Tough hydrogels enabled by transient entanglements

Domain: chemistry
Published: 2026-03-05
Editorial outcome: major_revision

Abstract
Achieving high toughness and strength simultaneously in single-covalent-network hydrogels remains a longstanding challenge. Herein, we report a simple yet effective strategy to resolve this strength-toughness conflict by constructing polyacrylamide (PAAm) networks with abundant dangling chains that form transient entanglements. Unlike permanently trapped entanglements, these transient entanglements can slip and fully disentangle upon loading, enabling highly efficient energy dissipation and stress redistribution over a broad range of strains. Besides, these networks exhibit superior homogeneity compared to other structures, effectively mitigating stress concentration. As a result, our single-covalent-network hydrogels exhibit good mechanical properties, including a fracture strain of 5071%, a fracture strength of 1.06 MPa, a fatigue threshold of 1968 J·m⁻², and a fracture energy of approximately 60,000 J·m⁻². Moreover, these hydrogels feature low friction and high wear-resistance. Such a simple yet robust design paradigm effectively overcomes the longstanding strength–toughness trade-off without the complexity of multi-network architectures, opening avenues for next-generation hydrogels in biomedicine, wearable electronics, and other demanding environments.

Introduction
Mechanically robust hydrogels that combine high toughness and strength are highly desirable for a wide range of applications, such as wearable electronics1,2, bioengineering3,4, actuators5,6, sensors7,8, and enhanced oil recovery9–11. However, achieving both properties simultaneously is a significant challenge, as toughness and strength are often seen as mutually exclusive in materials12–15. This trade-off is particularly pronounced in single-covalent-network hydrogels based on covalently cross-linked polyacrylamide (PAAm). While single-covalent-network PAAm hydrogels are relatively easy to prepare and most widely used, balancing toughness and strength remains difficult. To increase strength, a denser cross-linking network is usually required, but this often leads to embrittlement. According to the Lake-Thomas model16–18, a higher cross-linking density results in reduced ductility and toughness, making it challenging to achieve both high strength and toughness in a single network.

Over the past few decades, various strategies have been explored to reconcile the inherent strength-toughness trade-off in hydrogels, particularly through the design of multi-network hydrogels. These materials combine covalent cross-links with additional networks based on hydrogen bonding19–21, electrostatic interactions22,23, host–guest chemistry24,25, and crystallization26–28, providing both deformation resistance and energy dissipation. While multi-network designs can partially address the strength-toughness conflict, their construction is complex and often requires the introduction of functional monomers. A promising recent development involves molecular entanglements, which act as additional topological cross-links, restricting chain mobility and contributing to both elasticity and toughness29–32. However, tailoring entanglements in hydrogels is challenging due to the competition and repulsion of water molecules, which tend to weaken the entanglement effect33. Despite these challenges, careful structural design can engineer entanglements to enhance material properties. One such approach is the double-network (DN) design, in which polymer chains in a ductile matrix entangle with a rigid skeleton34,35. This allows the chains to slip and redistribute stress during deformation, thus improving both strength and toughness. A similar mechanism has been applied to macromolecular microsphere crosslinked hydrogels, where polymer chains interpenetrate and entangle within microspheres36,37. More recently, single-covalent-network PAAm hydrogels have been developed in which permanently trapped entanglements significantly outnumber covalent cross-links12. In these hydrogels, entanglements function as slip links, reinforcing the material without causing embrittlement. During deformation, entanglements slip first, and then transmit tension to other chains, dissipating energy when covalent bonds break. This approach has significantly improved the mechanical properties of PAAm hydrogels, achieving strengths of 400 kPa and fracture energies of 2200 J/m². However, these designs still rely on permanently trapped entanglements, which can only slip but cannot fully disentangle. This limits their energy dissipation capacity and overall toughness.

In contrast, introducing transient entanglements may offer a pathway for creating even tougher and stronger hydrogels. These entanglements can slip and disentangle during deformation, providing enhanced energy dissipation and stress redistribution across the material. In this study, we demonstrate an approach to resolving the strength-toughness conflict by fabricating a single-covalent-network PAAm hydrogel with abundant dangling chains that interlock to form transient entanglements. Unlike permanently trapped entanglements, these transient entanglements can not only slip but also fully disentangle under stress. This mechanism allows for superior energy dissipation and stress redistribution across a wide range of strain. As a result, our transiently entangled PAAm hydrogels exhibit good properties, including a fracture strain of 5071%, a fracture strength of 1.06 MPa, a fatigue threshold of 1968 J·m⁻², and a fracture energy of approximately 60,000 J·m⁻². Furthermore, these hydrogels also feature a more homogeneous network, with low friction and high wear-resistance, making them highly promising for biomedical applications and beyond. This simple yet effective approach provides a significant step forward in the development of tough, strong, and durable hydrogels.

Results
Synthesis of transiently entangled hydrogels.
We synthesized three types of single-covalent-network PAAm hydrogels: a regular hydrogel, a permanently entangled hydrogel, and a transiently entangled hydrogel (Fig. 1a, b). The regular hydrogel is cross-linked using N,N′-methylenebis(acrylamide) (MBA), where covalent cross-links dominate the network structure. The permanently entangled hydrogel features an ultra-high polymer concentration with fewer covalent cross-links, allowing the permanently trapped entanglements to outnumber the cross-links. During deformation, the entangled chains in the permanently entangled hydrogel slip to redistribute stress, and the covalently cross-linked chains eventually break, leading to significant damage to the hydrogel network (Fig. 1c, d). In contrast, the transiently entangled hydrogel allows its entangled chains to undergo both slip and disentanglement during deformation, effectively dissipating energy and enhancing the toughness (Fig. 1e).

To construct the transiently entangled hydrogel, a linear macromolecular cross-linker (LMC) is used to construct a network rich in dangling chains but with minimal chemical cross-linking. The LMC is polyallylamine (PAA) with double bonds on its side chains (Supplementary Fig. 1), synthesized by capping the amino groups with allyl glycidyl ether (AGE). The chemical structures of the reactants and final products are confirmed by proton nuclear magnetic resonance (1H NMR) spectroscopy (Supplementary Fig. 2), revealing an average of 0.9 unsaturated double bonds per PAA molecular repeat unit. The transiently entangled PAAm hydrogels are fabricated through in situ free radical polymerization of acrylamide (AAm) monomer in the presence of LMC. During polymerization, the PAAm chain radicals react with the double bonds of LMC to form dangling chains and LMC radicals. The LMC radicals can polymerize with AAm monomers to form reactive dangling chains, which either react with double bonds on other LMC molecules, creating chemical cross-links, or terminate via reaction with other PAAm chain radicals, forming additional dangling chains (Supplementary Fig. 3). The resulting network consists of numerous dangling chains that intertwine with each other or couple with the backbone chains, forming transient entanglements. Thus, both chemical cross-links and transient entanglements coexist within the PAAm hydrogel (Fig. 1b and Supplementary Fig. 3). The hydrogels are designated as LMC-m-AAm-n, where m and n represent the mass ratio of LMC cross-linker to AAm monomer and the molar concentration of AAm monomer, respectively. The compositions of the various hydrogels covered in this work are shown in Supplementary Table 1.

We summarize the fracture energy and ultimate strain on an Ashby plot to compare our materials with existing tough hydrogels and ionogels (Fig. 1f)12,27,31,37–43. The transiently entangled hydrogels exhibit superior toughness and ductility compared to most current tough hydrogels and ionogels. Remarkably, even when a rectangular sample is cut to 80% of its original width, the hydrogel still demonstrates exceptional tensile strength, stretching over 35 times its original length (Fig. 1g and Supplementary Fig. 4).

