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Concerning metallic nanoparticles, a statistical simulation method to predict the electron mean free path of a nanoparticleis developed. And the phonon-contributed specific heat and phonon group velocity are also analyzed. Then, the kinetic theory is used to obtain the electron thermal conductivity and the lattice thermal conductivity of the nanoparticles. The size dependence of these properties is further discussed. It turns out that the electron mean free path of a square nanoparticle approximates to that of a circle nanoparticle if nanoparticles are of the same characteristic length. The electron thermal conductivity is much higher than the lattice thermal conductivity on the nanoscale. Either electron or lattice thermal conductivity of nanoparticles declines with diameter decreasing, while the size dependence of electron thermal conductivity is more obvious. However, if the diameter decreases to quite a small size, the electron thermal conductivity will become as low as the lattice thermal conductivity. In addition, the electron/lattice thermal conductivity of a nanoparticle will become less size-dependent if its characteristic length is 4 times larger than corresponding bulk electron/phonon mean free path.
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Keywords:
- nanoparticle /
- thermal conductivity /
- electron mean free path /
- size effect
[1] Shi Z, Neoh K G, Kang E T 2004 Langmuir 20 6847
[2] Mei Y, Lu Y, Polzer F, Ballauff M, Drechsler M 2007 Chem. Mater. 19 1062
[3] Mei Y, Sharma G, Lu Y, Ballauff M, Drechsler M, Irrgang T, Kempe R 2005 Langmuir 21 12229
[4] Frederix F, Friedt J M, Choi K H, Laureyn W, Campitelli A, Mondelaers D, Maes G, Borghs G 2003 Anal. Chem. 75 6894
[5] Magdassi S, Grouchko M, Toker D, Kamyshny A, Balberg I, Millo O 2005 Langmuir 21 10264
[6] Zhou J,Yang J, Zhang Z, Liu W, Xue Q 1999 Mater. Res. Bull. 34 1361
[7] Esteban-Cubillo A, Pecharromán C, Aguilar E, Santarén J, Moya J S 2006 J. Mater. Sci. 41 5208
[8] Cioffi N, Torsi L, Ditaranto N, Tantillo G, Ghibelli L, Sabbatini L, Bleve-Zacheo T, D'Alessio M, Zambonin P G, Traversa E 2005 Chem. Mater. 17 5255
[9] Huang H, Remsen E E, Kowalewski T, Wooley K L. 1999 J. Am. Chem. Soc. 121 3805
[10] Prasher R, Bhattacharya P, Phelan P E 2005 Phys. Rev. Lett. 94 025901
[11] Zeng J L, Sun L X, Xu F, Tan Z C, Zhang Z H, Zhang J, Zhang T 2007 J. Therm. Anal. Cal. 87 369
[12] Yuan S P, Jiang P X 2006 Int. J. Thermophys. 27 581
[13] Flik M I, Tien C L 1990 J. Heat Transfer Trans. ASME 112 872
[14] Richardson R A, Nori F 1993 Appl. Phys. Lett. 63 2076
[15] Richardson R A, Nori F 1993 Phys. Rev. B 48 15209
[16] Krzysztof I 2010 Nanoelectronics: Nanowires, Molecular Electronics, and Nanodevices (McGraw-Hill Professional), p7
[17] Feng B, Li Z, Zhang X 2009 J. Phys. D: Appl. Phys. 42 055311
[18] Ashcroft N W, Mermin N D 1976 Solid State Physics (Holt, Rinehart and Winston, New York), p2
[19] Feng B, Li Z, Zhang X 2009 Thin Solid Films 517 2803
[20] Yarimbiyik A E, Schafft H A, Allen R A, Zaghloul M E, Blackburn D L 2006 Microelectron. Reliab. 46 1050
[21] Yang C C, Xiao M X, Li W, Jiang Q 2006 Solid State Commu. 139 148
[22] Liang L H, Li B W 2006 Phys. Rev. B 73 153303
[23] Jiang Q, Shi H X, Zhao M 1999 J. Chem. Phys. 111 2176
[24] Ashcroft N W, Mermin N D 1976 Solid State Physics (Holt, Rinehart and Winston, New York) p458
