Long chain branch polymer chain dimensions: application of topology to the Zimm–Stockmayer model

An explicit topological approach to the dimensions of LCB polymers is presented. It is based on the Wiener number, a topological descriptor which is shown in this study to be related to the topological radius of the macromolecule, the mean-square radius of gyration, the g-ratio, and the intrinsic viscosity within the Rouse–Zimm range. The new theory enables the treatment of the highly complex hyperbranched polymers, which are difficult to handle by the classical theory of Zimm and Stockmayer. The agreement with the measured g-values of model polyethylenes, synthesized by Hadjichristidis et al., is fairly good for star-like polymers and satisfactory for pom–pom type of structures, whereas for crowded comb-type species the calculated g-values are underpredicted. Extension of the approach is shown to cyclic structures for which the Kirchhoff number replaces the Wiener number.