Design principles for strong and tough hydrogels
强韧水凝胶的设计原则

Xueyu Li Jian Ping Gong
李雪雨 建平宫

Sections 部分

Introduction 介绍

Model of basic hydrogel mechanics
基础水凝胶力学模型

Design strategies 设计策略

Conclusions and outlook 结论和展望

As a combination of crosslinked solid and liquid components, hydrogels are similar to soft tissues in the human body and are promising materials for uses such as scaffolds in tissue engineering , medical implants or wound dressings . Many applications require hydrogels to bear mechanical loads and to resist failure under static or cyclic loading conditions. The macroscopic failure of materials originates from the growth of small defects. The ability to resist defect growth - the toughness - is correlated to the fracture energy of materials, which is the energy required for crack growth per unit area . Typically, loadbearing biological tissues have a high toughness. For instance, typical fracture energies are for skeletal muscle, for cartilage and for tendons . However, conventional synthetic hydrogels, which are composed of a single non-uniform network of hydrophilic polymers, are in general very weak, with low fracture energy . This poor mechanical performance greatly limits the application of such hydrogels. In addition to the toughness, elastic modulus (stiffness), fracture strength (strength), fracture stretch ratio (deformability) and fatigue threshold are important mechanical parameters for applications. For a simple polymer network material, these mechanical properties are correlated and conflicting. Increases in elastic modulus and strength result in decreases in deformability, fracture energy and fatigue threshold. Moreover, as hydrogels are polymer networks swollen in water (solvent), these mechanical parameters are strongly related to the swelling ratio of the hydrogels. At the equilibrium swelling, the swelling ratio is determined by the balance of osmotic pressure and network elasticity . Therefore, designing and developing hydrogels with high toughness without sacrificing the modulus and strength is a challenge.
作为交联固体和液体组分的组合物，水凝胶类似于人体软组织，是组织工程支架、医用植入物或伤口敷料等用途的有前途的材料。许多应用需要水凝胶承受机械载荷并在静态或循环加载条件下抵抗破坏。材料的宏观破坏源于小缺陷的增长。抵抗缺陷增长的能力 - 韧性 - 与材料的断裂能量相关，即单位面积裂纹增长所需的能量。通常，承载载荷的生物组织具有较高的韧性。例如，骨骼肌的典型断裂能量为，软骨为，肌腱为。然而，由一种非均匀网络组成的传统合成水凝胶通常非常脆弱，具有较低的断裂能量。这种劣质的机械性能极大地限制了这类水凝胶的应用。 除了韧性外，弹性模量 （刚度）、断裂强度 （强度）、断裂延展率 （可变形性）和疲劳阈值 是应用中重要的机械参数。对于简单的聚合物网络材料，这些机械性能是相关且矛盾的。弹性模量和强度的增加导致可变形性、断裂能量和疲劳阈值的降低。此外，由于水凝胶是在水（溶剂）中膨胀的聚合物网络，这些机械参数与水凝胶的膨胀比 强相关。在平衡膨胀时，膨胀比由渗透压和网络弹性平衡决定 。因此，设计和开发具有高韧性的水凝胶而不牺牲模量和强度是一个挑战。

The poor mechanical performance of conventional hydrogels is attributed to several intrinsic features. One is the network inhomogeneity in polymer density distribution and polymer strand length between the crosslinking points. Thus, hydrogels are susceptible to stress concentration at loading, initiating cracks. Another is the rubber-like elasticity caused by a lack of energy dissipation mechanisms, resulting in low resistance against crack propagation. In addition, conventional hydrogels usually contain abundant water. The low amount of load-bearing solid phase further results in weak and fragile mechanical properties. Since the 2000s, the development of mechanically strong and tough hydrogels has led to important advances in the study of soft materials and our understanding of their failure mechanisms. The main strategies to improve the mechanical properties of hydrogels through their structural components can be classified into three categories: the design of topological structures, such as slide-ring gels , homogeneous four-arm gels and highly entangled gels , to distribute stress in single-network systems; the introduction of energy dissipation mechanisms by sacrificial bonds, such as in double-network (DN) hydrogels and dual-crosslinked hydrogels ; and the introduction of high-order structures, such as microphase separations , microcrystals, and fibrils or fabrics . From the perspective of mechanical dynamics, they can be classified into elastic and viscoelastic hydrogels that are strain-rate independent and dependent, respectively, in the common observation window.
传统水凝胶的机械性能差主要归因于几个固有特征。 其中一个是聚合物密度分布和交联点之间聚合物链长度的网络不均匀性。 因此，水凝胶容易在加载时出现应力集中，从而引发裂纹。 另一个是由于缺乏能量耗散机制而导致的橡胶状弹性，从而使其抗裂纹传播能力较低。 此外，传统水凝胶通常含有大量水。 负载承载固相的少量进一步导致机械性能薄弱和脆弱。 自 2000 年代以来，机械强度和韧性水凝胶的发展已经在软材料研究和我们对其失效机制的理解方面取得了重要进展。 通过其结构组分改善水凝胶的力学性能的主要策略可分为三类：设计拓扑结构，如滑环凝胶 、均匀四臂凝胶 和高度纠缠凝胶 ，以在单网络系统中分布应力；通过牺牲键引入能量耗散机制，如双网络（DN）水凝胶 和双交联水凝胶 ；引入高阶结构，如微相分离 、微晶体和纤维或织物 。从力学动力学的角度来看，它们可以分为弹性和粘弹性水凝胶，在常见观察窗口中分别是应变速率独立和依赖的。

