Measuring the elastic properties of nanoparticles by time-resolved spectroscopy

The properties of many materials change when their dimensions approach the nanometer scale. The best-known example in chemistry is the size quantization effect observed in the optical spectra of semiconductor particles.¹ The mechanical properties of materials are also affected by size. For example, single crystal whiskers have superior stiffness and yield strengths when compared to bulk materials, due to their lack of growth defects.²

Recently, it has become possible to synthesize a wide range of nanostructures with excellent control of size, shape and crystal structure.³ These advances have stimulated interest in investigating the mechanical properties of nanomaterials.

For nanowires/nanotubes, the two most common approaches used to measure elastic constants are to bend the wire/tube with the tip of a scanning probe microscope and measure a forceversus distance curve,⁴ or to observe the amplitude of vibrations using transmission electron microscopy (TEM).^5,6 Both measurements require that the object be rigidly fixed at one end, that the point of contact be known, and that there are no substrate interactions. Bending is also required to occur only in one direction. However, these requirements can be difficult to achieve, and the results for ostensibly identical wires/tubes often show a large scatter.

Our approach to this problem is to use time-resolved spectroscopy to interrogate the vibrational modes of nanoparticles. Comparing the measured periods to continuum mechanics calculations allows the elastic constants of the particles to be determined.⁷ Our work has mainly been concerned with metals. In these experiments, an ultrafast laser pulse heats the electrons. The excitation energy flows into the vibrational modes on a picosecond timescale. This causes the particles to expand by an amount that depends on the thermal expansion coefficient (α) and the temperature rise in the lattice (ΔT). For particles larger than a few nanometers, the timescale for lattice heating is faster than the period of the vibrational mode that correlates with the expansion coordinate. This results in impulsive excitation of this mode. Figure 1 illustrates this process: the rapid laser-induced heating causes the particle to ‘ring’ around the new equilibrium radius R₀ + αΔT/3.

For metal particles, the coherently excited vibrational modes can be sensitively detected by monitoring the plasmon resonance (a collective oscillation of the conduction electrons). Figure 2 shows data for a gold nanorod sample, where the probe laser was tuned to the longitudinal plasmon resonance (LPR). Pronounced modulations due to the extensional mode can be observed. These modulations appear because the LPR depends on the aspect ratio of the rod, which is directly affected by the extensional mode. The period of this mode is related to the rod length L by ⁸

where E is Young's modulus and ρ is the density. Thus, these experiments also yield a value for Young's modulus.

The advantage of this all-optical method for measuring the elastic constants of nanomaterials is that the particles are freely suspended in solution: hence, the results are not affected by substrate interactions nor by how the particles are clamped. These experiments have shown that the elastic constants for spherical particles are the same as those for bulk metal.⁷ However, for nanorods, the measured value of Young' modulus is approximately 20% smaller than the value obtained for bulk gold.⁸ This is an unexpected result: nanomaterials should have superior mechanical properties because of elimination of defects.^2,4

We are currently investigating how the crystal structure and surface affect the elastic properties of nanorods. In addition, different shapes are being examined. Figure 3 shows transient absorption data obtained for nanocages⁹-which are hollow structures formed by etching silver nanocubes.³

For complex shapes like cubes or cages, analytical expressions for the period are not yet available. Thus, the experimental results must be compared to numerical simulations. Our goal is to explore how size, shape and crystal structure affect the elastic constants of such nanomaterials.

I would like to thank the students who have been involved in this work, notably Jose Hodak, Min Hu, and Hristina Petrova. I would also like to thank my collaborators (Paul Mulvaney, John Sader, Jorge Perez-Juste, Luis Liz-Marzan, and Younan Xia), and the National Science Foundation for support.