Mechanical properties and deformation morphologies of covalently bridged multi-walled carbon nanotubes: Multiscale modeling

We formulate a multiscale modeling framework to investigate the deformation morphologies and energetics of covalently bridged multi-walled carbon nanotubes (MWCNTs). The formulation involves extending a previously established quasi-continuum model by incorporating the inter-wall bridging energy density function into the constitutive relations via message passing from fully atomistic simulations. Using the extended numerical model, we studied the mechanical responses of the 10-walled MWCNT with varying inter-wall bridge densities under torsion, bending, and uniaxial compression. Our simulation results show that the presence of inter-wall covalent bridges not only enhances the post-buckling rigidities of the MWCNTs, but also modifies the deformation morphologies and morphology pathways. For bending and uniaxial compression, we constructed in the space of bridge density and applied strain the deformation morphology phase diagram, where three phases, uniformly deformed phase, rippling pattern, and diamond-shaped pattern, are identified and separated by linear phase boundaries. We attribute the deformation phase transitions to the interplay of inter-wall and intra-wall interaction energies. The multiple shape transitions of MWCNTs and the elastic nature of the deformation suggest that MWCNTs can be designed as shape-memory nanodevices with tunable stabilities.