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KARBON NANOTÜPLERİN ISI İLETİMİNİN UYGULANAN VOLTAJLAR ALTINDA ANALİTİK VE SAYISAL ANALİZİ

Year 2021, , 51 - 60, 30.04.2021

Yahya Öz

https://doi.org/10.47480/isibted.979332

Abstract

Karbon nanotüplerin (KNT) elektron alanı emisyonu deneyleri, ısı nedeniyle KNT'lerin uygulanan voltaj altında beklenenden daha hızlı bozulduğunu göstermektedir. Bu nedenle, değişen sıcaklık dağılımlarına sahip farklı sistemler, ısı akışı denklemini kullanarak analitik ve sayısal olarak değerlendirilmektedir. Bu metodoloji, KNT'lerin termoelektrik davranışının uygulanan voltaj altında fenomenolojik davranışını ve tanımını sağlamaktadır.

Keywords

Karbon Nanotüp Elektron Alan Emisyonu Isı İletimi

References

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  • Bilodeau G. G., 1962, The Weierstrass transform and Hermite polynomials, Duke Mathematical Journal, 29, 293-308.
  • Bocharov G. S. and Eletskii A. V., 2013, Theory of Carbon Nanotube (CNT)-Based Electron Field Emitters, Nanomaterials, 3, 393-442.
  • Bonard J., Dean K. A., Coll B. F. and Klinke C., 2002, Field Emission of Individual Carbon Nanotubes in the Scanning Electron Microscope, Physical Review Letters, 89, 197602.
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  • Charney J. G., Fjörtoft R. and J. Von Neumann, 1950, Numerical Integration of the Barotropic Vorticity Equation, Tellus, 2, 237-254.
  • Cheng Y. and Zhou O., 2003, Electron field emission from carbon nanotubes, Comptes Rendus Physique, 4, 1021-1033.
  • Chernozatonskii L. A., Gulyaev Y. V., Kosakovskaja Z. J., Sinitsyn N. I., Torgashov G. V., Zakharchenko Y. F., Fedorov E. A. and Val’chuk V. P., 1995, Electron field emission from nanofilament carbon films, Chemical Physics Letters, 233, 63-68.
  • Choi W. B., Chung D. S., Kang J. H., Kim H. Y., Jin Y. W., Han I. T., Lee Y. H., Jung J. E., Lee N. S., Park G. S. and Kim J. M., 1999, Fully sealed, high-brightness carbon-nanotube field-emission display, Applied Physics Letters, 75, 3129-3131.
  • Collins P. G., Hersam M., Arnold M., Martel R. and Avouris P., 2001, Current Saturation and Electrical Breakdown in Multiwalled Carbon Nanotubes, Physical Review Letters, 86, 3128-3131.
  • Crank J. and Nicolson P., 1996, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Advances in Computational Mathematics, 6, 207-226.
  • Croci M., Arfaoui I., Stöckli T., Chatelain A. and Bonard J., 2004, A fully sealed luminescent tube based on carbon nanotube field emission, Microelectronics Journal, 35, 329-336.
  • Curtright T. L. and Zachos C. K., 2013, Umbral Vade Mecum, Frontiers in Physics, 1, 15.
  • Dai H., Wong E. W. and Lieber C. M., 1996, Probing Electrical Transport in Nanomaterials: Conductivity of Individual Carbon Nanotubes, Science, 272, 523-526.
  • de Heer W. A., Châtelain A. and Ugarte D., 1995, A Carbon Nanotube Field-Emission Electron Source, Science, 270, 1179-1180.
  • de Jonge N., Allioux M., Oostveen J. T., Teo K. B. K. and Milne W. I., 2005, Optical Performance of Carbon-Nanotube Electron Sources, Physical Review Letters, 94, 186807.
  • Dehghani S., Moravvej-Farshi M. K. and Sheikhi M. H., 2012, Temperature dependence of electrical resistance of individual carbon nanotubes and carbon nanotubes network, Modern Physics Letters B, 26, 1250136.
