Computational studies of torsional properties of single-walled carbon nanotubes

Abstract

Current thesis presents computational studies of the torsional twist in single walled carbon nanotubes (SWCNTs). Since SWCNTs can be viewed as rolled up graphene sheets, our aim is to explain their torsion constants via shear mod- ulus of graphene in pristine, and single- and double vacancy cases. In addition, fundamental energy gap response to torsion is investigated. Calculations of defected structures is computationally expensive as it requires larger simula- tion cell with large number of atoms. To reduce the cost of computations we take the advantage of chiral symmetry of nanotubes instead of translational one, and faster performance of density-functional tight-binding method compared to other computational methods. Shear modulus calculations show that its value approaches that of graphene for large diameter tubes and is most sensitive to size in case of armchair tubes. Vacancies diminish shear modulus for most of the nanotubes and concentration-induced decrease has linear character regardless of chirality. Studies on direction-dependent shearing of graphene reveals that in the presence of double vacancy shear modulus has the biggest fluctuations from its average value compared to pristine and single vacancy instances. Torsion significantly modifies electronic structure as well - metallic tubes undergo tran- sition to semiconducting state, during which band gap change is linear, peaking and decreasing to zero again for most of the tubes. Results give the ground for assumption that for large diameter tubes the peak values, reached during torsion, converge.