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Determination of Elastic Properties of Graphene and Carbon-Nanotubes Using Brenner Potential: The Maximum Attainable Numerical Precision

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This paper explores the maximum attainable numerical precision in the computation of stiffness of graphene sheet and carbon nanotubes (CNTs) using Brenner potential and Cauchy-Born rule. The extent to which the round-off and truncation errors can affect the precision of computed stiffness values is demonstrated for a finite graphene sheet and CNT. Small displacement method, local potential-fit method, and finite difference method are employed to determine the stiffness. The optimum trial displacement value to be used in these methods are determined. The corresponding maximum attainable precision in the computed stiffness is reported. Instability of the small displacement method that could result from the use of non-equilibrium configuration of graphene/CNT is highlighted. A method to circumvent this instability is proposed.
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Keywords: BRENNER POTENTIAL; CARBON NANOTUBES; ERROR ANALYSIS; FINITE DIFFERENCE METHOD; GRAPHENE; NUMERICAL PRECISION; STIFFNESS

Document Type: Research Article

Publication date: 2006-06-01

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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