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Advances in Modelling of Size Effects in Graphene and Carbon...
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Advances in Modelling of Size Effects in Graphene and Carbon Nanotubes

A special issue of C (ISSN 2311-5629). This special issue belongs to the section "Carbon Skeleton".

Deadline for manuscript submissions: 30 June 2024 | Viewed by 7230

Special Issue Editors

Dr. Matteo Strozzi

E-Mail Website
Guest Editor
Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy
Interests: nonlinear dynamics; shells and plates; carbon nanotubes; functionally graded materials; vibration-based condition monitoring; mechanical systems modeling; stability analysis; damping
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ahmet Sinan Oktem

E-Mail Website
Guest Editor
Department of Mechanical Engineering, Gebze Teknik Üniversitesi, Kocaeli, Turkey
Interests: nano research; graphene production and modelling; composites; applied mechanics

Special Issue Information

Dear Colleagues,

The growing application of nano-electromechanical systems in various engineering fields. including civil, mechanics, electrical, medical, and aerospace, requires a correct modeling of their behavior. In order to model small-scale structures, both atomistic simulations and continuum mechanics can be adopted. On one hand, classical continuum mechanics models are simpler than atomistic models in modeling small-size structures. However, they present low accuracy, not taking into account the various size-dependent effects characteristic of nanostructures. To this end, several non-classical continuum mechanical models were introduced in the literature, such as nonlocal elasticity, strain gradient theory, and surface stress theory, which take into account the size-dependent effects.

The aim of the present Special Issue is to collect and share recent advances and developments in the theories and formulations that involve the modeling of the size effects in nanostructures, with specific reference to graphene and carbon nanotubes.

Dr. Matteo Strozzi
Prof. Dr. Ahmet Sinan Oktem
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. C is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nanostructures
  • graphene
  • carbon nanotubes

Published Papers (6 papers)

