THEORY OF BRANCHED POLYMERS ON FRACTAL LATTICES

A phenomenological approach, which takes into account the basic geometry and the topology of fractal lattices and of branched polymers, is used to derive a new expression for the Flory exponent describing the average radius of gyration of branched polymers on fractals. The mean-field version of this formula nicely reproduces the values of the Flory exponent, calculated using real-space renormalization group methods on several fractal lattices. This technique also allows the determination of the scaling exponent of the radius of gyration of branched polymers without excluded-volume interactions on fractal lattices. As an application, the findings are exemplified by analyzing the direct, incoherent energy transfer (via multipolar interactions and exchange) from excited donors to acceptors, which are attached to branched polymers. © 1990 American Institute of Physics.