Effective visco-elastic models of tough, doubly cross-linked, single-network polyvinyl alcohol (PVA) hydrogels Additively separable fractional derivative-based models for chemical and physical cross-links

An effective fractional derivative-based visco-elastic model of tough, doubly cross-linked, single-network polyvinyl alcohol (PVA) hydrogels, embodying both chemical and physical cross-links, is developed using a Mittag-Leffler relaxation function of order 1/2 while applying only three material parameters that are physically quantifiable, namely frequency for maximum loss modulus, equilibrium elastic modulus and relaxation intensity. The resulting 3-parameter shear modulus model is possible to additively split into chemical and physical parts; the split being the study focus. Physical explanations of the visco-elastic low-, mid- and high-frequency range properties, and their transitions between the frequency ranges, are given mainly in terms of the permanent chemical cross-links and the distinct adhesion-deadhesion processes of the transient physical cross-links. The latter are running from an associated Rouse mode low-frequency behaviour through a maximum adhesion-deadhesion dissipation and to an elastic, fully active cross-link high-frequency behaviour, while the former are displaying essentially an elastic, fully active cross-link behaviour throughout the frequency range. The developed model covers the full frequency range while matching measurements results remarkably well. Furthermore, the model is refined into a 4-parameter model by additively including an Abel relaxation function of order 1/2 to take into account the superimposed Rouse-type behaviour found in the measurements of the chemical cross-links in addition to their dominating elastic response, with the fourth parameter being a chemical Rouse stress intensity factor. The simple, effective visco-elastic models are suitable in predicting the mechanical properties of tough, doubly cross-linked, single-network PVA hydrogels with application potentials in tissue and noise abatement engineering.

Automated summary

An effective visco-elastic model based on fractional derivatives is developed for tough PVA hydrogels with both chemical and physical cross-links, which can be split into chemical and physical parts, mainly explained by permanent chemical cross-links and transient physical cross-links. The model covers the full frequency range and matches measurement results well, with potential applications in tissue and noise abatement engineering.