A polymeric gel consists of a polymer network swollen by small solvent molecules. It could be synthesized from a monomer solution through gelation or from a dry elastomer directly through swelling. The swelling capability attaches unique attributes to polymeric gels, such as 1) the extremely low stiffness, comparable to that of biological tissues, and 2) the coupling between deformation and solvent migration. However, swelling is also often accompanied with the reduction of both toughness and strength (Tsunoda 2000; Tanaka, 2000, Miquelard-Garnier, 2009), which could occur in gels obtained from either synthesis method. The fragility and weakness of gels hinder potential applications such as tissue replacement, tissue scaffold or as stimulus responsive material for sensors and actuators. In addition to promoting structural applications of gels, understand the fracture process of gels may also improve the handling and mouthfeel of many gel ingredients in foods (Lillfor, 2001; Foegeding, 2007) - an area less known to mechanical engineers.
Regular gels that are weak and brittle are often built upon a single type of polymer network. Some novel gels with modified network architecture show significant improve in strength, such as the double network gel (DN gel, Gong et al, 2003), the nano-composite gel (Haraguchi & Takisha, 2002), the topological gel (Mayumi & Ito, 2001), and the model network gel (Malkoch et al, 2006, Ossipov & Hilborun, 2006). This review aims to elucidate the current understanding of 1) the origin of fragility of simple gels 2) general toughening mechanisms of DN gel and nano-composite gel 3) the special role of swelling/diffusion coupling in fracture process of gels.
Swelling embrittlement
The rule of thumb for the strength requirement of polymeric gels in most biomedical applications is a level comparable to the load carrying capacity of nature tissues. For example, cartilage (Kempson 1982), aortic wall (Mohan & Melvin, 1982) and skin (Edwards & Marks 1995), could carry a load on the order of 10 MPa. However, the strength of a gel is usually dependent on the loading condition, sample geometry, and constraints, and thus may not be an objective measure.
The failure mechanisms of gels vary from localized flow (Moller, et al 2008), softening and yielding (Na et al, 2006; Webber et al 2007; Haraguchi 2006), cavitation (Kundo and Crosby, 2009), to fracture (Tanaka, 2000). If we limit the discussion to the macroscopic propagating cracks (with a length scale much larger than the mesh size of the polymer network), a suitable characteristic quantity is the fracture energy, namely the energy required to create unit area of fresh crack face.
To understand the reduction of fracture energy due to swelling, let us start from a generic conceptual picture: a mixture consists of homogeneous rubbery network with a viscous liquid. The cohesion of the material is provided solely from the polymer network, and a crack propagates by scissoring the polymer chains along its path. Besides a small amount of the excess energy of the surface itself, the fracture energy is mainly composed of two dissipation mechanisms. Firstly the energy of stretching an entire polymer chain to its elastic limit is dissipated irreversibly after subsequent chain rupture (Lake & Thomas 1967). Its magnitude is typically ~50 J/m2, and is often referred to as the intrinsic fracture energy. For dry polymers, the second means of dissipation is crystallization and viscoelastic dissipation of the highly stretched polymer network in front of crack tip due to interaction between closely packed chain strands, which is strongly rate dependent with the magnitude ranging from 0 to 105 J/m2 (Gent, 1996). The effect of this dissipation mechanism diminishes in a swollen gel when chains are diluted, and the fracture energy is shown to be strongly correlated with the dynamic loss modulus of a swollen elastomer (Tsunoda et al, 2000). At the high swelling limit (low elastomer fraction), the fracture energy becomes almost rate independent and reduced to the intrinsic fracture energy (Tsunoda et al, 2000; Tanaka 2007). The effect of dilution of chain density due to swelling could be easily corrected by converting the fracture energy into a value measured with respect to the corresponding area in the dry state.
Toughening of novel gels through distributed damage
Although simple polymer network tend to become very brittle when swollen, it has been demonstrated that by modifying the molecular and micro- structure of a gel, the deformation and energy dissipation mechanism could be changed, and the toughness may be increased by orders of magnitude (Tanaka et al, 2005; Lin et al 2010). The toughening mechanism in two tough gels, the DN gel and the nano-composite gel, are explained from a multi-scale perspective.