Fatigue resistance - that is, long-term stability under cyclic loadsis vital for some applications such as artificial cartilage. Since the initial work in 2017 (ref. 6), the study of fatigue-resistant mechanisms and the development of fatigue-resistant hydrogels have attracted considerable interest. Numerous antifatigue design strategies have been proposed. For elastic gels, these strategies involve modulations at the molecular level, such as lengthening the polymer chain , increasing entanglement , and unfolding or degrading the crosslinker . For viscoelastic gels, mesoscale modifications have been proposed, such as microphase separation , microcrystallization and fibrils , and nanocomposites . The fatigue threshold is greatly enhanced for gels with hierarchical structures , resolving the conflict between the modulus and the fatigue threshold.
疲劳抗性 - 即在循环载荷下的长期稳定性对于某些应用，如人工软骨至关重要。自 2017 年的最初研究以来（参考文献 6），对抗疲劳机制的研究和疲劳抗性水凝胶的开发引起了广泛关注。已提出了许多抗疲劳设计策略。对于弹性凝胶，这些策略涉及分子水平的调节，如延长聚合物链 ，增加纠缠 ，展开或降解交联剂 。对于粘弹性凝胶，已提出了介观尺度的修改，如微相分离 ，微晶化和纤维 ，以及纳米复合材料 。对于具有分层结构的凝胶，疲劳阈值得到了极大增强 ，解决了模量和疲劳阈值之间的冲突。

After about two decades of effort, nowadays the fracture energy and fatigue threshold of hydrogels can reach (refs. 16,44) and (ref. 18), respectively. Elastic modulus from submegapascal to hundreds of megapascals, strength from submegapascal to tens of megapascals, and stretching ratio from several to hundreds can be achieved. Moreover, taking inspiration frombiological systems, efforts have been made to develop self-healing hydrogels and anisotropichydrogels. Unlike other solid materials, hydrogels are permeable to small molecules. Thus, hydrogels could be used as an open system to develop mechanically triggered new networkgrowth. Self-growing and strengthening hydrogels based on mechanochemistry mechanisms have also attracted attention for the purpose of developing materials that adapt to their surrounding environment, resembling biological systems .
经过大约二十年的努力，如今水凝胶的断裂能量和疲劳阈值分别可以达到 （参考文献 16,44）和 （参考文献 18）。弹性模量从亚兆帕斯卡到数百兆帕斯卡，强度从亚兆帕斯卡到数十兆帕斯卡，拉伸比从几到数百 都可以实现。此外，受生物系统启发，人们努力开发自修复水凝胶和各向异性水凝胶。与其他固体材料不同，水凝胶对小分子具有渗透性。因此，水凝胶可以用作开放系统，以发展机械触发的新网络生长。基于机械化学机制的自生长和强化水凝胶也引起了人们的关注，目的是开发能够适应周围环境的材料，类似于生物系统 。

