Abstract
Different nanostructures of boron nitride have been observed experimentally such as fullerenes, tubes, cones, and graphene. They have received much attention due to their physical, chemical, and electronic properties that lead them to numerous applications in many nanoscale devices. Joining between nanostructures gives rise to new structures with outstanding properties and potential applications for the design of probes for scanning tunneling microscopy and other nanoscale devices, as carriers for drug delivery and liquid separation. This paper utilizes calculus of variations to model the joining between two types of BN nanostructures, namely, BN nanotubes and BN nanocones. Based on the curvature of the join curve, the joining of these structures can be divided into two models. Model I refers to when the join profile includes positive curvature only, and Model II contains both positive and negative curvatures. The main goal here is to formulate the basic underlying structure from which any such small perturbations can be viewed as departures from an ideal model. For this scenario of joining, we successfully present simple models based on joining BN nanotubes to BN nanocones with five different angles of the cone.