ORCID Profile
0000-0002-0662-7037
Current Organisation
University of Adelaide
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Publisher: Australian Mathematical Publishing Association, Inc.
Date: 04-07-2022
DOI: 10.21914/ANZIAMJ.V63.17079
Abstract: The chemical vapour deposition method is widely used to synthesise high quality graphene with a large surface area. However, the cooling process leads to the formations of ripples and wrinkles in the graphene structure. When a self-adhered wrinkle achieves the maximum height, it then folds onto the surface and leads to a collapsed wrinkle. The presence of such deformations often affects the properties of graphene. In this article, we describe a novel mathematical model to understand the formation and geometry of these wrinkles. The stability of these wrinkles is examined based on variational derivations for the energy of each structure. The model provides detailed explanations for the geometry of these wrinkles which would help in tuning their properties. References J. Aljedani, M. J. Chen, and B. J. Cox. Variational model for collapsed graphene wrinkles. Appl. Phys. A 127.11, 886 (2021), pp. 1–13. doi: 10.1007/s00339-021-05000-y A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau. Superior thermal conductivity of single-layer graphene. Nano Lett. 8.3 (2008), pp. 902–907. doi: 10.1021/nl0731872 S. Chen, Q. Li, Q. Zhang, Y. Qu, H. Ji, R. S. Ruoff, and W. Cai. Thermal conductivity measurements of suspended graphene with and without wrinkles by micro-Raman mapping. Nanotech. 23.36, 365701 (2012). doi: 10.1088/0957-4484/23/36/365701 on p. C85). B. J. Cox, T. Dyer, and N. Thamwattana. A variational model for conformation of graphene wrinkles formed on a shrinking solid metal substrate. Mat. Res. Express 7.8, 085001 (2020). doi: 10.1088/2053-1591/abaa8f A. K. Geim. Graphene: Status and prospects. Science 324.5934 (2009), pp. 1530–1534. doi: 10.1126/science.1158877 on p. C85). K. Kostarelos and K. S. Novoselov. Graphene devices for life. Nature Nanotech. 9 (2014), pp. 744–745. doi: 10.1038/nnano.2014.224 F. Long, P. Yasaei, R. Sanoj, W. Yao, P. Král, A. Salehi-Khojin, and R. Shahbazian-Yassar. Characteristic work function variations of graphene line defects. ACS Appl. Mat. Inter. 8.28 (2016), pp. 18360–18366. doi: 10.1021/acsami.6b04853 R. Muñoz and C. Gómez-Aleixandre. Review of CVD synthesis of graphene. Chem. Vapor Dep. 19.10–12 (2013), pp. 297–322. doi: 10.1002/cvde.201300051 L. Spanu, S. Sorella, and G. Galli. Nature and strength of interlayer binding in graphite. Phys. Rev. Lett. 103.19, 196401 (2009). doi: 10.1103/PhysRevLett.103.196401 T. Verhagen, B. Pacakova, M. Bousa, U. Hübner, M. Kalbac, J. Vejpravova, and O. Frank. Superlattice in collapsed graphene wrinkles. Sci. Rep. 9.1, 9972 (2019). doi: 10.1038/s41598-019-46372-9 C. Wang, Y. Liu, L. Li, and H. Tan. Anisotropic thermal conductivity of graphene wrinkles. Nanoscale 6.11 (2014), pp. 5703–5707. doi: 10.1039/C4NR00423J W. Wang, S. Yang, and A. Wang. Observation of the unexpected morphology of graphene wrinkle on copper substrate. Sci. Rep. 7.1 (2017), pp. 1–6. doi: 10.1038/s41598-017-08159-8 Y. Wang, R. Yang, Z. Shi, L. Zhang, D. Shi, E. Wang, and G. Zhang. Super-elastic graphene ripples for flexible strain sensors. ACS Nano 5.5 (2011), pp. 3645–3650. doi: 10.1021/nn103523t Y. Wei, B. Wang, J. Wu, R. Yang, and M. L. Dunn. Bending rigidity and Gaussian bending stiffness of single-layered graphene. Nano Lett. 13.1 (2013), pp. 26–30. doi: 10.1021/nl303168w Z. Xu and M. J. Buehler. Interface structure and mechanics between graphene and metal substrates: A first-principles study. J. Phys.: Cond. Mat. 22.48, 485301 (2010). doi: 10.1088/0953-8984/22/48/485301 Y. Zhang, N. Wei, J. Zhao, Y. Gong, and T. Rabczuk. Quasi-analytical solution for the stable system of the multi-layer folded graphene wrinkles. J. Appl. Phys. 114.6, 063511 (2013). doi: 10.1063/1.4817768 W. Zhu, T. Low, V. Perebeinos, A. A. Bol, Y. Zhu, H. Yan, J. Tersoff, and P. Avouris. Structure and electronic transport in graphene wrinkles. Nano Lett. 12.7 (2012), pp. 3431–3436. doi: 10.1021/nl300563h
Publisher: Royal Society of Chemistry (RSC)
Date: 2013
DOI: 10.1039/C3RA43991G
Publisher: Springer Science and Business Media LLC
Date: 11-2021
Publisher: Cambridge University Press (CUP)
Date: 04-2013
DOI: 10.1017/S1446181113000217
Abstract: We review the work of the present authors to employ variational calculus to formulate continuous models for the connections between various carbon nanostructures. In formulating such a variational principle, there is some evidence that carbon nanotubes deform as in perfect elasticity, and rather like the elastica, and therefore we seek to minimize the elastic energy. The calculus of variations is utilized to minimize the curvature subject to a length constraint, to obtain an Euler–Lagrange equation, which determines the connection between two carbon nanostructures. Moreover, a numerical solution is proposed to determine the geometric parameters for the connected structures. Throughout this review, we assume that the defects on the nanostructures are axially symmetric and that the into-the-plane curvature is small in comparison to that in the two-dimensional plane, so that the problems can be considered in the two-dimensional plane. Since the curvature can be both positive and negative, depending on the gap between the two nanostructures, two distinct cases are examined, which are subsequently shown to smoothly connect to each other.
