Physics and Astronomy Calendar

Advances in condensed matter physics and theoretical chemistry have made possible a comprehensive modeling of materials. We can adapt and apply these theoretical methods to study the amazing properties of nanostructures. I will discuss two examples where such theories helped the understanding of the mechanical response of carbon nanotubes (generally considered as a paradigm for nanoscale materials).

In materials modeling the most common way to implement molecular dynamics is via translational periodic boundary conditions. This is not the natural choice when modeling carbon nanotubes and other nanostructures. Appealing to the helical and rotational symmetries of the nanoscale graphitic tubules, molecular dynamics and structural relaxation can be done in a simplified way, on a modest number of atoms. This new method, termed objective molecular dynamics 1, is compatible with full quantum mechanics under the Born-Oppenheimer approximation. The utility of objective molecular dynamics will be presented in the context of studying the carbon nanotubes under elongation and twist.

Combining a probabilistic approach of the rate theory with detailed quantum mechanical computations of failure nucleation and transition-state barriers, allows for a comprehensive analysis of the underlying atomic mechanisms and evaluation of the yield strain for arbitrary nanotubes under realistic conditions 2. The numerical results are captured in a concise set of equations for the breaking strain, and reveal a competition between two alternative routes of brittle bond breaking and plastic relaxation. The employed probabilistic approach ultimately allows for the creation of a "strength map", which plots the likelihood that a nanotube will break – and how it's likely to break.

References
1 T. Dumitrica and R.D. James, Objective Molecular Dynamics, Journal of the Mechanics and Physics of Solids (submitted).
2 T. Dumitrica, M. Hua, and B.I. Yakobson, Symmetry, time-, and temperature-dependent strength of carbon nanotubes, Proc. Natl. Acad. Sci. USA 103, 6105 (2006).