FLORY THEORY REVISITED

The Flory theory for a single polymer chain is derived as the lowest o rder of a cumulant expansion. In this approach, the full original Flor y free energy (including the logarithmic term), is recovered. The crit ical exponent alpha comes out naturally as alpha = (nu -1/2)d, and is not related to nu by the hyperscaling relation alpha = 2 - nud. The pr efactors of the elastic and repulsive energy are calculated from the m icroscopic parameters. The method can be applied to other types of mon omer-monomer interactions, and the case of a single chain in a bad sol vent is discussed . The method is easily generalized to many chain sys tems (polymers in solutions), yielding the usual crossovers with chain concentration. Finally, this method is suitable for a systematic expa nsion around the Flory theory. The corrections to Flory theory consist of extensive terms (proportional to the number N of monomers ) and po wers of N2-nud. These last terms diverge in the thermodynamic limit, b ut less rapidly than the usual Fixman expansion in N 2-d/2.