Publisher: Elsevier BV
Date: 2011
Publisher: Springer Science and Business Media LLC
Date: 17-05-2011
Publisher: Elsevier BV
Date: 2011
Publisher: Cambridge University Press (CUP)
Date: 04-2008
Publisher: ASME International
Date: 11-2012
DOI: 10.1115/1.4007521
Abstract: In this paper, we investigate methane encapsulation in five spherical fullerenes C60,C240,C540,C960, and C1500. We exploit the 6–12 Lennard-Jones potential function and the continuum approximation to model the surface binding energies between methane and spherical fullerenes of varying sizes. Our results show that for a methane molecule interacting inside a spherical fullerene, the binding energies are minimized at locations which become closer to the fullerene wall as the size of the fullerene increases. However, we find that the methane molecule would require an applied external force to overcome the repulsive energy barrier in order to be encapsulated into a C60 fullerene. The present modeling indicates that the optimal minimum energy for methane storage in any spherical fullerene occurs for a fullerene with radius ≃6.17 Å, with a corresponding potential energy of ≃0.22 eV which occurs for a fullerene bigger than a C60 but slightly smaller than a C240 as the ideal spherical fullerene for methane encapsulation. Overall, our results are in very good agreement with other theoretical studies and molecular dynamics simulations, and show that fullerenes might be good candidates for gas storage. However, the major advantage of the approach adopted here is the derivation of explicit analytical formulae from which numerical results for varying physical scenarios may be readily obtained.
Publisher: IEEE
Date: 02-2008
Publisher: Royal Society of Chemistry (RSC)
Date: 2020
DOI: 10.1039/C9RA10439A
Abstract: A variational model is proposed to describe rippled graphene on a substrate, and obtain the relationship between total energy and substrate length.
Publisher: Informa UK Limited
Date: 07-05-2010
Publisher: Elsevier BV
Date: 07-2011
Publisher: Elsevier BV
Date: 09-2012
Publisher: SAGE Publications
Date: 26-07-2010
Abstract: Modelling molecular interactions in a benzene dimer is a typical ex le of a class of problems involving aromatic molecules. Although many studies on the benzene dimer have been carried out both theoretically and experimentally and energetically favorable structures of a benzene dimer have been found, an investigation of all equilibrium structures of a benzene dimer has not so far been done. Previously, the present authors investigated the interaction energy and geometries of a benzene dimer for the special case in which only one rotational angle is used to describe the relative position between two benzene molecules. In general, two rotational angles are necessary to describe the most general relative orientation. Here, we apply the same approach in which the discrete atomic structure of a benzene molecule is replaced by two continuous rings of atoms, namely an inner carbon ring and an outer hydrogen ring with average constant atomic densities and the molecular interaction forces are calculated from the Lennard-Jones potential function. An analytical expression for the interaction energy is obtained which we use to determine all equilibrium structures of a benzene dimer as well as to determine those domains in which certain configurations are more favorable than others. Our results show that parallel, T-shaped, parallel displaced and tilted structures are all possible configurations of a benzene dimer and they exist at different regions of vertical and offset distances at different energy levels.
Publisher: American Scientific Publishers
Date: 04-2011
Publisher: SAGE Publications
Date: 09-2010
Publisher: SAGE Publications
Date: 26-07-2010
Abstract: Nanotechnology is currently an area of intense research activity. To date there is some limited experimental data, and considerably more computational data arising from molecular dynamics simulations, but there is very little applied mathematical modelling from the disciplines associated with modelling, namely mathematics and mechanics. This paper reviews some of the mathematical and mechanical modelling contributions for interacting molecular structures. Modelling can indicate to the experimentalist materials and geometry where a certain outcome may be anticipated. A combined modelling—computational approach can make efficient a computational procedure that alone is not practical. The present review aims to provide an overview of contributions to date, but is necessarily focussed on the work of the present authors, since the number of mathematically orientated workers in the field is limited.
Publisher: The Royal Society
Date: 08-01-2008
Abstract: Carbon nanotubes are nanostructures that promise much in the area of constructing nanoscale devices due to their enhanced mechanical, electrical and thermal properties. In this paper, we examine a gigahertz oscillator that comprises a carbon nanotube oscillating in a uniform concentric ring or bundle of carbon nanotubes. A number of existing results for nanotube oscillators are employed to analyse the design considerations of optimizing such a device, and significant new results are also derived. These include a new analytical expression for the interaction per unit length of two parallel carbon nanotubes involving the Appell hypergeometric functions. This expression is employed to precisely determine the relationship between the bundle radius and the radii of the nanotubes forming the bundle. Furthermore, several pragmatic approximations are also given, including the relationships between the bundle radius and the constituent nanotube radius and the oscillating tube radius and the bundle nanotube radius. We also present a simplified analysis of the force and energy for a nanotube oscillating in a nanotube bundle leading to an expression for the oscillating frequency and the maximum oscillating frequency, including constraints on configurations under which this maximum is possible.
