Bruggeman model theory

Bergman effective medium theory, in conjunction with a model dielectric function for the particles, has been used. For the other layers the Bruggeman effective medium theory was used. After [Bel6]. 

The effective medium theory consists in considering the real medium, which is quite complex, as a fictitious model medium (the effective medium) of identical properties. Bruggeman [29] had proposed a relation linking the dielectric permittivity of the medium to the volumetric proportions of each component of the medium, including the air through the porosity of the powder mixture. This formula has been rearranged under a symmetrical form by Landauer (see Eq. (8), where e, is the permittivity of powder / at a dense state, em is the permittivity of the mixture and Pi the volumetric proportion of powder / ) and cited by Guillot [30] as one of the most powerful model. 

The understanding of factors that lead to enhanced band intensities and dispersive band shapes is of central interest in studies with nanostructured electrodes. Effective medium theory has often been employed to identify mechanisms for enhanced infrared absorption [28, 128, 172, 174, 175]. Osawa and coworkers applied Maxwell-Garnett and Bruggeman effective medium models in early SEIRAS work [28, 128]. Recently, Ross and Aroca overviewed effective medium theory and discussed the advantages and disadvantages of different models for predicting characteristics of SEIRAS spectra [174]. When infrared measurements on nanostructured electrodes are performed by ATR sampling, as is typically the case in SEIRAS experiments, band intensity enhancements occur, but the band shapes are usually not obviously distorted. In contrast, external... 

The phenomenon of surface-enhanced infrared absorption (SEIRA) spectroscopy involves the intensity enhancement of vibrational bands of adsorbates that usually bond through contain carboxylic acid or thiol groups onto thin nanoparticulate metallic films that have been deposited on an appropriate substrate. SEIRA spectra obey the surface selection rule in the same way as reflection-absorption spectra of thin films on smooth metal substrates. When the metal nanoparticles become in close contact, i.e., start to exceed the percolation limit, the bands in the adsorbate spectra start to assume a dispersive shape. Unlike surface-enhanced Raman scattering, which is usually only observed with silver, gold and, albeit less frequently, copper, SEIRA is observed with most metals, including platinum and even zinc. The mechanism of SEIRA is still being discussed but the enhancement and shape of the bands is best modeled by the Bruggeman representation of effective medium theory with plasmonic mechanism pla dng a relatively minor role. At the end of this report, three applications of SEIRA, namely spectroelectrochemical measurements, the fabrication of sensors, and biochemical applications, are discussed. 

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