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

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 ki and propagation kp. The modified Poisson distribution that results necessitates evaluation of rather complicated summations in order to characterize the number x̄n and weight average x̄w molecular weights. It is found that r = kp/ki as large as 106 still does not shift (x̄w/x̄n)max beyond the range 1.3 to 1.4. But under any circumstance, depletion of monomer assures homogeneous polymers, regardless of r.