Diffusing Wave Microrheology in Polymeric Fluids

Recently, there has been interest in determining the viscoelastic properties of polymeric liquids and other complex fluids by means of Diffusing Wave Spectroscopy (DWS). In this technique, light-scattering spectroscopy is applied to highly turbid fluids containing optical probe particles. The DWS spectrum is used to infer the time-dependent mean-square displacement and time-dependent diffusion coefficient $D$ of the probes. From $D$, values for the storage modulus $G'(\omega)$ and the loss modulus $G''(\omega)$ are obtained. This paper is primarily concerned with the inference of the mean-square displacement from a DWS spectrum. However, in much of the literature, central to the inference that is said to yield $D$ is an invocation $g^{(1)}(t) = \exp(- 2 q^{2} \overline{X(t)^{2}})$ of the Gaussian Approximation for the field correlation function $g^{(1)}(t)$ of the scattered light in terms of the mean-square displacement $\overline{X(t)^{2}}$ of a probe particle during time $t$. Experiment and simulation both show that the Gaussian approximation is invalid for probes in polymeric liquids and other complex fluids. In this paper, we obtain corrections to the Gaussian approximation that will assist in interpreting DWS spectra of probes in polymeric liquids. The corrections reveal that these DWS spectra receive contributions from higher moments $\overline{X(t)^{2n}}$, $n >1$, of the probe displacement distribution function.