Influence of microstructural parameters on mechanical behavior of polymer gels

This work extends our previous understanding concerning the nonlinear responses of entangled polymer solutions and melts to large external deformation in both simple shear and uniaxial extension. Many similarities have recently been identified for both step strain and startup continuous deformation, including elastic yielding, i.e., chain disentanglement after cessation of shear or extension, and emergence of a yield point during startup deformation that involves a deformation rate in excess of the dominant molecular relaxation rate. At a sufficiently high constant Hencky rate, uniaxial extension of an entangled melt is known to produce window-glass-like rupture. The present study provides evidence against the speculation that chain entanglements tie up into “dead knots” in constant-rate extension because of the exponentially growing chain stretching with time. In particular, it is shown that even Instron-style tensile stretching, i.e., extending a specimen by applying a constant velocity on both ends, results in rupture. Yet, in the same rate range, the same entangled melt only yields in simple shear, and the resulting shear banding is clearly not a characteristic of rupture. Thus, we conclude that chain entanglements respond to simple shear in the manner of yielding whereas uniaxial extension is rather effective in causing some entanglements to lock up, making it impossible for the entanglement network to yield at high rates.

ABSTRACTA non-Gaussian model is developed to precisely describe the chemo-mechanical coupled large deformation of responsive hydrogels. In this model, the free-energy density is composed of two parts, including the elastic energy due to stretching of cross-linked polymer networks described by Gent hyperelastic model, and the mixture energy of polymer network and described by Flory–Huggins theory. The effects of junction functionality and chain entanglements are investigated by analyzing free swelling of a cubic hydrogel and constrained swelling of a blanket layer of the gel. The present model is found to exhibit obvious hardening characteristic during large deformation of the hydrogel, and the considerations of functionality of junctions and chain entanglements are essential in the coupled chemo-mechanical deformation analysis of hydrogels.

Anisotropic strain hardening behavior in simple shear for cube textured aluminum alloy sheets

This articles is comprised of two parts: a) an experimental investigation on the behavior of an acrylic gel under DC electric field and b) a physico - mathematical description.a) Gel rods made of poly [acrylamide-co-bisacrylamide] were partially hydrolyzed to different extents at pH 12 by teteramethylethylene diamine. Equlibrium properties of the resulting gels rods (water content, number of carboxyl groups and pore size) were determined. Gel rods were then placed in water parallel to planar platinum electrodes. Under the field strengths geater than 2 V/cm the gels gradually bend towards cathode and after reaching a maximum, they traverse a smooth reverse deformation, finally bending towards anode. The speed and extent of these deformations depend on the electric field strergth; length, diameter, charge density (extent of hydrolysis) of the gel rods; temperature, and the pH of the bathing medium. In all cases the bending behavior follows the relation for the tree – point mechanical bending of solid rods. Anodic swelling and bending towards cathode is attributed to the difference in the osmotic pressure between the anodic and the cathodic sides of the gel, while the reverse deformation and bending towards anode is assigned to the migration of H+ ions from the anolyte into the gel and neutralization of COO¯ groups.b) Theoretical analysis: These attributes are quantitatively represented by a proper theoretical formulation based on Donnan and Flory-Huggins theories. The relation obtained for the osmotic pressure within the gels, in the absence of an electric field, is modified to include the ionic flux in response to concentration and electric field gradients. Considering the ionization of water and the network carboxyl groups, together with the principle of charge neutrality, and assuming Donnan equilibrium at the gel boundaries under the applied electric fields, the equations for ionic fluxes are derived and solved by Laplace transform. It is found that the concentration of cations decreases in the anodic side of the gel while it increases in the cathodic side, leading to an osmotic swelling gradient in the gel causing it to bend.

Swelling behavior of polyacrylamide (PAAm) and polyacrylamide-co-poly- acrylic acid (PAAm-co-PAAc) gels was investigated in aqueous solutions of monodis- perse PAAms with molecular weights (M V w) ranging from 1.5 1 10 3 to 5 1 10 6 g/mol. The volume of the gels decreases as the PAAm concentration in the external solution increases. This decrease becomes more pronounced as the molecular weight of PAAm increases. The classical Flory-Huggins (FH) theory correctly predicts the swelling behavior of nonionic PAAm gels in PAAm solutions. The polymer-polymer interaction parameter x23 was found to decrease as the molecular weight of PAAm increases. The swelling behavior of PAAm-co-PAAc gels in PAAm solutions deviates from the predictions of the FH theory. This is probably due to the change of the ionization degree of AAc units depending on the polymer concentration in the external solution. q 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1313-1320, 1998