  • Doytcheva M., Kaiser M. and de Jonge N., 2006, In situ transmission electron microscopy investigation of the structural changes in carbon nanotubes during electron emission at high currents, Nanotechnology, 17, 3226-3233.
  • Ebbesen T. W., Lezec H. J., Hiura H., Bennett J. W., Ghaemi H. F. and Thio T., 1996, Electrical conductivity of individual carbon nanotubes, Nature, 382, 54-56.
  • Fairchild S. B., Zhang P., Park J., Back T. C., Marincel D., Huang Z. and Pasquali M., 2019, Carbon Nanotube Fiber Field Emission Array Cathodes, IEEE Transactions on Plasma Science, 47, 2032-2038.
  • Flajolet P. and Sedgewick R., 1995, Mellin transforms and asymptotics: Finite differences and Rice's integrals, Theoretical Computer Science, 144, 101-124.
  • Fornberg B., 1988, Generation of finite difference formulas on arbitrarily spaced grids, Mathematics of Computation, 51, 699-706.
  • Fraser, D. C., 1909, On the Graphic Delineation of Interpolation Formulæ, Journal of the Institute of Actuaries, 43, 235-241.
  • Fujii M., Zhang X., Xie H., Ago H., Takahashi K., Ikuta T., Abe H. and Shimizu T., 2005, Measuring the Thermal Conductivity of a Single Carbon Nanotube, Physical Review Letters, 95, 065502.
  • Giubileo F., Di Bartolomeo A., Iemmo L., Luongo G. and Urban F., 2018, Field Emission from Carbon Nanostructures, Applied Sciences, 8, 526.
  • Ha J. M., Kim H. J., Raza H. S. and Cho S. O., 2013, Highly stable carbon nanotube field emitters on small metal tips against electrical arcing, Nanoscale Research Letters, 8, 355.
  • Hone J., Whitney M., Piskoti C. and Zettl A., 1999, Thermal conductivity of single-walled carbon nanotubes, Physical Review B, 59, R2514-R2516.
  • Huang N. Y., She J. C., Deng S. Z., Xu N. S., Bishop H., Huq S. E., Wang L., Zhong D. Y., Wang E. G. and Chen D. M., 2004, Mechanism Responsible for Initiating Carbon Nanotube Vacuum Breakdown, Physical Review Letters, 93,075501.
  • Jaluria Y. and Atluri S. N., 1994, Computational heat transfer, Computational Mechanics, 14, 385-386.
  • Jang W. Y., Kulkarni N. N., Shih C. K. and Yao Z., 2004, Electrical characterization of individual carbon nanotubes grown in nanoporous anodic alumina templates, Applied Physics Letters, 84, 1177-1179.
  • Karim S., Toimil-Molares M. E., Balogh A. G., Ensinger W., Cornelius T. W., Khan E. U. and Neumann R., 2006, Morphological evolution of Au nanowires controlled by Rayleigh instability, Nanotechnology, 17, 5954-5959.
  • Karim S., Toimil-Molares M. E., Ensinger W., Balogh A. G., Cornelius T. W., Khan E. U. and Neumann R., 2007, Influence of crystallinity on the Rayleigh instability of gold nanowires, Journal of Physics D: Applied Physics, 40, 3767-3770.
  • Lin C., Xiang Y. and Zhang J., 2019, Post-breakdown field emission behavior of a planar-structured single SWNT bundle in air, Journal of Micromechanics and Microengineering, 29, 065005.
  • Liu Z., Zhang Y., Zhao P., Ye Y., Chen J., Xu N. and Deng S., 2019, In situ study of field emission vacuum breakdown of individual multi-wall carbon nanotube, Micro & Nano Letters, 14, 206-210.
