5D Entanglement in Star Polymer Dynamics

TL;DR

This study reveals that star polymers relax through a 5D random walk mechanism, with faster simulations showing a power-law mean square displacement, challenging previous zero-scaling assumptions.

Contribution

The paper introduces a novel simulation approach that demonstrates star polymer relaxation follows a 5D random walk, providing new insights into their topological dynamics.

Findings

Mean square displacement scales with a power law 1/16 in time.

Star polymers relax via a 5D random walk.

Simulation speed exceeds previous studies by over a hundred times.

Abstract

Star polymers are within the most topologically entangled macromolecules. For a star to move the current theory is that one arm must retract to the branch point. The probability of this event falls exponentially with molecular weight, and a quicker relaxation pathway eventually takes over. With a simulation over a hundred times faster than earlier studies, we demonstrate that the mean square displacement scales with a power law 1/16 in time, instead of the previously assumed zero. It suggests that star polymer motion is the result of two linear relaxations coinciding in time. By analogy to linear polymers, which reptate with a random walk embedded in a 3D network, we show that star polymers relax by a random walk in a 5D network.