Assumption of separability of the excluded-volume interaction in polymer physics: Flory-Huggins theory reviewed

Rotational isomerism and the excluded-volume interaction are generally considered to be the two major factors in polymer crystallization, glass transition, etc. The calculations supporting this belief are based on the assumption that the contribution to the free energy from the excluded-volume interaction is separable from the rest of the interactions. This separability assumption is studied here by mapping a single-polymer-chain problem to a spin problem with a cluster interaction. Using a variational principle, which provides an upper bound to the free energy, it is shown that the separability assumption gives a qualitatively incorrect description of the system in the low-temperature region. The consequences of this result for general models are also discussed.