Ageing of glass: role of the Vogel–Fulcher–Tamman law

The ageing of various glass forming materials (polycarbonate, polystyrene, polyvinyl acetate and triphenylethene) has been studied by differential scanning calorimetry. The variation of the relaxation enthalpy ΔH with the ageing time measured in a large domain of time is compared to the variation of volume ΔV reported in the literature. Simple and complex thermal treatments (memory effect) can be distinguished.

In simple thermal treatments (annealing at a unique temperature) the following can be concluded.

(a) The glass at equilibrium is a liquid: the relaxation time τ_f to reach equilibrium, the saturation of enthalpy, is the time predicted by the Vogel–Fulcher–Tamman (VFT) law and the heat capacity is equal to that of the liquid.

(b) The kinetic laws giving the enthalpy, ΔH = k_H log t, and the volume, ΔV = k_V log t, are observed between the initial τ_i (H) and τ_i*(V) and final times τ_f (H) and τ_f* (V). For PS and PVAc we show that the times obtained by these two techniques are comparable, τ_i = τ_i* and τ_f = τ_f*. The initial relaxation times (or incubation times) follow the Arrhenius law and the final times (or equilibrium times) verify the VFT law. It is shown that for polymers the experimental slopes k_H and k_V can be deduced from this VFT (WLF) law, k_H = C₂ ΔC_p /C₁ and k_V = C₂ Δα/C₁, C₁ and C₂ being the coefficients of the WLF equation and ΔC_p and Δα being the jumps of the heat capacity and of the expansion coefficient at T_g.

In complex thermal treatments (annealing at two different temperatures) the enthalpy relaxation is compared to the volume relaxation (the memory effects) studied by Kovacs and Struik. In any case the kinetics presents two regimes, which defines an equivalent time t_eq; this is the annealing time necessary to erase the previous thermal history of the glass; the origin of this time is discussed. Above t_eq the kinetics is not different from that of simple treatments; below t_eq no variation of ΔH is observed.