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| Plasmon resonance tuning: Nanoparticle shape and structure | Prev topic | Next topic Fig. 1 |
Plasmon resonances of metallic particles can be modified by changing the particle shape/structure/orientation. For example, one can use spherical shell-shaped particles. The resonance of these particles can be tuned by varying the thickness of the shell or by changing the material in the core and/or the shell. Naomi Halas has performed numerous experiments in this field (for example, Loo C et al 2004, Oldenburg SJ et al 1998), while Malinsky MD et al 2001, for example, have calculated attenuation spectra for silver nanospheres with dielectric shells, by using the coated sphere theory. Results of that work indicate that the attenuation peak (plasmon resonance) shifts to the red (long wavelength) and becomes stronger as the shell thickness increases.
Ghodselahi et al 2009 have shown that the resonance for copper can be recovered by coating a copper core nanoparticle with copper oxide. The resonance is sensitive to both the size of the core and the thickness of the shell and disappears entirely when the core size is less than 2 nm.
The effect of particle shape on the plasmon resonance can be qualitatively understood by considering light scattering by spheroids in the small-particle (Rayleigh) limit (for example, van de Hulst HC 1981, section 6.1). For spheres, the resonance is a consequence of a zero in the denominator of the polarizability tensor α, of a sphere of radius a (for example, van de Hulst HC 1981, section 6.3):
| α = a3 |
|
(1) | |||
where m is the refractive index of the particle, relative to that of the surrounding medium. This factor appears in the Mie theory as well. Specifically, in the Rayleigh limit, the absorption efficiency of a particle, Qa, can be expressed as follows:
| Qa | = -4x Im |
|
|||
| = 4 πk / σg Re( iα ) | (2) | ||||
where k is the wavenumber and σg is the geometric cross section (equal to πa 2 for a sphere). Equation 1 for the polarizability, α, is a special case (spherical symmetry) of the equation for the three major axes (j = 1, 2, 3) of an ellipsoid of volume V. The polarizability tensor of an ellipsoid is expressed as follows:
| αj = V / (4π) |
|
(3) |
where the Lj's are three geometrical depolarization factors depending on the ratios of the axes (for example, Bohren CF and Huffman 1983, pp. 145-146). For a sphere, L1 = L2 = L3 = 1/3, independent of direction. The sum of the three factors Lj is always unity. For L1 ≠ L2 ≠ L3, the resonance is split into three distinct peaks, corresponding to the polarization of the incident radiation along each axis. The resonant absorption depends on the orientation of the particles with respect to the incident polarization. A zero in the denominator of Equation 3 identifies the resonance at m = -i√(1/Lj - 1). Therefore a shift of the resonance will result if the polarization of the incident light is rotated among the j axes, which effectively changes the particle size experienced by this polarization. Rotating the particle by 90° would effectively realign the incident polarization, causing a shift in the plasmon resonance. Clearly, the particle shape and orientation determine the absorption properties of the suspension (Figure 1). Furthermore, the absorption can be switched from a maximum to a minimum by switching the particle orientation or the incident polarization.
Yu YY et al 1997 have shown that the experimental absorption spectrum of gold nanorods randomly oriented in aqueus solution splits into two bands (which they call the transverse and the longitudinal) corresponding to the two orientations of the rods. They show absorption spectra for the rod aspect ratio of 1.8, 3, and 5.2. As the aspect ratio increases, the transverse peak (corresponding to polarization along the short axis) decreases but stays put while the longitudinal peak increases, broadens and red-shifts. The effect is even more pronounced in the data of Jana NR et al 2001 who show spectra for the aspect ratio of 4.6, 13, and 18. This is consistent with the results for increasing the size of a spherical particle (see Plasmon resonance tuning: Particle size). In fact, Schatz GC 2001 has theoretically shown that the absorption spectra of a judiciously chosen sphere approximates the spectra of spheroids with the aspect ratio of 5, which corresponds to the maximum aspect ratio in Yu's data.
The above treatment is only valid when all dimensions of the particle are much less than the wavelength of light. For larger particles, other techniques must be used, such as the discrete dipole approximation (DDA) (for example, Malinsky MD et al 2001). The DDA program code is freely available from its creators, Draine BT and Flatau PJ (user guide, see also Draine BT and Flatau 1994). Shatz GC 2001 has recently published a theoretical paper on the DDA with application to non-spherical metal nanoparticles. The DDA has also been used to calculate extinction spectra for gold nanosphere chains (Lazarides AA and Schatz 2000).
Experimental data for silver triangles and pentagons (Mock JJ et al 2002) and anisometric gold colloids (Wiesner J and Wokaun 1989) show that random orientation or randomly shaped particles generally broaden and red-shift the plasmon peak.
See plasmon resonance tuning by changing the particle size, medium surrounding the particle(s), and other factors. See also plasmon resonance for additional references.
| CITATION: Swanson N. L. 2008. Plasmon resonance tuning: Particle shape and structure (www.tpdsci.com/Tpc/PlasmResNptTunPtSha.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 25-Oct-2008 Modified: 19-Jun-2009 Peer-reviewed: PENDING |
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