Publisher: American Chemical Society (ACS)
Date: 29-06-2007
DOI: 10.1021/JP0721402
Publisher: Springer Science and Business Media LLC
Date: 11-2013
Publisher: Institution of Engineering and Technology (IET)
Date: 2010
Publisher: IOP Publishing
Date: 16-10-2007
Publisher: American Chemical Society (ACS)
Date: 27-06-2013
DOI: 10.1021/LA401446S
Abstract: The metal-organic framework beryllium benzene tribenzoate (Be-BTB) has recently been reported to have one of the highest gravimetric hydrogen uptakes at room temperature. Storage at room temperature is one of the key requirements for the practical viability of hydrogen-powered vehicles. Be-BTB has an exceptional 298 K storage capacity of 2.3 wt % hydrogen. This result is surprising given that the low adsorption enthalpy of 5.5 kJ mol(-1). In this work, a combination of atomistic simulation and continuum modeling reveals that the beryllium rings contribute strongly to the hydrogen interaction with the framework. These simulations are extended with a thermodynamic energy optimization (TEO) model to compare the performance of Be-BTB to a compressed H2 tank and benchmark materials MOF-5 and MOF-177 in a MOF-based fuel cell. Our investigation shows that none of the MOF-filled tanks satisfy the United States Department of Energy (DOE) storage targets within the required operating temperatures and pressures. However, the Be-BTB tank delivers the most energy per volume and mass compared to the other material-based storage tanks. The pore size and the framework mass are shown to be contributing factors responsible for the superior room temperature hydrogen adsorption of Be-BTB.
Publisher: IOP Publishing
Date: 07-10-2011
DOI: 10.1088/0957-4484/22/44/445707
Abstract: We investigate the van der Waals interaction of D,L-Ala cyclopeptide nanotubes and various ions, ion-water clusters and C(60) fullerenes, using the Lennard-Jones potential and a continuum approach which assumes that the atoms are smeared over the peptide nanotube providing an average atomic density. Our results predict that Li(+), Na(+), Rb(+) and Cl(-) ions and ion-water clusters are accepted into peptide nanotubes of 8.5 Å internal diameter whereas the C(60) molecule is rejected. The model indicates that the C(60) molecule is accepted into peptide nanotubes of 13 Å internal diameter, suggesting that the interaction energy depends on the size of the molecule and the internal diameter of the peptide nanotube. This result may be useful for the design of peptide nanotubes for drug delivery applications. Further, we also find that the ions prefer a position inside the peptide ring where the energy is minimum. In contrast, Li(+)-water clusters prefer to be in the space between each peptide ring.
Publisher: Elsevier BV
Date: 05-2011
Publisher: Cambridge University Press (CUP)
Date: 2018
DOI: 10.1017/S1446181117000396
Abstract: Macroscale “continuum” level predictions are made by a new way to construct computationally efficient “wrappers” around fine-scale, microscopic, detailed descriptions of dynamical systems, such as molecular dynamics. It is often significantly easier to code a microscale simulator with periodicity: so the challenge addressed here is to develop a scheme that uses only a given periodic microscale simulator specifically, one for atomistic dynamics. Numerical simulations show that applying a suitable proportional controller within “action regions” of a patch of atomistic simulation effectively predicts the macroscale transport of heat. Theoretical analysis establishes that such an approach will generally be effective and efficient, and also determines good values for the strength of the proportional controller. This work has the potential to empower systematic analysis and understanding at a macroscopic system level when only a given microscale simulator is available.
Publisher: Elsevier BV
Date: 12-2007
Publisher: Royal Society of Chemistry (RSC)
Date: 2015
DOI: 10.1039/C4RA13496F
Abstract: For nanoparticles penetrating biological tissue, modelling indicates that without external forces, carbon nanoparticles will remain trapped in lipid bilayers.
Publisher: Elsevier BV
Date: 04-2008
Publisher: American Institute of Physics
Date: 2009
DOI: 10.1063/1.3203251
Publisher: IOP Publishing
Date: 10-03-2008
Publisher: American Scientific Publishers
Date: 11-2013
Publisher: Springer Netherlands
Date: 2009
Publisher: Springer Science and Business Media LLC
Date: 20-12-2013
Publisher: Oxford University Press (OUP)
Date: 10-08-2011
DOI: 10.1093/QJMAM/HBR013
Publisher: Springer Science and Business Media LLC
Date: 22-06-2012
Publisher: Trans Tech Publications, Ltd.
