Scattering by deformed swollen gels: butterfly isointensity patterns

The influence of elongation-induced concentration fluctuations on segmental friction in polymer blends

Recent experimental studies have revealed a lack of universality in the extensional behavior of linear polymers, which is not envisioned by classical molecular theories. These surprising findings, particularly the sharp contrast between polymer melts and solutions, have catalyzed the development of new theoretical ideas, including the concept of friction reduction in highly stretched polymer melts. By presenting evidence from rheology and small-angle neutron scattering, this work shows that deformation-induced demixing, which is due to the viscoelastic asymmetry in binary mixtures, contributes to the observed nonuniversality. In the case of polystyrene/oligostyrene blends, demixing increases the effective glass transition temperature of the long chain, leading to an apparent friction enhancement. On the other hand, the opposite case is found for the polystyrene/poly(α-methylstyrene) blend. These results highlight the important influence of deformation-induced concentration fluctuations on polymer segmental friction.

Tri-branched gels: Rubbery materials with the lowest branching factor approach the ideal elastic limit

Unlike hard materials such as metals and ceramics, rubbery materials can endure large deformations due to the large conformational degree of freedom of the cross-linked polymer network. However, the effect of the network's branching factor on the ultimate mechanical properties has not yet been clarified. This study shows that tri-branching, which entails the lowest branching factor, results in a large elastic deformation near the theoretical upper bound. This ideal elastic limit is realized by reversible strain-induced crystallization, providing on-demand reinforcement. The enhanced reversible strain-induced crystallization is observed in the tri-branched and not in the tetra-branched network. A mathematical theory of structural rigidity is used to explain the difference in the chain orientation. Although tetra-branched polymers have been preferred since the development of vulcanization, these findings highlighting the merits of tri-branching will prompt a paradigm shift in the development of rubbery materials.

Theory of Flexible Polymer Networks: Elasticity and Heterogeneities

A review of the main elasticity models of flexible polymer networks is presented. Classical models of phantom networks suggest that the networks have a tree-like structure. The conformations of their strands are described by the model of a combined chain, which consists of the network strand and two virtual chains attached to its ends. The distribution of lengths of virtual chains in real polydisperse networks is calculated using the results of the presented replica model of polymer networks. This model describes actual networks having strongly overlapping and interconnected loops of finite sizes. The conformations of their strands are characterized by the generalized combined chain model. The model of a sliding tube is represented, which describes the general anisotropic deformations of an entangled network in the melt. I propose a generalization of this model to describe the crossover between the entangled and phantom regimes of a swollen network. The obtained dependence of the Mooney-Rivlin parameters C 1 and C 2 on the polymer volume fraction is in agreement with experiments. The main results of the theory of heterogeneities in polymer networks are also discussed.

Viscoelastic cluster densification in sheared colloidal gels

Many biological materials, consumer products and industrial formulations are colloidal suspensions where the suspending medium is itself a complex fluid, and such suspensions are effectively soft matter composites. At rest, the distortion of the microstructure in the suspending fluid by the particles leads to attractive interactions between them. During flow, the presence of a microstructure in the viscoelastic suspending medium changes the hydrodynamic forces due to the non-Newtonian and viscoelastic effects. However, little is known about the structural development, the rheology and the final properties of such materials. In the present study, a model flocculated suspension in both a Newtonian and a viscoelastic medium was studied by combined rheological and rheo-confocal methods. To this extent, micrometer-sized fluorescent PMMA particles were dispersed in polymeric matrices (PDMS). The effect of fluid viscoelasticity is studied by comparing the results for a linear and a branched polymer. Stress jump experiments on the suspensions were used to de-convolute the rate dependence of the viscous and elastic stress contributions in both systems. These results were compared to a qualitative and quantitative analysis of the microstructure during flow as studied by fast structured illumination confocal microscopy, using a counter-rotating rheometer. At comparable interaction strength, as quantified by equal Bingham numbers, the presence of medium viscoelasticity leads to an enhanced densification of the aggregates during steady-state flow, which is reflected in lower limiting high shear viscosities. Following a strong preshear, the structural and mechanical recovery is also altered between the Newtonian and viscoelastic matrix with an increase in the percolation threshold, but with the potential to build stronger materials exploiting the combination of processing history and medium rheology at higher volume fractions.

