Structure–property relations in linear viscoelasticity of supramolecular hydrogels

Extraordinary mechanical properties of supramolecular gels (fracture toughness, fatigue resistance, injectability and self-healing ability) are strongly affected by their viscoelastic response driven by rearrangement (association and dissociation) of physical bonds. The kinetics of rearrangement is traditionally studied in small-amplitude shear oscillatory tests by analyzing the effect of the frequency of oscillations ω on the storage G′ and loss G′′ moduli. Conventional Maxwell-type models describe observations rather poorly when the gels reveal a pronounced flattening of the graphs G′′(ω) at high frequencies. A simple model is derived in linear viscoelasticity of supramolecular gels. Its advantage is that the model reproduces experimental data correctly, on the one hand, and involves only four material constants, on the other. Based on the analysis of experimental data on gels cross-linked by coiled-coil complexes, covalent and ionic bonds, phenylboronic acid-diol complexes and metal–ligand coordination bonds, the model is applied to develop structure–property relations that describe the influence of chemical structure of supramolecular gels (concentration of polymer chains and type and molar fraction of temporary bonds) and environmental conditions (temperature, pH and ionic strength of buffer solutions) on their viscoelastic response.