The swelling and mechanical properties of networks are intimately tied together through the free energy function as it is affected either by chain stretching (elastic free energy) or through the mixing of the polymer with the solvent (usually through a Flory-Huggins estimate). Frenkel, then Flory and Rehner (FFR) developed a simple way of looking at this problem by simply balancing the elastic and mixing contributions to the chemical potential at swelling equilibrium. Much work has been done to examine this model, often in a way that suggests that something is missing or that the model itself is incorrect. In this presentation we examine the FFR model and show that it is correct for polymer networks swollen in organic liquids. We demonstrate that anomalous peaks in the swelling activity parameter S (or dilational modulus) are artifacts of experimental methods and we further show that, once the peak in S is removed, quantitative agreement is obtained between mixing and elastic contributions to the free energy with the simple addition of a cross-link dependent interaction parameter.

Slide-ring (SR) gels with movable cross-links along network strands have received much attention as a novel class of polymer gels. The network topology of SR gels is variable in response to imposed stress or deformation whereas that of classical gels with fixed cross-links is invariable. The polyrotaxane-based SR gels are synthesized by intermolecular cross-linking of alpha-cyclodextrin contained in poly(ethylene glycol). The SR gels are expected to exhibit novel properties and functions resulting from the movable cross-links. In this talk, we focus on the fluid-permeation behavior of the membranes of SR gels under imposed pressure (p), and the nonlinear elasticity revealed by biaxial stretching. It has been well known that the fluid permeation of classical gels obeys the Darcy's law: The steady-state fluid velocity (v) is linearly proportional to p. The proportionality constant (f) corresponding to the friction coefficient between gel network and fluid is independent of p for the classical gels. Here, we demonstrate that the membranes of SR gels exhibit a peculiar p dependence of f, where f sharply varies between two different values within a narrow p range. It indicates that SR gels are promising polymer membrane materials that enable the on-off control of fluid permeation by imposed pressure, which can be developed to separation membranes and drug delivery systems with novel functions. Further, we show a unique feature in nonlinear elasticity for SR gels revealed by the experiments using unequal biaxial strains. The effect of the strain in one direction on the stress in the other direction in SR gels is much smaller than that in classical gels. This feature results in no explicit strain-coupling term in the strain energy density function of SR gels.

Recently, we have developed a novel gel system (Tetra-PEG gel) by new network formation method, “AB-type crosslink-coupling”; the network is formed by the combination of two mutually reactive tetra-arm prepolymers with same shape. Our previous study revealed that the Tetra-PEG gel has a homogeneous polymer network with small amount of structural defects. Although the connectivity and spatial heterogeneity was observed, the degree of heterogeneity is extremely smaller than that of conventional gels. In this study, we focus on the correlation between mechanical properties and structural parameters of polymer gels. We tuned the structural parameters including the polymer volume fraction (f_0), polymerization degree of network strands (M = 5k-40k g/mol), and reaction conversion (p). We investigated the values of p by infrared (IR) measurement, elastic modulus (G) and ultimate elongation ratio (lambda;max) by stretching measurement, and fracture energy (T0) by tearing measurement.
First, we compared G measured by a stretching measurement, and that predicted from the reaction efficiency (p) using affine (G_af ) and phantom (G_ph) network models. As for the 10k and 20k Tetra-PEG gels, G_ph and G corresponded well with each other in a wider range than the other gels, suggesting that their elasticities is roughly predicted by the phantom network model. As for the 5k Tetra-PEG gel, the downward deviation of G from G_ph was increasingly pronounced with decreasing f_0. On the other hand, the 40k Tetra-PEG gel shows distinct behavior; G was above G_ph and near G_af. In order to discuss the whole tendency, G/G_af was plotted against f_0/ f*, f* is the overlapping polymer volume fraction of the prepolymer. In this figure, all of the data fall onto a single curve. In the range from f* to 3.0f*, the elastic moduli were well predicted by the phantom network model. The downward deviation below f* is due to the formation of elastically ineffective loops. In the range above 3.0f*, G = G_af increased with an increase in f_0 and approached to 1.0. This data strongly suggests that trapped entanglements are introduced to the network or that the model shifts to the affne network model, or both in the region above 3.0f*. Only from these results, we cannot distinguish whether the deviation from the phantom network model prediction is originated from trapped entanglements or from the change in models. Thus, we investigate the trapped entanglements by the tearing measurement. The results in tearing measurement indicated that there are few trapped entanglements. Taking into account these data, it is strongly suggested that the model predicting the elastic modulus shifts model with increasing _0 and N. In the presentation, the results of ultimate elongation ratio will be also discussed.

