Prediction of the effective thermal conductivityof composites with graphene inclusions


Аuthors

Lavrov I. V.*, Bardushkin V. V.**, Yakovlev V. B.***

Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, Moscow, Russia

*e-mail: iglavr@mail.ru
**e-mail: bardushkin@mail.ru
***e-mail: yakvb@mail.ru

Abstract

The article considers the problem of computing the effective thermal conductivity tensor of a sample of matrix composite with polymer matrix and multi-layer graphene inclusions, which shape is being modeled by the strongly squeezed spheroids (ellipsoid of rotation). These inclusions orientations are assumed to be of the probability distribution with the infinite order symmetry axis. The problem solution is being performed based on the generalized singular approximation, and matrix is assumed as a comparison medium. This approximation option corresponds to the Maxwell-Garnett approximation for computing effective dielectric characteristics of matrix composite. The representation theory of the SO(3) group is being applied to account for the probability distribution of the inclusions. Model computations of basic components of the effective thermal conductivity tensor of the composite sample with the ED-20 epoxy system as a matrix with graphene inclusions in dependence on the volume fraction of the inclusions were conducted. Computations are being performed at various aspect ratios of the inclusions and various scatters in the inclusions axes orientations, as well as uniform distribution of the inclusions orientations. The article demonstrates that adding a slight share of inclusions may lead to significant increase in the composite thermal conductivity, as well as strong anisotropy of the heat-conducting properties of the material.

Keywords:

tensor of effective thermal conductivity, composite, generalized singular approximation, distribution of inclusion orientations, SO(3) group representations

References

  1. Novoselov K.S., Geim A.K., Morozov S.V., Jiang D., Zhang Y., Dubonos S.V., Grigorieva I.V., Firsov A.A. Electric field effect in atomically thin carbon films. Science, 2004, vol. 306, iss. 5696, pp. 666–669. DOI: 10.1126/science.1102896

  2. Novoselov K.S. Grafen: materialy Flatlandii [Graphene: Materials in the Flatland]. Uspekhi fizicheskikh nauk, 2011, vol. 181, no. 12, pp. 1299–1311. (In Russ.). DOI: 10.3367/UFNr.0181.201112f.1299

  3. Bunch J.S., Van der Zande A.M., Verbridge S.S., Frank I.W., Tanenbaum D.M., Parpia J.M., Craighead H.G., McEuen P.L. Electromechanical resonators from graphene sheets. Science, 2007, vol. 315, iss. 5811, pp. 490–493. DOI: 10.1126/science.1136836

  4. Yan Zh., Nika D.L., Balandin A.A. Thermal properties of graphene and few-layer graphene: applications in electronics. IET Circuits, Devices & Systems, 2015, vol. 9, iss. 1, pp. 4–12. DOI: 10.1049/iet-cds.2014.0093

  5. Tkachev S.V., Buslaeva E.Y., Gubin S.P. Grafen — novyy uglerodnyy nanomaterial [Graphene: a novel carbon nanomaterial]. Neorganicheskiye materialy, 2011, vol. 47, no. 1, pp. 5–14. (In Russ.)

  6. Baimova Yu.A., Mulyukov R.R. Grafen, nanotrubki i drugie uglerodnye nanostruktury [Graphene, nanotubes and other carbon nanostructures]. Moscow, Russian Academy of Sciences, 2018, 212 p. (In Russ.). DOI: 10.31857/S9785907036369000001

  7. Eletskii A.V., Iskandarova I.M., Knizhnik A.A., Krasikov D.N. Grafen: metody polucheniya i teplofizicheskiye svoystva [Graphene: fabrication methods and thermophysical properties]. Uspekhi fizicheskikh nauk, 2011,181, no. 3, pp. 233–268. (In Russ.). DOI: 10.3367/UFNr.0181.201103a.0233

  8. Kolesnikov V.I. Teplofizicheskie protsessy v metallopolimernykh tribosistemakh [Thermophysical processes in metal-polymeric tribosystems]. Moscow, Nauka, 2003, 279 p. (In Russ.)

  9. Fokin A.G. Diehlektricheskaya pronitsaemost’ smesei [Dielectric Permittivity of Mixtures]. Zhurnal tekhnicheskoy fiziki, 1971, vol. 41, no. 6, pp. 1073–1079. (In Russ.)

  10. Shermergor T.D. Teoriya uprugosti mikroneodnorodnykh sred [Micromechanics of inhomogeneous medium]. Moscow, Nauka, 1977, 399 p. (In Russ.)

  11. Kolesnikov V.I., Yakovlev V.B., Bardushkin V.V., Lavrov I.V., Sychev A.P., Yakovleva E.N. Ob ob’yedinenii metodov otsenki effektivnykh dielektricheskikh kharakteristik geterogennykh sred na osnove obobshchennogo singulyarnogo priblizheniya [Association of evaluation methods of the effective permittivity of heterogeneous media on the basis of a generalized singular approximation]. Doklady Akademii nauk, 2013, vol. 452, no. 1, pp. 27–31. (In Russ.). DOI: 10.7868/S0869565213260083

  12. Lavrov I.V., Bardushkin V.V., Sychev A.P., Yakovlev V.B., Kirillov D.A. O vychislenii ehffektivnoi teploprovodnosti teksturirovannykh tribokompozitov [On calculation of the effective thermal conductivity of textured tribocomposites]. Ehkologicheskii vestnik nauchnykh tsentrov Chernomorskogo ehkonomicheskogo sotrudnichestva, 2017, no. 2, pp. 48–56. (In Russ.)