  • Milne W. I., Teo K. B. K., Chhowalla M., Amaratunga G. A. J., Lee S. B., Hasko D. G., Ahmed H., Groening O., Legagneux P., Gangloff L., Schnell J. P., Pirio G., Pribat D., Castignolles M., Loiseau, Semet V., Binh V. T., 2003, Electrical and field emission investigation of individual carbon nanotubes from plasma enhanced chemical vapour deposition, Diamond and Related Materials, 12, 422-428.
  • Park S., Chae S., Rhee J. and Kang S., 2010, A Study on Electrical and Thermal Properties of Polyimide/MWNT Nanocomposites, Bulletin of the Korean Chemical Society, 31, 2279-2282.
  • Purcell S. T., Vincent P., Journet C. and Binh V. T., 2002, Hot Nanotubes: Stable Heating of Individual Multiwall Carbon Nanotubes to 2000 K Induced by the Field-Emission Current, Physical Review Letters, 88, 105502.
  • Rinzler A. G., Hafner J. H., Nikolaev P., Nordlander P., Colbert D. T., Smalley, R. E., Lou L., Kim S. G. and Tománek D., 1995, Unraveling Nanotubes: Field Emission from an Atomic Wire, Science, 269, 1550-1553.
  • Sandomirskiĭ V. B., 1967, Quantum Size Effect in a Semimetal Film, Soviet Physics Journal of Experimental and Theoretical Physics, 25, 101-106.
  • Shannon C. E., 1949, Communication in the Presence of Noise, Proceedings of the IRE, 37, 10-21.
  • Sugie H., Tanemura M., Filip V., Iwata K., Takahashi K. and Okuyama, F., 2001, Carbon nanotubes as electron source in an x-ray tube, Applied Physics Letters, 78, 2578-2580.
  • Suzuura H. and Ando T., 2002, Phonons and electron-phonon scattering in carbon nanotubes, Physical Review B, 65, 235412.
  • Sveningsson M., Morjan R. E., Nerushev O. and Campbell E. E. B., 2004, Electron field emission from multi-walled carbon nanotubes, Carbon, 42, 1165-1168.
  • Tolman R. C., 1918, A General Theory of Energy Partition with Applications to Quantum Theory, Physical Review, 11, 261-275.
  • Vincent P., Purcell S. T., Journet C. and Binh V. T., 2002, Modelization of resistive heating of carbon nanotubes during field emission, Physical Review B, 66, 075406.
  • Wang Z. L., Gao R. P., de Heer W. A. and Poncharal P., 2002, In situ imaging of field emission from individual carbon nanotubes and their structural damage, Applied Physics Letters, 80, 856-858.
  • Wei W., Liu Y., Wei Y., Jiang K., Peng. L. and Fan S., 2007, Tip Cooling Effect and Failure Mechanism of Field-Emitting Carbon Nanotubes, Nano Letters, 7, 64-68.
  • Yang D. J., Zhang Q., Chen G., Yoon S. F., Ahn J., Wang S. G., Zhou Q., Wang Q. and Li J. Q., 2002, Thermal conductivity of multiwalled carbon nanotubes, Physical Review B, 66, 165440.
  • Yi W., Lu L., Dian-lin Z., Pan Z. W. and Xie S. S., 1999, Linear specific heat of carbon nanotubes, Physical Review B, 59, R9015-R9018.
  • Zachos C. K., 2008, Umbral deformations on discrete space-time, International Journal of Modern Physics A, 23, 2005-2014.
  • Zhang P., Park J., Fairchild S. B., Lockwood N. P., Lau Y. Y., Ferguson J. and Back T., 2018, Temperature Comparison of Looped and Vertical Carbon Nanotube Fibers during Field Emission, Applied Sciences, 8, 1175.
  • Zhang Y., Tan Y., Wang L., Li B., Ke Y., Liao M., Xu N., Chen J. and Deng S., 2020, Electron emission and structure stability of carbon nanotube cold cathode driven by millisecond pulsed voltage, Vacuum, 172, 109071.
  • Zhang J., Yang G., Cheng Y., Gao B., Qiu Q., Lee Y. Z., Lu J. P. and Zhou O., 2005, Stationary scanning x-ray source based on carbon nanotube field emitters, Applied Physics Letters, 86, 184104.

