Meander model of condensed polymers

Abstract

On the basis of the cluster-entropy hypothesis (CEH) the short-range order of polymer melts can be described by clusters of nearly parallel chain segments having similar conformations and holes in between these clusters. This bundle model allows the quantitative discussion of the melt transition as well as of the thermal properties of the melt. Within these bundles the molecules are assumed to fold back and forth in a one-dimensional statistical manner defined by the free energy of a tight chain fold. The bundle diameter, r, and the superfolding of bundles are derived by applying the CEH again. As primary blocks (5–30 nm, depending on the kind of polymer and molecular weight) coupled meander cubes are most probable. These are linked via their cube diagonals which serve as the axis of statistical rotation. Appropriate interaction between adjacent cubes may account for a liquid-crystalline transition, in which the paracrystalline but isotropic grains (0.3–3 µm) become nematically ordered. The diameters of these coarse grains (found in most amorphous polymers) depend on their grain boundary interaction. The shear deformations of the coupled cubes explain quantitatively the rubber-elastic compliances, J°_eN, of uncrosslinked polymer melts. Additionally, the unfolding of layers of meander-cubes into shear bands describes the stress–strain relation of high molecular weight polymer melts.