Diffusion of vibrated tethered granular chain in confinement

Abstract

Polymer physics have been used extensively to describe protein folding, rheological properties of fluids, and charge transport mechanisms in conducting polymers. Different models of polymers are available depending on the scale of dynamics being investigated – from quantum mechanical models to coarse-grained models.  In this study, the latter was considered by making use of a uniform granular chain as mechanical analog of bead-chain model of polymers.  We investigated the diffusion and conformation of a 20-bead granular chain with both terminal beads fixed on the containing circular wall.  The chain was vertically oscillated at different frequencies while keeping the amplitude constant. Angular separation between the terminal beads were also varied.  Effect of these factors on the diffusion coefficient of each bead were determined using video analysis. Results show that the diffusion coefficient profile depends on the frequency and angular separation.  Diffusion coefficient of each bead decreases with increasing frequency while it increases with increasing angular separation.  It was also observed that the diffusion coefficient profile along the chain follows a platykurtic distribution for both factors.  This behavior is attributed to chain geometry with respect to the dimension of the containing wall and to bead-to-bead interaction.  Contact map of the vibrated chain was made to visualize bead to bead interaction.  Our results may provide insight as to how biological systems like chromatins in cellular nucleus interact with the cell wall, other parts along the chromatin, and other chromatin.