The advancements in hydrogel design strategies, focusing on achieving comprehensive mechanical performance, have been summarized in several outstanding review papers, particularly those emphasizing the structure of polymer networks and the nonlinear elastic fracture mechanics . Given the importance of swelling and deswelling characteristics in hydrogels, and the practical need for hydrogels to be in an equilibrium state of swelling in a liquid medium, this Review explores design strategies to attain high mechanical performance with a focus on the perspective of swelling and deswelling. We initially use a basic hydrogel model to clarify the influences of the molecular structure and swelling or deswelling on the mechanical properties, encompassing the elastic modulus, extensibility, strength, toughness and fatigue resistance. We then discuss the main design strategies to obtain tough hydrogels, followed by advances in developing fatigue-resistant hydrogels and in understanding their underlying mechanisms. We highlight recently developed strategies for developing self-reinforcement hydrogels with tissue-like self-growing properties. To close, we emphasize challenges and trends in developing inelastic fracture mechanics theory to capture the large deformation behaviour and the next generation of tough hydrogels for practical biological applications.
水凝胶设计策略的进展主要集中在实现全面的力学性能上，已经在几篇杰出的综述论文中进行了总结，特别强调了聚合物网络结构和非线性弹性断裂力学。鉴于水凝胶中膨胀和脱胀特性的重要性，以及水凝胶在液体介质中处于膨胀平衡状态的实际需求，本综述探讨了通过关注膨胀和脱胀的角度来实现高力学性能的设计策略。我们首先使用基本水凝胶模型来阐明分子结构和膨胀或脱胀对力学性能的影响，包括弹性模量、延展性、强度、韧性和疲劳抗性。然后我们讨论了获得韧性水凝胶的主要设计策略，接着是发展抗疲劳水凝胶和理解其基本机制的进展。我们重点介绍了最近开发的具有组织样自生长特性的自强化水凝胶的策略。 总的来说，我们强调发展不可塑性断裂力学理论以捕捉大变形行为和下一代用于实际生物应用的坚韧水凝胶的挑战和趋势。

Various theoretical models, including the classic Flory-Rehner statistical model , Arruda-Boyce eight-chain constitutive model and Gent continuum mechanics model , along with their combination , have been explored to explain the swelling and large deformation of polymer networks. These models are discussed in reviews elsewhere . Here, we analyse a simple affine network to represent the structure of a hydrogel, and we discuss its rubber elasticity and fracture at different swelling states. The hydrogel features a uniform polymer network comprising strands characterized by the number of Kuhn monomers in each strand and the length of each monomer (b) (Fig. 1a). In the reference state, the end-to-end distance of each strand follows an ideal Gaussian chain, approximately given by , and the network has a strand density denoted as (refs. 76,83). On contact with water, the hydrogel undergoes a size change by a factor of in length ( 1indicates swelling, and indicates deswelling). Operating as an affine network, where the deformations of the bulk hydrogel and
各种理论模型，包括经典的 Flory-Rehner 统计模型 ，Arruda-Boyce 八链本构模型 和 Gent 连续力学模型 ，以及它们的组合 ，已被探讨用于解释聚合物网络的膨胀和大变形。这些模型在其他地方已经讨论过 。在这里，我们分析一个简单的仿生网络来代表水凝胶的结构，并讨论其橡胶弹性和在不同膨胀状态下的断裂。水凝胶具有由每个链中 Kuhn 单体的数量 和每个单体的长度（b）（图 1a）表征的均匀聚合物网络。在参考状态下，每个链的端到端距离 遵循理想的高斯链，近似为 ，并且网络具有一个链密度表示为 （参考文献 76,83）。与水接触时，水凝胶的尺寸会按长度因子 发生变化（ 表示膨胀， 表示收缩）。作为一个仿生网络，其中水凝胶的整体变形和

individual network strands are identical , the end-to-end distance of a strand becomes . Consequently, the strand density transforms to (Fig. 1a). Subsequently, we investigate the influence of on the elastic modulus, stretchability and fracture characteristics of the hydrogel in the absence of viscoelastic effect, unless specified.
个体网络链条是相同的 ，链条的端到端距离变为 。因此，链条密度转变为 （图 1a）。随后，我们研究了 对水凝胶的弹性模量、延展性和断裂特性的影响，在没有粘弹性效应的情况下，除非另有规定。

The Young's modulus ( ) of a hydrogel is determined by the product of the elasticity or stiffness per strand and the density of strands , expressed as . As the elasticity of a strand increases with swelling and strand number per volume decreases with swelling, exhibits a non-monotonic dependence on . In this context, we use the freely jointed chain model to represent the elastic energy of a strand, considering the finite extensibility effect (see Supplementary Information . By taking the second derivative of the elastic energy of a strand with respect to the stretching ratio, we derive the elasticity of the strand, expressed as:
年轻模量（ ）的水凝胶由弹性 或每股刚度与股密度 的乘积确定，表示为 。随着股的膨胀 和每单位体积的股数随膨胀减少， 对 表现出非单调依赖性。在这种情况下，我们使用自由联接链模型来表示股的弹性能量，考虑有限可伸展性效应（见补充信息 。通过对股的弹性能量关于拉伸比的二阶导数，我们推导出股的弹性，表示为：

where . Consequently, the Young's modulus of the hydrogel is given by:
在 。因此，水凝胶的杨氏模量由以下公式给出：

