When vertically aligned carbon nanotube microstructures lose verticality: experimental and computational insights...

Patterned vertically aligned carbon nanotube (VACNT) microstructures are promising building blocks for three-dimensional carbon architectures, yet the geometric conditions governing preservation of their as-grown verticality remain poorly resolved. Here, we systematically map the loss of verticality of square VACNT microstructures over 16 combinations of catalyst footprint and growth condition, spanning lateral dimensions of 12.5-75 µm and footprint-specific mean heights of approximately 24-231 µm. As-grown deformation was quantified from scanning electron microscopy images using a dimensionless projected relative displacement metric, D. Although deformation generally increased as the structures became more slender, the response did not follow a universal H̄/L scaling. Instead, distinct low, transition, and advanced-deformation regimes emerged, and geometries with nearly identical H̄/L ≈ 3 exhibited almost a sevenfold difference in median D. This breakdown of aspect-ratio-only scaling demonstrates that absolute footprint and height, and the growth-dependent evolution associated with them, remain important in determining the final morphology. Orthotropic finite element eigenvalue analysis nevertheless revealed a systematic reduction in critical pressure with increasing H̄/L and converged toward the shear-corrected Timoshenko response in the beam-column regime. The resulting susceptibility index showed a moderate positive association with experimental deformation (ρ _s = 0.58, n = 12), indicating that elastic instability provides an important geometric contribution but does not uniquely determine the as-grown state. These findings distinguish geometric susceptibility from final morphological evolution and provide a quantitative framework for designing patterned VACNT architectures that retain verticality.