Self-folding and unfolding of carbon nanotubes

Carbon nanotubes (CNTs) constitute a prominent example of nanomaterials. In most studies on mechanical properties, the effort was concentrated on CNTs with relatively small aspect ratio of length to diameters. In contrast, CNTs with aspect ratios of several hundred can be produced with today's experimental techniques. We report atomisticcontinuum studies of single-wall carbon nanotubes with very large aspect ratios subject to compressive loading. It was recently shown that these long tubes display significantly different mechanical behavior than tubes with smaller aspect ratios (Buehler, M. J., Kong, Y., and Guo, H., 2004, ASME J. Eng. Mater. Technol. 126, pp. 245-249). We distinguish three different classes of mechanical response to compressive loading. While the deformation mechanism is characterized by buckling of thin shells in nanotubes with small aspect ratios, it is replaced by a rodlike buckling mode above a critical aspect ratio, analogous to the Euler theory in continuum mechanics. For very large aspect ratios, a nanotube is found to behave like a wire that can be deformed in a very flexible manner to various shapes. In this paper, we focus on the properties of such wirelike CNTs. Using atomistic simulations carried out over a several-nanoseconds time span, we observe that wirelike CNTs behave similarly to flexible macromolecules. Our modeling reveals that they can form thermodynamically stable self-folded structures, where different parts of the CNTs attract each other through weak van der Waals (vdW) forces. This self-folded CNT represents a novel structure not described in the literature. There exists a critical length for self-folding of CNTs that depends on the elastic properties of the tube. We observe that CNTs fold below a critical temperature and unfold above another critical temperature. Surprisingly, we observe that self-folded CNTs with very large aspect ratios never unfold until they evaporate. The folding-unfolding transition can be explained by entropic driving forces that dominate over the elastic energy at elevated temperature. These mechanisms are reminiscent of the dynamics of biomolecules, such as proteins. The different stable states of CNTs are finally summarized in a schematic phase diagram of CNTs.