Хімія, фізика та технологія поверхні, 2016, 7 (3), 255-284.

Шарувато-неоднорідні об’єкти с поверхнями поділу. Застосування трансляційних матриць у прикладних задачах



DOI: https://doi.org/10.15407/hftp07.03.255

L. B. Lerman

Анотація


Досліджуються неоднорідні об’єкти: шарувато–неоднорідні наночастинки і шаруваті необмежені середовища. Наводиться загальна схема побудови трансляційних матриць. Із їх застосуванням розв’язані задачі розсіяння електромагнітних хвиль на багатошарових еліпсоїдальних наночастинках (в електростатичному наближенні), сферичних частинках (в електростатичному і хвильовому наближенні), знайдені вирази для визначення електричної енергії в шарах. Побудовано розв’язок задач на власні значення для плоскошаруватого тіла, отримано розрахункові співвідношення для визначення власних  частот коливань шаруватої плити з використанням рівнянь тривимірної теорії пружності. Наведено основні розрахункові формули і ілюстративний матеріал.

Ключові слова


шарувато-неоднорідні середовища; наночастинки; трансляційні матриці; електромагнітна енергія; теплопровідність, вільні коливання

Повний текст:

PDF (Русский)

Посилання


1. Venger E.F., Goncharenko A.V., Dmitruk M.L. Optics of small particles and dispersive media. (Kyiv: Naukova dumka, 1999). [in Ukrainian].

2. Boren C.F., Huffman D.R. Absorption and scattering of light by Small Perticles. (New York: Wiley, 1983).

3. Gaponenko S.V., Rozanov N.N., Ivchenko E.L., Fedorov A.V., Baranov A.V., Bonch-Bruevich A.M., Vartanyan T.A., Przhibelsky S.G. Opics of nanoctructures. (St. Petersburg: Nedra, 2005). [in Russian].

4. Bruggeman D.A.J. Berechnung verschiedener physicalischer Konstanten von heterigenen Substanzen. P.II. Ann. Phys. Leipzig. 1935. 24(8): 665. [in German]. https://doi.org/10.1002/andp.19354160802

5. Lichtenecker K. Die Dielectrizitatskonstante naturlicher und Kunstlicher Mischkorper. Physik Z. 1926. 27: 115. [in German].

6. Krivoruchko Ya.S. Determination of effective permeability of disperse media and use of radiometry to finding moisture content. Surface. 2011. 3(8): 22. [in Ukrainian].

7. Pecharromán C., Iglesias E. Effective dielectric properties of insulator particles. Phys. Rev. B. 1994. 49(11): 7137. https://doi.org/10.1103/PhysRevB.49.7137 

8. Jayannavar A.M., Kumar N. Generalization of Bruggeman's unsymmetrical effective–medium theory to a three–component composite. Phys. Rev. B. 1991. 44(21): 12014.  https://doi.org/10.1103/PhysRevB.44.12014

9. Wang J.R., Schmugge T.J. An Empirical Model for the Complex Dielectric Permittivity of Soils as a Function of Water Content. IEEE Transactions on Geoscience and Remote Sensing. 1980. GE–18(4): 2885.  https://doi.org/10.1109/tgrs.1980.350304 

10. Lerman L.B., Grischuk O.Yu., Shkoda N.G., Shostak S.V. Features of interaction electromagnetic radiation with small particles: theoretical aspects. Usp. Fiz. Met. 2012. 13: 73. [in Ukrainian].

11. Lerman L.B., Luschenko M.O., Krivoruchko Ya.S. Interaction electromagnetic radiation with metal nanoslabs on surface of a solid. Surface. 2009. 1(16): 271. [in Ukrainian].

12. Born M., Wolf E. Principles of optics. Second edition. (Oxford: Pergamon press, 1964).

13. Andreev L.V., Dashko A.L., Pavlenko I.D. Dynamics of plates and shells with concentrated masses. (Moscow: Mashinostroenie, 1988). [in Russian].

14. Amiro I.Ya., Zarutsky V.A., Palamarchuk V.G. Dynamics of ribbed shells. Layered mediums. (Moscow: Nauka, 1973). [in Russian].

15. Karmishin A.V., Lyaskovec V.A., Myachenkov V.I., Frolov A.N. Statics and dynamics jf thin-walled shell constractions. (Moscow: Mashinostroenie, 1975). [in Russian].

16. Brechovskih L.M. Waves in layered mediums. (Moscow: Nauka, 1973). [in Russian].

17. Brechovskih L.M., Godik O.A. Acoustics of layered mediums. (Moscow: Nauka, 1989). [in Russian].

18. Grigorenko Ya.M., Bespalova A.T., Kitaigorodsky A.B., Shinkar' A.I. Free vibrations of shell constractions elements. layered mediums. (Kyiv: Naukova Dumka, 1986). [in Russian].

