Simulating Carbon Nanotube Buckling

Carbon nanotubes (CNTs) are hexagonal structures of carbon atoms that are assembled to create single-wall (SW) or multiwalled (MW) filaments, with diameters measured in nanometers and lengths measured in micrometers.

Because of their well-defined shape and structure and remarkable physical characteristics, such as high mechanical strength and resilience, CNTs are in high demand for many industrial applications. Understanding how CNTs respond to primary deformations such as bending is critical knowledge for many areas of product development, especially nanoelectromechanical systems.

When subjected to large forces of bending or compression (for example, in a nanotube-tipped AFM cantilever setup), the carbon nanotube will buckle—a complex elastic deformation by which the nanotube loses its cylindrical shape at a particular spot.

“In the macroscopic world, buckling is quite a common elastic process,” says Traian Dumitrica Nelson, assistant professor of mechanical engineering at the University of Minnesota. “If one bends a drinking straw, at some point it will develop a kink. This is buckling. What is remarkable is that this happens in carbon nanotubes, structures that contain only a few dozen carbon atoms around the circumference.”

The Rippling Mode

Dumitrica has used objective molecular dynamics to systematically investigate elastic bending in carbon nanotubes up to 4.2 nm in diameter. “This research identified interesting contrasting behavior,” says Dumitrica. “While single-wall tubes buckle in a gradual way, with a clear intermediate regime before they fully buckle, multiwalled tubes with closed cores exhibit a rate- and size-independent direct transition to an unusual wavelike mode with a 1-nm characteristic length. This ‘rippling’ mode has a nearly linear bending response and causes a 35% reduction in the stiffness of the thickest multiwalled tubes.”

“Rippling,” a form of distributed buckling, also occurs when carbon nanotubes are subjected to torsional deformations. A rippled nanotube displays helicoidal ridges and furrows of positive and negative curvature, respectively. From a mechanical point of view, both buckling and rippling are responses to large applied forces that prevent the nanotube from breaking—a good thing. With increased stress, however, this resilience creates a structural weakness at the location of the buckling, eventually leading to structural failure of the CNT.

Buckling is a primary consideration in the design of structural members for bridges and machineries, but also is important at the nanoscale. Because buckling cannot really be avoided under large deformations, researchers are very interested in understanding how mechanical, electronic, and thermal properties of CNTs change when buckling occurs, as well as determining the physical thresholds (including temperature) below which buckling will not occur. 

Microscopic Simulations

Experiments that study buckling are difficult to undertake at this small scale. Therefore, researchers are attempting to understand the exact threshold at which buckling occurs, as well as the effects of buckling on the nanotube properties, through microscopic simulations.

“To simulate a carbon nanotube, one starts by considering its atomic structure,” says Dumitrica. “The only input in these simulations is the way atoms are interacting with each other to form chemical bonds. Finding out how they respond to buckling and rippling involves the explicit study of molecular bonds and atomic dynamics. By contrast, traditional ‘continuum’ engineering methodologies do not account explicitly for the atomistic discreteness.”

Microscopic simulation is a nontraditional research method for mechanical engineers but is beginning to gain popularity, as engineering moves toward smaller scales. Microscopic calculations can define both the morphological changes and the electronic behavior that occurs under buckling. Microscopic simulations also can provide guidance to electromechanical laboratory experiments on single- and multiwalled nanotubes. 

“For example, our simulations indicate that a multiwalled CNT structure provides robustness to electrical conductivity in the event of imposed large mechanical deformations," says Dumitrica. "In other words, the electronic conductivity is not negatively affected. Because of the support provided by the inner walls, the rippling is softened to the extent that its influence on the electronic conductivity is small.”

By contrast, the conductivity changes significantly when buckling and rippling develops in single-walled CNTs. “This finding suggests that multiwalled CNTs are best suited for nanoelectromechanical applications,” adds Dumitrica.

Because of the enormous interest in carbon nanotubes for use in electronic devices and nanoelectromechanical systems, understanding how different types of complex deformation impact the electromechanical characteristics of large-scale carbon nanotube assemblies and other individual nanoscale forms of carbon is a key area of research.

Mark Crawford is an independent writer.

The conductivity changes significantly when buckling and rippling develops in single-walled carbon nanotubes.