Anomalous Structure and Scaling of Ring Polymer Brushes

TL;DR

This study compares the structure and scaling behaviors of ring and linear polymer brushes using simulations, revealing similarities in density profiles but differences in transverse size scaling, with implications for understanding dense polymer systems.

Contribution

It provides a detailed comparison of ring and linear polymer brushes, highlighting differences in transverse scaling properties through advanced simulation methods.

Findings

Density profiles are nearly identical for rings and linear chains.

Gyration radii in the perpendicular direction scale linearly with chain length.

Transverse gyration radii scale differently: N^{0.4} for rings, N^{0.5} for linear chains.

Abstract

A comparative simulation study of polymer brushes formed by grafting at a planar surface either flexible linear polymers (chain length $N_L$) or (non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two distinct off-lattice models are studied, one by Monte Carlo methods, the other by Molecular Dynamics, using a fast implementation on graphics processing units (GPUs). It is shown that the monomer density profiles $\rho(z)$ in the $z$-direction perpendicular to the surface for rings and linear chains are practically identical, $\rho_R(2 N_L, z)=\rho_L(N_L, z)$. The same applies to the pressure, exerted on a piston at hight z, as well. While the gyration radii components of rings and chains in $z$-direction coincide, too, and increase linearly with $N_L$, the transverse components differ, even with respect to their scaling properties: $R_{gxy}^{(L)} \propto N_L^{1/2}$, $R_{gxy}^{(R)} \propto N_L^{0.4}$. These properties are interpreted in terms of the statistical properties known for ring polymers in dense melts.