We investigate the nonlinear shear and uniaxial extensional rheology of entangled polystyrene (PS) melts and solutions having the same number Z of entanglements, hence identical linear viscoelasticity. While experiments in extensional flows confirm that PS melts and solutions with the same Z behave differently, respective transient and steady data in simple shear over the largest possible range of rheometric shear rates (corresponding to Rouse−Weissenberg numbers from 0.01 to 40) demonstrate that melts and solutions exhibit identical behavior. Whereas the differences between melts and solutions in elongational flows are due to alignmentinduced friction reduction (more effective in melts than in solutions), in shear flows they disappear since the rotational component reduces monomeric alignment substantially. Recent molecular dynamics simulations of entangled polymers show that rotation induces molecular tumbling at high shear rates, and here a tube-based model involving tumbling effects is proposed in order to describe the response in shear. The main outcome is that tumbling can explain transient stress undershoot (following the overshoot) at high shear rates. Hence, the combination of tumbling in shear and friction reduction in extension successfully describes the whole range of experimental data and provides the basic ingredient for the development of molecular constitutive equations.

It is well accepted that adding nanoparticles (NPs) to polymer melts can result in significant property improvements. Here we focus on the causes of mechanical reinforcement and present rheological measurements on favourably interacting mixtures of spherical silica NPs and poly(2-vinylpyridine), complemented by several dynamic and structural probes. While the system dynamics are polymer-like with increased friction for low silica loadings, they turn network-like when the mean face-to-face separation between NPs becomes smaller than the entanglement tube diameter. Gel-like dynamics with a Williams–Landel–Ferry temperature dependence then result. This dependence turns particle dominated, that is, Arrhenius-like, when the silica loading increases to ∼31 vol%, namely, when the average nearest distance between NP faces becomes comparable to the polymer's Kuhn length. Our results demonstrate that the flow properties of nanocomposites are complex and can be tuned via changes in filler loading, that is, the character of polymer bridges which ‘tie' NPs together into a network.

We present systematic, unique linear and nonlinear shear rheology data of an experimentally pure ring polystyrene and its linear precursor. This polymer was synthesized anionically and characterized by interaction chromatography and fractionation at the critical condition. Its weight-average molar mass is 84 kg/mol; i.e., it is marginally entangled (entanglement number Z ≈ 5). Its linear viscoelastic response appears to be better described by the Rouse model (accounting for ring closure) rather than the lattice-animal-based model, suggesting a transition from unentangled to entangled ring dynamics. The failure of both models in the terminal region may reflect the remaining unlinked linear contaminants and/or ring–ring interpenetration. The viscosity evolution at different shear rates was measured using a homemade cone-partitioned plate fixture in order to avoid edge fracture instabilities. Our findings suggest that rings are much less shear thinning compared to their linear counterparts, whereas both obey the Cox–Merz rule. The shear stress (or viscosity) overshoot is much weaker for rings compared to linear chains, pointing to the fact that their effective deformation is smaller. Finally, step strain experiments indicate that the damping function data of ring polymers clearly depart from the Doi–Edwards prediction for entangled linear chains, exhibiting a weak thinning response. These findings indicate that these marginally entangled rings behave like effectively unentangled chains with finite extensibility and deform much less in shear flow compared to linear polymers. They can serve as guideline for further investigation of the nonlinear dynamics of ring polymers and the development of constitutive equations.

