The effect of physical ageing on the relaxation time spectrum of amorphous polymers: the fractional calculus approach

Empirical models corresponding to a constitutive equation with fractional derivatives are proposed for linear viscoelastic polymers. For these models, the relaxation modulus, the dynamic moduli, the relaxation time spectra, and other material functions can be calculated as a function of a few parameters that characterise the behaviour of a viscoelastic polymer. The fractional calculus approach allows us to calculate the relaxation time spectrum H() via the Stieltjes inversion in the linear viscoelastic zone. Polymethylmethacrylate (PMMA) is chosen as a model amorphous polymer in a temperature range from T_g + 90°C to T_g + 25°C. This polymer is characterised by a non-equilibrium state between at least the and relaxations. The structural recovery of PMMA has been investigated using dynamic mechanical thermal analysis (DMTA) by varying the preparational history. The effect of time and temperature on the model parameters and on the relaxation time spectra are also investigated in the neighbourhood of the glass transition.