Thermal accommodation coefficients for laser-induced incandescence sizing of metal nanoparticles in monatomic gases K. J. Daun • T. A. Sipkens • J. T. Titantah • M. Karttunen Received: 22 October 2012 / Accepted: 7 May 2013 / Published online: 22 May 2013 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract The capabilities of time-resolved laser-induced incandescence (TiRe-LII), a combustion diagnostic used almost exclusively to measure soot primary particles, could potentially be extended to size aerosolized metal nano- particles. In order to do this, however, it is necessary to characterize the thermal accommodation coefficient, a, which specifies the heat conduction rate between the laser- energized nanoparticles and the surrounding gas. This paper extends a molecular dynamics (MD) methodology to calculate a for Fe/He, Fe/Ar, Mo/He, and Mo/Ar systems. A comparative analysis of the results shows that a is most strongly influenced by the potential well between the gas molecule and nanoparticle surface. Finally, the MD- derived value for a is used to recover the nanoparticle size distribution for TiRe-LII measurements made on molyb- denum nanoparticles in argon. List of symbols a 0 Lattice parameter [A ˚ ] c Mean thermal speed [m/s] c p (T p ) Specific heat [J/(kg K)] C k Constant in Eq. (1) D Potential well depth [eV] d p Nanoparticle diameter [nm] d p,g Geometric mean nanoparticle diameter [nm] E(m k ) Absorption function of the complex refractive index I b,k Blackbody intensity [W/(m 2 sr lm)] J k Spectral incandescence Kn Knudsen number k B Boltzmann’s constant, 1.38 9 10 -23 [J/ (molecule K)] m g Gas molecular mass [kg/molecule] m s Surface atomic mass [kg/atom] m k Complex refractive index n Number density [molecules/m 3 ] N 00 Number flux [molecules/(m 2 s)] P(d p ) Probability density of nanoparticle diameter [nm -1 ] P Pressure [Pa] Q abs,k (d p ) Absorption efficiency q cond Conduction heat transfer [W] q evap Evaporation heat transfer [W] q rad Radiation heat transfer [W] r Radial distance [m] t Time [s] T Temperature [K] T eff Effective temperature [K] U Potential [eV] v Velocity [m/s] V ij (r ij ) Pairwise repulsive potential z Distance from surface [A ˚ ] a Thermal accommodation coefficient a n Normal thermal accommodation coefficient a t Tangential thermal accommodation coefficient k Wavelength l Reduced mass, m g /m s q Density [kg/m 3 ] q i Electron cloud density of ith atom K. J. Daun (&)  T. A. Sipkens Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada e-mail: kjdaun@uwaterloo.ca J. T. Titantah Department of Applied Mathematics, University of Western Ontario, London, ON, Canada M. Karttunen Department of Chemistry, University of Waterloo, Waterloo, ON, Canada 123 Appl. Phys. B (2013) 112:409–420 DOI 10.1007/s00340-013-5508-0