Light‐Scattering Properties of Representative, Morphological Rutile Titania Particles Studied Using a Finite‐Element Method

Abstract

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 lightscattering 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.

Influence of Multi-cycle Infiltration on Porosity and Optical Properties of Glassinfiltrated Alumina Biocomposites for Dental Restorations

“…This theory shows that scattering is a strong function of particle size and maximum scattering occurs when the particle size is close to the wavelength of the incident radiation [18]. The higher transmittance seen in specimens infiltrated with three cycles can be attributed to the reduction in residual porosity and also in pore fraction with diameter smaller than 3.2 µm.…”

Estudio de los factores que gobiernan la coloración de los esmaltes cerámicos

“…Más estudios en este sentido fueron desarrollados por Nakai y col (7). También se pueden citar los trabajos de Thiele y col. (8,9) donde se tienen en cuenta efectos debidos a la dispersión de la luz.…”

Near-field scattering by dielectric spheroidal particles with sizes on the order of the illuminating wavelength

“…This is known as the ES or non-retarded regime and occurs when the particle size is sufficiently small to satisfy both Rayleigh limit conditions [14], 2TTRJ\ < 1, \n r \2irRJ\ < 1, (13) where R eq is a characteristic length of the particle. For spheres it is simply the radius, and for spheroids R eq is taken as the radius of the volume-equivalent sphere [31].…”

“…Studies that go beyond these limitations, dealing with non-spherical objects with sizes on the order of or bigger than the wavelength, usually employ numerical grid-based approaches such as the finite difference time-domain [12] and finite element [13] methods. With mesh approaches it is usually difficult to resolve high field gradients that occur at the surface of particles that scatter highly resonantly with the incoming light.…”