Date: 09-2012
DOI: 10.4028/WWW.SCIENTIFIC.NET/MSF.700.96
Abstract: We examine a class of nano-oscillator comprising an outer carbon nanotube that isuncapped and xed, within which oscillates an inner nanotube. The inner tube is acted on byexcess van der Waals forces as well as an applied sinusoidal force, which may result from a timevarying external electric eld acting on ions functionalised to the inner nanotube. Although theequations of motion contain both a non-linear position dependence as well as a time-varyingterm by neglecting dissipative terms and considering the solution in di erent spatial domains,we reduce the problem to one with an analytical solution which we then evolve in time, solvingfor the domain boundaries to generate a full numerical solution.We nd a frequency dependenceon the maximum extrusion distance which is suggestive that the system may be used as the basisfor an accurate frequency detection device with sensitivity in the gigahertz range. We also notethat for a xed frequency of forcing, variations in the electric eld strength lead to changesin the litude and frequency of the response of the oscillator. Finally, we also commentthat an analysis of the position-momentum space reveals that in general the system occupiesall combinations of position and momentum inside a total energy envelop. However, carefullychosen initial conditions may lead to highly deterministic paths, where small perturbations tothese initial condtions quickly lead to a loss of order and thus we conclude these systems exhibitchaotic behaviour in these cases.
Publisher: Oxford University Press (OUP)
Date: 07-03-2007
DOI: 10.1093/QJMAM/HBM005
Publisher: IOP Publishing
Date: 23-03-2010
DOI: 10.1088/0957-4484/21/15/155305
Abstract: Experimental and predicted flow rates through carbon nanotubes vary considerably but generally are reported to be well in excess of that predicted by the conventional Poiseuille flow, and therefore nanotubes embedded in a matrix might provide membranes with exceptional mass transport properties. In this paper, applied mathematical modelling is undertaken to estimate the three forces acting on a nanotube bundle, namely the molecular interaction force, the viscous force, and the static pressure force. In deducing estimates of these forces we introduce a modification of the notion of the effective dead area for a carbon nanotube membrane, and we calculate the total forces necessary to push one or more of the nanotubes out of the bundle, thus creating a channel through which further enhancement of flow may take place. However, careful analysis shows that the nett dislodgement force is entirely independent on the useable flow area, but rather depends only on the total cross-sectional area perpendicular to the flow. This rather surprising result is a consequence of the flow being steady and a balance of the viscous and pressure forces.
Publisher: Informa UK Limited
Date: 12-08-2008
Publisher: IOP Publishing
Date: 30-12-2021
Abstract: A mathematical model is developed to study the folding behaviour of multi–layer graphene sheets supported on a substrate. The conformation of the fold is determined from variational considerations based on two energies, namely the graphene elastic energy and the van der Waals (vdW) interaction energy between graphene layers and the substrate. The model is nondimensionalized and variational calculus techniques are then employed to determine the conformation of the fold. The Lennard–Jones potential is used to determine the vdW interaction energy as well as the graphene–substrate and graphene–graphene spacing distances. The folding conformation is investigated under three different approximations of the total line curvature. Our findings show good agreement with experimental measurements of multi–layer graphene folds from the literature.
Publisher: IEEE
Date: 02-2010
Publisher: Elsevier BV
Date: 05-2008
Publisher: Royal Society of Chemistry (RSC)
Date: 2010
DOI: 10.1039/B9NR00433E
Abstract: In this paper, we survey a number of existing geometric structures which have been proposed by the authors as possible models for various nanotubes. Atoms assemble into molecules following the laws of quantum mechanics, and in general computational approaches to predicting the molecular structure can be arduous and involve considerable computing time. Fortunately, nature favours minimum energy structures which tend to be either very symmetric or very unsymmetric, and which therefore can be analyzed from a geometrical perspective. The conventional rolled-up model of nanotubes completely ignores any effects due to curvature and the present authors have proposed a number of exact geometric models. Here we review a number of these recent developments relating to the geometry of nanotubes, including both the traditional rolled-up models and some exact polyhedral constructions. We review a number of formulae for four materials, carbon, silicon, boron and boron nitride, and we also include results for the case when the bond lengths may take on distinct values.
Publisher: Springer Science and Business Media LLC
Date: 18-06-2013
Publisher: Springer Science and Business Media LLC
Date: 2015
DOI: 10.1007/S11538-014-0056-2
Abstract: Fullerenes have generated a great deal of interest in recent years, due to their properties and potential applications in many fields, including medicine. In this paper, we study an antiviral fullerene compound which may be used to treat the human immunodeficiency virus (HIV). We formulate a mathematical model which can describe the interaction energy between the C[Formula: see text] antiviral compounds and the HIV. In particular, this paper predicts the energy and force arising from the interaction between HIV active region and the antiviral molecule which is attached to the external surface of a fullerene C[Formula: see text]. These interactions are calculated based on the structure of the antiviral molecules. Our results show that the binding of fullerene C[Formula: see text] to the antiviral molecules increases the efficiency of the compound to prohibit the activity of HIV.
