Flory theory revisited

The Flory theory for a single polymer chain is derived as the lowest order of a cumulant expansion. In this approach, the full original Flory free energy (including the logarithmic term), is recovered. The critical exponent a comes out naturally as α=(v-1/2)d, and is not related to ν by the hyperscaling relation α=2-vd. The prefactors of the elastic and repulsive energy are calculated from the microscopic parameters. The method can be applied to other types of monomer-monomer interactions, and the case of a single chain in a bad solvent is discussed. The method is easily generalised to many chain systems (polymers in solutions), yielding the usual crossovers with chain concentration. Finally, this method is suitable for a systematic expansion around the Flory theory. The corrections to Flory theory consist of extensive terms (proportional to the number N of monomers) and powers of N 2-νd . These last terms diverge in the thermodynamic limit, but less rapidly than the usual Fixman expansion in N 2-d/2