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

Abstract

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.

A comprehensive assessment of empirical potentials for carbon materials

“…The armchair edge energy, E AC edge = 1.01 eV/Å, for graphene is lower than the zigzag edge energy, E ZZ edge = eV/Å, as predicted by DFT and consistent with the results obtained by Baran et al, 77 Li et al, 78 and Hedman and Larsson 79,80 Among the potentials, only GAP-20 and ReaxFF C2013 successfully predict this trend (E AC edge < E ZZ edge ). EDIP, LCBOP, ReacFF C2013 , and GAP-20 are within 5% of the DFT value for the armchair edge energy, but only GAP-20 is within 10% of the DFT calculated zigzag edge energy, showing that a high accuracy in energy is needed to correctly describe the relationship between armchair and zigzag edges.…”

Dynamics of growing carbon nanotube interfaces probed by machine learning-enabled molecular simulations

“…As shown, both growth and the formation and healing of interface defects occur at the tube-catalyst interface. Therefore, it becomes crucial to study how the tube-catalyst interface evolves, which has a direct impact on the current understanding of growth mechanisms [48][49][50][51][52] . By tracking the configuration of the SWCNT-edge during growth, the dynamics of the tube-catalyst interface can be studied.…”

Dynamics of growing carbon nanotube interfaces probed by machine learning-enabled molecular simulations

“…Later research recognized the importance of configurational entropy [81] and the impact of curvature and armchair/zigzag junctions [82,83]. More recent advances have extended the concept of configurational entropy to include edges of any cut where the number of edge atoms remains constant [84].…”