Topological effects in ring polymers: A computer simulation study

Abstract

Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for chains with up to N=512 statistical segments at a volume fraction \ensuremath{\Phi}=0.5 and show that rings in the melt are more compact than Gaussian chains. A careful finite-size analysis of the average ring size R\ensuremath{\propto}${\mathit{N}}^{\ensuremath{\nu}}$ yields an exponent \ensuremath{\nu}\ensuremath{\approxeq}0.39\ifmmode\pm\else\textpm\fi{}0.03 in agreement with a Flory-like argument for the topological interactions. We show (using the same algorithm) that the dynamics of molten rings is similar to that of linear chains of the same mass, confirming recent experimental findings. The diffusion constant varies effectively as ${\mathit{D}}_{\mathit{N}}$\ensuremath{\propto}${\mathit{N}}^{\mathrm{\ensuremath{-}}1.22(3)}$ and is slightly higher than that of corresponding linear chains. For the ring sizes considered (up to 256 statistical segments) we find only one characteristic time scale ${\mathrm{\ensuremath{\tau}}}_{\mathit{ee}}$\ensuremath{\propto}${\mathit{N}}^{2.0(2)}$; this is shown by the collapse of several mean-square displacements and correlation functions onto corresponding master curves. Because of the shrunken state of the chain, this scaling is not compatible with simple Rouse motion. It applies for all sizes of ring studied and no sign of a crossover to any entangled regime is found. \textcopyright{} 1996 The American Physical Society.