Effect of molar mass ratio of monomers on the mass distribution of chain lengths and compositions in copolymers: extension of the Stockmayer theory

In statistical copolymers, there exists a distribution according to molar mass as well as according to chemical composition. Stockmayer derived distribution functions, describing the relative weight of a particular molar mass and composition interval, assuming equal molar masses of the monomer units. In this article we present an extension of the distribution functions, suited for those cases where the aforementioned assumption is not valid. The final mathematical results is a product of the original Stockmayer distribution function and a correction function, due to the unequality of molar masses. It appears the correction function is dependent on the average composition, the composition deviation, and the ratio of molar masses of the monomers. Furthermore, a three-dimensional representation of distributions has been developed to get insight in the shape of the distributions.