The simple approach taken by Flory provides surprisingly good results - more modern theories/calculations provide R ~ N0.588. However, the success of the Flory theory is due to a cancelation of errors. The excluded volume contributions are overestimated as correlations between monomers (which decrease the probability of overlap) are not considered. At the same time, the entropic restoring force is also overestimated. Nevertheless, such approaches based on a mean field approximation of density combined with ideal chain conformation-derived entropy can provide quite useful results, for example in the case of an adsorbed chain.
The treatment of the case for v < 0 in the preceding simple manner leads to an aphysical result for the coil size that minimizes the total free energy. Stabilizing terms need to be considered [2].