Year: 2026
Type: article
Abstract: We study the Brownian motion of a rigid rod threading through a small fixed ring while the ring can freely rotate. We derive the distribution function for the sliding displacement and the unit vector along the rod both at equilibrium and non-equilibrium. The equilibrium distribution is quadratic in the sliding displacement and is controlled by the moment of inertia (mass distribution). Applying the Onsager variational principle, we derive a Smoluchowski equation in which sliding and rotational diffusion are coupled. The mean square displacement of sliding shows a metastable plateau in a certain time range before it approaches the final equilibrium value. The longest sliding relaxation time scales as α-1/2, where α is the dimensionless moment of inertia of the rod. The rotational relaxation time obtained from the orientational correlation function is longer than that of a rod with its center fixed but faster than a rod with one end fixed. These results may be useful in understanding the dynamics of polymers connected by sliding rings.
Source: The Journal of Chemical Physics
DOI: 10.1063/5.0322429
Authors: Zhongqiang Xiong, Shigeyuki Komura, Masao Doi
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7147378601