Mechanics of nanoscale orbiting systems

Chan, Yue; Thamwattana, Ngamta; Cox, Grant M.; Hill, James M.

doi:10.1007/s10910-008-9516-y

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…The equilibrium configurations of carbon atoms and C 60 fullerenes inside carbon nanotori have been determined by Hilder and Hill, [25][26][27] Chan and colleagues, 28,29 and Sumetpipat et al 30 Even though complicated analytical expressions are derived, the energy profiles are easily obtained utilizing algebraic packages such as Maple. Furthermore, the interaction energy between two nanocones has been investigated by Baowan and Hill [31][32][33] and Ansari et al, 34 where the spacing between the two cone surfaces is determined to be 3 Å .…”

Section: Mechanics Of Nanostructuresmentioning

confidence: 99%

“…The continuum or continuous approximation has been successfully applied to a number of systems, including the interaction energy between nanostructures of various types and shapes, namely, carbon fullerenes, 6,10,11 carbon nanotubes, 6,[12][13][14][15][16][17][18][19][20][21] carbon nanotube bundles, [22][23][24] carbon nanotori, [25][26][27][28][29][30] carbon nanocones, [31][32][33][34] carbon nanostacked cups, 35 fullerene-nanotube, 8,[36][37][38][39][40][41][42][43][44][45][46] and TiO 2 nanotubes. [47][48][49] Moreover, this method has also been used in systems involving proteins and enzymes, [50][51][52] DNA, [52][53]…”

Section: Lennard-jones Atomic Interaction Potential and The Continuous Approachmentioning

confidence: 99%

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Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications

Baowan

Hill

2016

Advances in Mechanical Engineering

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In many nanotechnology areas, there is often a lack of well-formed conceptual ideas and sophisticated mathematical modeling in the analysis of fundamental issues involved in atomic and molecular interactions of nanostructures. Mathematical modeling can generate important insights into complex processes and reveal optimal parameters or situations that might be difficult or even impossible to discern through either extensive computation or experimentation. We review the use of applied mathematical modeling in order to determine the atomic and molecular interaction energies between nanoscale objects. In particular, we examine the use of the 6-12 Lennard-Jones potential and the continuous approximation, which assumes that discrete atomic interactions can be replaced by average surface or volume atomic densities distributed on or throughout a volume. The considerable benefit of using the Lennard-Jones potential and the continuous approximation is that the interaction energies can often be evaluated analytically, which means that extensive numerical landscapes can be determined virtually instantaneously. Formulae are presented for idealized molecular building blocks, and then, various applications of the formulae are considered, including gigahertz oscillators, hydrogen storage in metal-organic frameworks, water purification, and targeted drug delivery. The modeling approach reviewed here can be applied to a variety of interacting atomic structures and leads to analytical formulae suitable for numerical evaluation.

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Section: Mechanics Of Nanostructuresmentioning

confidence: 99%

Section: Lennard-jones Atomic Interaction Potential and The Continuous Approachmentioning

confidence: 99%

Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications

Baowan

Hill

2016

Advances in Mechanical Engineering

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“…After the precession, if we apply an opposite retarding magnetic force at the contact point, then the molecule will return to its original standing position. We next investigate some nanoscale orbiting systems; in particular, we study an atom and a C 60 fullerene orbiting around a single infinitely long carbon nanotube and a C 60 fullerene orbiting around a C 1500 fullerene [3]. We find that the circular orbiting frequencies of the proposed nanosystems are in the gigahertz range and the classification of their orbiting paths is determined numerically.…”

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confidence: 99%

Some Mathematical Models Arising in Nano- And Bio-Technology

Chan

2010

Bull. Aust. Math. Soc.

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In this thesis, three mechanical models arising from nanoscale and biological systems are investigated, namely the dynamics of various nanostructures, the axial buckling of carbon nanotubes and nanopeapods, and the worm-like chain model for stretched semi-flexible molecules and the utilization of such a model for investigating molecular stretching in the connective tissue extracellular matrix. In nanomechanics, we investigate the motion of both a carbon atom inside a carbon nanotube and a C 60 fullerene inside a carbon nanotube [4]. We assume a continuous model for which the atoms are assumed to be smeared across the surface of the molecule, so that the pairwise molecular energy can be approximated by performing surface integrals. The spiral path of the atom is found to be stable, but the spiral path of the C 60 fullerene is shown to only exist for a few picoseconds. Next, we investigate the motion of a nanoscale tippe top spinning on the interior of a single-walled carbon nanotube in the presence of a variable magnetic field [5]. Unlike the classical tippe top, the nanoscale tippe top does not flip over since the gravitational effect is insignificant at the nanoscale. After the precession, if we apply an opposite retarding magnetic force at the contact point, then the molecule will return to its original standing position. We next investigate some nanoscale orbiting systems; in particular, we study an atom and a C 60 fullerene orbiting around a single infinitely long carbon nanotube and a C 60 fullerene orbiting around a C 1500 fullerene [3]. We find that the circular orbiting frequencies of the proposed nanosystems are in the gigahertz range and the classification of their orbiting paths is determined numerically.

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Restricted Three Body Problems at the Nanoscale

Chan

Thamwattana²,

Hill³

2009

Few-Body Syst

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In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C 60 fullerenes, and a carbon atom and two C 60 fullerenes. We model the van der Waals forces between the fullerenes by the Lennard-Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes are approximated by the continuous approach, so that the total molecular energy between two fullerenes can be determined analytically. Since we assume that such interactions between the molecules occur at sufficiently large distance, the classical three body problems analysis is legitimate to determine the collective angular velocity of the two and three C 60 fullerenes at the nanoscale. We find that the maximum angular frequency of the two and three fullerenes systems reach the terahertz range and we determine the stationary points and the points which have maximum velocity for the carbon atom for the carbon atom and the two fullerenes system.

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Mechanics of nanoscale orbiting systems

Cited by 4 publications

References 19 publications

Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications

Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications

Some Mathematical Models Arising in Nano- And Bio-Technology

Restricted Three Body Problems at the Nanoscale

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