# Examination of the thermal accommodation coefficient used in the sizing of iron nanoparticles by time-resolved laser-induced incandescence

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## Abstract

While time-resolved laser-induced incandescence (TiRe-LII) shows promise as a diagnostic for sizing aerosolized iron nanoparticles, the spectroscopic and heat transfer models needed to interpret TiRe-LII measurements on iron nanoparticles remain uncertain. This paper focuses on three key aspects of the models: the thermal accommodation coefficient; the spectral absorption efficiency; and the evaporation sub-model. Based on a detailed literature review, spectroscopic and heat transfer models are defined and applied to analyze TiRe-LII measurements carried out on iron nanoparticles formed in water and then aerosolized into monatomic and polyatomic carrier gases. A comparative analysis of the results shows nanoparticle sizes that are consistent between carrier gases and thermal accommodation coefficients that follow the expected trends with bath gas molecular mass and structure.

## Keywords

Nanoparticle Size Iron Nanoparticles Heat Transfer Model Molten Iron Nanoparticle Diameter## Notes

### Acknowledgments

This research was supported by the National Science and Engineering Research Council of Canada (NSERC), the Canadian Foundation for Innovation-Leaders Opportunity Fund (CFI-LOF), and the Waterloo Institute for Nanotechnology (WIN). Transmission electron microscopy was carried out using the facilities of the Canadian Centre for Electron Microscopy.