  13. Gel’fand I.M., Minlos R.A., Shapiro Z.Ya. Predstavleniya gruppy vrashchenii i gruppy Lorentsa [Representations of the rotation group and the Lorentz group]. Moscow, Gosudarstvennoye izdatel’stvo fiziko-matematicheskoy literatury, 1958, 294 p. (In Russ.)

  14. Lavrov I.V., Bardushkin V.V., Sychev A.P., Yakovlev V.B., Kochetygov A.A. O vychislenii ehffektivnoi teploprovodnosti teksturirovannykh matrichnykh kompozitov s vysokoi ob’emnoi dolei vklyuchenii [On calculation of the effective thermal conductivity of textured matrix composites with high volume fraction of inclusions]. Ehkologicheskii vestnik nauchnykh tsentrov Chernomorskogo ehkonomicheskogo sotrudnichestva, 2018, vol. 15, no. 3, pp. 92–101. (In Russ.). DOI: 10.31429/vestnik-15-3-92-101

  15. Zarubin V.S., Zimin V.N., Kuvyrkin G.N., Savelyeva I.Y., Novozhilova O.V. Two-sided estimate of effective thermal conductivity coefficients of a textured composite with anisotropic ellipsoidal inclusions. Zeitschrift für angewandte Mathematik und Physik (ZAMP), 2023, vol. 74, iss. 4 (139). DOI: 10.1007/s00033-023-02039-0

  16. Kartashov E.M., Kudinov V.A. Analiticheskie metody teorii teploprovodnosti i ee prilozhenii [Analytical methods of the theory of thermal conductance and its applications]. Moscow, Lenand, 2018, 1072 p. (In Russ.)

  17. Benveniste Y. On the effective thermal conductivity of multiphase composites. Zeitschrift für angewandte Mathematik und Physik (ZAMP), 1986, vol. 37, pp. 696–713. DOI: 10.1007/BF00947917

  18. Vinogradov A.P. Elektrodinamika kompozitnykh materialov [Electrodynamics of composite materials]. Moscow, Editorial URSS, 2001, 208 p. (In Russ.)

  19. Gel’fand I.M., Shilov G.E. Obobshchennye funktsii i deistviya nad nimi [Generalized functions. Properties and Operations]. Moscow, Gosudarstvennoye izdatel’stvo fiziko-matematicheskoy literatury, 1958, 440 p. (In Russ.)

  20. Lavrov I.V. Proizvol’no orientirovannyi diehlektricheskii ehllipsoid v anizotropnoi srede: metod neortogonal’nogo preobrazovaniya prostranstva [An arbitrarily oriented dielectric ellipsoid in an anisotropic medium: the non-orthogonal space transformation method]. Fundamental’nye problemy radioehlektronnogo priborostroeniya, 2013, vol. 13, no. 1, pp. 44–47. (In Russ.)

  21. Maxwell Garnett J.C. Colours in metal glasses and in metallic films. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 1904, vol. 203, pp. 385–420.

  22. Bohren C.F., Huffman D.R. Pogloshchenie i rasseyanie sveta malymi chastitsami [Absorption and Scattering of Light by Small Particles]. Moscow, Mir, 1986, 660 p. (In Russ.)

  23. Osborn J.A. Demagnetizing factors of the general ellipsoid. Physical Review, 1945, vol. 67, pp. 351–357. DOI: 10.1103/PhysRev.67.351

  24. Valiev K.A., Eskin L.D. O vrashchatel’noi diffuzii molekul i rasseyanii sveta v zhidkostyakh [On rotational diffusion of molecules and scattering of light in liquids]. Optika i spektroskopiya, 1962, vol. XII, iss. 6, pp. 758–764. (In Russ.)

  25. Valiev K.A., Ivanov E.N. Vrashchatel’noe brounovskoe dvizhenie [Rotational Brownian motion]. Uspekhi fizicheskikh nauk, 1973, vol. 109, iss. 1, pp. 31–64. (In Russ.)

  26. Lavrov I.V. Diehlektricheskaya pronitsaemost’ kompozitsionnykh materialov s teksturoi: ehllipsoidal’nye anizotropnye kristallity [Permittivity of composite material with texture: ellipsoidal anisotropic inclusions]. Ekologicheskii vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva, 2009, no. 1, pp. 52–58. (In Russ.)

  27. Grigor’ev I.S., Meilikhov E.Z. Fizicheskie velichiny: spravochnik [Physical Quantities: A Handbook]. Moscow, Energoatomizdat, 1991, 1232 p. (In Russ.)

  28. Lomovsky O.I., Dudina D.V., Suslyaev V.I., Korovin E.Yu., Bukhtoyarov V.A., Dorozkin K.V. Ehlektromagnitnyi otklik kompozitsionnykh sistem «uglerodnye nanotrubki — polimernaya matritsa» i «grafen — polimernaya matritsa», poluchennykh tverdofaznymi metodami [Electromagnetic response of composite systems: «carbon nanotubes — polymer matrix» and «graphene — polymer matrix» received solid phase method]. Izvestiya vuzov. Fizika, 2014, vol. 57, no. 9/2, pp. 86–91. (In Russ.)

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