Session J17: Elastomers & Gels

Depth Dependence of Shear Properties in Articular Cartilage

Articular cartilage is a highly complex and heterogeneous material in its structure, composition and mechanical behavior. Understanding these spatial variations is a critical step in designing replacement tissue and developing methods to diagnose and treat tissue affected by damage or disease. Existing techniques in particle image velocimetry (PIV) have been used to map the shear properties of complex materials; however, these methods have yet to be applied to understanding shear behavior in cartilage. In this talk, we will show that confocal microscopy in conjunction with PIV techniques can be used to determine the depth dependence of the shear properties of articular cartilage. We will show that the shear modulus of this tissue varies by over an order of magnitude over its depth, with the least stiff region located about 200 microns from the surface. Furthermore, our data indicate that the shear strain profile of articular cartilage is sensitive to both the degree of compression and the total applied shear strain. In particular, we find that cartilage strain stiffens most dramatically in a region 200-500 microns below the surface. Finally, we will describe a physical model that accounts for this behavior by taking into account the local buckling of collagen fibers just below the cartilage surface and present second harmonic generation (SHG) imaging data addressing the collagen orientation before and after shear.   

Determining Local Mechanical Properties of Soft Materials with Cavitation Rheology

To guide the development of tissue scaffolds and the characterization of naturally heterogeneous biological tissues, we have developed a method to determine the local modulus at an arbitrary point within a soft material. The method involves growing a cavity at the tip of a syringe needle and monitoring the pressure of the cavity at the onset of a mechanical instability. This critical pressure is directly related to the local modulus of the material. The results focus on the network development of poly(lactide)-poly(ethylene oxide)-poly(lactide) triblock copolymer and poly(vinyl alcohol) hydrogels. These materials serve as model materials for tissue scaffolds and soft biological tissues. This new method not only provides an easy, efficient, and economical method to guide the design and characterization of soft materials, but it also provides quantitative data of the local mechanical properties in naturally heterogeneous materials.   

Soft Segment Orientation Effects on the Morphology

A series of polyurethane elastomers were designed with varying poly(ethylene oxide) (PEO) lengths. Segmented polyurethanes containing higher soft segment molecular weight (4600 g/mol) demonstrated a lamellar morphology, a result of the highly crystalline hard and soft domains. Polyurethanes containing lower molecular weight PEO (1000 g/mol) showed less microphase segregation at similar hard segment contents, though shifting to a copolymer (PEO-PPO-PEO, 1900 g/mol) soft segment recovered domain segregation. High molecular weight PEO-containing polyurethanes showed a tendency to neck upon deformation, which likely resulted from the largely crystalline soft domains. Low molecular weight PEO-containing polyurethanes (1000 g/mol and 1900 g/mol) did not show a tendency to neck during deformation due to the lesser extent of microphase segregation and/or domain crystallinity. We have also investigated the effect of chemistry on morphology, thermal, and mechanical properties by varying chain extender, macrodiol, and isocyanate. Through these experiments, the goal was to determine the molecular mechanisms most responsible for mechanical property enhancement. Molecular architecture was shown to play a more prominent role in dynamic mechanical properties than hard segment percentage; amorphous polyurethane samples displayed drastic stiffness changes with strain rate.   

Structure and mechanical properties of hydrophobically modified hydrogels

Chemically crosslinked hydrogels based on polyacrylic acid chains modified with short hydrophobic C12 side groups have been synthesized in water at a polymer concentration varying between 4 and 10 {\%} in weight. In the absence of hydrophobic groups, the hydrogels behave as soft elastic solids with an elastic modulus in the few kPa range. With the introduction of even a few percent of C12 hydrophobic side chains, the dissipative component of the shear modulus increases by two orders of magnitude, while the elastic component remains unchanged. This causes a large increase in the hysteresis at large strains and an increase in the fracture toughness of the gel. We demonstrate that this change in properties is due to the formation of labile nanoclusters of the hydrophobic groups in the aqueous phase.   

