Mie resonance

The final size ofthe clusters depends on the metal it decreases as the initial polymer/ ion concentration ratio increases and with PVA lies in the nanometre range (1-10 nm).The radiolytic method has been used for the synthesis ofa great number of noble and non noble metal nanocolloids in various solvents, water, alcohols, liquid ammonia, etc. Their intense colours, due to a Mie resonance in light absorption by the electron pool of the particle, depend on the surrounding medium, on the cluster size and shape, and on the metal (Fig. 4) in water, yellow for Ag spheres of a few nm 380 nm), purple for Au ( max=520nm),... 

The SPR is then also called Mie resonance. For simple metals, the SPR absorption band has a Lorentzian shape peaked at oi p, the width of which is directly proportional to the collision constant E introduced in the Drude description of the metal dielectiic constant (Eq. 2). Of course, for noble metals the absorption due to interband transitions has to be taken into account in order to obtain the complete spectrum. 

Gold nanoparticles prepared within mesoporous silica monolith showed red-shift of the Mie-resonance absorption band with decreasing the Au particle size. Comparison with theoretical calculations of Mie-resonance for particles of... 

Linear response theory (TDLDA) applied to the jellium model follows the Mie result, but only in a qualitative way the dipole absorption cross sections of spherical alkali clusters usually exhibit a dominant peak, which exausts some 75-90% of the dipole sum rule and is red-shifted by 10-20% with respect to the Mie formula (see Fig. 7). The centroid of the strength distribution tends towards the Mie resonance in the limit of a macroscopic metal sphere. Its red-shift in finite clusters is a quantum mechanical finite-size effect, which is closely related to the spill-out of the electrons beyond the jellium edge. Some 10-25% of the... 

As compared to experiment, all spherical jellium calculations yield an insufficient redshift of the Mie resonance. This is connected to the low polarizability. Therefore, a jellium density with a smooth surface [52], or other corrections found to improve the polarizability, also improve the position of the dipole resonance. Replacing the LDA by a nonlocal description of exchange and... 

This model explains why SEIRA is observed in both s- and p- polarized IRRAS [384] and ATR [391, 405] spectra and in normal-incidence transmission spectra [377] and why the enhancement is not uniformly spread over each metal island but occurs mainly on the lateral faces of the metal islands [378, 384, 385]. The quasi-static interpretation of the SEIRA also defines the material parameters necessary for excitation and observation of SPR (1) The resonance frequency determined from the general Mie condition must be as low as possible and (2) Ime((Ures) must be as small as possible. The maximum enhancement effect should be observed for the absorption bands near the Mie (resonance) frequency of the particle. As mentioned in Section 3.9.1, the resonance frequencies of metal particles lie in the visual or near-IR range. However, they can be shifted into the mid-IR range by (1) increasing the aspect ratio of the ellipsoids, (2) adding the support to an immersion medium, (3) coating the particles by a dielectric shell [24, 406], or (4) varying the optical properties of the support [24, 349, 350, 384]. As emphasized by Metiu [299], the surface enhancement effect is not restricted to metals but can also be observed for such semiconductors as SiC and InSb. 

Figure 1.16 Imaginary part of the complex polarizability a o)) for an Na cluster with N = 198 in units of Effective single-pair excitations, as well as the surface plasmon and the volume plasmon, are clearly resolved. For comparison the result of the local Drude theory is also given. In this case there is only one mode of excitation, the classical surface-plasmon polariton or Mie-resonance at coply/3. Because the frequency is scaled with this frequency the Drude curve peaks trivially at 1. For more explanation see text. Reproduced with permission from Reference [5]. Copyright 1985 by the American Physical Society...

Here Im stands for the imaginary part, and e co) is the complex dielectric function. Using the experimental (o) for sodium [47] one obtains the absorption profile given as the last curve in Figure 5.10(d) (marked NaMie)- The calculated Mie resonance is narrower than the cluster plasmon peaks, but has nearly the same oscillator strength per electron. It has a maximum at Em c = 3.27 eV, which differs from the pure jellium result of 3.41 eV. The small but significant difference of 140 meV is attributed to core polarization effects, i.e. the... 

