Industrial applications of Photon Density Wave spectroscopy for in-line particle sizing [Invited]

Abstract

Optical spectroscopy in highly turbid liquid material is often restricted by simultaneous occurrence of absorption and scattering of light. Photon Density Wave (PDW) spectroscopy is one of the very few, yet widely unknown, technologies for the independent quantification of these two optical processes. Here, a concise overview about modern PDW spectroscopy is given, including all necessary equations concerning the optical description of the investigated material, dependent light scattering, particle sizing, and PDW spectroscopy itself. Additionally, it is shown how the ambiguity in particle sizing, arising from Mie theory, can be correctly solved. Due to its high temporal resolution, its applicability to highest particle concentrations, and its purely fiber-optical probe, PDW spectroscopy possesses all fundamental characteristics for optical in-line process analysis. Several application examples from the chemical industry are presented.

Particle sizing in highly turbid dispersions by Photon Density Wave spectroscopy: Bidisperse systems

“…To calculate theoretical μ 0 s;theo the refractive indices of the medium (water) n M and the particles (polystyrene) n p are required additionally. The refractive index of water was determined experimentally with a refractometer (DSR À λ, Schmidt þ Haensch GmbH & Co., Berlin, Germany; customer designed wavelength range) at seven discrete wavelengths in the range of 403-945 nm and intra-or extrapolated to the measurement wavelengths of PDW spectroscopy using a Cauchy formula [4]. The refractive index of polystyrene was taken from [18].…”

“…The refractive index of polystyrene was taken from [18]. The refractive index of the dispersion was then calculated by [4]: Eq. (7) is obtained from the well-known Lorentz-Lorenz equation discarding the local field correction [19, p. 201].…”

“…Therefore, scattering events are not independent any more leading to a non-linear dependency of μ 0 s on ϕ. For the monodisperse case μ 0 s reads [4,7]:…”

“…Limitations of other particle sizing methods are the disregard of particle interactions at high concentrations or the need for calibration. In contrast, Photon Density Wave (PDW) spectroscopy [2][3][4], based on multiple light scattering, is able to determine independently and without any calibration or dilution the absorption coefficient μ a and the reduced scattering coefficient μ 0 s of highly concentrated samples. While the absorption coefficient is related to chemical information of the sample, the reduced scattering coefficient provides access to the particle size, e.g.…”

“…However, due to the low interparticle distances at high concentrations appropriate models for particle interaction have to be considered additionally. In previous work [3,4], two different models for particle interaction, the Hard Sphere Model in the Percus-Yevick Approximation (HSPYA) and the Yukawa Model in the Mean Spherical Approximation (YMSA) were studied. Whereas the first one incorporates only hard sphere interaction between the spherical particles the second considers additionally electrostatic interaction from particle surface charges.…”