19. Hutchinson J.R. Vibration of plates. Boundary Elements. 1988. 4: 415.

20. Grigorenko Ya.M., Vasilenko A.T., Pankratova N.D. Statics of anisotropic thick-walled shells. (Kiev: Vyscha Shkola, 1985). [in Russian].

21. Asami K., Hanai T., Koizumi N. Dielectric Analysis of Escherichia Coli Suspension in the Light of the Theory of Interfacial Polarization. Biophys. J. 1980. 31(2): 215. https://doi.org/10.1016/S0006-3495(80)85052-1

22. Grecko L.G., Lerman L.B., Vodopianov D.L., Shostak S.V. Polarizability structural-nonuniform spherical particles. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics. 2007. 1: 416. [in Ukrainian].

23. Gurwich I., Kleiman M., Shiloah N., Cohen A. Scattering of electromagnetic radiation by multilayered spheroidal particles: recursive procedure. Appl. Opt. 2000. 39(3): 470.  https://doi.org/10.1364/AO.39.000470

24. Putilin E.S. Optical coatings. School-book on course «Optical coatings». (St. Petersburg: SPbGUITMO, 2005). [in Russian].

25. Atabekov G. Theoretical footings of electrical engineering. Linear electric circuits. (Publishing house. Lan. 7th edition, 2009). [in Russian].

26. He B., Rui X., Zhang H. Transfer Matrix Method for Natural Vibration Analysis of Tree System. Mathematical Problems in Engineering. 2012. 2012: Article ID 393204.

27. Khorasani S., Adibi A. Analytial solution of linear ordinary differential equations by differential transfer matrix method. Electronic J. of Differential Equatios. 2003. 2003(79): 1.

28. Samarsky A.A., Nikolaev E.S. Methods of grid equations solutions. (Moscow: Nauka, 1978). [in Russian].

29. Adams V., Askenazi A. Building Better Products with Finite Element Analysis PDF. (On Word Press; 1st edition. October 1, 1998.

30. Ainsworth M., Oden J., Tinsley A. Posterori Error Estimation in Finite Element Analysis DJVU. (John Wiley & Sons, Inc., 2000). https://doi.org/10.1002/9781118032824

31. Kantorovich L.V., Krylov A.I. Approximate methods of higher analysis. (Leningrad, Moscow: Gostechisdat, 1949). [in Russian].

32. Zuev V.E., Naats I.E. Inverse problems of laser probing. (Novosibirsk: Nauka, 1982). [in Russian].

33. Kokurin M.Yu., Paimerov S.K. Inverse Coefficient Problem for a Wave Equation in a Bounded Domain. Comput. Math. Math. Phys. 2008. 48(1): 109.  https://doi.org/10.1134/S0965542508010089

34. Lavrent'ev M.M., Romanov V.G., Shishatskii S.P. Ill–Posed Problems of Mathematical Physics and Analysis. (Moscow: Nauka, 1980. American Mathematical Society, Providence, R.I., 1986).

35. Romanov V.G. Stability of Inverse Problems. (Moscow: Nauchnyi Mir, 2005).

36. Denisov A.M. Introduction to the Theory of Inverse Problems. (Moscow: Mosk. Gos. Univ., 1994). [in Russian].

37. Lerman L.B., Luschenko M.A., Krivoruchko Ya.S., Skoda N.G., Shostak S.V. Inverse problems of optical and dielectrical spectroscopy of nanoparticles and dewy porous mediua. Chemistry, physics and technology of surface. 2008. 14: 101. [in Russian].

38. Krivoruchko Ya.S. Determination of effective permittivity of heterogeneous media and estimation of moisture content in soils. Surface. 2011. 3(18): 22. [in Ukrainian].

39. Krivoruchko Ya.S., Lerman L.B., Luschenko M.A., Yakymiv R.Ya. Determination of soils humidity of porous media (inverse problems). Bulletin of National Technical univercity "Kyivsky politechnichesky institut". Seria: Radio engineering.Radioinstrument-making. 2007. 35: 49. [in Ukrainian].

40. Grechko L.G., Eremenko A.M., Krylona G.V., Lerman L.B., Smirnova N.P., Shkoda N.G. Optical properties of small silver particles in colloidal solutions. Bulletin of Taras Shevchenko NationalUniversity of Kyiv. Series: Physics & Mathematics. 2004. 4: 450. [in Ukrainian].

41. Tichonov A.N., Arsenin V.Ya. Soution methods of incorrectly formulated problems. (Moscow: Nauka, 1986). [in Russian].

42. Shifrin K.S. Light scattering in turbid medium. (Moscow-Leningrad: GITTL, 1951). [in Russian].

43. Godunov S.K. Equations of mathematical physics. (Moscow: Nauka, 1982). [in Russian].

44. Tikhonov A.N., Samarsky A.A. Equations of mathematical physics. (Moscow: Nauka, 1972). [in Russian].

45. Koshlyakov N.S., Gliner E.B., Smirnov M.M. Equations in partial derivatives of mathematical physics. (Moskow: Vishaya shkola, 1970). [in Russian].