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Research

21 pages, 6477 KiB  
Article
Nonlocal-Strain-Gradient-Based Anisotropic Elastic Shell Model for Vibrational Analysis of Single-Walled Carbon Nanotubes
by Matteo Strozzi, Isaac E. Elishakoff, Michele Bochicchio, Marco Cocconcelli, Riccardo Rubini and Enrico Radi
C 2024, 10(1), 24; https://doi.org/10.3390/c10010024 - 07 Mar 2024
Viewed by 817
Abstract
In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strain–displacement relationships. Eringen’s nonlocal elasticity and Mindlin’s strain [...] Read more.
In this study, a new anisotropic elastic shell model with a nonlocal strain gradient is developed to investigate the vibrations of simply supported single-walled carbon nanotubes (SWCNTs). The Sanders–Koiter shell theory is used to obtain strain–displacement relationships. Eringen’s nonlocal elasticity and Mindlin’s strain gradient theories are adopted to derive the constitutive equations, where the anisotropic elasticity constants are expressed via Chang’s molecular mechanics model. An analytical method is used to solve the equations of motion and to obtain the natural frequencies of SWCNTs. First, the anisotropic elastic shell model without size effects is validated through comparison with the results of molecular dynamics simulations reported in the literature. Then, the effects of the nonlocal and material parameters on the natural frequencies of SWCNTs with different geometries and wavenumbers are analyzed. From the numerical simulations, it is confirmed that the natural frequencies decrease as the nonlocal parameter increases, while they increase as the material parameter increases. As new results, the reduction in natural frequencies with increasing SWCNT radius and the increase in natural frequencies with increasing wavenumber are both amplified as the material parameter increases, while they are both attenuated as the nonlocal parameter increases. Full article
(This article belongs to the Special Issue Advances in Modelling of Size Effects in Graphene and Carbon Nanotubes)
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12 pages, 2205 KiB  
Article
Thermodynamic Stability and Electronic Properties of Graphene Nanoflakes
by Raffaella Soave, Fausto Cargnoni and Mario Italo Trioni
C 2024, 10(1), 5; https://doi.org/10.3390/c10010005 - 03 Jan 2024
Viewed by 1362
Abstract
We conducted a large set of ab initio density functional theory computations to model a variety of hammer-terminated graphene nanoflakes—finite counterparts of armchair graphene nanoribbons. We focused on the relationships among the length and width of the nanoflakes, the stoichiometry and the [...] Read more.
We conducted a large set of ab initio density functional theory computations to model a variety of hammer-terminated graphene nanoflakes—finite counterparts of armchair graphene nanoribbons. We focused on the relationships among the length and width of the nanoflakes, the stoichiometry and the conformation of the hydrogen saturation of the caps, and the resulting electronic structure. The energetics and the thermodynamic stability of the nanoflakes were investigated as well. Based on this study, we provide a recipe for determining the most stable saturation of the dangling bonds at the caps, which is generally disregarded in theoretical studies, and we prove that this step is crucial for a reliable description of the electronic structure of these systems. Data analysis proved that flakes far from the most stable C–H pattern exhibited electronic properties that were typical of an unsaturated bonding structure. Based on thermodynamics, we also proved that, for any given flake, there was a well-defined hydrogen content and a conformation of H atoms at the caps, which were favored across a wide range of environmental conditions. Full article
(This article belongs to the Special Issue Advances in Modelling of Size Effects in Graphene and Carbon Nanotubes)
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15 pages, 1026 KiB  
Article
Large-Separation Behavior of the Casimir–Polder Force from Real Graphene Sheet Deposited on a Dielectric Substrate
by Galina L. Klimchitskaya and Vladimir M. Mostepanenko
C 2023, 9(3), 84; https://doi.org/10.3390/c9030084 - 31 Aug 2023
Viewed by 1136
Abstract
The Casimir–Polder force between atoms or nanoparticles and graphene-coated dielectric substrates is investigated in the region of large separations. Graphene coating with any value of the energy gap and chemical potential is described in the framework of the Dirac model using the formalism [...] Read more.
The Casimir–Polder force between atoms or nanoparticles and graphene-coated dielectric substrates is investigated in the region of large separations. Graphene coating with any value of the energy gap and chemical potential is described in the framework of the Dirac model using the formalism of the polarization tensor. It is shown that the Casimir–Polder force from a graphene-coated substrate reaches the limit of large separations at approximately 5.6 μm distance between an atom or a nanoparticle and graphene coating independently of the values of the energy gap and chemical potential. According to our results, however, the classical limit, where the Casimir–Polder force no longer depends on the Planck constant and the speed of light, may be attained at much larger separations depending on the values of the energy gap and chemical potential. In addition, we have found a simple analytic expression for the Casimir–Polder force from a graphene-coated substrate at large separations and determined the region of its applicability. It is demonstrated that the asymptotic results for the large-separation Casimir–Polder force from a graphene-coated substrate are in better agreement with the results of numerical computations for the graphene sheets with larger chemical potential and smaller energy gap. Possible applications of the obtained results in nanotechnology and bioelectronics are discussed. Full article
(This article belongs to the Special Issue Advances in Modelling of Size Effects in Graphene and Carbon Nanotubes)
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19 pages, 738 KiB  
Article
Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials
by César R. de Oliveira and Vinícius L. Rocha
C 2023, 9(3), 76; https://doi.org/10.3390/c9030076 - 08 Aug 2023
Viewed by 1007
Abstract
It is shown that it is possible to adapt the quantum graph model of graphene to some types of nonequilateral graphynes considered in the literature; we also discuss the corresponding nanotubes. The proposed models are, in fact, effective models and are obtained through [...] Read more.
It is shown that it is possible to adapt the quantum graph model of graphene to some types of nonequilateral graphynes considered in the literature; we also discuss the corresponding nanotubes. The proposed models are, in fact, effective models and are obtained through selected boundary conditions and an ad hoc prescription. We analytically recover some results from the literature, in particular, the presence of Dirac cones for α-, β- and (6,6,12)-graphynes; for γ-graphyne, our model presents a band gap (according to the literature), but only for a range of parameters, with a transition at a certain point with quadratic touch and then the presence of Dirac cones. Full article
(This article belongs to the Special Issue Advances in Modelling of Size Effects in Graphene and Carbon Nanotubes)
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17 pages, 1005 KiB  
Article
Casimir–Polder Force on Atoms or Nanoparticles from Gapped and Doped Graphene: Asymptotic Behavior at Large Separations
by Galina L. Klimchitskaya and Vladimir M. Mostepanenko
C 2023, 9(3), 64; https://doi.org/10.3390/c9030064 - 04 Jul 2023
Cited by 1 | Viewed by 1049
Abstract
The Casimir–Polder force acting on atoms and nanoparticles spaced at large separations from real graphene sheets possessing some energy gaps and chemical potentials is investigated in the framework of the Lifshitz theory. The reflection coefficients expressed via the polarization tensor of graphene, found [...] Read more.
The Casimir–Polder force acting on atoms and nanoparticles spaced at large separations from real graphene sheets possessing some energy gaps and chemical potentials is investigated in the framework of the Lifshitz theory. The reflection coefficients expressed via the polarization tensor of graphene, found based on the first principles of thermal quantum field theory, are used. It is shown that for graphene the separation distances, starting from which the zero-frequency term of the Lifshitz formula contributes more than 99% of the total Casimir–Polder force, are less than the standard thermal length. According to our results, however, the classical limit for graphene, where the force becomes independent of the Planck constant, may be reached at much larger separations than the limit of the large separations determined by the zero-frequency term of the Lifshitz formula, depending on the values of the energy gap and chemical potential. The analytic asymptotic expressions for the zero-frequency term of the Lifshitz formula at large separations are derived. These asymptotic expressions agree up to 1% with the results of numerical computations starting from some separation distances that increase with increasing energy gaps and decrease with increasing chemical potentials. The possible applications of the obtained results are discussed. Full article
(This article belongs to the Special Issue Advances in Modelling of Size Effects in Graphene and Carbon Nanotubes)
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10 pages, 3170 KiB  
Article
Single-Bilayer Graphene Test Structures for Kelvin Probe Microscopy
by Sergey P. Lebedev, Ilya A. Eliseyev, Mikhail S. Dunaevskiy, Ekaterina V. Gushchina and Alexander A. Lebedev
C 2023, 9(3), 62; https://doi.org/10.3390/c9030062 - 21 Jun 2023
Viewed by 1065
Abstract
A new technique for determining the point spread function, which is required for measuring the surface potential using Kelvin probe microscopy (KPM), is presented. The method involves using a silicon carbide substrate coated with single-layer and bilayer graphene as a test structure and [...] Read more.
A new technique for determining the point spread function, which is required for measuring the surface potential using Kelvin probe microscopy (KPM), is presented. The method involves using a silicon carbide substrate coated with single-layer and bilayer graphene as a test structure and obtaining KPM potential profiles in different directions on the surface. This makes it possible to determine the KPM point spread function, which can be used to perform deconvolution and accurately recover the surface potential. Full article
(This article belongs to the Special Issue Advances in Modelling of Size Effects in Graphene and Carbon Nanotubes)
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