Possible applications of graphene -- a sheet of bonded carbon atoms -- entail understanding and controlling the coupling between the mechanical deformation and electronic structure and transport properties. This coupling is not fully understood, in part because the basic mechanical response of interacting graphene sheets is not yet adequately described. Important for predicting this response are the nonlocal van der Waals forces between layers of graphene and between graphene and a supporting substrate. The aim of the project is to develop and investigate continuum models of graphene structures that incorporate van der Waals forces in a rigorous way, accounting for long-range ordering of atoms. Derived via a multiscale analysis, the continuum models are formulated within nonlinear rod and shell theories. Equilibrium configurations of various graphene structures -- involving multiple layers and different substrates -- under external loads are analyzed using the tools of bifurcation theory. Also, the thermal properties of nanotube composites are investigated within the framework of a network model taking into account the influence of van der Waals forces.
Interest in macromolecules composed of carbon atoms has stimulated a great deal of recent research in materials science and physics. Much of this work has focused on carbon nanotubes and, more recently, on the basic structural element of a nanotube -- graphene. Graphene is a single-atom-thick sheet of bonded carbon atoms. Despite many decades of effort, only within the last six years have scientists discovered methods for producing isolated individual graphene sheets. This discovery has stimulated a flurry of experimental and theoretical work on the exceptional mechanical, thermal, and electronic properties of graphene. Exploiting these properties could lead to significant advances in many technologies and yield, for example, more efficient solar cells, faster microprocessors, or lighter, stronger composite materials. The principal goal of this project is to employ mathematical modeling to gain a better fundamental understanding of how atomic-scale forces between layers of a carbon nanostructure influence its mechanical and thermal characteristics. The project investigators are developing and analyzing comprehensive multiscale models of interacting graphene layers by utilizing ideas at the forefront of existing theories as well as by introducing new mathematical tools.
Interest in macromolecules composed of carbon atoms has stimulated a great deal of recent research in materials science and physics. Much of this work has focused on carbon nanotubes and, more recently, on the basic structural element of a nanotube -- graphene. Graphene is a single-atom-thick sheet of bonded carbon atoms. Despite many decades of effort, only within the last ten years have scientists discovered methods for producing isolated individual graphene sheets. This discovery has stimulated a flurry of experimental and theoretical work on the exceptional mechanical, thermal, and electronic properties of graphene. Exploiting these properties could lead to significant advances in many technologies and yield, for example, more efficient solar cells, faster microprocessors, or lighter, stronger composite materials. Important for predicting the mechanical response of carbon nanostructures are the nonlocal van der Waals forces between layers of graphene and between graphene and a supporting substrate. In this project we developed and investigated continuum models of graphene structures that incorporate van der Waals forces in a rigorous way, accounting for long-range ordering of atoms. Derived via a multiscale analysis, the continuum models were formulated within nonlinear rod and shell theories. Equilibrium configurations of various graphene structures -- involving multiple layers and different substrates -- under external loads were analyzed using the tools of bifurcation theory. Among the particular issues that were addressed are (i) Derivation of a continuum model of a double-walled carbon nanotube and a graphene/susbstrate system starting from a microscopic atomistic model. The continuum model was shown to adequately predict experimentally observed effects, such as polygonization of nanotubes of a large diameter.; (ii) Analysis of stability of various carbon nanostructures: nanotubes with an imbedded core and nanotubes imbedded in another medium, graphene interacting with a susbtrate, etc.; (iii) Desing of a minimalistic model that reproduces the behavior of a graphene sheet to simplify the derivation of the corresponding continuum model. The methodology developed in the course of this project would have a direct impact in the disciplines where mechanincs of nanostructures is important. Eight Masters students theses were written on a subject related to this project and the work of six undergraduate was supported by the project. Among other venues, the project was discussed during an outreach lecture at the summer school for graduate students at Technion.
