Rigorous Accounting for Dependent Scattering in Thick and Concentrated Nanoemulsions

Concentrated and thick oil-in-water nanoemulsions have been observed to become more transparent with increasing oil volume fraction. This study demonstrates rigorously experimentally and numerically that such unusual behavior is due to dependent scattering including not only far-field but also near-field effects. Indeed, when the droplet concentration is sufficiently large, their interparticle distance becomes small compared to the wavelength of light and scattering by a given droplet may be affected by the proximity of others. This situation is referred to as dependent scattering. Light transfer through nanoemulsions and other colloids has previously been modeled by solving the radiative transfer equation accounting for dependent scattering using the static structure factor based on far-field approximations. Here, oil-in-water nanoemulsions were prepared with oil volume fraction ranging between 1 and 20% and a peak droplet radius of 16 nm. The spectral normal-hemispherical transmittance of the different nanoemulsions in 10 mm thick cuvettes was measured experimentally between 400 and 900 nm. Numerical predictions for nonoverlapping randomly distributed nanoscale oil droplets in water and accounting for dependent scattering including near-field effects-using the recently developed radiative transfer with reciprocal transactions (R²T²) method-were in excellent agreement with experimental measurements. Simulations revealed that assuming independent scattering underestimated the normal-hemispherical transmittance even for a relatively small oil volume fraction. Additionally, simulations using the dense medium radiative transfer (DMRT) and static structure factor predicted that dependent scattering prevailed for oil volume fractions slightly greater than those predicted by the R²T² method. Interestingly, the DMRT method predicted large increases in transmittance when the oil droplet size and volume fraction were larger than 10 nm and 10%, respectively. Finally, simulations also revealed that dependent scattering enables the design of oil-in-water nanoemulsions to backscatter or absorb light by tuning the oil droplet size and volume fraction. The results validate that the R²T² method could be used to characterize nanoemulsions or to investigate their formation, composition, and stability for drug delivery, food, and cosmetics applications. Future studies could extend the use of the R²T² method to colloidal suspensions with particles of arbitrary shapes and to radiation transfer of polarized light in turbid media.