Simulation of the thermal constituent of molecular crystals state equations

Yu. M. Kovalev   ; O. A. Shershneva

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 9 (2017) no. 4, pp. 43-51

Résumé

The analysis of existing approximations to describe the dependence of the heat capacity at a constant volume on the temperature of the molecular crystal has shown that the given approximations do not adequately describe the dependence of the heat capacity at a constant volume on the temperature. Therefore, in this paper for the heat capacity at a constant volume of a molecular crystal such approximation is given which makes it possible to describe both the low frequency and the high frequency parts of the vibrational spectra of molecular crystals and to obtain the temperature dependence of the heat capacity at a constant volume for molecular crystals of nitro compounds which is in line with the known dependencies. The knowledge of the dependence of the heat capacity at a constant volume on the temperature of a molecular crystal is of a great importance at the developing of the equations of state which are the closing relations of mathematical models rendering the propagation of shock waves, initiation of detonation in molecular crystals, etc. The separation of the frequencies of normal vibrations into intramolecular vibrational frequencies and the vibrations of the molecule as a whole (three vibrations of the center of gravity of the molecule and three vibrations of Euler angles) made it possible to use methods of quantum chemistry to determine the effect of intramolecular vibrations on the specific heat capacity at a constant volume. The analysis of the proposed approximation carried in the paper has shown that for molecular crystals of cyclonite, penthrite, tritol, tetryl and triaminobtrinitrobenzene the values of the relative heat capacity at a constant volume can be described by a universal curve with one parameter which is equal to 600 K.

Détail

Keywords: equation of state, molecular crystal, Helmholtz energy, Boltzmann's constant, Einstein's approximation.
Mots-clés : Planck's constant, Debye approximation

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