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A Mathematical Model of Graphene Nanostructures

Rhoads, Daniel Joseph
http://orcid.org/0000-0001-8294-0853
http://rave.ohiolink.edu/etdc/view?acc_num=akron1438978423

Abstract Details

2015, Master of Science, University of Akron, Applied Mathematics.
Having already shown great potential for novel engineering applications, graphene and other carbon-based nanostructures (CNSTR) are being investigated for use in nanotechnology and Nanoelectromechanical Systems. For the design of nanoscale devices, it is important to understand the geometries and behavior of CNSTR. We study an atomistic energy-based model for graphene. We model a graphene sheet as a two-dimensional sheet of atoms in ℜ³. We derive an expression for the total internal energy of a CNSTR considering only the energy of covalently bonded atoms, the energy of the local interaction between non-bonded atoms, and the energy due to the bending of adjacent atomic bonds. The configuration of a CNSTR is initialized, and we run simulations using gradient flow dynamics to minimize total energy and determine equilibrium configurations. Predictions from our model show that the structure of the final configuration depends on the relative strengths of the forces as well as the initial configuration.
Dmitry Golovaty, Dr. (Advisor)
Patrick Wilber, Dr. (Committee Member)
Malena Espanol, Dr. (Committee Member)
74 p.
Materials Science; Mathematics; Nanotechnology
mathematical model; carbon nanotube; carbon nanoribbon; carbon nanoscroll; graphene; nanostructure; gradient flow dynamics; minimize energy; atomistic model; discrete model; van der waals;

Recommended Citations

Citations

  • Rhoads, D. J. (2015). A Mathematical Model of Graphene Nanostructures [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1438978423

    APA Style (7th edition)

  • Rhoads, Daniel. A Mathematical Model of Graphene Nanostructures. 2015. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1438978423.

    MLA Style (8th edition)

  • Rhoads, Daniel. "A Mathematical Model of Graphene Nanostructures." Master's thesis, University of Akron, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=akron1438978423

    Chicago Manual of Style (17th edition)

akron1438978423
525
© 2015, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.