Dear Ruobing,

Thank you for your interest.

1. The material robustness may be roughly indicated by the stretchability of the material. Higher stretchability typically corresponds to longer polymer chains, which in turn leads to smaller chain diffusivity during the healing process. Under this logic, yes, we may roughly conclude that soft materials with better material robustness may heal more slowly. This point can also roughly verified by the data shown in Fig. 3. I guess one way to resolve this is to integrate multiple networks with different chain lengths. That is to say, using the short chains to dissipate energy and restore most of the strength, and using long chains to back the stretchability. The requirement is to involve non-covalent bonds in different networks.

2. Let me first try to understand what you mean here. Correct me if I understand incorrectly. I guess the shape-recovery capability is usually described as "resilience", meaning the capability of returning to its original shape after deformation. Quantitatively, it is described using the damping ratio, that is the ratio between the loss modulus and storage modulus. This is also a term to characterize the viscoelastic property. If the damping ratio is small, the material is very resilience, meaning that the shape immediately returns back to the original state once the applied load is relaxed. Self-healing polymers with non-covalent dynamic bonds usually feature large damping ratios because the dynamic bonds would easily break under deformation; thus, these polymers typically feature poorlow shape resilience.

Let us go back to Gong's paper: their gels are linked by two types of ionic bonds: strong ones and weak ones. From my understanding, the good shape resilience comes from the networks with strong ionic bonds which hold the shape and the weak ionic bonds break to dissipate the energy.

To answer your question regarding "How to theoretically or experimentally quantify this feature", the feature can be quantified using the term "damping ratio" as described above. In terms of theoretical modeling of the damping ratio, we may need to involve a formulation of viscoelastic theory within the time domain and integrate the bond-kinetics of the dynamic bonds in a certain loading rate. I believe this theoretical modeling can be done.

BTW, what you are talking here should not be related to the shape-memory effect of shape-memory polymers.

Hope these can answer your questions.

Best regards,

Qiming

Dear Qiming,

Thank you for sharing with us many exciting thoughts on the self-healing soft materials. I have two questions on which I hope you could share some thoughts.

1. Following Zheng's question, my impression of most self-healing materials is that many self-healing materials that can heal fast are typically soft and brittle, while self-healing materials that are mechanically robust often heal more slowly. Is this true? If so, is there any way to resolve this conflict?

2. I think another important feature required for many self-healing materials is the capability of shape recovery after healing. For example, a silly putty may heal immediately after fractured into two pieces, but it cannot recover its original shape. To enable this shape recovery, there must be some "memory" in the material of the original configuration, such as an elastic network that provides elasticity and motivates shape recovery. However, an elastic network made of C-C bonds is not healable anymore. A polyampholyte hydrogel by Prof. Jian Ping Gong's group [1] is both self-healing and capable of shape recovery due to the nonuniform distribution of bond strength in the network. How to theoretically or experimentally quantify this feature, and furthermore optimize the overall performance in a general self-healing material?

Thank you,

Ruobing

[1] Sun, T. L., Kurokawa, T., Kuroda, S., Ihsan, A. B., Akasaki, T., Sato, K., ... & Gong, J. P. (2013). Physical hydrogels composed of polyampholytes demonstrate high toughness and viscoelasticity. Nature materials, 12(10), 932.

Dear Zheng,

Thanks for your interest.

(1) The self-healing time is determined by two factors: chain diffusion and bond kinetics. With a similar bond type, we may assume they have similar bond kinetics; then the difference primarily comes from the chain diffusion. The chain diffusion is governed by two factors: chain length and friction coefficient. The chain diffusivity increases with decreasing chain lengths. The friction is mainly governed by the matrix character; for example, hydrogels may have smaller chain frictions, but stiff polymers may feature much higher chain frictions.

(2) I guess it is because of the low mobility of backbone structures of nanopapers and woods. The healing process requires the hydrogen-bond-anchered chains to flexibly diffuse and penetrate into the other matrix.

(3) I guess you may. Here I consider the healing process as a coupling of chain diffusion and bond reaction. If you consider the chain entanglement, you may not need to consider the bond reaction. Also, I need to point out that the healing physical picture due to chain entanglement in polymer melts has been proposed since 1980s. Here are some references:

[20]R. Wool and K. O’connor, J. Appl. Phys. 52, 5953 (1981).

[21]R. P. Wool, Soft Matter 4, 400 (2008).

(4) The partial healing is due to re-association of ionic bonds, while covalent bonds are permanently broken. There is no standard definition for self-healing polymer networks. Some researchers may still call particle self-healing as "self-healing". Here is an example from Dr. David Weitz group:

Wu, Jinrong, Li‐Heng Cai, and David A. Weitz. "Tough Self‐Healing Elastomers by Molecular Enforced Integration of Covalent and Reversible Networks." Advanced Materials 29.38 (2017): 1702616.

Best regards,

Qiming

Dear Teng,

Yes, I guess. The only requirement is that the self-healing material should be stiff enough. Here are two papers doing so, yet not with self-healing materials:

Cheung, Kenneth C., and Neil Gershenfeld. "Reversibly assembled cellular composite materials." science 341.6151 (2013): 1219-1221.

