Decrease of heat capacity on aging, long and linear extrapolations for fictive temperature, and the case of 20-million-year-old fossil-amber

Abstract

A glass and its melt have the same value of a physical property at fictive temperature, Tf, which is estimated by matching the area between two linearly extrapolated plots of the heat capacity, Cp, against temperature T, one from Cp of glass and the other from that of the melt. According to the DSC heating scans, the Cp values of 20-million-year-old fossil-amber and its melt-cooled fresh-amber are the same at T < 273 K, and Tf of fossil amber is 0.89 Tg→l, where Tg→l is the glass-liquid transition temperature of melt-cooled amber [Nat. Commun. 4 (2013) 1783]. A comparison of Tf with the variation of stress relaxation time with T led to the conclusion that relaxation dynamics of amber deviates from super-Arrhenius variation. Here we show that use of the same Cps of the two ambers at T > 0 K violates basic thermodynamics, and argue that Cp of (denser) fossil-amber would be less than that of fresh-amber at T < 273 K. The Cp,confof the melt, taken as the difference between the extrapolated Cps of fossil-amber and of its melt, increases by ∼13% on cooling from T= Tg→l to T= 0.72 Tg→l, and this increase and the corresponding increase of (Cp,conf/T)= (∂Sconf/∂T)p are too small to indicate an approach towards a second-order transition of the entropy theory. Hence we conclude that deviation from super-Arrhenius variation of relaxation time of amber is an artefact of a long and linear extrapolation of its melt's Cp used for determining Tf.