Step-Growth Polymerized Systems of General Type “AfiBgi”:A Method to Calculate the Bivariate (Molecular Size) × (Path Length) Distribution

Step-growth polymerized systems of general type “AfiBgi” are considered. The monomers bear one or more reactive groups of type A and/or B. An A group on one monomeric unit might react with a B group on another unit, thus coupling the two units. This process repeats itself randomly, and at a given degree of conversion, a wide range of polymeric molecules has formed, differing in both molecular size and in branching structure, determined by the laws of probability. In a slice of the molecular size distribution, all polymeric molecules have the same size, but differ in number and position of branching points. A method is presented to calculate the path length distribution for each such slice. Here, path length is the number of chemical bonds in the path connecting two monomeric units in the molecule. From the path length distribution, the light scattering function is calculated.