Responsively tough, injectable biomaterials are potentially useful for the minimally-invasive surgical implantation of durable matrices, either for delivering cellular or molecular cargo, or to act as robust fillers for soft tissue reinforcement. Associative protein hydrogels are well-suited for use as injectable materials, exhibiting cyto-protective shear-banding behavior and immediate recovery post-injection. However, the low yield stress required for the injectability of these materials is typically incompatible with the high resistance to deformation and fracture that is needed to maintain implant integrity under physiological stresses. One approach to accomplish both injectability and toughness is to engineer a shear thinning hydrogel with a low yield stress at low temperatures that is reinforced at body temperature due to thermoresponsive block copolymer self-assembly. Toward this end, triblock copolymer hydrogels containing artificially engineered associative protein midblocks and poly(N-isopropylacrylamide) (PNIPAM) endblocks have been developed, exhibiting responsive and reversible toughening over clinically-relevant temperature ranges. The PNIPAM endblocks exhibit lower critical solution behavior in this hybrid protein-polymer gel, and heating above the transition temperature to 37°C leads to endblock desolvation and aggregation into nanoscale domains. The formation of these reinforcing domains leads to large increases in the gel&’s elastic modulus and yield stress in shear, as well as improved resistance to compressive failure, erosion, and creep. The relationship between macromolecular design, nanostructure formation, and gel mechanics has been investigated in detail using small-angle neutron scattering (SANS) and oscillatory shear rheology, revealing important principles for controlling network self-assembly and achieving improved reinforcement. In particular, large micellar cores, high PNIPAM volume fractions, and high densities of midblock associations led to the stiffest hydrogels, with elastic moduli reinforced by a factor of 14 to approximately 130 kPa at 37°C. Stress relaxation times were seen to increase by up to 50-fold for gels with the largest micelles and packing fractions. For large enough endblocks, midblock associations were seen to promote endblock segregation even below the PNIPAM transition temperature, and these swollen micellar structures introduced long relaxation times into the gels. These studies demonstrate that control of the double network structure is critical for tuning the gel&’s mechanical behavior over a broad range for use in various biomedical applications.

We propose here a generic method to reinforce weak elastomers without using fillers. This method could be particularly interesting in the biomedical or high tech applications where pure polymers with specific physical properties (transparency, resistance to UV or temperature) are used but have poor mechanical properties.
In recent studies on the reinforement of hydrogels. Gong et al have shown that hydrogels synthesized with two interpenetrating networks with very different levels of crosslinking and conformations of chains have a fracture toughness significantly enhanced relative to a single homogeneous network[1][2][3]. Their mechanical properties are enhanced through breaking the bonds of the more crosslinked and highly stretched minority network while avoiding crack propagation through the less crosslinked and unstreched majority network[4].
We applied this method to acrylic elastomers and succesfully prepared poly(alkyl acrylate) elastomers containing isotropically prestretched chains at different volume fractions, using sequential swelling/polymerization steps. Samples containing prestretched chains show an impressive enhancement of properties compared to networks polymerized in one step. Both initial modulus and fracture toughness are enhanced while retaining a negligible hysteresis and residual deformation upon unloading, which is impossible in simple networks.. Our best samples show a 50 time increase in true stress at break and in fracture toughness, making those material as tough as some filled elastomers. Our methodology holds great promise to improve the extensibility, toughness and tune the non-linear elasticity of elastomers previously thought to be mechanically too weak to be used in mechanically demanding applications.

[1] Gong, J. P.; et al, Y. Adv. Mater. 2003, 15, 1155-1158.
[2] Tanaka, Y.; et al J. of Physical Chemistry B 2005, 109, 11559-11562.
[3] Gong, J. P. Soft Matter 2010, 6, 2583.
[4] Brown, H. R. Macromolecules 2007, 40, 3815-3818.

We investigated the effects of swelling and deswelling on the mechanical properties of Tetra-PEG ion gels with variable polymer volume fractions at the measured condition (phi;_m). Tetra-PEG gels were prepared by the AB type crosslink-coupling between the two symmetrical tetra-arm prepolymers with tuning the network strands length and polymer volume fractions. The use of an ionic liquid as diluent enables us to measure the mechanical properties of strongly deswollen Tetra-PEG gels above the melting point of PEG. The drastic increase in the elastic modulus was observed in the high phi;_m region due to the unusually contracted conformation of the network strands, called supercoiling. The Obukhov model, which predicts the elasticity of polymer networks using the concentration at preparation (phi;_0) and measured condition (phi;_m) as variables, can describe the phi;m-dependence of the elastic modulus in all phi;_m regions. Furthermore, we analyzed the stress-elongation relationships for the swollen and deswollen networks. We estimated the fractal dimensions based on the Pincus blob concept. We, for the first time, observed the crossover of the phi;_m-dependence of the fractal dimension from normal scaling to supercoiling, and the dependence of the fractal dimension on the strand length. The extensibility at break increased with an increase in phi;_m and an increase in the network strand length. These results did not obey the familiar Kuhn model, but were better explained by our model. These findings will help to understand the structure and formation mechanism of supercoiling.