Modelling the effect of hydrogen bonding on elongational flow of supramolecular polymer melts

Abstract

Hydrogen bonding is the most common noncovalent reversible interaction leading to supramolecular polymeric assemblies. Shabbir et al. (Macromolecules 48:5988–5996, 2015) reported both linear and nonlinear rheological data for a model system consisting of pure poly(n-butyl acrylate) (PnBA) homopolymer and three PnBA-poly(acrylic acid) (PnBA-PAA) copolymers with different numbers of acrylic acid (AA) side groups. Hydrogen bonds between the AA groups not only cause the storage and loss modulus to shift in the direction of a power law scaling of 0.5 in the terminal relaxation regime, but also the elongational viscosity shows increasing strain hardening with a strongly nonlinear dependence on the number of hydrogen bonding groups. Based on the “Sticky Rouse” model and a constitutive equation of the Doi-Edwards type with consideration of chain stretch, we model the effect of hydrogen bonding on the elongational viscosity of the PnBA-AA copolymers. We show that the elongational viscosity data are consistent with a Sticky Rouse relaxation modulus of the AA associations characterized by a constant modulus GA and a constant sticker life time τA, while the complexity of the hydrogen assemblies as quantified by the Sticky Rouse time increases with the concentration of AA groups from the order of seconds (3% AA) to hours (6%AA) and to 1 day (13%AA), and leads to extreme strain hardening. The elongational stress shows a steady state at large strains and the stretch reaches a limiting value independent of strain rate. At the highest concentration of AA groups investigated (38%AA), the PnBA-AA copolymer is a weak gel fracturing at a critical strain, and the sticker life time loses its significance. The effect of the Sticky Rouse time on self-healing is discussed.