Soft Materials by Design: Unconventional Polymer Networks Give Extreme Properties

Abstract

Hydrogels are polymer networks infiltrated with water. Many biological hydrogels in animal bodies such as muscles, heart valves, cartilages, and tendons possess extreme mechanical properties including extremely tough, strong, resilient, adhesive, and fatigue-resistant. These mechanical properties are also critical for hydrogels’ diverse applications ranging from drug delivery, tissue engineering, medical implants, wound dressing, and contact lenses to sensors, actuators, electronic devices, and soft robots. Whereas numerous hydrogels have been developed over the last few decades, a set of general principles that can rationally guide the design of hydrogels using different materials and fabrication methods for various applications remain a central need in the field of soft materials. This review is aimed to synergistically report: i). general design principles for hydrogels to achieve extreme mechanical and physical properties, ii). unconventional polymer networks to implement these design principles, and iii). future directions for the orthogonal design of hydrogels to achieve multiple combined mechanical, physical, chemical, and biological properties. Since these design principles and implementation strategies are based on generic polymer networks, they are also applicable to other soft materials including elastomers and organogels. Overall, the review will not only provide a comprehensive discussion on the rational design of soft materials, but also provoke interdisciplinary discussions on a fundamental question: why does nature select soft materials with unconventional polymer networks to constitute the major parts of animal bodies?

1. Introduction

As hydrophilic polymer networks infiltrated with water¹, hydrogels are the major components of animal bodies, constituting most of their cells, extracellular matrices, tissues, and organs. Not surprisingly, hydrogels have been widely used in biological and biomedical applications such as vehicles for drug delivery^2–5, scaffolds for tissue engineering^6–8, models for biological studies^9–13, medical implants^14,15, wound dressing^16–18, and contact lenses^15,19. More recently, intensive efforts have been devoted to exploring hydrogels’ emerging applications in devices and machines²⁰ such as hydrogel sensors^21–24, actuators^25–28, electronic devices^29–31, optical devices^32–34, iontronic devices^27,35, soft robots^26,36,37, batteries^38,39, super-capacitors⁴⁰, adhesives^41–43, and coatings^44,45.

The mechanical properties of hydrogels are crucial to the survival and wellbeing of animals, and greatly affect the abovementioned applications of hydrogels. The pioneering works in the field of polymers and soft materials have laid the foundation for understanding the elasticity, swelling, poroelasticity, viscoelasticity, fracture and fatigue of hydrogels (e.g., Ref.^46–59 and the references in them). However, the inverse question – how to design hydrogels that possess certain mechanical properties or certain properties in general – still poses a challenge in the field of polymers and soft materials^59–62. This challenge becomes even more daunting, when one targets at hydrogels’ extreme mechanical properties, such as extremely high values of fracture toughness⁶³, strength^64,65, resilience^66,67, interfacial toughness⁴³, fatigue threshold^68–70 and interfacial fatigue threshold⁷¹.

Despite the abovementioned grand challenge, the design of hydrogels with extreme mechanical properties is of both fundamental and practical importance. From the fundamental aspect, many biological hydrogels have achieved extreme mechanical properties necessary for their survival and well-being through evolution (Figure 1). For example, cartilage is a tough connective tissue that covers the surfaces of joints to provide reduced friction⁷². The human knee joint cartilage (i.e., articular cartilage) typically needs to sustain compressive stresses of 4–9 MPa for 1 million cycles per year, while maintaining high fracture toughness around 1,000 Jm^{−2 73}. The high fracture toughness of articular cartilage is mainly attributed to its abundant strong collagen fibers interpenetrated with proteoglycan macromolecules, which provides both viscoelasticity and poroelasticity for mechanical dissipation^74,75. The viscoelasticity of articular cartilage is mainly associated with local rearrangement of aggrecan, adhesive interactions of aggrecan, and reconfiguration of collagen⁷⁵; the poroelasticity of articular cartilage is governed by the interstitial fluid movement through the porous extracellular matrix⁷⁴. Tendon is a strong connective tissue that connects muscle to bone and muscle to muscle. The human patellar tendon can sustain a high tensile strength⁷⁶, owing to its unique hierarchical fibrous structure that enables the simultaneous stiffening of bundles of collagen fibers before their tensile failure^77,78. Heart valves generally possess both high resilience around 80% and high fracture toughness around 1,200 Jm^{−2 79,80}, which are two seemingly contradictory properties. The elastin and crimped collagen fibers in the heart valve are elastic and non-dissipative under moderate deformation giving the heart valve the high resilience (Figure 2)⁸¹, whereas under large deformation, the stiffening and fracture of the collagen fibers dissipate substantial mechanical energy making the heart valve tough as well⁸². The adhesion of soft connective tissues on bones can be extremely fatigue-resistant. For example, the cartilage-bone interface in the human knee joint can sustain compressive stresses of 1 MPa along with an interfacial toughness around 800 Jm⁻² over 1 million cycles of loads^73,83. The fatigue-resistant adhesion of soft tissues (e.g., tendons, ligaments, and cartilages) to rigid bones is commonly achieved through nanostructured interfaces of aligned collagen nano-fibrils and ordered hydroxyapatite nanocrystals^84–86. What are nature’s design principles, if any, for various biological hydrogels to achieve extreme mechanical properties? This is still a largely unanswered question, even in light of the pioneer works in the field of polymers and soft materials (e.g., Ref.^46–58 and the references in them).

Figure 1. Biological hydrogels in the human body can possess extreme mechanical properties.

Aorta with tensile strength of 0.2–3.7 MPa⁷³; heart valve with resilience above 80% and fracture toughness around 1,000 J m^{−2 79,80}; tendon with tensile strength of 10–100 MPa⁹⁶, fracture toughness of 20–30 kJ m⁻² and fatigue threshold of 1,000 J m^{−2 97}; skeletal muscle with fracture toughness around 2,490 J m⁻² and fatigue threshold around 1,000 J m^{−2 73}; articular cartilage with fracture toughness of 800–1,800 J m^{−2 98}; and tendon/cartilage/ligament-bone interfaces with interfacial fatigue threshold around 800 J m^{−2 71,83}.

Figure 2. Design principles and implementation strategies for various biological hydrogels to achieve extreme mechanical properties:

a. high toughness of cartilage due to viscoelastic and poroelastic dissipation of the polymer networks^75,99,100, b. high tensile strength of tendon due to simultaneous stiffening of multiple polymers in the fibrous hierarchical structure^77,96, c. high resilience and toughness of heart valve due to delayed mechanical dissipation^101,102, d. high interfacial fatigue threshold of cartilage-/ligament/tendon-bone interfaces due to intrinsically high-energy phases including nano-crystals and nano-fibers strongly bonded on the interfaces⁷¹. a is adopted from Ref⁹⁹. b is adopted from Ref⁷⁷. c is adopted from Ref^101,102. d is adopted from Ref⁷¹.

From the practical aspect, applications of hydrogels generally require the hydrogels to possess specific properties. For example, hydrogels designed with different moduli and viscoelastic properties have been used to regulate stem cell fate and activity^10,12,84,87. The applications of hydrogels as artificial cartilages and spinal discs require the hydrogels to be fatigue-resistant under cyclic mechanical loading^68,69,88,89. The mesh size of hydrogels’ polymer networks is critical to their applications in controlled drug delivery^33,90,91. More recent applications of hydrogels as various devices require the hydrogel to possess specific properties, for instance, stimuli-sensitivity for hydrogel sensors and actuators^37,92–94, strong adhesion for hydrogel coatings⁴³, optical transparency for hydrogel optics³³, electrical conductivity for hydrogel electronics³⁰, and water absorption/release for hydrogel water harvesters⁹⁵.

Over the last few decades, intensive efforts have led to the development of a plethora of hydrogels that possess extreme mechanical properties using diverse material candidates, including various natural and synthetic polymers, macro-/micro-/nano-fillers, and macro-/micro-/nano-fibers. Whereas the properties of these hydrogels are remarkable, their design often follows the Edisonian approach – trial and error with specific material candidates. As the field rapidly evolves, emerging applications of hydrogels in biomedicine pose escalating demands on the rationally-guided design of hydrogels beyond the Edisonian approach, requiring broad choices of material candidates and fabrication methods and achievements of multiple combined extreme properties. However, a set of general principles capable of rationally guiding the design of hydrogels using different materials and fabrication methods for various applications remain a central need in the field of soft materials. In this review, we aim to provide:

1. A set of general principles for the rational design of hydrogels to achieve extreme mechanical properties, including extremely high fracture toughness, tensile strength, resilience, interfacial toughness, fatigue threshold, and interfacial fatigue threshold; and extreme physical properties, including high electrical conductivity, patterned magnetization, high refractive index and transparency, tunable acoustic impedance, and self-healing. The design principles are generally based on fundamental mechanics and physics (beyond polymers) or inspired by biological hydrogels (e.g., muscles, cartilages, tendons, and heart valves) (Figure 3).

2. A set of unconventional polymer networks (UPNs) to implement the design principles discussed in i). using various material candidates and fabrication methods. The UPNs can be broadly categorized into: UPN architectures including ideal polymer networks, polymer networks with slidable crosslinks, interpenetrating and semi-interpenetrating polymer networks, polymer networks with high-functionality crosslinks, and nano-/micro-fibrous polymer networks; and UPN interactions including strong physical crosslinks, weak physical crosslinks, and dynamic covalent crosslinks (Figure 3).

3. A proposal of orthogonal design principles and synergistic implementation strategies for the design and fabrication of future hydrogels to achieve multiple combined mechanical, physical, chemical, and biological properties (Figure 3).

Figure 3.

This review summarizes the design principles and implementation strategies for soft materials including hydrogels, elastomers and organogels to achieve extreme properties.

Notably, since the aforementioned design principles and implementation strategies for hydrogels are based on generic polymer networks, they are also applicable to other soft materials comprised of polymer networks, including elastomers and organogels. In fact, many extreme mechanical and physical properties were first achieved in other soft materials than hydrogels. For example, high values of fracture toughness, tensile strength, resilience and interfacial toughness were realized in elastomers long before in hydrogels; ferromagnetic domains in soft materials were first programmed and 3D printed with elastomer inks as well.

The review is organized as the following. Section 2 will discuss common natural polymers, synthetic polymers, and permanent covalent crosslinks for hydrogels. Section 3 will introduce conventional polymer networks, and demonstrate that a number of mechanical properties of conventional polymer networks are coupled. Section 4 will define a set of unconventional polymer networks (UPNs), including both UPN architectures and UPN interactions, and then discuss that UPNs can provide decoupled mechanical properties. Thereafter, Sections 5 will systematically reveal the design principles for various extreme mechanical properties of hydrogels and implement strategies based on UPNs for each of the design principles; Sections 6 will briefly discuss the design principles and implementation strategies for hydrogels that possess a set of extreme physical properties. In Section 7, we will conclude the review by proposing orthogonal design principles and synergistic implementation strategies to design future hydrogels achieving multiple combined mechanical, physical, chemical and biological properties.

2. Polymers and crosslinks for hydrogels

A rich library of polymers and crosslinks have been used for the design and fabrication of various hydrogels. These polymers can be broadly categorized into natural polymers and synthetic polymers. In this section, we will briefly discuss the commonly-used natural polymers, synthetic polymers and permanent covalent crosslinks for hydrogels; we will discuss other types of crosslinks for hydrogels in Section 4.

2.1. Common natural polymers for hydrogels

Naturally derived polymers have been widely used to compose the polymer networks of hydrogels (Figure 4a). Hydrogels based on natural polymers usually possess biological properties compatible with extracellular matrices due to the similarity in their compositions. In addition, the natural polymer networks can often degrade in and be absorbed by the body through metabolism and tissue remodeling processes. Furthermore, the majority of natural polymers have reactive sites amenable to crosslinking and modification, which can endow the corresponding hydrogels with tailored biological and/or mechanical properties. In this subsection, we will briefly discuss a few natural polymers commonly-used for hydrogels. For more detailed discussions, a few classical reviews are recommended^4–6,61,103.

Figure 4.

Chemical structures and schematics of typical examples of a. common natural polymers, b. common synthetic polymers, and c. permanent covalent crosslinks for hydrogels. R represents an organyl substituent or hydrogen.

Alginate.

Alginate is a polysaccharide which is usually obtained from brown-algae cell walls and two kinds of bacteria, Azotobacter and Pseudomonas¹⁰⁴. Alginate is known to be a family of linear copolymers containing blocks of (1,4)-linked β-D-mannuronic (M) and α-L-guluronic acid (G) residues. The blocks are composed of consecutive G residues (GGGGGG), consecutive M residues (MMMMMM), and alternating M and G residues (GMGMGM)¹⁰⁵. Alginate hydrogels can be formed with various covalent and physical crosslinks. In particular, the ionic crosslinks have been widely used for alginate hydrogels, because the G blocks¹⁰⁶ (and GM blocks¹⁰⁷) in alginate can be readily bound with one another by divalent cations such as Ca²⁺, Mg²⁺, Ba²⁺, and Sr^{2+ 108–110}. The mechanical properties of alginate hydrogels can be easily tuned to match those of various tissues by changing different parameters, such as the molecular weight, polymer concentration, chemical modification, G/M ratio, and type or density of crosslinks^106,111. Alginate hydrogels have been widely used as scaffolds in tissue engineering, such as intervertebral disk regeneration¹¹², adipose tissue regeneration¹¹³, cardiac regeneration¹¹⁴, and liver regeneration¹¹⁵, since alginate allows the formation of hydrogels under physiological conditions and thus enables easy cell and drug encapsulation.

Hyaluronic acid.

Hyaluronic acid (also known as hyaluronan or hyaluronate) is a linear polysaccharide that consists of alternating units of a repeating disaccharide, β−1,4-D-glucuronic acid and β−1,3-N-acetyl-D-glucosamine^116,117. Hyaluronic acid is present in all mammals, especially in various soft connective tissues, acting as a space filler, lubricant, and osmotic buffer¹¹⁸. Hyaluronic acid can be covalently crosslinked into hydrogels by various hydrazide derivatives^119,120. The abundant carboxyl and hydroxyl groups on the polysaccharide structure of hyaluronic acid also offer many active sites for chemical modifications¹²¹. For example, hyaluronic acid can be modified with thiol^122,123, haloacetate¹²⁴, dihydrazide^119,125, aldehyde^126,127 and tyramine¹²⁸ groups, which can react with corresponding covalent crosslinkers through addition or condensation reactions¹²⁹. As another example, hyaluronic acid can also be modified by methacrylic anhydride or glycidyl methacrylate to possess reactive methacrylic groups, which can be polymerized by radical polymerization^130–132. Owing to the naturally-derived, nonimmunogenic, biodegradable, and nonadhesive properties^133–135, hyaluronic acid hydrogels have been widely used as scaffolds in cell therapy and tissue engineering, such as cell delivery¹³⁶, molecule delivery^137,138, stem cell therapy^139,140, cartilage engineering^137,141, cardiac repair¹⁴² and valvular engineering¹⁴³.

Collagen.

Collagen is one of the major proteins in animal bodies. There are approximately 29 types of collagens discovered so far¹⁴⁴. The structures of collagens can be defined at different levels, including primary structure (amino acid triplet), secondary structure (α-helix), tertiary structure (triple helix), and quaternary structure (fibril) ^145,146. The primary structure of collagen is the tripeptide sequence of –(Gly– X–Y–)_n–, where Gly is glycine, X, and Y are other amino acids than Gly. The sequence of the amino acids governs the peptide folding into a secondary structure, mainly left-handed α-helix, which is stabilized by the hydrogen bonds between amino acid residues¹⁴⁷. Three left-handed secondary α- polypeptide chains then form a tertiary structure by the aldol condensation crosslinking, aldehyde amine condensation crosslinking, and aldol histidine crosslinking¹⁴⁸. The triple strands can further self-assemble into a collagen fiber as the quaternary structure¹⁴⁹.

Acid-solubilized collagens can self-assemble to form physically-crosslinked hydrogels when the collagen solutions are neutralized and heated. Since the physically-crosslinked collagen hydrogels are usually mechanically weak and thermally unstable^150,151, they have been strengthened and stabilized with chemical crosslinks such as glutaraldehyde, genipin, carbodiimides or diphenylphosphoryl azide^152–154. Collagens can be biodegraded by collagenases and metalloproteases; the crosslinked collagens usually have slower degradation rates than the uncrosslinked collagens¹⁵⁵. Because collagens usually have low antigenicity, low inflammatory response, good biocompatibility and natural cell-adhesive motifs^156–158, collagen hydrogels have been widely used as scaffolds for drug and protein delivery^159,160 and reconstructions of liver¹⁶¹, skin¹⁶², blood vessel¹⁶³, and small intestine¹⁶⁴, cartilage¹⁶⁵, vocal cord¹⁶⁶, and spinal cord¹⁶⁷.

Gelatin.

Gelatins are naturally derived polymers obtained through breaking the triple-helix conformation of collagens into single-strand molecules. There are two types of gelatins, type A and type B, which are obtained with acid and alkaline treatments of collagens, respectively¹⁶⁸. Gelatins can be physically crosslinked by simply reducing the temperature of aqueous solutions of gelatins below a certain temperature^169,170. The physically-crosslinked gelatins are usually unstable for long-term biomedical applications under physiological conditions. To further stabilize the physically-crosslinked gelatin hydrogels, covalent crosslinkers¹⁷¹ such as aldehydes (e.g., formaldehyde, glutaraldehyde, and glyceraldehyde)^172,173, polyepoxides¹⁷⁴ and isocyanates¹⁷⁵ have been widely used to react with and bridge the free amine groups (from lysine and hydroxylysine) or free carboxylic acid (from glutamic and aspartic acid) on the gelatin molecules. Besides the introduction of covalent crosslinkers, the gelatin backbones can also be modified by methacrylates to form covalently-crosslinkable gelatin methacryloyl hydrogels¹⁷⁶. In addition, synthetic polymers can also be coupled on gelatin chains through grafting-from¹⁷⁷, grafting-to¹⁷⁸, and grafting-through¹⁷⁹ methods and enhance the mechanical properties of gelatin hydrogels. Furthermore, the gelatin molecules tend to form physical interactions with various dopants, such as carbon nanotubes¹⁸⁰, graphene oxide¹⁸¹, and inorganic nanoparticles or minerals^182,183. The aforementioned covalent crosslinks, modifications and/or interactions can significantly improve the mechanical properties of gelatin hydrogels^172,184. The easy gelation process and the excellent biocompatibility make gelatin hydrogels attractive for biomedical applications, such as drug delivery¹⁸⁵ and tissue engineering^186,187.

Fibrin.

Fibrin is a naturally-derived polymer obtained from thrombin-treated fibrinogen¹⁸⁸. Fibrin is involved in the natural wound healing process by forming extensive fibrous networks. Fibrin can form clots or hydrogels when mixing fibrinogen and thrombin solutions at room temperature¹⁸⁹. The resultant fibrin hydrogels usually have weak mechanical properties due to the nature of physical crosslinks. To improve the mechanical properties of fibrin hydrogels, chemical crosslinkers such as genipin can be introduced to crosslink the amine residues on fibrin proteins and form stable covalently-crosslinked networks¹⁹⁰. In addition, fibrin hydrogels can also be combined with synthetic polymers such as polyurethane¹⁹¹, polycaprolactone¹⁹², b-tricalciumphosphate¹⁹³ or polyethylene glycol¹⁹⁴ to enhance the mechanical strength of the hydrogels. Fibrin hydrogels have been widely used as sealants and adhesives to control bleeding in surgery¹⁹⁵, and as scaffolds for cardiac tissue engineering¹⁹⁶, neurological regeneration¹⁹⁷, ocular therapy¹⁹⁸, cartilage and bone reparation^199,200, muscle cells engineering²⁰¹, and exogenous delivery in wound healing²⁰². In particular, fibrin hydrogels can be produced autologously from a patient’s blood, thereby reducing the risk of foreign-body reactions²⁰³.

Agarose.

Agarose is a neutral polysaccharide composed of β-D-galactopyranosyl and 3,6-anhydro-α-L-galactopyranosyl, mainly extracted from red algae (Rhodophyceae)²⁰⁴. As a thermoresponsive polymer, agarose can be heated to dissolve in water, and then cooled down to form a hydrogel. During this gelation process, the agarose structure changes from a random-coil configuration to bundles of associated double helices with multiple-chain aggregation in the junction zone^205,206. The gelling temperature and mechanical properties of agarose hydrogels can be tuned by changing the concentration, molecular weight, and structure of the agarose in the hydrogels^207,208. Agarose hydrogels have been used as scaffolds for cell encapsulation²⁰⁹, cartilage reparation²¹⁰ and nerve regeneration²¹¹, due to its low immunoreaction in human bodies²¹². Notably, since the native agarose does not possess cell adhesion motifs, cell adhesion peptides have been covalently conjugated to the agarose backbone to enhance the interactions between cells and agarose hydrogels²¹³.

Chitosan.

