Home | Survey | Topics | Index | References | Dictionary | Contribute | Gallery | Community | Search
| Plasmon resonances of metal nanoparticles |
Prev topic | Next topic Fig. 1 |
Collective electronic excitations at the surface of metal are known as plasmons. The plasmons are not excited in a smooth surface, but in subwavelength surface structures and nanoparticles (for example, Zangwill A 1988, Ch. 7: "Optical properties"). Plasmon resonances have wide application in nanotechnology. Pitarke et al. 2007 have recently published a complete theoretical description of the subject. A good source for background material on bulk and surface plasmons is found in Zangwill A 1988 (Ch. 7).
An extremely strong (theoretically the Q-value can be infinite) plasmon resonance occurs for metallic particles and particle dispersions. This resonance manifests itself as a peak in the absorption spectrum. The form and wavelength of that peak is highly sensitive to the particle size and shape (see Plasmon resonance tuning).
To understand how this resonance arises in the Rayleigh limit (relative particle size x << 1; for example, van de Hulst HC 1981, section 6.1), we can consider the first term of the infinite series in x, for the attenuation efficiency, Qc, from the Mie theory:
| Qc = Qb + Qa ≅ Qa ≅ -4x Im |
|
(1) |
where Qa is the absorption efficiency, Qb is the scattering efficiency, and m is the refractive index of the particles relative to the surrounding medium. The first term in the series expansion of Qb has the same form but is proportional to x4, so the absorption will dominate attenuation of light by nanoparticles with relative size x << 1.
The denominator in the above equation is zero when the relative refractive index of the particle, m = -i√2. Because a purely imaginary refractive index is not considered physically possible, optical physicists ignored this resonance for a long time (Bohren and Huffman 1983, p. 327). Nevertheless, when the real part of m is small and the imaginary part is close to -√2, the absorption of electromagnetic radiation by nanoparticles of such material becomes very strong. These values for the refractive index can be realized for some metals and have been identified with excitations of surface plasmon modes (Kreibig U and Vollmer 1995, Chapter 2)
The situation is somewhat more palatable when looked at in terms of the dielectric function. Recall that the dielectric function, ε, of a material is related to the refractive index, m (relative to that of the vacuum), of that material by the following equation:
| m2= ε' - i ε" | (2) |
The denominator in Equation 1 is then (ε' - i ε" )/εm + 2 where ε' and ε" are the real and imaginary parts of the dielectric function of the particle material, and εm is the dielectric function of the medium, which is assumed to be real. The resonance condition then becomes
| ε' + 2εm - i ε" = 0, | (3) |
The resonance condition is nearly satisfied when ε" is small and ε' = -2εm. This condition is fulfilled for some alkali metals, like sodium, for which the energy of the surface plasmon resonance can be calculated from the free electron (Drude) model (for example, Kreibig U and Vollmer 1995, Sect. 2.1.1).
Conversely, the noble metals contain partly filled conduction bands, completely filled core states and empty excited bands. The interband contributions to the dielectric function shift the plasmon resonance to lower energy, as in silver (Figure 1) or shift and damp the resonance, as in gold and copper. For gold, the interband transition edge is very near the resonance energy (ε" grows large). Thus, the resonance is damped and shifted into the visible. In copper, ε" is large over most of the energy range, therefore the resonance is heavily damped and shifted.
In the above discussion we have assumed that the medium surrounding the particle is vacuum. The resonance can be enhanced by surrounding the metal nanoparticles with a medium of high refractive index, thereby shifting the resonance away from the interband transition region. The factor of 2 in the denominator of Equation 1 is a consequence of the spherical particle shape; it will have a different value for shapes other than spheres. The resonance can, therefore, be tuned by changing the shape or by changing the medium. These equations are only valid in the Rayleigh limit (relative particle size x << 1). For larger particles, higher order terms must be added, and the resonance shifts to lower energy (longer wavelength).
The above discussion is valid for single particles or dilute particle dispersions. For dense particle dispersions, the effective absorption efficiency, Qa, and thus the resonance, is not determined by the single-particle Qa alone, but also by optical interactions between the particles (see Single and multiple scattering), as characterized by the optical thickness (Swanson NL and Billard 2003). In general, as the particle concentration increases, the plasmon resonance is red-shifted (for example, Hussain S and Pal 2006).
| CITATION: Swanson N. L. 2008. Plasmon resonances of metal nanoparticles (www.tpdsci.com/Tpc/PlasmResNpt.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 25-Oct-2008 Modified: 05-Feb-2010 Peer-reviewed: 04-Feb-2010 |
| Journals | Journals search | Contributing | | | Menu |
| Copyright 2005-2012 TPDSci Inc. All rights reserved. | Terms of use | |