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 =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 ρ( z ) in the z -direction perpendicular to the surface for rings and linear chains are practically identical, ρ R (2 N L , z )=ρ L ( N L , z ). The same applies to the pressure, exerted on a piston at height z , as well. While the gyration radii components of rings and chains in the z -direction coincide, too, and increase linearly with N L , the transverse components differ, even with respect to their scaling properties: R gxy ( L ) ∝ N L 1/2 , R gxy ( R ) ∝ N L 0.4 . These properties are interpreted in terms of the statistical properties known for ring polymers in dense melts.