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When a poly mer net workis stretched, so me poly mer strands do not bearloads. Exa mplesinclude looped strands, dangling strands, and extre mely long strands. When the poly mer net work is sub mergedin asolvent, ho wever, allstrands mix withsolvent molecules. This distinction bet ween strandsthat bearloads andstrandsthat do notleads usto modifythe Flory-Rehner model. The modified modelhasthreeparameters:thedensityofload-bearingstrands, N,thedensityofall strands,M , andtheinteraction para meter,χ. For a poly mer net worksub mergedin areservoir of solvent and bearingtriaxialstresses,the modified model provides equations ofstate,relatingthe stressestostretches, as well asthe che mical potential ofsolvent molecules andte mperatureinthe reservoir. We synthesize polyacryla mide hydrogels using precursors of various concentrations of mono mer, crosslinker, and transfer agent. We deter mine the three para meters N, M , and χ by fittingthe modified modeltoseveral experi ments,includingfrees welling,fasttension, andstress relaxation. In all sa mples tested, M is several ti mes N , whereas χ is nearly constant. This work de monstrates the consequences of the notion that so me poly mer strands in a poly mer net work b e ar l o a ds, b ut all str a n ds c o ntri b ut e t o s w elli n g. 

"This paper studies the lap shear, in which both the adhesive and adherends are elastic, but the adhesive is much softer than the adherends. The shear lag model identifies a length, called the shear lag length Ls. The energy release rate of a debond crack is affected by the elasticity of both the adhesive and adherends. Their relative importance is characterized by the ratio of the length of the remaining joint, L, to the shear lag length, Ls. In the short-joint limit, L/Ls→0, the adherends do not deform, and the elasticity of the adhesive gives the energy release rate. In the long-joint limit, L/Ls→∞, the interior of the adhesive does not deform, and the elasticity of the adherends gives the energy release rate. The shear lag model gives an approximate expression of the energy release rate for all values of L/Ls. This expression is in excellent agreement with the results obtained by finite element calculations, so long as the crack is long compared to the thickness of the adhesive." 

Degradable polymers are under intense development for sustainability and healthcare. Evidence has accumulated that the chemical reaction that decomposes a polymer an also grow a crack. Even under a small load, the crack speed can be orders of magnitude higher than the overall rate of degradation, leading to premature failure. Here, we demonstrate that a crack slows down markedly in a composite of two degradable materials. In a homogeneous degradable material, the stress concentrates at the crack tip, so that a relatively small applied stretch induces a high stress and a high rate of reaction. The fracture behavior of a composite that consists of two degradable materials, a stiff material for the fibers and a compliant material for the matrix, with strong adhesion between both, is different: The soft matrix blunts the crack and distributes the stresses at the crack tip over a long length of the fibers. The same rate of reaction requires a larger applied stretch. This stress de-concentration retards crack growth in the composite. We demonstrate this concept using a composite made of stiff polydimethylsiloxane (PDMS) fibers in a soft PDMS matrix. In the presence of water molecules in the environment, siloxane bonds in the PDMS hydrolyze, causing hydrolytic crack growth. We show that a hydrolytic crack grows much more slowly in a PDMS composite than in homogeneous PDMS, and may even arrest in the composite. It is hoped that this concept will contribute to the development of degradable materials that resist premature failure. 

Lap shear and peel are common tests for soft materials. Their results, however, are rarely compared. Here we compare lap shear and peel as tests for measuring toughness. We prepare specimens for both tests by using stiff layers to sandwich a layer of a polyacrylamide hydrogel. We introduce a cut in the hydrogel by scissors, pull one stiff layer at constant velocity, and record the force. In lap shear, the force peaks and then drops to zero, the cut grows unstably through the entire hydrogel, and the peak force is used to determine toughness. In peel, the force peaks and then drops to a plateau, the cut grows in the hydrogel in steady state, and the plateau force is used to determine toughness. Our experimental data show that the average values of toughness determined by lap shear and peel are comparable. The peak forces in both tests scatter significantly, but the plateau force in peel scatters narrowly. Consequently, toughness determined by lap shear scatters more than toughness determined by peel. We hypothesize that the peak forces scatter mainly due to the statistical variation of the cuts made by scissors, and test the hypothesis using two additional sets of experiments. First, after a cut is made by scissors, we pre-peel the specimen to extend the cut somewhat, and then measure toughness by lap shear and peel. The peak force in lap shear scatters less, and the peak force in peel is removed. Second, we prepare cuts using spacers of various thicknesses, and find that the peak forces in both lap shear and peel vary with the thickness of the spacer. These findings clarify the use of lap shear and peel to characterize soft materials. 

Hydrogels are commonly integrated with other materials. In the one-pot synthesis of a hydrogel coating, polymerization, crosslink, and interlink are concurrent. This concurrency, however, is often inapplicable for integrating hydrogels to other materials. For example, a permeable substrate will absorb small molecules in the solution, causing side reactions and even toxicity. Here, we report a method to break the concurrency by using photoinitiator-grafted polymer chains (PGPCs). A type of photoinitiator is copolymerized with various monomers. The PGPCs are uncrosslinked during syn- thesis, have long shelf lives in dark storage, and can be applied to a substrate by brush, cast, spin, dip, spray, or print. Under ultraviolet light, the polymer chains crosslink into a network and interlink with the substrate. The cured PGPC hydrogels are characterized by me- chanical tests. Furthermore, the PGPCs are demonstrated to adhere wet materials, form hydrophilic coatings on hydrophobic substrates, and pattern functional groups on permeable substrates.