On the decrease of entropy on cooling polymer melts and an orientationally-disordered crystal

The heat capacity, C-p, measured on heating a glass in adiabatic and scanning calorimetry experiments generally shows an overshoot peak before the liquid state is reached. We argue that when estimates of S-liq, the entropy of a liquid, inadvertently include part of the C-p on the high temperature side of this peak, the decrease of S-liq with T is greater than the true decrease, and the downward curvature of the S-liq-T plot is, as an artefact, greater. This affects the super-linear extrapolation of Sliq to T below the glass to liquid transition temperature, which is basis of the theory for thermodynamic origin of glass formation. The artefact may be avoided by, (i) using the heat capacity of a liquid, C-p,C-liq, measured during cooling in a scanning calorimetry experiment and (ii) by directly determining the ratio, (C-p,C-liq /T) = (partial derivative S-liq / partial derivative T)(P). As examples, we analyze the C-p,C-liq data of two polymers measured during cooling of the melt and heating of the glass, the latter on the same time scale as used in adiabatic calorimetry, and compare the results against those obtained from dynamic measurements. We similarly analyze the C-p of an orientationally-disordered crystal. F. Simon (Z. Anorg. Allg. Chem. 203 (1931) 219-227) had provided a sigmoid shape extrapolation of C-p and sublinear extrapolation of S-exc (= S-liq - S-cryst) of glycerol down to T = 60 K. We discuss it in terms of (C-p,C-exc /T) = (partial derivative S-exc / partial derivative T)(P). Features of the (C-p,C-exc /T) against T plot agree with Simon's Sexc against T plot within experimental and analytical errors.

Automated summary

The overshoot peak observed in the heat capacity, C-p, during the heating of glass is caused by the inadvertent inclusion of part of the C-p on the high temperature side of the peak into the entropy estimate of the liquid state. This affects the decrease of the liquid entropy with temperature and the downward curvature of the entropy-temperature plot. By using the heat capacity of the liquid during cooling and directly determining the ratio (C-p,C-liq /T), this artifact can be avoided. Experimental data on polymers and an orientationally-disordered crystal are analyzed and compared to previous studies.