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It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length ξ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances r≫ ξ. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered. [ABSTRACT FROM AUTHOR]

Following the Flory ideality hypothesis intrachain and interchain excluded-volume interactions are supposed to compensate each other in dense polymer systems. Multichain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume (“hard monomers”) to no excluded volume (“phantom chains”). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions. [ABSTRACT FROM AUTHOR]

Abstract.: From equilibrium molecular dynamics (MD) simulations of a bead-spring model for short-chain glass-forming polymer melts we calculate several quantities characterizing the single-monomer dynamics near the (extrapolated) critical temperature Tc of mode-coupling theory: the mean-square displacement g0(t), the non-Gaussian parameter α2(t) and the self-part of the van Hove function Gs(r,t) which measures the distribution of monomer displacements r in time t. We also determine these quantities from a continuous-time random walk (CTRW) approach. The CTRW is defined in terms of various probability distributions which we know from previous analysis. Utilizing these distributions the CTRW can be solved numerically and compared to the MD data with no adjustable parameter. The MD results reveal the heterogeneous and non-Gaussian single-particle dynamics of the supercooled melt near Tc. In the time window of the early α relaxation α2(t) is large and Gs(r,t) is broad, reflecting the coexistence of monomer displacements that are much smaller (“slow particles”) and much larger (“fast particles”) than the average at time t, i.e. than r=g0(t)1/2. For large r the tail of Gs(r,t) is compatible with an exponential decay, as found for many glassy systems. The CTRW can reproduce the spatiotemporal dependence of Gs(r,t) at a qualitative to semiquantitative level. However, it is not quantitatively accurate in the studied temperature regime, although the agreement with the MD data improves upon cooling. In the early α regime we also analyze the MD results for Gs(r,t) via the space-time factorization theorem predicted by ideal mode-coupling theory. While we find the factorization to be well satisfied for small r, both above and below Tc, deviations occur for larger r comprising the tail of Gs(r,t). The CTRW analysis suggests that single-particle “hops” are a contributing factor for these deviations.Graphical abstract: [ABSTRACT FROM AUTHOR]