Publisher: Springer Science and Business Media LLC
Date: 30-03-2006
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 04-04-2018
Publisher: IOP Publishing
Date: 21-05-2008
Publisher: IOP Publishing
Date: 18-03-2009
DOI: 10.1088/0953-8984/21/14/144214
Abstract: In this paper, we investigate the mechanics of a nanoscaled gigahertz oscillator comprising a carbon molecule oscillating within the centre of a uniform concentric ring or bundle of carbon nanotubes. Two kinds of oscillating molecules are considered, which are a carbon nanotube and a C(60) fullerene. Using the Lennard-Jones potential and the continuum approach, we obtain a relation between the bundle radius and the radii of the nanotubes forming the bundle, as well as the optimum bundle size which gives rise to the maximum oscillatory frequency for both the nanotube-bundle and the C(60)-bundle oscillators. While previous studies in this area have been undertaken through molecular dynamics simulations, this paper emphasizes the use of applied mathematical modelling techniques, which provides considerable insight into the underlying mechanisms of the nanoscaled oscillators. The paper presents a synopsis of the major results derived in detail by the present authors (Cox et al 2007 Proc. R. Soc. A 464 691-710 and Cox et al 2007 J. Phys. A: Math. Theor. 40 13197-208).
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 28-02-2023
DOI: 10.21914/ANZIAMJ.V62.16642
Abstract: This is a report on the Lovells Springs challenge that was brought to the Mathematics in Industry Study Group at the University of Newcastle, Australia, in January 2020. The design of a furnace that heats steel rods to make them malleable and allow the reshaping of the rods into coiled springs is the challenge. Mathematical modelling of heat transport in the half-metre long furnace vestibule predicts the effect of vestibule geometry on the temperature of rods entering the furnace, and provides guidelines for deciding on the dimensions of the vestibule for improved energy efficiency of heating. Models considered include treating the rods as equivalent steel sheets, and as discrete steel rods. The relative importance of radiative and convective heat transfer mechanisms is considered. A longer vestibule, with length one or two metres, is recommended for improved heating efficiency of rods thicker than 25mm.
Publisher: Royal Society of Chemistry (RSC)
Date: 2015
DOI: 10.1039/C5RA08276E
Abstract: Variational calculus is employed to determine the folding behaviour of a single graphene sheet.
Publisher: American Chemical Society (ACS)
Date: 23-10-2009
DOI: 10.1021/JP904985R
Publisher: Royal Society of Chemistry (RSC)
Date: 2016
DOI: 10.1039/C6RA02126C
Abstract: Mathematical modelling, comprising Lennard–Jones potential and calculus of variations, is utilized to obtain the energy equations arising from AFM probe and substrate, leading to deflection equations of AFM cantilever.
Publisher: American Institute of Physics
Date: 2009
DOI: 10.1063/1.3203231
Publisher: AIP Publishing
Date: 10-04-2006
DOI: 10.1063/1.2185607
Abstract: The problem of electric field-induced force between spheres is fundamental to electrorheological fluids. Previously published experimental results indicate that the interaction force between two spheres under an external field is not adequately explained by the existing approximate and numerical methods. The specific models compared were dipole, dipole with local field corrections and a finite-element analysis. This letter employs an exact solution (via the equivalent multipole-moment method) to the electrostatic problem which accurately predicts the low-frequency experimental results at all measured interstices. The solution presented later is self-contained and addresses specifically the geometry of the previously mentioned experimental results. While more general solutions have been published previously, they are more complex than is required by this problem. The solution presented here is accurate for all sphere spacings, but in particular could apply to nano-spheres in close proximity.
Publisher: American Scientific Publishers
Date: 08-2015
Publisher: American Chemical Society (ACS)
Date: 25-09-2008
DOI: 10.1021/JP803023Q
Publisher: Springer Science and Business Media LLC
Date: 30-08-2010
Publisher: Springer Science and Business Media LLC
Date: 08-11-2014
DOI: 10.1007/S00249-013-0936-7
Abstract: Nanotechnology is a rapidly expanding research area, and it is believed that the unique properties of molecules at the nano-scale will prove to be of substantial benefit to mankind, especially so in medicine and electronics. Here we use applied mathematical modelling exploiting the basic principles of mechanics and the 6-12 Lennard-Jones potential function together with the continuum approximation, which assumes that intermolecular interactions can be approximated by average atomic surface densities. We consider the equilibrium offset positions for both single-strand and double-strand DNA molecules inside a single-walled carbon nanotube, and we predict offset positions with reference to the cross-section of the carbon nanotube. For the double-strand DNA, the potential energy is determined for the general case for any helical phase angle ϕ, but we also consider a special case when ϕ = π, which leads to a substantial simplification in the analytical expression for the energy. As might be expected, our results confirm that the global minimum energy positions for a single-strand DNA molecule and a double-strand DNA molecule will lie off axis and they become closer to the tube wall as the radius of the tube increases.
Publisher: Springer Science and Business Media LLC
Date: 21-12-2011
Publisher: IEEE
Date: 2006
Publisher: SPIE-Intl Soc Optical Eng
Date: 2007
Publisher: Elsevier BV
Date: 06-2007
Publisher: Elsevier BV
Date: 08-2011
Publisher: IEEE
Date: 2006
Publisher: MDPI AG
Date: 17-08-2018
DOI: 10.3390/NANO8080624
Abstract: The conventional rolled-up model for carbon nanocones assumes that the cone is constructed from a rolled-up graphene sheet joined seamlessly, which predicts five distinct vertex angles. This model completely ignores any effects due to the changing curvature, and all bond lengths and bond angles are assumed to be those for the planar graphene sheet. Clearly, curvature effects will become more important closest to the cone vertex, and especially so for the cones with the smaller apex angles. Here, we construct carbon nanocones which, in the assembled cone, are assumed to comprise bond lengths and bond angles that are, as far as possible, equal throughout the structure at the same distance from the conical apex. The predicted bond angles and bond lengths are shown to agree well with those obtained by relaxing the conventional rolled-up model using Lammps software (version: 11 September 2008). The major objective here is not simply to model physically realisable carbon nanocones for which numerical procedures are far superior, but rather, to produce an improved model that takes curvature effects close to the vertex into account, and from which we may determine an analytical formula which represents an improvement on the conventional rolled-up model.
