Dynamical Eigenmodes of Star and Tadpole Polymers

TL;DR

This paper analytically derives the dynamical eigenmodes of star and tadpole polymers in the overdamped limit, enabling precise calculations of their dynamic properties.

Contribution

It provides exact solutions for the eigenmodes of symmetric star and tadpole polymers, extending Rouse mode analysis to complex topologies.

Findings

Eigenmodes are derived exactly for star and tadpole polymers.

Analytical expressions for radius of gyration and mean square displacement are obtained.

Autocorrelation functions for star polymers are explicitly calculated.

Abstract

The dynamics of phantom bead-spring chains with the topology of a symmetric star with $f$ arms and tadpoles ($f=3$, a special case) is studied, in the overdamped limit. In the simplified case where the hydrodynamic radius of the central monomer is $f$ times as heavy as the other beads, we determine their dynamical eigenmodes exactly, along the lines of the Rouse modes for linear bead-spring chains. These eigenmodes allow full analytical calculations of virtually any dynamical quantity. As examples we determine the radius of gyration, the mean square displacement of a tagged monomer, and, for star polymers, the autocorrelation function of the vector that spans from the center of the star to a bead on one of the arms.