Related Experiment Video
Updated: Apr 8, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Fractal model of anomalous diffusion
1Institute of Chemistry, Warsaw University of Technology, 09-400, Plock, Poland. gmachowski@poczta.onet.pl.
Abstract:
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
More Related Videos
11:34Controlled Synthesis and Fluorescence Tracking of Highly Uniform PolyN-isopropylacrylamide Microgels
Published on: September 8, 2016
12:15Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
Published on: April 9, 2019
Related Concept Videos
Protein Diffusion in the Membrane
Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models
Theories of Dissolution: Diffusion Layer Model
This process starts with a thin layer, saturated with the drug, forming at the interface between the solid and liquid. The solute then diffuses from this layer into the main solution. The Noyes-Whitney equation suggests that the rate of dissolution relies on the diffusion...
Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion
The de Broglie Wavelength