Dynamics-based assessment of nanoscopic polymer-network mesh structures and their defects

Polymer-network gels often exhibit complex nanoscopic architectures. First, the polymer-network mesh topology on scales of 1-10 nm is usually not uniform and regular, but disordered and irregular. Second, on top of that, many swollen polymer networks display spatial inhomogeneity of their polymer segmental density and crosslinking density on scales of 10-100 nm. This multi-scale structural complexity affects the permeability, mechanical strength, and optical clarity of the polymer gels, which is of central relevance for their performance in popular applications. As a result, there is a need to characterize the polymer network structures on multiple scales. On the scale of the spatial inhomogeneity of crosslinking, 10-100 nm, scattering of neutrons, X-rays, and light has extraordinary utility and is well established. On the scale of the mesh topology, 1-10 nm, in contrast, experimental techniques are less established. This review intends to close this gap by reviewing two intrinsically dynamic methods that yield information on polymer network mesh structures. First, NMR-based assessment of residual dipolar proton-spin couplings, which arise upon the introduction of crosslinks into a liquidlike polymer system to impart partial solidlike characteristics, is suitable to quantitatively assess network meshes and local network defects. Second, diffusive penetration of molecular, macromolecular, and mesoscopic colloidal probes through a polymer gel provides insight into its obstructing network mesh structure and its potential irregularity. Either method is highly synergistic to scattering-based assessment of the network structures on larger scales, and in concert, a rich picture on the nano- and mesoscopic gel topology is obtained.

Tuning the Range of Polyacrylamide Gel Stiffness for Mechanobiology Applications

Adjusting the acrylamide monomer and cross-linker content in polyacrylamide gels controls the hydrogel stiffness, yet the reported elastic modulus for the same formulations varies widely and these discrepancies are frequently attributed to different measurement methods. Few studies exist that examine stiffness trends across monomer and cross-linker concentrations using the same characterization platform. In this work, we use Atomic Force Microscopy and analyze force-distance curves to derive the elastic modulus of polyacrylamide hydrogels. We find that gel elastic modulus increases with increasing cross-link concentration until an inflection point, after which gel stiffness decreases with increasing cross-linking. This behavior arises because of the formation of highly cross-linked clusters, which add inhomogeneity and heterogeneity to the network structure, causing the global network to soften even under high cross-linking conditions. We identify these inflection points for three different total polymer formulations. When we alter gelation kinetics by using a low polymerization temperature, we find that gels are stiffer when polymerized at 4 °C compared to room temperature, indicating a complex relationship between gel structure, elasticity, and network formation. We also investigate how gel stiffness changes during storage over 10 days and find that specific gel formulations undergo significant stiffening (1.55 ± 0.13), which may be explained by differences in gel swelling resulting from initial polymerization parameters. Taken together, our study emphasizes the importance of polyacrylamide formulation, polymerization temperature, gelation time, and storage duration in defining the structural and mechanical properties of the polyacrylamide hydrogels.

Extremely stretchable thermosensitive hydrogels by introducing slide-ring polyrotaxane cross-linkers and ionic groups into the polymer network

Stimuli-sensitive hydrogels changing their volumes and shapes in response to various stimulations have potential applications in multiple fields. However, these hydrogels have not yet been commercialized due to some problems that need to be overcome. One of the most significant problems is that conventional stimuli-sensitive hydrogels are usually brittle. Here we prepare extremely stretchable thermosensitive hydrogels with good toughness by using polyrotaxane derivatives composed of α-cyclodextrin and polyethylene glycol as cross-linkers and introducing ionic groups into the polymer network. The ionic groups help the polyrotaxane cross-linkers to become well extended in the polymer network. The resulting hydrogels are surprisingly stretchable and tough because the cross-linked α-cyclodextrin molecules can move along the polyethylene glycol chains. In addition, the polyrotaxane cross-linkers can be used with a variety of vinyl monomers; the mechanical properties of the wide variety of polymer gels can be improved by using these cross-linkers.

Microstructural evolution of a model, shear-banding micellar solution during shear startup and cessation

We present direct measurements of the evolution of the segmental-level microstructure of a stable shear-banding polymerlike micelle solution during flow startup and cessation in the plane of flow. These measurements provide a definitive, quantitative microstructural understanding of the stages observed during flow startup: an initial elastic response with limited alignment that yields with a large stress overshoot to a homogeneous flow with associated micellar alignment that persists for approximately three relaxation times. This transient is followed by a shear (kink) band formation with a flow-aligned low-viscosity band that exhibits shear-induced concentration fluctuations and coexists with a nearly isotropic band of homogenous, highly viscoelastic micellar solution. Stable, steady banding flow is achieved only after approximately two reptation times. Flow cessation from this shear-banded state is also found to be nontrivial, exhibiting an initial fast relaxation with only minor structural relaxation, followed by a slower relaxation of the aligned micellar fluid with the equilibrium fluid's characteristic relaxation time. These measurements resolve a controversy in the literature surrounding the mechanism of shear banding in entangled wormlike micelles and, by means of comparison to existing literature, provide further insights into the mechanisms driving shear-banding instabilities in related systems. The methods and instrumentation described should find broad use in exploring complex fluid rheology and testing microstructure-based constitutive equations.