Dong, Liang, Vikram Deshpande, and Haydn Wadley. "Mechanical response of Ti–6Al–4V octet-truss lattice structures." International Journal of Solids and Structures 60 (2015): 107-124.

It is really a tradeoff: slower for bigger structures or faster for smaller structures. It is a long-lasting debate in the field of additive manufacturing. That is also why there is an acute demand for large-scale additive manufacturing systems.

Best regards,

Qiming

Dear Qiming,

Thank you for this very informative and fantastic review on self-healing mechanics. I am particularly interested in the mechanism of self-healing:

(1) First of all, what determines the healing time? As evident in your Fig.3, some materials with dynamic covalent bonds heal themselves in 2-3 hours (Fig. 3B), while it takes 24 hours (Fig. 3A) for some other self-healing materials with the same bond type to fully recover its initial mechanical behavior. Why is that?

(2) Fig. 3C shows materials with hydrogen bonds heal in about 2-5 hours. Intriguingly, recent works found that nano-papers or densified woods which contain a high density of hydrogen bonds did not show obvious self-healing behavior (Processing bulk natural wood into a high-performance structural material, Nature, 554, 224-228 (2018); Anomalous scaling law of strength and toughness of cellulose nanopaper). Could you please shed some insights on this?

(2) Congrats on your great papers examining the self-healing behavior due to dynamic bonds. I wonder if the model can be also applied to decipher the self-healing via chain entanglement?

(3) It is known that the famous double-network hydrogel composed of polyacrylamide and alginate can recover its initial stress-strain response to some extent (not 100%) after a day. Can we also define it as a self-healing hydrogel?

Best regards,

Zheng

Dear Qiming,

Thanks for your very nice review. The self-healing performances of these polymers are really impressive. You already showed very promising methods of making 3D structures with self-healing polymers based on additive manufacturing. It seems still challenging to make large structures with additive manufacturing (3D printing), in terms of time and cost. By leveraging the self-healing properties, I was wondering whether it is possible to assemble small building blocks of self-healing polymers into a large structure (like building Lego) and then let the assembled structure heal to form a continuous 3D structure?

Best,

Teng

Dear Jingda,

Thank you for your interest.

(1) Stiff polymers/gels can also be self-healable. Here are two examples: [1-2]. You are right that the mobility of polymer chain is constrained by the matrix within these materials; therefore, external intervention is required to increase the chain mobility during the healing process, for example, heating, lighting, or applying catalyst.

(2) You have a great point. Most of the existing researchers in the field of self-healing materials use tensile strength as the indicator for the healing performance. Tensile strength can be a good indicator only when the sample number is large enough to eliminate the effect of material defects. Fracture toughness is a better indicator but the measurement is more challenging.

In terms of theoretical understanding, the fracture toughness should include two parts: intrinsic fracture energy due to dissociating or fracturing crossover chains and dissipating fracture energy due to the loading-unloading processing zone. Xuanhe and Rong did fantastic jobs in elucidating the mechanism of these two parts within the framework of fracture of soft materials [3-4]. To the best of my understanding, the current models are still semi-analytical as the processing zone is highly non-linear. I definitely expect the existing theories to be extended to understand the fracture energy of self-healing polymers. We are actually working on a theory to bridge the gap between the tensile strength and the fracture energy.

(3) Congratulations on your great work! According to Xuanhe's work [5], strong bonding/adhesion requires both strong bridges and tough matrix. Involving tough matrices may also be an important factor. Look forward to your future exciting work!

Best regards,

Qiming

Reference

[1] M. Burnworth et al., Nature 472, 334 (2011).

[2] Y. Yanagisawa et al., Science 359, 72 (2018).

[3] T. Zhang et al., Extreme Mechanics Letters 4, 1 (2015).

[4] Y. Qi, J. Caillard, and R. Long, J. Mech. Phys. Solids. 118, 341 (2018).

[5] H. Yuk et al., Nat. Mater. 15, 190 (2016).

Dear Qiming,

Thank you for the wonderful review. I studied nanocomposite hydrogel before, so I am very interested in the self-healing hydrogels. I have a few questions and comments and wish to hear your perspective.

(1) Many self-healing hydrogels are very soft, with a Young's modulus 1~dozens of kPa[1-2]. Can high-modulus hydrogels self-heal themselves? When the chains are long in soft hydrogels, it is easy for them to reconnect; while when the chains are short in stiff hydrogels, the network may constrain them to reconnect after fractured. Is this picture right?

(2) As you mentioned, most researchers use tensile strength as a benchmark to evaluate the self-healing capability of one material, is it possible to use the fracture energy as the parameter to evaluate? In this way, people may cut a crack in the specimen and measure the fracture energy before/after the healing.

(3) We just published a paper on the strong adhesion in the 3D printing of heteregeneous soft materials [3]. It may be possible to extend this technology to the self-healing bimaterials with strong adhesion.

[1] J. Insu, J.X.Cui, W.R. Illeperuma,J. Aizenberg, J. Vlassak. Adv.Mater. 28, 2016.

[2] K.Haraguchi et al, Macromol. Rapid Commun. 32, 2011.

[3] H. Yang et al, Adv.Funct. Mater.2019, 1901721.