Verification of transient entanglement structure.
To investigate the structure of transient entanglements in the hydrogels, we first conducted a stress relaxation experiment. Upon applying a step strain to the entangled PAAm hydrogels, all samples exhibit rapid relaxation behavior (Fig. 2a). Over time, the relaxation modulus, G(t), decrease and eventually reach a plateau, showing clear time dependence. The plateau value (G(t)/G₀) reflects the ratio between permanent cross-links and total cross-links. Due to the high water content, hydrogen bonds between PAAm chains are greatly weakened and contribute only marginally to the elasticity, so the dynamic cross-links are primarily attributed to transient entanglements, while the permanent cross-links involve covalent cross-links and permanently trapped entanglements (Supplementary Fig. 5). The G(t)/G₀ values range from 0.3 to 0.5, indicating that transient entanglements outnumber permanent cross-links. An increase in the cross-linker content results in higher G(t)/G₀ values, indicating a higher permanent cross-link density. In contrast, the regular hydrogel deforms immediately, with G(t) showing minimal variation over time (Supplementary Fig. 6), and the final G(t)/G₀ value is as high as 0.93, indicating high elasticity of network.

To determine the permanent cross-linking density of the hydrogels, we performed equilibrium swelling experiments. In the presence of a high amount of water, the transient entanglements disentangle, while the chemical cross-linkers and some permanently entangled chains become the primary components resisting swelling. As shown in Fig. 2b and Supplementary Table 2, increasing the amounts of chemical cross-linkers results in a decrease in the equilibrium swelling ratio, indicating a corresponding increase in the chemical cross-linking density. This result aligns with the findings from the stress relaxation behavior.

To confirm that the dynamic cross-links arise from entanglements of dangling chains, we performed ¹H Double-Quantum NMR (¹H DQ NMR) experiments on hydrogels with varying swelling ratios (Fig. 2c) and cross-linking densities (Fig. 2d). The ¹H DQ NMR results reveal that the DQ excitation curves of all samples show two distinct maxima at different excitation times (τ). These maxima suggest the presence of two networks within the hydrogels: chemical cross-linking network and transient entanglement network44. To distinguish the origins of these two maxima, we gradually increase the swelling ratio of the hydrogel, which progressively disentangles the transient entanglements. In Fig. 2c, the normalized DQ (nDQ) buildup curves of LMC-4.8-AAm-4.2 hydrogel at different swelling ratios show a sharp first maximum at a shorter τ (~2.2 ms). This maximum, corresponding to stronger dynamic constraints, does not shift with swelling. In contrast, the second maximum at a longer τ (~7.8 ms), corresponding to weaker confinement, broadens and shifts to longer τ as the swelling ratio increases. Herein, the polymer chain concentration-sensitive second peak can reasonably be attributed to the confinement effect induced by transient entanglements. Swelling decreases the polymer strand density (𝜌) and increases the tube diameter (α), following the relationship 𝛼 ∝ 𝜌−1/233. This ultimately reduces the number density of entanglements in the dangling chains, resulting in a disentangled-like phenomenon. Since the covalent cross-links remain unchanged during swelling, the first maximum, associated with shorter τ, corresponds to the rapid Rouse relaxation of chemically crosslinked network strands between adjacent covalent cross-linking points. Moreover, increasing the cross-linker content results in a negligible shift in the first maximum, while the second maximum shifts to a shorter τ (Fig. 2d). This suggests that with the increase of chemical cross-linking, the entanglements between dangling chains are enhanced, leading to more constrained segmental dynamics. This is further supported by spin echo experiments, which reveal an increase in the rigid fraction with increasing the content of cross-linkers (Supplementary Fig. 7 and Supplementary Table 3). In summary, these results demonstrate that the PAAm hydrogels possess numerous transient entanglements.

To further distinguish the contribution of entanglements and chemical cross-links to the elasticity of these hydrogels, we use the Mooney-Rivlin model
σ = Gc + Ge f(α), f(α) = 1/α - α⁻² (1)
where α and σ represent the elongation and the Mooney stress of the sample, respectively; Gc and Ge are the Mooney-Rivlin constants. Usually, Gc and Ge correspond to the contributions of permanent cross-linking and entanglements to the elastic modulus, respectively45. The Gc and Ge values of these transient hydrogels are shown in Fig. 2e, f and Supplementary Table 4. The higher Ge values of all these hydrogels indicate that entanglements play a dominant role in the stretching process, outweighing the contribution of covalent cross-linking. This suggests that while chemical cross-linking leads to stronger confinement, its contribution to elastic modulus is comparatively smaller. As the cross-linker content increases, Gc also increases, reflecting a higher density of chemical cross-links. On the other hand, Ge first increases and then decreases, indicating the number of branched chains in the network first increases and then decreases. This trend can be explained as follows: as more cross-linkers are added, the number of branching sites increases, leading to more dangling chains attached to the macromolecules. However, beyond a certain threshold, the increased number of growing chain radicals reduces the distance between free radicals, raising the probability of bimolecular coupling and forming more chemical cross-links instead of dangling chains46. Furthermore, we calculate the Ge/(Gc + Ge) values of transiently entangled hydrogel, regular hydrogel, and permanently entangled hydrogel to evaluate the contribution of entanglement to the elastic modulus. The Ge/(Gc + Ge) value of transiently entangled hydrogel is 96%, while the corresponding values for the regular hydrogel and permanently entangled hydrogel are 53% and 77%, respectively. This result indicates entanglement plays a more critical role in the transiently entangled hydrogel than that of regular and permanently entangled hydrogel (Fig. 2g, Supplementary Fig. 8 and Supplementary Table 4).

Transient entanglements also contribute to a highly homogeneous polymer network on scales larger than the mesh size, making the network optically transparent (Supplementary Fig. 9) and minimizing the inhomogeneity caused by the random distribution of chemical cross-links. Dynamic light scattering (DLS) tests, shown in Supplementary Fig. 10, provide typical scatter plots for the hydrogels. The time-average scattered intensity, 〈𝐼〉𝑇, of the regular hydrogel fluctuates significantly, whereas the permanently entangled and transiently entangled hydrogels exhibit much smaller fluctuations. The time-fluctuating intensity component, 〈𝐼𝐹〉𝑇, for these three types of PAAm hydrogels are nearly identical, as 〈𝐼𝐹〉𝑇 originates from excess scattering beyond the static scattering of the frozen structure and is only temperature dependent47. The static inhomogeneity, 〈𝐼𝐶𝐸(𝑝)〉, can be calculated by the equation:
〈𝐼𝐶𝐸(𝑝)〉 = 〈𝐼〉𝐸 − 〈𝐼𝐹〉𝑇 (2)
where 〈𝐼〉𝐸 is the ensemble-averaged scattered intensity. We summarize the 〈𝐼𝐶𝐸(𝑝)〉 values in Fig. 2h. It can be seen that the entanglements can effectively reduce the network inhomogeneity.

