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The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, implying a weak but persistent dynamic localization in real space. Comparison with a number of existing theoretical models of entangled polymers suggests that they cannot fully describe the spatial correlations revealed by simulations and experiments. In particular, the strict one-dimensional diffusion idea of the original tube model is shown to be flawed. The dynamic spatial correlation analysis demonstrated in this work provides a useful tool for interrogating the dynamics of entangled polymers. Lastly, the failure of the investigated models to even qualitatively predict the spatial correlations of collective single-chain density fluctuations points to a possible critical role of incompressibility in polymer melt dynamics.
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In this paper we study a system of entangled chains that bear reversible cross-links in a melt state. The cross-links are tethered uniformly on the backbone of each chain. A slip-link type model for the system is presented and solved for the relaxation modulus. The effects of entanglements and reversible cross-linkers are modelled as discrete form of constraints that influence the motion of the primitive path. In contrast to a non-associating entangled system the model calculations demonstrate that the elastic modulus has a much higher first plateau and a delayed terminal relaxation. These effects are attributed to the evolution of the entangled chains as influenced by tethered reversible linkers. The model is solved for the case when linker survival time $tau_s$ is greater than the entanglement time $tau_e$ but less than the Rouse time $tau_R$.
We present an extensive set of simulation results for the stress relaxation in equilibrium and step-strained bead-spring polymer melts. The data allow us to explore the chain dynamics and the shear relaxation modulus, $G(t)$, into the plateau regime for chains with $Z=40$ entanglements and into the terminal relaxation regime for $Z=10$. Using the known (Rouse) mobility of unentangled chains and the melt entanglement length determined via the primitive path analysis of the microscopic topological state of our systems, we have performed parameter -free tests of several different tube models. We find excellent agreement for the Likhtman-McLeish theory using the double reptation approximation for constraint release, if we remove the contribution of high-frequency modes to contour length fluctuations of the primitive chain.
For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together, leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and actions must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.
Significant progress was made in recent years in the understanding of the proton spin kinetics in polymer melts. Generally, the proton spin kinetics is determined by intramolecular and intermolecular magnetic dipole-dipole contributions of proton spins. During many decades it was postulated that the main contribution is a result of intramolecular magnetic dipole-dipole interactions of protons belonging to the same polymer segment. It appears that this postulate is far from reality. The relative weights of intra- and intermolecular contributions are time dependent and sensitive to details of polymer chain dynamics. It is shown that for isotropic models of polymer dynamics the influence of the intermolecular magnetic dipole-dipole interactions increases faster with increasing evolution time (i.e. decreasing frequency) than the corresponding influence of the intramolecular counterpart. On the other hand, an inverted situation is predicted by the tube-reptation model: here the influence of the intramolecular magnetic dipole-dipole interactions increases faster with time than the contribution from intermolecular interactions. The intermolecular contribution in the proton relaxation of polymer melts can experimentally be isolated using the isotope dilution technique and this opens a new perspective for experimental investigations of polymer dynamics by proton NMR.
The classical rheological theories of entangled polymeric liquids are built upon two pillars: Gaussian statistics of entanglement strands and the assumption that the stress arises exclusively from the change of intramolecular configuration entropy. We show that these two hypotheses are not supported by molecular dynamics simulations of polymer melts. Specifically, the segment distribution functions at the entanglement length scale and below deviate considerably from the theoretical predictions, in both the equilibrium and deformed states. Further conformational analysis reveals that the intrachain entropic stress at the entanglement length scale is substantially smaller than the total stress, indicative of a considerable contribution from interchain entropy. Lastly, the relation between entanglement strand entropic stress and macroscopic stress exhibits a bifurcation behavior during deformation and stress relaxation, which cannot be accounted for by the classical theories.
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