## References

- 1.L.A. Melton, Soot diagnostics based on laser heating. Appl. Opt.
**23**(13), 2201–2208 (1984)CrossRefADSGoogle Scholar - 2.S. Schraml, S. Will, A. Leipertz, Simultaneous measurement of soot mass concentration and primary particle size in the exhaust of a DI diesel engine by time-resolved laser-induced incandescence (TIRE-LII).
*SAE Paper,*no. 01-0146 (1999)Google Scholar - 3.B.F. Kock, T. Eckhardt, P. Roth, In-cylinder sizing of diesel particles by time-resolved laser-induced incandescence (TR-LII). Proc. Combust. Inst.
**29**(2), 2775–2782 (2002)CrossRefGoogle Scholar - 4.D.R. Snelling, G.J. Smallwood, F. Liu, O.L. Gulder, W.D. Bachalo, A calibration-independent laser-induced incandescence technique for soot measurement by detecting absolute light intensity. Appl. Opt.
**44**(31), 6773–6785 (2005)CrossRefADSGoogle Scholar - 5.R.L. Vander Wal, T.M. Ticich, J.R. West, Laser-induced incandescence applied to metal nanostructures. Appl. Opt.
**38**(27), 5867–5879 (1999)CrossRefADSGoogle Scholar - 6.A.V. Fillipov, M.W. Markus, P. Roth, In-situ characterization of ultrafine particles by laser-induced incandescence: sizing and particle structure determination. J. Aerosol Sci.
**30**(1), 71–87 (1999)CrossRefGoogle Scholar - 7.R. Starke, B. Kock, P. Roth, Nano-particle sizing by laser-induced incandescence (LII) in a shock wave reactor. Shock Waves
**12**(5), 260–351 (2003)CrossRefGoogle Scholar - 8.B.F. Kock, C. Kayan, J. Knipping, H.R. Orthner, P. Roth, Comparison of LII and TEM sizing during synthesis of iron particle chains. Proc. Combust. Inst.
**30**(1), 1689–1697 (2005)CrossRefGoogle Scholar - 9.A. Eremin, E. Gurentsov, C. Schulz, Influence of the bath gas on the condensation of supersaturated iron atom vapour at room temperature. J. Phys. D Appl. Phys.
**41**(5), 1–5 (2008)CrossRefGoogle Scholar - 10.A. Eremin, E. Gurentsov, E. Popova, K. Priemchenko, Size dependence of complex refractive index function of growing nanoparticles. Appl. Phys. B
**104**(2), 289–295 (2011)CrossRefADSGoogle Scholar - 11.A. Eremin, E. Gurentsov, E. Mikheyeva, K. Priemchenko, Experimental study of carbon and iron nanoparticle vaporisation under pulse laser heating. Appl. Phys. B
**112**(3), 421–432 (2013)CrossRefADSGoogle Scholar - 12.Y. Murakami, T. Sugatani, Y. Nosaka, Laser-induced incandescence study on the metal aerosol particles as the effect of the surrounding gas medium. J. Phys. Chem. A
**109**(40), 8994–9000 (2005)CrossRefGoogle Scholar - 13.T. Sipkens, G. Joshi, K.J. Daun, Y. Murakami, Sizing of molybdenum nanoparticles using time-resolved laser-induced incandescence. J. Heat Transf.
**135**(5), 052401 (2013)CrossRefGoogle Scholar - 14.J. Reimann, H. Oltmann, S. Will, C. Bassano, E.L. Lösch, S. Günther, Laser Sintering of Nickel Aggregates Produced from Inert Gas Condensation. in
*Proceedings of the World Conference on Particle Technology*, Nuremberg, Germany (2010)Google Scholar - 15.T. Lehre, H. Bockhorn, B. Jungfleisch, R. Suntz, Development of a measuring technique for simultaneous in situ detection of nanoscaled particle size distributions and gas temperatures. Chemosphere
**51**, 1055–1061 (2003)CrossRefGoogle Scholar - 16.S. Maffi, F. Cignoli, C. Bellomunno, S. De luliis, G. Zizak, Spectral effects in laser induced incandescence application to flame-made titania nanoparticles. Spectrochim. Acta B
**63**(2), 202–209 (2009)CrossRefADSGoogle Scholar - 17.F. Cignoli, C. Bellomunno, S. Maffi, G. Zizak, Laser-induced incandescence of titania nanoparticles synthesized in a flame. Appl. Phys. B
**96**(4), 593–599 (2008)CrossRefADSGoogle Scholar - 18.B. Tribalet, A. Faccinetto, T. Dreier, C. Schultz, Evaluation of particle sizes of iron-oxide nano-particles in a low-pressure flame-synthesis reactor by simultaneous application of TiRe-LII and PMS. in
*5th Workshop on Laser*-*Induced Incandescence*, Le Touquet, France (2012)Google Scholar - 19.I.S. Altman, D. Lee, J.D. Chung, J. Song, M. Choi, Light of absorption of silica nanoparticles. Phys. Rev. B
