Extending Time-Resolved LII to Metal Nanoparticles:
        Simulating the Thermal Accommodation Coefficient
           K. J. Dauna*, J. T. Titantahb, M. Karttunena and T. A. Sipkensa
                              a
                            University of Waterloo, Waterloo ON Canada
                         b
                          University of Western Ontario, London ON Canada
                           *Corresponding Author, kjdaun@uwaterloo.ca

There is growing interest in adapting time-resolved laser-induced incandescence
(TiRe-LII) to size metal nanoparticles, owing to their emerging applications in
materials science. Extending TiRe-LII to new aerosols requires a model for the heat
transfer between the laser-energized nanoparticles and the surrounding gas.
Unfortunately, the thermal accommodation coefficient, α, which defines the energy
transferred when a gas molecule scatters from the particle surface, is rarely
available. This parameter can sometimes be obtained from LII measurements made
on a reference aerosol sized using electron micrography, but this process is
notoriously time-consuming, and thermophoretic sampling of metal nanoparticles is
often problematic. These challenges have precluded interpretation of data from
several pioneering TiRe-LII studies on metal nanoparticles, including one by
Murakami et al. [1] that intended to determine how the bath gas influences the growth
of molybdenum nanoparticles formed through laser-induced photolysis of Mo(CO)6.

Alternatively, it is sometimes possible to estimate α using molecular dynamics (MD).
                                  In this technique, a pairwise potential between the gas
                                  molecule and metal atoms is derived from ab initio
                                  (generalized gradient approximations of density functional
                                  theory, GGA-DFT) calculations of the gas/surface
                                  potential. The potentials then differentiated to obtain
                                  forces, and Newton’s equations of motion are time-
                                  integrated to obtain atomic trajectories during a
                                  gas/surface scattering event. Finally, α is found through
MD simulation of an argon
                                  Monte Carlo integration over all incident gas molecular
molecule scattering from a laser- trajectories.
energized iron nanoparticle
                           This approach was initially used to characterize α between
soot and various gases, and is presently being extended to metal nanoparticles.
Preliminary results show that MD-derived Preliminary thermal accommodation coefficients for
accommodation coefficients are highly metal nanoparticles
sensitive to the potential well depth.                       αMD              αexp
                                                Ni/Ar     0.20±0.02
Unfortunately, a well-known limitation of
                                                Fe/He     0.07±0.01         0.01 [2]
GGA-DFT is that they cannot describe the
long-range        electron      correlations    Fe/Ar     0.04±0.01     0.1 [2], 0.13 [3]
responsible for van der Waals (vdW)            Mo/He     0.006±0.002
forces, which contribute to the potential       Mo/Ar     0.04±0.01
well. While the Ni/Ar interaction is dominated by a strong Casimir force, vdW forces
are thought to play a major role in other systems. Accordingly, true accommodation
coefficients are probably larger compared to ones found using ab initio derived gas-
surface potentials with no vdW correction. Current research is focused on identifying
an appropriate heuristic correction that can account for the dispersive forces.

[1] Y. Murakami, T. Sugatani, Y. Nosaka, J. Phys. Chem., 109 (2005) 8994.
[2] A. Eremin, E. Gurentsov, C. Schulz, J. Phys D: App. Phys, 41 (2008) 055203.
[3] B. F. Kock, C. Kayan, J. Knipping, H. R. Orthner, P. Roth, Proc. Comb. Inst., 30 (2005)
1689.

                 5th international workshop on Laser-Induced Incandescence
                  May 9-11, 2012, Palais des Congrès, Le Touquet, France