Autoacceleration in Free Radical Polymerization

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 $R_i$, in contrast to the $\sqrt{R_i}$ 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 $\overline{N}\sim \frac{1}{R_i}$.