Molecular Origins for the Superior Toughness of Double-Network Hydrogels

Double network hydrogels (DN-gels) are the toughest of crosslinked polymer networks which contain water at more than 90{\%} water by volume. The order-of-magnitude increase in the fracture toughness of a highly swollen but brittle polyelectrolyte network obtained from the addition of a linear polymer is non-intuitive and intriguing. Here, we present insights into the change in the total and the individual molecular structures of DN-gels obtained from recent neutron scattering measurements. The structure of individual components within the DN-gels was obtained by using a deuterium-labeled monomer in conjunction with contrast-matching methods. A working hypothesis for the toughening mechanism has been proposed based on the scattering data and other supporting measurements$.$   

Neutron scattering from polyelectrolyte solutions in the presence of a hydrophilic polymer

The structure of highly charged polyelectrolytes in water has been extensively studied. Existing models adequately describe the small-angle scattering from polyelectrolytes using characteristic physical parameters such as the Debye screening length. However, the influence of a hydrophilic polymer on the structure of a polyelectrolyte in solution such as the case of Double-Network Hydrogels has not been widely studied. Here, we present our recent neutron scattering results from such a multicomponent system. This talk discusses neutron scattering from a monovalent polyelectrolyte in water and in an aqueous solution of neutral polymer capable of hydrogen bonding. The thermodynamic parameters that govern the mutual interactions between the charged polyelectrolyte, neutral polymer, and water are used as parameters to successfully describe the observed neutron scattering results.   

Neutron scattering from double-network hydrogels subjected to uniaxial extension

Double-network hydrogels (DN-gels) are water swollen polymer networks with load bearing abilities similar to that of an articular cartilage. Our neutron scattering measurements offered important insights into the molecular origins for the superior toughness of DN-gels. Here, we discuss recent neutron scattering results from DN-gels subjected to uniaxial extension. These results are further supported by flow birefringence measurements on the solution equivalents of DN-gels subjected to uniaxial extension. The deformation behavior of DN-gels is contrasted with that of complex hydrogels containing nanosized inorganic fillers or figure-of-eight crosslinkers.   

The Conformational Elasticity Theory and Its Applications

A theory that physically describes rubber elasticity including large scale behavior, internal energy contribution and different elastic behaviors of chemically different polymers, so called ``conformational elasticity theory,'' has been recently developed with predicted stress as a function of axial ratio of ellipsoid model. Using short chain rotational isometric state (RIS) model we simulated 2-dimensional chain conformation distribution map (one axes is the end-to-end distance of a polymer chain and the other is the conformational energy). It is very important to propose a microscopic mechanism of the distribution evolution during the polymer deformation. The total tension, the internal energy force and the entropy force can be obtained in any elongation step, and very close to the experimental data. This theory includes interaction energy and distinguishes different chemical structures, thus providing the opportunity to make some efforts in analysis of the physical junction and the entanglement occurring to the system during elongation.   

Modeling mechanochemical transduction in chemo-responsive gels.

Using the recently developed gel lattice spring model, we study mechanochemical transduction in chemo-responsive gels undergoing the Belousov-Zhabotinsky reaction. More specifically, we examine how to harness an applied mechanical force to trigger the propagation of traveling chemical waves, which then lead to oscillations within gels that were initially non-oscillating. In our two dimensional simulations, we introduce the presence of an applied force by uniformly decreasing the thickness of the sample from its initial value. We isolate the system parameters for which the decreasing of the thickness of the sample cases causes the transition from the non-oscillatory to the oscillatory state. In addition, we illustrate that even if the system is not driven into the oscillatory state, the nature of the pressure-induced transient oscillations are of interest since the waves can indicate the strength of the mechanical impact. We define how this type of the mehanochemical transduction depends on the reaction parameters and on the gel's cross-link density. Our studies clarify the sensitivity of the chemo-responsive gel to mechanical deformation and indicate the extent to which the gels can be harnessed as sensors of the mechanical impact.   

Thermoreversible Ion Gels by Block Copolymer Self-assembly in Ionic Liquids

Ion gels, formed by swelling a polymer network with ionic liquids, have been shown to be promising candidates towards highly conductive solid-state electrolytes. Through the self-assembly of triblock copolymers in room-temperature ionic liquids, transparent ion gels could be obtained. Due to the low copolymer concentration, the ionic conductivity of the resulting ion gels is only modestly affected by the triblock copolymer network. By further selecting thermo-responsive end blocks in the triblock copolymers, thermoreversible ion gels were developed. The gelation behavior, ionic conductivity, rheological properties, and microstructure of the ion gels were investigated in detail. The results presented here suggest that triblock copolymer gelation is a promising way to develop highly conductive ion gels.   

