Delivered by Ingenta to: Nanyang Technological University IP: 91.236.120.137 On: Tue, 14 Jun 2016 08:15:59 Copyright: American Scientific Publishers RESEARCH ARTICLE Copyright © 2008 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Nanoscience and Nanotechnology Vol. 8, 6075–6081, 2008 Multi-Time Step Modeling of Plume Dynamics in Nanosecond-Scale Carbon Ablation Kedar Pathak and Alex Povitsky * Department of Mechanical Engineering, The University of Akron, Akron, OH 44325-3903, USA The time span of plume dynamics in laser ablation of carbon ranges from nanoseconds to millisec- onds. Multi-time step approach is developed to study the plume dynamics over this entire range with minimum requirements of numerical computational resources. This approach is applied to study one of the important aspects of nanosecond-scale laser ablation, namely the shielding of incident laser beam with previously ejected plumes. Capturing the shielding effect requires smaller than nanosecond-scale time step because of large velocity and pressure gradients in plume. Use of this time step over the entire domain needs enormous amount of computer time to cover the whole time span of plume dynamics. Multi-time step modeling for such an application is therefore useful. In general, for nanosecond-scale laser ablation this shielding is caused by ionized particles and by gas molecules. It is shown for carbon plume resulting from the nanosecond-scale lasers that the degree of ionization is small. Ionization of ablated carbon is estimated by Saha equation for the given initial plume conditions. The shielding of incident laser beam is therefore calculated by normal molecular absorption. The laser-light intensity that reaches the target for subsequent pulses is evaluated. Keywords: Multi-Time Step, Plume Dynamics, Shielding Effect, Carbon Ablation. 1. INTRODUCTION Plume dynamics in laser ablation in presence of back- ground gas has been studied experimentally 1–8 and theore- tically. 9–18 Nevertheless, the laser ablation in the process of production and synthesis of nanoparticles is still an open research field that is bursting with numerous impor- tant phenomena, which are still to be understood by researchers. 19–21 The entire process of laser ablation invol- ves numerous phenomena such as molecular bond break- ing, non-equilibrium electronic excitations, multi-photon or saturation processes, gas dynamics of plume, condensa- tion of metallic catalysts, nucleation of nanotubes etc. In general, the time scales that spans in laser ablation range from femtosecond-scale to millisecond-scale. In carbon nanotubes synthesis, it is of crucial impor- tance to know the dynamic behavior of the plume of ablated material in the laser ablation furnace. When a pow- erful laser illuminates the target, it sublimes the target surface and creates the high-pressure plume. The result- ing gas explosion produces a plume of rapidly expanding gaseous carbon with embedded catalyst particles. Lit- tle experimental information has been available for the * Author to whom correspondence should be addressed. initial conditions at the surface of the carbon target. 18 For complete description of gas dynamic and thermody- namic state of plume one needs to know the mass ablation rate, temperature, pressure, and the injection velocity with which the ablated plume emerges. Out of these parame- ters the only known experimental parameter is the mass ablation rate. 18 The estimations based on the ideal gas and the Clausius-Claperyon equations resulted in the initial gas pressure in the ablated plume of the order of 100 atm. 2 18 This pressure produces shock waves in the ambient fur- nace gas. The propagation of incident and reflected shock waves in a confined space of laser furnace affect the plume behind the incident shock wave. These effects of furnace geometry on plume evolution have been studied. 17 In the study, 22 the authors have obtained the temperature of the catalyst particles in plume, which is crucial for model- ing of growth of nanotubes. They show the influence of chamber pressure, injection velocity, and multiple ejec- tions of the plume on the temperature of particles, and discuss physical reasons for non-monotonic temperature behavior of catalyst particles. Their study included multi- ple plumes; however, they did not consider shielding effect and assumed the same mass ablation rate and injection velocity for all plumes. J. Nanosci. Nanotechnol. 2008, Vol. 8, No. 11 1533-4880/2008/8/6075/007 doi:10.1166/jnn.2008.SW20 6075