Theory For Spherical Particles Research Articles

Arctic aerosol and clouds studied by bistatic lidar technique

Aerosol and cloud studies were carried out with a polarimetric bistatic lidar setup at the Arctic Lidar Observatory for Middle Atmosphere Research (ALOMAR) in Andenes (69°N, 16E°), Norway. The measurements were performed from 10 to 23 October 2006 and covered altitudes between 1.5 and 11 km, corresponding to scattering angles between 130 and 170°. The degree of linear polarization, PL, calculated from the experiments was compared with light scattering calculations using Lorenz‐Mie theory for spherical particles, the T‐matrix approach for nonspherical rotationally symmetric particles, and a geometric optics ray‐tracing method. Average PL values between 0.61 and 0.72 were obtained for the background aerosol under cloud‐free conditions. The aerosol results may be qualitatively reproduced by standard aerosol types if a suitable combination of coarse‐ and fine‐mode spherical particles is assumed. The PL values obtained for thin and mildly opaque clouds were in the range from 0.21 to 0.38. These results were not well described by spherical particles, and the results for relatively small prolate and oblate particles studied with the T‐matrix method tended to be slightly higher than the experimental values. Geometric optics calculations for hexagonal column ice particles with surface roughness were able to reproduce the experimental cloud data. This does not rule out contributions from other types of particles, and particle orientation effects may also have influenced the results. We conclude that the experimental results are consistent with earlier in situ studies of cirrus clouds, and the further development and application of the bistatic lidar technique is discussed.

Nanofoam Porosity Measured by Infrared Spectroscopy and Refractive Index

AbstractInfrared spectroscopy and optical waveguide were used to determine the porosity of polymer nanofoams produced from block copolymers of an aromatic polyimide endcapped with either poly(propylene oxide) or poly(a-methylstyrene). The infrared absorption bands and film thickness were compared to those of the neat homopolymer to yield an accurate measure of the void content. The porosity was also determined by measuring the refractive index and using the Maxwell-Garnett effective medium theory for spherical particles. Both techniques are in quantitative agreement with density gradient methods.

Light scattering by nonspherical ice grains: An application to noctilucent cloud particles

The light scattered by noctilucent cloud particles is nearly fully polarized at scattering angles in the vicinity of 90 ‡. This was one of the reasons to conclude that the upper limit of their sizes is not larger than about 0.12 Μm. Nevertheless, this estimate was made on the basis of the Mie scattering theory for spherical particles, whereas many investigators noted usefulness of highly aspherical shapes of noctilucent cloud particles. In this paper, we used rigorous light scattering theory for randomly oriented nonspherical particles to calculate the degree of linear polarization of the scattered light for ice grains of different shape. By comparing these calculations with rocket polarization measurements of noctilucent clouds, we show that, as for spherical particles, the upper limit of particle equal-volume radii for slightly flattened and elongated grains is of about 0.12 Μm, while for highly aspherical plate-like and needle-like particles this upper limit is substantially larger and is of about 0.18–0.20 Μm. We also report calculations of the volumetric scattering cross-section for particles of different shape and show that randomly oriented spheroids have (slightly) smaller scattering cross section per unit particle mass than equal-volume spherical grains. Nevertheless, if in noctilucent clouds plate-like and needle-like grains grow to much larger sizes than spherical particles, their scattering efficiency may be much greater.

A b i n i t i o micromagnetic calculations for particles (invited)

We present the results of first-principles calculations of the magnetic behavior of particles of varying shapes (sphere, prolate spheroid, and rectangular particles of various aspect ratios) and sizes ranging from ≊0.1 to 10 μm. We use a numerical implementation of micromagnetics in which the only input quantities, aside from the particle geometry, are the material parameters and the magnetic history. We have obtained quantitative agreement with theory for spherical particles and qualitative agreement with experiment in the case of rectangular objects, and we have observed a variety of interesting reversible and irreversible phenomena accompanying magnetic reversal in all objects. We describe key aspects of the numerical implementation and survey selected results.

Scattering of polarised light by colloids containing anisotropic particles

It is only recently that the theoretical significance of the elliptic polarisation of light scattered by colloids containing particles of large size has been pointed out and an analysis made of the theoretical conclusions regarding ellipticity from Mie’s theory for spherical particles. The earlier qualitative measurements on ellipticity of the scattered light have been explained on the basis of these new ideas and the implications of Mie’s theory brought out more clearly. New experiments have been devised and used for measuring the constant phase difference δ that exists between the vertical and horizontal components of the transversely scattered light when the incident light is polarised in any azimuth. Measurements have been made both for systems of spherical particles and anisotropic particles. It is found that even in the case of large anisotropic particles δ is a constant. It follows therefore, that in the most general case of large anisotropic colloidal particles the polarised scattering due to finite size is elliptic in nature and is superposed on the depolarised part due to anisotropy.