Absorption/extinction cross section

Extinction Coefficient a measure of the ability of particles or gases to absorb and scatter photons from a beam of light a number that is proportional to the number of photons removed from the sight path per unit length. See absorption. Extinction Cross Section the amount of light scattered and absorbed by a particle divided by its physical cross section. 

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 ... 

It follows from (3.20) that the extinction cross section Cext may be written as the sum of the absorption cross section Cabs and the scattering cross section Csca ... 

The origin of the misconception that the absorption spectrum of particles in the Rayleigh limit is not appreciably different from that of the bulk parent material is easy to trace. Again, for convenience, let us take the particles to be in free space. In Chapter 3 we defined the volume attenuation coefficient av as the extinction cross section per unit particle volume if absorption dominates extinction, then av for a sphere is 3Qabs/4a, where a is the radius. If we assume that n k, which is true for most insulating solids at visible wavelengths, then... 

This calculated extinction cross section can then be compared with data measured via absorption spectroscopy. 

Conservation of energy requires that the light removed from the incident beam by the particle is accounted for by scattering in all directions and absorption in the particle. The combined effect of scattering and absorption is referred to as extinction, and an extinction cross section (Cext) can be defined by... 

Lahmani et al. (1980a) have shown that below 190 nm, the absorption of CH3ONO continues to decrease to a minimum at =>168 nm. It then increases to a maximum at 139 nm, which has an extinction cross section of (3.33 0.08)... 

Cext is the extinction cross-section of the spheres. The extinction efficiency factor which is the sum of scattering and absorption, is defined as the quotient of and the... 

The attenuation of light by a particle includes contributions from elastic scattering and absorption. The absorbed photons induce transitions leading to Raman or fluorescence scattering or contribute to the internal heating of the particle. The extinction cross section is the sum of the elastic-scattering cross section and the absorption cross section. The corresponding efficiency factors formed by... 

Figure 3.56. Calculated extinction cross section of CdTe sphere of radius 3 (jim with CdO coating of (a) 10 nm and b) 100 nm thick S and B denote surface and bulk mode absorption peaks, respectively. Reprinted, by permission, from R. Ruppin, Surf, Sci. 51,140 (1975), p. 145, Fig. 3. Copyright 1975 North-Flolland Publishing Company.

Because the extinction cross-section is a sum of the absorption and the scattering cross-sections, the absorption cross-section is obtained by subtracting the scattering from the extinction. 

The electronic plasmon absorption of a 6 nm Ag island film is shown in Figure 3. In the same figure, the extinction cross section calculated for a silver sphere and a silver prolate with a 3 1 aspect ratio, within the long wavelength limit of Mie theory, are included for comparison. The computation clearly illustrates the considerable shift to the red of the main plasmon absorption of the prolate spheroids in reference to the silver sphere. The broad plasmon absorption indicates a large distribution of sizes and shapes of Ag nanoparticles, and has a maximum at 494 nm. Notably, the SERS excitation profile follows closely the measured plasmon absorption, confirming the EM nature of the observed enhanced intensities. ... 

Figure 2. Calculated absorption, scattering, and extinction cross-section from a 40 nm diameter Ag particle and a 60 nm diameter Au particle. The spectrum from the silver particle has a sharp resonance and its extinction is equally split between scattering and absorption components, udiereas, the 60 nm diameter gold particle has a broader resonance and is dominated by absorption.

The intensity, number, and width of the surface plasmon resonances are very sensitive to the nanoparticle morphology. For metal nanoparticles whose shape deviates from that of a sphere, exact analj ic solutions of the extinction cross section are not available. Here we will describe, examples of absorption and scattering spectra obtained by discretizing the targets within the DDA framework... 

The equation for Mie scattering comes directly from solutions to Maxwell s equations applied to a spherical particle and the medium surrounding it (20), The extinction cross-section can further be defined as a combination of absorption and scattering, such that ... 

The amount of fluorescence emitted by a fluorophore is determined by the efficiencies of absorption and emission of photons, processes that are described by the extinction coefficient and the quantum yield. The extinction coefficient (e/M-1 cm-1) is a measure of the probability for a fluorophore to absorb light. It is unique for every molecule under certain environmental conditions, and depends, among other factors, on the molecule cross section. In general, the bigger the 7c-system of the fluorophore, the greater is the probability that the photon hitting the fluorophore is absorbed. Common extinction coefficient values of fluorophores range from 25,000 to 200,000 M 1 cm-1 [4],... 

Table I. Absorption Cross Sections (cJin) and Molar Extinction Coefficients (e) of Transition of ZnTPP...

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