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

TL;DR

This paper develops a theoretical framework to evaluate how the stagnant layer's thickness and refractive index affect photon mean-free-path in concentrated nanoparticle suspensions, accounting for many-particle effects beyond traditional approximations.

Contribution

It introduces a generalized model for photon scattering in dense suspensions, incorporating many-particle effects and providing insights into how stagnant layers influence light transport properties.

Findings

Photon mean-free-path decreases with higher stagnant layer refractive index.

Layer thickness affects mean-free-path differently depending on refractive index contrast.

Higher particle concentration correlates with increased mean-free-path due to correlation effects.

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. 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, $l$, is investigated 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, $l$ decreases because the suspension optical density increases. As a function of the layer thickness, $l$ reveals different types of behavior, depending on the relation between 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 $l$ with the particle concentration is explained as a manifestation of higher correlation effects. Our theory reveals that the stagnant layer make the situation more complicated, for both factors may either enhance or diminish each other.