polystyrene at 300 g/L polymer, kq decreases by a factor of 10 in going from MWs of 100 to 1000 g/mol; beyond 1000 g/mol, kq is nearly independent of chain length. Such effects indicate that the importance of oligomeric radical self‐diffusion and polymer radical chain‐end segmental mobility must be carefully considered in understanding the termination process in free radical polymerization. © 1996 John Wiley & Sons, Inc.

Bimolecular Free-Radical Termination at Low Conversion

“…Although they pointed out several weak aspects in the work of Horie and Mita regarding their polymer synthesis and data analyses (196), their findings with respect to the ratio of the rate of S-S quenching versus S-L quenching (196) and the scaling of k q with cooperative diffusion in the dilute regime (104) were similar to those of Horie and Mita. Interestingly, their quenching data for end-functional polystyrene in a dilute cyclohexane solution showed close agreement with predictions of the Smoluchowski equation using translational self-diffusion coefficients (117). For an L-L interaction between chains of equal length, k q scaled with 1/i 0.31 (20 < i < 2000), which compares favorably with the value of 0.29 obtained by Horie and Mita (116), although the latter workers reported this value for their experiments in a good solvent (benzene).…”

“…Further contributions to the field of phosphorescence quenching have come from the group of Torkelson (104,117,(190)(191)(192)(193)196). Although they pointed out several weak aspects in the work of Horie and Mita regarding their polymer synthesis and data analyses (196), their findings with respect to the ratio of the rate of S-S quenching versus S-L quenching (196) and the scaling of k q with cooperative diffusion in the dilute regime (104) were similar to those of Horie and Mita.…”

“…Among other things, they focused on the inter-and intramolecular quenching of a copolymer containing a small fraction of phenyl vinyl ketone. Results of the previously mentioned phosphorescence quenching technique, for instance, have shown that this is not an unreasonable assumption as polymer only acts as an obstacle for diffusion of small molecules (189)(190)(191)(192)(193) and references therein). † This is again in agreement with Eq.…”

“…They observed that the rate of intermolecular quenching between a small species and a large copolymer (S-L interaction) was approximately a factor of 2 lower than the interaction between two small species (an S-S interaction) (187,188). Torkelson and co- † For sake of simplicity, "small" may be considered as a "polymer" of chain length 1. workers have described this behavior in terms of free volume theories (190)(191)(192)(193). 12, again assuming the independence of the individual diffusion coefficients of the two species so that small species can freely diffuse through a large polymer coil.…”

Reaction kinetics in polymer melts

“…Hence during this regime ϕ is unimportant since it is much smaller than terms 1 and q t (0, 0) in eq. (7). Eq.…”