Chitosan is a linear polysaccharide composed of β-(1–4)-linked D-glucosamine and N-acetyl-D-glucosamine units, which is mainly prepared by partial deacetylation of chitin (obtained from crab and shrimp shells) to less than 40% of N-acetyl-D glucosamine residues^214,215. The physical, chemical and biological properties of chitosan materials are highly related to the molecular weight and the degree of deacetylation^216,217. Chitosan can form physically-crosslinked hydrogels by hydrophobic interaction, hydrogen bonding^218,219, metal coordination (with metal ions such as Pt(II), Pd(II), Mo(VI)^220,221), and electrostatic interaction (with multivalent anions such as sulfates, citrates and phosphates ions^222,223; with anionic polyelectrolytes²¹⁴ such as polysaccharides^224,225, proteins^226,227 and synthetic polymers²²⁸). These physically-crosslinked chitosan hydrogels usually have weak mechanical properties and short lifetime, which is also highly influenced by pH, temperature and environments^215,229. To enhance the mechanical properties of chitosan hydrogels, covalent crosslinkers have been introduced into the hydrogels. The commonly-used covalent crosslinkers include di-aldehydes^230,231, formaldehyde²³², di-glycidyl ether²³³ and genipin^234,235, which can react with the residual functional groups (such as OH, COOH, and NH₂) on chitosan backbones to form the amide bonds, ester bonds, and Schiff base linkages^218,236,237. In addition, chitosan can also be modified with methacrylate or aryl azide groups to form photo-crosslinkable macromers²³⁸. The gelation degree and mechanical properties of these chitosan hydrogels can be controlled by UV irradiation time and intensity^239–241. Furthermore, chitosan hydrogels can be modified with biofunctional ligands such as Arg-Gly-Asp (RGD) peptides to facilitate cell adhesion and proliferation^242,243. Chitosan hydrogels have been widely used in biomedical applications such as drug delivery²⁴⁴, cell encapsulation²⁴⁵, neural tissue engineering²⁴⁶ and bone regeneration²⁴⁵, owing to their excellent biocompatibility and biodegradability²⁴⁷.

Cellulose.

Cellulose is the most abundant natural polysaccharide, and the main constituent of plants and natural fibers such as cotton and linen^248–250. Some bacteria such as acetobacter xylinum are also able to produce cellulose²⁵¹. Cellulose has a chemical composite of 1,4-β-glucosidic linked glucose units, which results in high crystallinity (over 40%) and difficulty in dissolving in water and other common solvents²⁵². Solvents such as N-methylmorpholine-N-oxide^253,254, ionic liquids^255,256, and alkali/urea (or thiourea) aqueous^257,258 systems have been developed to dissolved native cellulose. Cellulose can also be modified through partly esterification or etherification of the hydroxyl groups on the backbones²⁴⁸. These cellulose derivatives, including methyl cellulose²⁵⁹, hydroxypropyl cellulose²⁶⁰, hydroxypropylmethyl cellulose^261,262 and carboxymethyl cellulose²⁶³ are easier to dissolve and process compared to the native cellulose.

Cellulose and its derivatives can be chemically crosslinked to form stable three-dimensional networks. Bifunctional or multifunctional molecules, such as 1,2,3,4-butanetetracarboxylic dianhydride²⁶⁴, succinic anhydride²⁶⁵, citric acid²⁶⁶, epichlorohydrin²⁶⁷, ethylene glycol diglycidyl ether²⁶⁸, and divinyl sulfone²⁶⁹ can form covalent ester or ether bonds between cellulose chains. Cellulose chains can also be covalently crosslinked by the irradiation of electron beam and gamma rays^270,271, which avoids the usage of toxic crosslinkers and allows the simultaneous sterilization of the resultant hydrogels. Cellulose and its derivatives can also be blended with natural polymers, such as chitosan²⁷², starch²⁷³, alginates²⁷⁴ and hyaluronic acid²⁷⁵, or synthetic polymers such as polyethylene glycol²⁷⁶, polyvinyl alcohol²⁷⁷ and poly(N,N-dimethylacrylamide)²⁷⁸ to form interpenetrating polymer networks with excellent mechanical properties. Notably, bacterial cellulose produced from certain bacterial species such as acetobacter xylinum can directly form cellulose hydrogels with high purity and tensile strength^279,280. Since cellulose-based hydrogels are proven to have superior hydrophilicity, biodegradability, biocompatibility, and transparency, they have been widely used in drug delivery²⁸¹, tissue engineering²⁸², blood purification²⁸³, strain sensor²⁸⁴ as well as water purification²⁸⁵.

2.2. Common synthetic polymers for hydrogels

In addition to the natural polymers, synthetic polymers have been widely used for the design and fabrication of hydrogels (Figure 4b). The synthetic polymer networks of hydrogels are commonly formed by copolymerization of monomers for the polymer backbones and crosslinkers, or by reactions of synthetic polymers, macromers and/or crosslinkers.

Poly(acrylic acid).

Poly(acrylic acid) (PAA) is a linear polymer prepared by radical polymerization of acrylic acid monomers. The backbone of PAA contains a large number of carboxyl groups. PAA can form hydrogels through covalent and physical crosslinking. Covalently-crosslinked PAA hydrogels are usually formed by copolymerization of di-/multi-vinyl crosslinkers together with acrylic acid monomers²⁸⁶. In addition, the carboxyl groups of PAA can form physical interactions with various doping agents such as clay²⁸⁷, graphene oxide²⁸⁸ and cations²⁸⁹, which can act as physical crosslinks for PAA hydrogels; the carboxyl groups can also form hydrogen bonds between PAA chains and introduce self-healing or self-adhesive properties to PAA hydrogels²⁹⁰. Furthermore, the abundant carboxyl groups on PAA can associate with water molecules to facilitate the absorption of water by PAA hydrogels²⁹¹. Since the carboxyl groups are sensitive to pH and ionic strength, the equilibrium swelling ratio of PAA hydrogels is affected by the pH and ionic strength of the solutions for the hydrogels^292,293. PAA hydrogels can also incorporate other linear polymers, such as biological polymers, to form various adhesives and hydrogels for biomedical applications^41,294.

Poly(2-hydroxyethyl methacrylate).

Poly(2-hydroxyethyl methacrylate) (PHEMA) hydrogels can be prepared by free-radical polymerization of 2-hydroxyethyl methacrylate (HEMA) monomers with covalent crosslinkers such as trimethylene glycol dimethacrylate (TEGDMA), initiators such as sodium pyrosulfite (SMBS), and catalysts such as ammonium persulfate (APS). The HEMA monomers can also be copolymerized with acrylic or acrylamide monomers to control the swelling and mechanical properties of the resultant hydrogels²⁹⁵. PHEMA hydrogels are optically transparent and mechanically stable in the physiological environments. Pure PHEMA hydrogels are also resistant to cell adhesion and difficult to degrade in the physiological environments; however, various biofunctional and bioactive motifs can be coupled onto the hydrogels to improve their cell interactions and degradability^296,297. PHEMA hydrogels are famous for their ophthalmic applications such as contact lens²⁹⁸ and artificial cornea²⁹⁹.

Poly(vinyl alcohol).

Poly(vinyl alcohol) (PVA) is mainly obtained from the partial hydrolysis of poly(vinyl acetate)³⁰⁰. PVA can form stable and elastic hydrogels through either physical or covalent crosslinking^301,302. The physically-crosslinked PVA hydrogels are commonly obtained by repeated freezing and thawing of PVA solutions³⁰³, which gives elastic, tough, strong and fatigue-resistant PVA hydrogels^69,71,304. PVA can also be covalently crosslinked through the use of difunctional crosslinkers such as glutaraldehyde, acetaldehyde, formaldehyde, epichlorohydrin, and other monoaldehydes^305,306. Electronbeam and gamma irradiation can also crosslink PVA to avoid residual covalent crosslinkers in the hydrogels³⁰⁷. Pure PVA hydrogels are nonadhesive to cells, but several oligopeptide sequences can be conjugated onto the backbones of PVA hydrogels to enhance their cellular interactions³⁰⁸. PVA hydrogels have been extensively studied and used in biomedical applications^309,310, such as articular cartilage replacement and regeneration^311,312.

Poly(ethylene glycol) or poly(ethylene oxide).

Poly(ethylene glycol) (PEG) is usually obtained from the anionic or cationic polymerization of ethylene oxide. When the PEG has a molecular weight more than 10 kDa, it is also named poly(ethylene oxide) (PEO) since the end groups are negligible³¹³. There are various methods to crosslink PEG polymers into hydrogels. The ends of PEG chains can be modified by unsaturated groups, such as acrylate or methacrylate ends, and then be used as macro-crosslinkers to form hydrogels with other unsaturated monomers by the photo-/UV-induced radical polymerization^314,315. PEG can also form hydrogels by electron beam irradiation via radiation-induced free radical processes³¹⁶. Furthermore, the end groups of the PEG chain can be modified with various reactive pairs, such as Nhydroxysuccinimide/NH₂³¹⁷, maleimide/thiol³¹⁸, and acetylene/azide³¹⁹. Since these functional chain-end motifs usually have high reaction efficiency and fast reaction kinetics, the obtained hydrogels by the coupling reactions of these groups can give relatively well-defined network architectures⁶⁷.

PEG polymers can also form physically-crosslinked networks. Similar to the chemical crosslinking method, the ends of PEG chains can be modified with various motifs for physical crosslinking. For example, nucleobase pairs of adenines and thymines³²⁰, ureido-pyrimidinone (UPy) units³²¹, or host-guest molecules³²² can be introduced onto the chain-ends of PEG molecules to prepare physically-crosslinked PEG hydrogels. These physically-crosslinked PEG hydrogels can exhibit switchable, self-healable or stimuli-responsive properties and high mechanical strength³²³. Besides the modification and utilization of chain-end groups, physically-crosslinked PEG hydrogel can also be prepared by using PEG block copolymers³²⁴. PEG-b-PPG (poly(propylene glycol)) is one of the most widely used PEG-derived block copolymers to prepare thermo-responsive physical hydrogels³²⁵. These physical hydrogels are formed by the hydrophobic interaction of PPG blocks. The phase transition behavior of these hydrogels can be optimized by balancing the hydrophobic PPG block and the hydrophilic PEG block. Based on the same gelation mechanism, PEG block copolymers with poly(DL-lactic acid) (PDLLA)³²⁶, poly(dl-lactic acid-coglycolic acid) (PLGA)^327,328, polylactide (PLA)³²⁹, poly(caprolactone)(PCL)³³⁰ and poly(propylene sulfide)(PPS)³³¹ can also form physically-crosslinked hydrogels with injectable or stimuli-responsive properties. PEG, as well as its derivatives, are widely used in biomedical applications due to their non-toxic and non-immunogenic properties³³². While the inert biological property of PEG hydrogels can prevent undesired interactions between native PEG hydrogels and cells^333,334, PEG hydrogels can also be modified with various bioactive conjugations such as growth factors ³³⁵ and cell-adhesive peptides³³⁶ through Michael-type addition^337,338or click chemistry³³⁴. PEG hydrogels with these bioactive molecules can facilitate their biomedical applications³³⁹ such as drug or cell delivery^340,341 and tissue engineering³⁴².

Poly (N-isopropylacrylamide).

Acrylamide and its derivatives have been widely used to prepare hydrogels by radical copolymerization with crosslinkers. One interesting hydrogel based on acrylamide and its derivatives is the poly(N-isopropylacrylamide) (PNIPAm) hydrogel. Uncrosslinked linear PNIPAm exhibits a coil-to-globule phase transition in aqueous solutions when the temperature is raised above a critical temperature^343,344. The PNIPAm can be covalently crosslinked by crosslinkers such as bis-acrylamide derivatives through the radical polymerization process. The crosslinked PNIPAm hydrogels also possess the reversible thermo-responsive behavior with a critical temperature of around 34 °C ³⁴⁵, above which the hydrogel structure will collapse and exude water^346,347. While the thermo-responsive behavior of PNIPAm hydrogels is usually slow, many studies have improved the phase-transition speed of PNIPAm hydrogels by incorporating porous structures during the hydrogel formation^348,349. The thermo-responsive PNIPAm hydrogels can be used as actuators for soft robotics³⁵⁰, injectable scaffolds for tissue engineering³⁵¹, and on-demand detachment of cell sheets^352,353.

Silicone.

Silicone hydrogels are hydrogels that contain silicone polymers as one of its polymer components³⁵⁴. Silicone polymers are commonly hydrophobic³⁵⁵. In order to form silicone hydrogels, hydrophilic monomers and/or polymers have been introduced into the silicone matrix by blending or copolymerization to improve the hydrophilicity of silicone hydrogels^356,357. For example, hydrophilic polymers such as PHEMA can be blended directly into the silicone polymer matrix, forming a hydrophilic interpenetrating polymer network³⁵⁸. Hydrophilic monomers such as N-vinylpyrrolidone (NVP) can be copolymerized with silicon-macromers to form hydrophilic silicone hydrogels³⁵⁹. Hydrophilic polymer segments such as PEG³⁶⁰ can also be copolymerized onto silicone segments to form block-modified^361,362 or graft-modified³⁶³ hydrophilic silicone hydrogels. Since these hydrophilic silicone hydrogels usually have excellent gas permeability as well good biocompatibility, they have been used in biomedical applications such as contact lenses^364,365, histological engineering materials^366,367, and drug-delivery carriers^368,369.

2.3. Common permanent covalent crosslinks for hydrogels

In this section, we will discuss permanent covalent crosslinks that are commonly used in hydrogels (Figure 4c); we will discuss other types of crosslinks in Section 4. The energy of permanent covalent crosslinks ranges from 220 kJ/mol to 570 kJ/mol (Figure 5)^370–372.

Figure 5.

Bond energies of various types of permanent covalent crosslinks^370–372, weak physical crosslinks ^373–376, and dynamic covalent crosslinks^{372,377–381}.

Carbon-carbon bonds.

The energy of the carbon-carbon bond is around 300 to 450 kJ/mol^370–372. Hydrogels covalently crosslinked by carbon-carbon bonds are usually formed by radical copolymerization of monomers and di-/multi-vinyl crosslinkers. The crosslinkers can be small molecules with two double bonds such as N,N’-Methylenebisacrylamide (MBA) or macromolecules with several acrylate groups^6,382. These crosslinkers are compatible with various initiation and polymerization systems^4,237,383. For example, photo-radical initiators can be added into the pre-polymerization solution together with monomers and di/multi-vinyl crosslinkers^302,384,385. Once the initiator is irradiated by UV light, radicals will be generated to initiate the polymerization of the double bonds on monomers as well as crosslinkers^386,387. As a result, hydrogels can be formed in-situ and with patterned structures or biology functions^384,388. The polymerization of vinyl monomers and crosslinkers can also be carried out with a system composed of peroxydisulfate and N,N,N′N′-tetramethylene-diamine (TEMED), where TEMED can accelerate the decomposition of peroxydisulfate to generate a large number of radicals³⁸⁹. This initiation and polymerization system can effectively and rapidly form various hydrogels under room temperature.

The carbon-carbon crosslinks of hydrogels can also be formed by high-energy irradiation (e.g., gamma and electron beams). Similar to UV light, high-energy radiation can be used to polymerize unsaturated compounds such as monomers and crosslinkers with vinyl groups or acrylate groups^390,391. High-energy radiation can also crosslink polymers without unsaturated bonds³⁹², because radicals can be generated from the homolytic scission of the polymer chains under high-energy radiation. The radiolysis of water molecules in the solvent can also generate hydroxyl radicals that attack polymer chains to form macroradicals³⁹³. These radicals can then undergo recombination and termination to form covalent polymer networks crosslinked by carbon-carbon bonds.

Carbon-nitrogen bonds.

The energy of the carbon-nitrogen bond is around 300 to 430 kJ/mol^370,372. Hydrogels covalently crosslinked by carbon-nitrogen bonds are usually formed by highly effective chemical reactions of complementary groups. For example, the amide bonds have been widely used as the covalent crosslinks for hydrogels by the condensation reactions between amines with carboxylic acids and derivatives³⁹⁴. N-hydroxysuccinimide (NHS) and N,N-(3-dimethylaminopropyl)-N-ethyl carbodiimide (EDC) are widely used to facilitate the condensation reaction of amines with carboxylic acids⁶⁷. The addition of NHS and EDC will also suppress possible side-reactions and give better control of the crosslink density in the hydrogels³⁹⁵. The carbon-nitrogen bonds can also be formed through the addition reactions of amines with electrophiles such as adipic acid dihydrazide and diisocyanates crosslinkers^6,103,396. These di-functional crosslinkers have been widely used to crosslink natural macromolecules due to the high reaction efficiency. The mechanical properties of the resultant hydrogels can be controlled by tuning the concentration and ratio of the polymers and the crosslinking agents. Another category of reactions that can form carbon-nitrogen crosslinks for hydrogels is the azide-alkyne cycloaddition reaction, which is one typical click reaction to connect alkyne and azide into triazole. The click reaction has high efficiency without side reactions³⁹⁷. Furthermore, the azide-alkyne cycloaddition can be conducted in the absence of metal catalysis³⁹⁸, expanding the applicability of the azide-alkyne cycloaddition for preparing biocompatible hydrogels.

Carbon-oxygen bonds.

The energy of the carbon-oxygen bond is around 280 to 370 kJ/mol^370–372. The most common carbon-oxygen bond is the ester bond formed by the reactions between hydroxyl groups and carboxylic acids or derivatives³⁹⁹. Such ester crosslinks can be hydrolyzed easily and make the hydrogels degradable under ambient temperature and physiological conditions. Besides the ester crosslinks, the carbon-oxygen bonds are also present in ether groups and urethane groups, which can become crosslinks due to the reaction between side groups on polymers (such as hydroxyl groups on polysaccharides or PVA) and reactive crosslinkers (such as glutaraldehyde^400,401, divinyl sulfone⁴⁰², dibromide⁴⁰³ or diisocyanate⁴⁰⁴).

Carbon-sulfide bonds.

The energy of the carbon-sulfide bond is around 220 to 310 kJ/mol³⁷². The covalent crosslinking of hydrogels through carbon-sulfide bonds are mainly formed by the thiol-click reactions^405,406. The inherent electron density of the sulfide atom makes thiols prone to react with many functional groups through a radical or catalyzed process^407,408. Thiol groups can be easily converted into nucleophilic thiolates or electrophilic thiyl radicals, which then proceed with nucleophilic reactions or radical chain processes to achieve the thiol-click reactions⁴⁰⁹. Specifically, for the radical thiol-click reactions, the thiol group can be activated by heat and/or UV light to generate radicals that initiate the radical-mediated thiol-ene or thiol-yne reactions⁴¹⁰; for the nucleophilic thiol-click reactions initiated by strong bases, the thiol groups can readily react with electron-poor ene-functional compounds through the Michael addition, with isocyanates derivatives through carbonyl addition, with halide through S_N2 nucleophilic substitution, and with epoxies motifs through S_N2 ring-opening reactions^411–414. The thiol-click reactions commonly have high efficiency and high conversion rate without any side products, even in the presence of water, ions, and oxygen. The thiol-click reactions have been extensively used to prepare hydrogels for various biomedical applications^415,416.

Silicon-oxygen bonds.

The energy of the silicon-oxygen bond is around 420 to 570 kJ/mol^370–372. The silicon-oxygen bonds are mainly used in the formation of silicone-based hydrogels^360,417,418, and can usually enhance the mechanical properties of the silicone-based hydrogels⁴¹⁹. In addition, silicon-oxygen bonds have been widely used to form strong bonding between hydrogels and diverse engineering materials with modified surfaces such as salinized surfaces⁴³.

3. Conventional polymer networks

3.1. Conventional polymer networks in the dry state

As illustrated in Figure 6, a conventional polymer network is defined as long-chain polymers crosslinked via permanent covalent bonds into a network, in which entanglements and reversible crosslinks of the polymer chains are negligible^47,50,55. Conventional polymer networks have provided the basic models for the development of unentangled rubber elasticity including the affine network model and the phantom network model^47,50,55. Conventional polymer networks have also been widely adopted in synthetic hydrogels, although biological hydrogels (Figures 1 and 2) usually reply on more complex polymer networks.

Figure 6.

Schematics of a conventional polymer network a. in the dry state and b. covalently bonded on a substrate, and c. in the swollen state and d. covalently bonded on a substrate.

In the dry state (Figure 6a), a conventional polymer network contains n polymer chains per unit volume, where a chain is defined as the segment of polymer between two successive covalent crosslinks. Each polymer chain contains N Kuhn monomers, and the length of each Kuhn monomer is b. The end-to-end distances of a polymer chain at the relaxed and fully stretched states are $\sqrt{Nb}$ and Nb, respectively. Therefore, the stretch limit of polymer chains ${\lambda }_{\lim }$ in the dry polymer network can be calculated as^47,50,55

$${\lambda }_{\lim }=\frac{Nb}{\sqrt{Nb}}=N^{1/2}$$ (1)

The stretch limit of the bulk polymer network scales with ${\lambda }_{\lim }$, and the pre-factor of the scaling relation depends on the polymer network architecture⁵⁴.

Assuming that the dry polymer network follows the affine network model, the shear modulus of the network under initial deformation can be expressed as^47,50,55,

$$G=nkT$$ (2)

where k is the Boltzmann constant and T is the absolute temperature.

Following the Lake-Thomas model⁴⁹, the fracture toughness of the dry polymer network is its intrinsic fracture energy ${\mathrm{\Gamma }}_0$, which is the energy required to fracture a single layer of polymer chains per unit area,

$${\text{Γ}}_0=n\sqrt{N}b\cdot N{U}_f=nb{N}^{3/2}{U}_f$$ (3)

where $n\sqrt{N}b$ is the number of polymer chains per unit area, $N{U}_f$ is the energy required to fracture a polymer chain, and $U_f$ is the energy required to fracture a single Kuhn monomer.

Also based on the Lake-Thomas model^48,49, the fatigue threshold of the dry polymer network is the intrinsic fracture energy ${\mathrm{\Gamma }}_0$. If the dry polymer network is covalently bonded on a substrate (Figure 6b), both the interfacial toughness and the interfacial fatigue threshold of the adhesion are on the level of ${\mathrm{\Gamma }}_0$ as well^43,71,420.

By substituting the typical ranges of b, N, n, kT and U_f into Eqs. 1–3, we can estimate that the shear modulus G can be on the order of kilopascals to megapascals, the chain stretch limit ${\lambda }_{\lim }$ can reach up to a few tens (without chain entanglement), and the intrinsic fracture energy ${\mathrm{\Gamma }}_0$ can reach up to a few hundreds of joule per meter squared⁵⁵.

The mechanical properties of the dry polymer network are coupled with one another. It is commonly assumed that the polymer chains occupy the major volume of the polymer network in the dry state, and therefore the volume conservation of the polymer network gives

$$Nnv=1$$ (4)

where v is the volume of a Kuhn monomer.