In Fig. 1a, we depict as a function of for 20 as a representative example. Here is the Young's modulus of the hydrogel at the reference state . The curve in Fig. 1a illustrates the non-monotonic evolution of the elastic modulus with swelling ratio. For small or modest , where is much smaller than the contour length of the strand , polymer strands can be approximated as Gaussian chains, and the elasticity is proportional to . Therefore, decreases as increases because the strand density is proportional to . For large where approaches , the stiffness of strands increases rapidly owing to the limited extensibility of the strand . The increase of strand stiffness with is much stronger than , surpassing the effect from the decrease of strand density and resulting in an increase of with .
在图 1a 中，我们以 20 为代表性例子，将 描绘为 的函数。这里 是水凝胶在参考状态 的杨氏模量。图 1a 中的曲线说明了弹性模量随着膨胀比的非单调演变。对于小或适度 ，其中 远小于链 的轮廓长度，聚合物链可以近似为高斯链，弹性与 成正比。因此， 随着 的增加而减少，因为链密度与 成正比。对于大 ，其中 接近 ，由于链 的有限延展性，链的刚度迅速增加。链刚度随 的增加要比 强得多，超过了链密度减少的影响，导致 随 的增加而增加。

For a deswelling hydrogel , when there are physical interactions between polymer strands, the elastic modulus comprises two terms, , where is from the primary network and increases with deswelling (Fig. 1a, regime C), and is from dynamic crosslinking of interstrand physical bonds and changes with the observation time (or strain rate ) relative to the characteristic relaxation time ( ) of the viscoelastic hydrogel. At low strain rate ( ), the dynamic bonds have little contribution to the modulus, and the hydrogel behaves as a soft solid with elastic modulus , like the elastic hydrogel. At high strain rate ( ), the dynamic bonds play a similar role to the permanent crosslinking, and the hydrogel behaves as a hard elastic solid with a large . In the intermediate strain rate, the modulus increases as the strain rate increases (viscoelastic regime). The modulus of viscoelastic hydrogels typically follows the time-temperature superposition principle, as the bond association time is strongly temperature dependent and influences (refs. ).
对于脱肿水凝胶 ，当聚合物链之间存在物理相互作用时，弹性模量包括两个项 ，其中 来自主要网络并随脱肿增加（图 1a，区域 C）， 来自链间物理键的动态交联，并随观察时间（或应变速率 ）相对于粘弹性水凝胶的特征弛豫时间（ ）而变化。在低应变速率（ ）下，动态键对模量的贡献很小 ，水凝胶表现为弹性模量 的软固体，类似于弹性水凝胶。在高应变速率（ ）下，动态键起到类似于永久交联的作用，水凝胶表现为具有大 的硬弹性固体。在中等应变速率下，模量随着应变速率的增加而增加（粘弹性区域）。粘弹性水凝胶的模量通常遵循时间-温度超定位原则，因为键的结合时间强烈依赖于温度并影响 （参考文献 ）。

The theoretical maximum stretching ratio ( ) and engineering stress strongly depend on the swelling behaviour. Here we use a simple model to see the effect of on and . Under deformation, the maximum stretch ratio of a single strand, which goes from to its physical limit or contour length ( ), is
理论最大拉伸比（ ）和工程应力 高度依赖于膨胀行为。在这里，我们使用一个简单的 模型来观察 对 和 的影响。在变形下，单根纤维的最大拉伸比，从 到其物理极限或轮廓长度（ ），是

The maximum engineering stress, which is the product of a single strand's rupture force and the areal density of strands crossing the plane perpendicular to the loading direction in the undeformed state , is given by
最大工程应力，即单股断裂力 与垂直于加载方向的平面上穿过股的面密度 的乘积，在未变形状态下给出

Here, the monomer concentration in the as-synthesized state is . From equations (3) and (4), the true maximum stress ) of the simple hydrogel is proportional to the bond rupture force and bond density of the network , independent of .
在这里，合成状态下的单体浓度为