The mechanical behavior of bovine articular cartilage in shear was measured and related to its structure through the depth of the tissue. To make these measurements, we designed an apparatus that could apply controlled shear displacement and measure the resulting shear force on cartilage specimens. Shear displacement and shear strain were obtained from confocal images of photobleached lines on fluorescently stained deformed samples. Depth-dependent collagen structure was obtained using compensated polarized light microscopy. Depth-dependent shear behavior and structure of samples from two animals were measured (group A and B). Both animals were 18-24months old, which is the range in which they are expected reach skeletal maturity. In mature samples (group A), the stiffest region was located beneath the superficial zone, and the most compliant region was found in the radial zone. In contrast, in samples that were in the process of maturing (group B) the most compliant region was located in the superficial zone. Compensated polarized light microscopy suggested that the animal from which the group A samples were obtained was skeletally mature, whereas the animal yielding the group B samples was in the process of maturing. Compensated polarized light microscopy was an important adjunct to the mechanical shear behavior in that it provided a means to reconcile differences in observed shear behavior in mature and immature cartilage. Although samples were harvested from two animals, there were clear differences in structure and shear mechanical behavior. Differences in the depth-dependent shear strain were consistent with previous studies on mature and immature samples and, based on the structural variation between mature and immature articular cartilage, their mechanical behavior differences can be tenable. These results suggest that age, as well as species and anatomic location, need to be considered when reporting mechanical behavior results.

Analysis of texture perception of geometry of artificial skin and lubricant

Intranetwork phase separation in polyelectrolyte gels

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theorry of axion field arising from Type IIB string theory compactified to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For massless axion field, in all these three formalism, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.

Swollen physical magneto-responsive gels were obtained by self-assembly of triblock copolymers containing dispersed soft magnetic particles. When subject to simple shear cyclic loading–unloading cycles in the presence of a magnetic field, magnetorheological (MR) gels show a stress hardening behavior. The stress-hardening was characterized by the increase of the maximum stress against the number of cycles. Most of the stress increases are achieved in the first and second cycles and only minor effects take place in the subsequent ones. The cyclic behaviour of MR gels with dilute particle volume fraction is also studied with the help of a homemade shear cell mounted on an optical microscope. Despite the difference of particle volume fraction, we are able to relate cyclic stress hardening to the change in particle–particle distribution observed directly at the microscopic scale. While anisotropic particle strings created by a pre-structuring process (original sample alignment) still has many defects, the history of simple shear in the presence of the magnetic field gradually removes the defects of the particle strings and helps them to relax towards a zipped cluster. We show here the first directly observed example of the shear-annealing effect in MR gels. The shear induced rearrangement of the particle network serves as the microscopic origins of the above mentioned cyclic stress hardening behavior of MR gels and seems to be fully reversible after the removal of the magnetic field. Results show that a slow quiescent process also takes place and it is suggested to be related to solvent flow outwards of the clusters, while they get more compact. Interestingly, all directly observed rearrangements including string breaking seem to be fully reversible after removal of the magnetic field.

Transition of polymers from the fluid to the forced high-elastic and leathery states at temperatures above the glass transition temperature

This study presents a new scheme for performing integration point constitutive updates for anisotropic, small strain, non-linear viscoelasticity, within the context of implicit, non-linear finite element structural analysis. While the basic scheme has been presented earlier by the authors for linear viscoelasticity, the present work illustrates the generality of the underlying fundamentals by extending to Schapery's non-linear model. The method features a judicious choice of state variables, a stable backward Euler integration step, and a consistent tangent operator. Its greatest strength lies in ready incorporation into existing FEM codes. Numerical examples involving homogeneous stress states such as uniaxial extension and simple shear, and non-uniform stress states such as a beam under tip load, were carried out by incorporating the present scheme into a general purpose FEM package. Excellent agreement with analytical results is observed. Copyright © 1999 John Wiley & Sons, Ltd.

Ultimate regimes of deformation of linear flexible chain fluid polymers

We introduce a class of continuum mechanical models aimed at describing the behavior of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant material parameters is able to qualitatively reproduce a number of experimental observations in both simple shear and extensional flows, including linear viscoelastic properties, the rate dependence of steady-state material functions, the stress overshoot in incipient shear flows, and the difference in shear and extensional rheological curves. Furthermore, by allowing the relaxation time of the model to depend on the total strain, we can reproduce some experimental observations of the non-attainability of steady flows in uniaxial extension and link this to a concept of polymeric jamming or effective solidification. Remarkably, this modeling framework helps in understanding the interplay between different mechanisms that may compete in determining the rheology of non-Newtonian materials.

Exact large strain analysis for the Poynting effect of freely twisted thin-walled tubes made of highly elastic soft materials