**63**(16), 161402 (2001)CrossRefADSGoogle Scholar - 20.T.A. Sipkens, R. Mansmann, K.J. Daun, N. Petermann, J.T. Titantah, M. Karttunen, H. Wiggers, T. Dreier, C. Schulz, In situ particle sizing of silicon nanoparticles by time-resolved laser-induced incandescence. Appl. Phys. B
**116**(3), 623–636 (2014)CrossRefADSGoogle Scholar - 21.S. Krishnan, K.J. Yugawa, P.C. Nordine, Optical properties of liquid nickel and iron. Phys. Rev. B
**55**(13), 8201–8206 (1997)CrossRefADSGoogle Scholar - 22.J.C. Miller, Optical properties of liquid metals at high temperatures. Philos. Mag.
**20**(168), 1115–1132 (1969)CrossRefADSGoogle Scholar - 23.K.M. Shvarev, V.S. Gushchin, B. Baum, The effect of temperature on optical constants of iron. High Temp.
**16**(3), 441–446 (1978)Google Scholar - 24.K.K. Nanda, F.E. Kruis, H. Fissan, Evaporation of free PbS nanoparticles: evidence of the Kelvin effect. Phys. Rev. Lett.
**89**(25), 256103 (2002)CrossRefADSGoogle Scholar - 25.K. Daun, B. Stagg, F. Liu, G. Smallwood, D. Snelling, Determining aerosol particle size distributions using time-resolved laser-induced incandescence. Appl. Phys. B
**87**(2), 363–372 (2007)CrossRefADSGoogle Scholar - 26.T.C. Bond, R.W. Bergstrom, Light absorption by carbonaceous particles: an investigative review. Aerosol Sci. Technol.
**40**, 27–67 (2006)CrossRefGoogle Scholar - 27.M.F. Modest,
*Radiative Heat Transfer*, 3rd edn. (Academic Press, San Diego, 2013)Google Scholar - 28.J.A. Creighton, D.G. Eadon, Ultraviolet–Visible absorption spectra of the colloidal metallic elements. J. Chem. Soc., Faraday Trans.
**87**, 3881–3891 (1991)CrossRefGoogle Scholar - 29.M. Quinten,
*Optical Properties of Nanoparticle Systems: Mie and Beyond*(Wiley, New York, 2011)CrossRefGoogle Scholar - 30.C.F. Bohren, D.R. Huffman,
*Absorption and Scattering of Light by Small Particles*(Wiley, New York, 1983)Google Scholar - 31.M.P. Marder,
*Condensed Matter Physics*, 2nd edn. (Wiley, New York, 2010)CrossRefGoogle Scholar - 32.Y. Liu, S.A. Majetich, R.D. Tilton, D.S. Scholl, G.V. Lowry, TCE dechlorination rates, pathways, and efficiency of nanoscale iron particles with different properties. Environ. Sci. Technol.
**39**(5), 1338–1345 (2005)CrossRefADSGoogle Scholar - 33.F. He, D. Zhao, Manipulating the size and dispersibility of zerovalent iron nanoparticles by use of carboxyl cellulose stabilizers. Environ. Sci. Technol.
**41**(17), 6216–6221 (2007)CrossRefADSGoogle Scholar - 34.M. W. Chase,
*NIST*-*JANAF Thermochemical Tables*, 4th edn. American Institute of Physics (1998)Google Scholar - 35.H. Kobatake, H. Khosroabadi, H. Fukuyama, Normal spectral emissivity measurement of liquid iron and nickel using electromagnetic levitation in direct current magnetic field. Metall. Mater. Trans. A
**43A**, 2466–2472 (2012)CrossRefADSGoogle Scholar - 36.K.J. Daun, T.A. Sipkens, J.T. Titantah, M. Karttunen, Thermal accommodation coefficients for laser-induced incandescence sizing of metal nanoparticles in monatomic gases. Appl. Phys. B
**112**(3), 409–420 (2013)Google Scholar - 37.F. Liu, K.J. Daun, D.R. Snelling, G.J. Smallwood, Heat conduction from a spherical nanoparticle: status of modeling heat conduction in laser-induced incandescence. Appl. Phys. B
**83**, 355–382 (2006)CrossRefADSGoogle Scholar - 38.K.J. Daun, Thermal accommodation coefficients between polyatomic gas molecules and soot in laser-induced incandescence experiments. Int. J. Heat Mass Transf.
