Aerosol synthesis of silicon nanoparticles with narrow size distribution—Part 2: Theoretical analysis of the formation mechanism

This work investigates the mechanisms which lead to the formation of silicon nanoparticles with narrow size distributions by means of population balance modeling. The model accounts for the full aerosol process, including chemical reaction, nucleation from supersaturated vapor, growth and agglomeration. The results are in good agreement with experimental data. The effects of the process parameters temperature, silane concentration and reactor total pressure are systematically investigated. The simulation allows an in-depth insight into the particle formation mechanism and reveals the key requirements which are necessary for the generation of narrow particle size distributions. In this mechanism, only a short nucleation burst occurs, while surface growth plays the dominant role in silane precursor consumption. A key role is attributed to condensation, because the numerical calculations can only reflect the experimental observations, if the condensation mechanism is included in the model.     

Computational Modeling of Silicon Nanoparticle Synthesis: II. A Two-Dimensional Bivariate Model for Silicon Nanoparticle Synthesis in a Laser-Driven Reactor Including Finite-Rate Coalescence

In this work, a two-dimensional model was developed for silicon nanoparticle synthesis by silane thermal decomposition in a six-way cross laser-driven aerosol reactor. This two-dimensional model incorporates fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics, with particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, coagulation, and coalescence processes. Because of the complexity of the problem at hand, the simulation was carried out via several sub-models. First, the chemically reacting flow inside the reactor was simulated in three dimensions in full geometric detail, but with no aerosol dynamics and with highly simplified chemistry. Second, the reaction zone was simulated using an axisymmetric two-dimensional CFD model, whose boundary conditions were obtained from the first step. Last, a two-dimensional aerosol dynamics model was used to study the silicon nanoparticle formation using more complete silane decomposition chemistry, together with the temperature and velocities extracted from the reaction zone CFD simulation. A bivariate model was used to describe the evolution of particle size and morphology. The aggregates were modeled by a moment method, assuming a lognormal distribution in particle volume. This was augmented by a single balance equation for primary particles that assumed locally equal number of primary particles per aggregate and fractal dimension. The model predicted the position and size at which the primary particle size is frozen in, and showed that increasing the peak temperature was a more effective means of improving particle yield than increasing silane concentration or flowrate.     

Numerical modeling of silicon oxide particle formation and transport in a one-dimensional low-pressure chemical vapor deposition reactor

A numerical model is presented for particle formation and transport during low-pressure chemical vapor deposition of silicon dioxide films from silane and oxygen. A detailed chemical kinetics approach was used to model silicon oxide clustering that leads to homogeneous nucleation. A moment-type aerosol dynamics model was developed, which includes particle growth by surface reactions and coagulation, and particle transport by convection, diffusion and thermophoresis, assuming a lognormal particle size distribution function. A chemical clustering mechanism was coupled to the aerosol dynamics model in an axisymmetric stagnation–flow reactor. Simulations were conducted to predict steady-state spatial distributions of major particle characteristics such as particle concentration, diameter and volume fraction. The effects of various system parameters were assessed for conditions around $\text{1.5}\text{Torr}$ $\text{(200}\text{Pa}\text{)}$, 800°C, $\text{200}\text{sccm}$ and an inlet oxygen-to-silane ratio of 20. Model predictions are shown to be in good agreement with experimental data and indicate that, unlike the case of particle formation in silane pyrolysis, the results are relatively insensitive to temperature. On the other hand, we observe a large sensitivity to pressure change, which is corroborated by experiment.     

Computational Modeling of Silicon Nanoparticle Synthesis: I. A General Two-Dimensional Model

A two-dimensional model has been developed for silicon nanoparticle synthesis by silane thermal decomposition driven by laser heating in a tubular reactor. This fully coupled model includes fluid dynamics, laser heating, gas phase and surface phase chemical reactions, and aerosol dynamics which includes particle transport and evolution by convection, diffusion, thermophoresis, nucleation, surface growth, and coagulation processes. A moment method, based upon a lognormal particle size distribution, and a sectional method are used to model the aerosol dynamics. The simulation results obtained by the two methods are compared. The sectional method is capable of capturing the bimodal behavior that occurs locally during the process, while the moment method is computationally more efficient. The effect of operating parameters, such as precursor concentration, gas phase composition, inlet gas velocity and laser power input, on the characteristics of the particles produced are investigated. Higher temperature generates more large particles with higher precursor conversion. Shorter residence time, from high inlet velocity, produces more small particles at the cost of lower precursor conversion. Increasing H₂ concentration suppresses particle formation by reducing the rates of gas phase and surface reactions, leading to fewer and smaller particles. In addition, the relative importance of the interconnected mechanisms involved in the particle formation is considered. The results make clear that spatial variations in reaction conditions are the primary source of size polydispersity and generation of non lognormal overall size distributions in a laser-driven process like that considered here.     

