Significant Structure Theory of Molecules Having Hindered Intermolecular Rotation in the Condensed Phases

Abstract

Significant structure theory leads to a partition function which accounts for all three phases of simple substances and in particular describes rather accurately the liquid and dense gas regions.' In the case of polyatomic molecules, additional degrees of freedom not possessed by monatomic molecules must be taken into account, and for light molecules like hydrogen, quantum effects must be considered.2 We present here a modification of the basic partition function to account for hindered intermolecular rotation.The Significant Structure Model (refs. 1 and 2).-The problem of describing a condensed system is really the problem of determining the distribution of the normal modes of motion of the molecules. This distribution follows from our liquid model, according to which all the molecules vibrate much as in a solid except for molecules jumping into vacancies. The result is that a vacancy surrounded by molecules converts three vibrational degrees into translations, and in so doing the vacancy behaves as a gas molecule. Since vacancies are of molecular size, the number of moles of vacancies in a mole of liquid is V -V,/VS, where V is the molar volume of the liquid and V, is the molar volume of the solid at the melting point. A vacancy surrounded by other vacancies is without dynamic properties, but when it is completely surrounded by other molecules, it acts like a gas molecule. Since the fraction of the positions next to a vacancy filled by molecules is V8/V, we write (V8/V). (V -V./V.) = (V -V8/V) for the fraction of gaslike molecules, with the remaining fraction VS/V being solidlike. Accordingly, for simple molecules like liquid argon, our model leads to the partition functionwhere the numerical value of all parameters is calculated from the model. This formula should apply equally well for polyatomic molecules if proper account is taken of hindered rotation and of the internal vibrations. The internal vibrations are practically unchanged by any phase change so that they offer no difficulty.A Simplified Partition Function for Hindered Rotation.-Some solids show higherorder transitions below the melting point which have been interpreted to be due to the onset of molecular rotation.3 Some members of series of similar compounds do not show any transitions below the melting point but do have large entropies of

Phase change materials for thermal energy storage: A perspective on linking phonon physics to performance

“…Less fundamental but more easily applied and quantitatively fairly accurate , Eyring developed a purely analytical model [28][29][30][31] that provides a quantitative description of the liquid state. Qualitatively, Eyring assumes that a liquid has a mixture of solid-like and gas-like characteristics such that it supports both conventional solid-like phonon transport and gas-like ballistic transport.…”