ANALYTICAL AND NUMERICAL ANALYSES OF THE HEAT CONDUCTION OF CARBON NANOTUBES UNDER APPLIED VOLTAGES

Year 2021, , 51 - 60, 30.04.2021

Yahya Öz

https://doi.org/10.47480/isibted.979332

Abstract

Electron field emission experiments of carbon nanotubes (CNT) show that due to heat CNTs breakdown faster under applied voltage than expected. Therefore, different systems with varying temperature distributions are considered analytically and numerically by use of the heat conduction equation. This methodology yields a phenomenological understanding and description of the thermoelectric behavior of CNTs under applied voltage

Keywords

Carbon Nanotubes Electron Field Emission Heat Conduction

References

  • Aizen A. M., Redchits I. S. and Fedotkin I. M., 1974, On improving the convergence of series used in solving the heat-conduction equation, Journal of Engineering Physics, 26, 453-458.
  • Bachtold A., Strunk C., Salvetat J., Forró L., Nussbaumer T. and Schönenberger, 1999, Aharonov–Bohm oscillations in carbon nanotubes, Nature, 397, 673-675.
  • Bilodeau G. G., 1962, The Weierstrass transform and Hermite polynomials, Duke Mathematical Journal, 29, 293-308.
  • Bocharov G. S. and Eletskii A. V., 2013, Theory of Carbon Nanotube (CNT)-Based Electron Field Emitters, Nanomaterials, 3, 393-442.
  • Bonard J., Dean K. A., Coll B. F. and Klinke C., 2002, Field Emission of Individual Carbon Nanotubes in the Scanning Electron Microscope, Physical Review Letters, 89, 197602.
  • Bonard J., Kind H., Stöckli T. and Nisson L., 2001, Field emission from carbon nanotubes: the first five years, Solid-State Electronics, 45, 893-914.
  • Bonard J., Klinke C., Dean K. A. and Coll B. F., 2003, Degradation and failure of carbon nanotube field emitters, Physical Review B, 67, 115406. Charlier J., Blasé X. and Roche S., 2007, Electronic and transport properties of nanotubes, Reviews of Modern Physics, 79, 677-732.
  • Charney J. G., Fjörtoft R. and J. Von Neumann, 1950, Numerical Integration of the Barotropic Vorticity Equation, Tellus, 2, 237-254.
  • Cheng Y. and Zhou O., 2003, Electron field emission from carbon nanotubes, Comptes Rendus Physique, 4, 1021-1033.
  • Chernozatonskii L. A., Gulyaev Y. V., Kosakovskaja Z. J., Sinitsyn N. I., Torgashov G. V., Zakharchenko Y. F., Fedorov E. A. and Val’chuk V. P., 1995, Electron field emission from nanofilament carbon films, Chemical Physics Letters, 233, 63-68.
  • Choi W. B., Chung D. S., Kang J. H., Kim H. Y., Jin Y. W., Han I. T., Lee Y. H., Jung J. E., Lee N. S., Park G. S. and Kim J. M., 1999, Fully sealed, high-brightness carbon-nanotube field-emission display, Applied Physics Letters, 75, 3129-3131.
  • Collins P. G., Hersam M., Arnold M., Martel R. and Avouris P., 2001, Current Saturation and Electrical Breakdown in Multiwalled Carbon Nanotubes, Physical Review Letters, 86, 3128-3131.
  • Crank J. and Nicolson P., 1996, A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type, Advances in Computational Mathematics, 6, 207-226.
  • Croci M., Arfaoui I., Stöckli T., Chatelain A. and Bonard J., 2004, A fully sealed luminescent tube based on carbon nanotube field emission, Microelectronics Journal, 35, 329-336.
  • Curtright T. L. and Zachos C. K., 2013, Umbral Vade Mecum, Frontiers in Physics, 1, 15.
  • Dai H., Wong E. W. and Lieber C. M., 1996, Probing Electrical Transport in Nanomaterials: Conductivity of Individual Carbon Nanotubes, Science, 272, 523-526.
  • de Heer W. A., Châtelain A. and Ugarte D., 1995, A Carbon Nanotube Field-Emission Electron Source, Science, 270, 1179-1180.
