Abstract
The influence of the internal structure of inhomogeneous particles on their radiative properties is an open issue repeatedly questioned in many fields of science and technology. The importance of a refined description of the particle composition and structure, going beyond mean-field approximations, is generally recognized. Here, we focus on describing internal inhomogeneities from a statistical point of view. We introduce an analytical description based on the two-point density-density correlation function, or the corresponding static structure factor, to calculate the extinction cross sections. The model agrees with numerical predictions and is validated experimentally with colloidal aggregates in the 0.3–6 μm size range, which serve as an inhomogeneous model system that can be characterized enough to work without any free parameters. The model can be tightly compared to measurements with single particle extinction and scattering and spectrophotometry and suggests a simple behavior for 90° scattering from fractal aggregates as a function of extinction, which is also confirmed experimentally and numerically. We also discuss the case of absorbing particles and report the experimental results for water suspensions of black carbon for both the forward and 90° scattering properties. In this case, the total scattering and the extinction cross sections determine the single scattering albedo, which agrees with numerical simulations. The three parameters necessary to feed radiative transfer models, namely, extinction, asymmetry parameter, and single scattering albedo, can all be set by the analytical model, with explicit dependence on a few parameters. Results are applicable to radiative transfer problems in climate, paleoclimate, star and planetary formation, and nanoparticle optical characterization for science and industry, including the intercomparison of different optical methods such as those adopted by ISO standards.
Highlights
Dust, powders, and micro- and nanoparticles of natural and anthropogenic origin have been the subject of extensive research due to their ubiquity and potential industrial applications
The optical properties of dust are paramount in our understanding of a widespread class of systems, such as the influence of eolian dust on climate balance and remote sensing (Mishchenko et al 1995; Claquin et al 1998; Bigler et al 2011; Kemppinen et al 2015; Wu et al 2016; Doner and Liu 2017), dust grains in the solar system, protoplanetary accretion disks, and star-forming clouds (Bazell and Dwek 1990; Kozasa et al 1992; Stognienko et al 1995; Fogel and Leung 1998; Voshchinnikov et al 2000; Shen et al 2008; Köhler et al 2011; Ormel et al 2011; Kataoka et al 2014; Min et al 2016)
Three general cases where optical properties are the cornerstones of the analysis can be identified: i) Interpreting data from optical instruments based on the measurement of light emitted by one or a collection of particles ii) Interpreting data from light scattering in dust clouds iii) Modeling physical systems where the light is emitted, scattered, and possibly absorbed by dust grains
Summary
Powders, and micro- and nanoparticles of natural and anthropogenic origin have been the subject of extensive research due to their ubiquity and potential industrial applications. As discussed in the literature (Sorensen 2001), the structure factor can be fitted by several functions that depend on a small set of parameters, such as the number of primary particles (N), the fractal dimension (df), and the gyration radius (Rg). The following scaling relation can be derived (Sorensen 2001; Potenza and Milani 2014) This scaling law obtained from the MFA is in open contrast with the result reported above for the aggregates, where Re Sð0Þ and Im Sð0Þ are both proportional to the number of monomers and the slope does not depend on df. A homogeneous spherical particle deriving from the MG model (case 3.3 above, Fig. 1c) can be related to each fractal and uncorrelated particle, obtaining a triplet of particles with a different morphology but described by the same set of parameters, which give the same particle density (or volume fraction)
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