Normal Modes of Rouse-Ham Symmetric Star Polymer Model

TL;DR

This paper develops methods to construct normal modes for symmetric star polymers in the Rouse-Ham model, enabling analysis of their dynamics with arbitrary arm numbers using permutation, Hadamard, and DFT matrices.

Contribution

It introduces new techniques to construct normal modes for symmetric star polymers, including a general DFT-based method for any number of arms.

Findings

Normal modes can be constructed using permutation or Hadamard matrices for specific arm numbers.

A general method using the discrete Fourier transform matrix is applicable for any number of arms.

The proposed methods produce symmetric, orthogonal modes suitable for analyzing star polymer dynamics.

Abstract

The Rouse-Ham model is a simple yet useful dynamics model for an unentangled branched polymer. In this work, we study the normal modes of the Rouse-Ham type coarse-grained symmetric star polymer model. We model a star polymer by connecting multiple arm beads to a center bead by harmonic springs. In the Rouse-Ham model, the dynamics of the bead positions can be decomposed into the normal modes, which are chosen to be orthogonal to each other. Due to the existence of degenerate eigenvalues, the eigenmodes do not directly correspond to the normal modes. We propose several methods to construct the normal modes for the coarse-grained symmetric star polymer model. We show that we can construct the normal modes by using a simple permutation or the Hadamard matrix. These methods give symple and highly symmetric orthogonal modes, but work just for a special number of arms. We also show that we can construct the normal modes by using the discrete Fourier transform (DFT) matrix. This method is applicable for an arbitrary number of arms.