Application of fractional calculus to viscoelastic behaviour modelling and to the physical ageing phenomenon in glassy amorphous polymers

Abstract A model based on the concept of fractional calculus is proposed to predict the viscoelastic behaviour of amorphous polymers in the temperature range from T g −190°C to T g +25°C. Poly methyl methacrylate (PMMA) has been chosen as a model amorphous polymer. PMMA has been studied by dynamic mechanical spectrometry and the experimental data have been compared with the fractional calculus model proposed. An agreement between experiments and model has been achieved. PMMA is characterised by an unstable non-equilibrium state, at least between the main secondary relaxation ( β ) and the main relaxation ( α ). All molecular mobility phenomena are affected by this structural recovery that itself exists because of molecular mobility. One of the objectives of this work is to give some ideas of this important phenomenon and quantify its influence on the parameters of the viscoelastic model proposed.