To investigate the dynamics of physical entanglements formed by dangling chains, we measured the intensity time-averaged correlation functions (ICFs) (Fig. 2i and Supplementary Fig. 11). The ICFs of the regular hydrogel shows a single relaxation event around 20 μs. In contrast, both the transiently entangled and permanently entangled hydrogels exhibit an additional, slower relaxation mode. According to the work of Amis et al.48, these relaxation modes, i.e., the fast and slow modes, are attributed to the collective motion of entangled chains and the translational diffusion of gel clusters, respectively. Fig. 2i presents the G(Γ) of these three hydrogels, obtained by performing an inverse Laplace transform of ICFs. The slower relaxation mode is more clearly resolved in this figure. The single relaxation with a relaxation time of ~27 μs for the regular hydrogel reflects local fluctuations in polymer chain concentration, a behavior commonly observed in many hydrogels49. For the entangled hydrogels, a broader and weaker peak appears, corresponding to a slow mode with a relaxation time of ~1250 μs, which is associated with the diffusion of entangled dangling chains. This diffusion is hindered by factors such as entanglement and friction between molecular chains, as noted by Gong et al50. Additionally, the relaxation time of slow mode is sensitive to the covalent cross-link density; in the permanently entangled hydrogel, the movement of dangling chains is even more restricted, leading to a slight increase in the relaxation time.

Characterization of mechanical properties.
Transient entanglements significantly enhance both the strength and elongation of hydrogels, as shown by comparing the transiently entangled hydrogel with the permanently entangled hydrogel and the regular hydrogel (Fig. 3a). The ultimate strength and strain for the transiently entangled hydrogel are 1.06 MPa and 3184%, respectively, compared to 0.39 MPa and 404% for the permanently entangled hydrogel, and 0.22 MPa and 1215% for the regular hydrogel. To investigate the fracture mechanics of these hydrogels, pure shear tests were performed. All transiently entangled hydrogels demonstrated high fracture energy and resistance to notch propagation (Fig. 3b, c). Notably, the fracture energy of LMC-4.8-AAm-4.2 hydrogel is 6.02×10⁵ J·m⁻², which is higher than that of many reported single-covalent-network PAAm hydrogels12,31,51,52. This value is only slightly lower than those of some ionogels and hierarchical poly(vinyl alcohol) hydrogels27,53. Furthermore, the fracture energy is proportional to n and inversely proportional to m, scaling as 𝛤 ~ 80−2.3𝑚 when n = 5.0.

The superior fracture energy indicates that transiently entangled hydrogels possess overall better performance compared to both permanently entangled hydrogels and regular hydrogels. For hydrogels, increasing cross-link density usually raises Young’s modulus and ultimate tensile strength, but it also restricts reptation and disentanglement, curtails sacrificial dissipation pathways, and suppresses crack-tip blunting. These effects elevate the elastic energy-release rate while reducing available inelastic dissipation, so toughness declines even as modulus and strength increase. Therefore, regular hydrogels often face a strength-toughness trade-off, where toughness (represented by Γ, or fracture energy) is inversely related to strength (represented by σ or yield strength σy, which reflects cross-link density). This relationship is described as 𝛤 ~ 𝜎−2.63, indicating that chemical cross-links increase strength but also make the hydrogels more brittle. In contrast, permanently entangled hydrogels partially overcome this issue. The permanently trapped entanglements stiffen the hydrogels but do not significantly compromise their toughness, following the scaling 𝛤 ~ 𝜎−1.52. Transiently entangled hydrogels, however, show minimal strength-toughness conflict, with a scaling of 𝛤 ~ 𝜎−0.61. Notably, even with nearly an order of magnitude increase in the σ value, the Γ value only changes slightly, indicating that transient entanglements effectively enhance strength without leading to brittleness (Fig. 3d and Supplementary Fig. 12).

To capture genuine fatigue durability under successive tensile loading-unloading rather than single-shot fracture behavior, we determined the fatigue threshold (Γ₀) by measuring the crack expansion of the transiently entangled hydrogel at different energy release rate amplitudes (Fig. 3e). Linear regression of the data yields a Γ₀ of 1968 J·m⁻², which is much higher than that of pure natural rubber (~50 J·m⁻²), the permanently entangled hydrogel (~200 J·m⁻²), and the regular hydrogel (~10 J·m⁻²). Plotted on an Ashby map of fatigue threshold versus fracture energy, the transiently entangled hydrogel outperforms most existing tough hydrogels (Fig. 3f) 12,14,27,28,31,54–58. Notably, even materials with appreciable fracture energies, such as natural rubber (~10⁴ J·m⁻²) and the permanently entangled hydrogel (~1460 J·m⁻²), exhibit much lower fatigue thresholds, underscoring the exceptional fatigue resistance enabled by the transiently entangled network.

To optimize the mechanical properties, transiently entangled hydrogels were developed with varying values of m and n. The ultimate stress is maximized at m = 9.6‰ and n = 4.2 M (Supplementary Table 5). When m is varied from 1.2‰ to 14.4‰, both tensile strength and toughness first increase and then decrease, reaching maximum values of 1.06 MPa and 10.65 MJ·m⁻³ at m = 9.6‰, while the strain decreases from 5071% to 2666% (Fig. 3g-i). While the modulus typically correlates with cross-linker content, in this case, it first increases and then decreases with higher cross-linker concentrations. As noted, both chemical cross-links and dynamic cross-links contribute to the modulus. Cross-linker content below the threshold favors the formation of dangling chains, while above the threshold, it results in more chemical cross-links. This interplay leads to the unique modulus behavior observed in these hydrogels. These hydrogels also exhibit distinct yielding behavior. At m = 4.8‰ and n = 4.2 M, yielding is most pronounced, with a maximum yield strength of 0.07 MPa. At m = 14.4‰, the yielding phenomenon becomes much less noticeable, suggesting that disentanglement of transient entanglements is the main origin of the yielding behavior. Moreover, as the strain rate increases, transient entanglements do not have sufficient time to disentangle and therefore behave as effective load-bearing constraints, increasing the modulus and strength while reducing the fracture strain (Supplementary Fig. 13).

The effect of n on the mechanical properties shows analogous non-monotonic trend. The modulus increases while stretchability decreases, with strength and toughness peaking near n = 5.0 M and then falling due to network densification at high solids (Supplementary Fig. 14).

As far as we know, pure PAAm hydrogels typically cannot achieve a tensile strength above the megapascal level, nor do they display strains at break exceeding 5000%. The transiently entangled hydrogels in this study represent a significant advancement for PAAm-based hydrogels, offering both ultra-high strength and strain. Additionally, all transiently entangled hydrogels exhibit high compression strength (~1.0 MPa at 90% strain) and quickly return to their original shape once the compressive stress is removed (Supplementary Fig. 15). At small strains, the transient entanglements dissipate energy by sliding and uncoiling twisted dangling chains, while the network chains absorb energy as they straighten from a curved to a linear configuration. At larger strains, more transient entanglements are untangled, and the chemical cross-links begin to rupture. These unique behaviors contribute to the hydrogels’ superior mechanical properties. Moreover, these hydrogels' storage modulus exhibits an order of magnitude higher than its loss modulus (Supplementary Fig. 16), and it is accompanied by linear viscoelasticity and a low apparent activation energy of only 34 kJ·mol⁻¹ (Supplementary Fig. 17). Some single-covalent-network polyelectrolyte hydrogels can also be constructed using this strategy to introduce transient entanglements, thereby improving comprehensive mechanical properties (Supplementary Fig. 18).

