Molcular Weight Distribution in Di Metal Cyanide Catalyzed Polymerization 1: Fundamental Distribution for Length Dependent Propagation Constant and Segments

Di metal cyanide (DMC) catalyzed living polymerization is characterized by a) the “catch‐up” kinetics with a length dependent propagation rate constant kP≈n−2 (n: chain length), favoring the growth of small molecules and b) segmental growth caused by the repeated attachment and detachment of a growing end to a catalyst site. Whereas the inverse square law reduces polydispersity, growth in segments increases it. Analytic expressions of “catch‐up” molecular weight distributions (MWD) are given for kP≈n0,n−1, and n−2. To include segments, the theory originally developed for quasi living polymerizations is generalized to arbitrary distributions for the number of segments as well as the MWD of the segments themselves. General simple relationships allow calculating the moments of composite distributions in terms of the moments of the underlying distributions. The heterogeneous DMC catalysis with a length dependent propagation rate gives polymers with an extremely narrow molecular weight distribution. This narrowing together with a broadening due to segmental growth are studied. Analytical solutions are provided, allowing a fast prediction of polydispersity and a fast analysis of experiments. Extensions to high molecular weight tailing will be given in part 2.