The article by Natasha Hjerrild and Robert Taylor about nanofluids for solar-to-thermal energy conversion (Physics Today, December 2017, page 40) was very interesting. Their review has introduced a promising energy technology.

To explain fundamental concepts of nanoparticle plasmon resonances, Hjerrild and Taylor use analogies to excitation processes in dipolar absorbers. The analogies are appealing in terms of pedagogy and intuitiveness and are also somewhat common in lay descriptions of plasmonics. However, such loose conceptual descriptions can lead to inaccurate physical understanding and incorrect predictions. I would like to point readers to physical models that are more representative of plasmonic excitations in nanoparticles.

As the authors indicate, silver nanoparticles can indeed exhibit higher-quality localized surface plasmon resonances (LSPRs) than can comparably sized nanoparticles of other metals, including gold and copper. The reason is not the higher free-electron density of silver. In fact, silver is known to have a free-electron density similar to that of gold and lower than that of copper. However, silver differs in terms of its interband electronic transitions. In gold and copper, those transitions overlap with the LSPRs in part of the visible-frequency range and dampen the resonances at those frequencies. In silver, they are limited to the UV.

Interband transitions are also responsible for the LSPRs of gold and copper nanospheres being at longer wavelengths than those of silver nanospheres of comparable size. Were it not for interband transitions, the LSPR frequency would depend primarily on the square root of the free-electron density and would therefore be quite close for nanoparticles of the three metals. Depending on the particles’ size and shape, the LSPRs and absorption maxima of gold and copper nanoparticles can span from the visible (around 500 nm) to the IR.

The size dependence of the LSPR frequency is also well understood. The longer-wavelength resonance for a larger nanoparticle is not the result of increased charge separation distance, even though such an explanation seems intuitive. Rather, the size effect is an outcome of increased electromagnetic retardation as the size of a nanoparticle increases and approaches the wavelength of the driving electromagnetic field of the incident light.

As for the shape effect, as the authors state, a nanorod has an LSPR, polarized along the long axis, that peaks at a longer wavelength than the LSPR of a nanosphere. However, that effect is not simply due to the increased charge-separation distance in the nanorod. If it were, the long-axis LSPR of a nanorod 30 nm long would have a similar wavelength to the LSPR of a nanosphere 30 nm in diameter, which is generally not true. The nanorod LSPR’s longer wavelength—or lower photon energy—is due to the nanorod’s higher surface curvature, which makes the electrons more easily polarizable along its long axis.

In fact, the LSPR wavelength depends not only on the nanorod’s length but also on its aspect ratio. The aspect ratio encodes the degree of surface curvature and the resulting electronic polarizability of the nanorod, as shown beautifully by the Gans model for ellipsoidally shaped metal nanoparticles.1 

For similar reasons, the LSPR modes in nanodisks have different wavelength maxima and absorption cross sections than those in nanospheres of comparable radii—not because of the confinement of electrons along the thickness dimension, as the authors suggest. Nanodisks typically have thicknesses of several nanometers, and quantum confinement of electrons is not important in that range in metals. There is no general rule for a nanodisk’s absorption cross section to be twice that of a nanosphere of similar radius. The absorption cross section is likely to depend instead on the nanodisk’s aspect ratio.

Regardless of the need for more rigorous conceptual explanations, I found Hjerrild and Taylor’s article compelling. My discussion above highlights the field’s multidisciplinary nature and the need for collaboration among physical chemists, physicists, materials scientists, and engineers. And the article does an excellent job of speaking to that broad community and generating excitement about the energy-harvesting potential of nanofluids.

Natasha E.
Robert A.
Physics Today