**52**, 5081–5089 (2009)CrossRefMATHGoogle Scholar - 39.K.J. Daun, G.J. Smallwood, F. Liu, Investigation of thermal accommodation coefficients in time-resolved laser-induced incandescence. J. Heat Trans.
**130**(12), 121201 (2008)CrossRefGoogle Scholar - 40.K.J. Daun, G.J. Smallwood, F. Liu, Molecular dynamics simulations of translational thermal accommodation coefficients for time-resolved LII. Appl. Phys. B
**94**(1), 39–49 (2009)CrossRefADSGoogle Scholar - 41.K.J. Daun, J.T. Titantah, M. Karttunen, Molecular dynamics simulation of thermal accommodation coefficients for laser-induced incandescence sizing of nickel particles. Appl. Phys. B
**107**(1), 221–228 (2012)CrossRefADSGoogle Scholar - 42.K.M. Watson, Thermodynamics of the liquid state. Ind. Eng. Chem.
**35**(4), 398–406 (1943)CrossRefGoogle Scholar - 43.D.A. Young, B.J. Alder, Critical point of metals from the van der Waals model. Phys. Rev. A
**3**(1), 364–371 (1971)CrossRefADSGoogle Scholar - 44.D. Lide (ed.),
*CRC Handbook of Chemistry and Physics*, 95th ed., (CRC Press, Boca Raton, 2014–2015)Google Scholar - 45.W. Forsythe,
*Smithsonian Physical Tables*, 9th ed., Knovel (2003)Google Scholar - 46.P.D. Desai, Thermodynamic properties of iron and silicon. J. Phys. Chem. Ref. Data
**15**(3), 967–983 (1986)CrossRefADSGoogle Scholar - 47.S.A. Kuhlmann, J. Reimann, S. Will, On heat conduction between laser-heated nanoparticles and a surrounding gas. J. Aerosol Sci.
**37**(12), 1696–1716 (2006)CrossRefGoogle Scholar - 48.B.J. Keene, Review of data for the surface tension of iron and its binary alloys. Int. Mater. Rev.
**33**(1), 1–37 (1988)CrossRefGoogle Scholar - 49.R.C. Tolman, The effect of droplet size on surface tension. J. Chem. Phys.
**17**(3), 333–337 (1949)CrossRefADSGoogle Scholar - 50.K. Koga, X.C. Zeng, A.K. Shchekin, Validity of Tolman’s equation: how large should a droplet be? J. Chem. Phys.
**109**(10), 4063–4070 (1998)CrossRefADSGoogle Scholar - 51.T. Mohri, T. Horiuchi, H. Uzawa, M. Ibaragi, M. Igarashi, F. Abe, Theoretical investigation of L10-disorder phase equilibria in Fe–Pd alloy system. J. Alloys Compd.
**317**, 13–18 (2001)CrossRefGoogle Scholar - 52.Y.A. Lei, T. Bykov, S. Yoo, X.C. Zeng, The Tolman length: is it positive or negative? J. Am. Chem. Soc.
**127**(44), 15346–15347 (2005)CrossRefGoogle Scholar - 53.H.M. Lu, Q. Jiang, Size-dependent surface tension and Tolman’s length of droplets. Langmuir
**21**(2), 779–781 (2005)CrossRefGoogle Scholar - 54.A.R. Nair, S.P. Sathian, Studies on the effect of curvature on the surface properties of nanodrops. J. Mol. Liq.
**195**, 248–254 (2014)CrossRefGoogle Scholar - 55.J.H. Shin, M.R. Deinert, A model for the latent heat of melting in free standing metal nanoparticles. J. Chem. Phys.
**140**(16), 164707 (2014)CrossRefADSGoogle Scholar - 56.A. Alqudami, S. Annapoorni, Fluorescence from metallic silver and iron nanoparticles prepared by exploding wire technique. Plasmonics
**2**, 5–13 (2007)CrossRefGoogle Scholar - 57.R.L. Vander Wal, Laser-induced incandescence: excitation and detection conditions, material transformations and calibration. Appl. Phys. B
**96**(4), 601–611 (2009)CrossRefADSGoogle Scholar - 58.T. Phenrat, H.J. Kim, F. Fagerlund, T. Illangasekare, R.D. Tilton, G.V. Lowry, Particle size distribution, concentration, and magnetic attraction affect transport of polymer-modified Fe0 nanoparticles in sand columns. Environ. Sci. Technol.
**43**(15), 5079–5085 (2009)CrossRefADSGoogle Scholar - 59.B.M. Crosland, M.R. Johnson, K.A. Thomson, Analysis of uncertainties in instantaneous soot volume fraction measurements using two-dimensional, auto-compensating, laser-induced incandescence (2D-AC-LII). Appl. Phys. B
**102**, 173–183 (2011)CrossRefADSGoogle Scholar - 60.J. Kaipio, E. Somersalo,
*Statistical and Computational Inverse Problems*(Springer, Berlin, 2005)MATHGoogle Scholar