An Explanation for the High-Frequency Elastic Response of Dilute Polymer Solutions

Abstract

The behavior of polymer molecules in dilute solutions under high-frequency oscillations is revisited, with consideration given to the barriers to bond rotation that we argue can make the chain dynamically rigid at high frequency. Thus, the dynamical Kuhn length of the chain exceeds the static one, and the chain at high frequencies acts like a freely jointed chain of “bent rigid wires” in which each bent rigid wire is a “dynamical Kuhn length” containing many static Kuhn lengths connected together in a rigid random walk. We show that this model is consistent with anomalous high-frequency behavior of polystyrene solutions under shear observed by Schrag and co-workers1-3 and Amelar et al.4 and predicts that there is a minimum “spring” size corresponding roughly to exp[ΔEa/(3ν + 1)kBT] Kuhn steps that will behave elastically at high frequencies, where ΔEa is the barrier to bond rotation, and ν = 0.5−0.6 is the Flory exponent.