Non-Steady State Free Radical Polymerization Kinetics at High Conversions:  Entangled Regimes

Abstract

We present a theory of non-steady state free radical polymerization kinetics at high conversions where entanglements are present. Our immediate aim is to explain apparently infinite experimental living chain lifetimes at conversions that are high, but very far from the onset of glassy behavior. In these “posteffect” studies, the time dependence of the total number of living chains is measured, after the steady state is interrupted by switching off primary radical production at t = 0. We find that infinite lifetimes are inevitable in posteffect when entanglements are present. Our starting point is a previous theoretical study of steady state entangled polymerizations according to which the principle termination mechanism for the majority long entangled chains is provided by the small population of short mobile unentangled chains. In posteffect, we find that the entire short living chain population disappears after a time scale τshort ≈ z/v p, where z is the conversion-dependent threshold for entanglement-dominated reaction kinetics and v p is the rate at which monomers add to a living chain. For t < τshort the situation is essentially unchanged from steady state and the terminated fraction R t grows linearly in time t. But by τshort all short chains have either grown to become long or have terminated through interpolymeric radical−radical reactions. Consequently, the net termination rate is drastically suppressed for t > τshort, decaying as 1/t 1/2. Correspondingly, R(t) increases as t 1/2. At the longest times, t > τrad, where τrad is the mean steady state living chain lifetime, termination saturates: in the presence of entanglements, the living population is infinitely long-lived and the final terminated fraction is of order (z/N̄)1/2 ≪ 1, where N̄ is the steady state living chain length. Our intermediate time prediction, R(t) ∼ t 1/2, is consistent with experiment.

Free Radical Photopolymerization of Multifunctional Monomers

“…Under illumination (stationary conditions), at the early and medium polymerization stages, the bimolecular termination is dominated by reactions involving newly formed mobile short-chain radicals able to diffuse and to react with themselves or with macroradicals connected to the network. Mobility of macroradicals drops rapidly, which immediately affects the bimolecular process [56]. The entire living population is growing longer.…”

Reexamination of the Pyrolysis of Polyethylene: Data Needs, Free-Radical Mechanistic Considerations, and Thermochemical Kinetic Simulation of Initial Product-Forming Pathways

“…A summary of more recent speculations based on the transition 127 from Rouse 128 to reptation chain dynamics 95,96 and its effects on chain mobility and diffusion is given in the Supporting Information. [129][130][131][132][133][134][135][136][137][138] The common assumption has been that R p • is the major terminating species. Yet the estimated inequality k < k H (F/m 0 ) (see above and below) suggests that [R s • ] > [R p • ], such that R s • should dominate termination (unless it suffers significantly greater diffusional constraints than R p • ; see next paragraph).…”

Termination mechanism during the photo-induced radical cross-linking polymerization in the presence and absence of oxygen

“…The entire living population is growing longer (including the short-chains not terminated before) and mobilities of macroradicals are dropping rapidly, which immediately affects the bimolecular process. 33 As a result, k b t rapidly decreases with the increase in conversion in the dark 33,34 and only a small fraction of living chain radicals is able to terminate in bimolecular reaction. The higher the conversion the smaller this fraction becomes.…”