Modeling of Particle Formation in Arc Discharges by Monte-Carlo Based Population Balance Modeling
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Modeling of Particle Formation in Arc Discharges by Monte-Carlo Based Population Balance Modeling Gregor Kotalczyk, Ivan Skenderovic and Frank Einar Kruis Institute of Technology for Nanostructures (NST) and Center for Nanointegration DuisburgEssen (CENIDE), University Duisburg-Essen, Duisburg, D-47057, Germany ABSTRACT A simulation method is presented which encompasses all relevant mechanisms, which are necessary for the description of the early stages of particle formation in arc discharges. Next to discrete coagulation and nucleation events, a continuous surface growth process is included into the simulation, making thus the description of the evaporation of thermodynamic unstable particles possible. The driving force for the nucleation and growth/evaporation is coupled to the monomer concentration in the gaseous phase and thus subject to change in the further course of the simulation. It is shown, that the simulation results gained by the incorporation of all three of these processes cannot be reproduced, if one of those processes is not simulated. INTRODUCTION The scale-up of the production of metallic nanoparticles can be done efficiently by means of arc discharge in an inert carrier gas. The use of many single production units in parallel, which can be thoroughly optimized and tested on a lab scale for a given material, ensures that a highly effective scale-up of the synthesis process in terms of cost and energy consumption is possible. We demonstrated the integration of this technology in the aerotaxy production line for solar cells, direct deposition of nanoparticles on textiles, nanocomposites, deposition of nanoparticles within periodic arrays for photonics, higher heat transfer with nanoparticle dispersions and direct deposition of catalytic nanoparticles on membrane structures. [1] This work addresses the problems which appear when modeling the particle formation from an atomic vapor, formed by plasma evaporation from a melt as in the case of arc discharge. The modeling of particle formation initiated by a physically induced nucleation controlled by the local temperature, is especially challenging due to a strong variation of the Kelvin diameter which makes it almost impossible to apply conventional discrete-sectional population balances. Inclusion of nucleation in a Monte-Carlo approach is challenging as the number of simulation particles which can be used is limited. The application of weighted simulation particles offers here a practical solution. Keeping the number of simulation particles constant requires strategies to discard other simulation particles while keeping the loss of information to a minimum, merging techniques show here the best performance. Another challenge is the modeling of condensational growth, here the continuous variation of the Kelvin diameter, induced by e.g. temperature variation or monomer depletion, has to be taken into account. Care has to be taken that particles smaller than the Kelvin diameter effectively evaporate while large ones grow. Although many recent works deal
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