Optical Microrheology of Gelling Biopolymer Solutions Based on Diffusing Wave Spectroscopy - Food Colloids: Self-Assembly and Material Science - page 321

21.4 Diffusing Wave Spectroscopy Based on Optical
Microrheology
DWS is the extension of dynamic light scattering (DLS) to soft materials
exhibiting strong multiple scattering. 6 It has been shown that DWS allows
monitoring of the displacement of micrometre-sized particles with sub-nanome-
tre precision. In recent years significant progress has been made in the develop-
ment of the DWS approach, 15,16 and it has been successfully applied to the study
of fluid and solid media, e.g., colloidal suspensions, gels, and biocolloids
(yoghurt and cheese), and also ceramic slurries and green bodies. 17-24
In a DWS experiment, coherent laser light impinges on one side of a turbid
sample and the intensity fluctuations of the light propagated through the
sample are analysed either in transmission or in a back-scattering geometry.
A diffusion model is used to describe the propagation of photons across the
sample, where the diffusion approximation allows determination of the distri-
bution of scattering paths and calculation of the temporal autocorrelation of
the intensity fluctuations. DWS provides quantitative information on the
average mean-square displacement of the scattering particles from the meas-
ured intensity autocorrelation function (ICF) over a very broad range of
timescales. Analogous to DLS, for the case of noninteracting particles, we
can express the measured ICF,
g 2 (t) 1 ¼h I(t)I(t + t) i / h I i 2 1,

(1)

in terms of the mean-square displacement of the scattering particles:

2
4

3
5

2

Z

1

dsP ð s Þ exp s = l Þ k 2 Dr 2 ð t Þ g 2 ð t Þ 1 ¼ ð : ð 2 Þ

0

The quantity k ¼ 2 p n/ l is the wave number of light in a medium of refractive index
n. The function P(s) is the distribution of photon trajectories of length s in the
sample, which can be calculated within the diffusion model by taking the
experimental geometry into account. The transport mean free path l* character-
izes the typical step length of the photon random walk, as given by the individual
particle scattering properties and the particle concentration. The value of l* can be
determined independently, and it enters the analysis as a constant parameter.
From Equation (2) it is possible to calculate the particle mean-square displace-
ment ( h Dr 2 (t) i ) numerically from the measured autocorrelation function g 2 ( t ).
From the Laplace transform of the particle mean-squared displacement,

D r 2 ð s Þ , the complex modulus of the sample can be determined via a gener-
alized Stokes-Einstein relation using s ¼ i o :

k B T
p a i o Dr 2 ð i o Þ

G ð o Þ¼

i ¼ G 0 ð o Þþ iG 00 ð o Þ:

ð 2 Þ

h

The details of this procedure can be found elsewhere. 1,25