Mechanics of in-surface buckling of one dimensional nanomaterials on elastomeric substrates

In this recently published paper on Nanotechnology, we studied the in-surface buckling mechanics of one dimensional nanomaterials on elastomeric substrates.  Simple analytical solutions are obtained for buckling wavelength and amplitude, which can be easily applied to the in-surface buckling of different nanomaterials, such as nanowires and nanotubes.  It is shown that in-surface buckling of nanomaterials has lower energy than out-of-surface buckling, which explains the experimental observance of in-surface buckling of silicon nanowires.  However, single-walled carbon nanotubes (SWNTs) are reported to buckle out-of-surface on PDMS substrates (Khang et al., 2007 Nano Lett.).  This is due to that the energy difference  between two buckling modes of SWNTs is so small that PDMS surface roughness prevents the in-surface buckling.  For multi-walled carbon nanotubes and nanotube bundles, the energy difference between two buckling modes can be very large, and therefore their in-surface buckling is possible to be observed in experiment.