Verification of branch point withdrawal in elongational flow of pom-pom polystyrene melt

Abstract

According to tube model ideas, chain stretch at deformation rates below the inverse Rouse time of the chain, is only possible for polymer topologies with two or more branch points. The basic topologies, which embody this idea, are the H molecule with two side chains, and the pom-pom molecule with q>2 side chains at each end of the backbone. According to the pom-pom hypothesis, maximum chain stretch of the backbone is limited by branch point withdrawal, i.e., the side chains are drawn into the tube of the backbone as soon as the relative tension in the backbone reaches a value of q. This hypothesis, which has never been verified before, can now be tested by considering recent elongational experiments by Nielsen et al. [Macromolecules 39, 8844–8853 (2006)] on a nearly monodisperse polystyrene pom-pom melt with q=2.5. The analysis presented is based on the original integral version of the pom-pom model, and on the molecular stress function (MSF) model with strain-dependent tube diameter. The material strain measure determined from the experiments is found to be consistent with a constant maximum stretch, independent of the elongation rate, which is, however, significantly larger than q. To achieve quantitative agreement between experiment and modeling, (1) dynamic dilution of the backbone, which increases the tube diameter of the backbone and reduces equilibrium tension in the backbone, (2) finite extensibility effects, (3) stretch relaxation causing a transition from chain stretch to tube squeeze at lower strain rates, and (4) the dynamics of branch point withdrawal need to be considered. Integrating all of these features in a MSF stretch evolution equation with multiple time scales, the fundamental pom-pom hypothesis is confirmed.