  • de Jonge N., Allioux M., Oostveen J. T., Teo K. B. K. and Milne W. I., 2005, Optical Performance of Carbon-Nanotube Electron Sources, Physical Review Letters, 94, 186807.
  • Dehghani S., Moravvej-Farshi M. K. and Sheikhi M. H., 2012, Temperature dependence of electrical resistance of individual carbon nanotubes and carbon nanotubes network, Modern Physics Letters B, 26, 1250136.
  • Doytcheva M., Kaiser M. and de Jonge N., 2006, In situ transmission electron microscopy investigation of the structural changes in carbon nanotubes during electron emission at high currents, Nanotechnology, 17, 3226-3233.
  • Ebbesen T. W., Lezec H. J., Hiura H., Bennett J. W., Ghaemi H. F. and Thio T., 1996, Electrical conductivity of individual carbon nanotubes, Nature, 382, 54-56.
  • Fairchild S. B., Zhang P., Park J., Back T. C., Marincel D., Huang Z. and Pasquali M., 2019, Carbon Nanotube Fiber Field Emission Array Cathodes, IEEE Transactions on Plasma Science, 47, 2032-2038.
  • Flajolet P. and Sedgewick R., 1995, Mellin transforms and asymptotics: Finite differences and Rice's integrals, Theoretical Computer Science, 144, 101-124.
  • Fornberg B., 1988, Generation of finite difference formulas on arbitrarily spaced grids, Mathematics of Computation, 51, 699-706.
  • Fraser, D. C., 1909, On the Graphic Delineation of Interpolation Formulæ, Journal of the Institute of Actuaries, 43, 235-241.
  • Fujii M., Zhang X., Xie H., Ago H., Takahashi K., Ikuta T., Abe H. and Shimizu T., 2005, Measuring the Thermal Conductivity of a Single Carbon Nanotube, Physical Review Letters, 95, 065502.
  • Giubileo F., Di Bartolomeo A., Iemmo L., Luongo G. and Urban F., 2018, Field Emission from Carbon Nanostructures, Applied Sciences, 8, 526.
  • Ha J. M., Kim H. J., Raza H. S. and Cho S. O., 2013, Highly stable carbon nanotube field emitters on small metal tips against electrical arcing, Nanoscale Research Letters, 8, 355.
  • Hone J., Whitney M., Piskoti C. and Zettl A., 1999, Thermal conductivity of single-walled carbon nanotubes, Physical Review B, 59, R2514-R2516.
  • Huang N. Y., She J. C., Deng S. Z., Xu N. S., Bishop H., Huq S. E., Wang L., Zhong D. Y., Wang E. G. and Chen D. M., 2004, Mechanism Responsible for Initiating Carbon Nanotube Vacuum Breakdown, Physical Review Letters, 93,075501.
  • Jaluria Y. and Atluri S. N., 1994, Computational heat transfer, Computational Mechanics, 14, 385-386.
  • Jang W. Y., Kulkarni N. N., Shih C. K. and Yao Z., 2004, Electrical characterization of individual carbon nanotubes grown in nanoporous anodic alumina templates, Applied Physics Letters, 84, 1177-1179.
  • Karim S., Toimil-Molares M. E., Balogh A. G., Ensinger W., Cornelius T. W., Khan E. U. and Neumann R., 2006, Morphological evolution of Au nanowires controlled by Rayleigh instability, Nanotechnology, 17, 5954-5959.
  • Karim S., Toimil-Molares M. E., Ensinger W., Balogh A. G., Cornelius T. W., Khan E. U. and Neumann R., 2007, Influence of crystallinity on the Rayleigh instability of gold nanowires, Journal of Physics D: Applied Physics, 40, 3767-3770.
  • Lin C., Xiang Y. and Zhang J., 2019, Post-breakdown field emission behavior of a planar-structured single SWNT bundle in air, Journal of Micromechanics and Microengineering, 29, 065005.
  • Liu Z., Zhang Y., Zhao P., Ye Y., Chen J., Xu N. and Deng S., 2019, In situ study of field emission vacuum breakdown of individual multi-wall carbon nanotube, Micro & Nano Letters, 14, 206-210.
  • Milne W. I., Teo K. B. K., Chhowalla M., Amaratunga G. A. J., Lee S. B., Hasko D. G., Ahmed H., Groening O., Legagneux P., Gangloff L., Schnell J. P., Pirio G., Pribat D., Castignolles M., Loiseau, Semet V., Binh V. T., 2003, Electrical and field emission investigation of individual carbon nanotubes from plasma enhanced chemical vapour deposition, Diamond and Related Materials, 12, 422-428.