Versatile supramolecular cross-linker: a rotaxane cross-linker that directly endows vinyl polymers with movable cross-links

A supramolecular cross-linked cross-linker, capable of introducing rotaxane cross-links to vinyl polymers, has been developed for the rational synthesis of polyrotaxane networks. The experimental results reveal that the combination of an oligocyclodextrin (OCD) and a terminal bulky group-tethering macromonomer (TBM) forms a polymer-network structure having polymerizable moieties through supramolecular cross-linking. Radical polymerization of a variety of typical vinyl monomers in the presence of the vinylic supramolecular cross-linker (VSC) afforded the corresponding vinyl polymers cross-linked through the rotaxane cross-links (RCP) as transparent stable films in high yields under both photoinitiated and thermal polymerization conditions. A poly(N,N-dimethylacrylamide)-based hydrogel synthesized by using VSC, RCPDMAAm , displayed a unique mechanical property. The small-angle X-ray scattering (SAXS) results, indicating patterns characteristic of a polyrotaxane network, clearly suggested the presence and role of the rotaxane cross-links. The confirmation of the introduction of rotaxane-cross-links into vinyl polymers strongly reveals the significant usefulness of VSC.

Structure and properties of aqueous methylcellulose gels by small-angle neutron scattering

Cold, semidilute, aqueous solutions of methylcellulose (MC) are known to undergo thermoreversible gelation when warmed. This study focuses on two MC materials with much different gelation performance (gel temperature and hot gel modulus) even though they have similar metrics of their coarse-grained chemical structure (degree-of-methylether substitution and molecular weight distribution). Small-angle neutron scattering (SANS) experiments were conducted to probe the structure of the aqueous MC materials at pre- and postgel temperatures. One material (MC1, higher gel temperature) exhibited a single almost temperature-insensitive gel characteristic length scale (ζ(c) = 1090 ± 50 Å) at postgelation temperatures. This length scale is thought to be the gel blob size between network junctions. It also coincides with the length scale between entanglement sites measured with rheology studies at pregel temperatures. The other material (MC2, lower gel temperature) exhibited two distinct length scales at all temperatures. The larger length scale decreased as temperature increased. Its value (ζ(c1) = 1046 ± 19 Å) at the lowest pregel temperature was indistinguishable from that measured for MC1, and reached a limiting value (ζ(c1) = 450 ± 19 Å) at high temperature. The smaller length scale (ζ(c2) = 120 to 240 Å) increased slightly as temperature increased, but remained on the order of the chain persistence length (130 Å) measured at pregel temperatures. The smaller blob size (ζ(c1)) of MC2 suggests a higher bond energy or a stiffer connectivity between network junctions. Moreover, the number density of these blobs, at the same reduced temperature with respect to the gel temperature, is orders of magnitude higher for the MC2 gels. Presumably, the smaller gel length scale and higher number density lead to higher hot gel modulus for the low gel temperature material.

Effect of network topology on phase separation in two-dimensional Lennard-Jones networks

We generate two-dimensional Lennard-Jones networks with random topology by preparing a perfect four-functional network of identical harmonic springs and randomly cutting some of the springs. Using molecular-dynamics simulations we find that the fraction p of active springs affects both the temperature of phase separation and the type of structures observed below this temperature, from networklike high-density patterns at p>0.5 ("gel") to dropletlike structures at p<0.5 ("sol"). In the gel domain, these patterns are determined by the interplay between free energy and network topology, with the former dominant as p-->1 and the latter as p-->0.5 .

Soft elasticity of RNA gels and negative Poisson ratio

We propose a model for the elastic properties of RNA gels. The model predicts anomalous elastic properties in the form of a negative Poisson ratio and shape instabilities. The anomalous elasticity is generated by the non-Gaussian force-deformation relation of single-stranded RNA. The effect is greatly magnified by broken rotational symmetry produced by double-stranded sequences and the concomitant soft modes of uniaxial elastomers.

Butterfly patterns in crystalline polymers under uniaxial stretch

We investigate the density fluctuations in crystalline polymers under uniaxial stretch in the order of submicrons to microns with two-dimensional ultrasmall-angle x-ray scattering. Before uniaxial stretch, we found isotropic density fluctuations obeying the mass fractal with the fractal dimension 2.6. After uniaxial stretch, the isotropic scattering pattern was transformed into the butterfly pattern. The butterfly pattern is caused by the stress-induced density fluctuations and the heterogeneous deformation associating with the spatial heterogeneity of stress field due to the distribution of crystalline and amorphous regions.

Particle structuring under the effect of an uniaxial deformation in soft/hard nanocomposites

A model nanocomposite sample, made of rigid monodisperse spherical inclusions in a deformable matrix, was uniaxially stretched. The displacement field of the particles at the sample surface is analyzed using atomic force microscopy. It is shown that its 2D structure factor presents most of the characteristic features previously described from scattering experiments on similar materials. At the scale of the particles, distortions from affinity are observed. They can be explained by the radial interactions between neighboring inclusions, related to the mechanical confinement of the matrix between particles. At larger scales, remarkable alignments of particles are observed along a direction which is roughly perpendicular to the stretching direction. We show that this effect is found in other soft/hard nanocomposites. It may contribute to the mechanical properties of this class of heterogeneous materials.