Step-Growth Polymerized Systems of Type “A1+A2+A3”: A Method to Calculate the Bivariate (Molecular Size) × (Path Length) Distribution

Step-growth polymerizing systems of type “A1+A2+A3” are considered. The monomers bear one (A1), two (A2), or three (A3) identical reactive sites. In the reactor vessel, 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 (i.e., are built up by the same number of monomeric units), but differ in number and position of branching points (A3's). 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. The shape and moments of this distribution may help rheologists and polymer manufacturers in improving the properties of their products. The system “A1+A2+A3” is the most simple representative of the more general step-growth polymerizing systems of type “Afi,” and of type “AfiBgi.” Extension of this calculation method to these for the chemical industry more relevant systems is intended.