  • Park S., Chae S., Rhee J. and Kang S., 2010, A Study on Electrical and Thermal Properties of Polyimide/MWNT Nanocomposites, Bulletin of the Korean Chemical Society, 31, 2279-2282.
  • Purcell S. T., Vincent P., Journet C. and Binh V. T., 2002, Hot Nanotubes: Stable Heating of Individual Multiwall Carbon Nanotubes to 2000 K Induced by the Field-Emission Current, Physical Review Letters, 88, 105502.
  • Rinzler A. G., Hafner J. H., Nikolaev P., Nordlander P., Colbert D. T., Smalley, R. E., Lou L., Kim S. G. and Tománek D., 1995, Unraveling Nanotubes: Field Emission from an Atomic Wire, Science, 269, 1550-1553.
  • Sandomirskiĭ V. B., 1967, Quantum Size Effect in a Semimetal Film, Soviet Physics Journal of Experimental and Theoretical Physics, 25, 101-106.
  • Shannon C. E., 1949, Communication in the Presence of Noise, Proceedings of the IRE, 37, 10-21.
  • Sugie H., Tanemura M., Filip V., Iwata K., Takahashi K. and Okuyama, F., 2001, Carbon nanotubes as electron source in an x-ray tube, Applied Physics Letters, 78, 2578-2580.
  • Suzuura H. and Ando T., 2002, Phonons and electron-phonon scattering in carbon nanotubes, Physical Review B, 65, 235412.
  • Sveningsson M., Morjan R. E., Nerushev O. and Campbell E. E. B., 2004, Electron field emission from multi-walled carbon nanotubes, Carbon, 42, 1165-1168.
  • Tolman R. C., 1918, A General Theory of Energy Partition with Applications to Quantum Theory, Physical Review, 11, 261-275.
  • Vincent P., Purcell S. T., Journet C. and Binh V. T., 2002, Modelization of resistive heating of carbon nanotubes during field emission, Physical Review B, 66, 075406.
  • Wang Z. L., Gao R. P., de Heer W. A. and Poncharal P., 2002, In situ imaging of field emission from individual carbon nanotubes and their structural damage, Applied Physics Letters, 80, 856-858.
  • Wei W., Liu Y., Wei Y., Jiang K., Peng. L. and Fan S., 2007, Tip Cooling Effect and Failure Mechanism of Field-Emitting Carbon Nanotubes, Nano Letters, 7, 64-68.
  • Yang D. J., Zhang Q., Chen G., Yoon S. F., Ahn J., Wang S. G., Zhou Q., Wang Q. and Li J. Q., 2002, Thermal conductivity of multiwalled carbon nanotubes, Physical Review B, 66, 165440.
  • Yi W., Lu L., Dian-lin Z., Pan Z. W. and Xie S. S., 1999, Linear specific heat of carbon nanotubes, Physical Review B, 59, R9015-R9018.
  • Zachos C. K., 2008, Umbral deformations on discrete space-time, International Journal of Modern Physics A, 23, 2005-2014.
  • Zhang P., Park J., Fairchild S. B., Lockwood N. P., Lau Y. Y., Ferguson J. and Back T., 2018, Temperature Comparison of Looped and Vertical Carbon Nanotube Fibers during Field Emission, Applied Sciences, 8, 1175.
  • Zhang Y., Tan Y., Wang L., Li B., Ke Y., Liao M., Xu N., Chen J. and Deng S., 2020, Electron emission and structure stability of carbon nanotube cold cathode driven by millisecond pulsed voltage, Vacuum, 172, 109071.
  • Zhang J., Yang G., Cheng Y., Gao B., Qiu Q., Lee Y. Z., Lu J. P. and Zhou O., 2005, Stationary scanning x-ray source based on carbon nanotube field emitters, Applied Physics Letters, 86, 184104.
There are 55 citations in total.

Details

Primary Language English
Subjects Mechanical Engineering
Journal Section Research Article
Authors

Yahya Öz This is me 0000-0003-3784-0495

Publication Date April 30, 2021
Published in Issue Year 2021

Cite

APA Öz, Y. (2021). ANALYTICAL AND NUMERICAL ANALYSES OF THE HEAT CONDUCTION OF CARBON NANOTUBES UNDER APPLIED VOLTAGES. Isı Bilimi Ve Tekniği Dergisi, 41(1), 51-60. https://doi.org/10.47480/isibted.979332