The role of polymer architecture in determining the static and dynamic properties of polymers in the melt

The static and dynamic properties of ring polymers and three-arm star polymers are investigated via computer simulation. Ring and star polymer simulations have been performed for both melts and single chains.; We find that rings in the melt are smaller and more compact than corresponding linear chains: for rings and linear chains in the melt the mean-square radius of gyration scales with degree of polymerization as $R2g\propto N0.82$ and $R2g\propto N$, respectively. Simulations in which bonds are allowed to cross show that the smaller ring size is a consequence of the constraint of non-concatenation: for crossing rings in the melt the mean-square radius of gyration scales as $R2g\propto N$.; We find that rings in the melt have faster dynamics than linear chains of comparable N. For rings the self-diffusion coefficient and orientational relaxation time scale as $D\propto N-1.6$ and $tee\propto N2.5$, respectively. Faster ring dynamics is shown to persist for ring sizes up to twenty times greater than the entanglement crossover chain length for linear chains. For crossing rings in the melt we find that the self-diffusion coefficient and orientational relaxation time scale as $D\propto N-1$ and $tee\propto N2.0$, respectively.; For crossing and non-crossing single rings we find that the scaling of the mean-square radius of gyration is identical in both cases, $R2g\propto N1.17$. Additionally we find that for both crossing and non-crossing single rings the self-diffusion coefficient and orientational relaxation time scale identically as $D\propto N-1$ and $tee\propto N2.1$, respectively.; For three-arm star polymers in the melt we find that the mean-square radius of gyration scales as $R2g\propto N$. For the dynamics we observe a possible non-power-law dependence of the self-diffusion coefficient on star size. The limited range of star sizes simulated precludes any stronger comment; however, we argue that the largest star lies in at least a semi-entangled dynamics regime.; For the simulations of single stars we find that the mean-square radius of gyration scales as $R2g\propto N1.2$, and that the self-diffusion coefficient and relaxation time scale as $D\propto N-1$ and $tce\propto N2.3$, respectively.