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.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Materialteknik -- Textil-, gummi- och polymermaterial (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Materials Engineering -- Textile, Rubber and Polymeric Materials (hsv//eng)

Nyckelord

Abel relaxation function

Chemical cross-link

Doubly cross-linked

single-network hydrogel

Mittag–Leffler relaxation function

Physical cross-link

Rouse mode

Additives

Adhesion

Elastic moduli

Hydrogels

Noise abatement

Polyvinyl alcohols

Tissue engineering

Viscoelasticity

Fractional derivatives

Full frequency ranges

Physical cross-links

Poly (vinyl alcohol) (PVA)

Relaxation functions

Relaxation intensity

Rouse modes

Single networks

Crosslinking

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