Tough transiently entangled hydrogels with multifunctions.
Tough transiently entangled hydrogels with tunable mechanical properties and numerous hydrophilic dangling polymer chains can serve as an effective lubricating coating that lubricate the hydrogel surface and reduce friction. Owing to their much more dangling chains compared to a regular hydrogel, the transiently entangled hydrogel achieves a significantly lower friction coefficient of 0.0025 (Fig. 4a). This value is approximately 2.7 times lower than that of the permanently entangled hydrogel, 9.6 times lower than that of the regular hydrogel, and even 16 times lower than some common plastics59 (Supplementary Fig. 19 and 20). The combination of low friction, high toughness, and fatigue resistance allows this hydrogel to exhibit good resistance to wear (Fig. 4b, c). While the regular hydrogel fails after just 3.5 hours of shearing in a rheometer test, the transiently entangled hydrogel remains intact after 6 hours, demonstrating a superior wear resistance compared to most elastomers and hydrogels12. These make the transiently entangled hydrogel ideal for modifying the surfaces of medical devices. To evaluate its lubrication performance, we tested the hydrogel films under various conditions, including sliding frequency and applied load (Fig. 4d, e). Both factors affect the friction coefficient, but it consistently remains low. Continuous friction tests at 1 N and 1 Hz show that the hydrogel maintains lubricity for at least 480 cycles (Fig. 4f), with a friction coefficient of approximately 0.0025, demonstrating the long-term stability of the hydrogel as a lubricant.

To further assess the lubrication properties, the hydrogel was used to modify the surfaces of catheters. Using water as a lubricant to analyze the lubricating properties of two hydrogel-modified catheter. The average friction coefficients of the bare PVC catheter (Fig. 4g-i) and the latex catheter without gel coating (Fig. 4j-l) were 3.21 and 1.73, respectively. After applying the hydrogel coatings, the friction coefficients were reduced to 0.037 for the SPVC catheter and 0.041 for the latex catheter, demonstrating the good lubrication performance of the modified catheters. Both catheters exhibit conformal and continuous contact with the coatings at the interface. A direct comparison between the transiently entangled hydrogel and a composition-matched regular hydrogel underscores the factors governing lubrication. In the transiently entangled hydrogel, densely distributed and hydrophilic dangling chains stabilize a water-rich interfacial film, providing fluid-film lubrication and yielding an ultra-low friction coefficient (Fig. 4m). Crucially, the transiently entangled hydrogel retains this hydration layer: after a continuous 4 hour sliding test, it preserved 90.5% of its initial water content, whereas the regular hydrogel retained only 70.7% (Fig. 4n, o). These results confirm that a persistent surface-hydration layer is the key to the transiently entangled hydrogel’s remarkable, long-lived lubricity.

Methods
Materials.
Polyallylamine (PAA, Mn = 15000, 30 wt%) was purchased from Zouping Mingyuan Import & Export Trading Co., China. Acrylamide (AAm, ≥99%) was provided by Chengdu Huaxia Chemical Reagent Co., Ltd, China. Allyl glycidyl ether (AGE, 99%), potassium persulfate (KPS, ≥99.5%), tetramethylenediamine (TMEDA, 99%), N,N′-methylenebis(acrylamide) (MBA, ≥99%), deuterium oxide (D2O, 99.9%) were purchased from Adamas, China. Deionized water (H2O) was obtained from Chengdu Chron Chemical Co., China. Hydroxy silicone oil was received from Wacker Chemical Co., Ltd, Germany. All the chemicals and solvents were used as received without further purification.

Preparation of linear macromolecular cross-linker (LMC).
LMC was prepared in three steps. Firstly, 3.39 g of PAA and 100 g of H2O were added into a 250 mL three-necked bottle and stirred for 10 min. Then, 2.0 g of AGE was added into the mixed solution and the solution was heated to 60°C for 6 hours with mechanical stirring. Lastly, the as-prepared dispersion was dialyzed in a dialysis bag with a molecular weight cutoff of 3000 Da for two weeks with refreshing deionized water once a day for subsequent use. The final mass concentration of LMC solution is 1.38%.

Preparation of hydrogels.
The typical transiently entangled hydrogels were prepared by free in situ radical polymerization. Prescribed amounts of AAm, LMC solution, TMEDA were dissolved in deionized water. After dissolving completely, a vacuum pump was used to remove the dissolved oxygen for 15 min. After that, a given amount of KPS aqueous solution as initiator was added into the precursor solution and stirred for another 2 min. At last, the reaction solution was transferred to a reaction box consisting of the organic glass mold with 1 mm spacing and kept at 25°C for 12 h. The regular hydrogel and permanently entangled hydrogel were prepared with reference to Suo et al. The synthesis steps are consistent with those of the transiently entangled hydrogels. The detail compositions of these hydrogels covered in this work are shown in Supplementary Table 1.

Nuclear magnetic resonance spectra (1H NMR) test.
The 1H NMR of PAA, AGE and LMC were recorded on a spectrometer operating (AV III HD 400 MHz, Bruker, Germany). Before test, the LMC solution was completely lyophilized in a vacuum freeze dryer and then dissolved in D2O.

1H Double-Quantum NMR (1H DQ NMR) test.
The 1H DQ NMR experiments were performed at 9.4 T magnetic field on a JEOL JNM-ECZR400R/M1 spectrometer, equipped with a 3.2 mm HXY MAS probe (JEOL RESONANCE Inc., Japan). The 1H π/2 pulse length is about 2.2 μs. A well-established offset-compensated Baum-Pine pulse sequence was adapted to excite double-quantum (DQ) coherences. For 1H Hahn Echo (spin echo) mode, using 90° pulse width of 2.3 us, 180° pulse width of 4.6us, the upper and lower limits of the sampling time (τ) are 0.002 ms and 500 ms, respectively, and take 39 sampling points.

Rheological test.
Rheological behaviors of the hydrogels were analyzed by a rotational rheometer (AR2000ex, TA Instrument, USA) with a suit of 40 mm diameter parallel-plates. The thickness of the samples was 1 mm. To keep hydrogels hydrated, the samples were smeared with a thin layer of low-viscosity silicone oil during the testing. Stress relaxation experiments were carried out with a constant strain of 5% for 60 min at 25°C. Frequency sweeps with variable temperature ranging from 25 to 75°C were performed to the sample at an immobile strain of 1%. The apparent activation energies were calculated from the slope of the master curves according to Arrhenius' plot.

Swelling ratio and cross-linking density.
The swelling ratio and cross-linking density of the hydrogel was calculated based on the equilibrium swelling method. The sample with a thickness of 1mm was cut into small cubes of about 10×10 mm and then placed in deionized water for swelling, during which the change in the mass of the sample was recorded at regular intervals. Until the quality of the hydrogel no longer changes, to reach the equilibrium swelling. The swelling ratio (Qw) is calculated as Qw=(Ws/Wd)×100%, where Qw is the equilibrium swelling ratio, Ws is the mass of the hydrogel after equilibrium swelling, and Wd is the mass of the dry gel before swelling test. The cross-linking density can be calculated according to the Flory-Rehner equation. Details are show in Supplementary material.

Dynamic light scattering (DLS) test.
DLS experiments were performed using a BI-200SM instrument manufactured by Brookhaven, USA, using a He-Ne laser (2 mW, wavelength λ of 633 nm) with a detection angle of 90°, and the instrument was fitted with a rotating stage. The time-averaged scattering intensity ⟨I⟩T and the time-averaged correlation function (ICF) were tested by rotating the rotating stage arbitrarily at 100 different positions for 30 s for each run, and the temperature was kept constant during the test. The overall average scattering intensity ⟨I⟩E, defined as the average of the time-averaged scattering intensity ⟨I⟩T measured at 100 points, consists of two components, which can be expressed by the following equation: 〈𝐼𝐶𝐸(𝑝)〉 = 〈𝐼〉𝐸 − 〈𝐼𝐹〉𝑇, ⟨IF⟩T is the time-averaged scattering intensity caused by the dynamically fluctuating component, similar to the concentration fluctuation of the liquid component, which is ergodic in nature, and 〈𝐼𝐶𝐸(𝑝)〉 is the static time-averaged scattering intensity caused by spatial inhomogeneities arising from cross-linking processes. Details are show in Supplementary material.

