Entangled Structures as High Cycle Compression Springs

Polymer, 1986

This paper presents a theory of rubber elasticity based on the concept of entanglements. It is shown that for small deformation the molecular mechanism of stretching is dominated by the slippage of chains. Hardening of the rubber at a high deformation is due to inextensibility as described by the tube concept. This free energy of deformation agrees well with experiment. The resulting free energy is F _~Nc] 1 log 1-~z~),2 + kBT .= If,{ ."+""'-:' +½N~ il + q2~)(1-~2Z2~) i +log(1 + q2~)}-log(1-~2Z2z)] where ~ is a measure of the inextensibility and ~/of the slippage, Nc is the number of crosslinks and N~ the number of slip links.

Rheologica Acta, 2000

Different blending laws have been proposed in the literature to describe the polydispersity effect on the rheological behavior of polymer melts. In this paper predictions of linear viscoelastic properties of entangled polydisperse polymers have been derived from the double reptation mixing rule. The results in terms of the relaxation modulus, the zero shear-rate viscosity, η0, and the steady-state compliance, J e 0, have been obtained using three different relaxation functions for the monodisperse fractions, namely the Tuminello step function, the single exponential function and the BSW function. Both discrete and continuous molecular weight distributions (MWDs) have been investigated. The Generalized Exponential Function (GEX) has been considered in the continuous case. The results showed that, in systems with a large number of components, the predictions of linear viscoelastic properties mainly depend on the double reptation mixing rule assumption, while the choice of the relaxation function is not crucial. In particular, the mathematical simplicity of the Tuminello step relaxation function has allowed analytical computation of the linear viscoelastic properties in closed form. Indeed, the analytical results indicated a dependence of η0 on the MWD that could be expressed in terms of (M z/M w)0.8, in agreement with experimental results reported in the literature. In the case of J e 0, the analytical model defines a dependence on (M z/M w)5.5, i.e. as expected a strong dependence on the MWD is predicted for the steady-state compliance. Finally, dynamic moduli have been computed from the relaxation modulus and their predictions have been favorably compared with experimental results from the literature.

Granular Matter

We study the transmission of compressive and tensile stresses, and the development of stress - induced anisotropy in entangled granular structures composed of nonconvex S-shaped hooks and staples. Utilizing discrete element simulations, we find that these systems exhibit fundamentally different behavior compared to standard convex particle systems, including the ability to entangle which contributes to a lower jamming packing fraction and facilitates the transmission of tensile stresses. We present direct evidence of tensile stress chains, and show that these chains are generally sparser, shorter and shorter-lived than the compressive chains found in convex particle packings. We finally study the probability distribution, angular density and anisotropic spatial correlation of the minor (compressive) and major (tensile) particle stresses. The insight gained for these systems can help the design of reconfigurable and recyclable granular structures capable of bearing considerable loads...

Macromolecules, 2012

Using four entangled 1,4-polybutadiene solutions as model systems, we carry out rate-switching startup shear and elastic recovery tests to probe the state of chain entanglement during startup continuous shear and after shear cessation, respectively. Specifically, we apply a second startup shear of higher rate either during the first startup shear or after cessation of the first shear. The nonmonotonic response (overshoot) to the startup shear is evaluated to elucidate the effect of any preceding shear on the entanglement structure. In a second type of experiments, at different strains during and after shear or relaxing for a certain amount of time after shear cessation we set the shear stress free to determine the amount of elastic recoil, which can also reveal the status of chain entanglement interactions. Consistent with the emerging theoretical interpretations, these multistep rheometric procedures allow us to learn more about (a) elastic yielding during relaxation after cessation of shear that is produced at a low rate, (b) existence of a critical strain amplitude for the elastic yielding, (c) nonmonotonic evolution of the chain entanglement upon startup shear, and (d) yielding of the entanglement network at the point of shear stress overshoot.

