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Light‐Scattering Properties of Representative, Morphological Rutile Titania Particles Studied Using a Finite‐Element Method
Author(s) -
Thiele Erik S.,
French Roger H.
Publication year - 1998
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1151-2916.1998.tb02364.x
Subject(s) - mie scattering , light scattering , scattering , materials science , isotropy , optics , light scattering by particles , particle (ecology) , scattering theory , anisotropy , molecular physics , ray , physics , oceanography , geology
The light‐scattering performance of TiO 2 pigment depends intimately upon particle size, size distribution, shape and dispersion quality. TiO 2 particles exhibit complex shapes and have anisotropic optical constants, and particulate dispersions of TiO 2 are characterized by complicated microstructures such as aggregates and agglomerates. Despite this complexity, the theoretical understanding of light scattering by white pigment has been based upon Mie theory, which is restricted to the case of a single, optically isotropic sphere. We utilize a finite‐element method which produces rigorous solutions to Maxwell's equations to determine computationally the light‐scattering properties of complex particulate microstructures. This represents a significant step beyond the restrictions of Mie theory, providing a method to determine quantitatively the effects of particle shape, optical anisotropy, and interactions between neighboring particles upon the light‐scattering properties of white pigments in coatings. In the present study, we use the finite‐element method first to compute the light‐scattering properties of a single, morphological rutile particle with a representative size and shape. These results are compared to the light‐scattering properties of the optically isotropic, equivalent volume sphere using Mie theory. Neither the average index nor the weighted sum approximation offers clear advantages in this case. Second, the far‐field light‐scattering properties of two such particles interacting at near field are determined as a function of the interparticle separation. The agglomerated pair of particles exhibits a 20% decrease relative to the single particle in the scattering parameter associated with the hiding power of a paint film. The basis for this decrease is the same as for the crowding effect observed in extensive paint films. The results of both sets of computations are compared to Mie theory to determine the sizes of spherical particles with equivalent scattering cross sections. These comparisons highlight the inherent difficulties in using Mie theory to evaluate particle size by light‐scattering methods.