Why polymer chains in a melt are not random walks

Abstract

A cornerstone of modern polymer physics is the `Flory ideality hypothesis'\nwhich states that a chain in a polymer melt adopts `ideal' random-walk-like\nconformations. Here we revisit theoretically and numerically this pivotal\nassumption and demonstrate that there are noticeable deviations from ideality.\nThe deviations come from the interplay of chain connectivity and the\nincompressibility of the melt, leading to an effective repulsion between chain\nsegments of all sizes $s$. The amplitude of this repulsion increases with\ndecreasing $s$ where chain segments become more and more swollen. We illustrate\nthis swelling by an analysis of the form factor $F(q)$, i.e. the scattered\nintensity at wavevector $q$ resulting from intramolecular interferences of a\nchain. A `Kratky plot' of $q^2F(q)$ {\\em vs.} $q$ does not exhibit the plateau\nfor intermediate wavevectors characteristic of ideal chains. One rather finds a\nconspicuous depression of the plateau, $\\delta(F^{-1}(q)) = |q|^3/32\\rho$,\nwhich increases with $q$ and only depends on the monomer density $\\rho$.\n