Brownian motion is perhaps best described as the never-ceasing phenomenon responsible for
self-diffusion occurring although there is no temperature or concentration gradients. The
distribution of the steps P(r) is vital in order to see the underlying mechanism of diffusion.
Normal diffusion is characterised by having Gaussian distributions of the step lengths.
Diffusion can be classified as either normal or anomalous depending on how the mean square
displacement is related to time:
If a = 1, diffusion is classified as normal diffusion. With a > 1 , there is superdiffusion. When
a < 1 , subdiffusion takes place. In order to replace normal diffusion by anomalous diffusion,
pathologies must be present. Most anomalous diffusion takes the shape of subdiffusion
Video-based fluorescence microscopy is the basis for all experimental work and has
successfully been used earlier [3-5]. For each concentration the trajectories of 60 probes were
determined using the built-in Particle Analysis function in Aquacosmos 2.6. The 6000 data
points collected were used to extract both the coefficient G and the exponenta .
Relatively few studies have been devoted to tell normal diffusion from anomalous diffusion in
real chemical systems. In this study the probe is a fluorescent labeled latex particle, the matrix
was changed in different ways. Unlabelled latex particles, DoTAB (a cationic surfactant),
cationic starch of different molecular weight were all used to alter the sample.
The conclusion is that it is safe to assume a = 1 in all cases except for very high
concentrations of starch, where diffusion is hindered by the viscous matrix, which gives rise
to subdiffusion. Moreover, all distributions are Gaussian except for the highest concentrations
of starch and latex. In these latter cases, distributions appear as truncated normal distributions
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 Fredriksson L., Bsc thesis, Karlstad university, 2010
 Fredriksson L., Msc thesis, Karlstad university, 2010