Anomalous Structure and Scaling of Ring Polymer Brushes

Daniel Reith, Andrey Milchev, Peter Virnau, Kurt Binder
Institut fur Physik, Johannes Gutenberg-Universitat, D-55099 Mainz, Staudinger Weg 7, Germany
arXiv:1104.4943v1 [cond-mat.soft] (26 Apr 2011)


   author={Reith}, D. and {Milchev}, A. and {Virnau}, P. and {Binder}, K.},

   title={“{Anomalous Structure and Scaling of Ring Polymer Brushes}”},

   journal={ArXiv e-prints},




   keywords={Condensed Matter – Soft Condensed Matter, Condensed Matter – Materials Science, Condensed Matter – Statistical Mechanics},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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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.
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