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.