Scale-free center-of-mass displacement correlations in dense polymer solutions and melts without topological constraints and momentum conservation: A bond-fluctuation model study

By Monte Carlo simulations of a variant of the bond-fluctuation model without topological constraints we examine the center-of-mass (COM) dynamics of polymer melts in $d=3$ dimensions. Our analysis focuses on the COM displacement correlation function $\text{CN}(t)\approx {\mathrm{\partial }}_t^2\text{MSDcmN}(t)\mathrm{/}2$, measuring the curvature of the COM mean-square displacement $\text{MSDcmN}(t)$. We demonstrate that $\text{CN}(t)\approx -(\text{RN}\mathrm{/}\text{TN}{)}^2(\text{rhostar}\mathrm{/}\rho )f(x=t\mathrm{/}\text{TN})$ with $N$ being the chain length ($16\le N\le 8192$), $\text{RN}\sim N^{1\mathrm{/}2}$ the typical chain size, $\text{TN}\sim N^2$ the longest chain relaxation time, $\rho$ the monomer density, $\text{rhostar}\approx N\mathrm{/}{\text{RN}}^d$ the self-density and $f(x)$ a universal function decaying asymptotically as $f(x)\sim x^{-\omega }$ with $\omega = (d+2) \times \alpha$where$\alpha = 1/4$for$x \ll 1$and$\alpha = 1/2$for$x \gg 1$. We argue that the algebraic decay $N\text{CN}(t)\sim -t^{-5\mathrm{/}4}$ for $t\ll \text{TN}$ results from an interplay of chain connectivity and melt incompressibility giving rise to the correlated motion of chains and subchains.