Statistics of Polymer Molecular Size Distribution for an Invariant Number of Propagating Chains

Abstract

A detailed study of the polymer statistics for a reaction system resembling the ethylene oxide initiator case is made allowing for different rates of initiation k_i and propagation k_p. The modified Poisson distribution that results necessitates evaluation of rather complicated summations in order to characterize the number x̄_n and weight average x̄_w molecular weights. It is found that r = k_p/k_i as large as 10⁶ still does not shift (x̄_w/x̄_n)_max beyond the range 1.3 to 1.4. But under any circumstance, depletion of monomer assures homogeneous polymers, regardless of r.