The residual configurational entropy below the glass transition: Determination for two commercial optical glasses

Essentially from differential scanning calorimetry and viscosimetry, the residual configurational entropy below the glass transition is determined for two linearly cooled commercial optical glasses, K7™ and N-LaK12™ from SCHOTT. The procedure is according to the conventional understanding of glass entropy and the conventional description of the configurational state by a distribution of fictive temperatures. For a cooling rate of 10 K/min, the residual entropy values found below the glass transition are 0.146 J/(g K) for K7™ and 0.148 J/(g K) for N-LaK12™. The result is discussed comparing with both the lower limit for the residual entropy resulting from the reversibly exchanged heat (∫dq/T∫dq/T, ‘Clausius limit’) and the upper limit given by the configurational entropy of an equilibrium liquid with the same fictive temperature. The difference between the residual entropy and its lower limit is equal to the entropy generation due to the fall-out from equilibrium during linear cooling. The difference between the residual entropy and its upper limit is the driving force of the crossover- (or Kovacs-) effect. It turns out that the difference between the residual entropy and the Clausius limit is very small. The values found amount to less than 0.0001 J/(g K) for both glasses. Therefore, this difference can be neglected concerning the extrapolation of the Adam–Gibbs relation to low temperatures.