Dependent Scattering in Thick and Concentrated Colloidal Suspensions

This study demonstrates numerically and experimentally that dependent scattering occurs in colloidal suspensions and can, counterintuitively, cause their transmittance to increase with increasing particle volume fraction. Radiation transfer through colloidal suspensions has been modeled with the radiative transfer equation (RTE) assuming independent scattering. Then, the effective absorption and scattering coefficients of the disperse medium are predicted as the sum of the cross sections of all particles divided by the volume of suspension. However, this approach is not valid when the average interparticle distance is on the same order of magnitude as the wavelength, corresponding to large particle concentrations. The latter situation is referred to as dependent scattering. Rigorously accounting for dependent scattering requires solving Maxwell's equations, but is limited to relatively thin suspensions. Here, we extend the Radiative Transfer with Reciprocal Transactions (R2T2) method to predict the normal-hemispherical transmittance of thick and concentrated plane-parallel slabs of nonabsorbing nanoparticle suspensions and to rigorously account for dependent scattering effects. The radiation characteristics of a large number of particle ensembles were estimated using the superposition T-matrix method and the RTE was solved using Monte Carlo method combined with strategies for sampling the previously computed radiation characteristics. A wide range of particle size parameter, volume fraction, and optical properties as well as colloidal suspension thickness were investigated. Dependent scattering effects were found to prevail for particle volume fractions as low as 1% depending on the particle size and refractive index. Evidences of dependent scattering were also observed experimentally in the visible normal-hemispherical transmittance of 10 mm thick colloidal suspensions of silica nanoparticles with diameter between 16 and 30 nm and particle volume fraction ranging from 2% to 15%. Moreover, good agreement was found between experimental measurements and numerical predictions from the R2T2 method. By contrast, assuming independent scattering underestimated systematically the normal-hemispherical transmittance, especially for large particle volume fraction. As such, this paper presents, for the first time, experimental validation of the R2T2 method and its ability to account for dependent scattering.