Numerical investigation on new configurations for vapor-phase aerosol reactors

Non-ideal aerosol reactors for synthesizing nano- and micro-metal-oxide powders can currently be accurately designed by means of computational fluid dynamics (CFD) models instead of an expensive trial-and-error experimental technique. According to a multi-scale approach, fluid dynamics of the reacting volume is modeled by an appropriate population balance equation (PBE) coupled to momentum, energy and chemical species conservative equations. The present work refers to the modeling of non-ideal vapor-phase aerosol reactors, in particular to the numerical investigation on the effects of feeding nozzle arrangement, where the most significant gradients and aerosol phenomena occur. The described aerosol CFD model, which a priori assumes a log-normal particle size distribution (PSD), has been validated against both an experimental and an industrial case, and therefore it has been applied to the study of new reactor configurations. Numerical results show that traditional axial-symmetric and jet-opposed nozzle arrangements can be improved adopting a tangential geometry.     

Simulation of aerosol dynamics and transport in chemically reacting particulate matter laden flows. Part II: Application to CVD reactors

A highly computationally efficient and accurate semi-implicit numerical technique based on the concept of operator splitting (described in detail in Part I of this paper) has been used to solve the General Dynamic Equation in complex, non-isothermal reacting flows to predict aerosol dynamics and particle deposition rates. The numerically efficient algorithm has made it possible to solve the GDE in complex two-dimensional and three-dimensional simulations, hitherto not done due to the computational intensiveness. Simulations have been performed to elucidate the role of different process parameters on aerosol dynamics and particle deposition rates in idealized and commercial horizontal single wafer CVD reactors. Specifically, it has been demonstrated that the gas phase kinetics, particle formation, growth and deposition rates result in very complex aerosol size distributions in the reactor that cannot be captured with simplistic models that do not couple the GDE to the detailed flow field simulations. Guidelines for minimizing particle contamination in CVD reactors on the basis of the simulation results are presented.     

Approaches to increasing yield in evaporation/condensation nanoparticle generation

With the recent interest in the chemical, electronic and optical properties of nanometer scale metal particles, there is now interest in manufacturing these materials in larger quantities. Since both small particle size and high particle number concentrations are sought, there is a need for improved particle generation reactors that can realize both goals. Here, results are presented for the synthesis of indium metal nanoparticles in an evaporation/condensation aerosol generator. Size distributions were measured for metal nanoparticles formed using a standard flow configuration, as well as using several variations on the standard configuration. The aim of the modifications is to increase the cooling rate and thus, to increase the nucleation rate of the nanoparticles. An increase in the number concentration of particles and, in some cases, a significant decrease in average particle size was observed when the modified reactor configurations were used. These results can be explained by the changes in the time–temperature history of the nanoparticles resulting from the modifications to the aerosol generator. A monodisperse model of nanoparticle formation and growth, accounting for nucleation, condensation and coagulation, was used to describe particle formation in the standard flow configuration, to guide the modifications, and to describe particle formation in one of the modified configurations, with qualitative agreement seen between measured and predicted particle sizes.     

化学气相淀积反应器中成核与成膜控制

基于气溶胶动力学和化学反应动力学,建立了化学气相淀积(CVD)反应器中普适动力学方程,导出了CVD反应器中超细颗粒粒径分布谱函数和薄膜淀积速率的计算方法;研究了操作参数对钛酸丁酯高温裂解过程中成核与成膜的影响.用成核与成膜竞争判据——H准数,研究了CVD反应器中成核与成膜的控制策略.     

The Behavior of Constant Rate Aerosol Reactors

An aerosol reactor is a gaseous system in which fine particles are formed by chemical reaction in either a batch or flow process. The particle sizes of interest range from less than 10 Å (molecular clusters) to 10μm. Such reactors may be operated to study the aerosol formation process, as in a smog reactor, or to generate a product such as a pigment or a catalytic aerosol. Aerosol reactors can be characterized by three temporal or spatial zones or regions of operation for batch and flow reactors, respectively. In zone I, chemical reaction results in the formation of condensable molecular products which nucleate and form very high concentrations of small particles. The number density depends on the concentration of preexisting aerosol. Zone II is a transition region in which the aerosol number concentration levels off as a result of hetergeneous condensation by the stable aerosol. In zone III coagulation becomes sufficiently rapid to reduce the particle number concentration. There may be a zone IV in which agglomerates form. Chemical reaction may continue to generate condensable material throughout the various zones. This paper deals with reactors in which aerosol material is generated at a constant rate. Design parameters of interest are the particle size distribution, number density, surface area, and mass loadings. For ideal systems composed of spherical coalescing particles, these can be predicted theoretically for certain limiting cases. However, the irregular agglomerates which may form in zone IV are more difficult to characterize theoretically.     

