Collapsed adhesion of carbon nanotubes on silicon substrates: continuum mechanics and atomistic simulations

Carbon nanotubes (CNTs) can undergo collapse from the ordinary cylindrical configurations to bilayer ribbons when adhered on substrates. In this study, the collapsed adhesion of CNTs on the silicon substrates is investigated using both classical molecular dynamics (MD) simulations and continuum analysis. The governing equations and transversality conditions are derived based on the minimum potential energy principle and the energy-variational method, considering both the van der Waals interactions between CNTs and substrates and those inside CNTs. Closed-form solutions for the collapsed configuration are obtained which show good agreement with the results of MD simulations. The stability of adhesive configurations is investigated by analyzing the energy states. It is found that the adhesive states of single-walled CNTs (SWCNTs) (n, n) on the silicon substrates can be categorized by two critical radii, 0.716 and 0.892 nm. For SWCNTs with radius larger than 0.892 nm, they would fully collapse on the silicon substrates. For SWCNTs with radius less than 0.716 nm, the initial cylindrical configuration is energetically favorable. For SWCNTs with radius between two critical radii, the radially deformed state is metastable. The non-contact ends of all collapsed SWCNTs are identical with the same arc length of 2.38 nm. Finally, the role of number of walls on the adhesive configuration is investigated quantitatively. For multi-walled CNTs with the number of walls exceeding a certain value, the cylindrical configuration is stable due to the increasing bending stiffness. The present study can be useful for the design of CNT-based nanodevices.