Eighth International Symposium on Scale Modeling (ISSM-8) Portland, Oregon, USA, Sept 12-14, 2017 Activation Energy of Carbon Materials Formation from Xylene Wahed Wasel a , Kazunori Kuwana b,* , Kozo Saito a a Department of Mechanical Engineering, University of Kentucky, 151 RGAN Building, Lexington, KY 40506-0503, USA b School of Engineering, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan * E-mail address: k-kuwana@t-adm.t.u-tokyo.ac.jp Abstract Rcent studies discuss the formation mechanism of carbon nanotubes (CNTs) in chemical vapor deposition (CVD) reactors based on the measured activation energies of CNT formation. In most cases, the activation energies are simply calculated from Arrhenius plots of CNT yield (or CNT length) vs. 1/T (T, temperature) at different reaction temperatures. Reaction conditions such as gas-phase species and their molar concentrations, however, are different at different temperatures, possibly causing errors in the calculation of activation energies by these simple methods. We propose an inverse method that considers the effect of gas-phase reactions to calculate the activation energies. To demonstrate the method, we measured gas-phase concentrations in a CVD reactor and calculated the activation energy of carbon materials formation from xylene using the measured gas concentrations. Nomenclature dp particle diameter T temperature z height  collision frequency function  gas mean free path subscripts g gas phase p particle Introduction Hydrocarbon decomposition in flames has been studied in relation to soot formation [1], but there is a lag in similar studies for synthesis of carbon nanotubes (CNTs). CNT, since its discovery by Iijima [2], has attracted the interest of many researchers due to its unique mechanical and electrical properties [3, 4]. CNTs can be synthesized by different methods such as arc discharge [5], flame [6, 7], and chemical vapor deposition (CVD) [8], which is considered one of the most scalable methods that can be used commercially in producing large amounts of CNTs. Therefore, the formation and growth mechanisms of CNTs in CVD reactors are subjects of current intense research. There are a number of papers [9–14] that discuss the formation mechanism of CNTs based on measured activation energies of CNT growth. Typically, activation energies of CNT formation in CVD reactors are about 140 kJ/mol, which is similar to those for carbon diffusion in metal catalyst, suggesting that the carbon diffusion may be a rate-limiting process. The activation energies are often calculated in a simple way, that is, Arrhenius plots of CNT yield. This, however, might be a source of error. For example, our study [15, 16] showed that gas-phase species that were present in a CVD reactor could be significantly different at different reaction