Mechanical properties tests.
All the mechanical properties of the hydrogels were measured by a commercial tensile tester (5567, Instron, USA). For the uniaxial tensile test, the as-prepared dumbbell shape hydrogel samples with a length of 20 mm, a width of 2 mm, and a thickness of 1 mm were tested at room temperature with a given crosshead velocity. The tensile rate is 100 mm/min when not otherwise specified.

For pure shear test, the samples were cut into a rectangle shape with a cross-section of 35×1 mm (i.e. a0 × b0), the gauge length is 7 mm and the tensile rate is 100 mm/min. The fracture energy was calculated via equation: 𝛤 =U(Lc)/(a0 × b0), where U(Lc) denotes the work done to stretch the unnotched sample to Lc, Lc denotes the tensile displacement of the notched sample (notch length: 17.5 mm) at the onset of crack expansion, a0 and b0 denote the width and thickness of the sample, respectively.

For fatigue resistance test, fatigue thresholds were tested via the single-notch method in a customized temperature and humidity controlled closed acrylic plate. The size of the rectangular gel samples used was consistent with the pure shear test. The sample was prepped with a 7-mm notch and subjected to continuous loading-unloading cyclic tests at 600% strain (ε), and the value of the change in notch size was recorded (c). This value was then divided by the number of cycles N to give the crack extension value (dc/dn) for each cycle. The energy release rate (G) was calculated according to the equation G = 2kcW. where k is a function of strain, empirically determined to be 𝑘 =3/(𝜀+1)1/2, c is the crack length, and W is the work of fracture of an unnotched sample of the same size stretched to the same strain ε. The critical energy release rate (G), i.e., the inflection point of the dc/dn vs. G curve is the fatigue threshold.

Friction coefficient test.
The friction coefficient of the hydrogel was measured using a rheometer consistent with the rheological tests. The torque was measured at a specific applied load and frequency. The friction coefficient (µ) was calculated by the following equation: µ=8T/T3DP, where T is the torque, D is the diameter of the parallel-plates, and P is the applied axial force.

Lubrication coating test.
Before testing the friction coefficient, PVC catheter and latex catheter were washed with alcohol and deionized water under ultrasound conditions for 40 min, which were followed by drying with N2 flow for 2 min. Subsequently, both catheters were cut into 8 mm diameter discs using a scalpel. The friction coefficients of the outer surfaces of the samples were tested using a rheometer. In order to modify the surface of the catheter via hydrogel coating, we placed the catheter in a customized ring column consisting of 2 layers of cylindrical glass. Then, the reaction precursor solution was transferred into the ring column and left at 25°C for 12 h. After the reaction was completed, the modified catheter with gel coating was cut into 8 mm diameter discs and tested the friction coefficient using the same method.

