Geodesic
An algorithm for calculating the movements of diatomic gases molecules
Matematičeskoe modelirovanie, Tome 33 (2021) no. 1, pp. 53-62.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of modeling the properties of diatomic gases by molecular dynamics methods is considered. Such studies are traditional for the physics of matter. Currently, there is an increased interest in this problem in connection with the development of nanotechnologies and their implementation in various industrial branches. In the proposed work, the question of clarifying the original classical model of Newton's dynamics is considered. In particular, a technique is discussed for taking into account additional degrees of freedom that characterize the rotational motions of diatomic molecules. This is due to the need to correctly calculate the heat capacity. To solve this problem, it was proposed to add equations for the angular momentum and rotational velocities of molecules to the molecular dynamics model. For such an extended formulation, a special numerical algorithm has been developed that generalizes the Verlet scheme. A computational program has been developed on the basis of the proposed algorithm. It was used to calculate the heat capacity curve for nitrogen in the temperature range 100-400 K at a pressure of 1 atm. The calculated data obtained agree with the known data from reference books.
Keywords: properties of technical gases, molecular dynamics, translational and rotational degrees of freedom, numerical algorithm for calculation. 
@article{MM_2021_33_1_a3,
     author = {S. V. Polyakov and V. O. Podryga},
     title = {An algorithm for calculating the movements of diatomic gases molecules},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {53--62},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_1_a3/}
}
TY  - JOUR
AU  - S. V. Polyakov
AU  - V. O. Podryga
TI  - An algorithm for calculating the movements of diatomic gases molecules
JO  - Matematičeskoe modelirovanie
PY  - 2021
SP  - 53
EP  - 62
VL  - 33
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2021_33_1_a3/
LA  - ru
ID  - MM_2021_33_1_a3
ER  - 
%0 Journal Article
%A S. V. Polyakov
%A V. O. Podryga
%T An algorithm for calculating the movements of diatomic gases molecules
%J Matematičeskoe modelirovanie
%D 2021
%P 53-62
%V 33
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2021_33_1_a3/
%G ru
%F MM_2021_33_1_a3
S. V. Polyakov; V. O. Podryga. An algorithm for calculating the movements of diatomic gases molecules. Matematičeskoe modelirovanie, Tome 33 (2021) no. 1, pp. 53-62. http://geodesic.mathdoc.fr/item/MM_2021_33_1_a3/

[1] I.K. Kikoin (red.), Tablitsy fizicheskikh velichin. Spravochnik, Atomizdat, M., 1976, 1008 pp.

[2] E. B. Winn, “The Temperature Dependence of the Self-Diffusion Coefficients of Argon, Neon, Nitrogen, Oxygen, Carbon Dioxide, and Methane”, Phys. Rev., 80:6 (1950), 1024–1027 | DOI

[3] F. Hutchinson, “Self-Diffusion in Argon”, J. Chem. Phys., 17:11 (1949), 1081–1086 | DOI

[4] V. G. Fastovskii, A. E. Rovinskii, IU. V. Petrovskii, Inertnye gazy, Atomizdat, M., 1972, 352 pp.

[5] N. B. Vargaftik, Spravochnik po teplofizicheskim svoistvam gazov I zhidkostei, izdanie vtoroe, dopolnennoe, Nauka, M., 1972, 720 pp.

[6] V. V. Sychev, A. A. Vasserman, A. D. Kozlov, G. A. Spiridonov, V. A. Tsymarnyi, Termodinamicheskie svoistva azota, GSSSD. Seriia monografiia, Izd-vo standartov, M., 1977

[7] GSSSD 4-78. Azot zhidkii I gazoobraznyi. Plotnost, entalpiia, entropiia I izobarnaia teploemkost pri temperaturakh 70–1500 K i davleniiakh 0.1–100 MPa, Izd-vo standartov, M., 1978

[8] A. A. Vigasin, V. E. Liusternik, L. R. Fokin, GSSSD 49-83. Azot. Vtoroi virialnyi koeffitsient, koeffitsienty dinamicheskoi viazkosti, teploprovodnosti, samodiffuzii i chislo Prandtlia razrezhennogo gaza v diapazone temperatur 65-2500 K. Tablitsy standartnykh spravochnykh dannykh, Izd-vo standartov, M., 1984

[9] A. D. Kozlov, V. M. Kuznetsov i dr., GSSSD 89-85. Azot. Koefficienty dinamicheskoi viazkosti i teploprovodnosti pri temperaturakh 65...1000 K i davleniiakh ot sostoianiia razrezhennogo gaza do 200 MPa. Tablitsy standartnykh spravochnykh dannykh, Izd-vo standartov, M., 1986

[10] V. M. Zhdanov, M. IA. Alievskii, Protsessy perenosa i relaksatsii v molekuliarnykh gazakh, Nauka, M., 1989, 336 pp.