By substituting Eq. 4 into Eqs. 1–3, we can express the chain stretch limit ${\lambda }_{\lim }$, shear modulus G and intrinsic fracture energy ${\mathrm{\Gamma }}_0$ of a conventional polymer network in the dry state as functions of its polymer-chain length N,

$${\lambda }_{\lim }=N^{1/2},G=N^{-1}{v}^{-1}kT,{\text{Γ}}_0=N^{1/2}{v}^{-1}b{U}_f$$ (5)

From Eq. 5, it is evident that enhancing the polymer-chain length N increases the chain stretch limit ${\lambda }_{\lim }$ and intrinsic fracture energy ${\mathrm{\Gamma }}_0$ but decreases the shear modulus G of the conventional polymer network in the dry state. These mechanical properties of the conventional polymer network in the dry state are coupled through the following relation,

$${\lambda }_{\lim }\sim {\text{Γ}}_0\sim G^{-1/2}$$ (6)

3.2. Conventional polymer networks in the swollen state

A dry conventional polymer network with the physical parameters discussed in Section 3.1 can imbibe water and swell into a hydrogel composed of the conventional polymer network and water (Figure 6c). The swelling of the dry polymer network stretches polymer chains in the network by a ratio of λ_s, named the chain stretch of swelling.

Since the swelling of the dry polymer network stretches its polymer chains by a ratio of λ_s, the end-to-end distance of a polymer chain in the hydrogel at the relaxed and fully stretched states are ${\lambda }_s\sqrt{Nb}$ and Nb, respectively. Therefore, the stretch limit of polymer chains ${\lambda }_{\lim }$ in the hydrogel can be calculated as,

$${\lambda }_{\lim }=\frac{Nb}{{\lambda }_s\sqrt{Nb}}=N^{1/2}{\lambda }_s^{-1}$$ (7)

The stretch limit of the bulk hydrogel scales with ${\lambda }_{\lim }$, and the pre-factor of the scaling relation depends on the polymer network architecture⁵⁴.

The swelling of the dry polymer network reduces its shear modulus by a ratio of λ_s⁴⁷. Therefore, the shear modulus of the hydrogel under initial deformation can be expressed as,

$$G=nkT{\lambda }_s^{-1}$$ (8)

Note that n in Eq. 8 is the number of polymer chains per unit volume of the dry polymer network.

The swelling of the dry polymer network reduces the number of polymer chains per unit area by a ratio of ${\lambda }_s^2$ but does not significantly change the energy required for fracturing a polymer chain in the network. Therefore, the intrinsic fracture energy ${\mathrm{\Gamma }}_0$ of the hydrogel can be calculated as,

$${\text{Γ}}_0=\frac{n\sqrt{N}b}{{\lambda }_s^2}\cdot N{U}_f=nb{N}^{3/2}{U}_f{\lambda }_s^{-2}$$ (9)

The fracture toughness and fatigue threshold of a hydrogel with the conventional polymer network are the hydrogel’s intrinsic fracture energy ${\mathrm{\Gamma }}_0$^48,49. If the hydrogel’s polymer network is covalently bonded on a substrate (Figure 6d), both the interfacial toughness and interfacial fatigue threshold of the adhesion are on the order of the hydrogel’s intrinsic fracture energy ${\mathrm{\Gamma }}_0$ as well^43,71,420.

By comparing Eqs. 1–3 and Eqs. 7–9, we can see that swelling the dry polymer network into the hydrogel reduces the stretch limit ${\lambda }_{\lim }$, shear modulus G and intrinsic fracture energy ${\mathrm{\Gamma }}_0$ of the dry network by factors of λ_s, λ_s and ${\lambda }_s^2$, respectively^47,50,55. By substituting the typical ranges of λ_s, b, N, n, kT and U_f into Eqs. 7–9, we estimate that the shear modulus G of the hydrogel with the conventional polymer network can be on the order of pascals to megapascals, the chain stretch limit ${\lambda }_{\lim }$ can reach up to a few times (without chain entanglement), and the intrinsic fracture energy ${\mathrm{\Gamma }}_0$ can reach a few tens of joule per meter square.

By substituting Eq. 4 into Eqs. 7–9, we can express the chain stretch limit ${\lambda }_{\lim }$, shear modulus G and intrinsic fracture energy ${\mathrm{\Gamma }}_0$ of the hydrogel with the conventional polymer network as functions of its polymer-chain length N,

$${\lambda }_{\lim }=N^{1/2}{\lambda }_s^{-1},G=N^{-1}{v}^{-1}kT{\lambda }_s^{-1},{\text{Γ}}_0=N^{1/2}{v}^{-1}b{U}_f{\lambda }_s^{-2}$$ (10)

From Eq. 10, it is evident that enhancing the polymer-chain length N increases the chain stretch limit ${\lambda }_{\lim }$ and the intrinsic fracture energy ${\mathrm{\Gamma }}_0$ but decreases the shear modulus G of the hydrogel with the conventional polymer network. These mechanical properties of the hydrogel are coupled through the following relation,

$${\lambda }_{\lim }\sim {\text{Γ}}_0\sim G^{-1/2}$$ (11)

Notably, the chain stretches due to equilibrium swelling of a conventional polymer network can be calculated. Without loss of generality, let consider a dry conventional polymer network with a cubic shape. When the polymer network reaches the equilibrium state in water, one side of the cube increases its length from the dry state by a ratio of ${\lambda }_{eq}$. At the equilibrium state, the Helmholtz free energy for stretching polymer chains $W_{stretch}$ and for mixing polymers and water per unit volume of the dry polymer network can be expressed as^47,421,

$$W_{stretch}=\frac{1}{2}nkT\left(3{\lambda }_{eq}^2-3-2\log {\lambda }_{eq}^3\right)$$ (12a)

$$W_{mix}=-\frac{kT}{v_s}\left[\left(1-{\lambda }_{eq}^3\right)\log \left(1-{\lambda }_{eq}^{-3}\right)+\chi {\lambda }_{eq}^{-3}\right]$$ (12b)

where χ is the Flory polymer-solvent interaction parameter and v_s is the volume of a solvent molecule. Subsequently, the Helmholtz free energy per unit volume of the dry polymer network can be expressed as^47,421,

$$W=W_{stretch}+W_{mix}$$ (13)

When the polymer network reaches the equilibrium state in water, ${\lambda }_{eq}$ minimizes the Helmholtz free energy^47,421,

$$\frac{\partial W}{\partial {\lambda }_{eq}}=0$$ (14)

By solving Eq. 14, one can obtain ${\lambda }_{eq}$ of the hydrogel at the equilibrium swollen state. The chain stretch of the hydrogel at the equilibrium swollen state scales with ${\lambda }_{eq}$, and the pre-factor of the scaling relation depends on the polymer network architecture⁵⁴. While Eqs. 12–14 assume that the polymer network of the hydrogel is uncharged, the effect of charges on the equilibrium swelling of hydrogels can be accounted for by introducing additional terms to the Helmholtz free energy function^47,422. It should be noted that hydrogels are not necessary to reach the equilibrium swollen state in many situations, for example, when the hydrogels are insulated from water or do not have sufficient time to equilibrate with water.

4. Unconventional polymer networks

Section 3 has established that hydrogels with conventional polymer networks have intrinsically coupled mechanical properties, including shear modulus, stretch limit, fracture toughness, fatigue threshold, interfacial toughness and interfacial fatigue threshold of adhesion (Eq. 11). This section will discuss unconventional polymer networks (UPNs), which constitute most biological hydrogels (Figures 1 and 2) and have been widely used in synthetic hydrogels to achieve extreme mechanical properties.

The UPNs are defined as polymer networks that are different from the conventional polymer networks in terms of the architectures of polymer networks and/or the interactions among polymer chains in the networks^63,423–431. Therefore, the UPNs can be broadly classified into two categories: the UPN architectures and the UPN interactions.

4.1. Unconventional polymer network architectures

As illustrated in Figure 7, the UPN architectures are dramatically different from the architecture of the conventional polymer networks composed of randomly-crosslinked polymer chains (Figure 4). Almost all biological tissues (Figures 1 and 2) possess UPN architectures. Over the last few decades, multiple UPN architectures have been proposed and synthesized for soft materials including elastomers and hydrogels to achieve extreme properties. Based on their topologies, the typical UPN architectures can be classified into a number of categories, including ideal polymer networks, polymer networks with slidable crosslinks, interpenetrating polymer networks, semi-interpenetrating polymer networks, polymer networks with highfunctionality crosslinks, nano-/micro-fibrous polymer networks, and bottlebrush polymer networks.

Figure 7.

Schematics of unconventional polymer network architectures, including ideal polymer networks, polymer networks with slidable crosslinks, interpenetrating polymer networks, semi-interpenetrating polymer networks, polymer networks with high-functionality crosslinks, nano-/micro-fibrous polymer networks, bottlebrush polymer networks, and future new UPN architectures.

4.1.1. Ideal polymer networks.

Ideal polymer networks are polymer networks that have uniform chain length, uniform functionality, and no defect (Figure 7)³¹⁷. Following the pioneer work by Sakai et al.^{317,432–434}, the ideal polymer networks have been commonly fabricated using multi-arm macromers, where the arms of adjacent macromers are crosslinked into polymer chains. Because the lengths of the macromer arms are uniform and the reaction efficiency of the crosslinking is high, various ideal polymer networks with uniform chain length, uniform functionality, and almost no defect have been achieved^{67,317,435–445}. The tetra-arm PEG^317,446,447 is among the most frequently used macromers for the fabrication of hydrogels with ideal polymer networks. The ends of the PEG macromers are commonly modified with pairs of reaction groups such as N-hydroxysuccinimide and amine^67,317,448, tetrabenzaldehyde and tetrabenzaacylhydrazide⁴⁴⁹, maleimide and thiol⁴⁵⁰, or boronic acid and diol^435,439,446. Due to the almost defect-free nature, the ideal polymer networks have been made highly stretchable and resilient⁶⁷. It should be noted that, although the conventional polymer networks usually have non-uniform chain lengths and topological defects, their mechanical properties are commonly calculated based on the models of ideal polymer networks as discussed in Section 3. Therefore, the ideal polymer networks by themselves still have coupled mechanical properties.

4.1.2. Polymer networks with slidable crosslinks

A slidable crosslink, commonly in the form of two covalently-crosslinked polymer rings, can interconnect two polymer chains that thread through and slide inside the rings (Figure 7)⁴⁵¹. Polymer networks with slidable crosslinks are both mechanically stable and reconfigurable due to the permanent and slidable nature of the crosslinks, respectively. Under mechanical loads, the slidable crosslinks tend to reconfigure the polymer network in a way that the polymer chains in the network sustain the same level of forces, approximating an ideal polymer network.

The polymer networks with slidable crosslinks are mainly synthesized from cyclodextrins-based polyrotaxanes^452–454. Cyclodextrins are a series of cyclic oligosaccharides with 6, 7, or 8 glucose units (named α-, β-, or γ- cyclodextrin, respectively); cyclodextrins-based polyrotaxanes are inclusion complexes composed of linear polymer chains that are threaded through the cyclodextrin molecules and then capped by bulky groups at the chain ends^454–456. The formation of cyclodextrins-based polyrotaxanes mainly depends on the size matching between the interior cavities of the cyclodextrins and the cross-section of the polymer chains⁴⁵⁷. Many polymer chains have been investigated to form cyclodextrin-based polyrotaxanes including linear homopolymers, linear block copolymers as well as branched polymers⁴⁵⁷. The αcyclodextrin has the smallest cavity size and can form inclusion complexes with PEG or PCL, but not with PPO chains^458,459. While the β-cyclodextrin can form complexes with PCL or PPO but not PEG^458,460,461. The γ-cyclodextrin, which has the largest cavity size, can thread through a PPO chain or two chains of PEG or PCL⁴⁶². The cyclodextrins can be crosslinked with each other to interconnect the threaded polymer chains and form the polymer networks with slidable crosslinks^60,356. Because a polymer network with slidable crosslinks under mechanical loads approximates an ideal polymer network, the mechanical properties of the polymer network with slidable crosslinks are usually coupled with one another as discussed in Section 3^{451,463–465}.

4.1.3. Interpenetrating and semi-interpenetrating polymer networks

Interpenetrating polymer networks are comprised of two or more interpenetrated polymer networks, which are individually crosslinked but not joint together (Figure 7); semi-interpenetrating polymer network are comprised of two or more interpenetrated polymer networks, in which at least one network is uncrosslinked and others are individually crosslinked but not joint together (Figure 7)^{356,383,466–473}. The interpenetrating and semi-interpenetrating polymer networks are entangled or interlocked in a way that they cannot be pulled apart unless the networks are broken^470–473. Hydrogels based on the interpenetrating and semi-interpenetrating polymer networks are commonly prepared following the sequential or simultaneous method. In the sequential method, one polymer network is first prepared and then immersed into a solution of monomers, initiators and/or crosslinkers for another polymer network. Thereafter, the interpenetrating or semi-interpenetrating polymer network is formed by polymerizing the second polymer network within the first network. As a remarkable example, Gong et al. have adopted the sequential method to fabricate the so-called double-network hydrogels with high fracture toughness⁶³. In the simultaneous method, a mixture of the polymers, monomers, initiators and crosslinkers for all polymer networks form the interpenetrating or semi-interpenetrating polymer networks in one step or one pot⁴⁷⁴. This one-step or one-pot fabrication process is a merit for the simultaneous method compared to the sequential method. One remarkable example of the simultaneous method is the simple fabrication of the polyacrylamide-alginate hydrogel with high stretchability and fracture toughness⁴⁷⁵. A wide range of material candidates including both natural and synthetic polymers as discussed in Section 2^{60,356,383,467–469,475–477} have been used to synthesize hydrogels with interpenetrating and semi-interpenetrating polymer networks via various crosslinking strategies^{237,383,469,478}. As will be discussed in Section 4.4, the interpenetrating and semi-interpenetrating polymer networks can provide decoupled and extreme mechanical properties for hydrogels, such as extremely high stretchability and fracture toughness^{63,475,479–481}.

4.1.4. Polymer networks with high-functionality crosslinks.

The functionality of a crosslink refers to the number of polymer chains interconnected at the crosslink. Common covalent crosslinks as discussed in Section 2.3 usually have relatively low functionality (e.g., less than 10), and there is usually a single polymer chain bridging between two adjacent covalent crosslinks. To dramatically enhance the functionality of a polymer network, various types of high-functionality crosslinks can be introduced into the polymer networks, including crystalline domains^{215,300,302,482}, glassy nodules^483,484, nano-/micro-particles^{356,383,477,482,485–487}, and micro-phase separations^488–490 (Figure 7). For example, poly(vinyl alcohol) can form crystalline domains to crosslink the polymer networks through the freeze-thaw method^302,491; poly(methyl methacrylate) can form glassy spheres and crosslink poly(methyl methacrylate)-based block copolymers into networks⁴⁹²; exfoliated particles, such as nano-clays⁴⁹³, graphene oxide⁴⁹⁴ or stratified lamellar bilayers⁴⁹⁵, can crosslink polyacrylamide into mouldable or self-healable hydrogels; mixtures of styrene, butyl acrylate, and acrylic acid can form microspheres and crosslink the residual polymer chain into microsphere composite hydrogels⁴⁹⁶.

Multiple polymer chains (e.g., over 10) can be interconnected at each high-functionality crosslink (Figure 7). In addition, there can be multiple polymer chains bridging between two neighboring high-functionality crosslinks, where the lengths of the polymer chains can be highly non-uniform^60,436. As will be discussed in Section 4.4, the polymer networks with high-functionality crosslinks can provide decoupled and extreme mechanical properties for hydrogels, such as extremely high fracture toughness, resilience, tensile strength and fatigue resistance.

4.1.5. Nano-/micro-fibrous polymer networks

Both synthetic and natural polymers can assemble into fibers (or fibrils referring to short fibers) with diameters ranging from nanometers to micrometers via covalent or physical bonds. The nano-/micro-fibers can further entangle, aggregate, and crosslink into percolated polymer networks^{6,64,497–502} (Figure 7). In biological organisms, cells can secrete proteins (e.g., collagens) and polysaccharides (e.g., celluloses), which then assemble into nano-/micro-fibrous polymer networks^{103,250,503–506}. These naturally-derived fibers and fibrous networks have been widely harnessed for the fabrication of hydrogels with nano-/micro-fibrous polymer networks^{382,507–510}. In addition, a wide range of natural and synthetic polymers have been fabricated into nano-/micro-fibrous polymer networks with the spinning techniques^511–513, among which the electrospinning is most popular due to its simplicity, low cost, and wide applicability⁵¹⁴. In particular, the diameter, alignment and density of the fibers can be readily controlled by tuning the parameters of the electrospinning process^515–519. As will be discussed in Section 4.4, the nano-/micro-fibrous polymer networks can provide decoupled and extreme mechanical properties for hydrogels, such as extremely high fracture toughness, tensile strength, resilience and fatigue resistance^520,521.

4.1.6. Other UPN architectures

Many other types of UPN architectures can provide extraordinary mechanical properties as well. For example, the bottlebrush polymer networks (Figure 7) have shown extremely low shear moduli and tissue-like stress-strain relations in the solvent-free state^522,523. Although these UPN architectures have not been widely used in hydrogels, they may be exploited for the design of hydrogels in future⁵²⁴. Furthermore, it is also expected that new UPN architectures will be invented together with the development of polymers and hydrogels.

4.2. Unconventional polymer network interactions

As illustrated in Figure 8, the UPN interactions are defined as inter-polymer and intra-polymer interactions that are different from those in the conventional polymer networks (i.e., permanent covalent crosslinks, excluded volumes, and osmotic interactions) (Figure 8). The UPN interactions are vastly abundant in biological organisms⁵²⁵, and they have been intensively studied for the design of soft materials such as elastomers and hydrogels to achieve extreme mechanical properties among many other purposes²³⁷. Based on the nature of the UPN interactions, they can be broadly classified into three categories⁵⁵: strong physical crosslinks, weak physical crosslinks, and dynamic covalent crosslinks.

Figure 8.

Schematics of unconventional polymer network interactions including a. strong physical crosslinks, b. weak physical crosslinks, and c. dynamic covalent crosslinks.

4.2.1. Strong physical crosslinks

In addition to the permanent covalent crosslinks discussed in Section 2.3, various types of strong physical bonds can act as effectively permanent crosslinks in polymer networks. Typical examples of strong physical crosslinks include crystalline domains, glassy nodules, and helical structures. The energy of strong physical crosslinks is similar to that of permanent covalent crosslinks.

Crystalline domain.

A specific subset of synthetic and natural polymers can form crystalline domains under appropriate conditions. A crystalline domain, with the size from nanometers to micrometers, can serve as a strong physical crosslink for multiple amorphous polymer chains connected to it (Figure 8). As an example in synthetic polymers, PVA can form crystalline domains by repeated freeze-thaw cycles or by annealing at temperatures above its glass transition temperature^300,302,482. The formation of PVA crystalline domains is mainly due to the hydrogen-bonding interactions of the hydroxyl groups on PVA chains⁴. As an example in natural polymers, chitin and chitosan can form semi-crystalline polymer networks with crystalline domains crosslinking amorphous chains by treating the chitin and chitosan with strongly acidic or basic solutions to overcome the inter-chain electrostatic repulsions^215,218. As another example in natural polymers, cellulose can also form highly crystalized nanofibers due to the strong interaction between glucose units⁵²⁶. These cellulose nanofibers can further aggregate and form a stable network by alkaline treatments^497,527. It should be noted that heating the abovementioned semi-crystalline polymer networks above their melting temperatures can destroy the crystalline domains in the networks, although most crystalline domains are stable at room and body temperatures.

Because a crystalline domain usually interconnects multiple polymer chains, they often act as highfunctionality crosslinks in the polymer networks as discussed in Section 4.1. In addition, the energy required to pull a polymer chain out of a crystalline domain is much higher than that required to fracture the same polymer chain⁷¹; therefore, crystalline domains can also introduce intrinsically high-energy phases into the polymer networks. These attributes of crystalline domains have endowed the hydrogels containing crystalline domains with extreme mechanical properties, such as tough, strong and fatigue-resistant, which will be discussed in Section 5.

Glassy nodule.

Glassy nodules are formed by the reversible liquid-glass transition of amorphous polymers when the temperature is decreased below their glass-transition temperatures⁵²⁸. In order to harness glassy nodules as strong physical crosslinks, block copolymers that contain at least one segment with a high glass-transition temperature have been commonly used. As the temperature reduces to room or body temperature, the segments with the high glassy-transition temperature form glassy nodules that effectively crosslink the adjacent amorphous polymer chains (Figure 8)⁵²⁹. For example, the polystyrene segments in the polystyrene-b-poly(N-isopropylacrylamide)-b-polystyrene copolymers can form glassy nodules at room temperature to crosslink the block copolymers chains into a polymer network⁵³⁰. As another example, poly(methyl methacrylate) has a glass transition temperature around 115 °C⁵³¹; therefore, the poly(methyl methacrylate) segments in the poly(methyl methacrylate)-b-poly(n-butyl acrylate) copolymers can form glassy spheres at room temperature to crosslink the polymer network⁴⁹². Similar to crystalline domains, glassy nodules can also act as high-functionality crosslinks and intrinsically high-energy phases in polymer networks to give the corresponding hydrogels extreme mechanical properties, which will be discussed in Section 5.

Helical association.

Many natural polymers, due to their precisely-controlled structures, can assemble into nanometer-scale helical fibers (or fibrils), which then can aggregate or entangle to form a crosslinked network (Figure 8)^{103,507,509,510}. For example, the well-known triple-helix structure of type I collagen is formed by the self-assembly of three peptide strands. These collagen triple helices can pack together to form collagen nanofibers and further self-assemble into an interconnected hydrogel network^532,533. As another example, the linear agarose chains are disordered coils in aqueous solutions at high temperatures, and can form double-helix strings⁵³⁴ or simple helical chains⁵³⁵ when the temperature is decreased to room or body temperature. These stings or chains can associate to form agarose fibers through hydrogen bonding and further be entangled to form the interconnected hydrogel network⁵³⁶.

