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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. Daun
  • N. Petermann
  • J. T. Titantah
  • M. Karttunen
  • H. Wiggers
  • T. Dreier
  • C. Schulz
Article

Abstract

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.

Keywords

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

cg,t

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

co

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

cp

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

cv,t

Thermal speed of evaporating atoms (m s−1)

dp

Nanoparticle diameter (nm)

E(mλ)

Complex absorption function

h

Planck’s constant (6.626 × 10−34 J s)

ΔHv

Heat of vaporization (J mol−1)

Ib,λ

Spectral blackbody intensity (W)

Jevap

Evaporating mass flux (kg s−1)

Jλ

Spectral incandescence (a.u.)

kB

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

mv

Mass of vaporized atoms (kg)

mg

Molecular mass of the gas (kg)

mλ

Complex index of refraction

Ng

Incident number flux of gas molecules

Nv

Number flux of vaporized atoms

ng

Number density of gas molecules

nv

Number density of evaporated vapor

P(dp)

Probability density of particle diameters

pg

Gas partial pressure (Pa)

pv

Vapor pressure (Pa)

Qabs,λ

Spectral absorption efficiency

qcond

Conduction heat transfer (W)

qevap

Evaporation heat transfer (W)

qrad

Radiation heat transfer (W)

R

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

Rs

Specific gas constant (J kg−1 K−1)

Tcr

Critical temperature of liquid silicon (K)

Teff

Pyrometrically defined effective temperature (K)

Tg

Gas temperature (K)

ti

Discrete time (ns)

Ti

Initial temperature (K)

Tm

Melting temperature of silicon (K)

Tp

Nanoparticle temperature (K)

Ts

Surface temperature (K)

Uij

Interatomic potential between atoms i and j (eV)

v1

Incident gas velocity (m s−1)

v2

Scattering gas velocity (m s−1)

vxy

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

vz

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

x

Particle size parameter

X

Uniformly distributed random number

α

Thermal accommodation coefficient

δ

Tolman length (nm)

γ

Specific heat ratio

γs

Surface tension of silicon (N m−1)

λ

Wavelength (nm)

μ

Ratio of gas atom mass to surface atom mass

ρ

Nanoparticle density (kg m−3)

ξ

Sticking coefficient

Notes

Acknowledgments

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 (www.sharcnet.ca) 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
  • 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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