NONEQUILIBRIUM STOCHASTIC-THEORY OF POLYMERIZATION PROCESSES

A new, nonequilibrium stochastic theory of polymerization processes is developed. For complex polymerization reactions as those involving cyclization, size dependent reactivity, or diffusion effects, existing statistical and kinetic theories do not predict equivalent results. In the present work a unified and internally consistent procedure is developed for the analysis of size distributions resulting from such complex polymerization reactions. Our starting point is the Kolmogorov stochastic differential equations with the generator depending explicitly on the transition matrix for multifunctional systems. The functional form of the generator is derived for systems with equal reactivity and then extended to systems with unequal reactivity. The solution to the equations yields the Flory-Stockmayer distributions when the assumption of equal reactivity is valid. Statistical and kinetic theories are re-covered as special cases of the present theory.