Affiliation:
1. Hillegers Consult Batterijstraat 32 Maastricht 6211 SH The Netherlands
2. Eindhoven University of Technology Department of Mathematics and Computer Science PO Box 513 Eindhoven 5600 MB The Netherlands
Abstract
AbstractStep‐growth polymerized systems of type “A3 + A1” are considered. The monomers bear, respectively, 3 or 1 reactive A group. During the reaction, an A group on one monomeric unit might react with an A group on another such unit, thus chemically coupling the two units involved. Complexly structured polymeric molecules are formed. The A3's act as branching points; the A1's as end cappers. At the end of the reaction, the population of molecules present in the reactor vessel varies in size and branching structure. A method is presented to calculate the bivariate (molecular size) × (square radius of gyration) number distribution. It is shown that within the class of molecules of the same size, their square radius of gyration follows a shifted gamma distribution. Two new molecular parameters are introduced: the D index and the G index. The method uses bivariate generating functions.