A constant number Monte Carlo approach to examine Non-Isothermal nucleation and growth in a limited vapor system

Nucleation and growth are the central reactions in gas phase nanomaterial synthesis reactors. When particles collisionally grow, latent heat release occurs, which can lead to particle elevated thermal energies, and in turn greatly affect particle size distribution evolution. Unfortunately, particle heating during growth is difficult to probe experimentally, and atomistic scale simulations accounting for heating are computationally expensive. Here, we devise a constant number Monte Carlo simulation approach to study particle growth, permitting growing particles to be in thermal non-equilibrium with their gaseous surroundings. To examine how non-isothermal effects influence particle growth, we studied the nucleation of gold particles in a closed system with high initial saturation ratio and variable background gas temperatures. Particles evolve by condensation, coagulation, and evaporation. The model also incorporates collisional or dissociative latent to sensible heat conversion, heat transfer between particles and surrounding gas, and black body radiation, which are difficult to incorporate in traditional population balance studies. Simulations clearly demonstrate how the system temperature, pressure, initial saturation ratio, heat transfer rate affect the particle size distribution evolution, thermal energy distributions, and the inferred system nucleation rates. Using Jaccard and Frobenius similarities, we also developed metrics of the “non-isothermalness” of particle evolution processes by comparing non-isothermal nucleation size distributions with their isothermal counterparts. We find that a simple dimensionless ratio between gas cooling rate to condensational heating rate can serve as a guide in evaluating the necessity of non-isothermal heat transfer model in gas phase synthesis reactions.