Nanostructure Distortions Simulated Effectively: The Technique and its Nanocarbon Applications

Hefty commercial potential of nanotechnology drives great research interest to nanoscience. This is also the case in the fields of bendable electronics, conformational sensors, and nanoelectromechanical systems (NEMS), where structural distortions play a key role. Distortions are ever-present in nature and difficult to avoid in experiments: being low-dimensional, nanostructures are often flexible, and hence get distorted easily. Carbon nanostructures, known for their unique properties, get distorted particularly easily. Yet, distortions are hard and expensive to study computationally. Moreover, they are tiresome to control experimentally, which is why they are often unexplored. The work presented in this Thesis is a twofold attempt in the fields of nanocarbon and computational research to recognize that structures under realistic conditions get distorted. In the first part, we present a powerful simulation technique to model structural distortions. By revising the traditional periodic boundary conditions technique and the underlying Bloch theorem, we developed a unified simulation framework valid for symmetries beyond translational ones, which allowed modeling distortions such as twisting, stretching, and bending in a local, but natural, easy, and efficient way. We also went beyond exact symmetries and established usage of approximate symmetries, which allowed modeling thin nanostructures warped to arbitrary curvature. So as to illustrate the technique and explore nanocarbon, we extended and implemented generalized symmetries into the density-functional tight-binding method. Since its idea lies in nothing but symmetry or generalized boundary conditions being imposed on a physical problem, the technique is universal. It is valid from classical to fully quantum-mechanical treatments, it allows studying electronic and structural properties simultaneously, it works beyond nanoscale, and it enables reduction in simulation costs by orders of magnitude. In the second part, we investigated distortions and transformations of carbon nanostructures. First, we predicted that certain kinds of narrow stripes of graphene—graphene nanoribbons—get twisted spontaneously. Second, we demonstrated outstanding flexibility of graphene while accomplished estimation of its Gaussian curvature modulus. Third, we actualized the traditional yet experimentally unrealized view on carbon nanotubes as being rolled-up from graphene. Namely, we predicted how graphene could be transformed into carbon nanotubes by means of twisting. The nanotube fabrication method we predict could enable unprecedented control of nanotube chirality, which is important since chirality control after two decades from nanotube discovery still remains experimentally challenging. In all these cases, not only did we simulate the phenomena on atomistic quantum-mechanical level, we also explained them on continuum-elasticity level, which thus suggested that our findings are valid beyond nanocarbon. Within and beyond distortions, the developed technique will be useful in diverse physical, chemical, biological, and medical applications, both scientific and engineering ones, while the gained nanocarbon insights are to bring ambitious nanotechnological dreams closer to reality. Keywords: nanoscience, graphene, carbon nanotubes, twisting, bending, stretching, Gaussian curvature, symmetry, revised periodic boundary conditions, RPBC, elasticity theory