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A complete form of the van der Waals dispersion interaction between an infinitely long anisotropic semiconducting/insulating thin cylinder and an anisotropic half space is derived for all separations between the cylinder and the half space. The derivation proceeds from the theory of dispersion interactions between two anisotropic infinite half spaces as formulated in Phys. Rev. A 71, 042102 (2005). The approach is valid in the retarded as well as nonretarded regimes of the interaction and is coupled with the recently evaluated ab initio dielectric response functions of various semiconducting/insulating single wall carbon nanotubes, enables the authors to evaluate the strength of the van der Waals dispersion interaction for all orientation angles and separations between a thin cylindrical nanotube and the half space. The possibility of repulsive and/or nonmonotonic dispersion interactions is examined in detail.

When film coatings are made of pigment particles embedded in a transparent resin, the optical characteristics of the resulting film are determined not only by the bulk optical properties of the constituent materials, but also by the spatial distribution of the light scattered from small particles. If the particles are separated by distances comparable to their diameter, as is the case for high particle concentrations or agglomerated systems, the near-field interactions between the radiation fields of the particles can strongly influence the resulting far-field intensity distribution. In this work we have used full-field finite-element solutions of Maxwell’sequations to calculate the near- and far-field scattering patterns for single 500 nm quinacridone spheres and for pairs of particles. We find that the scattered intensity forms a forward-directed plume that extends far beyond the particle surface, especially at short wavelengths and where the absorption is large. This results in near-field interactions between pairs of particles that can either increase or decrease the scattering (both the total scattering and the fraction of the scattered light that is directed into the backward hemisphere), depending on the orientation of the particle pair relative to the direction of the incident light. In some cases, particularly if the particles are aligned along the incident direction, the two spheres can produce a far-field scattering distribution that is approximately that of a single, larger (sometimes much larger) sphere. If the particles are aligned perpendicular to the incident direction, the strength of the scattering per particle volume is roughly the same as for a single particle, but the scattering is more forward directed. These interaction effects occur even though the surface-to-surface separation of the particles is larger than the distance for which a single particle shows significant scattered intensity. These near-field and far-field phenomena are beyond the limitations of single-scattering and independent multiple-scattering approaches, and the near-field interactions can have a significant effect on the scattering of light from films containing such particles, especially if they tend to form oriented clusters.

In the optical analysis of collections of particles embedded in a matrix, the ultimate goal is to predict the optical properties of the final film, given the optical characteristics of the materials of which it is made, the particle size, and the fraction of the volume occupied by the particles. The first task in the pursuit of this goal is to make connections between the optical properties of the bulk materials of which the particles and medium are made and the spatial distribution of the scattered intensity from the individual particles. The second is to relate the calculated far-field scattering and absorption cross sections for a single particle to the measured optical characteristics of real films. Here we accomplish these tasks for a regime that is rarely considered in the literature but is quite important in applications. This regime is characterized by three conditions: (a) the extinction coefficient of the particle is significant; (b) the particle size is comparable to the wavelength in the medium; and (c) the optical density of the films is large enough that multiple scattering is significant, and yet direct transmission of collimated radiation through the film is not negligible. We have measured the visible diffuse reflectance and transmission of films of quinacridone particles in a transparent resin at various particle volume concentrations, and used the Kubelka–Munk formalism as a parametrization method to extract scattering and absorption parameters for this strongly absorbing, multiple-scattering system in the resonant regime. We have modeled the scattering parameter S * as a convolution of the angular distribution of the scattering from a single particle (derived from Mie theory) and a multiple-scattering function that characterizes the effects of the concentration and arrangement of the particles in the film. We find that the multiple-scattering function has an angular distribution that is strongly peaked in the backscattering direction. This accounts for the transformation of the collimated and strongly forward-scattered light in the top layers of the film into diffusely reflected light as the film is traversed. The multiple-scattering function also accounts for the differences in diffuse reflection observed for films of identical volume fraction occupied by particles (particle volume concentration) but different grinding time. This method of analysis begins to allow one to make an explicit connection between the fundamental optical properties of the particles and the experimentally accessible parameters. We have thus developed a way to begin to bridge the gap between the fundamental physics of the scattering of light from individual particles and the practical characterization of a film using the simple Kubelka–Munk analysis.

Master of Science