Analytical modelling of single-walled carbon nanotube energies: the impact of curvature, length and temperature

Recent breakthroughs in the field of single-walled carbon nanotube (SWCNT) growth have been achieved by combining theoretical models with experiments. Theoretical models rely on accurate energies for SWCNTs, obtained via first principle calculations in the form of density functional theory (DFT). Such calculations are accurate, but time and resource intensive which limits the size and number of systems that can be studied. Here, we present a new analytical model consisting of three fundamental energy expressions, parametrized using DFT, for fast and accurate calculation of SWCNT energies at any temperature. Tests against previously published results show our model having excellent accuracy, with an root mean square error in total energies below 2 meV per atom as compared to DFT. We apply the model to study SWCNT growth on Ni catalysts at elevated temperatures by investigating the SWCNT/catalyst interface energy. Results show that the most stable interface shifts towards chiral edges as the temperature increases. The model’s ability to perform calculations at any temperature in combination with its speed and flexibility will allow researcher to study more and larger systems, aiding future research into SWCNT growth.