4.2.2. Weak physical crosslinks

Compared to the strong physical crosslinks, many other physical crosslinks in polymer networks are relatively weak, transient and reversible. Typical examples of weak physical crosslinks include hydrogen bond, electrostatic interaction, metal coordination, guest-host interaction, hydrophobic association, and π-π stacking. The energy of weak physical crosslinks is usually lower than that of strong physical crosslinks and permeant covalent crosslinks.

Hydrogen bond.

The energy of a single hydrogen bond ranges from 0.8 kJ mol⁻¹ to 167 kJ mol⁻¹ (Figure 5) ^373,374. Many natural polymers can form hydrogels by the intermolecular hydrogen bonds. For example, gelatin can form polymer networks of helical structures crosslinked by hydrogen bonds¹⁷⁰; certain types of polysaccharides, such as agarose, amylose, amylopectin and carrageenan, can also form helical structures in solutions and crosslinked into hydrogels by hydrogen bonds⁵³⁷. A number of synthetic polymers are also capable of forming physical hydrogels via hydrogen bonds. For example, PVA hydrogels can be obtained by forming hydrogen bonds between polymer chains through repeated freezing and thawing of PVA solutions³⁰³. PAA or polymethacrylic acid (PMA) can form complexes with PEG by hydrogen bonds between the oxygen groups of PEG and the carboxyl groups of PMA⁵³⁸ or PAA⁵³⁹.

Despite the abundance of hydrogen-bond groups (-OH, -NH, -C=O, -C-O) in natural and synthetic polymers, the hydrogen-bond interactions in hydrogels are usually screened due to the water molecules in hydrogels. To enable effective hydrogen-bond crosslinks, hydrophobic moieties with multiple self-complementary hydrogen-bond groups have been introduced^478,540,541. For instance, functionalizing PEG, PHMEA and PNIPAM with amine triazine or diamino triazine groups enables the formation of triple hydrogen bonds per crosslink^{478,490,540,542}. Similarly, the introduction of ureidopyrinimidone (UPy) groups onto PEG, PHMEA, PNIPAM, PAA and PDMAA chains gives quadruple hydrogen bonds per crosslink^478,540,541. Complementary DNA base pairs (A-T, C-G) can also serve as hydrogen-bond motifs when attached to polymer chains⁵⁴³.

Electrostatic interaction.

The energy of electrostatic interactions ranges from 5 kJ mol⁻¹ to 200 kJ mol⁻¹ (Figure 5)³⁷⁵. Natural and synthetic polymers with fixed charges, named polyelectrolytes, can be physically crosslinked by electrostatic interactions^{105,475,544,545}. As a typical example of the anionic polyelectrolytes, alginate has been physically crosslinked with a wide range of divalent cations such as Ca²⁺, Ba²⁺ and Mg²⁺. Although the energy of a single ionic bond in alginate is relatively low, multiple (e.g., over 20) adjacent ionic crosslinks on the alginate chains can form a densely-crosslinked region following the “eggbox” model^{6,103,105,546}, giving relatively stable alginate hydrogels. As a typical example of the cationic polyelectrolytes, chitosan has been crosslinked by multivalent anions such as citrate and tripolyphosphate^547–549. Electrostatic interactions of oppositely charged polyelectrolytes can also give physically-crosslinked hydrogels. For example, anionic poly(L-glutamic acid) and cationic poly(L-lysine) can form an injectable hydrogel by simply mixing them in phosphate buffered saline solutions⁵⁴⁴. As another example, poly(3-(methacryloylamino) propyl-trimethylammonium chloride) and poly(sodium p-styrenesulfonate) can form polyion complexes and give a series of tough and self-healing hydrogels by the stepwise polymerization of the oppositely charged monomers⁵⁵⁰. It should be noted that the formation of ionic crosslinks usually requires low ionic strength of the solvents for the hydrogels to avoid charge shielding.

Coordination complex.

A coordination complex consists of a central metal ion, especially transition metal ion, and a surrounding array of organic ligands^551,552. The energy of coordination complexes ranges from 100 kJ mol⁻¹ to 300 kJ mol⁻¹ (Figure 5) ³⁷⁵. Coordination bonds provide structural support in many living tissues, such as human bone⁵⁵³, insect mandible⁵⁵⁴ as well as mussel byssal thread⁵⁵⁵. Hydrogels crosslinked by coordination complexes are primarily achieved by functionalizing polymer backbones with chelating ligands, which then form coordination complexes with metal ions. Bisphosphonate^556–558, catechol^559–561, histidine^562–564, thiolate^565,566, carboxylate^567,568, pyridine⁵⁶⁹, bipyridine⁵⁷⁰, and iminodiacetate^564,571 have been widely used as the chelating ligands; Cu²⁺, Zn²⁺, Fe³⁺, Co²⁺ and Ni²⁺ are the commonly-used metal ions. Bisphosphonate ligands can be modified onto hyaluronan⁵⁷², gelatin⁵⁷³ or PEG⁵⁵⁷ to form coordination complex with Ca²⁺, Mg²⁺ or Ag⁺. Besides bisphosphonate, catechol ligands are also widely used to functionalize various polymers such as PEG^574,575, gelatin⁵⁷⁶, hyaluronic acid⁵⁷⁷, chitosan⁵⁷⁸, polyacrylamide⁵⁶⁰, and PAA⁵⁶¹. As a typical example, PEG-modified with 3,4dihydroxyphenyl-L-alanine (DOPA) residues can form coordination complexes with metal ions (Cu²⁺, Zn²⁺ and Fe³⁺ ions) when the pH is above 8^478,575. In natural proteins, the histidine amino acid can give an imidazole ligand residue⁵⁹, which is one of the most important chelators in the human body⁵⁷⁹. PEG-modified with histidine can form coordination complexes with metal ions (Cu²⁺, Co²⁺ and Ni²⁺ ions) to achieve the physically crosslinking of the PEG hydrogels^478,580. The mechanical properties of the hydrogels crosslinked by coordination complexes can be tuned by varying the metal ions and/or the chelating ligands^562,581.

Host-guest interactions.

Host-gust interactions refer to two or more molecules or ions that are held together in unique structural relationships by forces other than those of covalent bonds^461,582,583. The two most common host moieties are cyclodextrins and curcubit[n]urils. Cyclodextrins (CDs) are cyclic oligosaccharides which compose of 6 to 8 D-glucose repeating units linked by α−1,4-glucosidic bonds^584,585. Commonly-used CDs include α-, β-, and γ-CDs which are composed of 6, 7, and 8 D-glucose repeating units, respectively. These CDs have a truncated cone shape with the secondary and primary hydroxyl groups on the smaller cone rim exposed to the solvent⁵⁸³, which makes the CDs show a relatively hydrophobic inner cavity and a relatively hydrophilic outer surface. Therefore, these CDs can act as the host molecules for various hydrophobic guest molecules with appropriate molecular sizes through hydrophobic and van der Waals interactions^383,457,461. For example, common guests for α-CD include azobenzene⁵⁸⁶ and ferrocene⁵⁸⁷; common guests for β-CD include adamantane⁵⁸⁸, benzimidazole⁵⁸⁹, 3-(Trimethylsilyl)propionic acid⁵⁹⁰, azobenzene⁵⁸⁶, ferrocene⁵⁹¹, bipyridine⁵⁹², phenolphthalein⁵⁹³ and cholesterol⁵⁹⁴; common guests for γ-CD include ferrocene⁵⁸⁷. Among various guest molecules, adamantane is widely regarded as having one of the greatest affinities due to its complementary size for β-CD and high hydrophobicity⁵⁹⁵. In addition, the complexation of azobenzene or ferrocene to CDs is responsive to light⁵⁹⁶ or redox conditions^597,598, respectively.

The cucurbit[n]urils (CB[n, n=5–8]) are pumpkin-shaped macrocyclic oligomers made from the condensation reactions of formaldehyde and glycoluril^583,599. The CB[n]s usually have a structure of a rigid hydrophobic cavity with two identical hydrophilic polar carbonyl groups surrounding the portals. The cavity size ranges from 4.4 to 8.8 A° (for CB[n], n = 5–8) and the portal diameter ranges from 2.4 to 6.9 A°⁶⁰⁰. The binding affinities of CBs are often greater than that of other cavitands⁶⁰¹, mainly due to the formation of the strong charge–dipole, hydrogen bonding, and hydrophobic/hydrophilic interactions by the rigid inner cavities and the negative portals of CB[n]s⁶⁰². In particular, CB[7] can form strong 1:1 complexes with positively charged amphiphilic guests including adamantane, ferrocene, p-xylylene and trimethylsilyl derivatives containing one or two amino groups, as well as viologen derivatives^603,604. CB[8] also displays remarkable binding affinities towards positively charged and relatively large guests such as amantadine derivatives. Furthermore, the cavity of CB[8] is large enough to accommodate two organic guests simultaneously, thus forming highly stable ternary complexes. For example, CB[8] can form stable complexes with two doubly-charged 2,6-bis(4,5-dihydro-1Himidazol-2-yl)naphthalene molecules⁶⁰⁵, or one viologen (paraquat) and one 2,6-dihydroxynaphthalene together⁶⁰⁶.

Hydrogels crossslinked by the host-guest interactions are usually constructed with polymer networks modified by the guest molecules and/or host molecules. For example, monomers, host molecules, and guest molecules can be copolymerized into polymer networks crossslinked by the host-guest interactions⁶⁰⁷. The host/gust molecules can also be attached to the backbones or ends of polymers such as PEG, PDMAA, hyaluronic acid and PAA, and then the addition of the corresponding difunctional gust/host crosslinkers will crosslink the polymer network⁵⁸³. Alternatively, guest-functionalized and hostfunctionalized polymers can also be synthesized separately, and a mixture of the two types of polymers gives hydrogels crosslinked by the host-guest interactions^608,609. Supramolecular hydrogels with these host-guest interactions have been extensively utilized to fabricate responsive materials⁶¹⁰ and other dynamically assembling systems^457,611.

Hydrophobic association.

The physical crosslink of hydrophobic association relies on the microphase separation and aggregation of hydrophobic domains of the polymer chains^478,490. The energy of hydrophobic association ranges from 0.1 kJ mol⁻¹ to 20 kJ mol⁻¹ (Figure 5) ³⁷⁵. The hydrophobic domains can be introduced by post-polymerization modification (e.g., via the grafting-to approach) or by copolymerizing hydrophobic monomers within the polymer chains, either randomly or as blocks⁶¹². These modifications usually require the usage of non-aqueous solvents, mixed solvents, or micellar systems^488,613. As a typical example of introducing the hydrophobic domains, hydrophobic stearyl acrylate monomers have been copolymerized within polyacrylamide (PAAm) chains⁴⁸⁸. Another example of introducing the hydrophobic domains is the synthesis of multiblock copolymers with hydrophobic n-alkyl acrylate end blocks and a large middle block of PEG, PAAm, PAA and PHEMA polymers^614–616. Notably, because one hydrophobic association can interconnect multiple polymer chains, the hydrophobic association has also been used as high-functionality crosslinks in hydrogels^290,617, although the energy of hydrophobic association is usually lower than that of crystalline domains and glassy nodules.

π-π stacking.

The π-π stacking interaction is a type of noncovalent interaction which refers specifically to the attractive interactions between π electrons in the aromatic groups⁶¹⁸ The π-π interactions can be divided into the edge-to-face stacked (T-shaped), offset stacked, and face-to-surface stacked due to the geometry of the aromatic interactions⁶¹⁹. The energy of π-π stacking ranges from 1 kJ to 50 kJ mol⁻¹ (Figure 5) ³⁷⁶. Natural amino acids with aromatic rings, such as phenylalanine, tyrosine and tryptophan, and the other compounds with conjugate structures such as fluorenylmethyloxycarbonyl (Fmoc), 1pyrenebutyric acid, 2-naphthalene acetic acid and nitrophenyl methacrylate can be used to design and prepare polymers with aromatic moieties for gelation by the π-π stacking interaction^499,620,621. For example, aromatic moiety containing short peptides and N-terminal Fmoc-amino acids can self-assemble into robust supramolecular architectures⁴⁹⁹. In addition, carbon nanotubes^622,623, polythiophene^30,624, and graphene-based nanomaterials^625,626 (including single-layer graphene, multilayer graphene, graphene oxide, and reduced graphene oxide) are also capable to form π-π interactions, which is useful in preparing electrically conductive hydrogels^627,628.

4.2.3. Dynamic covalent crosslinks

In addition to the weak physical bonds, dynamic covalent bonds can also act as reversible crosslinks that are cleavable by external stimuli. The energy of dynamic covalent bonds is usually similar to or lower than that of permanent covalent bonds⁶²⁹, and higher than that of weak physical bonds (Figure 5). Typical examples of dynamic covalent crosslinks in hydrogels include imine bond, boronate ester bond, disulfide bond, cyclohexenes hydrazone bond, oxime bond, and reversible Diels-Alder reaction.

Imine bond.

An imine is a compound with a carbon-nitrogen double bond, which is commonly formed by reactions between amine and aldehyde or ketone⁶³⁰. In particular, the imine crosslinks in hydrogels are usually formed through the Schiff base reactions, which give aliphatic Schiff bases or aromatic Schiff bases^631–634. The reversible nature of the imine crosslinks endows the resultant hydrogels with properties such as mechanical dissipation, self-healing and stimuli responses⁶³⁵. The energy of the Schiff bases ranges from 67 kJ mol⁻¹ to 477 kJ mol⁻¹ (Figure 5)^372,377. The aromatic Schiff bases usually have higher energy and stability than the aliphatic Schiff bases^636,637.

The imide bonds are particularly useful for preparing biopolymer-based hydrogels, because most biopolymers such as proteins contain amine groups. These amines can form imide bonds with various aldehydic crosslinkers at mild conditions^635,638. The obtained hydrogels with imine bonds are usually sensitive to various chemical and biological stimuli, including pH, free amine, and free aldehydes⁶³⁷. These hydrogels can be used as self-healing materials and injectable scaffolds in biomedical applications^639–641.

Boronate ester bond.

The dynamic boronate ester bonds are formed by the reaction of diols and boronic acid^642–644. The energy of boronate ester bonds ranges from 27.2 kJ mol⁻¹ to 93.3 kJ mol⁻¹ (Figure 5) ³⁷⁸, highly dependent on pH and temperature^645–647. The boronic acid can be introduced into hydrogels by polymerizing boronic acid-containing monomers together with other monomers, such as acrylamide (AAm)⁶⁴⁸ and N-isopropylacrylamide (NIPAM)⁶⁴⁹. Alternatively, boronic acid functional groups can also be grafted onto pre-formed polymer chains through the carbodiimide chemistry^650,651.

The boronic acid-containing polymers can react with polymers having diol functional groups. For example, polymers modified with salicyl hydroxamic acid groups or catechol groups can form the dynamic boronate ester crosslinks with boronic acid-containing polymers in acidic environment^646,652 or alkaline environment^574,653,654, respectively. As another example, polyhydroxy polymers such as PVA^655,656, alginate^657,658, and cellulose⁶⁵⁹ can also be crosslinked into dynamic hydrogels by mixing with boronic acid-containing polymers in aqueous solutions. The transient boronate ester networks usually can dynamically restructure after broken, making the resultant hydrogels injectable and self-healing^660,661. In addition, the boronate ester crosslinked hydrogels are also glucose-sensitive, because glucose can compete with diol groups to form boronate–glucose complexes and therefore de-crosslink the hydrogels⁶⁵⁵. These glucosesensitivity hydrogels, based on the boronate ester bonds, have been used for self-regulated insulin release and glucose sensing^{383,650,655,662}.

Disulfide bond.

Disulfide bonds are dynamic covalent bonds based on thiol-thiol interactions at slightly alkaline environments or at mild oxidative conditions^663,664. The energy of disulfide bonds is around 425kJ mol⁻¹ (Figure 5)^372,379. Many natural polymers have disulfide bonds to stabilize their structures such as fibrinogen⁶⁶⁵ and collagen⁶⁶⁶. The disulfide bond can also be introduced into polymers by using disulphide-bond containing crosslinkers such as 3,3’-dithiobis(propanoic dihydrazide)^667,668 and N, N’-cystamine-bisacrylamide^669–671. The thiol-thiol reaction has relatively fast kinetics and can be used to prepare dynamic hydrogels^672,673. Hydrogels crosslinked by disulfide bonds can be used to encapsulate various types of cells, due to the mild reaction conditions^674,675. In addition, the disulfide bonds are sensitive to pH and can be cleaved by reducing agents such as tris(2-carboxyethyl)phosphine⁶⁷⁶, 1,4-dithiothreitol⁶⁷⁷, and glutathione^672,678.

Hydrazone bond.

Hydrazone bonds are formed by the reaction of aldehyde and hydrazine groups⁶⁷⁹. Polymers with hydroxyl groups, such as PEG⁶⁸⁰, cellulose⁶⁸¹ and polysaccharide⁶³², can be easily modified with the aldehydes and reactive hydrazines, especially acylhydrazine or hydrazide motifs. The reversible hydrazone bonds can be formed by simply mixing the aldehyde and hydrazine containing polymers under physiological conditions^682–684.

Hydrogels crosslinked by the hydrazine bonds can exhibit reversible sol-gel transition properties by changing the pH^680,685. Aliphatic aldehyde-derived hydrazone has a more rapid rate of formation and hydrolysis than the aryl aldehyde-derived hydrazone at neutral pH^686,687. Hydrogels crosslinked by hydrazone bonds can be used for in situ cell encapsulation due to the cytocompatibility and fast gelation kinetics of aldehyde and hydrazine coupling^688,689. The mechanical properties of these hydrogels can be easily tuned, which facilitates the study of the relationships between cell behaviors and mechanics (such as stress-relaxation kinetics) of the hydrogels⁶⁹⁰. Hydrazone bonds can also be used to prepare self-healing and injectable hydrogels based on the reversibility of hydrazone bonds at the mildly acid environment (pH 4.0–6.0)^682,684,686.

Oxime bond.

Oxime bonds are formed by the reaction between hydroxylamine and aldehyde or ketone with high efficiency under mild conditions⁶⁹¹. The reactive aldehyde or ketone groups can be modified onto polymers through radical polymerization⁶⁹² or oxidation^693,694, while the hydroxylamine motif is mainly modified onto hydroxyl-containing polymers through a sequential N-hydroxyphthalimide induced Mitsunobu reaction and hydrazine reduction⁶⁹⁵. Then, the oxime bonds can be formed by mixing the aldehyde or ketone-containing polymers with the hydroxylamine-containing polymers at a neutral or slightly acid aqueous solution⁶⁹⁶. This reaction is biocompatible without cytotoxic side products and can be used to crosslink biopolymers into hydrogels^695,697. Due to the dynamic nature, oxime bonds have been used for building self-healing and injectable hydrogels which show higher hydrolytic stability than the hydrogels crosslinked by imines and hydrazones^696,698.

Reversible Diels–Alder reaction.

Diels-Alder reaction is a click reaction between diene and dienophile groups^699,700. The energy of Diels-Alder bonds ranges from 37.6 kJ mol⁻¹ to 130 kJ mol⁻¹ (Figure 5)^380,381. To harness the dynamic Diels-Alder reaction as reversible crosslinks for hydrogels, natural polymers (such as hyaluronic acid⁷⁰¹, cellulose⁷⁰² and other polysaccharides⁷⁰³) and synthetic polymers (such as PNIPAM⁷⁰⁴and PEG⁷⁰⁵) can be modified with diene (such as furan) functional groups and dienophile (such as maleimide) functional groups on their backbones or chain ends. The equilibrium of the Diels-Alder linkage is thermally responsive; for example, the adducted Diels-Alder linkage can reform maleimide and furan moieties when increasing the temperature^706,707. The Diels-Alder reaction can be performed in aqueous media at physiologically compatible conditions without any side reactions or byproducts^708–711. Therefore, the Diels-Alder reaction has been used for preparing self-healing or adaptable hydrogels for biological applications in drug delivery and tissue engineering^701,711,712.

4.3. Synergy of unconventional polymer network architectures and interactions

It is not uncommon for an unconventional polymer network to simultaneously possess both UPN architectures and UPN interactions. In some cases, the UPN architectures and interactions are interdependent. The formation of certain UPN architectures requires certain UPN interactions, or certain UPN interactions naturally lead to the self-assembly of polymers into certain UPN architectures. For example, the strong physical crosslinks such as crystalline domains and glassy nodules mostly have high functionalities, giving rise to UPNs with high-functionality crosslinks. As another example, the selfassembly of polymer chains into nano-/micro-fibers usually requires the UPN interactions such as weak physical crosslinks. In other cases, specific types of UPN architectures and interactions can be intentionally designed and integrated into the same UPN. For example, weak physical crosslinks and dynamic covalent crosslinks have been introduced into various UPN architectures in order to design tough hydrogels⁴⁷⁵, because the dissociation and reformation of these reversible crosslinks can dissipate mechanical energy to toughen the hydrogels.

4.4. Decoupled mechanical properties

Decoupled mechanical properties of hydrogels with UPN architectures.

Polymer chains in the ideal polymer networks have uniform chain lengths (i.e., the same N), and the polymer networks with slidable crosslinks also tend to give relatively uniform chain lengths under mechanical loads. These polymer networks with relatively uniform chain lengths are named as unimodal polymer networks (Figure 9a)^53,56,428. Because the shear moduli, stretch limits and intrinsic fracture energy of conventional polymer networks have been derived based on unimodal polymer networks, these mechanical properties are still coupled in hydrogels with the ideal polymer networks and the polymer networks with slidable crosslinks.

Figure 9. The UPN architectures decouple mechanical properties of hydrogels:

a. unimodal polymer networks such as ideal polymer networks and the polymer networks with slidable crosslinks give coupled mechanical properties; b. multimodal polymer networks such as interpenetrating polymer networks, semiinterpenetrating polymer networks and polymer networks with high-functionality crosslinks can decouple the mechanical properties.

