Nonlinear Relaxation of Unentangled Associative Polymers: Strain-Induced Hardening and Softening

Nonlinear stress relaxation under step strain γ was examined for two types of ionomers, sulfonated polystyrene (SPS) having either zinc (Zn) or sodium (Na) as the counter-cation. These SPS samples were of low molecular weight (M_w = 11 kg mol^–1) and in the unentangled state by themselves but had, on average, two associating salt groups (stickers) per chain thereby forming a transient network sustained by aggregates of those stickers. The thermal dissociation of the stickers from those aggregates was much slower than the intrinsic Rouse motion of the chain backbone between the stickers because of a large energy required for the stickers to escape from their aggregates. Thus, for both SPS-Zn and SPS-Na ionomers, the terminal relaxation was much slower than the intrinsic Rouse relaxation. For small γ (=0.5) in the linear viscoelastic regime, this terminal relaxation was almost single-Maxwellian, possibly because the ionomer backbone had only two stickers (on average) and the dissociation of one sticker allowed the whole backbone to relax. For large γ (still below 2), both SPS-Zn and SPS-Na ionomers exhibited strain-hardening at short times t followed by a fast modulus decay and the strain-softening in the terminal relaxation zone at long t. In this terminal relaxation zone, the nonlinear relaxation modulus G(t,γ) was found to obey the time-strain separability, G(t,γ) = G(t)h(γ) with G(t) and h(γ) being the linear relaxation modulus and the damping function, respectively. These nonlinear features were discussed in relation to strain-induced changes in the associative network structure. The hardening at short t was not attributable to the finite extensible nonlinear elasticity (FENE), because the chain backbone between the stickers was too long to exhibit a significant FENE effect at γ < 2. Instead, the hardening was related to strain-induced enhancement of aggregation of the stickers not involved in large and stable aggregates before imposition of the strain. Correspondingly, the fast stress decay after the hardening was attributed to mechanical rupture of the aggregates formed by those stickers. After this rupture, the transient network sustained by the surviving aggregates would have relaxed through the thermal dissociation of those aggregates. This thermal process should have been very similar to that at equilibrium, which resulted in the time-strain separability of G(t,γ) at long t. These structural arguments of the nonlinearities were in harmony with a double-step reverse strain test as well as a model analysis assuming the mechanical rupture and successive equilibration of the aggregates.