The configurational free energy of a polymer chain

Abstract

The configurational, or elastic, free energy Ael of a polymer chain is discussed in terms of the Fourier configurational approach. The importance of accounting for all degrees of freedom of the chain is shown in comparison with affine mean-field theories and with scaling theories of chain expansion and contraction. In case of strong contraction the chain does show neither affinity nor self-similarity, and we get Ael ∼ N1/3, N being the number of chain bonds. Conversely, in case of good-solvent expansion we find Ael ∼ N. The same result holds in the vicinity of the Θ-temperature, where Ael is also proportional to [(T − Θ)/T]2.