Publisher: IOP Publishing
Date: 05-2021
Abstract: We present a novel analytical prediction for the effective bending rigidity γ eff of multi–layer graphene sheets. Our approach involves using a variational model to determine the folding conformation of multi–layer graphene sheets where the curvature of each graphene layer is taken into account. The Lennard–Jones potential is used to determine the van der Waals interaction energy per unit area and the spacing distance between graphene layers. The mid–line of the folded multi–layer graphene is described by a solution derived in previous work for folded single– and multi–layer graphene. Several curves are obtained for the single–layer solution using different values of the bending rigidity γ , and compared to the mid–line of the folded multi–layer graphene. The total area between these curves and the mid–line is calculated, and the value of γ eff is determined by the single–layer curve for which this area is minimized. While there is some disagreement in the literature regarding the relationship between the bending rigidity and the number of layers, our analysis reveals that the bending rigidity of multi–layer graphene follows an approximate square–power relationship with the number of layers N , where N 7. This trend is in line with theoretical and experimental studies reported in the literature.
Publisher: Informa UK Limited
Date: 2012
Publisher: Springer Science and Business Media LLC
Date: 08-12-2007
Publisher: Springer Science and Business Media LLC
Date: 28-06-2011
Publisher: Elsevier BV
Date: 10-2007
Publisher: Springer Science and Business Media LLC
Date: 27-03-2014
Publisher: Elsevier BV
Date: 10-2010
Publisher: Elsevier BV
Date: 12-2015
DOI: 10.1016/J.JTBI.2015.09.020
Abstract: Nanoparticles have considerable promise for many applications in electronics, energy storage, bioscience and biotechnologies. Here we use applied mathematical modelling to exploit the basic principles of mechanics and the 6-12 Lennard-Jones potential function together with the continuum approach, which assumes that a discrete atomic structure can be replaced by an average constant atomic surface density of atoms that is assumed to be smeared over each molecule. We identify a circular hole in a graphene sheet as a nanopore and we consider the molecular interaction energy for both single-strand and double-strand DNA molecules assumed to move through the circular hole in a graphene sheet to determine the radius b of the hole that gives the minimum energy. By minimizing the interaction energy, we observe that the single-strand DNA and double-strand DNA molecules penetrate through a graphene nanopore when the pore radii b> 7.8Å and b> 12.7Å, respectively. Our results can be adopted to offer new applications in the atomic surface processes and electronic sensing.
Publisher: Springer Science and Business Media LLC
Date: 30-12-2010
Publisher: MDPI AG
Date: 16-07-2018
DOI: 10.20944/PREPRINTS201807.0272.V1
Abstract: The conventional rolled-up model for carbon nanocones assumes that the cone is constructed from a rolled-up graphene sheet joined seamlessly, which predicts five distinct vertex angles. This model completely ignores any effects due to the changing curvature and all bond lengths and bond angles are assumed to be those for the planar graphene sheet. Clearly curvature effects will become more important closest to the cone vertex, and especially so for the cones with the smaller apex angles. Here we construct carbon nanocones which in the assembled cone are assumed to comprise bond lengths and bond angles which are, as far as possible, equal throughout the structure at the same distance from the conical apex. Predicted bond angles and bond lengths are shown to agree well with those obtained by relaxing the conventional rolled-up model using the LAMMPS software. The major objective here is not simply to model physically realisable carbon nanocones for which numerical procedures are far superior, but rather to produce an improved model that takes into account curvature effects close to the vertex, and from which we may determine an analytical formula which represents an improvement on that for the conventional rolled-up model.
Publisher: Institution of Engineering and Technology (IET)
Date: 02-2014
Publisher: Inderscience Publishers
Date: 2008
Publisher: Springer Science and Business Media LLC
Date: 09-2014
Publisher: Informa UK Limited
Date: 11-2011
Publisher: Springer Science and Business Media LLC
Date: 22-03-2018
DOI: 10.1007/S00894-018-3630-Y
Abstract: The low bending rigidity of graphene facilitates the formation of folds into the structure. This curvature change affects the reactivity and electron transport of the sheet. One novel extension of this is the intercalation of small molecules into these folds. We construct a model incorporating a single-walled carbon nanotube into a sheet of folded graphene. Variational calculus techniques are employed to determine the minimum energy structure and the resulting curves are shown to agree well with molecular dynamics study. Graphical Abstract Using calculus of variations, the elastic bending energy and van der Waals energy are minimised giving rise to Euler-Lagrange equation for which analytical solutions are derived to determine the optimal curved sturctures of graphene wrapped around carbon nanotubes . Overall agreement between the analytical solutions (with different values of bending rigidities) and results from molecular dynamics simulations (grey) is shown here for (6,6), (8,8) and (10,10) armchair nanotubes, respectively.
