Journal of Nanoparticle Research

, Volume 10, Issue 2, pp 333–340 | Cite as

Radiation model for nanoparticle: extension of classical Brownian motion concepts

Research Paper


Emissive power per unit area of a blackbody has been modeled as a function of frequency using quantum electrodynamics, semi-classical and classical approaches in the available literature. Present work extends the classical lumped-parameter systems model of Brownian motion of nanoparticle to abstract an emissive power per unit area model for nanoparticle radiating at temperature greater than absolute zero. The analytical model developed in present work has been based on synergism of local deformation leading to local motion of nanoparticle due to photon impacts. The work suggests the hypothesis of a free parameter f′ characterizing the damping coefficient of resistive forces to local motion of nanoparticle and the manipulation of which is possible to realize desired emissivity from nanoparticles. The model is validated with the well established Planck’s radiation law.


Blackbody radiation Planck’s law Nanoparticle Brownian motion Systems modeling Numerical simulation 


  1. Beiser A (1987) Concepts of modern physics. McGraw-HillGoogle Scholar
  2. Berggren KK (2004) Quantum computing with superconductors. Proc IEEE 92(10):1630–1638CrossRefGoogle Scholar
  3. Boyer TH (1969) Derivation of the blackbody radiation spectrum without quantum assumption. Phys Rev 182(5):1374–1383CrossRefGoogle Scholar
  4. Boyer TH (1976) Equilibrium of classical electromagnetic radiation in the presence of non-relativistic nonlinear electric dipole oscillator. Phys Rev D 13(10):2832–2845CrossRefGoogle Scholar
  5. Boyer TH (1979) Equilibrium distribution for relativistic free particles in thermal radiation with classical electrodynamics. Phys Rev A 20(3):1246–1259CrossRefGoogle Scholar
  6. Boyer TH (1980) Thermal effects of acceleration through random classical radiation. Phys Rev D 21(8):2137–2148CrossRefGoogle Scholar
  7. Boyer TH (1980) In: Barut AO (ed) Foundation of radiation theory and quantum electrodynamics, Springer; (April 1, 1980) ISBN-10:0306402777; ISBN-13: 978-0306402777Google Scholar
  8. Boyer TH (1983) Derivation of Planck radiation spectrum as an interpolation formula in classical electrodynamics with classical electrmagnetic zero point radiation. Phys Rev D 27(2):2906–2911CrossRefGoogle Scholar
  9. Boyer TH (1984) Derivation of the blackbody radiation spectrum from the equivalence principle in classical physics with classical electromagnetic zero- point radiation. Phys Rev D 29(6):1906–1908Google Scholar
  10. Cole DC (1992) Reinvestigation of the thermodynamics of blackbody radiation via classical physics. Phys Rev A 45(12):8471–8489CrossRefGoogle Scholar
  11. Gordon JP (1975) Neoclassical physics and blackbody radiation. Phys Rev A 12(6):2487–2497CrossRefGoogle Scholar
  12. Hansen K, Campbell EEB (1998) Thermal radiation from small particles. Phys Rev E 58(5):5477–5482CrossRefGoogle Scholar
  13. Kuhn TS (1978) Blackbody theory and the quantum discontinuity 1894–1912. Oxford University Press, NYGoogle Scholar
  14. Lin S-Y, Moreno J, Fleming JG (2003) Three-dimensional photonic-crystal emitter for thermal photovoltaic power generator. Appl Phys Lett 83:380–382CrossRefGoogle Scholar
  15. Lin S-Y, Fleming JG, El-Kady I (2003) Three-dimensional photonic-crystal emission through thermal excitation. Opt Lett 28(20):1909–1911CrossRefGoogle Scholar
  16. Luo C, Narayanswamy A, Chen G, Joannopoulos JD (2004) Thermal radiation from photonic crystals: a direct calculation. Phys Rev Lett 93(21):213905 (1–4)Google Scholar
  17. Mitzner R, Campbell EEB (1995) Optical emission studies of laser desorbed C 60. J Chem Phys 103:2445–2453CrossRefGoogle Scholar
  18. Planck M (1991) Wärmestrahlung (1914) translated in the theory of heat radiation. Dover Publication, Reprint edition (August 28, 1991) ISBN-10:0486668118; ISBN-13: 978-0486668116Google Scholar
  19. Purcell EM (1984), Ch. 9, Electricity & magnetism. McGraw-HillGoogle Scholar
  20. Rohlfing EA (1988) Optical emission studies of atomic, molecular and particulate carbon produced from a laser vaporization cluster source. J Chem Phys 89(10):6103–6112CrossRefGoogle Scholar
  21. Scholl R, Weber B (1992) In: Physics and chemistry of finite systems; from clusters to crystals, vol. 374 of NATO Advanced Study Institute Series C, Physics, Kluwer Academics, NY, pp 1275Google Scholar
  22. Sharma NN, Mittal RK (2005) Brownian motion of nanoparticle considering non rigidity of matter–systems modeling approach. IEEE Tr Nanotechnol 4(2):180–186CrossRefGoogle Scholar
  23. Sharma NN, Ganesh M, Mittal RK (2004) Non-Brownian motion of nanoparticle—an impact process model. IEEE Tr Nanotechnol 3(1):180–186CrossRefGoogle Scholar
  24. Theimer O (1971) Derivation of the blackbody radiation spectrum by classical statistical mechanics. Phys Rev D 4(6):1597–1601CrossRefGoogle Scholar
  25. Theimer O, Peterson PR (1974) Statistics of classical blackbody radiation with ground state. Phys Rev D 10(12):3962–3971CrossRefGoogle Scholar
  26. Theimer O, Peterson PR (1977) Semiclassical stochastic radiation theory. Phys Rev A 16(5):2055–2067CrossRefGoogle Scholar
  27. Tsallis C, SaBarreto FC (1995) Generalization of the Planck radiation law and application to the cosmic microwave background radiation. Phys Rev E 52(2):1447–1451CrossRefGoogle Scholar
  28. Uhlenbeck GE, Ornstein LS (1930) On the theory of Brownian motion. Phys Rev 36:823–841CrossRefGoogle Scholar
  29. Ustinov A (2003) Quantum computing using superconductors. In: Waser R (ed) Nanoelectronics and information technology. Wiley-VCH GmbH, pp 463–471Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Mechanical Engineering GroupBirla Institute of Technology & SciencePilaniIndia

Personalised recommendations