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

The heat capacity, Cp, 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 Sliq, the entropy of a liquid, inadvertently include part of the Cp on the high temperature side of this peak, the decrease of Sliq with T is greater than the true decrease, and the downward curvature of the Sliq - 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, Cp,liq, measured during cooling in a scanning calorimetry experiment and (ii) by directly determining the ratio, (Cp,liq /T) = (∂Sliq /∂T)P. As examples, we analyze the Cp,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 Cp of an orientationally-disordered crystal. F. Simon (Z. Anorg. Allg. Chem. 203 (1931) 219–227) had provided a sigmoid shape extrapolation of Cp and sublinear extrapolation of Sexc (= Sliq – Scryst) of glycerol down to T = 60 K. We discuss it in terms of (Cp,exc /T) = (∂Sexc /∂T)P. Features of the (Cp,exc /T) against T plot agree with Simon's Sexc against T plot within experimental and analytical errors.