The interpenetrating polymer networks, semi-interpenetrating polymer networks and polymer networks with high-functionality crosslinks can integrate polymer chains with dramatically varying chain lengths (i.e., different N) into the same polymer networks, which are often named as multimodal polymer networks (Figure 9b)^53,56,428. Let’s classify the polymer chains in a multimodal polymer network into different types based on their chain lengths (Figure 9b). For the ith type of polymer chains, the number of the polymer chains per unit volume of the polymer network in the dry state, the number of Kuhn monomers per polymer chain, and the volume of the Kuhn monomer are denoted as n_i, N_i and v_i, respectively.

The multimodal polymer network (Figure 9b) can be designed such that the corresponding hydrogel can sustain its integrity up to the stretch limit of the longest polymer chains, which can be expressed as^63,475,

$${\lambda }_{\lim }=\sqrt{N_{\max }}{\lambda }_s^{-1}$$ (15)

where N_max is the number of Kuhn monomers on the longest polymer chain, and ${\lambda }_s^{-1}$ accounts for the effect of swelling on the stretch limit. The stretch limit of the bulk hydrogel scales with ${\lambda }_{\lim }$, and the pre-factor of the scaling relation depends on the polymer network architecture⁵⁴.

Based on the affine network model, the shear modulus of the hydrogel with the multimodal polymer network (Figure 9b) can be expressed as

$$G=\sum n_{i}kT{\lambda }_s^{-1}$$ (16)

where n_i and ${\lambda }_s^{-1}$ account for the effects of the ith type of polymer chains and swelling on the initial shear modulus of the hydrogel.

Following the Lake-Thomas model, the intrinsic fracture energy of the hydrogel with the multimodal polymer network (Figure 9b) can be calculated as,

$${\text{Γ}}_0=\sum n_i{b}_i{N}_i^{3/2}{U}_i{\lambda }_s^{-2}$$ (17)

where b_i and U_i are the length and fracture energy of a Kuhn monomer on the ith type of polymer chain, respectively, and ${\lambda }_s^{-2}$ accounts for the effect of swelling on the intrinsic fracture energy. It should be noted that the fracture toughness and interfacial fracture toughness of the multimodal polymer network (Figure 9b) can be much higher than the intrinsic fracture energy, which will be discussed in Section 5.

It is commonly assumed that the polymer chains occupy the major volume of the polymer network in the dry state, and therefore the volume conservation of the multimodal polymer network (Figure 9b) gives

$$\sum N_i{n}_i{v}_i=1$$ (18)

Despite the relation of Eq. 18, the stretch limit, shear modulus and intrinsic fracture energy of a hydrogel with the multimodal polymer network (Figure 9b) can be decoupled and independently designed. Without loss of generality, let’s consider a hydrogel with bimodal distribution of polymer-chain lengths as an example (Figure 9b). A high density of the short polymer chains can give a high initial shear modulus of the hydrogel. While these short chains will be fractured when the hydrogel is highly stretched, the long polymer chains can still maintain the integrity and high stretch limit of the hydrogel^63,475. Similarly, the long polymer chains can give high intrinsic fracture energy of the hydrogel⁷¹³.

The mechanical properties of the nano-/micro-fibrous polymer networks are determined by their fibers, interactions of the fibers (e.g., crosslinks between fibers), and topologies of the fibrous polymer networks. Therefore, the stretch limit, shear modulus and intrinsic fracture energy of nano-/micro-fibrous hydrogels do not follow the coupling relations for conventional polymer networks (Eqs. 13 and 14), and they can be independently designed.

Decoupled mechanical properties of hydrogels with UPN interactions.

The crystalline domains and glassy nodules have been widely used as the high-functionality crosslinks in UPNs, whose stretch limit, shear moduli and intrinsic fracture energy are decoupled as discussed above (Figure 9b).

The weak physical crosslinks and dynamic covalent crosslinks can act as reversible crosslinks in polymer networks, leading to decoupled mechanical properties of the resultant hydrogels (Figure 10). Without loss of generality, let’s consider a conventional polymer network with long polymer chains (i.e., polymer networks sparsely crosslinked by permanent covalent bonds that give high N value), whose stretch limit, shear modulus and intrinsic fracture energy are given by Eqs. 7–9, respectively. We next introduce reversible crosslinks such as weak physical crosslinks and dynamic covalent crosslinks into the polymer network. When the polymer network undergoes initial small deformation, the reversible crosslinks act as additional crosslinks⁴³⁵, increasing the effective chain density of the polymer network to $n_{eff}$. Therefore, the shear modulus of the hydrogel with the reversible crosslinks under initial deformation increases to

$$G=n_{eff}kT{\lambda }_s^{-1}$$ (19)

Figure 10. The UPN interactions decouple the mechanical properties of hydrogels.

The reversible crosslinks give an effectively high density of short chains for the high modulus, and the sparse covalent crosslinks give long chains for high stretchability and intrinsic fracture energy.

As the hydrogel is highly stretched, the reversible crosslinks can be de-crosslinked. However, the covalently-crosslinked long polymer chains (i.e., high N ) still endow the hydrogel with high stretch limit and high intrinsic fracture energy according to Eq. 13.

5. Design of hydrogels with extreme mechanical properties

While numerous UPN architectures and interactions have been developed over the last few decades, the design of hydrogels that possess extreme mechanical properties has largely followed an Edisonian approach – trial and error with specific materials. The rational design of hydrogels with different polymers and fabrication methods for various applications remains a central need of the field. In this section, we will summarize a set of general design principles for hydrogels to achieve the corresponding extreme mechanical properties, including extremely high fracture toughness, tensile strength, resilience, interfacial toughness, fatigue-threshold, interfacial toughness, and interfacial fatigue threshold. Then, we will discuss the implementations of these design principles with the UPN architectures and/or the UPN interactions.

5.1. Tough: Build dissipation into stretchy polymer networks

Fracture toughness.

Fracture toughness has been widely used to characterize a material’s capability to resist fracture under mechanical loads. One common definition for the fracture toughness of a material is the energy required to propagate a crack in the material over a unit area measured in the undeformed state (Figure 11a) which can be quantitatively expressed as,

$$\text{Γ}=G_c=-\frac{dU}{dA}$$ (20)

where U is the total potential energy of the system, A is the crack area measured in the undeformed state, and G_c is the critical energy release rate that drives crack propagation. According to Eq. 20, the unit for the fracture toughness is joule per meter squared (i.e., J m⁻²).

Figure 11. Design principle for tough hydrogels – build dissipation into stretchy polymer networks.

a. definition of fracture toughness and the pure-shear test to measure the fracture toughness. When a notched sample with height H at the undeformed state is stretched by a critical ratio of λ_c under pure-shear deformation, the crack begins to propagates (top). The relation of the nominal stress s and the stretch λ is measured for an un-notched sample (otherwise the same as the notched sample) under pure-shear deformation (bottom). The fracture toughness can be calculated as $\text{Γ}=H{\int }_1^{{\lambda }_c}sd\lambda$ based on the measured λ_c and s vs λ relation in the pure-shear tests. b. the intrinsic fracture energy ${\mathrm{\Gamma }}_0$ from fracturing a layer of polymer chains. c. the mechanical dissipation in the process zone around the crack tip dramatically contributes to the fracture toughness by ${\text{Γ}}_D$. The mechanical dissipation manifests as a hysteresis loop on the stress-stretch curve. The total fracture toughness of the tough hydrogel is $\text{Γ}={\text{Γ}}_0+{\text{Γ}}_D$.

The fracture toughness of soft materials such as elastomers and hydrogels has been measured with many experimental methods such as the pure-shear test and the single-notch test, which have been summarized in a few recent review papers^60,714,715. For example, in the pure-shear test, two identical pieces of a hydrogel are fabricated with the same thickness T, width W and height H, where W >> H >> T (Figure 11a). Both pieces of samples are clamped along their long edges (i.e., along the width direction) with rigid plates. A notch with a length of ~0.5W is introduced into the first sample, which is then gradually pulled to a stretch of λ_c times of its undeformed height until a crack begins to propagate from the notch (Figure 11a). The second sample without notch is uniformly stretched above the critical stretch λ_c to measure the nominal stress s - stretch λ relation (Figure 11a). Thereafter, the fracture toughness of the hydrogel can be calculated as $\text{Γ}=H{\int }_1^{{\lambda }_c}sd\lambda$, based on the measured λ_c and s-λ relation in the pure-shear tests.

As discussed in Section 3, the fracture toughness of a conventional polymer network is its intrinsic fracture energy ${\mathrm{\Gamma }}_0$, which is the energy required to fracture a layer of polymer chains over a unit area (Figure 11b). Evaluated with typical parameters of conventional polymer networks, the fracture toughness of the corresponding hydrogels is commonly limited to a few tens of joule per meter squared. In addition, the fracture toughness of hydrogels with conventional polymer networks is also coupled with their stretch limits and shear moduli (Eqs. 11). For example, in order to increase the fracture toughness of a conventional polymer network, the polymer-chain length (i.e., N) and thus the stretch limit of the polymer network need to be increased. Consequently, the polymer-chain density (i.e., n) and thus the shear modulus of the polymer network will be decreased.

Design principle.

The design principle for tough hydrogels is the same as the principle for toughening various engineering materials such as metals⁷¹⁶, ceramics ⁷¹⁷, composites⁷¹⁸ and polymers⁵⁷ and various biological tissues such as tendons, cartilages, muscles and blood vessels (Figure 2)⁷¹⁹. That is to integrate both ductility and mechanical dissipation in the same material, so that a process zone with substantial mechanical dissipation develops around the crack tip prior to crack propagation (Figure 11c). The mechanical dissipation of a material manifests as the hysteresis loop on its stress-stretch curve under a loading-unloading cycle (Figure 11c); the ductility of hydrogels generally relies on the high stretchability (or the high stretch limit) of their polymer networks. Overall, the design principle for tough hydrogels is to build dissipation into stretchy polymer networks^60,720. Quantitatively, the total fracture toughness of a hydrogel with the capability of mechanical dissipation can be expressed as ^60,721

$$\text{Γ}={\text{Γ}}_0+{\text{Γ}}_D$$ (21)

where $\text{Γ}$, ${\mathrm{\Gamma }}_0$, and ${\text{Γ}}_D$ are the total fracture toughness, the intrinsic fracture energy, and the contribution of mechanical dissipation in the process zone to the total fracture toughness, respectively. While the intrinsic fracture energy for hydrogels is usually limited to a few tens of joule per meter squared, the contribution of the process-zone dissipation can be extremely high because both the dissipated energy per volume of the process zone and the size of the process zone can be large values (Figure 11c). Indeed, the fracture toughness of tough hydrogels has exceeded 10,000 Jm⁻², orders of magnitude higher than that of hydrogels with conventional polymer networks⁶⁰.

Implementation with UPNs.

The design principle for tough hydrogels requires: i). at least one polymer network in the hydrogel maintains a high stretch limit ${\lambda }_{\lim }$ and thus the polymer chains in that polymer network need to have a high N value according to Eq. 7; and ii). at least one component in the hydrogel dissipates substantial mechanical energy under the deformation typically experienced in the process zone. The design principle for tough hydrogels has been widely implemented with diverse types of UPN architectures and UPN interactions. We will discuss a few examples in the following paragraphs.

The interpenetrating polymer networks and semi-interpenetrating polymer networks have been widely used for the design of tough hydrogels since the pioneer work of double-network hydrogels by Gong et al. in 2003 (Figure 12a)⁶³. A typical double-network hydrogel interpenetrates a long-chain network (high N) and a short-chain network (low N)⁶³. As the double-network hydrogel deforms, the short-chain network fractures and dissipates substantial mechanical energy, while the long-chain network maintains the integrity of the hydrogel even under high stretches, implementing the design principle for tough hydrogels (Figures 12f and g)^63,720,722. Gong et al first demonstrated that the fracture toughness of double-network hydrogels can exceed 1,000 Jm^{2 63}. Other interpenetrating and semi-interpenetrating polymer networks such as the triple-network architecture have also been developed for tough hydrogels⁷²⁴ and elastomers⁷²⁵, implementing the design principle. Notably, since the fracture of the short-chain network is usually irreversible, these hydrogels’ capability of mechanical dissipation may be substantially reduced after a few cycles of large deformation⁷²¹.

Figure 12. Implementation of the design principle for tough hydrogels– build dissipation into stretchy polymer networks.

Schematics of the implementation strategies with a. interpenetrating or semiinterpenetrating polymer networks, b. polymer networks with high-functionality crosslinks, c. nano-/micro-fibrous polymer networks, and d. polymer networks with reversible crosslinks. e. nominal stress s-stretch λ relations for a PAAm-alginate hydrogel under loading and unloading⁴⁷⁵. f. microscope image of the process zone around the crack in a PAMPS-PAAm hydrogel⁷²². g. microscope image of a fibrous fibrin hydrogel⁷²³. e is adopted from Ref⁴⁷⁵. f is adopted from Ref⁷²². g is adopted from Ref⁷²³.

The polymer networks with high-functionality crosslinks have given tough hydrogels based on various types of polymers and crosslinks. There are multiple polymer chains (e.g., over 10) bridging between two adjacent high-functionality crosslinks, and the lengths of these polymer chains are usually non-uniform (Figure 12b). As the hydrogel deforms, the relatively short polymer chains fracture or detach from the crosslinks, while the relatively long polymer chains maintain the integrity and high stretchability of the hydrogel, implementing the design principle for tough hydrogels. The bonds between the polymer chains and the high-functionality crosslinks can be permanent covalent crosslinks⁷²⁶, strong physical crosslinks^727,728, weak physical crosslinks^729,730, and dynamic covalent crosslinks^731,732, or a combination of them⁷³³. Depending on the number and lengths of polymer chains between adjacent crosslinks and the types of bonds between polymer chains and crosslinks, the corresponding hydrogel can have different capabilities of mechanical dissipation and stretchability and therefore different fracture toughness.

The nano-/micro-fibrous hydrogels have also been used to implement the design principle for tough hydrogels. The nano-/micro-fibers can be made intrinsically stretchable (Figure 12c), and their reorientation and re-alignment in hydrogels under deformation further enhance the stretchability of the hydrogels (Figure 12g)^{723,728,731,734–736}. The fracture of the nano-/micro-fibers and pull-out of the nano/micro-fibers from the hydrogel matrices can dissipate substantial mechanical energy. A combination of the high stretchability and the mechanical dissipation enabled by the nano-/micro-fibrous polymer networks implements the design principle for tough hydrogels.

In addition to the abovementioned UNP architectures, the UPN interactions have also been widely used to implement the design principle for tough hydrogels⁷³⁷. The strong physical crosslinks such as crystalline domains and glassy nodules naturally act as high-functionality crosslinks for the corresponding UPN architectures (Figure 12b), which lead to tough hydrogels as discussed above.

The weak physical crosslinks^{550,568,607,738–745} and dynamic covalent crosslinks⁷³¹ have been added into polymer networks with long chains (i.e., uncrosslinked or sparsely-crosslinked polymer networks) to design tough hydrogels. The weak physical crosslinks and dynamic covalent crosslinks act as reversible crosslinks in these hydrogels (Figure 12d). As the hydrogel deforms, many of these reversible crosslinks dissociate or de-crosslink to dissipate substantial mechanical energy and the sparsely-crosslinked longchain polymer network still sustains the high stretchability of the polymer network (Figure 12d). A synergy of the mechanical dissipation and the high stretchability enabled by the hybrid reversible and covalent crosslinks implements the design principle for tough hydrogels.

The weak physical crosslinks and dynamic covalent crosslinks have also been added into UPN architectures such as the interpenetrating polymer networks (Figure 12a)^{475,547,746–753}, polymer networks with high-functionality crosslinks (Figure 12b)^{727,729,730,754–757}, and nano-/micro-fibrous polymer networks (Figure 12c)^{734,735,755,758} to further toughen the resultant hydrogels, leveraging these reversible bonds’ capability of dissipating additional mechanical energy. Furthermore, unlike irreversibly-fractured polymer chains, the dissociated weak physical crosslinks and dynamic covalent crosslinks may re-associate due to their reversible nature, potentially endowing the tough hydrogels with recoverable dissipation over cyclic loads⁴⁷⁵. For further detailed discussion on the design principle and implementation strategies for tough hydrogels, a recent review paper is recommended⁶⁰.

5.2. Strong: Synchronize stiffening and fracture of multiple polymer chains

Tensile strength.

Multiple types of strengths such as tensile strength, compressive strength and shear strength have been used to characterize the strength of a material. We will focus on tensile strengths of hydrogels in this paper, because the tensile strength is easier to measure than the shear strength and less affected by boundary conditions in the measurement (such as friction) than the compressive strength. Since soft materials such as elastomers and hydrogels usually do not yield plastically, their tensile strengths are commonly defined as the stresses at which the ultimate tensile failure occurs in the uniaxial tensile test. In addition, since the hydrogel samples usually undergo large deformation before failure, the tensile strength can be defined based on either the nominal stress or the true stress (Figure 13a),

$$s_f=\frac{F_f}{A},{\sigma }_f=\frac{F_f}{a}$$ (22)

where $F_f$ is the tensile force at the failure of the sample, A and a are the cross-section areas of the sample in the reference (undeformed) and current states, respectively, and $s_f$ and ${\sigma }_f$ are the nominal and true tensile strengths, respectively. The nominal tensile strengths of hydrogels with conventional polymer networks and even tough hydrogels are commonly lower than 1 MPa^63,475, much lower than the tensile strengths of engineering materials such as metals and biological tissues such as tendons.

Figure 13. Design principle for strong hydrogels – synchronize stiffening and fracture of multiple polymer chains:

a. definition and measurement of the tensile strength. A and a are the cross-section areas of the sample in the undeformed and deformed states, and F is applied tensile force. b. the simultaneous stiffening and fracture of substantial polymer chains give a high tensile strength⁷⁵⁹. F_f is the tensile force at the failure of the sample. c. the nominal tensile strength s_c increases with the decrease of the defect size D up to a critical value D_c, below which the tensile strength is defect-insensitive^760,761.

Design principle.

A generic principle for the design of strong hydrogels is to make a substantial number of polymer chains in the polymer network to stiffen and fracture simultaneously (Figure 13b). Following this principle, the nominal and true tensile strengths of the polymer network can be evaluated as

$$s_f=M_f{f}_f,{\sigma }_f=m_f{f}_f$$ (23)

where $f_f$ is the force required to fracture a single polymer chain, which is on the order of a few nanonewton³⁷⁰, and $M_f$ and $m_f$ are the numbers of simultaneously fractured polymer chains per unit area of the hydrogel at the reference and deformed states, respectively. It has been evaluated that s_f and σ_f can reach up to 1 GPa and 10 GPa, respectively, in an ideal scenario where all polymer chains in a polymer network fracture simultaneously⁷⁵⁹.

In realistic situations, almost all materials contain defects in the forms such as notches, microcracks, cavities, impurities, and missing polymer chains or crosslinks. The presence of defects usually significantly reduces the tensile strengths of the materials^760–762. Without loss of generality, let’s assume the largest defect in the tensile sample is a notch with length D in the undeformed state perpendicular to the tensile direction (Figure 13c). The tensile strength of the sample generally increases with the decrease of the defect size D up to a critical value D_c, below which the tensile strength is defect-insensitive (Figure 13c). A scaling relation for the critical defect size D_c can be expressed as^760,761

$$D_c\sim \frac{\text{Γ}}{W_c}$$ (24)

where W_c is the work for tensile failure of a unit volume of the defect-insensitive sample, and $\text{Γ}$ is the fracture toughness of the sample.

In order to achieve strong hydrogels, it is highly desirable for the hydrogel samples to have defectinsensitive tensile strengths⁷⁵⁹. According to Eq. 24, a tougher material (i.e., higher $\text{Γ}$) can be insensitive to larger defects due to a larger critical defect size D_c. For example, the critical defect size is on the order of a few nanometers for glass and ceramics, a few micrometers for brittle hydrogels, and a few millimeters for tough elastomers and hydrogels^760,761. Furthermore, it is a common strategy to set the characteristic size of the sample (e.g., the diameter of the sample in Figure 13c) to be similar to or smaller than the critical defect size D_c, so that the tensile strength of the sample is guaranteed to be insensitive to any possible defect in the sample⁷⁵⁹.

Implementation.

The UPNs with high-functionality crosslinks such as crystalline domains have been widely used for the design of strong hydrogels⁶⁸. As the hydrogels undergo large deformation, relatively short polymer chains are gradually pulled out of the crystalline domains, so that the polymer chains bridging adjacent crystalline domains tend to have similar lengths and therefore stiffen and fracture simultaneously – implementing the design principle for strong hydrogels (Figure 14a).

Figure 14. Implementation of the design principle for strong hydrogels – synchronize stiffening and fracture of multiple polymer chains.

Schematics on the implementation with a. polymer networks with high-functionality crosslinks, b. nano-/micro-fibrous polymer networks. c. confocal (left) and SEM (right) images of a fibrous PVA hydrogel with aligned fibers⁶⁹. d. nominal stress-stretch curves of the fibrous PVA hydrogels with aligned and randomly-oriented fibers⁶⁹. c and d are adopted from Ref⁶⁹.

The nano-/micro-fibrous polymer networks is another type of UPN architecture that implements the design principle for strong hydrogels (Figure 14b). The diameters of the nano-/micro-fibers can be readily controlled below the critical defect sizes. Bundles of polymer chains in the nano-/micro-fibers can be designed to stiffen and fracture simultaneously to endow the fibers with high tensile strengths up to the ideal strengths (Figure 14b)^{69,728,731,736,763}. Consequently, the resultant nano-/micro-fibrous hydrogels can reach extremely high tensile strengths (Figures 14c and d). Notably, biological hydrogels such as tendons, ligaments and muscles commonly adopt nano-fibers and micro-fibers, often in hierarchical architectures, to achieve high tensile strengths (Figure 2).

