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Many naturally occurring particles are aggregates of smaller units, also referred to as primary particles. Such aggregates occur in natural waters (for example, Jackson and Burd 1998, Alldredge and Silver 1988) and the atmosphere (soot aggregates - for example, Xiong C and Friedlander 2001, ice crystals in snow - for example, Westbrook CD et al 2002). These particles have random shapes frequently characterized by fractal geometry (for example, http://en.wikipedia.org/wiki/Fractal). Their properties are tractable essentially in terms of ensemble averages of the respective properties of the particles of a dispersion.
From the point of view of the light scattering process, an aggregate is a complex particle. When illuminated by an electromagnetic wave, its primary particles each scatter light in response to the local electromagnetic field, which is the sum of that of the incident wave and those of waves scattered by all other primary particles of the aggregate. The scattered waves interfere to produce the observed scattering/absorption of light by the aggregate. Such a viewpoint is the basis of the discrete dipole approximation (DDA, for example, Mulholland GW et al 1994). The incoherent-scattering version of this approach, has also been used in a Monte Carlo modeling of light scattering by a fractal aggregate of spheres (for example, Deng X et al 2004).
If an aggregate is “tenuous”, i.e. the refractive index of its components is close to that of the surrounding medium and the phase shift parameter of the whole aggregate is much less than unity, then the primary particles can be regarded as independent scatterers. In that case, the scattering of light by the aggregate is the result of interference of waves scattered by the primary particles, accounting only for geometry-related phase delays of the scattered waves (Fig. 1 in Significance of the scattering vector). This is referred to as the Rayleigh-Gans-Debye approximation (RGD, for example, Bohren CF and Huffman 1983, Ch. 6). Applications of this model to aggregates are reviewed, for example, by Sorensen CM 2001 (see also scattering models, nonspherical/inhomogeneous particles, aggregates, RGD).
Fractal aggregates merit a special mention. The spatial arrangement of primary particles within a fractal aggregate has specific geometrical properties (for example, Meakin P 1988b). Given the role of geometry of a particle in light scattering, one may suspect that the structure of fractal aggregates affects light scattering properties of these aggregates is a specific way. It can be simply demonstrated by using the RGD model that this is in fact the case (for example, Sorensen CM 2001).
Light scattering by an aggregate with the relative size much less than unity can be evaluated (for example, Mackowski 1995) by using the Rayleigh model, the i.e. the electrostatic approximation (for example, Bohren CF and Huffman 1983, Ch.5). Mackowski concludes that although the aggregate behaves as a single dipole in this model, the optical properties (for example, absorption cross section) of the aggregate may be significantly influenced by interaction of the primary particles, i.e. multiple scattering within it.
Aggregates of spheres are specific but ubiquitous type of aggregates (for example, soot). The problem of scattering of light by such aggregates has been solved, for example, by Xu YL 1997, 1995 and Fuller and Kattawar 1988b (arbitrary aggregate size/configuration), 1988a (linear chains), and Fuller 1991 (two spheres).
Light scattering by an aggregate has also been modeled in the first approximation by taking a simpler approach based on the porous sphere model with a radius equal to the radius of gyration of the aggregate, rg (Dobbins and Megaridis 1991). The effective refractive index of the porous sphere is calculated by using an effective medium theory. Note that for fractal aggregates, the model of a constant density sphere leads to an incorrect dependence of the angular scattering pattern on the magnitude of the scattering vector, q, for q > 1 / rg (for example, Sorensen CM 2001). In addition, a simple application of an effective medium theory does not account for interaction between the primary particles. Lazarides AA et al 2000 suggested to compensate for this latter neglect by choosing the polarizability of the primary particles so that a lattice of these particles, each approximated by an electric dipole, becomes optically equivalent to a continuum of the dipoles. Such equivalence has been shown by Draine BT and Goodman 1993 in the context of the DDA method.
See also Scattering calculations methods for nonspherical/inhomogeneous particles.
| CITATION: Jonasz M. 2008. Light scattering by aggregates: Calculation methods (www.tpdsci.com/Tpc/ScaAgg.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 12-Jan-2008 Modified: 19-Feb-2008 Peer-reviewed: 26-Feb-2008 |
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