Other tests.
Ultraviolet absorption spectroscopy (UV 3600, Shimadzu, Japan) in diffuse reflection mode was used to characterize the optical transparency of hydrogel. Attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR, Nicolet 6700, Thermo Scientific, USA) was used to test the water content on the surface of the hydrogel. The micrograph of the sample was observed by Scanning electron microscopy (SEM, ThermoFisherScientific, Apreo S HiVov, USA), atomic force microscope (AFM, Smart SPM, AIST-NT, USA) and Polarizing microscope (Leica, DM4P, Germany).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Yuan et al. report developing tough yet stiff single-network polyacrylamide (PAAm) hydrogels through transient\nentanglements. While the authors demonstrate impressive mechanical properties with a record-high fracture energy of\n60,000 J·m² and strain over 5000%, several critical issues regarding the fundamental science and practical applications\nneed to be addressed.\n1. The most critical concerns relate to the sensing applications. The authors fail to explain the fundamental mechanism of\nelectrical conductivity in these hydrogels, and crucial electrical characterization data is missing. This absence of essential\nelectrical properties makes evaluating the material's true potential as a sensor impossible.\n2. The sensor fabrication process reveals significant limitations. The encapsulation of hydrogels between polyethylene films\nraises serious concerns about mechanical performance. The authors neither address how this encapsulation affects the\nmechanical properties nor explain how it impacts the claimed advantages of the transient entanglement structure. Given that\nPE films likely restrict the hydrogel's deformation, this oversight represents a fundamental flaw in the sensor design.\n3. A critical disconnect exists between the exceptional mechanical properties achieved and their practical necessity. The\ndemonstrated sensing applications involve only minor deformations, monitoring simple body movements that could likely be\nachieved with conventional hydrogels. The authors fail to justify why such high mechanical properties (>5000% strain) are\nessential for these applications, where the actual deformation is minimal.\n4. Similarly, the catheter coating application demonstrates poor utilization of the material's unique properties. While showing\nimproved lubrication, the authors have not demonstrated why such exceptional mechanical properties are necessary for this\napplication. The lack of comparison with simpler hydrogel systems and the absence of long-term durability data weaken this\napplication's significance.\n5. The broader applicability of this approach remains questionable. While the authors suggest their strategy could be applied\nto other monomer systems beyond PAAm, they provide experimental validation with other hydrogels. The mechanism of\ntransient entanglement formation and its relationship to molecular structure remains inadequately explained, making it\ndifficult to evaluate the generalizability of this approach.\n6. Some technical points:\n• Absolute resistance values should be given\n• Detailed sensor fabrication protocols is missing.\n• Comparative studies with conventional hydrogels for those applications", "reviewer_2": "This paper reported a simple and general method for the fabrication of a single-network PAAm hydrogels with numerous\ntransient entanglements that can slip and disentangle to dissipate energy upon deformation. The resultant transiently\nentangled hydrogels effectively resolve the longstanding stiffness–toughness conflict, achieving high toughness and low\nhysteresis alongside excellent fatigue resistance. The paper could merit the level of Nature Communications if the following\nminor issues are fully addressed:\nFirst, the author claimed that “The plateau value (G(t)/G₀) reflects the ratio between dynamic cross-links and permanent\ncross-links.” To be understood easier, the author should explain why G(t)/G₀ can reflect the ratio and what is the behind\nmechanism?\nSecond, why did the authors use Mooney-Rivlin model to distinguish the contribution of entanglements and chemical cross-\nlinks to the elasticity of these hydrogels? why do (cid:1)(cid:2) and (cid:1)(cid:3) correspond to the contributions of permanent cross-linking and\nentanglements to the elastic modulus respectively?\nThird, ¹H Double-Quantum NMR (¹H DQ NMR) experiments showed that the increase of chemical cross-linking leads to\nenhanced entanglements between dangling chains. However, Mooney-Rivlin model showed that as the cross-linker content\nincreases, (cid:1)(cid:3) (corresponding to the contributions of entanglements) first increases and then decreases. These seem to be\ndifferent conclusions.", "reviewer_3": "Although the author repeatedly emphasizes the mechanical advantages of its materials, unfortunately there are many key\nissues or mechanisms that have not been explained clearly, which has led me to question the reliability of the test data.\nI think the author should focus on one key breakthrough point in the framework of the paper to demonstrate its scientific value.\nEspecially, I am confused about how sensor application relates to the main argument of the paper? Besides,the author\nexcessively referenced previously published papers in terms of data organization.At present, it is difficult for me to support its\npublication in NC.\n（1）Firstly, the authors believe that their hydrogel has excellent mechanical properties, which is also a major emphasis in\nthe article. However, the testing method used is completely incorrect. The authors used rectangular samples instead of the\nstandard dumbbell-shaped test specimens, which always leads to larger deformations at the points where the sample is\nfixed to the material testing apparatus during the test. This often results in significant difference between the sample's strain-\nstress and the real results, typically manifesting as more higher fracture strains and toughness in the calculation process.\nTherefore, we do not trust the mechanical values reported in the author's article.（a fracture strain of 5071%, a fracture\nstrength of 1.06 MPa, a fatigue threshold of 1968 J·m2）Although many papers may misuse this standard test and avoid\ndiscussing its impact, in high-level journals like Nature Communications, we believe it is essential to clarify this point.\n（2）In the paper, the authors consider elasticity/stiffness and toughness to be contradictions, but in fact, referring to\nelasticity alone is unfair. In materials science, strength and toughness often constitute a pair of contradictions. (\"The conflicts\nbetween strength and toughness.\" Nature Materials, 2011.) Additionally, in the context of hydrogels, this contradictory\nrelationship is even more complex: \"Design principles for strong and tough hydrogels.\" Nature Reviews Materials, 2024.\n（3）The authors state, \"tailoring entanglements in hydrogels is challenging due to the competition and repulsion of water\nmolecules, which tend to weaken the entanglement effect.\" This is one of the foundational elements of the author's paper.\nWe hope that the authors can provide specific references or specific chapters from textbooks, rather than merely citing the\ntextbook (\"The Theory of Polymer Dynamics,\" 1988) in general.\n（4）The authors said that due to the high water content, hydrogen bonding between PAAm chains is negligible, and thus\nthe dynamic cross-links are primarily attributed to transient entanglements，Figure 2a. This is a problem. Hydrogen bonding\nin PAAm gel is very important. For example, PVA hydrogels often have a water content of 90%, yet their hydrogen bonding\nnetwork plays a significant role.\n（5）The authors have conducted extensive characterizations to describe the entanglement mechanism. We believe that ¹H\nDouble-Quantum NMR alone is sufficient. The additional model fittings in Figure efg, along with DLS and the intensity time-\naveraged correlation functions, only serve to complicate the article further and dilute the emphasis on the mechanical\nproperties that the article aims to highlight. The framework of the figure should change a little.and this make this paper more\nsuitable for more suitable for the specialized journal of polymer physics like Macromolecules\n（6）As mentioned above, because the samples used by the authors are not standard, the samples exhibit greater strains\nand phenomena such as yielding and plasticization during testing, which can be seen in the tensile curves. Therefore, some\nof the subsequent calculations are problematic. Additionally, regarding the fatigue performance emphasized by the authors,\nthere are discrepancies with some data and reference literature. For example, the PAAm/alginate/Ca gel mentioned in the\nauthors' literature does not include fatigue performance data (\"Highly stretchable and tough hydrogels,\" Nature, 2012).\nFurthermore, the reference for fatigue performance data on double network hydrogels is also problematic, as the cited\nliterature does not describe fatigue data either (\"Why are double network hydrogels so tough?\" Soft Matter, 2010).\nSystematic studies on gel fatigue began only after Suo Zhigang's research later than 2015.\n（7）The tunability of mechanical properties and Figure 4, should be integrated with Figure 3 to ensure the logical\nconsistency of the paper. Additionally, some of the data should be moved to the supplementary information.\n（8）In Figure 4g, the gel shows significant hysteresis and yielding at strains exceeding 200%. Are you sure this is normal\nfor hydrogels that are designed to resist fatigue?\n（9）For the friction coefficient testing, it is essential to specify the surface roughness of the sample, the material and\nroughness of the friction counterpart, and the load applied. Additionally, hydration lubrication is crucial for hydrogel\nlubrication. The authors mention the material's excellent frictional performance and the application of a lubricating coating,\nbut they do not discuss the characterization of the lubrication mechanism. The authors should carefully review the relevant\nliterature and supplement the characterization of hydration lubrication.