FORMATION OF SULPHURIC ACID AEROSOLS AND CLOUD CONDENSATION NUCLEI: AN EXPRESSION FOR SIGNIFICANT NUCLEATION AND MODEL COMPRARISON

A new analytical expression has been derived to predict atmospheric conditions where homogeneous water–sulphuric acid nucleation will have a significant effect on aerosol and cloud condensation nuclei population. In the expression, the condensational sink due to pre-existing aerosol particles and source due to chemical production of sulphuric acid have been taken into account. The analytical expression has been derived using a sectional aerosol dynamic model including nucleation, condensation, coagulation, deposition and sulphuric acid formation in the gas phase. In the present study we have also compared the sectional model with modal and monodisperse models. All models may be used for predicting the onset of significant new particle formation. However, the computationally more efficient models—monodisperse, modal, and sectional with low number of sections—over- or underpredict particle formation in some situations.     

Simulation of nanoparticle synthesis in an aerosol flame reactor using a coupled flame dynamics–monodisperse population balance model

Flame aerosol synthesis is one of the commonly employed techniques for producing ultra fine particles of commodity chemicals such as titanium dioxide, silicon dioxide and carbon black. Large volumes of these materials are produced in industrial flame reactors. Particle size distribution of product powder is the most important variable and it depends strongly on flame dynamics inside the reactor, which in turn is a function of input process variables such as reactant flow rate and concentration, flow rates of air, fuel and the carrier gas and the burner geometry. A coupled flame dynamics–monodisperse population balance model for nanoparticle synthesis in an aerosol flame reactor is presented here. The flame dynamics was simulated using the commercial computational fluid dynamics software CFX and the particle population dynamics was represented using a monodisperse population balance model for continuous processes that predicts the evolution of particle number concentration, particle volume and surface area. The model was tested with published experimental data for synthesis of silica nanoparticles using different burner configurations and with different reactor operating conditions. The model predictions for radial flame temperature profiles and for the effects of process variables like precursor concentration and oxygen flow rate on particle specific surface area and mean diameter are in close agreement with published experimental data.     

Modeling Multicomponent Aerosol Particle Growth By Vapor Condensation

A new “moving-sectional” method is presented to solve the dynamics of multicomponent aerosol particle growth by vapor condensation in a closed system. The method controls numerical diffusion and stiffness by adapting the method of characteristics to a sectional representation of the aerosol. An exact solution for a closed system is presented, and the “moving-sectional” method gives excellent agreement when tested against this solution. Four cases are presented to demonstrate the importance of the solute, Kelvin, and latent heat effects.     

Modeling Oxidation of Soot Particles Within a Laminar Aerosol Flow Reactor Using Computational Fluid Dynamics

This work examines the measurement of surface specific soot oxidation rates with the High Temperature Oxidation-Tandem Differential Mobility Analyzer (HTO-TDMA) method. The Computational Fluid Dynamics package CFD-ACE⁺ is used to understand particle flow, oxidation and size dependent particle losses in the laminar aerosol flow reactor using an Eulerian-Lagrangian framework. Decrease of DMA selected mono-disperse particle size distribution due to oxidation within the aerosol tube is modeled using fitted kinetic soot oxidation parameters. The effects of Brownian diffusion and thermophoresis on particle flow and loss to the reactor walls are evaluated. The position of peak particle diameter, which is used as an indicator to determine oxidation rate, is found to be independent of diffusion, thermophoresis and secondary flow effects, thus validating its use in deriving kinetic soot oxidation parameters. Diffusion does not affect the evolution of particle size distribution within the reactor. However, thermophoresis is found to be the dominant mechanism influencing both shape of particle size distribution and particle loss to the walls of the aerosol reactor. Simulations show reduced effects of secondary recirculating flows on the particle flow trajectories in a vertical furnace as compared to horizontal furnace orientation. This work highlights the importance of making accurate measurements of temperature within the modeling domain. Since gas temperature within the flow tube could not be measured with high radial resolution using radiation shielded thermocouple, the derived soot oxidation rate may be uncertain by a factor of 2. Importantly, CFD simulations suggest that a distribution of temperature and size-dependent particle reactivities may be present in the reactor, requiring further theoretical and experimental investigation.     