Publisher: Cambridge University Press (CUP)
Date: 07-2015
Publisher: Springer Science and Business Media LLC
Date: 28-04-2016
Publisher: American Scientific Publishers
Date: 05-2016
Publisher: IOP Publishing
Date: 31-01-2008
DOI: 10.1088/0957-4484/19/7/075704
Abstract: For future nanoelectromechanical signalling devices, it is vital to understand how to connect various nanostructures. Since boron nitride nanostructures are believed to be good electronic materials, in this paper we elucidate the classification of defect geometries for combining boron nitride structures. Specifically, we determine possible joining structures between a boron nitride nanotube and a flat sheet of hexagonal boron nitride. Firstly, we determine the appropriate defect configurations on which the tube can be connected, given that the energetically favourable rings for boron nitride structures are rings with an even number of sides. A new formula E = 6+2J relating the number of edges E and the number of joining positions J is established for each defect, and the number of possible distinct defects is related to the so-called necklace and bracelet problems of combinatorial theory. Two least squares approaches, which involve variation in bond length and variation in bond angle, are employed to determine the perpendicular connection of both zigzag and armchair boron nitride nanotubes with a boron nitride sheet. Here, three boron nitride tubes, which are (3, 3), (6, 0) and (9, 0) tubes, are joined with the sheet, and Euler's theorem is used to verify geometrically that the connected structures are sound, and their relationship with the bonded potential energy function approach is discussed. For zigzag tubes (n,0), it is proved that such connections investigated here are possible only for n isible by 3.
Publisher: Royal Society of Chemistry (RSC)
Date: 2012
DOI: 10.1039/C2NR00042C
Abstract: We survey various molecular structures which have been proposed as possible nanocontainers for methane storage. These are molecular structures that have been investigated through either experiments, molecular dynamics simulations or mathematical modelling. Computational simulation and mathematical modelling play an important role in predicting and verifying experimental outcomes, but both have their limitations. Even though recent advances have greatly improved computations, due to the large number of atoms and force field calculations involved, computational simulations can still be time consuming as compared to an instantaneous mathematical modelling approach. On the other hand, underlying an ideal mathematical model, there are many assumptions and approximations, but such modelling often reveals the key physical parameters and optimal configurations. Here, we review methane adsorption for three conventional nanostructures, namely graphite, single and multi-walled carbon nanotubes, and nanotube bundles (including interstitial and groove sites), and we survey methane adsorption in other molecular structures including metal organic frameworks. We also include an examination of minimum binding energies, equilibrium distances, gravimetric and volumetric uptakes, volume available for adsorption, as well as the effects of temperature and pressure on the adsorption of methane onto these molecular structures.
Publisher: The Royal Society
Date: 03-10-2012
Abstract: We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light, and that are complementary to the Lorentz transformation, giving rise to the Einstein special theory of relativity that applies to relative velocities less than the speed of light. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but, most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions. Making use of the dependence on relative velocity of the Lorentz transformation, the paper provides an elementary derivation of the new transformations between inertial frames for relative velocities v in excess of the speed of light c , and further we suggest two possible criteria from which one might infer one set of transformations as physically more likely than the other. If the energy–momentum equations are to be invariant under the new transformations, then the mass and energy are given, respectively, by the formulae and where denotes the limiting momentum for infinite relative velocity. If, however, the requirement of invariance is removed, then we may propose new mass and energy equations, and an ex le having finite non-zero mass in the limit of infinite relative velocity is given. In this highly controversial topic, our particular purpose is not to enter into the merits of existing theories, but rather to present a succinct and carefully reasoned account of a new aspect of Einstein's theory of special relativity, which properly allows for faster than light motion.
Publisher: Springer Science and Business Media LLC
Date: 16-10-2010
Publisher: Elsevier BV
Date: 2016
Publisher: IOP Publishing
Date: 13-01-2009
DOI: 10.1088/0953-8984/21/7/075301
Abstract: In this paper, we introduce an idealized model of silicon nanotubes comprising an exact polyhedral geometric structure for single-walled silicon nanotubes. The silicon nanotubes considered here are assumed to be formed by sp(3) hybridization and thus the nanotube lattice is assumed to comprise only squares or skew rhombi. Beginning with the three postulates that all bond lengths are equal, all adjacent bond angles are equal, and all atoms are equidistant from a common axis of symmetry, we derive exact formulae for the geometric parameters such as radii, bond angles and unit cell length. We present asymptotic expansions for these quantities to the first two orders of magnitude. Because of the faceted nature of the polyhedral model we may determine a perceived inner radius for the nanotube, from which an expression for the wall thickness emerges. We also describe the geometric properties of some ultra-small silicon nanotubes. Finally, the values of the diameters for the polyhedral model are compared with results obtained from molecular dynamics simulations and some limited numerical calculations are undertaken to confirm the meta-stability of the proposed structures.
