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

Abstract

The ageing of various glass forming materials (polycarbonate, polystyrene,polyvinyl acetate and triphenylethene) has been studied by differentialscanning calorimetry. The variation of the relaxation enthalpy ΔH with theageing time measured in a large domain of time is compared to the variation of volumeΔVreported in the literature. Simple and complex thermal treatments (memoryeffect) can be distinguished.In simple thermal treatments (annealing at a unique temperature) the followingcan be concluded.(a) The glass at equilibrium is a liquid: the relaxation time τfto reach equilibrium, the saturation of enthalpy, is the time predicted by theVogel–Fulcher–Tamman (VFT) law and the heat capacity is equal to that of theliquid.(b) The kinetic laws giving the enthalpy, ΔH = kH log t,and the volume, ΔV = kV log t, are observed betweenthe initial τi (H)and τi*(V) andfinal times τf (H)and τf* (V).For PS and PVAc we show that the times obtained bythese two techniques are comparable, τi = τi* and τf = τf*.The initial relaxation times (or incubation times) follow the Arrheniuslaw and the final times (or equilibrium times) verify the VFTlaw. It is shown that for polymers the experimental slopes kH andkVcan be deduced from this VFT (WLF) law, kH = C2 ΔCp /C1 and kV = C2 Δα/C1,C1 andC2being the coefficients of the WLF equation and ΔCp and Δαbeing the jumps of the heat capacity and of the expansion coefficient atTg.In complex thermal treatments (annealing at two different temperatures)the enthalpy relaxation is compared to the volume relaxation (thememory effects) studied by Kovacs and Struik. In any case thekinetics presents two regimes, which defines an equivalent timeteq;this is the annealing time necessary to erase the previous thermalhistory of the glass; the origin of this time is discussed. Aboveteqthe kinetics is not different from that of simple treatments; belowteq no variationof ΔHis observed.