Macromolecules, 2017

The dynamics of chain entanglement/disentanglement in concentrated polymer solutions are matters of current debate. We report the results of step strain rate experiments in uniaxial extensional flow on a well-characterized polymer solution containing about 22 entanglements per chain which allows these dynamics to be probed. In these experiments the polymer solution is subjected to homogeneous stretching at a given strain rate up until a predetermined value of strain. After this strain is reached, the strain rate is changed to a new value, and stretching is continued until steady state is acquired in the extensional stress. The strain rates are increased in step-up experiments and decreased in stepdown experiments. The strain rates are adjusted so that both the orientation and the stretching dynamics can be probed. Additionally, the predictions of two recent single-mode molecular models are evaluated against the experimental data. These models include the effects of entanglement dynamics in their predictions in an ad hoc manner. This leads to only a qualitative improvement in the predictive capacity of one of the models and reduces that of the other. Slip-link simulations using the primitive chain network model are also included for further insight into the underlying dynamics. The models are found to yield qualitative predictions of the experimental observations.

Smart Materials and Structures, 2007

Magnetorheological elastomers (MRE) are interesting candidates for active vibration control of structural systems. In this study, spring elements consisting of magnetorheological elastomer were prepared and tested in dynamic compression to study the changes in their stiffness and vibration damping characteristics under the influence of a magnetic field. Aligned and isotropic magnetorheological elastomer composites were prepared using room temperature vulcanizing silicone elastomer as the matrix material and carbonyl iron as the magnetizable filler. Aligned MREs were prepared by curing the material under an external magnetic field. Aligned MREs were tested and the results were compared with isotropic composites with no preferred orientation.

Macromolecules, 1987

Experimental swelling data are used to compare theoretical models of rubber elasticity. Of the nine models that were examined, only the Gaylord and Marrucci tube models, the modified Graessley primitive path model, and the Flory-Erman constrained junction fluctuation model provide even qualitative agreement with the observed network behavior. Quantitative agreement is impossible for the Flory-Erman model and requires physically unrealistic parameter values for the other three models. The assumed separability of elastic and mixing free energy terms remains questionable.

Journal of Non-Crystalline Solids, 2000

The non-linear stress±strain relation for cross-linked polymer networks is studied using molecular dynamics simulations. Previously we demonstrated the importance of trapped entanglements in determining the elastic and relaxational properties of networks. Here, we present new results for the stress versus strain for both dry and swollen networks. Models which limit the¯uctuations of the network strands like the tube model are shown to describe the stress for both elongation and compression. For swollen networks, the total modulus is found to decrease like V 0 aV 2a3 and goes to the phantom model result only for short strand networks. Ó

Macromolecules, 2016

The present rheological study reveals for the first time that entangled polymer solutions made of linear polystyrene or poly(methyl methacrylate) can exhibit strain hardening due to non-Gaussian stretching during startup shear at sufficiently high rates and temperatures well above their overall glass transition temperatures: T g,solute > T exp > T g,solution. The solutions made of high-T g polymers only show partial yielding in the sense that both shear and normal stresses grow monotonically in time until a point of rupture, signified by an emergent cusp in the stress vs strain curve and macroscopic breakup along a shear plane. The shear softening-to-hardening transition, which occurs as a function of the applied shear rate, happens at lower equivalent rate with decreasing temperature, violating the time−temperature superposition principle.

Acta Mechanica, 2004

Experimental testing of piano hammers, which consist of a wood core covered with several layers of compressed wool felt demonstrates, that all hammers have the hysteretic type of the forcecompression characteristics. It is shown, that different mathematical hysteretic models can describe the dynamic behavior of the hammer felt. In addition to the four-parameter nonlinear hysteretic felt model, another new three-parameter hysteretic model is presented. Both models are based on the assumption that the hammer felt made of wool is a microstructured material possessing history-dependent properties. The equivalence of these models is proved for all realistic values of hammer velocity.