Sectional Modeling of Aerosol Dynamics in Multi-Dimensional Flows

The integration of computational fluid dynamics (CFD) with computer modeling of aerosol dynamics is needed in several practical applications. The use of a sectional size distribution is desirable because it offers generality and flexibility in describing the evolution of the aerosol. However, in the presence of condensational growth the sectional method is computationally expensive in multidimensional flows, because a large number of size sections is required to cope with numerical diffusion and achieve accuracy in the delicate coupling between the competing processes of nucleation and condensation. The present work proposes a methodology that enables the implementation of the sectional method in Eulerian multidimensional CFD calculations. For the solution of condensational growth a number conservative numerical scheme is proposed. The scheme is based on a combination of moving and fixed particle size grids and a re-mapping process for the cumulative size distribution, carried out with cubic spline interpolation. The coupling of the aerosol dynamics with the multidimensional CFD calculations is performed with an operator splitting technique, permitting to deal efficiently with the largely different time scales of the aerosol dynamics and transport processes. The developed methodology is validated against available analytical solutions of the general dynamic equation. The appropriateness of the methodology is evaluated by reproducing the numerically demanding case of nucleation-condensation in an experimental aerosol reactor. The method is found free of numerical diffusion and robust. Good accuracy is obtained with a modest number of size sections, whereas the computational time on a common personal computer remained always reasonable.     

Modeling of the monomer role and the coalescence limitation in primary particle growth

The general dynamic equation (GDE) has been numerically solved to simulate the growth of ultrafine particles (UFPs) in a tubular aerosol reactor, approximating the particle size distribution by a lognormal function. The GDE includes all the terms describing diffusion, thermophoresis, nucleation, condensation and coagulation. We have also considered the efficiency of liquid-like coagulation to primary particles. The data calculated from our model were compared with those from the previous model and also with some experimental results from a TiO₂ UFP generator. The condensation term, which we split from a single coagulation term in the previous model, well described the monomer contribution to the particle growth. Introduction of one adjustable parameter, the efficiency of coagulation, was successful in limiting the growth of primary particles and fit the experimental data.     

Evolution of atmospheric aerosol particle size distributions via Brownian coagulation numerical simulation

Current atmospheric observations tend to support the view that continental tropospheric aerosols, particularly urban aerosols, show multimodal mass distributions. One of the obvious mechanisms causing the multimodality is the mixing of different primary sources. Other modes involve dissimilar aerosol formation processes in the atmosphere. Fine aerosol particles are generated from secondary processes such as nucleation, condensation and chemical reaction, whereas coarse particles usually consist of dust, fly ash and mechanically generated aerosols. With the use of a newly developed computer code GROWTH in our laboratory, we report here the simulated results of Brownian coagulation dynamics involving multimodal mass density functions for long periods of time. In our model calculations we assume that the aerosol particles are well mixed in an atmospheric volume so that spatial variation in the distribution is negligible. Our accurate numerical simulation of the Brownian coagulation dynamics indicates that once formed, an atmospheric multimodal aerosol distribution in the range 0.1 to 100 μm will maintain its identity for a very long period of time (at least hours) unless “atmospheric perturbations” such as meteorological instabilities, rain-washout and gravitational settling occur. It is our belief that understanding the complex domain of atmospheric aerosols requires systematic investigation of each process. This paper is a continuation of such an investigation.     

Aerosol synthesis of silicon nanoparticles with narrow size distribution—Part 1: Experimental investigations

A study on the feasibility of aerosol processing of nearly monodisperse silicon nanoparticles via pyrolysis of monosilane in a hot wall reactor is presented. For optimal conditions silicon nanoparticles with a geometric standard deviation of 1.06 were synthesized at a production rate of 0.7 g/h. The size of the particles could be precisely controlled in the range of 20–40 nm, whilst maintaining a geometric standard deviation in the range of 1.06–1.08, by proper choice of the governing parameters temperature, residence time and precursor concentration. The results show that narrow particle size distributions can only be obtained in the temperature range between 900 and 1100 °C, as long as both the initial silane concentration (1 mbar silane partial pressure) and the reactor total pressure are low (25 mbar). This regime for the production of narrow particle size distributions has not been identified in prior work on the thermal decomposition of silane. Narrowly distributed particles can be obtained under conditions where nucleation and particle growth are separated and the agglomeration rates are negligible.