A series of homologous dendronized polymers (DPs) with generations (g) 1−3 and backbone nominal degrees of polymerization (P n ) in the range 50−3000 have been synthesized and characterized in order to investigate the g-and P n -dependent viscoelastic properties and packing of this class of densely grafted, associating and effectively "thick" macromolecules in their molten state. Rheological measurements reveal an unusually long thermal equilibration time, attributed to (i) the tendency of DPs to minimize local density gradients, as realized via their mutual weak interpenetration, and (ii) the intermolecular DP−DP correlations and inter-and intramolecular hydrogen bonding and π−π stacking interactions. With the help of simulations and X-ray scattering measurements, a scenario emerges, according to which DPs interact via local cooperative rearrangements of the dendrons, akin to a Velcro fastening process. In this picture, neighboring bonds accelerate the local interpenetration process. Results from X-ray scattering show increased lateral backbone−backbone correlations with a columnar arrangement of backbones and a liquid crystalline underlying order. Linear viscoelasticity is characterized by plateau moduli which originate from intermolecular bonding and whose extent in frequency and absolute value depends on P n and g and can be lower than or comparable to that of the backbone. Very long relaxation times can be probed (sometimes via creep measurements) and attributed to the lifetime of the bonds. The nonlinear shear rheology data suggest a resemblance in behavior to unentangled linear chains with finite extensibility and point to reduced deformability of the DPs in flow. These findings indicate that DPs constitute a promising class of functional macromolecules with tunable properties.

Steady-state shear viscosity η­(γ̇) of unconcatenated ring polymer melts as a function of the shear rate γ̇ is studied by a combination of experiments, simulations, and theory. Experiments using polystyrenes with Z ≈ 5 and Z ≈ 11 entanglements indicate weaker shear thinning for rings compared to linear polymers exhibiting power law scaling of shear viscosity η ∼ γ̇–0.56 ± 0.02, independent of chain length, for Weissenberg numbers up to about 102. Nonequilibrium molecular dynamics simulations using the bead-spring model reveal a similar behavior with η ∼ γ̇–0.57 ± 0.08 for 4 ≤ Z ≤ 57. Viscosity decreases with chain length for high γ̇. In our experiments, we see the onset of this regime, and in simulations, which we extended to Wi ∼ 104, the nonuniversality is fully developed. In addition to a naive scaling theory yielding for the universal regime η ∼ γ̇–0.57, we developed a novel shear slit model explaining many details of observed conformations and dynamics as well as the chain length-dependent behavior of viscosity at large γ̇. The signature feature of the model is the presence of two distinct length scales: the size of tension blobs and much larger thickness of a shear slit in which rings are self-consistently confined in the velocity gradient direction and which is dictated by the size of a chain section with relaxation time 1/γ̇. These two length scales control the two normal stress differences. In this model, the chain length-dependent onset of nonuniversal behavior is set by tension blobs becoming as small as about one Kuhn segment. This model explains the approximate applicability of the Cox–Merz rule for ring polymers.

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We investigate the influence of the environment on the relaxation dynamics of well-defined Hpolymers diluted in a matrix of linear chains. The molar mass of the linear chain matrix is systematically varied and the relaxation dynamics of the H-polymer is probed by means of linear viscoelastic measurements, with the aim to understand its altered motion in the different blends, compared to its pure melt state. Our results indicate that short unentangled linear chains accelerate the relaxation of both the branches and the backbone of the H-polymers by acting as an effective solvent.On the other hand, the relaxation of the H-polymer in an entangled matrix is slowed-down, with the degree of retardation depending on the entanglements number of the linear chains. We show that this retardation can be quantified by considering that the H-polymers are moving in a dilated tube at the rhythm of the motion of the linear matrix.

We present a comprehensive experimental rheological dataset for purified entangled ring polystyrenes and their blends with linear chains in nonlinear shear and elongation. In particular, data for shear stress growth coefficient, steady-state shear viscosity, and first and second normal stress differences are obtained and discussed as functions of shear rate as well as molecular parameters (molar mass, blend composition and decreasing molar mass of linear component in blend). Over the extended parameter range investigated, rings do not exhibit clear transient undershoot in shear, in contrast to their linear counterparts and ring-linear blends. For the latter, the size of the undershoot and respective strain appear to increase with shear rate. Universal scaling of strain at overshoot and fractional overshoot (ratio of maximum to steady-state shear stress growth coefficient) indicates subtle differences in the shear-rate dependence between rings and linear polymers or their blends.