A clean nanotube shorter than its phonon mean free path conducts ballistically: phonons cross end to end without scattering, and the “effective conductivity” extracted from its conductance keeps growing with length. Long tubes flatten onto the diffusive plateau set by the intrinsic mean free path. Drag Λ — a cleaner tube — and watch the crossover march right; the marker shows your device length and how far below the plateau it sits.
Textbook ballistic-diffusive interpolation k_eff = k∞·L/(L+Λ) with a single gray-phonon mean free path. It qualitatively illustrates the crossover only; real tubes carry a mean-free-path spectrum plus chirality, contact and defect physics that reshape the curve as well as its scale.