In addition to the abovementioned UPN architectures, the UPN interactions facilitate the implementation of the design principles for strong hydrogels. The strong physical crosslinks such as crystalline domains allow the pull-out of polymer chains from them to achieve simultaneous stiffening and fracture of multiple polymer chains (Figure 14a)⁶⁸. The weak physical crosslinks such as the hydrogen bonds can facilitate the alignment and self-assembly of polymer chains into bundles (Figure 14b), which tend to stiffen and fracture simultaneously to give high tensile strengths of the hydrogels.

On a structural level, high-strength fibers made of polymers^764,765, steel⁷⁶⁶, glass^767,768 and wood⁷⁶⁹ have been utilized to strengthen hydrogels, and the tensile strengths of the resultant hydrogels are primarily determined by the strengths of the fibers.

Resilience.

Resilience of soft materials such as elastomers and hydrogels is commonly defined as the ratio of energy released in deformation recovery to the energy required to induce the deformation of the materials⁷⁷⁰. Let’s consider a cylindrical sample under the uniaxial tensile test over a loading-unloading cycle (Figure 15a). The energy released in the unloading and the dissipated energy per unit volume of the sample are denoted as $W_R$ and $W_D$, respectively. Therefore, the resilience R and hysteresis ratio H of the material can expressed as (Figure 15a)^66,770

$$R=\frac{W_R}{W_R+W_D},H=\frac{W_D}{W_R+W_D}=1-R$$ (25)

Figure 15. Design principle for resilient and tough hydrogels – delay dissipation:

a. definition and measurement of resilience. The relation of nominal stress s and stretchλ of a sample is measured under uniaxial tension in a loading-unloading cycle. W_R and W_D are the energy released in the unloading and the dissipated energy per unit volume of the sample, respectively. The resilience can be calculated as $R=W_R/\left(W_R+W_D\right)$. b. when the stretch is below a critical stretch λ_R, the hydrogel releases most of the stored elastic energy during deformation recovery, giving high resilience; when the stretch is above λ_R, the hydrogel dissipates substantial mechanical energy, giving high fracture toughness⁶⁶. c. the stretch in the process zone around the crack is usually much higher than λ_R, dissipating substantial mechanical energy and giving high fracture toughness⁶⁶. b and c are adopted from Ref⁶⁶.

The resilience R and the hysteresis ratio H depend on the material properties and the loading conditions such as the applied stretch and the applied stretch rate. The resilience of soft materials has been measured with many experimental methods such as the cyclic tensile test and the dropping-ball test^66,770.

Design principle.

Once a material is deformed to fracture, the elastic energy stored in the material is mostly dissipated^66,67,771, giving low energy recovery and thus low resilience. Therefore, the high resilience of hydrogels can only be designed up to the failure of the hydrogels. A generic principle for the design of resilient hydrogels is to minimize the mechanical dissipation of the hydrogels within certain ranges of deformation that is commonly experienced by the hydrogels, or in short, to delay dissipation⁶⁶. Without loss of generality, we define a critical stretch for polymer chains in a hydrogel λ_R, below which the hydrogel can release most of the stored elastic energy during deformation recovery (i.e., $W_D\approx 0$, Figure 15b)⁶⁶. Therefore, according to Eq. 25, the hydrogel will give a high resilience under the condition,

$$\lambda \le {\lambda }_R\le {\lambda }_{\lim }$$ (26)

where λ and ${\lambda }_{\lim }$ are the stretch and stretch limit of polymer chains in the hydrogel.

The design principle for resilient hydrogels also reconciles a pair of seemly contradictory properties, fracture toughness and resilience in the following manner. The hydrogel is highly resilient under common deformation with $\lambda \le {\lambda }_R$ (Figure 15b); however, when a crack attempts to propagate in the hydrogel, the chain stretch in the process zone around the crack tip can be higher than λ_R, inducing substantial mechanical dissipation to toughen the hydrogel (Figure 15c). Indeed, biological hydrogels such as heart valves delay the mechanical dissipation up to supraphysiological deformation levels to achieve both high fracture toughness (e.g., over 1,000 Jm⁻²) and high resilience (e.g., over 99%) (Figure 2)^772,773. Synthetic elastomers⁷⁷⁴, hydrogels⁶⁶ and hydrogel composites⁷⁰ have also been made both tough and resilient by following the design principle of delaying dissipation.

Implementation.

The ideal polymer networks are one common UPN architecture to implement the design principle for resilient hydrogels^67,771. Because the polymer chains in the ideal polymer networks have relatively uniform lengths and no entanglement, the hydrogels with the ideal polymer networks usually can be deformed without significant mechanical dissipation up to stretch limits, giving high resilience^67,771. It is also expected that the polymer networks with slidable crosslinks may be able to implement the design principle for resilient hydrogels, because the energy dissipated for sliding the crosslinks during their reconfiguration may be negligibly low. Despite being resilient, the ideal polymer networks and polymer networks with slidable crosslinks are not tough, since their fracture toughness is still the intrinsic fracture energy ${\text{Γ}}_0$ for fracturing a layer of polymer chains as discussed in Section 4.1.

The multimodal polymer networks including the interpenetrating polymer networks, semiinterpenetrating polymer networks, and polymer networks with high-functionality crosslinks usually begin to dissipate mechanical energy at very small deformation, because of the fracture and/or de-crosslink of very short polymer chains in the polymer networks. Such “early” dissipation gives narrow ranges of deformation for the hydrogels to be resilient in practical applications⁶⁶. To address the issue of “early” dissipation, Lin et al. have pre-stretched the interpenetrating polymer networks up to λ_R over multiple cycles to fracture and/or de-crosslink susceptible short polymer chains and thus deplete possible dissipation mechanism within the deformation range of λ_R (Figure 16b)⁶⁶. In subsequent tests or applications, if the chain stretch in the hydrogel is below λ_R, the hydrogel is highly resilient, due to the lack of mechanical dissipation within this range (Figures 16b and f). However, as the polymer chains are stretched beyond λ_R, for example, in the process zone around the crack tip, some of the polymer chains will be further fractured and de-crosslinked to dissipate mechanical energy and toughen the hydrogel (Figures 16b and f–h). It is expected that other multimodal polymer networks such as the semi-interpenetrating polymer networks and polymer networks with high-functionality crosslinks⁷⁷⁵ can be pre-stretched in a similar way to implement the design principle for resilient hydrogels (Figure 16c). Notably, when pre-stretching the multimodal polymer networks, the fracture and de-crosslink of polymer chains should be irreversible, so that the dissipation mechanism is irrecoverable once depleted⁶⁹.

Figure 16. Implementation of the design principle for resilient and tough hydrogels – delay dissipation:

a. ideal polymer networks are resilient up to fracture due to the lack of dissipation mechanism. b. pre-stretching interpenetrating polymer networks to λ_R can make them both resilient and tough. c. prestretching polymer networks with high-functionality crosslinks to λ_R can make them both resilient and tough⁶⁶. d. nano-/micro-fibrous polymer networks with resilient fibers can be both resilient and tough. e. the nominal stress-stretch curve of a resilient and tough fibrous PVA hydrogels⁶⁹. f. the nominal stressstretch curves of a PAAm-alginate hydrogel with λ_R =5 ⁶⁶. g. the measured strain field around a crack in the PAAm-alginate hydrogel with λ_R =5. h. the stretch in the process zone can be much higher than λ_R = 5 ⁶⁶. e is adopted from Ref⁶⁹. f, g and h are adopted from Ref⁶⁶.

The nano-/micro-fibrous polymer networks can naturally implement the design principle for resilient hydrogels by constituting them with resilient nano-/micro-fibers and eliminating dissipation mechanisms (Figures 16d and e)⁶⁹. In addition, because the energy required to fracture and pull out the nano-/micro-fibers can be much higher than the energy for fracturing amorphous polymer chains, resilient nano-/micro-fibrous hydrogels can also be tough⁶⁹.

Besides the abovementioned UPN architectures, some UPN interactions also facilitate the implementation of the design principles for resilient hydrogels. The strong physical crosslinks such as crystalline domains provide the high-functionality crosslinks for some UPN architectures, which can be pre-stretched to give resilient hydrogels (Figure 16c)⁶⁸. On the other hand, the weak physical crosslinks and dynamic covalent crosslinks are not suitable to implement the design principle for resilient hydrogels, because of their reversible and dissipative nature⁶⁶.

On a structural level, resilient elastomeric fibers have been embedded into resilient hydrogel matrices to give resilient yet tough hydrogel composites⁷⁰ to implement the design principle for resilient hydrogels⁶⁹.

5.4. Tough adhesion: Integrate tough dissipative hydrogels and strong interfacial linkages

Interfacial toughness.

Interfacial toughness, or so-called practical work of adhesion, has been commonly used to characterize the capability of the interface of two adhered materials to resist fracture under mechanical loads. One common definition for the interfacial toughness between two adhered materials is the energy required to propagate a crack along the interface or in either material over a unit area measured in the undeformed state of the materials (Figure 17a)⁷⁷⁶. Depending on whether the crack propagates along the interface or in either material, the failure mode is called an adhesive failure or cohesive failure, respectively (Figure 17a). Quantitatively, the interfacial toughness ${\text{Γ}}^{\text{inter}}$ can be expressed as,

$${\text{Γ}}^{\text{inter}}=G_c=-\frac{dU}{dA}$$ (27)

where U is the total potential energy of the system, A is the crack area measured in the undeformed state, and G_c is the critical energy release rate that drives interfacial crack propagation. According to Eq. 27, the unit for the interfacial toughness is joule per meter squared (i.e., J m⁻²).

Figure 17. Design principle for tough adhesion of hydrogels – integrate tough dissipative hydrogels and strong interfacial linkages.

a. definition of interfacial toughness and the 90-degree peeling test to measure the interfacial toughness. F is the peeling force, $F_{plateau}$ is the plateau peeling force, and W is the width of the sample. The interfacial toughness can be calculated as ${\text{Γ}}^{\text{inter}}=F_{platenu}/W$ based on the values of $F_{plateau}$ and W measured in the 90-degree peeling test. b. weak interface can give the adhesive failure mode. c. brittle hydrogel matrix can give the cohesive failure mode. d. integration of tough dissipative hydrogels and strong interfacial linkages gives tough adhesion of hydrogels⁴³. The contributions of strong interfacial linkages and mechanical dissipation in the process zone to the total interfacial toughness are ${\text{Γ}}_0^{\text{inter}}$ and ${\text{Γ}}_D^{\text{inter}}$, respectively. The total interfacial toughness of the tough adhesion is ${\text{Γ}}^{\text{inter}}={\text{Γ}}_0^{\text{inter}}+{\text{Γ}}_D^{\text{inter}}$ d is adopted from Ref⁴³.

The interfacial toughness of soft materials such as elastomers and hydrogels has been measured with many experimental methods such as the 90-degree peeling test, the T-peeling test and the lap-shear test^714,776. For example, in the 90-degree peeling test, a layer of a hydrogel with thickness T, width W and length L (L >> W >> T) is bonded on a substrate, and a notch is introduce on the interface along the length direction (Figure 17a). The detached part of the hydrogel is further peeled off the substrate, while maintaining vertical to the substrate (Figure 17a). The measured force reaches a plateau $F_{plateau}$ as the peeling process enters the steady state, and the interfacial toughness is determined by dividing the plateau force $F_{plateau}$ by the width of the hydrogel sheet W, i.e. ${\text{Γ}}^{\text{inter}}=F_{plateau}/W$.

If a hydrogel with a conventional polymer network is strongly bonded on a substrate (e.g., via covalent bonds), the interfacial toughness is on the level of the hydrogel’s fracture toughness or intrinsic fracture energy ${\mathrm{\Gamma }}_0$. This is because the fracture toughness of the hydrogel poses an upper limit for the interfacial toughness, since the cohesive failure mode may occur (Figure 17c)⁴³. Therefore, evaluated with typical parameters of conventional polymer networks, the interfacial toughness of the hydrogel is bounded by a few tens of joule per meter squared. If the hydrogel is adhered on the substrate via a low density of weak physical crosslinks such as hydrogen bonds and electrostatic interactions, the interfacial toughness can be even lower, since the adhesive failure mode may occur (Figure 17b)⁴².

Design principle.

As discussed in the previous part, if a hydrogel adheres to a substrate via a low density of weak physical crosslinks, a crack can easily propagate along the hydrogel-substrate interface, resulting in low interfacial toughness (Figure 17b). Therefore, the design of tough adhesion of hydrogels first requires strong interfacial linkages between the hydrogels and the adhered substrates, such as covalent bonds^43,777,778, strong physical crosslinks^42,71,779, connector polymers^{26,775,780,781}, and mechanical interlocks^782,783. In addition, because the interfacial crack can tilt into the bulk hydrogel and develop the cohesive failure mode (Figure 17c), the design of tough adhesion of hydrogels further requires high fracture toughness of the hydrogel matrices by themselves⁴³.

Overall, the design principle for tough adhesion of hydrogels is to integrate tough dissipative hydrogel matrices and strong interfacial linkages⁴³. When attempting to detach the tough hydrogel from the substrate, the strong interfacial linkages will hold the interfacial crack tip, allowing the bulk hydrogel to develop a process zone with substantial mechanical dissipation (Figure 17d). Quantitatively, the total interfacial toughness can be expressed as^43,778

$${\text{Γ}}^{\text{inter}}={\text{Γ}}_0^{\text{inter}}+{\text{Γ}}_D^{\text{inter}}$$ (28)

where ${\text{Γ}}^{\text{inter}}$, ${\text{Γ}}_0^{\text{inter}}$, and ${\text{Γ}}_D^{\text{inter}}$ are the total interfacial toughness, the intrinsic interfacial toughness due to strong interfacial linkages, and the contribution of mechanical dissipation in the process zone to the total interfacial toughness, respectively.

Tough adhesion of biological hydrogels in animal bodies such as cartilages, tendons and ligaments on bones generally relies on the integration of tough hydrogels and strong interfacial linkages. However, only recently has this design principle been proposed⁴³ and implemented^{26,41,43,775,777,780,781,784} for tough adhesion of synthetic hydrogels on diverse substrate materials, including metals, ceramics, glass, silicone, elastomers, hydrogels and biological tissues, partially because the role of tough dissipative hydrogel matrices has been underexplored or underestimated in adhesion^43,785,786. Notably, strong interfacial linkages and/or bulk dissipation of the adherents have also been widely employed for tough bonding of engineering materials such as metals⁷⁸⁷ and rubbers^788,789 on substrates.

Implementation.

Since the implementation of tough hydrogels has been discussed in Section 5.1, we will focus on how to implement the strong interfacial linkages to bond tough dissipative hydrogels on various substrates in this section. In order to achieve tough adhesion, the intrinsic interfacial toughness ${\text{Γ}}_0^{\text{inter}}$ of the interfacial linkages should at least reach the level of the intrinsic fracture energy ${\mathrm{\Gamma }}_0$ of tough hydrogels, i.e. over a few tens of joule per meter squared⁷⁹⁰. Given this requirement on the intrinsic interfacial toughness, the strong interfacial linkages have been commonly implemented with covalent bonds, strong physical crosslinks, connector polymers, and mechanical interlocks.

Covalent bonds have been widely adopted to strongly anchor polymer chains in tough hydrogels’ UPNs (as discussed in Section 5.1) on various substrates. The commonly-used covalent bonds for tough adhesion of hydrogels include carbon-carbon, carbon-nitrogen, carbon-sulfide, carbon-oxygen, siloxane bonds (Figure 4c)⁷⁹¹. In order to form these covalent bonds, the hydrogels and substrates are usually designed to possess functional groups such as radical crosslinkable unsaturated bond (to form carboncarbon bond)⁷⁹², amine group (to form carbon-nitrogen bond)⁴³, thiol group (to form carbon-sulfide bond)⁷⁹³, hydroxyl and carboxyl group (to form carbon-oxygen bond), and silanol group (to form silicon-oxygen bond)⁷⁹⁴ (Figure 18a). According to the Lake-Thomas model, the intrinsic interfacial toughness ${\text{Γ}}_0^{\text{inter}}$ of polymer chains covalently anchored on a substrate can be expressed as

$${\text{Γ}}_0^{\text{inter}}=M^{\text{inter}}N{U}_f$$ (29)

where $M^{\text{inter}}$ is the number of covalently-anchored polymer chains on a unit area of the substrate in the undeformed reference state, N is the number of Kuhn monomers per polymer chain, and U_f is the lower value of the energy required to fracture either the Kuhn monomer or the covalent bond on the substrate. According to Eq. 29, anchoring longer polymer chains with a higher density of covalent bonds on a substrate will give a higher value of the intrinsic interfacial toughness^778,790.

Figure 18. Implementation of the design principle for tough adhesion of hydrogels – integrate tough hydrogels and strong interfacial linkages.

The tough UPNs are bonded on substrates via various types of strong interfacial linkages: a. covalent bonds, b. strong physical crosslinks, c. bridging polymers, and d. mechanical interlocks. e. catechol interactions can implement various types of strong interfacial linkages. e is adopted from Ref^808,811.

Strong physical crosslinks including crystalline domains, glassy nodules, and high-density physical bonds such as hydrogen bonds can also strongly adhere tough hydrogels on substrates (Figure 18b)^{71,745,793–801}. Since the crystalline domains and glassy nodules usually act as high-functionality crosslinks, each of them may anchor multiple polymer chains on the substrate, further enhancing the intrinsic interfacial toughness ${\text{Γ}}_0^{\text{inter}}$.

Connector polymers^788,802 have been employed to strongly bond elastomers and hydrogels on substrates (Figure 18c). In this case, the substrates usually take the form of polymer networks (i.e., elastomers and hydrogels) as well. To provide strong interfacial linkages, the connector polymers can form covalent crosslinks^775,803, interlocked loops^{780,781,793,797,804}, and/or strong physical bonds⁷⁸¹ with the polymer networks of both the hydrogels and the substrates. Specifically, strong physical interactions can be crystalline domains, glassy nodules, and/or high-density weak physical crosslinks⁷⁸¹. The connector polymers can be polymerized from monomers across the interface of the two polymer networks^780,794,803 or can be directly added on the interface to diffuse into the two polymer networks⁷⁸¹.

Mechanical interlocks between tough hydrogels and substrates usually occur at length scales from micrometers to millimeters (Figure 18d). One commonly-used method is to impinge precursor solutions of tough hydrogels into porous substrates and then form tough hydrogels that are mechanically interlocked with the substrates⁷⁸². Similarly, the surfaces of the substrates can be roughened or patterned to enhance the strength of mechanical interlocks with tough hydrogels^783,805,806. As a special yet interesting case, hydrogels have been fabricated into dried microneedles, which can pierce into a soft substrate such as biological tissues and then swell to form mechanical interlocks⁸⁰⁷.

Inspired by the adhesive proteins found in mussels, catechol chemistry has been widely adopted to achieve various types of interfacial linkages between hydrogels and substrates (Figure 18e)^563,779. Catechol can form both covalent and physical crosslinks with various functional groups (Figure 18e). Upon oxidation to quinone, catechol can form a covalent bond with nucleophiles (e.g, amine and thiol) via Michael addition as well as a strong coordination complex with metal oxides⁸⁰⁸. The hydroxyl groups of catechol can form electrostatic interaction with metal oxides as well as hydrogen bonds with hydrophilic substrates. The benzene ring of catechol can further form cation- π interaction with positively charged functional groups, π-π stacking with benzene functional groups, and hydrophobic interaction with hydrophobic functional groups on substrates^779,808. While catechol chemistry has been widely utilized for adhesion of hydrogels to various substrates, the interfacial toughness of the adhesion achieved only by catechol-based interfacial linkages is not high⁸⁰⁹, highlighting the importance of tough dissipative hydrogel matrices on top of the interfacial linkages to achieve tough adhesion⁸¹⁰.

5.5. Fatigue-resistant: Pin fatigue cracks by intrinsically high-energy phases

Fatigue threshold.

The word “fatigue” has been used to describe many symptoms observed in materials under prolonged loads, including materials with or without precut cracks under prolonged static or cyclic loads^812,813. In this section, we will focus on the fatigue fracture of hydrogels with precut cracks under cyclic loads (Figure 19a), because this is one of the most common failure modes of hydrogels used in mechanically dynamic environments such as artificial cartilages⁸¹⁴ and soft robots²⁶. Fatigue threshold has been commonly used to characterize a material’s resistance to fatigue crack propagation under cyclic loads. The fatigue threshold is defined as the minimal fracture energy at which fatigue crack propagation occurs under infinite cycles of loads^48,49. Quantitatively, the fatigue threshold ${\text{Γ}}_{FT}$ can be expressed as,

$${\text{Γ}}_{FT}=G_c(dc/dN=0)$$ (30)

where G is the energy release rate to drive crack propagation under each cycle of load, G_c is the minimal energy release rate at which crack propagation occurs under infinite cycles of loads,c is the length of the crack, N is the cycle number of the applied load, and dc /dN gives the crack extension per cycle.

Figure 19. Design principle for fatigue-resistant hydrogels – pin cracks by intrinsically high-energy phases.

a. definition of fatigue threshold and the pure-shear method to measure fatigue threshold. G is the energy release rate, c is the crack length, and N is the cycle number. The fatigue threshold ${\text{Γ}}_{FT}$ is determined by intersecting the curve of dc / dN vs G with the G axis. b. dissipation mechanisms such as reversible crosslinks in tough hydrogels are depleted over cyclic loads, not contributing to the fatigue threshold. c. fatigue crack is pinned by intrinsically high-energy phases in fatigue-resistant hydrogels⁶⁸. b and c are adopted from Ref⁶⁸.

