Modeling of heating of energy materials

Yu. M. Kovalev   ; E. V. Pomykalov   ; O. A. Shershneva

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 14 (2022) no. 2, pp. 72-79

Résumé

An analysis of the known approximations for describing the dependence of the heat capacity at a constant volume of energetic materials (molecular crystals) on the crystal temperature has shown that there are reliable approximations of the dependence of the heat capacity at a constant volume that do not require complex quantum mechanical calculations to determine the frequencies of normal vibrations, both intermolecular and inside the molecule. To obtain the dependence of the thermal part of the internal energy of a molecular crystal, which is responsible for heating the material, it is required to integrate the heat capacity expression at constant volume over temperature. In this work, calculations have been made for the dependence of the thermal part of the internal energy of a molecular crystal in case when it is calculated through the frequencies of normal vibrations, and in case when it is calculated by integrating the heat capacity at a constant volume with respect to temperature using approximation formulas. When solving the spectral problem of determining the frequencies of normal vibrations within the molecule, the PM3 and DFT quantum chemical methods have been used. The paper presents the dependences of the thermal part of the internal energy of molecular crystals on temperature, calculated for different methods of determination, and a comparative analysis, which has shown that the difference has equaled less than 1%.

Détail

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

Bibliographie

[1] E.E. Son, “Sovremennye issledovaniya teplofizicheskikh svoistv veschestv (na osnove poslednikh publikatsii v TVT) (Obzor)”, Teplofizika vysokikh temperatur, 51:3 (2013), 392–411

[2] S.V. Stankus, R.A. Khairulin, V.G. Martynets, P.P. Bezverkhii, “Issledovaniya teplofizicheskikh svoistv veschestv i materialov v Novosibirskom nauchnom tsentre SO RAN v 2002–2012 godakh”, Teplofizika vysokikh temperatur, 51:5 (2013), 769–786 | DOI

[3] M.M. Budzevich, A.C. Landerville, M.W. Conroy et al., “Hydrostatic and uniaxial compression studies of 1,3,5-triamino- 2,4,6- trinitrobenzene using density functional theory with van der Waals correction”, J. Appl. Phys., 107:11 (2010), 113524 | DOI

[4] A.A. Rykounov, “Investigation of the pressure dependent thermodynamic and elastic properties of 1,3,5-triamino-2,4,6-trinitrobenzene using dispersion corrected density functional theory”, J. Appl. Phys., 117:21 (2015), 215901 | DOI

[5] D. Bedrov, O. Borodin, G.D. Smith et al., “A molecular dynamics simulation study of crystalline 1,3,5-triamino-2,4,6- trinitrobenzene as a function of pressure and temperature”, J. Chem. Phys., 131:22 (2009), 224703 | DOI

[6] H.C. Andersen, “Molecular Dynamics Simulations at Constant Pressure and/or Temperature”, J. Phys. Chem., 72:4 (1980), 2384 | DOI

[7] M. Parrinello, A. Rahman, “Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method”, J. Appl. Phys., 52:12 (1981), 7182 | DOI

[8] Y.S. Wei, R.J. Sadus, “Equations of State for the Calculation of Fluid-Phase Equilibria”, J. Am. Inst. Chem. Eng., 46:1 (2000), 169–196 | DOI | MR

[9] K.V. Khischenko, V.E. Fortov., “Issledovanie uravnenii sostoyaniya materialov pri vysokoi kontsentratsii energii”, Izvestiya Kabardino-Balkarskogo gosudarstvennogo universiteta, IV:1 (2014), 6–16

[10] G.I. Kanel, S.V. Razorenov, A.V. Utkin, V.E. Fortov, Udarno-volnovye yavleniya v kondensirovannykh sredakh, «Yanus-K», M., 1996, 407 pp.

[11] Yu.M. Kovalev, “Opredelenie temperaturnoi zavisimosti izobaricheskogo koeffitsienta ob'emnogo rasshireniya dlya nekotorykh molekulyarnykh kristallov nitrosoedinenii”, Inzhenerno-fizicheskii zhurnal, 91:6 (2018), 1653–1663

[12] Yu.M. Kovalev, “Uravneniya sostoyaniya dlya opisaniya izotermicheskogo szhatiya nekotorykh molekulyarnykh kristallov nitrosoedinenii”, Inzhenerno-fizicheskii zhurnal, 93:1 (2020), 229–239

[13] Yu.M. Kovalev, V.F. Kuropatenko, “Opredelenie temperaturnoi zavisimosti teploemkosti dlya nekotorykh molekulyarnykh kristallov nitrosoedinenii”, Inzhenerno-fizicheskii zhurnal, 91:2 (2018), 297–306 | MR

[14] Kompyuternaya khimiya, Mir, M., 1990, 381 pp.

[15] N.F. Stepanov, Yu.V. Novakovskaya., “Kvantovaya khimiya segodnya”, Ros. khim. zhurnal, LI:5 (2007), 5–17

[16] T.R. Gibbs, A. Popolato, Last Explosive Property Data. Los Alamos Series on Dynamic Material Properties, University of California Press, Berkeley–Los Angeles–London, 1980

[17] V.G. Schetinin, “Raschet teploemkosti organicheskikh veschestv v udarnykh i detonatsionnykh volnakh”, Khimicheskaya fizika, 18:5 (1999), 90–95