（\"Hydration lubrication in biomedical applications:\nFrom cartilage to hydrogels.\" Accounts of materials research 2022.，\"Recent progress in cartilage lubrication.\" Advanced\nMaterials 2021.Liu, J., Qu, S., Suo, Z., & Yang, W. (2021).）\n(10)Additionally, regarding the demonstration of sensing, we believe it is not related to the main mechanical theme of the\narticle, thereby diluting the content. Moreover, for hydrogel sensing, the authors need to measure the electrochemical\nproperties of hydrogels, as well as the micro-mechanisms of impedance changes. Merely using tests of resistance signal\nchanges is insufficient. For intelligent monitoring, only observing signal curve changes is not adequate; the authors should\nalso incorporate AI and machine learning for analysis assistance. The authors' demonstration of sensing does not meet the\nstandards of Nature Communications."}, "author_response": "Point-by-point response to the reviewers’ comments\nReviewer #1 (Remarks to the Author)\nI cannot recommend acceptance of this manuscript in its current form. The\ninappropriate citations undermine the scientific rigor of the work. If the authors believe\ntheir conductivity originates from residual ions, they must provide experimental\nevidence, not fabricated literature support.\nThe sensing application requires either proper validation or removal.\nAuthors’ response: Dear reviewer, we sincerely appreciate you for your time and effort\nin reviewing our manuscript again. We have revised the manuscript after carefully\nconsidering your comments and suggestions. All modifications are shown in red in the\nrevised manuscript and a detailed list to answer each of the questions is provided below.\nWe agree that (i) all citations must be directly relevant and (ii) any claim regarding\nthe origin of electrical conductivity must be supported by experimental evidence rather\nthan inferred or indirectly cited. We are sorry for the previously inappropriate literature\nsupport and we have performed the direct quantitative measurements of residual ions\nin the hydrogel.\nIn this revision, to keep the manuscript focused on the mechanical and lubrication\nadvances enabled by transient entanglements, we have therefore removed the sensing\napplication and all sensor-related claims and data from the manuscript and\nSupplementary Information.\n1) The authors claim (page 2 of rebuttal)\"Similar levels of conductivity from residual\ninitiator ions have been reported for neutral PAAm hydrogels (Adv. Mater. 2023,\n2210021; ACS Appl. Mater. Interfaces 2019, 11, 7405).\" This reference does NOT\nsupport the authors' claim about conductivity from residual ions. The authors cannot\nclaim literature support when the cited papers do not address the topic (A paper about\nelectronic conductivity in CNT composites).\nAuthors’ response: Thank you for your professional comments. We agree and sincerely\napologize for the inappropriate citations in our previous rebuttal. The references we\ncited (Adv. Mater. 2023, 2210021; ACS Appl. Mater. Interfaces 2019, 11, 7405) do not\nprovide direct support for ionic conductivity originating from residual initiator ions in\nneutral PAAm hydrogels. In the revised manuscript, we have removed these\ninappropriate citations and the discussion on sensing application to avoid any\nmisleading effect of literature support. We appreciate you again for your guidance and\nprofessional suggestions for improving our manuscript.\nRevisions: We have deleted the sensing application in the manuscript (Tough\ntransiently entangled hydrogels with multifunctions, Results; intelligent sensors, line 11,\nConclusion; Multifunctional sensor test, Methods) and the Supplementary Information\n(The previous version's Supplementary Note 7 and Supplementary Fig. 18).\n2) The claimed conductivity (σ = 1.5 × 10⁻² S/m) remains unvalidated. While typical\nresidual initiator concentrations is very low, the claimed conductivity is comparable to\nthe intentionally added salt system of higher concentration. The authors need to perform\nquantifying K⁺/SO₄²⁻ concentrations with ICP-MS or a control experiment by removing\nremaining initiators.\nAuthors’ response: Thank you for your insightful comment. We agree that direct\nquantitative evidence is essential. Following the suggestion, we have now quantified\nthe residual ionic species introduced by the KPS/TEMED redox initiation system and\nconfirmed their presence using three independent methods:\n(i) Ion chromatography (IC) for sulfate (SO 2-): using ion chromatography with solid-\n4\nphase extraction (SPE) pretreatment, we measured the SO 2- content in the hydrogel\n4\n(freeze-dried gel powder) as 1099 mg·kg-1 (Figure R1 and Table R1 as below).\n(ii) Inductively coupled plasma-mass spectrometry (ICP-MS) for potassium (K+):\nusing ICP-MS with acid digestion pretreatment, we measured the K+ content as 556\nmg·kg-1. (Table R2 as below)\n(iii) Energy-dispersive X-ray spectrometer (EDS) elemental analysis: EDS further\nconfirms the presence of K and S elements in the hydrogel, consistent with residual\npotassium sulfate species derived from the initiator (Figure R2 as below).\n(iiii) Quantitative validation of conductivity. To assess whether the measured residual\nions can generate a conductivity on the order of 10⁻² S·m⁻¹, we estimated the ionic\nconductivity using the Kohlrausch law of independent ionic migration at 25 °C,\nemploying limiting molar ionic conductivities at infinite dilution. From CRC Handbook\nof Chemistry and Physics (P. Vanýsek, Ionic Conductivity and Diffusion at Infinite\nDilution, 1993), the limiting ionic molar conductivities are 𝜆0 =\n𝐾+\n73.48 𝑆 𝑐𝑚2 𝑚𝑜𝑙−1 and 𝜆0 = 160 𝑆 𝑐𝑚2 𝑚𝑜𝑙−1 . Using the K⁺ and SO₄²⁻\n𝑆𝑂2−\n4\nconcentrations converted from our IC and ICP–MS measurements, the calculated\nconductivity is 8.63 × 10⁻² S/m. This estimated value represents an upper-bound\nbecause it is based on infinite-dilution molar conductivities, whereas in real hydrogels\nion mobility is reduced by non-ideal effect. Therefore, it is expected that the\nexperimentally measured conductivity is lower. Importantly, the calculation\ndemonstrates that the quantified residual ions are sufficient to account for the measured\nconductivity (1.5 × 10⁻² S/m), supporting an ionic conduction mechanism without\ninvoking electronic pathways.\nFinally, to maintain a rigorous and focused manuscript aligned with the core\nmechanical theme, we have removed all sensing-related results and discussions from\nboth the manuscript and the Supplementary Information.\nRevisions: All sensing demonstrations and conductivity-based application claims\nhave been removed from the manuscript and Supplementary Information (Tough\ntransiently entangled hydrogels with multifunctions, Results; intelligent sensors, line 11,\nConclusion; Multifunctional sensor test, Methods; The previous version's\nSupplementary Note 7; Supplementary Fig. 18).\nFigure R1. IC spectrum for detecting SO 2- content.\nWeight Time Area Height Amount\nNO. volume after dilution factor\nm0 (g) (min) (μS·min) S (mg/kg)\nV0 （mL) (mg/L) f\n1 0.0996 25 11.16 0.5185 4.377246 1 1.171 1098.706\nTable R2. Summary of the detected K+ concentration as determined by ICP-MS analysis\nConstant Concentration of Dilution Concentration of K+ Average\nWeight Content of K+\nNO. volume K+ in solution factor in digestion solution value\nm0 (g) Cx (ug/kg)\nV0 （mL) C0 (ug/L) f C1 (ug/L) (mg/kg)\n1 0.1011 25 2264.2531 1 2264.2531 559904.3249\n555.628\n2 0.1011 25 2226.3737 1 2226.3737 550537.5124\n5\n3 0.1011 25 2213.8619 1 2213.8619 547443.5979\nFigure R2. EDS spectrum and corresponding S and K element mapping.\nWe thank you for identifying this critical issue and professional suggestion again. By\ncorrecting the inappropriate citations, providing direct quantitative evidence for\nresidual ions, and removing sensor-related data that is irrelevant to the topic of our\nmanuscript, we believe the revised submission now meets the scientific rigor.\nReviewer #2 (Remarks to the Author)\nNow, the paper can be accepted by Nature Communications.\nAuthors’ response: We sincerely thank Reviewer #2 for the positive assessment and for\nrecognizing the improvements in the revised manuscript.\nReviewer #3 (Remarks to the Author)\nCompared with the previous manuscript, the authors have made substantial efforts to\nrevise the work and have addressed most of the controversial points. However, several\nissues still need to be resolved:\nAuthors’ response: Dear reviewer, we sincerely appreciate you for your time and effort\nin reviewing our manuscript again. And we appreciate you for acknowledging the\nsubstantial revisions. After carefully considering your comments and suggestions, we\nhave addressed the remaining concerns by adding rate-dependent mechanical validation,\nmicrograph of the crack tip, clarifying terminology regarding “single-network” and\nrevising the key trade-off plot to strength–toughness. All modifications are shown in\nred in the revised manuscript and a detailed list to answer each of the questions is\nprovided below.\n1) The authors propose an “transient entanglement” mechanism. If this is the case, the\ntime-dependent mechanical performance—such as fracture and fatigue resistance—\nmust be evaluated. Testing at different loading rates (1 mm/min, 10 mm/min, 100\nmm/min, and 1000 mm/min) should clearly demonstrate the effectiveness of the\ntransient-entanglement strategy.\nAuthors’ response: Thank you for your precious suggestion. To address the time-scale\ndependence expected for a transiently entangled network, we have performed rate-\ndependent uniaxial tensile tests on dumbbell specimens at the four crosshead speeds (1,\n10, 100 and 1000 mm/min). Using the gauge length of the dumbbell specimen, these\nspeeds correspond to strain rates of 0.00083, 0.0083, 0.083 and 0.83 s-1, respectively.