A mechanochemical model of growth termination in vertical carbon nanotube forests

Understanding the mechanisms by which vertical arrays of carbon nanotube (CNT) forests terminate their growth may lead to the production of aligned materials of infinite length. We confirm through calculation of the Thiele modulus that several prominent systems reported in the literature to date are not stunted by diffusion limitations. Evidence also suggests that, for many systems, the growth-termination mechanism is spatially correlated among nanotubes, making spontaneous, random catalytic poisoning unlikely as a dominant mechanism. We propose that a mechanical coupling of the top surface of the film creates an energetic barrier to the relative displacement between neighboring nanotubes. A Monte Carlo simulation based on this premise is able to qualitatively reproduce characteristic deflections of the top surface of single- and doubled-walled CNT (SWNT and DWNT) films near the edges and corners. The analysis asserts that the coupling is limited by the enthalpy of the carbon-forming reaction. We show that for patterned domains, the resulting top surface of the pillars is approximately conic with hyperbolic cross sections that allow for empirical calculation of a threshold force (F(max) = 34-51 nN for SWNTs, 25-27 nN for DWNTs) and elastic constant (k, 384-547 N/m for SWNTs and 157-167 N/m for DWNTs) from the images of experimentally synthesized films. Despite differences in nanotube type and precursor chemistry, the values appear consistent supporting the validity of the model. The possible origin of the mechanical coupling is discussed.