Publisher: Springer Science and Business Media LLC
Date: 27-07-2013
Publisher: The Royal Society
Date: 11-10-2007
Abstract: The discovery of carbon nanotubes and C 60 fullerenes has created an enormous impact on possible new nanomechanical devices. Owing to their unique mechanical and electronic properties, such as low weight, high strength, flexibility and thermal stability, carbon nanotubes and C 60 fullerenes are of considerable interest to researchers from many scientific areas. One aspect that has attracted much attention is the creation of high-frequency nanoscale oscillators, or the so-called gigahertz oscillators, for applications such as ultrafast optical filters and nano-antennae. While there are difficulties for micromechanical oscillators, or resonators, to reach a frequency in the gigahertz range, it is possible for nanomechanical systems to achieve this. This study focuses on C 60 –single-walled carbon nanotube oscillators, which generate high frequencies owing to the oscillatory motion of the C 60 molecule inside the single-walled carbon nanotube. Using the Lennard-Jones potential, the interaction energy of an offset C 60 molecule inside a carbon nanotube is determined, so as to predict its position with reference to the cross-section of the carbon nanotube. By considering the interaction force between the C 60 fullerene and the carbon nanotube, this paper provides a simple mathematical model, involving two Dirac delta functions, which can be used to capture the essential mechanisms underlying such gigahertz oscillators. As a preliminary to the calculation, the oscillatory behaviour of an isolated atom is examined. The new element of this study is the use of elementary mechanics and applied mathematical modelling in a scientific context previously dominated by molecular dynamical simulation.
Publisher: Springer Science and Business Media LLC
Date: 04-05-2011
DOI: 10.1007/S00894-011-1086-4
Abstract: Due to the large number of possible applications of nanoparticles in cosmetic and medical products, the possible hazards of nanoparticles in the human body are a major concern. A worst-case scenario is that nanoparticles might cause health issues such as skin damage or even induce cancer. As a first step to study the toxicity of nanoparticles, we investigate the energy behaviour of a C(60) fullerene interacting with a lipid bilayer. Using the 6-12 Lennard-Jones potential function and the continuous approximation, the equilibrium spacing between the two layers of a bilayer is predicted to be 3.36 Å. On assuming that there is a circular hole in the lipid bilayer, a relation for the molecular interaction energy is determined, involving the circular radius b of the hole and the perpendicular distance Z of the spherical fullerene from the hole. A graph of the minimum energy location Z ( min ) verses the hole radius b shows that a C(60) fullerene first penetrates through a lipid bilayer when b > 6.81 Å, and shows a simple circular relation [Formula: see text] for Z ( min ) positive and b ≤ 6.81 Å. For b > 6.81, the fullerene relocates from the surface of the bilayer to the interior, and as the hole radius increases further it moves to the centre of the bilayer and remains there for increasing hole radii. Accordingly, our modelling indicates that at least for the system with no external forces, the C(60) fullerene will not penetrate through the lipid bilayer but rather remains encased between the two layers at the mid-plane location.
Publisher: The Royal Society
Date: 11-10-2007
Abstract: Owing to their unusual properties, carbon nanostructures such as nanotubes and fullerenes have caused many new nanomechanical devices to be proposed. One such application is that of nanoscale oscillators which operate in the gigahertz range, the so-called gigahertz oscillators. Such devices have potential applications as ultrafast optical filters and nano-antennae. While there are difficulties in producing micromechanical oscillators which operate in the gigahertz range, molecular dynamical simulations indicate that nanoscale devices constructed of multi-walled carbon nanotubes or single-walled carbon nanotubes and C 60 fullerenes could feasibly operate at these high frequencies. This paper investigates the suction force experienced by either an atom or a C 60 fullerene molecule located in the vicinity of an open end of a single-walled carbon nanotube. The atom is modelled as a point mass, the fullerene as an averaged atomic mass distributed over the surface of a sphere. In both cases, the carbon nanotube is modelled as an averaged atomic mass distributed over the surface of an open semi-infinite cylinder. In both cases, the particle being introduced is assumed to be located on the axis of the cylinder. Using the Lennard-Jones potential, the van der Waals interaction force between the atom or C 60 fullerene and the carbon nanotube can be obtained analytically. Furthermore, by integrating the force, an explicit analytic expression for the work done by van der Waals forces is determined and used to derive an acceptance condition, that is whether the particle will be completely sucked into the carbon nanotube by virtue of van der Waals interactions alone, and a suction energy which is imparted to the introduced particle in the form of an increased velocity. The results of the acceptance condition and the calculated suction energy are shown to be in good agreement with the published molecular dynamical simulations. In part II of the paper, a new model is proposed to describe the oscillatory motion adopted by atoms and fullerenes that are sucked into carbon nanotubes.
Publisher: IEEE
Date: 02-2008
Publisher: Elsevier BV
Date: 2016
Publisher: IOP Publishing
Date: 14-01-2009
Publisher: Trans Tech Publications, Ltd.
Date: 09-2012
DOI: 10.4028/WWW.SCIENTIFIC.NET/MSF.700.104
Abstract: We investigate the prospect of methane gas storage in carbon nanotubes, and in particular we determine the interaction energy between a methane molecule and (9, 5), (8, 8) and (10,10) carbon nanotubes. Employing the Lennard-Jones potential together with the continuous approximation, we determine analytically the interaction energy for a methane molecule inside a carbon nanotube. Our results indicate that larger tubes are highly favoured sites for methane storage although smaller tubes might be superior for methane adsorption at higher temperatures, especially in the range 400 − 500 K.
Publisher: Informa UK Limited
Date: 17-03-2010
Publisher: American Chemical Society (ACS)
Date: 29-11-2011
DOI: 10.1021/JP2069094
No related grants have been discovered for Barry Cox.