Why polymer chains in a melt are not random walks

A cornerstone of modern polymer physics is the ‘Flory ideality hypothesis’ which states that a chain in a polymer melt adopts ‘ideal’ random-walk-like conformations. Here we revisit theoretically and numerically this pivotal assumption and demonstrate that there are noticeable deviations from ideality. The deviations come from the interplay of chain connectivity and the incompressibility of the melt, leading to an effective repulsion between chain segments of all sizes s. The amplitude of this repulsion increases with decreasing s where chain segments become more and more swollen. We illustrate this swelling by an analysis of the form factor F (q), i.e. the scattered intensity at wavevector q resulting from intramolecular interferences of a chain. A ‘Kratky plot’ of qF (q) vs. q does not exhibit the plateau for intermediate wavevectors characteristic of ideal chains. One rather finds a conspicuous depression of the plateau, δ(F(q)) = |q|/32ρ, which increases with q and only depends on the monomer density ρ. Polymer melts are dense disordered systems consisting of macromolecular chains. Theories that predict properties of chains in a melt or concentrated solutions generally start from the ‘Flory ideality hypothesis’ [1]. The hypothesis states that polymer conformations correspond to those of ‘ideal’ random walks on length scales much larger than the monomer diameter [1–3]. The commonly accepted justification is that intrachain and interchain excluded volume forces compensate each other in dense systems [2, 3]. This compensation has several important consequences. For instance, the radius of gyration R(s) of chain segments of curvilinear length s ≤ N scales as R(s) = as, where N denotes the number of monomers per chain and a the statistical segment length of the chain. This result holds provided s is sufficiently large for all local correlations to be neglected. For s = N , it implies that the radius of gyration of the total chain obeys Rg = R(s = N) = a √ N [3]. A further consequence of chain ideality is that the intrachain scattering function, the ‘form factor’ F (q), is given by the Debye formula, F (q) = 2N ( exp(−(qRg))− 1 + (qRg) ) /(qRg) 4 [3]. For intermediate wavevectors, 1/Rg ≪ q ≪ 1/a, F (q) reduces to the power law F (q) ≈ 2/(qa). Due to this power-law behavior, we refer to the latter q-regime as ‘scale-free regime’ in the following. Neutron scattering experiments have been extensively used to test Flory’s hypothesis [4]. This technique allows one to extract F (q) from the total scattered intensity of a mixture of deuterated and hydrogenated polymers. One E-mail: [email protected] to ta l c ha in c (s) a b density ρ