46. Kartashov E.M. Integral transform method in analytical theory of heat conduction of solids. Proceedings of the Russian Academy of Sciences. Energy. 1993. 2: 99.

47. Kamke E. Gewöhnliche differentialgleichungen. (Leipzig, 1959). [in German].

48. Korn G.A., Korn M.S. Mathematical handbook for scientists and ingineers. Second,enlargend and reviesed edition. (New York: McGraw Hill Book Company, 1968).

49. Tugolukov E.N. Solving of thermal conductivity problems by finite integral transform method. School-book. (Tambov: Publishing house of Tambov State Technical University, 2005). [in Russian].

50. Drexler K.E. Nanosystems. Molecular Machinery, Manofacturing, and Computation. (New York: Wiley, 1992).

51. Kik P.G. Surface Plasmon Nanofotonics. (Springer, 2007).

52. Giharev I.V., Lyashenko V.I. Nanotechnology in the world and in the Ukraine. Donetsk Reional Economics Bulletin. 2007. 1: 117. [in Russian].

53. Krushenko G.G. Some aspects of use of nanotechnology. Nanotechnology. 2008. 1(13): 9.

54. Hutter B.E., Fendler J.H. Exploitation of localized surface plasmon resonance. Advanced Materials. 2004. 16(19): 1685. https://doi.org/10.1002/adma.200400271

55. Kelly K.L., Coronado E., Zhao L.L., Schatz G.C. The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment. J. Phys. Chem. B. 2003. 107(3): 668.  https://doi.org/10.1021/jp026731y 

56. Noguez C. Surface plasmons on metal nanoparticles: the influence of shape and physical environment. J. Phys. Chem. C. 2007. 111(14): 3606.  https://doi.org/10.1021/jp066539m

57. Lee K.S., El-Sayed M.A. Gold and silver nanoparticles in sensing and imaging: sensitivity of plasmon response to size, shape, and metal composition. J. Phys. Chem. B. 2006. 110(39): 19220. https://doi.org/10.1021/jp062536y

58. Motl N.E., Ewusi-Annan E., Sines I.T., Jensen L., Schaak R.E. Au-Cu alloy nanoparticles with tunable compositions and plasmonic properties: experimental determination of composition and correlation with theory. J. Phys. Chem. C. 2010. 114(45): 19263. https://doi.org/10.1021/jp107637j 

59. Blaber M.G., Arnold M.D., Ford M.J. A review of the optical properties of alloys and intermetallics for plasmonics. J. Phys. Condens. Matter. 2010. 22(14): Article ID 143201. https://doi.org/10.1088/0953-8984/22/14/143201

60. Mischenko M.I., Hovenier I.V., Travis L.D. Light Scatterring by Nonspherical Particles. Theory, Measurements, and Applications. (New York: Academic press, 2002).

61. Wen-Chi Hung. A Steady of Surface Plasmon Effect Exited on Metal Nanoparticles. − A thesis submitted in partical Sulilment of the requrements for the degree of Doctor of Philosophy. (Inst. of Electro–Optical Engineering National Sun Yat-sen University Kaohsiung. Taivan, R.O.C., 2008).

62. Mischenko M.I. Doctor (Doctor of Physics and Mathematics Science). Thesis. (Kyiv–New York, 2007).

63. Grecko L.G., Lerman L.B., Shkoda N.G. Multi-layere ellipsoid in electrical field. Bulletin of Taras Shevchenko NationalUniversity of Kyiv. Series: Physics & Mathematics. 2004. 1: 386. [in Ukrainian].

64. Grecko L.G., Lerman L.B., Bilokrinithka L.M., Shostak S.V. Surface modes in multi-layere particles of ellipsoidal form. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics. 2006. 4: 416. [in Ukrainian].

65. Grecko L.G., Lerman L.B., Shkoda N.G. Scattering of electromagnetic radiation on multi-layere sphere. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics. 2004. 3: 376. [in Ukrainian].

66. Jonson P.B., Christy R.W. Optical Constants of the Noble Metals. Phys. Rev. B. 1972. 6(12): 4370. https://doi.org/10.1103/PhysRevB.6.4370

67. Palik E.D. Handbook of Optical Constants of Solids. (New York: Academic Press, 1985).

68. Lerman L.B. Generation of additional plasmon resonances in layered small particles. Nanosystems, nanomaterials, nanotechnologies. 2009. 7: 37.

69. Lerman L.B. Generation of additional plasmon resonances in small particles with shell. Chemistry, Physics and Technology of Surface. 2008. 14: 91.