The fatigue threshold of soft materials such as elastomers and hydrogels have been measured with various experimental methods such as the pure-shear fatigue-fracture test and the single-notch fatigue-fracture test⁶⁸. For example, in the pure-shear fatigue-fracture test, two identical pieces of a hydrogel are fabricated with the same thickness T, width W and height H, where W >> H >> T (Figure 19a). Both pieces of samples are clamped along their long edges (i.e., along the width direction) with rigid plates. The first sample is repeatedly pulled to a stretch of ${\lambda }_{applied}$ times of its undeformed height to measure the nominal stress s - stretch λ relation, and the corresponding energy release rate can be calculated as $G=H{\int }_1^{{\lambda }_{applied}}sd\lambda$, which is a function of the cyclic number N (Figure 19a). Thereafter, a notch with a length of ~0.5W is introduced into the second sample, which is then repeatedly pulled to the same stretch ${\lambda }_{applied}$ to measure the crack length c as a function of the cyclic number N. The pure-shear fatigue-fracture tests are repeated for different values of the applied stretch ${\lambda }_{applied}$ (i.e., energy release rate G), and a curve of dc / dN vs. G can be obtained (Figure 19a). The fatigue threshold ${\text{Γ}}_{FT}$ is then determined by intersecting the curve of dc / dN vs. G with the G axis (i.e., when dc / dN= 0). Notably, the fatigue fracture tests of hydrogels are commonly carried out in aqueous environments to avoid dehydration of the hydrogels under prolonged loads^68,69. For further discussion on the theory and experiments for the fatigue of hydrogels, a comprehensive review paper on this topic is recommended⁸¹³.

Design principle.

As discussed in Section 5.1, a hydrogel can be designed tough by building mechanical dissipation into stretchy polymer networks⁶⁰. The mechanical dissipation in the process zone around the crack tip can dramatically enhance the fracture toughness of the hydrogel (by ${\text{Γ}}_D$ in Eq. 21). However, the mechanisms for irreversible dissipation such as fracturing polymer chains in the process zone are usually depleted under cyclic loads. The mechanisms for reversible dissipation such as reversible crosslinks, once depleted, usually cannot recover in time to resist fatigue crack propagation in future cycles of loads (Figure 19b)^48,49,815. Consequently, the fatigue threshold of hydrogels and rubbers is their intrinsic fracture energy^48,49,815,

$${\text{Γ}}_{FT}={\text{Γ}}_0$$ (31)

Therefore, it is clear that the design of fatigue-resistant hydrogels generally cannot rely on mechanical dissipation in the bulk hydrogel matrices.

The design principle for fatigue-resistant hydrogels is to make the fatigue crack encounter and fracture objects with energies per unit area much higher than that for fracturing a single layer of polymer chains, or in short, to pin fatigue crack by intrinsically high-energy phases (Figure 19c)⁶⁸. The intrinsically high-energy phases that have been exploited for the design of fatigue-resistant hydrogels include nanocrystalline domains (Figure 20a)⁶⁸, nano-/micro-fibers (Figure 20b)⁶⁹, microphase separations (Figure 20c)^813,816, and macroscale composites (Figure 20d)⁷⁰. In addition, because the design of fatigue-resistant hydrogels does not rely on mechanical dissipation in the bulk hydrogels, fatigue-resistant hydrogels usually also demonstrate low hysteresis ratio H and high resilience R (Eq. 23)^68,69,817. Notably, biological hydrogels such as muscles, tendons and ligaments commonly possess intrinsically high-energy phases such as nano/micro-fibers, usually arranged in hierarchical architectures, to achieve a high fatigue threshold (Figure 2).

Figure 20. Implementation of the design principle for fatigue-resistant hydrogels – pin cracks by intrinsically high-energy phases.

Fatigue cracks can be pinned by intrinsically high-energy phases including a. nano-crystalline domains⁶⁸, b. nano-/micro-fibers⁶⁹, c. micro-phase separations⁸¹⁶, d. macro-fibers⁷⁰. e. Molecular dynamic simulation of the energy for pulling a polymer chain out of a PVA nano-crystalline domain and for fracturing the same polymer chain⁷¹. d is the displacement of one end of the polymer chain, and U is the energy required to achieve the displacement. f. confocal microscope image of a crack pinned by nano-fibers in a nano-fibrous PVA hydrogel, and g. measurement of the fatigue threshold of the nano-fibrous PVA hydrogel⁶⁹. G is the energy release rate, c is the crack length, and N is the cycle number. a is adopted from Ref⁶⁸, b is adopted from Ref⁶⁹, c is adopted from Ref⁸¹⁶, d is adopted from Ref⁷⁰, e is adopted from Ref⁷¹, f and g are adopted from Ref⁶⁹.

Implementation.

The design principle for fatigue-resistant hydrogels has been implemented with the UPNs that possess intrinsically high-energy phases^{68–70,813,816}. In order to effectively pin fatigue cracks, the density of the intrinsically high-energy phases in the UPNs should be sufficiently high⁶⁸.

High-functionality crosslinks such as crystalline domains can effectively play the role of intrinsically high-energy phases in the UPNs (Figure 20a). The energy required to pull out a polymer chain from a crystalline domain can be multiple times of that to fracture the same polymer chain, and the energy required to mechanically damage the crystalline domains can be multiple times of that to fracture the corresponding amorphous polymer chains (Figure 20e)⁷¹. Consequently, it has been shown that enhancing the crystallinity of a PVA hydrogel from 0.2 wt. % to 18.9 wt. % by dry-annealing can increase its fatigue threshold from 10 Jm⁻² to 1,000 Jm⁻², reaching the level of fatigue-resistant biological hydrogels such as cartilages for the first time⁶⁸. Since the size of the crystalline domains in the PVA hydrogel has been measured to be a few nanometers, it is the nano-crystalline domains that play the role of intrinsically high-energy phases here (Figure 20a). It is expected other UPNs with sufficiently high densities of high-functionality crosslinks such as crystalline domains and glassy nodules can also implement the design principle for fatigue-resistant hydrogels. It should be further noted that hydrogels with high densities of rigid crystalline domains and glassy nodules can be much stiffer than common hydrogels⁶⁸, and such high stiffness may be undesirable for many applications of hydrogels.

Nano-/micro-fibers can also act as intrinsically high-energy phases in the UPNs to implement the design principle for fatigue-resistant hydrogels (Figure 20b). The energy required to fracture a nano/micro-fiber can be much higher than that to fracture the corresponding amorphous polymer chains, because of the synergistic elongation and stiffening of bundled polymer chains in the fiber⁶⁹. Based on this implementation strategy, it has been shown that introducing nano-fibers into a PVA hydrogel by freeze-thawing the hydrogel can enhance its fatigue threshold from 10 Jm⁻² to 310 Jm^-2. In particular, if the nanofibers are aligned perpendicular to the fatigue crack by pre-stretching the hydrogel, the measured fatigue threshold further increases to 1,250 Jm⁻² (Figures 20f and g) ⁶⁹. In addition, because the nano-fibers can be made compliant, stretchable and strong by using a low density of nano-crystalline domains to bundle polymer chains (Figure 14b), the resultant nano-fibrous hydrogel integrates high compliance, stretchability and strength together with high fatigue threshold – mimicking the combinational mechanical properties of biological muscles⁶⁹.

Phase separations in hydrogels can also enhance the fatigue threshold of the hydrogels^813,816, possibly because the energy required to fracture the separated phases is higher than that to fracture the corresponding amorphous polymer chains. The UPN interactions including reversible covalent bonds and weak physical crosslinks play critical roles in inducing the phase separations in the hydrogels^813,816.

On a structural level, macroscale resilient elastomer fibers have been embedded in a resilient hydrogel to form a macroscale composite⁷⁰. Since it requires much higher energy to fracture the elastomer fibers than a layer of amorphous polymer chains, a fatigue threshold over 1,000 Jm⁻² has been achieved for the macroscale composite⁷⁰.

5.6. Fatigue-resistant adhesion: Strongly bond intrinsically high-energy phases on interfaces

Interfacial fatigue threshold.

The interfaces of adhered materials can suffer from fatigue failure under prolonged loads, including interfaces with or without precut cracks under prolonged static or cyclic loads. In this section, we will focus on the fatigue fracture of hydrogels adhering to substrates with precut cracks on their interfaces under cyclic loads (Figure 21a). Depending on whether the fatigue crack propagates along the interface or tilts into the hydrogel under cyclic loads, the failure mode is called adhesive failure or cohesive failure, respectively (Figure 21a)⁷¹. Interfacial fatigue threshold has been commonly used to characterize the capability of adhered materials to resist interfacial fatigue crack propagation following either failure mode under cyclic loads. The interfacial fatigue threshold is defined as the minimal fracture energy at which interfacial crack propagation occurs under infinite cycles of loads^71,818–820. Similar to the fatigue threshold, the interfacial fatigue threshold ${\text{Γ}}_{FT}^{\text{inter}}$ can be expressed as,

$${\text{Γ}}_{FT}^{\text{inter}}=G_c(dc/dN=0)$$ (32)

where G is the energy release rate to drive interfacial crack propagation under each cycle of load, G_c is the minimal energy release rate at which interfacial crack propagation occurs under infinite cycles of loads, c is the length of the crack, N is the cycle number of the applied load, and dc / dNgives the crack extension per cycle.

Figure 21. Design principle for fatigue-resistant adhesion of hydrogels – strongly bond intrinsically high-energy phases on interfaces:

a. definition of interfacial fatigue threshold and the 90-degree cyclic peeling test to measure the interfacial fatigue threshold. F is the applied peeling force, W is the width of the sample, G is the energy release rate, c is the crack length, and N is the cycle number. The interfacial fatigue threshold ${\text{Γ}}_{FT}^{\text{inter}}$ is determined by intersecting the curve of dc / dN vs G with the G axis. b. fatigue-crack propagation along the interface giving adhesive failure. c. fatigue-crack propagation in the hydrogel giving cohesive failure. d. fatigue-crack pinned by intrinsically high-energy phases on the interface and in the bulk hydrogel⁷¹. d is adopted from Ref⁷¹.

The interfacial fatigue threshold of soft materials such as elastomers and hydrogels has been measured with many experimental methods such as the cyclic 90-degree peeling test, the cyclic T-peeling test and the cyclic lap-shear test^71,818–820. For example, in the cyclic 90-degree peeling test^71,818, a layer of a hydrogel with thickness T, width W and length L (L >> W >> T) is bonded on a substrate, and a notch is introduce on the interface along the length direction (Figure 21a). A force F is repeatedly applied on the detached part of the hydrogel, while maintaining the detached part vertical to the substrate (Figure 21a). The applied force F gives the energy release rate ${\text{Γ}}_{FT}^{\text{inter}}$, where W is the width of the hydrogel sheet. The interfacial crack length c is then measured as a function of the cyclic number N. The cyclic 90-degree peeling test are repeated for different values of the applied force F (i.e., energy release rate G), and a curve of dc / dN vs.G can be obtained (Figure 21a). The interfacial fatigue threshold ${\text{Γ}}_{FT}^{\text{inter}}$ is determined by intersecting the curve of dc / dN vs. G with the G axis (i.e., when dc / dN = 0). Notably, the interfacial fatigue fracture tests of hydrogels are commonly carried out in aqueous environments to avoid dehydration of the hydrogels under prolonged loads⁷¹.

Design principle.

As discussed in Section 5.4, tough adhesion of hydrogels on substrates relies on the integration of tough dissipative hydrogel matrices and strong interfacial linkages (Figure 17)⁴³. The strong interfacial linkages can hold the interfacial crack tip, while the mechanical dissipation in the process zone around the crack tip can dramatically enhance the interfacial toughness of the adhesion. However, similar to the situation in fatigue of hydrogels^48,49,815, because the mechanical dissipation in bulk hydrogel matrices is usually depleted or not timely accessible after cyclic loads, such dissipation generally cannot contribute to resisting interfacial fatigue crack propagation (Figures 21b and c)^71,820. Consequently, the interfacial fatigue threshold of hydrogels and elastomers is their intrinsic interfacial toughness^71,820,

$${\text{Γ}}_{FT}^{\text{inter}}={\text{Γ}}_0^{\text{inter}}$$ (33)

Therefore, the design of fatigue-resistant adhesion of hydrogels generally cannot rely on mechanical dissipation in the bulk hydrogel matrices.

Because interfacial cracks can tilt into bulk hydrogels and develop the cohesive failure mode (Figure 21c), the design of fatigue-resistant adhesion of hydrogels requires fatigue-resistant hydrogel matrices that possess sufficiently high densities of intrinsically high-energy phases⁶⁸. Notably, hydrogel matrices that are only tough but not fatigue-resistant are unsuitable for the design of fatigue-resistant adhesion, owing to the depletion of dissipation over cyclic loads. To further avoid the adhesive failure mode under cyclic loads (Figure 21b), fatigue cracks on the interfaces need to be pinned by intrinsically high-energy phases strongly bonded on the interfaces as well (Figure 21d).

Therefore, the design principle for fatigue-resistant adhesion of hydrogels, in short, is to strongly bond intrinsically high-energy phases on interfaces⁷¹. While the intrinsically high-energy phases that have been employed for the design of fatigue-resistant adhesion include nano-crystalline domains⁷¹ and exceptionally long polymer chains (in unfully swollen sate)⁸¹⁹, other candidates such as nano-/micro-fibers can be explored in the future. Not surprisingly, biological hydrogels including tendons, ligaments and cartilages all rely on strongly bonding crystalline domains and nano-/micro-fibers throughout their interfaces with bones to achieve fatigue-resistant adhesion⁷⁴⁵.

Implementation.

The design of fatigue-resistant hydrogels relies on achieving sufficiently high densities of intrinsically high-energy phases in the UPNs, as discussed in Section 5.6. In this section, we will focus on how to strongly bond intrinsically high-energy phases on substrates to implement the design principle for fatigue-resistant adhesion.

High-functionality crosslinks such as crystalline domains usually can play the role of intrinsically high-energy phases in the UPNs. Nano-crystalline domains in PVA hydrogels have been strongly bonded on diverse substrates including glass, ceramics, metals and elastomers via high-density hydrogen bonds (Figure 22a)⁷¹. The molecular dynamic simulation shows that the energy required to pull a polymer chain out of the interface is even higher than that to pull the same polymer chain out of the nano-crystalline domain, implying high intrinsic interfacial toughness of the adhesion ${\text{Γ}}_0^{\text{inter}}$ ⁷¹. As a result, the interfacial fatigue threshold of the PVA-substrate systems measured in phosphate-buffered saline reaches up to 800 Jm⁻², similar to those of tendon/ligament/cartilage-bone interfaces (Figures 22d and e). In addition, the failure mode of the PVA-substrate systems observed in the interfacial fatigue fracture tests follows the cohesive failure, indicating the critical role of intrinsically high-energy phases in the bulk hydrogels (i.e., fatigue-resistant hydrogels) for the design of fatigue-resistant adhesion⁷¹.

Figure 22. Implementation of the design principle for fatigue-resistant adhesion of hydrogels – strongly bond intrinsically high-energy phases on interfaces:

The intrinsically high-energy phases can be bonded on the substrates via a. high-density physical bonds such as hydrogen bonds⁷¹, b. covalent bonds, and c. mechanical interlocks. d. measurements of the fatigue thresholds of tough adhesion and fatigueresistant adhesion of hydrogels on substrates⁷¹. e. photos of interfacial crack propagation in a cyclic peeling test for tough adhesion (top) and fatigue-resistant adhesion (bottom) of hydrogels on substrates⁷¹. a, d and e are adopted from Ref⁷¹.

Covalent bonds are also expected to be able to strongly bond the intrinsically high-energy phases such as nano-crystalline domains and nano-/micro-fibers on substrates (Figure 22b). In addition, curing precursor solutions of fatigue-resistant hydrogels on porous, roughened or patterned substrates can lead to mechanical interlocks that may strongly bond intrinsically high-energy phases on the hydrogel-substrate interfaces (Figure 22c)⁸²¹.

5.7. Implementation with unconventional polymer networks

While the implementation of each design principle for the corresponding extreme property has been discussed in Sections 5.1–5.6, we will provide an overview of the design process and implementation strategy in this section.

Since the design principles discussed in Sections 5.1–5.6 are general and abstract, it is usually more intuitive to begin the design process with specific UPN architectures and/or UPN interactions than with a design principle. The commonly-used UPN architectures that can give extreme mechanical properties include interpenetrating polymer networks, semi-interpenetrating polymer networks, polymer networks with high-functionality crosslinks, and nano-/micro-fibrous polymer networks. The commonly-used UPN interactions that can give extreme mechanical properties include various types of strong physical crosslinks and weak reversible crosslinks. Let’s imagine that the selected UPN is subjected to the relevant modes of mechanical loads such as tension, compression, shear, fracture, fatigue and/or peeling. If the selected UPN under mechanical loads seems to be able to implement the design principle for the desired property, one can proceed to select polymers and crosslinks such as those discussed in Section 2 and Section 4 for the design and fabrication of the hydrogel. Furthermore, it may be difficult to initiate the design process by considering both UPN architectures and UPN interactions simultaneously; in this case, we can first test whether a UPN architecture will likely implement the design principle, and then further add UPN interactions into the UPN architecture to facilitate the implementation. For example, in order to design a fatigue-resistant hydrogel, we can begin with a polymer network with high-functionality crosslinks, because a sufficiently high density of high-functionality crosslinks can act as intrinsically high-energy phases to pin fatigue cracks. Furthermore, strong physical crosslinks such as crystalline domains and glassy nodules can be added into the polymer network as the intrinsically high-energy phases to facilitate the implementation of the design principle. Indeed, dry-annealed PVA with high densities of nano-crystalline domains has been selected to implement the design principle of fatigue-resistant hydrogels⁶⁸.

Alternative design and implementation strategy are through the mimicry of the UPNs of biological hydrogels that possess the extreme mechanical properties to be designed for synthetic hydrogels (Figure 2). Because biological hydrogels have exploited various types of UPNs to implement the design principles discussed in Sections 5.1–5.6, we can simply begin the design process by replicating biological hydrogels’ UPNs (Figure 2). Notably, the biological UPNs, commonly featuring hierarchical and gradient structures (Figure 2), can be more complex than the UPNs discussed in Section 4; therefore, we should only mimic the essential characteristics of the biological UPNs that enable the desired mechanical properties. As an example, tendons, ligaments and cartilages all feature fatigue-resistant adhesion on bones, owing to nano/micro-fibers and nano-crystalline domains strongly anchored on the interfaces (Figure 2). Such fatigueresistant adhesion of PVA hydrogels on diverse solid substrates have been recently achieved by strongly anchoring nano-crystalline domains in PVA hydrogels on the substrates via densely-distributed hydrogen bonds (Figures 22d and e)⁷¹.

6. Design of hydrogels with extreme physical properties

In addition to the extreme mechanical properties discussed in Section 5, the design of hydrogels that possess extreme physical properties has attracted escalating research interests in recent years. Examples of hydrogels’ extreme physical properties under development and exploration include high electrical conductivity⁶²⁷, patterned magnetization⁸²², high refractive index and transparency^823,824, tunable acoustic impedance⁸²⁵, and self-healing⁸²⁶. Unlike the extreme mechanical properties discussed in Section 5, many of the extreme physical properties do not have embodiments in biological hydrogels. Nevertheless, these extreme physical properties can be of similar importance as the extreme mechanical properties to hydrogels’ various applications, especially to the nascent applications of hydrogel machines²⁰. In this section, we will briefly discuss the design principles and implementation strategies for hydrogels to possess these extreme physical properties, while bearing in mind that many works in this field are still in the initial stage of developments.

6.1. Electrically conductive: Percolate electrically conductive phases

Electrical conductivity is critical for hydrogels’ nascent applications such as bioelectrodes for stimulation and recording of neural activities in bioelectronics⁶²⁷ and electrodes for supercapacitors and batteries in energy storage^20,827. However, the electrical conductivity of common hydrogels is less than a few Siemens per meter, on the same level as that of water or saline water⁶²⁷. Compared to metals, carbon and conducting polymers, common hydrogels are usually deemed to be electrically nonconductive.

The design principle for electrically conductive hydrogels is to embed electrically conductive phases such as liquid metals, metallic nanowires, carbon nanotube, graphene and conducting polymers in hydrogel matrices and make the conductive phases form percolated networks, or in short, to percolate electrically conductive phases (Figure 23a)^627,828,829. In particular, conductive hydrogels based on conducting polymers have attracted great interests recently, owing to their unique polymeric nature as well as favorable electrical and mechanical properties, stability, and biocompatibility^{29,30,480,624,830–833}. For example, poly(3,4-ethylenedioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) has been made into pure conducting polymer hydrogels that achieve high electrical conductivity over a few thousand Siemens per meter and superior biocompatibility (Figure 23c)^29,30,624. In addition to electrically conductive hydrogels, ionically conductive hydrogels have also been intensively developed as stretchable and transparent ionic conductors for various applications (Figure 23b)²⁷. The conductive phases in ionically conductive hydrogels are usually high concentrations of salt ions. For a further detailed discussion on various types of conductive hydrogels, a recent review paper is recommended⁶²⁷.

Figure 23. Design of hydrogels with high electrical conductivity – percolate electrically conductive phases.

a. hydrogels with percolated electrically conductive fillers. b. hydrogels with ionically conductive salt solvents. c. hydrogels based on conducting polymers. The bottom panel of a is adopted from Ref⁸²⁹. The bottom panel of b is adopted from Ref²⁷. The bottom panels of c are adopted from Ref⁸³⁴ (left) and Ref²⁹ (right).

6.2. Magnetized: Embed magnetic particles and pattern ferromagnetic domains

Soft materials such as elastomers and hydrogels with ferromagnetic domains or magnetization have been intensively developed and explored for biomedical applications such as drug delivery and minimally invasive surgery^{28,822,835–839}, owing to their mechanical compliance, potential biocompatibility, and capability of fast deformation under applied magnetic fields. Common hydrogels are usually diamagnetic and do not contain ferromagnetic domains, possessing similar magnetic properties as water. Therefore, subjected to applied magnetic fields, common hydrogels cannot be actuated to deform, exert forces, or release substances.

