Relaxation times and viscosity

Abstract

On the basis of parallel Maxwell models having partial shear moduli G i and relaxation times τ i , mechanical relaxation processes including viscous flow can be easily described. Viscosity, e.g., equals the sum of the products of the above quantities, i.e. η = Σ G i τ i . The temperature dependence of each i term rigorously follows Arrhenius' las as log τ i = logτ i, ∞ + Q i / MRΘ. The assumption that a relation log τ ∞ = f( Q) exists between the activation energy Q i and the relaxation time limit τ ∞ correlated to Θ = ∞ and that it varies with composition and cooling rate of the glass, proves useful. The usual function for the distribution of shear moduli over relaxation times [ φ(log τ) ≡ G −1d G/dlog τ] can thus be complemented by a corresponding one for the distribution over activation energies [ Ψ( Q) ≡ G −1d G/d Q]; which is temperature independent — the same as log τ ∞( Q) The corresponding functions Ψ ( Q) are determined for the solid (−100 deg/h) and ‘liquid’ (L) glass states. Measurements of relaxation and viscosity are employed for that purpose. Application of the temperature-dependent functions log τ ∞ ( Q) and Ψ ( Q) are useful in several respects, as exemplified by calculating the freezing temperature, the change of activation energy with cooling rate, and the damping of mechanical vibrations in the transformation range.