Concurrent quantum/continuum coupling analysis of nanostructures

A general multiscale computational framework that concurrently couples the quantum-mechanical model with the continuum model is developed. This approach is then used to study the electronic properties of single-walled carbon nanotubes (CNTs) influenced by geometry and deformation. The electronic properties of the CNT, such as the band structure and band gap, are intimately connected to its electrical and thermal properties, mechanical stiffness, failure strength, chemical reactivities and many others. The CNT geometry is featured by a cylindrical-shaped structure, which leads to a mixture of the electronic structures that were originally present in graphite. These important effects are incorporated in a coarse-grained tight-binding model based on an extension to the Bloch theorem and the virtual atom cluster model developed previously by the authors. With this approach, we study the correlation among the electronic structures/properties, CNT geometry and applied deformation for a wide variety of tubes. The major technical ingredients and findings are(1)Compared with the computational cost of O(ne3) of the full-scale tight-binding calculation with ne being the electronic base functions used, we have developed an efficient concurrent approach as it scales with O(NG) with NG being the number of quadrature points;(2)We have established a new coarse-grained cluster model that provides a direct way of coupling deformation mapping with the quantum-mechanical model. A unique feature of this coarse-grained model is that it does not use any stress and strain concepts as in a standard continuum approach;(3)We report strong influences of CNT geometry on its electronic properties. For zigzag tubes with chiral index of (n, 0) and radius r, the band gap Eg ∝ r−0.695 when the remainder of n divided by 3 (mod(n, 3)) is 1 and Eg ∝ r−1.109 when mod(n, 3) = 2;(4)We report significant changes in the band gap and electrical conductance as functions of the applied tensile strain and twist. Transitions from metal to semiconductor and vice versa are observed;(5)There is a weak coupling between the band gap, electrical conductance and applied bending angle.Based on extensive studies, we conclude that the electron–mechanical coupling relations obtained in this work are more robust than the previous analytical studies in that it takes into account the important effects of curvature and relaxation. The simulation results highlight the importance of the concurrent coupling among the electronic properties, CNT geometry and mechanical deformation.