Thermodynamic Analysis for Carbon Nanotube Growth Mechanism in Combustion-Based Environment

Abstract Comprehending the favourable conditions for CNT growth in flames requires a thermodynamic analysis based on an integrated framework that comprises a coupled computation of flame-scale and kinetic-based particle-scale models. However, the lack of such investigations hampers a deeper understanding of the CNT growth mechanism in a heterogeneous flame environment. In the present study, a coupled computation of computational fluid dynamics (CFD) and a kinetic-based growth rate model was performed for an inverse diffusion flame fuelled by a 30% methane − 5% ethylene mixture. Flame parameters (temperature and combustion species) and CNT growth rate were resolved by CFD and the growth rate model, respectively, and were further related within a thermodynamic framework through Arrhenius and Van’t Hoff plots. Additionally, combustion reactions comprising of three carbon monoxide (CO) - based reactions and five hydrocarbon (C $$_m$$ H $$_n$$ ) - based reactions were analysed using Gibbs free energy plots to identify the favourable dissociation reactions for CNT growth. Arrhenius plots at locations 8, 13, and 18 mm downstream of the burner exhibit Arrhenius behaviour in the low temperature range (700–850 K) and anti - Arrhenius behavior in the high temperature regime (850–1000 K). This observation of a mixed Arrhenius and anti - Arrhenius behaviour provides a unified explanation for both CNT growth and catalyst deactivation, corresponding respectively to the lower and higher temperature regions of the flame. Based on the Arrhenius plots, the activation energy for CNT growth in the present work is determined to be 40–50 kJ/mol, providing the first quantitative estimate of CNT growth activation energy for flame - based synthesis. Thermodynamic analysis based on Arrhenius and Van’t Hoff plots suggests that CNT growth driven by the production of methane is more favourable than that through the production of carbon monoxide. The analysis is extended to Gibbs free energy plots, which indicate that hydrocarbon in particular methane-based dissociation reactions are highly favourable pathways for CNT growth in flames. Although the same analysis also supports CO-based dissociation reactions as favourable, the relatively lower abundance of CO resulting from the combustion of the present fuel makes the contribution of CO to CNT growth secondary compared to methane.