Breathing mode vibrations and elastic properties of single-crystal and penta-twinned gold nanorods.

The acoustic vibrations of individual single-crystal and penta-twinned gold nanorods with widths from ∼7 to ∼26 nm are studied using atomic-level simulations and finite element calculations. It is demonstrated that the continuum model in the limit of an infinite rod length could be used to describe the breathing periods of nanorods with an aspect ratio as small as ∼2.5, in combination with bulk material elastic constants. The elastic moduli of gold nanorods are determined via their atomistically simulated extensional periods and the dispersion relation based on long-wavelength approximation. The twinned nanorods become stiffer as the width is reduced, which is in contrast to the size dependence of the modulus in single-crystal nanorods. Further finite element calculations for the breathing periods of nanorods are performed using isotropic elastic constants of bulk gold. We find that the breathing vibrations of the penta-twinned nanorods are more affected by the crystal structure effect than those of single-crystal nanorods, because a smaller range of crystal directions perpendicular to the long axis is involved in the breathing vibrations of twinned nanorods.