Abstract

In many reversible or irreversible jelling materials the time evolution of the shear stress relaxation modulus is described by a power law. This peculiar viscoelastic behaviour is related to a continuous relaxation time spectrum (i.e. no characteristic relaxation time) and observed not only in gelling materials, but also at various levels of organization in biological phenomena. Classical viscoelastic models, based on association of springs and dashpots, leading to a single discrete sum of relaxation times are inadequate to describe such behaviour at least without a large number of material parameters. On the contrary fractional order parameters used in the viscoelastic constitutive laws allows to reduce significantly the number of parameters and therefore to describe the behaviour of viscoelastic materials with damping properties (or energy dissipation)

We have used the fractional calculus approach to predict the power law relaxation modulus of both critical gel, near the sol-gel transition and the gel state after transition. We will show that the critical gel (gel at Sol Gel Transition) can be associated to a single fractional element and the gel in the post SGT state to a fractional Kelvin-Voigt model. In this case it is possible to give a physical interpretation to the fractional derivative order. It is associated to the power law exponent of the shear modulus related to the fractal dimension of the critical gel.

This theoretical description has been applied experimental data obtained on silica alkoxide-based systems and biogels of chitosan by different experimental methods (rheology, compression, X-Rays diffusion and small angle neutron scattering).