Introduction Metal nanoparticles interact with light more strongly than any other chromophore Optical cross-section is greater than the geometrical cross-section
Plasmon resonance Oscillating electric field causes the conduction electrons to oscillate coherently. Oscillation frequency determined by Density of electrons Effective electron mass Shape and size of the charge distribution
Localized surface plasmons Limited dimension of an nanoparticle prohibit the plasmon waves from propagating. The excited state is not stable and decays Radiatively -> Scattering of photons Non-radiatively -> Absorption and conversion to heat Scattering + Absorption = Extinction All conductive materials support LSPs Ag, Au and Cu most studied as their plasmon resonance frequency is near to that of visible light.
Mie-theory Exact solution to Maxwell’s equations for the case of a sphere Input: Wavelength, particle radius, particle’s dielectric function and the dielectric function of the environment. Output: Exact extinction, scattering and absorption cross- sections, internal and external field intensities The theory states that the scattering cross-section varies with r 6 while absorption cross-section varies with r 3 -> Absorption becomes more dominant as particle size decreases
Mie-theory No intrinsic restriction on particle size or wave length, however: d Surface scattering must be taken into account d Classical electrodynamics no longer valid Experimentally derived coefficients -> No information on the underlying mechanism i.e. LSPs For particles with arbitrary shapes, computationally demanding numerical methods are needed
Size Two types of size effects, threshold for the two regimes dependent on the metal Extrinsic (Above threshold): Related to the diameter and bulk dielectric function. Redshifting and broadening of the resonance peak with increasing particle sizes Intrinsic (Below threshold): Attenuation and broadening of the resonance peak due to surface scattering of electrons.
Size With increasing sizes, the retardation effect may lead to higher-order oscillations -> additional peaks at shorter wavelengths
Shape Peak position shift correlates with the increased number of sharp tips or edges Surface roughness results in redshifting
Shape More complex shapes can feature distinct LSPs on different surfaces Core-shell NPs, Nanorings Coupling of two surfaces leads to alteration of the overall optical response
Environment The scattering spectrum redshifts as the refractive index of the surrounding medium increases NPs often deposited on a substrate prior to analysis -> May distort the results. A transition metal substrate dampens LSPs
Interparticle coupling Properties of a group of NPs can differ from a single one even if the group is homogenous Closely spaced particle pairs exhibit a strong polarization sensitivity Polarization of the incidence light perpendicular to the center-to-center line -> Blueshift P0larization along the line -> Redshift Periodically ordered NPs act as a grating
Characterization Geometrical measurements SEM TEM AFM Optical properties Spectrophotometry LSP resonance maximum at transmission minimum Near and far field optical microscopy for single particles
Applications Optoelectronics Solar cells Biomedical Biolabelling Cure for cancer!
Summary The optical properties of metal nanoparticles arise from localized plasmon resonance. Spherical particles can be modeled analytically with Mie-theory, other shapes require numerical methods. The optical properties are influenced by particle material, size, shape, environment and interaction with other particles. Characterization with spectrophotometry and optical microscopy. Applications range from optoelectronics to biomedicine.
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