Optical Properties of Metal Nanoparticles

In this section, we describe theoretical methods that describe the macroscopic optical properties of metal nanoparticles (a.k.a quantum dots). Recently, silver and gold nanoparticles have foimd tremendous use in biological assays, detection, labelling and sensing because of their sensitive optical spectra. While some works in the literature refer to these as quantum dots , in optical absorption experiments their quantized energy structure is not probed. The spectrum is a probe of the localized surface plasmon phenomenon, a collective electronic excitation that is localized in spatial extent owing to the small size of the nanoparticle compared with the wavelength. 

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The optical properties of metal nanoparticles have traditionally relied on Mie tlieory, a purely classical electromagnetic scattering tlieory for particles witli known dielectrics [172]. For particles whose size is comparable to or larger tlian tire wavelengtli of the incident radiation, tliis calculation is ratlier cumbersome. However, if tire scatterers are smaller tlian -10% of tire wavelengtli, as in nearly all nanocrystals, tire lowest-order tenn of Mie tlieory is sufficient to describe tire absorjDtion and scattering of radiation. In tliis limit, tire absorjDtion is detennined solely by tire frequency-dependent dielectric function of tire metal particles and the dielectric of tire background matrix in which tliey are... 

Kelly, K.L., Coronado, E., Zhao, L.L. and Schatz, G.C. (2003) The optical properties of metal nanoparticles the influence of size, shape, and dielectric environment. The Journal of Physical Chemistry B, 107, 668-677. 

Optical properties of metal nanoparticles embedded in dielectric media can be derived from the electrodynamic calculations within solid state theory. A simple model of electrons in metals, based on the gas kinetic theory, was presented by Drude in 1900 [9]. It assumes independent and free electrons with a common relaxation time. The theory was further corrected by Sommerfeld [10], who incorporated corrections originating from the Pauli exclusion principle (Fermi-Dirac velocity distribution). This so-called free-electron model was later modified to include minor corrections from the band structure of matter (effective mass) and termed quasi-free-electron model. Within this simple model electrons in metals are described as... 

Sosa, I. O., Noguez, C., and Barrera, R. G. (2003). Optical Properties of Metal Nanoparticles with Arbitrary Shapes. J. Phys. Chem. B 107 6269-6275. 

The fascinating optical properties of metal nanoparticles have caught the attention of many researchers from the pioneering and almost parallel works of G. Mie and J.C. Maxwell-Garnett at the beginning of the twentieth century. These original properties, like many other phenomena specifically appearing in matter divided to the nanoscale, are linked with confinement effects, since quasi-free conduction 461... 

As several works devoted to the nonlinear optical properties of metal nanoparticles include a size dependence of the linear dielectric function, it seems to us relevant to introduce and briefly comment now the most widespread approach used to describe such a dependence. It consists in modifying the phenomenological collision factor F in the Drude contribution (Eq. 2) as ... 

Most of the studies devoted to the nonlinear optical properties of metal nanoparticles use the notation x (<>>) to refer to the susceptibility for the optical Kerr effect. Unless otherwise specified, we will also adopt this simplified designation in the following. Let us just recall that it corresponds, in fact, to an experimental situation where a unique plane wave, linearly polarized (or three plane waves with same polarization and frequency), generates the third-order nonlinear optical phenomenon in an isotropic medium at the same frequency, and that the susceptibility is a priori a complex quantity. 

Intrinsic nonlinear optical properties of metal nanoparticles... 

Pinchuk A, Kreibig U, Hilger A. 2004. Optical properties of metallic nanoparticles Infiuence of interface effects and interband transitions. Surface Sci. 557 269-280. 

The optical properties of metal nanoparticles embedded in an insulating host differ substantially from the optical properties of bulk metals. Under the influence of an electrical field, there is a plasmon excitation of the electrons at the particle surface. This resonance, which takes place at a certain energy of the incident light, results in an optical absorption, the so-called plasmon absorption or plasma resonance absorption [1,2]. 

A dielectric oxide layer such as silica is useful as shell material because of the stability it lends to the core and its optical transparency. The thickness and porosity of the shell are readily controlled. A dense shell also permits encapsulation of toxic luminescent semiconductor nanoparticles. The classic methods of Stober and Her for solution deposition of silica are adaptable for coating of nanocrystals with silica shells [864,865]. These methods rely on the pH and the concentration of the solution to control the rate of deposition. The natural affinity of silica to oxidic layers has been exploited to obtain silica coating on a family of iron oxide nanoparticles including hematite and magnetite [866-870]. The procedures are mostly adaptations of the Stober process. Oxide particles such as boehmite can also be coated with silica [871]. Such a deposition process is not readily extendable to grow shell layers on metals. The most successful method for silica encapsulation of metal nanoparticles is that due to Mulvaney and coworkers [872—875]. In this method, the smface of the nanoparticles is functionalized with aminopropyltrimethylsilane, a bifunctional molecule with a pendant silane group which is available for condensation of silica. The next step involves the slow deposition of silica in water followed by the fast deposition of silica in ethanol. Changes in the optical properties of metal nanoparticles with silica shells of different thicknesses were studied systematically [873 75]. This procedure was also extended to coat CdS and other luminescent semiconductor nanocrystals [542,876-879]. 

I. O. Sosa, C. Noguez and R. G. Barrera, Optical properties of metal nanoparticles with arbitrary shapes. Journal of Physical Chemistry B, 107(26), 6169-6275 (2003). 

Theoretically, the sensitivity of the optical properties of metal nanoparticles to the refractive index of the surrotmding medium is described by simplified Mie theory. Plasmons resonate in a nanoparticle when the denominator in Eq. (1) is at a minimum, as shown below... 

Gonzalez, A. L., and Noguez, C. [2007] Influence of morphology on the optical properties of metal nanoparticles, / Comput. Theor. Nanosci., 4, 231-238. 

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