This asymptotic trend is indicated by the dotted continuation of the peak frequency. It becomes more than obvious that the limitation of nuclear sizes inhibits a clear empirical confirmation of this trend. The Mie resonance in the clusters, on the other hand, approaches a finite value in the bulk limit. This is due to the long-range Coulomb force, which generally produces a plasmon dispersion co a q. The overall trends for very large clusters complies with a linear growth of the surface plasmon frequency. 

In its basic expression, the Drude model does not predict that the absorption bandwidth is affected by particle size. Experimentally, colloidal systems having a weak cluster-matrix interaction show a well-established inverse correlation with respect to the plasmon bandwidth with particle size. In order to describe the bandwidth dependency on particle size. Hovel et al. [47] proposed a classical view of free-electron metals here, the scattering of electrons with other electrons, phonons, lattice defects and impurities leads to a damping of the Mie resonance. Briefly, in realistic metals, the dielectric function is composed of contributions from both interband transitions and the free-electron portion [48]. The free-electron dielectric function can be modified by the Dmde model to account for this dependency, giving [47-50]... 

The theory of isolated resonances is well understood and is discussed below. Mies and Krauss [79, ] and Rice [ ] were pioneers m treating unimolecular rate theory in temis of the decomposition of isolated Feshbach resonances. 

Mies F H 1969 Resonant scattering theory of association reactions and unimolecular decomposition. Comparison of the collision theory and the absolute rate theory J. Cham. Phys. 51 798-807... 

In this Section we want to present one of the fingerprints of noble-metal cluster formation, that is the development of a well-defined absorption band in the visible or near UV spectrum which is called the surface plasma resonance (SPR) absorption. SPR is typical of s-type metals like noble and alkali metals and it is due to a collective excitation of the delocalized conduction electrons confined within the cluster volume [15]. The theory developed by G. Mie in 1908 [22], for spherical non-interacting nanoparticles of radius R embedded in a non-absorbing medium with dielectric constant s i (i.e. with a refractive index n = Sm ) gives the extinction cross-section a(o),R) in the dipolar approximation as ... 

Mies FH (1968) Configuration interaction theory, effects of overlapping resonances. Phys Rev 175 164... 

The sensitivity of a prism-coupled microtube resonator can be evaluated by employing the Mie theory70. For this calculation, the optical field in air is modified as ... 

Using the Mie scattering method, the resonant wavelength shift due to the adsorbed lipid membrane onto the tube wall is simulated with the microtube dimensions identical to the previous simulations. The refractive index of lipid bilayer is assumed to be 1.46. When the inner surface of a tube is coated with lipid membrane, the magnetic field for TE mode can be described in the following form ... 

The absence of an absorption peak arising from Mie plasmon resonance (around 570 nm) [124] indicates that the Cu clusters are smaller than the Mie-onset particle diameter of about 4 nm [124-126]. Plasmon resonance cannot be detected for very small metal clusters because the peak is flattened due to the large imaginary dielectric constant of such materials [122]. 

Chylek et al. (1983) showed that, by comparing experimental resonance spectra with spectra computed using Mie theory, the size and refractive index of a microsphere can be determined to about one part in 10. Numerous investigators have used resonance spectra to determine the optical properties of microspheres since Ashkin and Dziedzic observed resonances. A recent example is the droplet evaporation study of Tang and Munkelwitz (1991), who measured the vapor pressures of the low-volatility species dioctyl phthalate (DOP), glycerol, oleic acid, and methanesulfonic acid (MSA). This... 

The outer and core radii were determined from optical resonance measurements using Mie theory solutions (Aden and Kerker, 1951 Bohren and Huffman, 1983) for concentric spheres to interpret the resonance spectra. Figure 36 presents some of the data of Ray et al. for a pure component glycerol droplet and for a coated droplet having an initial coating thickness given by yo = 0-321. Here y is a reduced thickness defined by y = (a - aj/a. 

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