70. Porod'ko L.V., Lerman L.B. Electrodynnamic energy in spherical layered particles. Technological audit and production reserves. 2013. 6/1(14): 41.

71. Luschenko M.A., Lerman L.B., Krivoruchko Ya.S. Interaction electromagnetic radiation with alyered spherical lens. Bulletin of National Technical univercity "Kyivsky politechnichesky institut". Seria: Radio engineering. Radioinstrument-making. 2007. 34: 54. [in Ukrainian].

72. Prashant K.J., Ivan H.El−Sayed, Mostafa A.El−Sayed. Au nanoparticles target cancer. Nanotoday. 2007. 2(1). 18. https://doi.org/10.1016/S1748-0132(07)70016-6

73. Hongxing Xu. Surface plasmon Photonics. Thesis for the degree of doctor of philosophy. (Geteborg University, 2002).

74. Chatterjee K., Banerjee S., Chakravorty D. Plasmon resonance shifts in oxide–coated silver nanoparticles. Phys. Rev. B. 2002. 66: 085421−1.  https://doi.org/10.1103/PhysRevB.66.085421

75. Zhu J. Theoretical study of the optical absorption properties of Au–Ag bimetalic nanospheres. Physica E. 2005. 27(1–2): 296. https://doi.org/10.1016/j.physe.2004.12.006

76. Huazhong S., Lide S., Weiping C. Composition modulation of optical absorption in AgxAu1–x alloy nanocrystals in suti within pores of nanopores silica. J. Appl. Phys. 2000. 87(3): 1572. https://doi.org/10.1063/1.372053

77. Grechko L.G., Lerman L.B., Koretskyi S.L., Krivoruchko Ya. S., Shostak S.V.  Absorption of electromagnetic irradiation by bimetall particles and matrix disperse systems with such inclusion. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics. 2008. 4: 260. [in Ukrainian].

78. Lerman L.B., Luschenko M.A., Krivoruchko Ya.S. Interaction of electromagnetic irradiation with bimetallic particles near surface of solid. Chemistry, physics and technology of surface. 2009. 15: 15. [in Russian].

79. Moroz A. A recursive transfer–matrix solution for a dipole radiating and outside a stratified sphere. Annal. Phys. 2005. 315: 352.  https://doi.org/10.1016/j.aop.2004.07.002

80. Wu Z.S., Wang Y.P. Electromagnetic scattering for multi–layered sphere: recursive algorithm. Radio Sci. 1991. 26: 1393. https://doi.org/10.1029/91RS01192

81. Gurwich I. Kleiman M., Shiloah N., Cohen A. Scattering of electromagnetic radiation by multilayered spheroidal particles: recursive procedure. Appl. Opt. 2000. 39(3): 470. https://doi.org/10.1364/AO.39.000470

82. Averitt R.D., Sarcar D., Halas N.J. Plasmon Resonance Shifts of Au-Coated Au2S Nanoshells: Insight into Multicomponent Nanoparticle Growth. Phys. Rev. Lett. 1997. 78(22): 4217. https://doi.org/10.1103/PhysRevLett.78.4217

83. Roth J., Digman M.J. Scattering and extinction sections fof a spherical particles coated with an oriented molecular layer. J. Opt. Soc. Am. 1973. 63(3): 308. https://doi.org/10.1364/JOSA.63.000308 

84. Lopatin V.N., Sydko F.Ya. Introduction to optics cell suspensions. (Novosibirsk: Nauka, 1988). [in Russian].

85. Barber P.W. Light Scattering by Particles: Computational Methods. V.2. (Singapore, New Jersy, London, Hong Kong: World Scientific, 1990).

86. Lerman L.B. Oscillation of flat layered shells with local elastic supports. Int. Appl. Mech. 1994. 30(2): 129. https://doi.org/10.1007/BF00848511

87. Lerman L.B. Application of planar elasticity equations to the investigation of vibrations of extended multilayered slabs with internal line supports. Int. Appl. Mech. 1994. 30(7): 530. https://doi.org/10.1007/BF00847248

88. Silveirinha M.G., Alu A., Engheta N. Parallel Plate Metamaterials for Cloaking Structures. Phys. Rev. E. 2007. 75(036603): 1. https://doi.org/10.1103/physreve.75.036603

89. Tricarico S., Bilotti F., Vegni L. Scattering cancellation by metamaterial cylindrical multilayers. JEOS: RP. 2009. 4: 0921-1.

90. Qiu Ch.-W., Yao H.-Y., Burocur S.-N. Electromagnetic Scattering Properties in a Multilayered Metamaterial Cylinder. IEICE Trans. Commun. 2007. E90-B(9): 2423. https://doi.org/10.1093/ietcom/e90-b.9.2423




DOI: https://doi.org/10.15407/hftp07.03.255

Copyright (©) 2016 L. B. Lerman