A DN gel consists of interpenetration networks of a highly extended 1st network of crosslinked polyelectrolyte, and a coiled 2nd network of neutral chains (Gong et al, 2003). The 1st network ruptures with microcracks prior to the 2nd network at finite deformation. Under an increasing deformation, the multiplication of microcracks or damage in 1st network proceeds stably, while the 2nd network remains almost intact, due to the double network topology, even after the 1st network has been shattered into small islands with percolated microcracks (Nakajima et al, 2008). Recently, a new type of DN gel is developed with the 1st network crosslinked by reversible ionic crosslinks (Sun et al,2012). This new DN gel achieves a much higher toughness and has a self-healing capability due to the reforming of the ionic crosslinks. A nano-composite gel undergoes a different damage process. A nano-composite gel consists of a swollen single network imbedded with nano-clay particles (Haraguchi & Takehisha, 2002). The polymer chains absorb and form physical bonds with clay particle, i.e. the clay acts as weak physical crosslinking points attached with a large amount of short chains, and breaks easily before the final failure of the main backbone (Nishida et al 2009). A signature for the damage of stress-active chains in the network for both materials is the significant hysteresis and softening in simple mechanical tests such uniaxial tension and compression (Webber et al, 2007; Zhu et al, 2006; Xiong et al 2008). Both materials are highly heterogeneous before and after damage. For example, the typical length scale for the island structure a damaged DN gel (Nakajima et al, 2008) (and other derivatives based on this structure such as micro-gel reinforced gels (Hu et al, 2012), and micro-voids reinforced gels ((Nakajima et al, 2011)) is on the order of microns, and the typical size of a nano-composite-reinforced gel is in the submicron region (Haraguchi et al, 2006).
For the problem of an advancing macroscopic crack, the microstructural damage leads to the formation of an extended damage zone ahead of the crack tip. The fracture energy has the additional contribution from the dissipation in the damage zone. While the intrinsic fracture energy corresponds to the dissipation at a region of size comparable to merely the mesh size of polymer network (Lake & Thomas, 1967; Hui, 2003), the damage of sacrificial bonds occurs on a much larger length scale, typically several hundreds of microns, which has been observed directly under optical micro scope for double network gels (Yu et al, 2009; Liang et al, 2011). Thus comparing to the rupture a single layer of chains in a simple gel, the fracture energy is amplified by orders of magnitudes.
The toughening effect is determined form the competing process of an extending damage zone against the propagation the actual crack. For a DN gel, it has been shown experimentally that the fracture energy increases with the average chain length of the 2nd network (Nakajima et al, 2009). On the other hand, it is also found that that the fracture energy could be further increased by increase the heterogeneity and weakening of the 1st network, which enables the formation of damage zone at lower strain (Nakajima et al, 2011). Simple models have been developed to relate the energy dissipation in the hysteresis of a simple test to that in the damage zone (Brown 2007; Tanaka 2007). The general mechanism of toughening in all these gels are the same: to sacrifice part of the gel structure (1st network, crosslinks, clay particles, etc) as much as possible in a stable way. The weaker the sacrifice, the larger the damage zone, the tougher the composite gel would be.
Weakening effect of heterogeneity
A simple gel, even without any visible flaw, often breaks easily due to the large amount of defects and heterogeneities in the network, especially for those formed by regular gelation methods such as radical polymerization (Cohen et al,1992; Ikkai & Shibayama 2004). It is found that the magnitude of heterogeneity tends to be amplified by swelling or deformation (Mendes et al, 1996; Basu et al, 2011, Shibayama 2011), which eventually leads to the formation of microcracks.
On the other hand, both the topological network defect and heterogeneous crosslinking problem could be avoided by producing a nearly-homogeneous network using methods such as ‘click chemistry' (Malkoch et al, 2006, Ossipov & Hilborun, 2006), and combining star polymers of the same size (Sakia et al, 2008). Alternatively, one can also enable the network crosslinking point to slide with deformation by producing a ‘topological gel'. Both types of gels could survive much larger stretch than a regular single gel, to almost the ultimate stretch of each chain. These homogeneous gels are, however, not much tougher, and are expected to fracture at a much lower stretch when a notch in the geometry is present.
Effect of solvent
The effect of the solvent and solvent-network interactions to the strength and toughness of gels is relatively less studied. Firstly, solvent may induce a frictional drag on the polymer chains, especially for those dangling chains formed during damage. Secondly, the highly concentrated hydrostatic tension near a crack tip lower the local solvent chemical potential, and causes a converging solvent flow (Wang & Hong, 2012). Despite the diffusional origin of the second effect, the redistribution of solvent takes as short as milliseconds near a microcrack. While the first effect generally stabilizes the fracture process, the second softens the crack tip and promotes fracture (at constant load).
Experiments on highly viscous physical gel has shown that the wetting of propagating crack in dry air could lead to a decrease in fracture energy (Baumberger et al, 2006), increase in propagation velocity of steady state cracks (Baumberger & Ronsin, 2009, 2010), and the initiation of secondary cracks (Baumberger & Ronsin, 2010). Simple analytical model shows that these effects are partly due to the stress-assisted dissociation of physical crosslinks, and the friction between polymer chains and solvent (Baumberger & Ronsin, 2009). While solvent friction is also present in a permanently crosslinked gel (Tanaka et al, 2000), similar observation has not been reported on chemical gels.
The effect of solvent on a weak simple gel may seem minor. However, it could lead to a large improvement on the performance of tough gels by stabilizing crack propagation and increase the damage-zone size. For example, it has been shown that by increasing the viscosity of the swelling medium, the fracture energy of a DN gel could be further improved (Liang et al, 2012).
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