Simple Estimation of Nanoparticle Diameter Produced in a Flow Tube Reactor
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Simple Estimation of Nanoparticle Diameter Produced in a Flow Tube Reactor Kazunori Kuwana and Kozo Saito Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506-0503, U.S.A. ABSTRACT In many carbon nanotube synthesis methods, catalyst nanoparticles are formed via pyrolysis of a precursor such as ferrocene. Since the diameter of a carbon nanotube is usually determined by the diameter of the catalyst nanoparticle, it is of great importance to control the size of nanoparticles. To do so, it is necessary to identify the key reaction parameters that influence nanoparticle size. For engineering purposes, a simple analytical model offers a convenient first estimation of particle diameter. It also clarifies the dependence of nanoparticle diameter on each reaction parameter and enhances our understanding of the formation mechanism of nanoparticles. This paper presents a simplified model that can calculate the diameter of particles and the model’s analytical solutions. INTRODUCTION Continuous, large-scale production of carbon nanotubes (CNTs) is a subject of intense current research [1]. To properly scale up a process, the correct understanding of the process is essential, thus requiring an accurate, predictive model. The final goal of our research project is to develop a model that can simulate the synthesis of CNTs in a chemical vapor deposition (CVD) reactor and to scale up the reactor based on the model’s predictions. The CVD reactor that we have been modeling is the one developed by Andrews et al. [1], which can produce multiwalled CNTs at a reaction temperature of about 1000 K using xylene as the carbon source and ferrocene as the catalyst precursor. We divided the CVD process into four basic subprocesses: (1) flow and heat transfer, (2) gas-phase reactions, (3) catalyst particle formation, and (4) nanotube growth on the surface of catalyst particles; we developed a computational model for each subprocess. A brief overview of these models is provided in the next section. These computational models provide us with detailed information about the CVD reactor. Conducting a series of computational simulations is, however, sometimes time-consuming. On the other hand, an analytical model and its solution can offer a convenient first estimation of the process in a timely manner. The model and its solution also clarify the influence of each reaction parameter such as temperature and feed rate. This paper presents one such analytical model, i.e., a simple model that can predict the formation and the growth of catalyst particles in the CVD reactor. OVERVIEW OF CNT-CVD MODELS Flow and heat transfer
We used computational fluid dynamics (CFD) to calculate the flow and temperature fields in the reactor [2−4]. It was found that the buoyant force might generate a nonuniform flow in the
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reactor, causing a nonuniform distribution of local CNT yield [2]. However, a preheating system was found to yield a very uniform flow pattern in the reactor [3]. Gas-phase reactions
CNT deposit
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