Applied Physics B

, Volume 116, Issue 3, pp 623–636 | Cite as

In situ nanoparticle size measurements of gas-borne silicon nanoparticles by time-resolved laser-induced incandescence

  • T. A. Sipkens
  • R. Mansmann
  • K. J. DaunEmail author
  • N. Petermann
  • J. T. Titantah
  • M. Karttunen
  • H. Wiggers
  • T. Dreier
  • C. Schulz


This paper describes the application of time-resolved laser-induced incandescence (TiRe-LII), a combustion diagnostic used mainly for measuring soot primary particles, to size silicon nanoparticles formed within a plasma reactor. Inferring nanoparticle sizes from TiRe-LII data requires knowledge of the heat transfer through which the laser-heated nanoparticles equilibrate with their surroundings. Models of the free molecular conduction and evaporation are derived, including a thermal accommodation coefficient found through molecular dynamics. The model is used to analyze TiRe-LII measurements made on silicon nanoparticles synthesized in a low-pressure plasma reactor containing argon and hydrogen. Nanoparticle sizes inferred from the TiRe-LII data agree with the results of a Brunauer–Emmett–Teller analysis.


Nanoparticle Size Credible Interval Accommodation Coefficient Nanoparticle Diameter Nanoparticle Size Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Thermal molecular speed of the gas at equilibrium (m s−1)


Speed of light in a vacuum (2.998 × 108 m s−1)


Specific heat of the nanoparticle (J kg−1 K−1)


Thermal speed of evaporating atoms (m s−1)


Nanoparticle diameter (nm)


Complex absorption function


Planck’s constant (6.626 × 10−34 J s)


Heat of vaporization (J mol−1)


Spectral blackbody intensity (W)


Evaporating mass flux (kg s−1)


Spectral incandescence (a.u.)


Boltzmann constant (1.38 × 10−23 J molecule−1 K−1)


Mass of vaporized atoms (kg)


Molecular mass of the gas (kg)


Complex index of refraction


Incident number flux of gas molecules


Number flux of vaporized atoms


Number density of gas molecules


Number density of evaporated vapor


Probability density of particle diameters


Gas partial pressure (Pa)


Vapor pressure (Pa)


Spectral absorption efficiency


Conduction heat transfer (W)


Evaporation heat transfer (W)


Radiation heat transfer (W)


Universal gas constant (8.314 J mol−1 K−1)


Specific gas constant (J kg−1 K−1)


Critical temperature of liquid silicon (K)


Pyrometrically defined effective temperature (K)


Gas temperature (K)


Discrete time (ns)


Initial temperature (K)


Melting temperature of silicon (K)


Nanoparticle temperature (K)


Surface temperature (K)


Interatomic potential between atoms i and j (eV)


Incident gas velocity (m s−1)


Scattering gas velocity (m s−1)


Gas atom velocity parallel to surface (m s−1)


Gas atom velocity perpendicular to surface (m s−1)


Particle size parameter


Uniformly distributed random number


Thermal accommodation coefficient


Tolman length (nm)


Specific heat ratio


Surface tension of silicon (N m−1)


Wavelength (nm)


Ratio of gas atom mass to surface atom mass


Nanoparticle density (kg m−3)


Sticking coefficient



This research was supported by grants from the Natural Science and Engineering Council of Canada (NSERC) and the Deutsche Forschungsgemeinschaft (DFG). One of the authors (TA Sipkens) was also supported by a scholarship from the Government of Ontario. Compute Canada and SharcNet ( provided the computational resources.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • T. A. Sipkens
    • 1
  • R. Mansmann
    • 2
    • 3
  • K. J. Daun
    • 1
    Email author
  • N. Petermann
    • 2
    • 3
  • J. T. Titantah
    • 4
  • M. Karttunen
    • 4
    • 5
  • H. Wiggers
    • 2
    • 3
  • T. Dreier
    • 2
    • 3
  • C. Schulz
    • 2
    • 3
  1. 1.Department of Mechanical and Mechatronics EngineeringUniversity of WaterlooWaterlooCanada
  2. 2.Institute for Combustion and Gas Dynamics – Reactive Fluids (IVG)University of Duisburg-EssenDuisburgGermany
  3. 3.Center for Nanointegration Duisburg-Essen (CENIDE)University of Duisburg-EssenDuisburgGermany
  4. 4.Department of Applied MathematicsWestern UniversityLondonCanada
  5. 5.Department of ChemistryUniversity of WaterlooWaterlooCanada

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