The configurational entropy theory and the heat capacity decrease of orientationally disordered crystals on cooling to 0K

Abstract

The validity of the Kauzmann extrapolation in the entropy theory for kinetic freezing of orientational disordered crystals is examined. It is found that the theory itself does not support this extrapolation nor does it lead to the inference of an Ehrenfest-type thermodynamic transition in the equilibrium state at a temperature above 0 K. It is argued that the heat capacity C p and entropy S of the equilibrium disordered state of a crystal would decrease along a stretched sigmoid shape curve to their zero values at 0 K, while the enthalpy H and volume would remain higher than in the ordered crystal state. This is elaborated by interpolating C p between 0 K and the available high-temperature C p values of the equilibrium state of ®ve substances, four orientationally disordered crystals and one nematic liquid crystal. The calculated H of the equilibrium state at 0 K is 20±41% of the enthalpy of transformation. The role of vibrational and con®gurational entropies has been discussed, and it is shown that the con®gurational part of C p and S would not diverge at any temperature, nor would the con®gurational entropy be proportional to the excess entropy of the equilibrium disordered state over the ordered state. The manner of decreases in C p , S and H of the kinetically frozen state towards the equilibrium state in our interpolation is characteristically di erent from the corresponding decrease in the Kauzmann equilibrium state.

Many Faces of Entropy or Bayesian Statistical Mechanics

“…[28] Still, it does not seem to ever be acceptable to everybody, because of the huge essential difficulty with any ultimate experimental check: It is practically impossible to achieve the absolute zero of temperature (a detailed discussion on this topic can be found in refs. [27,29]). …”

“…This is in fact a much stronger statement than merely the third law of thermodynamics -and, in effect, it is rooted in the microscopic, quantum nature of the matter [27], but can nonetheless be mathematically derived just from the macroscopic expressions for the 1 st and the 2 nd laws of thermodynamics without any further assumptions and/or empirical data/experience [28]. Still, it does not seem to be ever acceptable by everybody, because of the huge essential difficulty with any ultimative experimental check: It is practically impossible to achieve the absolute zero of temperature (for example, there is a detailed discussion on this topic in the works [27,29]); a) when absolute temperature goes to infinity, entropy and heat capacity become more and more decorrelated, so that the derivative of heat capacity with respect to entropy tends to zero (this is just the reflection of the fact that heat capacity tends to its maximum value, whereas entropy does not have any limit).…”