Abstract
The light scattering performance of TiO2 pigment
depends intimately upon particle size, size distribution, shape, and dispersion
quality. TiO2 particles exhibit complex shapes and have anisotropic
optical constants, and particulate dispersions of TiO2 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.
Figure 10. Finite element model
cross section and near field scattering results for two anisotropic
morphological rutile particles in n=1.514 resin for light incident normal to the
cross section shown and with a wavelength of 560 nm. The interparticle spacing
is 0.5 m m.
Figure 11. Finite element model cross section and near field
scattering results for two anisotropic morphological rutile particles in n=1.514
resin for light incident normal to the cross section shown and with a wavelength
of 560 nm. The interparticle spacing is 0.2 m m.
Figure 12. Finite element model
cross section and near field scattering results for two anisotropic
morphological rutile particles in n=1.514 resin for light incident normal to the
cross section shown and with a wavelength of 560 nm. The interparticle spacing
is 0 m m.
Figure 13. Scattering coefficient
S for two morphological rutile particles as a function of interparticle
separation. The horizontal line shows the results for two non-interacting
morphological rutile particles.
Figure 14. Angle-weighted
scattering coefficient s for two morphological rutile
particles as a function of interparticle separation. The horizontal line shows
the results for two non-interacting morphological rutile particles.
