Willmore energy for joining of carbon nanostructures

Advances in Mathematical Physics

2020

Boron nitride (BN) nanomaterials such as boron nitride graphenes, boron nitride nanotubes, and boron nitride nanocones are attracting attention among the most promising nanomaterials due to their physical, chemical, and electronic properties when compared to other nanomaterials. BN nanomaterials suggest many exciting potential applications in various fields. Joining between BN nanostructures gives new enhanced structures with outstanding properties and potential applications for design of probes for scanning tunnelling microscopy and other nanoscale devices. This paper uses calculus of variations to model the joining between BN graphene with other BN nanostructures: BNNTs and BNNCs. Furthermore, during the joining between these BN nanostructures, this research examines two models which are depending on the curvature of the join profile. For the first case, Model I refers to when the join profile only includes positive curvature where for the second case, Model II is considered for both positive and negative curvatures. Thus, the purpose of this research is to formulate the basic underlying structure to present simple models based on joining BN graphene to other BN nanostructures.

Section: Introductionmentioning

confidence: 61%

Mathematical Modelling for Joining Boron Nitride Graphene with Other BN Nanostructures

Advances in Mathematical Physics

2020

“…This demonstrates the joining surface, as a catenoid, between two nanostructures. For more details of derivation, we refer the reader to [ 29 ].…”

Section: Modelmentioning

confidence: 99%

“…As a result of this method, many carbon nanostructures have been connected, such as carbon nanotubes and graphene, nanotubes and fullerenes, nanotubes and nanocones, fullerenes and graphenes as two fullerenes, two nanocones, nanocones and fullerenes, nanocones and fullerenes, and two parallel sheets of graphene, as detailed in [ 9 , 11 , 24 ] and [ 2 ]. Furthermore, another method was utilized to connect carbon nanostructures, that is, the Willmore energy [ 29 ]. This method supports the argument that considers the rotational curvature because it has a similar size.…”

Section: Introductionmentioning

confidence: 99%

“…As a natural generalization of elastic energy, the Willmore energy, which involves axial curvature and rotational curvature, is used to determine the surface connection of two carbon nanoscale structures. As a result of this energy, carbon nanostructures have been joined and connected, for example, carbon nanotubes to fullerenes and two fullerenes to each other, as detailed in [ 29 ]. Furthermore, another study used this energy to join a carbon nanotorus and a nanotube [ 30 ].…”

Section: Introductionmentioning

confidence: 99%

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Mathematical energy minimization model for joining boron nitride fullerene with several BN nanostructures

2021

J Mol Model

Nanoscale materials have gained considerable interest because of their special properties and wide range of applications. Many types of boron nitride at the nanoscale have been realized, including nanotubes, nanocones, fullerenes, tori, and graphene sheets. The connection of these structures at the nanoscale leads to merged structures that have enhanced features and applications. Modeling the joining between nanostructures has been adopted by different methods. Namely, carbon nanostructures have been joined by minimizing the elastic energy in symmetric configurations. In other words, the only considerable curvature in the elastic energy is the axial curvature. Accordingly, because it has nanoscale structures similar to those in carbon, BN can also be joined and connected by using this method. On the other hand, different methods have been proposed to consider the rotational curvature because it has a similar size. Based on that argument, the Willmore energy, which depends on both curvatures, has been minimized to join carbon nanostructures. This energy is used to identify the joining region, especially for a three-dimensional structure. In this paper, we expand the use of Willmore energy to cover the joining of boron nitride nanostructures. Therefore, because catenoids are absolute minimizers of this energy, pieces of catenoids can be used to connect nanostructures. In particular, we joined boron nitride fullerene to three other BN nanostructures: nanotube, fullerene, and torus. For now, there are no experimental or simulation data for comparison with the theoretical connecting structures predicted by this study, which is some justification for the suggested simple model shown in this research. Ultimately, various nanoscale BN structures might be connected by considering the same method, which may be considered in future work.

“…We comment that this model does not take into account the chemical issues, such as positions of atoms and bonds. Finally, using Willmore energy which depends on the axial and rotational curvatures to determine the joining between nanostructures gives rise to similar joining profiles of using elastic energy as studied in [15]. Furthermore, similar techniques have been used and investigated by many researches such as in [16][17][18] and [19].…”

Section: Introductionmentioning

confidence: 99%

Joining between Boron Nitride Nanocones and Nanotubes

Advances in Mathematical Physics

2020

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.