Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications
© 2016 The Author(s). 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 insigh...
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th-mahidol.436292019-03-14T15:04:41Z Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications Duangkamon Baowan James M. Hill Mahidol University South Carolina Commission on Higher Education University of South Australia Engineering © 2016 The Author(s). 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. 2018-12-11T02:46:39Z 2019-03-14T08:04:41Z 2018-12-11T02:46:39Z 2019-03-14T08:04:41Z 2016-11-01 Review Advances in Mechanical Engineering. Vol.8, No.11 (2016), 1-16 10.1177/1687814016677022 16878140 16878132 2-s2.0-85002168881 https://repository.li.mahidol.ac.th/handle/123456789/43629 Mahidol University SCOPUS https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85002168881&origin=inward |
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© 2016 The Author(s). 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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Mahidol University |
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Mahidol University Duangkamon Baowan James M. Hill |
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Review |
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Duangkamon Baowan James M. Hill |
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Duangkamon Baowan |
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Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications |
title_short |
Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications |
title_full |
Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications |
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Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications |
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Mathematical modeling of interaction energies between nanoscale objects: A review of nanotechnology applications |
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mathematical modeling of interaction energies between nanoscale objects: a review of nanotechnology applications |
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2018 |
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https://repository.li.mahidol.ac.th/handle/123456789/43629 |
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