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Normal and anomalous diffusion
Karlstad University, Faculty of Technology and Science, Paper Surface Centre. Karlstad University, Faculty of Technology and Science, Department of Chemistry and Biomedical Sciences. Karlstad University, Faculty of Technology and Science, Materials Science.ORCID iD: 0000-0001-7235-0905
Karlstad University, Faculty of Technology and Science, Department of Chemistry and Biomedical Sciences. Karlstad University, Faculty of Technology and Science, Materials Science.ORCID iD: 0000-0002-0995-3823
2010 (English)Conference paper, Published paper (Refereed)
Abstract

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

[1, 2].

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

[6,7].

References

[1] Klafter J., Blumen A., Zumofen g. Shlesinger M.f., Physica A., 1990, 168, 637-645

[2] Ott A., Bouchaud J.P., Langevin D., Urbach W., Phys. Rev. Lett., 1990, 65, 2201-2204

[3] Carlsson G., Warszynski P., van Stam J., J. Colloid Interface Sci., 2003, 267, 500-508

[4] Carlsson G., van Stam J., Nord. Pulp Pap. Res. J., 2005, 20, 192-199

[5] Carlsson G., Järnström L., van Stam J., J. Colloid Interface Sci., 2006, 298, 162-171

[6] Fredriksson L., Bsc thesis, Karlstad university, 2010

[7] Fredriksson L., Msc thesis, Karlstad university, 2010

Place, publisher, year, edition, pages
2010.
Keywords [en]
fluorescence microscopy, image analysis, brownian motion, diffusion
National Category
Chemical Sciences
Research subject
Chemistry
Identifiers
URN: urn:nbn:se:kau:diva-10509OAI: oai:DiVA.org:kau-10509DiVA, id: diva2:494049
Conference
Molecular Processes at Solid Surfaces 10th Annual Surface and Colloid Symposium, 24-26 November 2010, Lund
Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2014-09-10Bibliographically approved

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