E5 Optical Properties: Surface Plasmon

Topic

When visible light strikes this metallic nanoparticle, it excites a collective oscillation of its conduction electrons within the particle: the oscillating electric field of the visible light drives these conduction electrons—acting in unison—to shift back and forth across the nanoparticle, periodically moving away from the positive lattice ions left behind and being drawn back toward them by the electrostatic force generated by that very displacement. Higher-intensity visible light striking the nanoparticle causes this collective oscillation of conduction electrons to occur with greater amplitude.

This collective oscillation of conduction electrons enters into resonance with the visible light—forming the nanoparticle's surface plasmon—when the frequency of the incident light matches the oscillation's natural frequency, as defined by the Fröhlich resonance condition; this condition determines the natural frequency based on the dielectric constants of the metal and the surrounding medium. A change in the dielectric constant of the surrounding medium results, according to the Fröhlich resonance condition, in a corresponding change in the surface plasmon's frequency.

Thus, this model—based on the collective oscillation of conduction electrons and the surface plasmon—determines the observed color of the colloidal suspension via the extinction cross-section described by Mie theory (within the dipole approximation). This extinction cross-section reaches its maximum at the surface plasmon frequency; this frequency of maximum extinction determines which color of the incident visible light is most strongly absorbed or scattered by the metallic nanoparticle and, consequently, which color is perceived by the naked eye in the colloidal suspension. The fact that this surface plasmon—at the frequency determined by the Fröhlich resonance condition—is experimentally detected by another model in this set (which uses UV-Vis spectroscopy to record the shift of this same plasmon peak as a function of nanoparticle size) means that this model directly confirms both the existence of the surface plasmon and its size dependence.

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