[25] Liang L H,Wei Y G, Li B W 2008 J. Appl. Phys. 103 084314
[26] Mamand S M, Omar M S, Muhammad A J 2012 Mater. Res. Bull. 47 1264
[27] Fuchs K 1938 Proc. Camb. Phil. Soc. 34 100
[28] Sondheimer E H 1952 Adv. Phys. 1 1
[29] Tien C L, Majumdar A, Gerner F M 1998 Microscale Energy Transport (Washington, DC: Taylor and Francis)
[30] Shapira Y, Deutscher G 1984 Phys. Rev. B 30 166
[31] Stojanovic N, Maithripala D H S, Berg J M, Holtz M 2010 Phys. Rev. B 82 075418
[32] Jiang Q, Zhou X H, Zhao M 2002 J. Chem. Phys. 117 10269
[33] Heino P, Ristolainen E 2003 Microelectron. J. 34 773
[34] Zhou Y, Anglin B, Strachan A 2007 J. Chem. Phys. 127 184702
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[1] Shi Z, Neoh K G, Kang E T 2004 Langmuir 20 6847
[2] Mei Y, Lu Y, Polzer F, Ballauff M, Drechsler M 2007 Chem. Mater. 19 1062
[3] Mei Y, Sharma G, Lu Y, Ballauff M, Drechsler M, Irrgang T, Kempe R 2005 Langmuir 21 12229
[4] Frederix F, Friedt J M, Choi K H, Laureyn W, Campitelli A, Mondelaers D, Maes G, Borghs G 2003 Anal. Chem. 75 6894
[5] Magdassi S, Grouchko M, Toker D, Kamyshny A, Balberg I, Millo O 2005 Langmuir 21 10264
[6] Zhou J,Yang J, Zhang Z, Liu W, Xue Q 1999 Mater. Res. Bull. 34 1361
[7] Esteban-Cubillo A, Pecharromán C, Aguilar E, Santarén J, Moya J S 2006 J. Mater. Sci. 41 5208
[8] Cioffi N, Torsi L, Ditaranto N, Tantillo G, Ghibelli L, Sabbatini L, Bleve-Zacheo T, D'Alessio M, Zambonin P G, Traversa E 2005 Chem. Mater. 17 5255
[9] Huang H, Remsen E E, Kowalewski T, Wooley K L. 1999 J. Am. Chem. Soc. 121 3805
[10] Prasher R, Bhattacharya P, Phelan P E 2005 Phys. Rev. Lett. 94 025901
[11] Zeng J L, Sun L X, Xu F, Tan Z C, Zhang Z H, Zhang J, Zhang T 2007 J. Therm. Anal. Cal. 87 369
[12] Yuan S P, Jiang P X 2006 Int. J. Thermophys. 27 581
[13] Flik M I, Tien C L 1990 J. Heat Transfer Trans. ASME 112 872
[14] Richardson R A, Nori F 1993 Appl. Phys. Lett. 63 2076
[15] Richardson R A, Nori F 1993 Phys. Rev. B 48 15209
[16] Krzysztof I 2010 Nanoelectronics: Nanowires, Molecular Electronics, and Nanodevices (McGraw-Hill Professional), p7
[17] Feng B, Li Z, Zhang X 2009 J. Phys. D: Appl. Phys. 42 055311
[18] Ashcroft N W, Mermin N D 1976 Solid State Physics (Holt, Rinehart and Winston, New York), p2
[19] Feng B, Li Z, Zhang X 2009 Thin Solid Films 517 2803
[20] Yarimbiyik A E, Schafft H A, Allen R A, Zaghloul M E, Blackburn D L 2006 Microelectron. Reliab. 46 1050
[21] Yang C C, Xiao M X, Li W, Jiang Q 2006 Solid State Commu. 139 148
[22] Liang L H, Li B W 2006 Phys. Rev. B 73 153303
[23] Jiang Q, Shi H X, Zhao M 1999 J. Chem. Phys. 111 2176
[24] Ashcroft N W, Mermin N D 1976 Solid State Physics (Holt, Rinehart and Winston, New York) p458
[25] Liang L H,Wei Y G, Li B W 2008 J. Appl. Phys. 103 084314
[26] Mamand S M, Omar M S, Muhammad A J 2012 Mater. Res. Bull. 47 1264
[27] Fuchs K 1938 Proc. Camb. Phil. Soc. 34 100
[28] Sondheimer E H 1952 Adv. Phys. 1 1
[29] Tien C L, Majumdar A, Gerner F M 1998 Microscale Energy Transport (Washington, DC: Taylor and Francis)
[30] Shapira Y, Deutscher G 1984 Phys. Rev. B 30 166
[31] Stojanovic N, Maithripala D H S, Berg J M, Holtz M 2010 Phys. Rev. B 82 075418
[32] Jiang Q, Zhou X H, Zhao M 2002 J. Chem. Phys. 117 10269
[33] Heino P, Ristolainen E 2003 Microelectron. J. 34 773
[34] Zhou Y, Anglin B, Strachan A 2007 J. Chem. Phys. 127 184702
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