Density-Driven Buckling Instabilities and Negative Stiffness in Patterned CNT Forest Architectures

We demonstrate a scratch-lithography method in which spatially confined carbon nanotube (CNT) forests are synthesized within shallow (∼100 nm) scratches on (0001) C-cut sapphire substrates. Linear scratches in close proximity facilitate low-density CNT forests that exhibit negative differential stiffness and bistable mechanical behavior. While the native (0001) sapphire plane natively resists CNT growth, scratches expose subsurface crystallographic planes that provide preferential catalyst adhesion sites during CVD, enabling robust CNT nucleation exclusively within the scratched regions. By varying the spacing between scratches, we systematically control the areal density of CNT forests and observe a linear correlation between CNT density and yield stress. All patterned structures exhibit pronounced mechanical nonlinearity, including negative stiffness behavior associated with snap-through. The scratched substrates remained active for more than ten growth cycles, establishing a scalable and reproducible route for architected CNT assemblies whose density and mechanical response are tunable through simple physical surface modification.