Size- and edge-effect cohesive energy and shear strength between graphene, carbon nanotubes and nanofibers: Continuum modeling and molecular dynamics simulations

Explicit expressions for the size- and edge-effect cohesive energy and shear stress between two finite-sized graphene (graphene/graphene), two finite-sized carbon nanotubes (CNTs) (CNT/CNT) and two finite-sized nanofibers (nanofiber/nanofiber) are obtained through continuum modeling of van der Waals (vdW) interactions between them. The close-form solutions of the cohesive energy and shear stress between these structures at different positions are derived by using Gaussian quadrature. The analytical results of the edge-effect cohesive energy show that both of the maximum repulsive and attractive shear stresses are always close to the initial intersecting positions between them. Checking against present molecular dynamics (MD) calculations and available experimental results shows that the continuum solutions are reasonable, in which the main reason of their difference is also revealed in detail. The obtained analytical solutions should be of great help for understanding the size- and edge-effect interactions between these nanostructures and designing nanoelectronic devices.