IntroductionHyperbranched macromolecules are of great interest to industry in view of their favorable rheological properties, one of these being improved melt strength. In earlier work [1] we showed that it was possible to obtain the bivariate CLD/ DBD from the basic kinetics of a system. This was illustrated on ldPE, which from experiments and computations proved to possess significant concentrations of large polymer molecules, carrying some thousands of branches. In subsequent work [2] we demonstrated that it was possible to synthesize full molecular topologies, in terms of Summary: Hyperbranched molecules like low-density polyethylene (ldPE) adopt a huge variety of molecular architectures. Previous work has shown that it is possible to computationally synthesize these architectures and to characterize them according to radius of gyration. Here, a method is presented and applied on ldPE to characterize populations using rheological quantities in terms of comb-shaped and Cayley tree structures. Interbranch segments are assigned seniority and priority values that quantify their behavior in relaxation and elastic deformation processes. New generalpurpose algorithms have been developed to derive the full bivariate seniority/priority distribution using a representation from the graph theory of branched architectures. This paper describes the computation of bivariate chain length/degree of branching distributions (CLD/DBD) using a Galerkin finite element method for two scission mechanisms: linear and topological scission. The DBD is calculated using pseudodistributions. Random scission is treated with fragment length and branch point redistribution functions as obtained from scission statistics of branched molecules, preferentially yielding short and long fragments. Reactor populations of ldPE architectures are then obtained using computational synthesis. The seniority and priority distributions calculated indeed prove to be an adequate characterization method. They show good comparison, although not a complete overlap, with size characterization using a variant of the radius of gyration. It was possible to calculate a full bivariate seniority/ priority fraction distribution, but due to the limited sample size its surface was not smooth. Subsequent work has shown the consequences for the prediction of rheological properties.Seniority/priority values for segments of molecules for one chain length/number of branch points combination.
400Full Paper monomer units with branch points and the numbers of monomer units between branch points, from the CLD/ DBD. We employed a computational method involving Monte Carlo sampling from pre-specified chain lengthnumber of branches combinations, while applying a representation technique from graph theory. A crucial element revealed by these studies was the extremely wide variability in the topologies obtained when dealing with such a truly hyperbranched system as ldPE. This variability is usually expressed in terms of two extremes: combs and Cayley trees. We calculated that the numb...