Strain Hardening and Strain Softening of Reversibly Cross-Linked Supramolecular Polymer Networks

Abstract

The large amplitude oscillatory shear behavior of metallo-supramolecular polymer networks formed by adding bis-Pd(II) cross-linkers to poly(4-vinylpyridine) (PVP) in dimethyl sulfoxide (DMSO) solution is reported. The influence of scanning frequency, dissociation rate of cross-linkers, concentration of cross-linkers, and concentration of PVP solution on the large amplitude oscillatory shear behavior is explored. In semidilute unentangled PVP solutions, above a critical scanning frequency, strain hardening of both storage moduli and loss moduli is observed. In the semidilute entangled regime of PVP solution, however, strain softening is observed for samples with faster cross-linkers (kd ∼ 1450 s−1), whereas strain hardening is observed for samples with slower cross-linkers (kd ∼ 17 s−1). The mechanism of strain hardening is attributed primarily to a strain-induced increase in the number of elastically active chains, with possible contributions from non-Gaussian stretching of polymer chains at strains approaching network fracture. The divergent strain softening of samples with faster cross-linkers in semidilute entangled PVP solutions, relative to the strain hardening of samples with slower cross-linkers, is consistent with observed shear thinning/shear thickening behavior reported previously and is attributed to the fact that the average time that a cross-linker remains detached is too short to permit the local relaxation of polymer chain segments that is necessary for a net conversion of elastically inactive to elastically active cross-linkers. These and other observations paint a picture in which strain softening and shear thinning arise from the same set of molecular mechanisms, conceptually uniting the two nonlinear responses for this system.

pH‐Based Regulation of Hydrogel Mechanical Properties Through Mussel‐Inspired Chemistry and Processing

“…Purely synthetic materials have been designed with covalent networks strengthened by non‐covalent interactions, such as hydrophobic bonds49, 50 and hydrogen bonding,51–53 in an analogous way to achieve unique physical properties. Metal coordination interactions appear to have this function also, as illustrated here and by others 30, 54…”

Rheological Properties of Cysteine-Containing Elastin-Like Polypeptide Solutions and Hydrogels

“…The nonlinear strain sweep results are similar to the nonlinear steady shear results shown in Figure 6, and although we do not pursue it further here, we therefore infer that the strain hardening is also caused by nonlinear high tension along stretched polymer chains. 31 …”

Network Topology in Soft Gels: Hardening and Softening Materials

“…When rescaling the differential modulus K by the low frequency elastic modulus G 0 and the stress measured by σ c , we can directly compare the non-linear response of gels at different volume fractions, independently of their different stiffness in the linear response regime. Fig.3 (a) shows how, for relatively small volume fraction (φ = 5% and φ = 7.5%), the gels exhibit a linear elastic response at small deformations (the initial flat part of K/G 0 as a function of σ/σ c ), followed by a pronounced softening before entering a strain-hardening regime at larger deformations [13,14,49,50]. The strain hardening is characterized by a power law scaling K/G 0 ∼ (σ/σ c ) α , similar to the one found in semiflexible polymer networks [51,52] with an exponent α = 3/2, at φ = 0.05, 0.075.…”