Anomalous Structure and Scaling of Ring Polymer Brushes

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 $N_R=2N_L$) 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, ${\rho }_R(2N_L,z)={\rho }_L(N_L,z)$. 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: $R_{gxy}^{(L)}\propto N_L^{1\mathrm{/}2}$, $R_{gxy}^{®} \propto N_L^{0.4}$. These properties are interpreted in terms of the statistical properties known for ring polymers in dense melts.