Ideal Linear Chain Polymers with Fixed Angular Momentum

TL;DR

This paper derives the exact radius of gyration for a linear polymer with fixed angular momentum, compares it with simulations, and explores the anisotropic effects of spinning polymers, revealing universal scaling behavior.

Contribution

It provides an exact analytical solution for the radius of gyration of spinning polymers and validates it with simulations, highlighting anisotropic scaling effects.

Findings

Analytical radius of gyration matches simulations.

Polymer size exhibits universal scaling with angular momentum.

Spinning induces anisotropic shape changes in polymers.

Abstract

The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This result is then compared to simulations done with a large number of non-interacting rigid links at fixed angular momentum. The simulation agrees with the theory up to finite size corrections. The simulations are also used to investigate the anisotropic nature of a spinning polymer. We find universal scaling of the polymer size along the direction of the angular momentum, as a function of rescaled angular momentum.