User:Drfg90/Plasmonic Nanoparticles

Plasmonic nanoparticles are particles whose electron density can couple with electromagnetic radiation of wavelengths that are far larger than the particle due to the nature of the dielectric-metal interface between the medium and the particles: unlike in a pure metal where there is a maximum limit on what size wavelength can be effectively coupled based on the material size.

What differentiates these particles from normal surface plasmons is that plasmonic nanoparticles also exhibit interesting scattering, absorbance, and coupling properties based on their geometries and relative positions. These unique properties have made them a focus of research in many applications including solar cells, spectroscopy, signal enhancement for imaging, and cancer treatment.

Background
Plasmons are the oscillations of free electrons which are the consequence of the formation of a dipole in the material due to electromagnetic waves. The electrons migrate in the material to restore its initial state; however, the light waves are constantly oscillating leading to a constant shift in the dipole, so the electrons are forced to oscillate at the same frequency as the light. This coupling only occurs when the frequency of the light is equal to or less than the plasma frequency and is greatest at the plasma frequency and is therefore called the resonant frequency.

Nanoparticle plasmons have the additional property of being dependent on their geometry and size, the scattering and absorbance cross-sections describe the intensity of a given frequency to be scattered or absorbed.

Many fabrication processes exist for fabricating the nanoparticles depending on the desired size and geometry.

Theory
The equations that describe the scattering and absorbance cross-sections for spherical nanoparticles are as follows

$${{\sigma }_{scatt}}=\frac{8\pi }{3}{{k}^{4}}{{R}^{6}}{{\left| \frac{{{\varepsilon }_{particle}}-{{\varepsilon }_{medium}}}{{{\varepsilon }_{particle}}+2{{\varepsilon }_{medium}}} \right|}^{2}}$$

$${{\sigma }_{abs}}=4\pi k{{R}^{3}}Im\left| \frac{{{\varepsilon }_{particle}}-{{\varepsilon }_{medium}}}{{{\varepsilon }_{particle}}+2{{\varepsilon }_{medium}}} \right|$$

where k is the wavenumber of the electric field, R is the radius of the particle, $${{\varepsilon }_{medium}}$$ is the relative permittivity of the dielectric medium and $${{\varepsilon }_{particle}}$$ is the relative permittivity of the nanoparticle defined by

$${{\varepsilon }_{particle}}=1-\frac{\omega _{p}^{2}}$$

also known as the Drude Model for free electrons where $${{\omega }_{p}}$$ is the plasma frequency and ω is the frequency of the electromagnetic radiation. This equation is the result of solving the differential equation for a harmonic oscillator with a driving force proportional to the electric field that the particle is subjected to. A more thorough derivation is provided here.

It logically follows that the resonance conditions for these equations is reached when the denominator is around zero such that

$${{\varepsilon }_{particle}}+2{{\varepsilon }_{medium}}\approx 0$$

When this condition is fulfilled the cross-sections are at their maximum.

It should be kept in mind that these cross-sections are for single, spherical particles and that the equations change when particles are non-spherical, or are coupled to 1 or more other nanoparticles i.e. when their geometry changes. This principle is important for several applications.

Plasmonic Solar Cells
Due to their ability to scatter with light back into the photovoltaic structure and low absorption, plasmonic nanoparticles are being investigated as a method for increasing solar cell efficiency. By forcing more light to be absorbed by the dielectric the effeciency of the device goes up.

Spectroscopy
In the past 5 years plasmonic nanoparticles have been explored as a method for high resolution spectroscopy. One group utilized 40 nm gold nanoparticles that had been functionalized such that they would bind specifically to epidermal growth factor receptors to determine the density of those receptors on a cell. This technique relies on the fact that the effective geometry of the particles change when they get within one particle diameter (40 nm) of each other. If the particles are within that range, quantitative information on the EGFR density in the cell membrane can be retrieved based on the shift in resonant frequency of the plasmonic particles.

Cancer Treatment
Preliminary research indicates that the absorption of gold nano rods functionalized with epidermal growth factor is enough to amplify the effects of low power laser light such that it can be used for targeted radiation treatments of cancer.