Branching - the long and short of it

Gregory Beaucage (Prof. of Chemical and Materials Engineering University of Cincinnati)

Complex branched structures can be described in terms of scaling features to yield surprising insight into the static and dynamic properties and mechanisms of formation. This scaling model considers that ramified structures can be decomposed into a topological network of branch sites and a tortuous path through the structure. In polymers this simple decomposition allows the resolution of thermodynamic and topological features, for example. We find that weakly branched (long chain branched) polymers display a tortuous path identical with linear chains. In these cases the tortuous path allows quantification of the mole fraction branching. While the model is general; specific emphasis will be given to a discussion of the use of this model in static neutron and x-ray scattering (SANS and SAXS). The scaling description can be applied to a wide range of structures and examples will be given from hyperbranched polymers, cyclic polymers, long chain branched polyolefins, star polymers, ceramic and carbon aggregates, vesicles and proteins (if there is time). The limitations of this approach, especially for extremely polydisperse systems and systems with collapsed 3d structures such as some dendrimers will be discussed.

Beaucage G, Phys. Rev. E 70 031401 (2004).
Kulkarni AS, Beaucage G J. Polym. Sci. Polym. Phys. 44 1395 (2006).
Kulkarni AS, Beaucage G Macromol. Rapid Commun. (2007 in press).

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