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SUMMARY:Fractional calculus approach for viscoelasticity at the sol-gel tr
 ansition: application to sol-gel materials and biogels - Alain Ponton\, Ma
 tière et Systèmes Complexes\, UMR 7057 CNRS & Université Denis Diderot-
 Paris 7\, Paris\, France
DTSTART:20070524T131500Z
DTEND:20070524T141500Z
UID:TALK7377@talks.cam.ac.uk
CONTACT:Dr Kalin Dragnevski
DESCRIPTION:In many reversible or irreversible jelling materials the time 
 evolution of the shear stress relaxation modulus is described by a power l
 aw. This peculiar viscoelastic behaviour is related to a continuous relaxa
 tion time spectrum (i.e. no characteristic relaxation time) and observed n
 ot only in gelling materials\, but also at various levels of organization 
 in biological phenomena. Classical viscoelastic models\, based on associat
 ion of springs and dashpots\, leading to a single discrete sum of relaxati
 on times are inadequate to describe such behaviour at least without a larg
 e number of material parameters. On the contrary fractional order paramete
 rs used in the viscoelastic constitutive laws allows to reduce significant
 ly the number of parameters and therefore to describe the behaviour of vis
 coelastic materials with damping properties (or energy dissipation)\n\nWe 
 have used the fractional calculus approach to predict the power law relaxa
 tion modulus of both critical gel\, near the sol-gel transition and the ge
 l state after transition. We will show that the critical gel (gel at Sol G
 el Transition) can be associated to a single fractional element and the ge
 l in the post SGT state to a fractional Kelvin-Voigt model. In this case i
 t is possible to give a physical interpretation to the fractional derivati
 ve order. It is associated to the power law exponent of the shear modulus 
 related to the fractal dimension of the critical gel. \n\nThis theoretical
  description has been applied experimental data obtained on silica alkoxid
 e-based systems and biogels of chitosan by different experimental methods 
 (rheology\, compression\, X-Rays diffusion and small angle neutron scatter
 ing).      \n
LOCATION:IRC in Superconductivity Seminar Room\, Cavendish Laboratory
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