Diffusing diffusivity: Rotational diffusion in two and three dimensions

• Published in: The Journal of chemical physics Vol. 146; no. 21; pp. 214102 - 214111
• Main Authors: Jain, Rohit, Sebastian, K. L.
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 07.06.2017; AIP Publishing LLC
• Subjects: Brownian motion; Computer simulation; Diffusion; Diffusivity; Distribution functions; Mathematical models; Physics; Probability distribution functions; Three dimensional motion; Time dependence
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/1.4984085

We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, α r o t , 2 D and α r o t , 3 D , which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.