Microscopic Theory for the “Lozenge” Contour Plots in Scattering from Stretched Polymer Networks

Extensional Flow-Induced Concentration Gradient in Entangled Polymer Solutions with Chemically Identical Species

Entangled polymer solutions show different rheological behavior from melts in fast extensional flow. This discrepancy is not expected according to the classic tube model and is an urgent issue to be solved in polymer physics. While in the tube model the polymer concentration is considered to be homogeneous, we show that extensional flow-induced concentration gradient may happen in polymer solutions even with chemically identical solutes and solvents. Through labeling an aggregation-induced emission (AIE) probe on oligomeric solvents, the flow-induced concentration gradient is visualized by combining extensional rheology and ex situ fluorescence microscopy. Microdomains of oligomeric solvents with a length scale of tens of micrometers are observed, and their influence on rheological behavior cannot be ignored.

Nematic effects and strain coupling in entangled polymer melts under strong flow

We use small-angle neutron scattering (SANS) to study labeled short chains with and without the influence of an entangled and highly stretched surrounding environment of longer chains. We find unequivocal evidence of nematic effects as the blend chains in steady state flow are stretched a factor ∼1.5 more from the presence of the long chain nematic field. In the pure melt we confirm that the nonaffine mean-field result ν=0.5 for the strain coupling is still valid for very fast flows, while in the nematic system our analysis predicts an increased coupling constant. We provide a structural explanation for the two first regimes of the nonlinear relaxation, particularly a transition regime where the long chains are relaxing in a sea of reptating short chains.

Direct observation of nonaffine tube deformation in strained polymer networks

We present a one-to-one comparison of polymer segmental fluctuations as measured by small angle neutron scattering in a network under deformation with those obtained by neutron spin echo spectroscopy. This allows an independent proof of the strain dependence of the chain entanglement length. The experimentally observed nonaffine square-root dependence of the tube channel on strain is in excellent agreement with theoretical predictions and permits us to exclude an often invoked nondeformed as well as affinely deformed tube.

Topological versus rheological entanglement length in primitive-path analysis protocols, tube models, and slip-link models

We show that the front factor appearing in the shear modulus of a phantom network, G(ph) = (1-2/f)(ρk(B)T)/N(s), also controls the ratio of the strand length, N(s), and the number of monomers per Kuhn length of the primitive paths, N(ph)(PPKuhn), characterizing the average network conformation. In particular, N(ph)(PPKuhn) = N(s)/(1-2/f) and G(ph) = (ρk(B)T)/N(ph)(PPKuhn). Neglecting the difference between cross-links and slip-links, these results can be transferred to entangled systems and the interpretation of primitive path analysis data. In agreement with the tube model, the analogy to phantom networks suggest that the rheological entanglement length, N(e)(rheo) = (ρk(B)T)/G(e), should equal N(e)(PPKuhn). Assuming binary entanglements with f = 4 functional junctions, we expect that N(e)(rheo) should be twice as large as the topological entanglement length, N(e)(topo). These results are in good agreement with reported primitive path analysis results for model systems and a wide range of polymeric materials. Implications for tube and slip-link models are discussed.

Segmental order in end-linked polymer networks: a Monte Carlo study

Segmental order in end-linked monomodal and bimodal polymer networks is investigated by means of bond-fluctuation Monte Carlo simulations. The tensor order parameter, which is a central observable in NMR experiments, is not uniquely related to simple vectorial order. The relaxation of NMR-detected tensorial interactions towards their finite long-time limit is best described by a power law and occurs over much longer time scales than the relaxation of vectorial order. The well-known prediction for the segmental order of Gaussian chains as a simple function of the segment number between constraints is not straightforwardly obeyed, neither in dry nor in swollen networks. Excluded-volume interactions tend to significantly reduce the tensorial order, as is clearly observed in single-chain simulations. A distribution extends along the chain, where order is increased in a region of 30-40 bonds around the cross-links in networks. The dominating contribution to the order parameter distribution arises from the frozen-in distribution of end-to-end separations. We find strong deviations from the Gamma distribution, which has so far been implicitly used in most NMR works, as it is a straightforward consequence of a Gaussian distribution of end separations. Specifically, we find narrower distributions, as small values of the tensor order parameter are strongly suppressed, most probably as a result of trapped entanglements. The markedly subaffine behavior of the average order parameter and the changes in its distribution on swelling are assigned to orientation processes of strands which compensate for the non-affine local deformation. Our central observations and interpretations are well supported by our previous experimental and theoretical work.

Strain-dependent localization, microscopic deformations, and macroscopic normal tensions in model polymer networks

We use molecular dynamics simulations to investigate the microscopic and macroscopic response of model polymer networks to uniaxial elongations. By studying networks with strand lengths ranging from N(s)=20 to 200 we cover the full crossover from cross-link to entanglement dominated behavior. Our results support a recent version of the tube model which accounts for the different strain dependence of chain localization due to chemical cross-links and entanglements.

Neutron-Mapping Polymer Flow: Scattering, Flow Visualization, and Molecular Theory

Flows of complex fluids need to be understood at both macroscopic and molecular scales, because it is the macroscopic response that controls the fluid behavior, but the molecular scale that ultimately gives rise to rheological and solid-state properties. Here the flow field of an entangled polymer melt through an extended contraction, typical of many polymer processes, is imaged optically and by small-angle neutron scattering. The dual-probe technique samples both the macroscopic stress field in the flow and the microscopic configuration of the polymer molecules at selected points. The results are compared with a recent "tube model" molecular theory of entangled melt flow that is able to calculate both the stress and the single-chain structure factor from first principles. The combined action of the three fundamental entangled processes of reptation, contour length fluctuation, and convective constraint release is essential to account quantitatively for the rich rheological behavior. The multiscale approach unearths a new feature: Orientation at the length scale of the entire chain decays considerably more slowly than at the smaller entanglement length.