[11] A. P. Babichev, N. A. Babushkina, A. M. Bratkovskii i dr., Fizicheskie velichiny. Spravochnik, eds. I.S. Grigorev, E.Z. Meilihov, Energoatomizdat, M., 1991, 1232 pp.

[12] M. S. Cramer, “Numerical estimates for the bulk viscosity of ideal gases”, Physics of fluids, 24 (2012), 066102, 23 pp. | DOI

[13] J. O. Hirschfelder, C. F. Curtiss, R. B. Bird, Molecular Theory of Gases and Liquids, Wiley Sons, NY., 1964, 1249 pp.

[14] M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids, Oxford University Press, NY, 1987, 385 pp. | MR | Zbl

[15] A. N. Lagar'kov, V. M. Sergeev, “Molecular dynamics method in statistical physics”, Sov. Phys. Usp., 21:7 (1978), 566–588

[16] J. M. Haile, Molecular Dynamics Simulations. Elementary Methods, John Wiley Sons Inc., NY, 1992, 489 pp.

[17] D. Frenkel, B. Smit, Understanding Molecular Simulation. From Algorithm to Applications, Academic Press, NY, 2002, 638 pp.

[18] D. C. Rapaport, The Art of Molecular Dynamics Simulations, Second Edition, Cambridge University Press, 2004, 565 pp.

[19] G. E. Norman, V. V. Stegailov, “Stochastic theory of the classical molecular dynamics method”, Mathematical Models and Computer Simulations, 5:4 (2013), 305–333 | DOI | MR | Zbl

[20] L. Verlet, “Computer «experiments» on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules”, Phys. Rev., 159 (1967), 98–103 | DOI

[21] H. J. C. Berendsen, J. P.M. Postma, W. F. van Gunsteren et al., “Molecular dynamics with coupling to an external bath”, J. Chem. Phys., 81 (1984), 3684–3690 | DOI

[22] J. E. Lennard-Jones, “Cohesion”, Proc. of the Physical Soc., 43:5 (1931), 461–482 | DOI

[23] G. Von Mie, “Zur kinetischen theorie der einatomigen korper”, Ann. Phys. Leipzig, 11:8 (1903), 657–697

[24] L. R. Fokin, A. N. Kalashnikov, “The transport properties of an N2-H2 mixture of rarefied gases in the EPIDIF database”, High Temperature, 47:5 (2009), 643–655 | DOI

[25] L. R. Fokin, A. N. Kalashnikov, A. F. Zolotukhina, “Transport properties of mixtures of rarefied gases. Hydrogen-methane system”, J. of Eng. Phys. Therm., 84:6 (2011), 1408–1420 | DOI

[26] L. R. Fokin, A. N. Kalashnikov, “Transport properties of a rarefied CH4-N2 gas mixture”, Journal of Engineering Physics and Thermophysics, 89:1 (2016), 249–259 | DOI

[27] K. Meier, A. Laesecke, S. Kabelac, “Transport coefficients of the Lennard-Jones model fluid. III. Bulk viscosity”, J. Chem. Phys., 122:1 (2005), 014513 | DOI

[28] K. Meier, Computer Simulation and Interpretation of the Transport Coefficients of the Lennard-Jones Model Fluid, PhD Thesis, Shaker Publishers, Aachen, 2002, 265 pp.

[29] D. Levesque, L. Verlet, J. Kurkijarvi, “Computer “experiments” on classical fluids. IV. Transport properties and time-correlation functions of the Lennard-Jones liquid near its triple point”, Phys. Rev. A, 7:5 (1973), 1690–1700 | DOI

[30] V. O. Podryga, “Opredelenie makroparametrov realnogo gaza metodami molekuliarnoi dinamiki”, Matematicheskoe modelirovanie, 27:7 (2015), 80–90 | MR | Zbl

[31] V. O. Podryga, E. V. Vikhrov, S. V. Polyakov, “Molecular dynamic calculation of macroparameters of technical gases by the example of argon, nitrogen, hydrogen, and methane”, Mathematical Models and Computer Simulations, 12:2 (2020), 210–220 | DOI | MR | Zbl

[32] E. W. Lemmon, M. O. McLinden, D. G. Friend, Thermophysical Properties of Fluid Systems, NIST Chemistry WebBook, NIST Standard Reference Database Number 69, eds. P.J. Linstrom, W.G. Mallard, National Institute of Standards and Technology, Gaithersburg MD, 20899 http://webbook.nist.gov | Zbl