Polymer Physics: Phenomenology of Polymeric Fluid Simulations -- Chapter: Collective Coordinates and Collective Models

TL;DR

This chapter reviews collective coordinate methods for polymer chain modeling, focusing on Fourier, Rouse, and Haar wavelet coordinates, and discusses their roles in understanding polymer dynamics.

Contribution

It introduces and compares various collective coordinate frameworks, including Rouse and Haar wavelets, for analyzing polymer chain motion and dynamics.

Findings

Rouse coordinates effectively simplify polymer dynamics analysis.

Haar wavelets enable regional analysis of polymer chains.

The Rouse model provides a foundational understanding of polymer motion.

Abstract

Polymer Physics: Phenomenology of Polymeric Fluid Simulations is a review volume that I am writing. I anticipate it will take a while to complete, so I am supplying individual chapters when each is more-or-less completed. This Chapter considers collective coordinates and collective models for isolated polymer chains. Collective coordinates can be effective tools for isolating aspects of polymer motion that are less obvious if only the Cartesian coordinates of the individual atoms or monomers are viewed. I treat Fourier, Rouse, and Haar wavelets as suppliers of collective coordinates. One of the sets of collective coordinates that i consider, the Rouse coordinates, follows naturally from the Rouse model of polymer dynamics. We therefore consider the Rouse model as well as its more important predecessor, the Kirkwood-Riseman model. Haar wavelets are noteworthy because they allow one to isolate individual regions of a polymer