Diblock copolymers containing compositionally-uniform poly(HEMA-co-DMAEMA)

Hydroxyethyl methacrylate (HEMA) and dimethylaminoethyl methacrylate (DMAEMA) have been investigated as precursors for pH-responsive hydrogels. DMAEMA contains tertiary amine functionality that is reversibly protonated below its pKa. The swelling characteristics of poly(HEMA-co-DMAEMA) hydrogels are dependent on the distribution of DMAEMA, which in turn depends on the monomer composition and the monomer reactivity ratios. We find that the reactivity ratios are highly solvent dependent. Gradient copolymers are favored in most solvents at all monomer compositions. In dimethylsulfoxide, however, the reactivity ratios are near unity; compositionally-uniform poly(HEMA-co-DMAEMA) copolymers can therefore be synthesized at any composition. We have synthesized diblock copolymers containing poly(HEMA-co-DMAEMA) by a combination of atom transfer radical polymerization and click chemistry. The resulting diblock copolymers have controlled molecular weights, molecular weight distributions, and comonomer distributions, and they form well-defined periodic nanoscale structures consistent with their molecular characteristics.   

Small Angle Neutron Scattering Studies of the Counterion Effects on the Molecular Conformation and Structure of Charged G4 PAMAM Dendrimers in Aqueous Solutions

The structural properties of generation 4 (G4) poly(amidoamine) starburst dendrimers (PAMAM) with an ethylenediamine (EDA) central core in D$_{2}$O solutions have been studied by small angle neutron scattering (SANS). Upon the addition of DCl, SANS patterns show pronounced inter-particle correlation peaks due to the strong repulsion introduced by the protonation of the amino groups of the dendrimers. By solving the Ornstein-Zernike integral equation (OZ) with hypernetted chain closure (HNC), the dendrimer-dendrimer structure factor S(Q) is determined and used to fit the experimental data. Quantitative information such as the effective charge per dendrimer and its conformational change at different pH values is obtained. The results show clear evidence that significant counterion association occurs, strongly mediating the inter-dendrimer interaction. The influence of interplay between counterions and molecular protonation of dendrimers imposes a strong effect on the dendrimer conformation and effective interaction.   

Creasing of soft surfaces under compression

The surface of a soft material may form sharp creases when placed under compression. Though this mechanical instability was first recognized over 40 years ago, very little is known about the structures that result. In particular, we focus on the creasing of surface-attached hydrogels, materials that provide an excellent means of controlling properties such as biocompatibility, adhesion, and tribology. Large compressive stresses are generated within such gels upon swelling, leading to formation of creases that can dramatically alter surface properties. This instability may be exploited to enable the reversible formation of topographic patterns to actively control surface properties. We will present measurements of the critical compression at which surface creases form and how the soft surfaces deform as they fold, and will describe the preparation of surfaces that reversibly fold and flatten in response to external stimuli.   

Schallamach Wave Periodicity in Soft Elastomer Friction

From the dynamics of biomaterial interfaces to the interpretation of nanoscale characterization of polymer interfaces, the friction of soft polymer layers is critical to a wide range of advanced materials. A dominant mechanism in the friction of soft material interfaces is the onset and propagation of Schallamach waves. Schallamach waves are ``tunnels'' of air that provide relative displacement between the slider and the substrate rather than the instantaneous interfacial failure involved with stick-slip. We present a fundamental relationship between the periodicity of Schallamach waves ($\lambda )$ and the ratio of interfacial adhesion (G$_{c})$ over complex elastic modulus (E*). This deconvolution of bulk and interfacial contributions to the friction of soft materials leads to interesting predictions that will impact material design for a wide range of applications.   

Complex diffusion in biopolymer networks with added molecular crowding

Intra- and extracellular diffusion can depend sensitively on the environmental details. In general the diffusion is hindered and can be subdiffusive, varying heterogeneously due to molecular crowding and interactions with an immobile polymer network. We study the combined effects of polymer-hindrance and molecular crowding using particle tracking and correlation analyses applied to microspheres diffusing in Type I collagen with added polyethylene glycol.