The design principle for hydrogels to possess patterned magnetization is to embed magnetic components such as hard-magnetic, soft-magnetic and super-paramagnetic particles in the hydrogels matrices where ferromagnetic domains may be further patterned, or in short, to embed magnetic particles and pattern ferromagnetic domains (Figure 24) ^{822,835–839}. In particular, hard-magnetic particles such as neodymium iron boron (NdFeB) particles after magnetic saturation can retain their magnetization under actuation magnetic fields, because of the high coercivity of the hard-magnetic particles (Figure 24a). Therefore, patterned ferromagnetic domains can be programmed into elastomers and hydrogels embedded with hard-magnetic particles. Subjected to actuation magnetic fields, the elastomers and hydrogels with the patterned ferromagnetic domains can quickly transform among various shapes ^835–839. Recently, 3D printing has been further exploited as an effective method to program complex 3D shapes as well as domain patterns in ferromagnetic elastomers and hydrogels (e.g., Figures 24b and c)^836,839. It should be noted that magnetic particles can be corrosive in the aqueous environments of hydrogel matrices. To enhance their chemical stability in hydrogel matrices, the magnetic particles have been coated with protective layers such as silica layers (Figures 24b and c)⁸³⁵.

Figure 24. Design of hydrogels and elastomers with patterned magnetization – embed magnetic particles and pattern ferromagnetic domains.

a. typical relations of applied magnetic field H and magnetization M for paramagnetic, soft-magnetic, and hard-magnetic materials. M_r and H_c are the residual magnetization and coercivity of the hard-magnetic material, respectively. b. hard-magnetic particles can be embedded into an elastomer/hydrogel matrix, in which ferromagnetic domains can be patterned by 3D printing. c. Photos of the resultant magnetic soft material before and after magnetic actuation. a is adopted from Ref⁸⁴⁰. b and c are adopted from Ref⁸⁴¹.

6.3. High reflective index and transparency: Uniformly embed high-refractive-index non-scattering nano-phases.

Various optical applications of hydrogels such as ophthalmic lenses^21,364,842 and optical fibers^33,843 require high refractive indices and high transparency of the hydrogels (Figure 25a). The refractive indices of common hydrogels are around 1.333, similar to that of water. One general strategy to enhance the refractive indices of hydrogels is to uniformly embed nano-phases such as nano-particles^823,824 and nano-crystalline domains with high refractive indices in the hydrogel matrices. However, the refractive-index mismatch between the nano-phases and hydrogel matrices may lead to substantial undesirable light scattering, reducing the transparency of the hydrogels (Figure 25b). It has been found that decreasing the size of the nano-phases below one-tenth of the light wavelength (e.g., zinc sulfide nanoparticles with 3 nm diameter) can effectively diminish light scattering to achieve hydrogels with a high refractive index (i.e., 1.49) and high transparency (Figures 25b–d)⁸²³. Overall, the design principle for hydrogels with high refractive indices and transparency is to uniformly embed high-refractive-index non-scattering nano-phases in hydrogel matrices.

Figure 25. Design of hydrogels with high reflective indices and transparency – uniformly embed high-refractive-index non-scattering nano-phases.

a. high contrast between reflective indices of the hydrogel fiber ${\eta }_{HF}$ and tissue fluid ${\eta }_{TF}$ can give minimal light leakage. b. uniformly embedding nano-phases such as nano-particles with high refractive indices in the hydrogel matrices can enhance the refractive index of the hydrogel. The size of the nano-phases d_NC should be much smaller than the light wavelength λ for minimal scattering and high transparency. c. hydrogels with high reflective indices and transparency can be used as optical fibers in living tissues. d. photo of a hydrogel optical fiber⁸⁴³. d is adopted from Ref⁸⁴³.

6.4. Tunable acoustic impedance: Tune densities and bulk moduli of effectively homogeneous hydrogels

Hydrogels have been widely used as the media for sound-wave transmissions such as the coupling agents for imaging and therapeutic ultrasounds. It is highly desirable to design hydrogels that possess tunable acoustic impedance to match the impedance of different materials or varying environments^26,825. The acoustic impedance Z of a homogenous material can be expressed as

$$Z=\sqrt{{\rho }_{eff}{K}_{eff}}$$ (34)

where ${\rho }_{eff}$ and $K_{eff}$ are the effective density and bulk modulus of the material, respectively. Because the density and bulk modulus of common hydrogels are almost the same as those of water, the acoustic impedance of common hydrogels also approximates that of water. To achieve tunable acoustic impedance, fluidic channels have been patterned into tough hydrogel matrices recently (Figure 26a)⁸²⁵. By infusing the air, water or liquid metal (i.e., eutectic gallium-indium) into the fluidic channels, the effective density, bulk modulus and thus acoustic impedance of the hydrogel can be dramatically varied to approximate the acoustic impedance of air, water and many solids on demand (Figure 26b) ⁸²⁵. In order to approximate a homogeneous material, the fluidic channels should be uniformly distributed in the hydrogel and the characteristic sizes of the fluidic channels (i.e., channel diameter and distance between adjacent channels) should be much smaller than the acoustic wavelengths. Overall, a generic design principle for hydrogels with tunable acoustic impedance is to tune densities and bulk moduli of effectively homogeneous hydrogels.

Figure 26. Design of hydrogels with tunable acoustic impedance – tune densities and bulk moduli of effectively homogeneous hydrogels.

a. by infusing air, water or liquid metal (i.e., eutectic gallium-indium) into the fluidic channels inside a hydrogel matrix, the effective density, bulk modulus and thus acoustic impedance of the hydrogel can be dramatically varied. b. the hydrogel can approximate the acoustic impedance of air, water and many solids on demand⁸²⁵. a and b are adopted from Ref⁸²⁵.

6.5. Self-healing: Form crosslinks and/or polymers at damaged regions

A salient feature of many biological hydrogels is their capability of healing after injury. The capability of self-healing can potentially bestow synthetic hydrogels with the merits such as damage mitigation and long-term robustness. However, the healing processes in biological hydrogels mostly rely on the functions of biological cells, which do not exist in synthetic hydrogels. In absence of living components, a generic strategy to achieve self-healing in engineering materials is to form new materials and/or interactions in the vicinity of damaged regions in the materials⁸⁴⁴.

Specifically for soft materials such as elastomers and hydrogels, the new materials formed in the vicinity of damaged regions are usually new crosslinks and/or polymer chains. Therefore, the design principle for self-healing hydrogels is to form new crosslinks and/or polymers at damaged regions (Figure 27a). The commonly-used crosslinks for self-healing of hydrogels include weak physical crosslinks such as hydrogen bonds^{738,753,755,845}, ionic bonds^288,481,846, metal coordination^288,755,832, hydrophobic interactions⁸⁴⁷ and guest-host interactions⁷⁴⁰; and dynamic covalent bonds such as olefin metathesis^848,849. Once two newly-formed surfaces in a damaged hydrogel are brought into contact with each other under certain conditions such as specific temperature and pH, new crosslinks can form on the interface, endowing the hydrogel with the self-healing capability (Figure 27c). Besides reversible crosslinks, the crack healing of hydrogels can be achieved through interdiffusion of polymer chains to form entangled chains that span the crack surfaces^850,851. Furthermore, some self-healing processes in hydrogels involve both mechanisms of chain entanglement and reversible crosslinking⁸⁵². When the surfaces of two intact self-healing hydrogels are in contact, new interfaces can also be formed in between to adhere the two hydrogels together. Therefore, strictly speaking, most of the existing self-healing hydrogels are self-adhesive hydrogels, because the damage of the hydrogels is not required to induce the process of self-healing. Recently, Matsuda et al. have reported a self-growing or self-reinforcing hydrogel, in which the scission of polymer chains can induce mechanoradicals that trigger the polymerization of monomers in the solvent of the hydrogel (Figure 27b)⁸⁵³. Consequently, the hydrogel self-grows or self-reinforces after moderate damage, analogous to mechanical training of a muscle (Figure 27d). This strategy may be adopted for the future design of truly self-healing (instead of self-adhesive) hydrogels where the healing is triggered by the damage. For a further detailed discussion on various types of self-healing hydrogels, a recent review paper is recommended⁸²⁶.

Figure 27. Design of self-healing hydrogels – form crosslinks and/or polymers at damaged regions.

a. reversible crosslinks form on the interfaces between two pieces of hydrogels for self-healing or selfadhesion. b. damage of a hydrogel induces new polymerization and crosslinking, giving self-reinforcement or self-growth⁸⁵³. c. photos of a self-healing hydrogel based on oppositely charged polyelectrolytes^481,854. d. photos of a self-reinforcing or self-growing hydrogel⁸⁵³. b and d are adopted from Ref⁸⁵³. c is adopted from Ref⁸⁵⁴.

6.6. Implementation with unconventional polymer networks

While the implementation of design principles for hydrogels with extreme mechanical properties exploits various types of UPNs as discussed in Section 5, it seems hydrogels with extreme physical properties mainly reply on one implementation strategy: functional nano-/micro-/macro-fillers. The functional fillers range from percolated conductive phases for high electrical conductivity, to magnetic particles for magnetization, to high-refractive-index non-scattering nano-phases for high refractive index and transparency, to fillers with tunable densities and bulk moduli for tunable acoustic impedance, and to reversible crosslinks and polymerization triggered by damages for self-leading capability.

7. Design of hydrogels with multiple combined properties

In addition to the extreme mechanical and physical properties discussed in Sections 5 and 6, respectively, chemical and biological properties of hydrogels also play critical roles in various applications of hydrogels. In fact, many nascent applications of hydrogels such as hydrogel living devices commonly require that a set of combined mechanical, physical, chemical and biological properties simultaneously coexist in hydrogels^20,24,849. In order to achieve multiple combined properties, we will propose a general strategy for the orthogonal design of hydrogels guided by the corresponding design principles, which will then be implemented with UPNs in a synergistic manner.

7.1. Orthogonal design principles

In Sections 5 and 6, we have discussed the design principles for hydrogels to achieve a variety of extreme mechanical and physical properties, which are summarized as the following.

• Tough: build dissipation into stretchy polymer networks.

• Strong: synchronize chain stiffening and fracture.

• Resilient: delay dissipation.

• Tough adhesion: integrate tough dissipative hydrogels and strong interfacial linkages.

• Fatigue-resistant: pin fatigue cracks with intrinsically high-energy phases.

• Fatigue-resistant adhesion: strongly bond intrinsically high-energy phases on interfaces.

• Electrically conductive: percolate electrically conductive phases.

• Magnetization: embed magnetic particles and pattern ferromagnetic domains.

• High reflective index and transparency: uniformly embed high-refractive-index non-scattering nano-phases.

• Tunable acoustic impedance: tune densities and bulk moduli of effectively homogeneous hydrogels.

• Self-healing: form crosslinks and/or polymers at damaged regions.

Since the abovementioned design principles are general and material-independent, they have been widely deployed for the design of biological hydrogels, synthetic hydrogels, and other engineering materials. In addition, based on the discussions in Sections 5 and 6, these design principles do not contradict or exclude one other in general. For example, the seeming contradiction between high toughness and high resilience of hydrogels has been reconciled by the design principles of building dissipation into stretchy polymer networks and delaying dissipation, respectively. Therefore, the design of multiple combined mechanical and physical properties of hydrogels can potentially follow the corresponding design principles in an orthogonal and independent manner as illustrated in Figure 28a. For example, a tough, electrically conductive, and self-healing hydrogel can be potentially designed by following the orthogonal design principles of building dissipation into stretchy polymer networks, percolating electrically conductive phases, and forming crosslinks and/or polymers at damaged regions, respectively³⁰ (Figure 28b). The hydrogel can further form tough adhesion on substrates by following the design principle of integrating tough hydrogels and strong interfacial linkages⁸³¹.

Figure 28. Orthogonal design principles and synergistic implementation strategies for the design of hydrogels with multiple combined properties.

a. schematics of the orthogonal design principles and synergistic implementation strategies. b. example of the design of a tough, self-healing and electrically conductive hydrogel.

In addition, although chemical and biological properties of hydrogels are beyond the scope of the current review, it is expected that the design of hydrogels’ chemical and biological properties will likely follow a set of design principles that are orthogonal with one another and with the design principles for mechanical and physical properties as well. Consequently, a set of orthogonal design principles will potentially guide the rational design of future hydrogels that possess multiple combined mechanical, physical, chemical and biological properties (Figure 28).

7.2. Synergistic implementation strategy

The orthogonal design principles for hydrogels to achieve multiple combined properties will be implemented with UPNs in a synergistic manner, meaning that one type of UPN can implement multiple design principles. As discussed in Section 4, the commonly-used UPNs include the UPN architectures:

• Ideal polymer networks

• Polymer networks with slidable crosslinks

• Interpenetrating and semi-interpenetrating polymer networks

• Polymer networks with high-functionality crosslinks

• Nano-/micro-fibrous polymer networks

and the UPN interactions:

• Strong physical crosslinks

• Weak physical crosslinks

• Dynamic covalent crosslinks.

Each UPN architecture or interaction usually can implement (or facilitate the implementation of) multiple design principles. For example, the nano-/micro-fibrous polymer networks can integrate high stretchability and mechanical dissipation (Section 5.1), delay dissipation (Section 5.3), synchronize stiffening and fracture of polymer chains (Section 5.2), and act as intrinsically high-energy phases (Section 5.5) to implement the design principles for tough, resilient, strong, and fatigue-resistant hydrogels, respectively. By strongly bonding the nano-/micro-fibers on substrates (Section 5.4 and Section 5.6), the corresponding nano-/micro-fibrous polymer networks can achieve tough and fatigue-resistant adhesion as well. Furthermore, the nano-/micro-fibers can also be made functional such as electrically conductive or high reflective index (Section 6.1) to implement the design of extreme physical properties. Not surprisingly, biological hydrogels indeed frequently employ nano-/micro-fibrous polymer networks, supplemented by other UPN architectures and interactions, to achieve multiple combined extreme mechanical and physical properties necessary for their robustness and well-being over the lifetime (Figure 2).

Last but not least, it should be emphasized that the design principles and implementation strategies for hydrogels discussed in this paper are based on generic polymer networks; therefore, they should be applicable to other soft materials comprised of polymer networks including elastomers and organogels as well. For example, the design principle and implementation strategy for tough hydrogels have been used to design tough elastomers⁷²⁵. We expect the current review will provide a solid foundation for rational design of various types of polymeric soft materials such as hydrogels, elastomers and organogels to achieve multiple combined extreme properties for diverse applications. Furthermore, we hope the current review will provoke interdisciplinary discussions on a fundamental question: why does nature select soft materials, especially hydrogels embodied in unconventional polymer networks (Figures 1 and 2), to constitute the major parts of animal bodies?

Table 1.

Examples of unconventional polymer network architectures.

UPN architectures	Examples	References
Ideal polymer networks	Covalently-crosslinked 4-arm end-functionalized PEG; Reversibly-crosslinked 4-arm end-functionalized PEG	67,317,356,435–450.
Polymer networks with slidable crosslinks	PEG with polyrotaxanes as slidable crosslinks; PCL with polyrotaxanes as slidable crosslinks; PPO with polyrotaxanes as slidable crosslinks	60,356,451,454–458,460–465
Interpenetrating polymer networks	Covalently-crosslinked PAMPS interpenetrated with covalently-crosslinked PAAm; Covalently-crosslinked polysaccharide interpenetrated with covalently-crosslinked PHEMA, PEG, PAAm, PNIPAm, and PDMA	60,63,356,383,467–470,476
Semi-interpenetrating polymer networks	Covalently-crosslinked PAAm interpenetrated with reversibly-crosslinked or uncrosslinked PVA, alginate, chitosan, and hyaluronan; Covalently-crosslinked gelatin interpenetrated with reversibly-crosslinked or uncrosslinked alginate; Covalently-crosslinked PEG-DA gelatin interpenetrated with reversibly-crosslinked or uncrosslinked alginate, chitosan, and hyaluronan; Covalently-crosslinked PAAm interpenetrated with reversibly-crosslinked or uncrosslinked PVA	60,63,356,383,466,468,469,475,477
Polymer networks with high-functionality crosslinks	PVA with crystalline domains as high-functionality crosslinks; Poly(methyl methacrylate) with glassy spheres as high-functionality crosslinks; Polyacrylamide with exfoliated particles as high-functionality crosslinks; Mixtures of polystyrene, poly(butyl acrylate), and poly(acrylic acid) with microsphere composites as high-functionality crosslinks	60,215,300,302,356,383,436,477,478,482,485,488–496
Nano-/microfibrous polymer networks	Cellulose, cellulose-derivative, collagen, gelatin, fibrin and elastin nano-/micro-fibrous networks	6,103,382,507–521
Other UPN architectures	Poly(dimethylsiloxane) bottlebrush; Poly(n-butyl acrylate) bottlebrush; Poly polylactic acid-b-polyethylene glycol-b-poly(N-isopropylacrylamide) triblock bottlebrush	522–524

Table 2.

Examples of unconventional polymer network interactions.

UPN interactions		Examples	References
Strong physical crosslinks	Crystalline domain	PVA treated by freeze-thawing or annealing	4,300,302,482
		Chitin and chitosan treated by acidic or basic solutions	215,218
		Cellulose treated by alkalines	497,526,527
	Glassy nodule	Polystyrene-b-poly(N-isopropylacrylamide)-bpolystyrene	530
		Poly(methyl methacrylate)-b-poly(n-butyl acrylate)	492
	Helical association	Self-assemble of agarose or gelatin	6,103,534,535
		Self-assemble of collagen or fibrinogen	6,103,532,533.
		Self-assemble of elastin-like polypeptides	507,510
Weak physical crosslinks	Hydrogen bond	PAA or polymethacrylic acid (PMA) with PEG	478,538–540
		PEG, PHEMA, PNIPAM with self-complementary hydrogen-bond groups (triazine moieties or ureido pyrinimidone moieties)	478,490,540–542
	Electrostatic interaction	Alginate with Ca2+, Ba2+, Mg2+, Zn2+	6,103,105,546
		Chitosan with tripolyphosphate, citrate ions	547–549
		Cationic polyelectrolytes with anionic polyelectrolytes	544,550
	Coordination complex	Bisphosphonate containing polymers with metal ions (Ca2+, Mg2+ or Ag+)	557,572,573
		Catechol containing polymers with metal ions (Cu2+, Zn2+ and Fe3+)	478,574–577,580 560,561,578
		Histidine containing polymers with metal ions (Cu2+, Co2+ and Ni2+)	478,579,58059
	Host-guest interaction	Polymers containing β-CD moieties with azobenzene group, adamantyl group, ferrocene group, t-butyl group, cyclohexyl(ester) group, cyclododecyl(amide) group, benzyl group, 2naphthylmethyl group, 1-pyrenylmethyl group	383,457,478,540,586,588–594
		Polymers containing α-CD moieties with n-butyl group, adamantyl group, benzyl group, trans- azobenzene group	383,478,540,586,587;
		Polymers containing curcubit[n]uril moieties with spermine, diaminohexane, viologens, naphtalenes	383,540,605,606.
	Hydrophobic association	PEG, PAAm, PNIPAM, PDMAA, PVA containing hydrophobic moieties (octylphenol-PEG acrylate, stearyl acrylate, lauryl acrylate)	478,488,490 488,612,613
		Triblock amphiphilic copolymers with PEG, PAAm, PVA, PHEMA middle blocks and n-alkyl acrylate end blocks	614–616
	π - π stacking	Polymers modified with aromatic moiety containing short peptides and N-terminal Fmoc- amino acids	499,620,621
		Hydrogels containing carbon nanotubes, polythiophene, and graphene-based nanomaterials	30,622–626
Dynamic covalent crosslinks	Imine bond	Polymers containing amine and aldehyde (or ketone) functional groups	383,631–635,637–641
	Boronate ester bond	Polymers containing boronic acid and diol functional groups	383,644,650,655,656,662
	Disulfide bond	Polymers containing disulfide functional groups	383,615,668,674,675,679
	Hydrazone bond	Polymers containing hydrazide and aldehyde (or ketone) functional groups	679,680,682–686,688–690
	Oxime bond	Polymers containing hydroxylamine and aldehyde (or ketone) functional groups	695–698,706
	Reversible Diels–Alder reaction	Polymers containing diene and dienophile functional groups	701,711,712

Acronym

APS

ammonium persulfate

CB[n]

cucurbit[n]uril

CD

cyclodextrin

CNT

carbon nanotubes

DOPA

3,4-dihydroxyphenyl-L-alanine

EDC

1-ethyl-3-(3-dimethylaminopropyl)carbodiimide

Fmoc

fluorenylmethyloxycarbonyl

G

α-L-guluronic acid

GO

graphene oxide

M

β-D-mannuronic

MBA

N,N’-Methylenebisacrylamide

NdFeB

neodymium iron boron

NHS

N-hydroxysuccinimide

NVP

N-vinylpyrrolidone

PAA

poly(acrylic acid)

PAAm

polyacrylamide

PCL

poly(caprolactone)

PDLLA

poly(DL-lactic acid)

PDMA

poly(N,N-Dimethylacrylamide)

PEDOT

PSS: poly(3,4-ethylenedioxythiophene):poly (styrene sulfonate)

PEG

poly(ethylene glycol)

PEO

poly(ethylene oxide)

PHEMA

poly(2-hydroxethyl methacrylate)

PLA

polylactide

PLGA

poly(DL-lactic acid-co-glycolic acid)

PMA

polymethacrylic acid

PNIPAm

poly(N-isopropylacrylamide)

PPG

poly(propylene glycol)

PPS

poly(propylene sulfide)

PVA

poly(vinyl alcohol)

RGD

Arg-Gly-Asp

TEGDMA

trimethylene glycol dimethacrylate

TEMED

N,N,N′N′-tetramethylene-diamine

UPN

unconventional polymer network

UPy

ureido-pyrimidinone