Physical interpretation of the rheological behaviour of amorphous polymers through the glass transition

Overview & Synopsis

The purpose of the present work is to predict, from physical bases, the mechanical behaviour of amorphous polymers resulting from the application of a periodic stress through the glass transition range (a relaxation). A theory of the non elastic deformation is developed from a model of molecular mobility. The amorphous polymer is described in terms of a close packing of monomers in which there are sites corresponding to density fluctuations : these sites, exhibit an excess of enthalpy (and entropy) and are hereafter called « defects ». The concentration of defects is calculated from thermodynamic arguments usual in physical metallurgy. The application of a stress results in the nucleation of shear-microdomains (Smd) around the defects where the resistance to shear is weaker. Thus, the non elastic deformation has two components : one is anelastic due to the nucleation of the Smd (characteristic time τ1), the other is viscoplastic due to the expansion of the Smd until annihilation of the line bordering them (time τ2). Both τ1 and τ 2 are related to a unique characteristic time τmax thanks to the application of the hierarchical (or series) correlation concept introduced earlier by Palmer et al. The dynamic modulus (G' and G") and tan ϕ are calculated. The parameters appearing in the equations thus obtained can be known from independent experimental ways and all have a precise physical meaning : the concentration of defects Cd, the mechanical relaxation time τmr linked to τmax ∼ τ mol which is a life time for monomer diffusion and two coefficients, k and h, indicating the effectiveness of correlation effects existing, on the one hand, during preliminary molecular movements (reversible expansion of Smd) and, on the other hand, during longer distance movements implying the annihilation of lines bordering the Smd. After determining the different physical parameters the comparison between theoretical and experimental results is made. Thus the physical origin of stretched exponentials (Kohlrausch or Williams-Watt's equation) as well as the high values of the apparent activation energy (which, moreover depend on T) can be explained.