Transition from diffusing to dynamic light scattering in solutions of monodisperse polystyrene spheres

Abstract

Light scattering in the backscattering geometry, and transmission measurements are used to size monodisperse spherical particles in solutions. The concentration of spheres spans the scattering to range from single scattering to very highly multiple scattering. These experiments were performed by varying volume fractions of polystyrene latex spheres of nominal diameter 0.136 and 1.015 m. Transmission measurements were performed as a function of particle size, volume fraction, and sample thickness with a spectrophotometer equipped with an integrating sphere. The data show that for thin samples the percent transmission is nearly independent of particle size and depends only on L/l*, the ratio of the sample thickness L to the transport mean free path l*. By fitting the autocorrelation functions of samples obtained from known sphere sizes to a generalized cumulants model, which describes both the highly multiple scattering regime and the singly scattering regime, parameters were found that allow particle sizes to be determined over a wide range of scattering strengths. For samples of unknown size, this method can size monodisperse spherical particles in highly scattering solutions to better than 10%.

Scattering of low coherence radiation and applications

“…Originally, DLS applications were limited to weakly scattering media, where the light propagation could be described by a single-scattering model. An important breakthrough in the field of dynamic light scattering is represented by the extension of DLS to strongly scattering media [40][41][42][43][44][45][46][47][48][49][50][51]. The technique is referred to as diffusing wave spectroscopy (DWS).…”

“…However, many of the dynamic systems of practical interest, although multiple scattering, are not optically diffusive, and, therefore, cannot be characterized by the DWS treatment presented above. The region of transition from single to diffusive scattering regime, in the context of dynamic light scattering experiments, has been studied and the experimental data have been described using a combination of cumulants weighted by empirical constants [47]. More recently, the theory of DWS was extended using the Poisson photon distribution and numerical solutions to the transport equation [48].…”

“…In order to compute the real and imaginary parts of the response function, we used the functional forms obtained from the fit over the frequency domain where they describe the experimental results accurately. This result, in combination with equations (46,50), leads directly to χ (ω), from which one then obtains the memory component χ (ω) using the Kramers-Kronig relation, equation (47).…”

“…In order to perform the Kramers-Kronig integration in equation (47), the power-law dependence of P (ω) on frequency has been assumed to be valid beyond the actual frequency interval measured. This is a common procedure necessary to avoid the effects of a limited bandwidth.…”

Dynamic light scattering in localized coherence volumes

“…DLS of coherent light in this regime has been described by use of a combination of cumulants weighted by empirical constants. 9 It is of considerable interest to be able to optically probe the scattering systems that lie in this intermediate regime of optical densities in a consistent manner.…”