Joining curves between nano-torus and nanotube: mathematical approaches based on energy minimization

Sripaturad, Panyada; Baowan, Duangkamon

doi:10.1007/s00033-020-01451-0

Cited by 4 publications

(4 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additionally, R denotes the major radius of the torus, and a denotes the minor radius of the torus. Thus, the equation of the torus in cylindrical coordinates is ( r − R ) 2 + z 2 = a 2 , which can be written as where D is a constant that can be determined by the position of the torus along the negative z -axis [ 30 ]. Now, at the joining point ( r 1 , z 1 ), considering the negative sign of Eq.…”

Section: Resultsmentioning

confidence: 99%

“…where D is a constant that can be determined by the position of the torus along the negative z-axis [30]. Now, at the joining point (r 1 , z 1 ), considering the negative sign of Eq.…”

Section: Joining a Bn Fullerene And Bn Nanotorusmentioning

confidence: 99%

“…This nanostructure has been studied in many studies based on its structure and unique properties. Different applications have been found in the literature, such as in ultrafast optical filters and nanoantennas sensitive to high-frequency electromagnetic signals [ 18 , 30 ].…”

Section: Introductionmentioning

confidence: 99%

“…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 ]. In addition, similar techniques have been utilized and investigated by other researchers, for example, in [ 22 ] and [ 21 ].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Alshammari

2021

J Mol Model

View full text Add to dashboard Cite

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.

show abstract

Section: Resultsmentioning

confidence: 99%

“…where D is a constant that can be determined by the position of the torus along the negative z-axis [30]. Now, at the joining point (r 1 , z 1 ), considering the negative sign of Eq.…”

Section: Joining a Bn Fullerene And Bn Nanotorusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Alshammari

2021

J Mol Model

View full text Add to dashboard Cite

show abstract

Two energies for conjoining boron nitride nanotorus and nanotube

Alshammari

2023

J Math Chem

View full text Add to dashboard Cite

Owing to a variety in nanoscale material applications, the conjunction of two nanostructures is frequently researched for potential new applications. Numerous methods are used to model this conjunction process. One such method, the minimization of elastic energy, only considers the axial curvature when modeling conjoined structures. Another method minimizes the Willmore energy, which depends on both the axial and rotational curvatures. In particular, because the catenoid is an absolute minimizer of Willomre energy, a catenoid section can be utilized to conjoin nanostrucrures. Owing to the similarities among carbon nanostructures, we expanded the use of two different energies to join a boron nitride nanotube with a boron nitride nanotorus. The primary objective of this study was to formulate a basic underlying structure from which any small perturbations can be viewed as departures from an ideal model. Accordingly, elastic energy was used to determine the conjunction region for two-dimensional structures, whereas Willmore energy was used to determine the conjunction region for three-dimensional structures. This approach may be extended to produce other hybrid nanoscale structures.

show abstract

Design of schwarzite templates based on energy minimization of surfaces

Sriphathurat

Baowan

2021

Carbon Trends

View full text Add to dashboard Cite

Joining curves between nano-torus and nanotube: mathematical approaches based on energy minimization

Cited by 4 publications

References 17 publications

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

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

Two energies for conjoining boron nitride nanotorus and nanotube

Design of schwarzite templates based on energy minimization of surfaces

Contact Info

Product

Resources

About