We present a theory of the "autoacceleration" of polymerization rates during free radical polymerization, known as the gel effect. Termination reactions between long living chains are so retarded by entanglements that "short-long" terminations provide the fastest mechanism. Consistent with several experiments, this leads to polymerization rates independent of the radical production rate R;, in contrast to the~R; dependence in the classical theory. For long chains, the instantaneous polymer product is a copy of the living population, following an exponential distribution with mean length N -1/R;. PACS numbers: 82.35.+t, 05.40.+j, 05.70.Ln The structure and properties of polymeric materials are governed to a large degree by the kinetics of their synthesis, in general, highly nonequilibrium polymerization processes. This has motivated a huge body of interdisciplinary research into the most widely employed method of polymer synthesis, free radical polymerization (FRP) [1 -10]. FRP kinetics determine [11] molecular weight distributions, chemical sequences in statistical and graft copolymers, gel structures, and many other characteristics
Molecular weight distributions during autoacceleration in free radical polymerization are calculated within the framework developed in part 1. Most macroradicals (living chains) are so immobilized by entanglements that they terminate with short mobile unentangled chains with rate constants independent of their own lengths. In some respects, Flory's "equal reactivity" hypothesis is recovered, leading to a Flory (exponential) distribution of the living population for most chain lengths N. The instantaneous distribution of the polymer product, $& is a copy of the living one. Its mean length is Nd -1/Ri where & is the initiation rate. For the shortest chains, $d exhibits power law behavior with exponents determined by short chain termination kinetics and vanishes at N = 0. It follows that $d is peaked at N = z, the characteristic short chain length.
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.
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