The effect of the stagnant layer on the photon mean-free-path length in concentrated suspensions of nanoparticles

Abstract

We analyze the possibility of evaluation of the thickness and refractive index of the stagnant layer in concentrated suspensions of nanoparticles through the transport characteristics of scattered light photons. The analysis is based on a physically-transparent generalization of the concept of the single scattering intensity off systems in which the number of particles within regions with linear sizes of order of the wavelength in the medium greatly exceeds unity. This generalization is carried out within the notion of compact groups of particles, makes it possible to go beyond the traditional Born approximation, and take into account many-particle effects contributed from those ranges of integration variables in the terms of the iteration series for the scattered field where the internal propagators have delta-function-type behavior. As a result, the evaluation of the photon transport characteristics becomes possible without a detailed modeling of many-particle scattering and correlation processes in the system. 
 The photon mean-free-path length is investigated theoretically as a function of the stagnant refractive index and that of the layer thickness to show a noticeable effect of both parameters on it. As the layer refractive index is increased at a fixed layer thickness, the mean-free-path length decreases because the suspension optical density increases. As a function of the layer thickness, the photon mean-free-path length reveals different types of behavior, depending on the relation between the refractive indices of the stagnant layer and base liquid. If the former is smaller than the latter, this behavior is increasing; in the opposite case, it is decreasing. An experimentally observed increase of the photon mean-free-path length with the particle concentration is usually explained as a manifestation of higher correlation effects. Our theory reveals that the presence of the stagnant layer make the situation more complicated, for both factors may either enhance or diminish each other. To resolve the issue, new specially-designed experiments are required to be set up.