Diffusion controlled termination of linear polystyrene radicals in linear, 4-Arm, and 6-Arm star polymer matrices in dilute, semidilute, and concentrated solution conditions

The effect of polymer matrix architecture (polystyrene stars) on the termination of linear polystyrene radical chains was studied in a continually evolving polymer−solvent mixture using the robust and accurate RAFT−CLD−T method. It was found that four distinct regions were observed for the stars analogous to the linear RAFT-mediated polymerizations with chain length dependencies (where kti,ii-α) for the 4-arm and 6-arm stars in the dilute regime similar to that found for the linear polymer (with αS and αL equal to 0.53 and 0.15, respectively). However, the gel onset conversion (xgel) increased with the greater number of arms on the star, in agreement with the Zimm−Stockmayer prediction and in excellent agreement with the theoretical overlap concentration c*. This supports our previous work that claimed chain overlap is the main cause of the onset of the gel effect in free-radical polymerizations. In concentrated solutions the chain length dependent exponents for linear radicals were much greater in solutions of 4-arm and 6-arm star polymers (with αgel close to 1.82x for both) when compared with linear polymer solutions (αgel = 1.22x). Because of the increased topological constraints in star polymer solutions, termination was expected to be controlled by reptation (which expects dependencies of 1.5 or 2). However, the dependencies predicted by reptation will only be reached at high conversions (close to the glass transition), suggesting that although solutions of star polymers are more constrained than their linear counterparts, there is still a great deal of matrix mobility on the time scale required for diffusion. The RAFT−CLD−T method also provided a means to determine diffusion coefficients for chain length i using Smoluchowski's equation in the regions where translational diffusion is rate determining