Modeling of nonbonded interactions in graphene and carbon nanotubes

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GolovatyDMS-1009849 Possible applications of graphene -- a sheet of bondedcarbon atoms -- entail understanding and controlling the couplingbetween the mechanical deformation and electronic structure andtransport properties. This coupling is not fully understood, inpart because the basic mechanical response of interactinggraphene sheets is not yet adequately described. Important forpredicting this response are the nonlocal van der Waals forcesbetween layers of graphene and between graphene and a supportingsubstrate. The aim of the project is to develop and investigatecontinuum models of graphene structures that incorporate van derWaals forces in a rigorous way, accounting for long-rangeordering of atoms. Derived via a multiscale analysis, thecontinuum models are formulated within nonlinear rod and shelltheories. Equilibrium configurations of various graphenestructures -- involving multiple layers and different substrates-- under external loads are analyzed using the tools ofbifurcation theory. Also, the thermal properties of nanotubecomposites are investigated within the framework of a networkmodel taking into account the influence of van der Waals forces. Interest in macromolecules composed of carbon atoms hasstimulated a great deal of recent research in materials scienceand physics. Much of this work has focused on carbon nanotubesand, more recently, on the basic structural element of a nanotube-- graphene. Graphene is a single-atom-thick sheet of bondedcarbon atoms. Despite many decades of effort, only within thelast six years have scientists discovered methods for producingisolated individual graphene sheets. This discovery hasstimulated a flurry of experimental and theoretical work on theexceptional mechanical, thermal, and electronic properties ofgraphene. Exploiting these properties could lead to significantadvances in many technologies and yield, for example, moreefficient solar cells, faster microprocessors, or lighter,stronger composite materials. The principal goal of this projectis to employ mathematical modeling to gain a better fundamentalunderstanding of how atomic-scale forces between layers of acarbon nanostructure influence its mechanical and thermalcharacteristics. The project investigators are developing andanalyzing comprehensive multiscale models of interacting graphenelayers by utilizing ideas at the forefront of existing theoriesas well as by introducing new mathematical tools.