A simple model for polymeric fractals in a good solvent and an improved version of the Flory approximation

We define a r-fractal as a self-similar structure built from N basic units, and with a maximum gyration radius scaling like Nr. We assume that r is a superuniversal exponent, independent of the space dimension d and verifying 1/d≤r≤1. We determine the equilibrium fractal dimension, the spectral and spreading dimensions, etc... as a function of r and d. These r-fractals seem to offer a simple picture of actual polymers, with r = 1 for chains and r = 3/4 for branched polymers. We reinterpret the Flory approximation as giving an oversimplified expression for the statistical distribution of the gyration radius of r-fractals. The correct expression leads to an improved version of the Flory model, whose success is (tentatively) explained by the rather unexpected behaviour of an exponent ratio which stays very close to its ideal value in a wide range of r and d.