Population Balance-Monte Carlo Simulation for Gas-to-Particle Synthesis of Nanoparticles

Abstract

The process simulation of nanoparticle synthesis via the gas-phase method is essential to understanding the detailed dynamic evolution of nanoparticles within a very short time period under high temperature. The task is, however, very challengeable up to now as the conversion of the gaseous precursor to the end-use nanoparticle is a complex physicochemical process involving nucleation of the particulate phase, agglomeration between particles and sintering under industrial production conditions. In this article, we extended the differentially weighted Monte Carlo method for population balance to simulate the dynamic evolution of titania (TiO 2 ) nanoparticles synthesized by gas-to-particle conversion in a single aerosol reactor, considering simultaneous nucleation, agglomeration, and sintering. The simulated size distribution of TiO 2 agglomerate and primary particles produced by the thermal decomposition of titanium tetraisoproxide agreed well with the experimental data. In the simulation, the fast population balance-Monte Carlo method was utilized to accelerate the process simulation on a desktop PC. Results were obtained up to 178 times faster than that of a normal Monte Carlo method. The inhomogeneous internal structure of primary particles was considered through solving population balance of polydisperse primary particles within agglomerate. It was found the polydisperse model could predict the primary particle size distribution better. Simulation results revealed a complex competition relation among nucleation, agglomeration and sintering.

Identification of the compensation effect in the characteristic sintering time model for population balances

“…PBM is a powerful tool for general simulation, which has been applied by many groups (Hao et al, 2013;Kostoglou & Konstandopoulos, 2001;Kostoglou et al, 2006;Mukherjee, Sonwane, & Zachariah, 2003;Rosner & Yu, 2001;Tandon & Rosner, 1999) to agglomeration or sintering. The PBM is capable of directly describing the dynamic evolution of internal variables (e.g., size and surface area) of each simulation particle (it represents a certain number of real particles having similar state with the simulation particle) (Zhao & Zheng, 2006.…”

“…In our previous work (Hao et al, 2013), this polydispersed model was employed to simulate the synthesis process of TiO 2 via gas-phase method. The simulation results for the synthesis process involving nucleation, agglomeration and sintering agree well with the experimental measurements.…”

“…The advantage of population balance modeling lies in their simplicity (Xu, Zhao, & Zheng, 2015;Zhao, Kruis, & Zheng, 2010;Zhao & Zheng, 2009). Furthermore, the discrete nature of the particles used to represent the system is very useful for multivariate population balances, i.e., containing other particle properties than particle size alone (Hao, Zhao, Xu, & Zheng, 2013;Xu, Zhao, & Zheng, 2014). In this paper the uncertain kinetic parameters in the classical characteristic sintering time equation of TiO 2 and SiO 2 nanoparticles were identified to examine if the compensation effect exists or not.…”

Kinetic Monte Carlo simulation for homogeneous nucleation of metal nanoparticles during vapor phase synthesis

“…Numerous studies have investigated the evolution of aerosol size distributions using MC methods that have shown the capabilities of MC approach to approximate aerosol growth processes. Generally, MC methods can be divided into two classes: Constant‐Volume ( Constant‐V ) and Constant‐Number ( Constant‐N ).…”

Methods of Moments for Resolving Aerosol Dynamics

“…These applications include the derivation of coagulation kernel under different mechanisms, the solution of the governing equations within the Smoluchowski mean-field theory, and the application of Smoluchowski mean-field theoretical model to predict the behavior of aerosol multiphase system. In fact, within the Smoluchowski mean-field theory, some important phenomena such as self-preserving distribution [15][16][17], and gelation or asymptotic behavior [18][19][20][21] have been thoroughly studied using state-of-the-art technologies such as the method of moments (MOM) [17,[19][20][21][22][23], sectional method (SM) [24][25][26][27][28][29][30], stochastic particle method [31][32][33][34][35], and Monte Carlo method [36][37][38][39][40][41][42]. The method of moments is more widely used than other methods due to that it requires the least requirement for computational cost as well as the relative simplicity of implementation [36].…”