From linear viscoelasticity to the architecture of highly branched polyethylene

In this work, the linear viscoelastic behavior of some low-density polyethylene in the melt is used to obtain their architecture. In this way, the number of branches per molecule and long chain branching (LCB) content is determined. For this purpose, a method based on the molecular dynamics of simple star-shaped molecules is presented. It allows one to infer the topology of an average molecule through a set of 2Nc parameters {Cni, the number concentration of a level i} and {Mbi, the mass of a segment of level i} representing an irregular Cayley tree with Nc levels. The inverse problem uses the complex shear modulus as a function of the frequency data along with a minimization algorithm. Results from the present method are compared with NMR and SEC measurements of the level of branching. It appears that SEC and rheology leads to similar results on the determination of LCB while NMR overestimate the number of branch points per molecule. Moreover, rheology allows one to go further than the basic evaluation of LCB content and shows a picture of the structure of the molecules that is in agreement with the kinetics of free radical polymerization of polyethylene.