Surface Effects on the Coherent Reflection of Light From a Polydisperse Colloid

Abstract

We consider the coherent reflection of light from a dilute polydisperse random system of particles. We focus our attention on the effects of the variation of the size distribution function induced near a flat solid interface. We also present a comparison of the theory with experimental results of the coherent reflectance of light in an internal reflection configuration. Introduction The coherent reflection and transmission of light in random systems of particles is potentially a useful tool to characterize highly scattering particles, colloids and composite materials. By coherent we mean the wave corresponding to the average electromagnetic field which is obtained by averaging over all possible configurations of the system (configurational average). The coherent transmission of electromagnetic waves through random systems of particles has been studied by several authors since long ago (1). More recently, the coherent reflection of an electromagnetic wave from a half space of randomly located particles has been studied using a very intuitive approach (3), which turned out to be closely related to the so called effective-field approximation (4) and valid only for a dilute suspension of particles. We will call this approach the coherent-scattering model. For relatively dense systems a more elaborate procedure, called the quasi-crystalline approximation (2), has been also developed. This latter approximation is rather intensive numerically, and since we are exploring here the importance of surface effects on the reflectance, we will restrict ourselves to dilute colloidal systems where the inversion of experimental data can be easily done. We should also add that we have performed already experiments to test and to validate the coherent-scattering model finding that it can reproduce well the experimental data (5). However, when dealing with polydisperse systems of particles in the presence of a flat interface between the matrix material and a homogeneous medium, the mere presence of the interface changes the density and size distribution over a region of the order of the width of the size distribution function. This region of variable density and size distribution may be called the surface region. In this paper we propose an iterative procedure to take into account in the reflectance calculations the presence of the surface region and compare its effects with the ones of a simpler approximation that we call the sharp-surface approximation. Finally, we also present a comparison between reflectance calculations using the coherent-scattering model and experimental data of light reflectance from a polydisperse colloidal suspension of latex particles, in an internal-reflection configuration.