skip to main content

Title: Small and large particle limits of single scattering alb e do for homogeneous, spherical particles
The aerosol single scattering albedo (SSA) is the dominant intensive particle parameter determining aerosols direct radiative forcing. For homogeneous spherical particles and a complex refractive index in- dependent of wavelength, the SSA is solely dependent on size parameter (ratio of particle circumference and wavelength) and complex refractive index of the particle. Here, we explore this dependency for the small and large particle limits with size parameters much smaller and much larger than one. We show that in the small particle limit of Rayleigh scattering, a novel, generalized size parameter can be introduced that unifies the SSA dependence on particle size parameter independent of complex refractive index. In the large particle limit, SSA decreases with increasing product of imaginary part of the refractive index and size parameter, another generalized parameter, until this product becomes about one, then stays fairly constant until the imaginary part of the refractive index becomes comparable with the real part minus one. Beyond this point, particles start to acquire metallic character and SSA quickly increases with the imaginary part of the refractive index and approaches one.
Authors:
;
Award ID(s):
1649783
Publication Date:
NSF-PAR ID:
10056818
Journal Name:
Journal of Quantitative Spectroscopy & Radiative Transfer
Volume:
204
Page Range or eLocation-ID:
250-255
ISSN:
0022-4073
Sponsoring Org:
National Science Foundation
More Like this
  1. Biomass burning (BB) aerosols contribute to climate forcing, but much is still unknown about the extent of this forcing, owing partially to the high level of uncertainty regarding BB aerosol optical properties. A key optical parameter is the refractive index (RI), which influences the absorbing and scattering properties of aerosols. This quantity is not measured directly, but it is obtained by fitting the measured scattering cross section and extinction cross section to a theoretical model using the RI as a fitting parameter. We used the Rayleigh–Debye–Gans (RDG) approximation to retrieve the complex RI of freshly emitted BB aerosol from two fuels (eucalyptus and olive) from Africa in the spectral range of 500–580 nm. Experimental measurements were carried out using cavity ring-down spectroscopy to measure extinction over the range of wavelengths of 500–580 nm and nephelometry to measure scattering at three wavelengths of 450, 550, and 700 nm for size-selected BB aerosol particles. The fuels were combusted in a tube furnace at a temperature of 800 °C, which is representative of the flaming stage of burning. Filter samples were collected and imaged using tunneling electron microscopy to obtain information on the morphology and size of the particles, which was used inmore »the RDG calculations. The mean radii of the monomers were 27.8 and 31.5 nm for the eucalyptus and the olive fuels, respectively. The components of the retrieved complex RI were in the range of 1.31 ≤ n ≤ 1.56 and 0.045 ≤ k ≤ 0.468. The real and complex parts of the RI increase with increasing particle mobility diameter. The real part of the RI is lower, and the imaginary part is higher than what was recommended in literature for black carbon generated by propane or field measurements from fires of mixed wood samples. Fuel dependent results from controlled laboratory experiments can be used in climate modeling efforts and to constrain field measurements from biomass burning.« less
  2. We present measurements of the scattered light intensity by aerosolized hematite aggregate particles. The measurements were made at a wavelength of 532 nm in the scattering angle range from 0.32 °to 157 °. Hematite has high values of the real and imaginary parts of the refractive index m = n + i κ= 3 + i0.5 at the studied wavelength. Scanning electron micrographs (SEM) indicated that the particles were aggregates whereas the optical microscope pictures showed that the aerosol had a bimodal distribution with effective mean diameters of roughly 1 and 10 μm. This is consistent with the light scattering results which displayed two Guinier regimes. The aggregates were composed of smaller grains with an approximate size of 200 nm. Ultra Small-Angle X-ray Scattering (USAXS) indicate that the aggregates were uniform and non-fractal. Mie calculations for a sphere equivalent to the aggregate size were compared to the experimentally observed results. The observed results showed an enhanced backscattering, whereas the Mie calculations did not due to the large imaginary part of the refractive index. Hematite aggregates were simulated by assuming they were composed of spherical monomers inside a spherical volume. Then the light scattering was calculated using the T-matrix method formore »these simulated aggregates. The calculated results show an enhanced backscattering. We present a dimensional analysis to estimate the extent of multiple scattering within the aggregate and find a correlation between the average number of scattering events within the aggregate and the enhancement in the backscattering.« less
  3. We present measurements of light scattering intensity from aerosolized, micron sized, irregularly shaped, molybdenum disulfide (MoS 2 ) particles in order to study the effects of a refractive index, m = n + i κ, with large real and imaginary parts. Light scattering was measured over a range of angles from 0.32 °to 157 °. Calibration was achieved by scattering with micron sized, spherical silica particles. Light scattering for both particle types was compared to theoretical Mie scattering calculations using size distributions deter- mined by an aerodynamic particle sizer. Effects of the intensity weighted size distribution are discussed. We find that scattering by these irregularly shaped, highly refractive particles is well described by Mie scattering. We also find that when the quantity κkR, where kR = 2 πR/ λis the size parameter, is greater than one, there is no enhancement in the backscattering. Finally, we show that Guinier analysis of light scattering by highly refractive particles yields intensity weighted mean sizes of reasonable accuracy for any shape.
  4. The scattered intensity from large spheres with a real part of the refractive index ofn=1.33,1.5,2.0is investigated as the radiusRand an imaginary part of the refractive indexκ<#comment/>are varied. It is shown that the product ofκ<#comment/>and the size parameterkR,κ<#comment/>kR, is a universal parameter describing the quenching of the refraction phenomenon of the scattered light: the refraction hump, the generalized rainbows, and the glory. The physical reason for this is thatκ<#comment/>kRis the inverse of the relative skin depth of light penetration into the sphere, which is demonstrated by calculations of the internal fields that darken universally asκ<#comment/>kRincreases.

  5. We show that for spherical particles greater than ca. 5 µm, the differential scattering cross section is only weakly dependent on the real and imaginary parts of the refractive index (m=n+iκ<#comment/>) when integrated over angle ranges near37±<#comment/>5∘<#comment/>and115±<#comment/>5∘<#comment/>, respectively. With this knowledge, we set up an arrangement that collects scattered light in the ranges37±<#comment/>5∘<#comment/>,115±<#comment/>5∘<#comment/>, and80±<#comment/>5∘<#comment/>. The weak functionality on refractive index for the first two angle ranges simplifies the inversion of scattering to the particle properties of diameter and the real and imaginary refractive indices. Our setup also uses a diamond-shaped incident beam profile that allows us to determine when a particle went through the exact center of the beam. Application of our setup to droplets of an absorbing liquid successfully determined the diameter and complex refractive index to accuracies ranging from a few to ten percent. Comparisons to simulated data derived from the Mie equations yielded similar results.