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Journal of Nanoparticle Research

, Volume 7, Issue 1, pp 29–41 | Cite as

Formation of Si-nanoparticles in a microwave reactor: Comparison between experiments and modelling

  • B. Giesen
  • H. Wiggers
  • A. Kowalik
  • P. Roth*
Article

Abstract

The formation and growth of silicon-nanoparticles from silane in a microwave reactor was investigated. Experiments were performed for the following conditions: precursor concentration 380–2530 ppm, pressures of 20–30 mbar, microwave powers 120–300 W. The formed particles were examined in-situ with a particle mass spectrometer. Additionally, particles were collected on grids and analyzed by transmission electron microscopy, X-ray diffraction, and by determining the specific surface area by BET. The particle size was found to be in the range of 5–8 nm in diameter. A simple model was used to simulate the particle formation processes taking place inside the reactor. The microwave energy coupled into the reactor flow was treated as a spatially distributed energy source resulting in a local temperature increase. The particles were assumed to have a monodisperse size distribution. To allow an approximation of their shape they were characterized by their volume and surface area. The model takes nucleation, convection, coagulation, and coalescence into account. The fluid flow inside the microwave reactor was simulated with the commercial CFD-code Fluent.

Keywords

silicon microwave reactor population balance nanoparticles aerosols numerical simulation 

Nomenclature

ap0

surface area of a monomer [m2]

A

total surface area per unit volume [1/m]

Amin

minimal total surface area per unit volume [1/m]

ci

concentration of species i [mol i /m3]

D

diffusion coefficient for the user defined scalar in Fluent

Dgb

grain boundary diffusion coefficient [m2/s]

dpp

diameter of a primary particle [m]

\(\vec{f}\)

flux function for the user defined scalar in Fluent

J

nucleation rate [kg/m3s]

Kn

Knudsen number

k

reaction coefficient

kB

Boltzman constant [J/K]

L

average grain size [m]

N

number concentration of the agglomerates [1/m3]

NA

Avogadro constant [1/mol]

npp

number of primary particles of an agglomerate

PMW

power of the microwave generator [W]

p

pressure [mbar]

R

gas constant [J/mol K]

R

reaction rate [mol/m3s]

S

source term for the user defined scalar in Fluent

T

temperature [K]

t

time [s]

V

total particle volume per unit volume [1]

VMW

volume into which the microwave energy is coupled [m3]

vpp

volume of a primary particle [m3]

vp

particle volume [m3]

\(v_{\rm p}^0\)

volume of a monomer [m3]

\(\vec{w}\)

velocity of the aerosol [m/s]

w

grain boundary width [m]

Greek letters

\(\beta_{v_{\rm p}}\)

collision kernel of two particles with volume v p [m3/s]

γ

surface tension [J/m2]

μG

viscosity of the gas phase [Pas]

ϕ

user defined scalar in Fluent

ρ

density of the aerosol [kg/m3]

\(\rho_{\rm p}^0\)

density of the particle material [kg/m3]

τ

characteristic sintering time [s]

Ω

molar volume of diffusing species [m3/kg]

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References

  1. Edelstein, A.Cammarata, & R. eds. 1996Nanomaterials: Synthesis, Properties and ApplicationsInstitute of Physics Publishing LtdBristolGoogle Scholar
  2. Fluent 2000. Fluent User’s Guide, Version 5.5. Fluent Inc., Computational Fluid Dynamics Software, Centerra Resource Park, 10 Cavendish Court, Lebanon, NH 03766Google Scholar
  3. Janzen C., H. Wiggers, J. Knipping & P. Roth, 2001. J. Nanosci. Nanotechnol. 1, 221Google Scholar
  4. Kleinwechter, H., Janzen, C., Knipping, J., Wiggers, H., Roth, P. 2002Formation and properties of ZnO nano-particles from gas phase synthesis processesJ. Mater. Sci.3743494360Google Scholar
  5. Kruis, F., Kusters, K., Pratsinis, S., Scarlett, B. 1993A simple model for the evolution of the characteristics of aggregate particles undergoing coagulation and sinteringAerosol Sci. Technol.19514526Google Scholar
  6. Lindackers D., C. Janzen, B. Rellinghaus, E. Wassermann & P. Roth, 1998, Nanostruct. Mater. 10, 1247Google Scholar
  7. Lindackers D., M. Strecker, P. Roth, C. Janzen & S. Pratsinis, 1997. Combust. Sci. Technol. 123, 287Google Scholar
  8. Melinon, P., Paillard, V., Dupuis, V., Perez, A., Jensen, P., Hoareau, A., Perez, J., Tuaillon, J., Broyer, M., Vialle, J., Pellarin, M., Baguenard, B., Lerme, J. 1995From free clusters to cluster-assembled materialsInt. J. Mod. Phys. B9339397Google Scholar
  9. Proot J., C. Delerue, & G. Allan, 1992. Appl. Phys. Lett. 61, 1948Google Scholar
  10. Roth P. & A. Hospital, 1994. J. Aerosol Sci. 25, 61Google Scholar
  11. Warren, B. 1969X-Ray DiffractionDover Publications, Inc.New York259Google Scholar
  12. Woiki, D., Kunz, A., Roth, P. 2000Chemicl reactions of aerosol precursorsJ. Aerosol Sci. Suppl1212213Google Scholar
  13. Xing, Y., Rosner, D. 1999Prediction of spherule size in gas phase nanoparticle synthesisJ. Nanoparticle Res.1277291Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Institut für Verbrennung und GasdynamikUniversität Duisburg–EssenDuisburgGermany

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