Mathematical modelling of the carbon nanotubes synthesis by methane pyrolysis on a copper catalyst based on the approximation approach

Abstract

We present the mathematical model concepts for the synthesis of carbon nanotubes by catalytic pyrolysis of methane, based on the analysis and approximation of the dependence of the process stages on the gas phase composition and temperature. The process was considered to consist of three successive stages that include the linear stage of initial growth with a constant specific rate, the stage of growth retardation due to the catalyst active site deactivation, and the stage close to linear, occurring after equilibrium of the accompanying sorption-desorption processes on the active sites is reached. Based on the available experimental studies on a specific catalyst, a step-by-step search for mathematical patterns describing the selected phases of a typical nanotubes growth curve was performed. We have determined and confirmed the criteria for the dependence of the proposed equations parameters on the gas phase composition. The article also discusses the advantages of the proposed approach for modeling complex processes in comparison with traditional physicochemical approaches.