Rayleigh extinction

For convenience, a megameter, denoted Mm and equal to 1000 km, is often used as the unit of distance in this unit the sea-level Rayleigh extinction coefficient is 13 Mm 1. 

Classical electrodynamics is the theoretical treatment used to describe the LSPR effect. The shape and size of the nanoparticles define the resonant response, as well as the theoretical treatment. Mie theory solves the sphere case, while almost no analytic calculations have been established for other nonspher-ical particles. When particles are small enough with respect to incident wavelength (X) (j = (InanmlX) 1, where a is the size of the particle and m is the surrounding media refractive index), same approximations can be achieved and Rayleigh extinction (Cext) cross section expression is obtained ... 

Rayleigh scattering accounts for only a minor part of the extinction, except on the clearest days. It is a function of atmospheric pressure alone and... 

The Rayleigh scattering extinction coefficient for particle-free air is 0.012 km for "green" light (y = 0.05 /rm) at sea level (4). This permits a visual range of —320 km. The particle-free, or Rayleigh scattering, case represents the best visibility possible with the current atmosphere on earth. 

A glance at the curves in Fig. 11.15 reveals extinction characteristics similar to those for spheres at small size parameters there is a Rayleigh-like increase of Q a with x followed by an approximately linear region broad-scale interference structure is evident as is finer ripple structure, particularly in the curves for the oblate spheroids. The interference structure can be explained... 

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... 

Measurements of extinction by small particles are easier to interpret and to compare with theory if the particles are segregated somehow into a population with sufficiently small sizes. The reason for this will become clear, we hope, from inspection of Fig. 12.12, where normalized cross sections using Mie theory and bulk optical constants of MgO, Si02, and SiC are shown as functions of radius the normahzation factor is the cross section in the Rayleigh limit. It is the maximum infrared cross section, the position of which can shift appreciably with radius, that is shown. The most important conclusion to be drawn from these curves is that the mass attenuation coefficient (cross section per unit particle mass) is independent of size below a radius that depends on the material (between about 0.5 and 1.0 fim for the materials considered here). This provides a strong incentive for deahng only with small particles provided that the total particle mass is accurately measured, comparison between theory and experiment can be made without worrying about size distributions or arbitrary normalization. 

Figure 12.12 Maximum infrared extinction cross sections of spheres normalized by the value in the Rayleigh limit.

Figure 2. Ratio of DNA dose with aerosols to DNA dose in aerosol-free atmosphere (Rayleigh visual range of 386 km), for different aerosol loadings. The lower scale gives the ground level total extinction coefficient at 550 nm, while the upper scale gives the corresponding visual range, (from figure 2 of Liu et al. 1991).

By first considering the Rayleigh regime and expanding the complex scattering coefficients in power series of a, it can be shown that the extinction can be approximated by (1, 3, 17)... 

Therefore, in principle, the parameters of the particle size distribution can be estimated from specific turbidity measurements at different wavelengths. This is not true, however, in the Rayleigh regime (i.e. small particles, (D/Am) less than 0.1). In this case, the extinction coefficient is proportional to (D/Am)4 and... 

Values of both Rayleigh and aerosol extinction at the surface for a clear day are given in Table V. For the detailed altitude behavior of these coefficients and their integrated extinction, the reader should refer to the reports by Elterman (55,56). 

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