An explicit topological approach to the dimensions of LCB polymers is prese
nted. It is based on the Wiener number, a topological descriptor which is s
hown in this study to be related to the topological radius of the macromole
cule, the mean-square radius of gyration, the g-ratio, and the intrinsic vi
scosity within the Rouse-Zimm range. The new theory enables the treatment o
f the highly complex hyperbranched polymers, which are difficult to handle
by the classical theory of Zimm and Stockmayer. The agreement with the meas
ured g-values of model polyethylenes, synthesized by Hadjichristidis et al.
, is fairly good for star-like polymers and satisfactory for pom-pom type o
f structures, whereas for crowded comb-type species the calculated g-values
are underpredicted. Extension of the approach is shown to cyclic structure
s for which the Kirchhoff number replaces the Wiener number. (C) 2001 Elsev
ier Science Ltd. All rights reserved.