NANO LETTERS
Determination of the Elastic Constants of Gold Nanorods Produced by Seed Mediated Growth
2004 Vol. 4, No. 12 2493-2497
Min Hu, Patrick Hillyard, and Gregory V. Hartland* Department of Chemistry and Biochemistry, UniVersity of Notre Dame, Notre Dame, Indiana 46556-5670
Thomas Kosel Department of Electrical Engineering, 275 Fitzpatrick Hall, UniVersity of Notre Dame, Notre Dame, Indiana 46556
Jorge Perez-Juste and Paul Mulvaney School of Chemistry, UniVersity of Melbourne, Australia Received September 16, 2004; Revised Manuscript Received October 21, 2004
ABSTRACT The extensional and breathing modes of gold nanorods in aqueous solution have been examined by time-resolved spectroscopy. These experiments yield values for the elastic constants for the rods. The results show that gold nanorods produced by wet chemical techniques have a smaller Young’s modulus than bulk gold. HRTEM and SAED studies show that the rods have a 5-fold twinned structure with growth along the [110] crystal direction, consistent with previous reports. However, neither the growth direction nor the twinning provide a simple explanation for the reduced elastic moduli measured in our experiments.
Small whiskers are often added to materials to improve mechanical properties, such as their strength and stiffness.1,2 However, relatively little is known about the mechanical properties of the whiskers themselves-especially when their dimensions are on the nanometer scale. This is because the measurement of the mechanical properties of nanometer sized objects is a formidable experimental challenge. For relatively long nanowires/nanotubes, analysis of thermal vibrations using TEM,3,4 or the force versus distance response by AFM,5 can yield estimates of Young’s modulus (E). The results of these measurements show that nanowires are typically stiffer (higher value of E) than the corresponding bulk material; which has been attributed to the elimination of defects in the nanowires (see ref 5 and the references therein). Young’s modulus of nanometer sized objects can also be estimated by nanoindentation. Recent experiments on single silver nanowires determined a value of E that is comparable to bulk silver.6 However, all these measurements typically have fairly large uncertainties - sometimes greater than the difference between the measured value of Young’s modulus for the nanowires and the bulk value. This is due both to limitations of the techniques and to the heterogeneity of the samples.4 10.1021/nl048483i CCC: $27.50 Published on Web 11/12/2004
© 2004 American Chemical Society
In our laboratory we use an approach based on timeresolved spectroscopy to measure the elastic properties of nanoparticles and nanorods.7,8 In these experiments acoustic vibrations are coherently excited in the particles by laser induced heating, and the period is analyzed to determine the elastic constants. This technique relies on having accurate information about the size and shape of the particles, as well as a way of connecting the measured period to the elastic constants of the particle (typically through continuum mechanics). For spherical particles the symmetric breathing mode is excited.7,8 The period of this mode depends on the radius and the longitudinal and transverse speeds of sound.9 Results from our group and others show that for spherical particles larger than ∼6 nm diameter the speeds of sound, and therefore the elastic moduli, are the same as those for the bulk material.7,8 The measurements are quite accurate because many particles are interrogated; however, information about differences between different particles in the sample is lost. In comparison to the AFM and TEM approaches, these measurements are better suited to smaller objects that can be easily dispersed in solution or a solid matrix. They also do not rely on having one end of the particle anchored to a surface, a limitation that can introduce
Figure 1. Period versus average length for a series of gold nanorods samples produced by the seed mediated growth technique. The solid line is a fit to the data using eq 1 and allowing E to vary. The dashed lines show calculations for different crystal direction, see text for details.
uncertainty in the measured elastic constants4 and precludes measurements for particles with low aspect ratios. In a recent paper, we reported measurements of the fundamental extensional mode of gold nanorods with lengths between 40 and 110 nm.10 The rods were synthesized using a wet chemical, seed-mediated growth technique.11-13 The samples consisted of relatively monodisperse rods, but with a significant fraction (∼50%) of spheres.10 The measured periods are plotted versus the average length of the rods (determined by TEM) in Figure 1. The period of the fundamental extensional mode is given by10,14 T(0) ext ) 2L/xE/F
(1)
where L is the rod length and F is the density. Thus, these measurements can be used to estimate Young’s modulus for the rods. The solid line in Figure 1 shows a fit to the data that yields a value of Young’s modulus of E ) 64 ( 8 GPa (in this calculation we assumed that the density of the nanorods is the same as the bulk value).10 The value of E obtained from the fit is significantly lower (∼19%) than the room-temperature value for bulk gold of E ) 79 ( 1 GPa.15 The lower value of Young’s modulus is in contrast to the normal results for nanomaterials of a larger Young’s modulus compared to bulk.5 In our previous report this difference was attributed to the structure of the rods, i.e., that they grow in a specific way and are not isotropically elastic.10 In ref 10 we also considered the possibility that the decrease in Young’s modulus arises from size effects (i.e., the contribution from surface energy to the overall cohesive energy of the particles), analogous to the well-known decrease in melting point for small spherical metal particles.16,17 However, the decrease in melting point is only significant for particle sizes