\nThe resulting stress–strain curves and the extracted modulus, tensile strength, and strain\nare summarized in the newly added figure (Supplementary Fig. 13)\nAs shown in the Supplementary Fig. 13, the transiently entangled hydrogel exhibits\ncharacteristic rate dependence of a network governed by reversible topological\nconstraint. As the strain rate increase, the small-strain modulus and ultimate tensile\nstrength increases, but the strain at break decreases. This trend is fully consistent with\nthe proposed transient entanglement mechanism: at higher deformation rates, transient\nentanglements do not have sufficient time to disentangle and therefore behave as\neffective load-bearing constraints, leading to higher modulus and strength; at lower\nrates, these entanglements have enough time to progressively relax and disentangle,\nresulting in lower modulus and strength but higher extensibility.\nRegarding fatigue resistance, our manuscript already evaluates fatigue behavior\nusing cyclic crack-growth measurements to determine the fatigue threshold, which is\nintrinsically a time-dependent fracture metric. We have now explicitly state in the\nrevised manuscript that the high fatigue threshold obtained from long-cycle crack-\ngrowth measurements reflects genuine fatigue durability rather than single-shot fracture\nbehavior.\nWe have supplemented the data and related descriptions in the revised manuscript\nand Supplementary Fig. 13. Details are as follows:\n(line 14, paragraph 4, Characterization of mechanical properties, Results):\nMoreover, as the strain rate increases, transient entanglements do not have sufficient\ntime to disentangle and therefore behave as effective load-bearing constraints,\nincreasing the modulus and strength while reducing the fracture strain (Supplementary\nFig. 13)\n(line 1, paragraph 3, Characterization of mechanical properties, Results): To capture\ngenuine fatigue durability under successive tensile loading-unloading rather than\nsingle-shot fracture behavior, we determined the fatigue threshold (Γ ) by measuring\n0\nthe crack expansion of the transiently entangled hydrogel at different energy release\nrate amplitudes (Fig. 3e). Linear regression of the data yields a Γ of 1968 J·m⁻²,\n0\nwhich is much higher than that of pure natural rubber (~50 J·m⁻²), the permanently\nentangled hydrogel (~200 J·m⁻²), and the regular hydrogel (~10 J·m⁻²). Plotted on an Ashby map\nof fatigue threshold versus fracture energy, the transiently entangled hydrogel\noutperforms most existing tough hydrogels (Fig. 3f). Notably, even materials with\nappreciable fracture energies, such as natural rubber (~104 J·m⁻²) and the permanently\nentangled hydrogel (~1460 J·m⁻²), exhibit much lower fatigue thresholds,\nunderscoring the exceptional fatigue resistance enabled by the transiently entangled network.\nSupplementary Figure 13\nTensile stress-strain curves of the transiently entangled hydrogels upon different\nstrain rate. a) Tensile stress–strain curves and b) corresponding modulus, c) tensile\nstrength and d) fracture strain parameters of the transiently entangled hydrogel (LMC-\n4.8-AAm-4.2). The hydrogel exhibits characteristic rate dependence of a network\ngoverned by reversible topological constraint. As the strain rate increase, the small-\nstrain modulus and ultimate tensile strength increases, but the strain at break decreases.\nThis trend is fully consistent with the proposed transient entanglement mechanism: at\nhigher deformation rates, transient entanglements do not have sufficient time to\ndisentangle and therefore behave as effective load-bearing constraints, leading to higher\nmodulus and strength; at lower rates, these entanglements have enough time to\nprogressively relax and disentangle, resulting in lower modulus and strength but higher\nextensibility.\nWe thank you again for your suggestions, making the transient entanglement\nmechanism clearer and more comprehensive.\n2) The definition of a double-network hydrogel remains problematic. The authors\nemphasize that their material is a single-network system. However, if the physical\ncrosslinking network (formed by noncovalent, weak interactions) is considered as\nanother network, the system is in fact a multi-network structure. For example, even a\nsingle PVA network can exhibit a fatigue threshold as high as 10,500 J/m² (“Strong\ntough hydrogels via the synergy of freeze-casting and salting out”). Therefore, we\nbelieve the authors should not insist on claiming a single-network design. In addition,\nin Figure 3f, a complete Ashby plot should be provided for comparison, rather than a\nselective comparison.\nAuthors’ response: Thank you for your professional comment. In the revised\nmanuscript, we have revised the wording to avoid ambiguity and to align with broader\nusage. Specifically, we now describe our material as a “single-covalent-network PAAm\nhydrogel” in which transient entanglements act as reversible topological constraints,\nrather than insisting on “single-network” in an absolute sense. We explicitly distinguish\nthis design from classical double-network gels that contain two interpenetrating\npolymer networks with distinct crosslinking chemistries and permanent connectivity.\nIn addition, we have revised Fig. 3f to provide a complete Ashby plot of fatigue\nthreshold versus fracture energy of transiently entangled hydrogel, other reported tough\nhydrogels and natural rubber (Fig. 3f).\nAnd we have revised the descriptions in the revised manuscript: (line 6, paragraph\n3, Characterization of mechanical properties, Results): Plotted on an Ashby map of\nfatigue threshold versus fracture energy, the transiently entangled hydrogel outperforms\nmost existing tough hydrogels (Fig. 3f). Notably, even materials with appreciable\nfracture energies, such as natural rubber (~104 J·m⁻²) and the permanently\nentangled hydrogel (~1460 J·m⁻²), exhibit much lower fatigue thresholds,\nunderscoring the exceptional fatigue resistance enabled by the transiently entangled network.\nFig. 3 ∣ Characterization of mechanical properties. f) an Ashby plot of fatigue\nthreshold versus toughness (fracture energy) of transiently entangled hydrogel, other\nreported tough hydrogels and natural rubber.\n3) In the notched sample images in Figure 1g, the crack tip does not appear sufficiently\nsharp. This can lead to significant deviations in fracture and fatigue measurements.\nAuthors’ response: Thank you for your insightful comment. We agree that crack-tip\nsharpness is critical. In our experiments, the notch was introduced using a fresh\nmicrotome blade, and the crack-tip radius was controlled to be as small as possible. To\nremove any ambiguity, we have now added an enlarged optical micrograph of the crack\ntip in the revised Supplementary Information (Supplementary Fig. 4), which shows that\nthe crack tip of the sample is sufficiently sharp. At λ=2 (Fig. 1g), the crack tip does not\nappear sharp (slightly blunt area, which is actually light spot) due to the lighting and\nreflection during photography, rather than an actual rounded notch. Consistent with this\ninterpretation, no blunt area is observed at λ=4 (Figure R3 as below) and higher stretch\n(λ=10, 15 and 35, Fig. 1g), where the crack front is clearly resolved. Therefore, the\nreported fracture and fatigue values are not samples of blunt notches. We appreciate\nyour guidance again and believe the clarified wording and added micrograph resolve\nthe concern.\nSupplementary Figure 4\nMicrograph of the crack tip of the transiently entangled hydrogel. We used a\npolarizing microscope to record the crack tip of the pre-notched samples, which is\nsufficiently sharp.\nFigure R3. Photographs of a notched transiently entangled hydrogel (notch width ≈ 80%\nof sample width) stretched to 2 and 4 times.\n4) Although the authors have revised the description and now emphasize the strength–\ntoughness trade-off, Figure 3d still presents modulus–toughness data. We recommend\nthat the authors provide strength–toughness data instead, as this is central to the main\nclaim of the paper.\nAuthors’ response: We appreciate your constructive suggestion and fully agree that the\nstrength–toughness relationship is more directly aligned with the central claim of our\nmanuscript. Accordingly, we have revised the figures and the associated discussion as\nfollows：\ni) Strength–toughness plot added to the manuscript. We have added a new plot\nshowing fracture energy (𝛤) versus tensile strength (𝜎) for the three hydrogel classes\n(regular, permanently entangled, and transiently entangled), which now serves as the\nprimary trade-off map in the revised manuscript (Fig. 3d). This presentation directly\nsupports our key message that transient entanglements enable a markedly improved\nstrength–toughness balance compared to conventional networks.\nii) Modulus-toughness plot was modified to yield strength vs. toughness plot.\nBecause yielding is a characteristic mechanical feature of transient-entanglement\nnetworks, serving as an important descriptor to demonstrate the hydrogel’s strength and\nstiffness, we revised the original modulus-toughness based comparison into a yield\nstrength vs. toughness plot and moved it to the Supplementary Information\n(Supplementary Fig. 12).\nAnd we have revised related descriptions in the revised manuscript: (line 7,\nparagraph 2, Characterization of mechanical properties, Results): Therefore, regular\nhydrogels often face a strength-toughness trade-off, where toughness (represented by\nΓ, or fracture energy) is inversely related to strength (represented by σ or yield strength\nσ , which reflects cross-link density). This relationship is described as Γ ~ σ⁻2.63,\ny\nindicating that chemical cross-links increase strength but also make the hydrogels more\nbrittle. In contrast, permanently entangled hydrogels partially overcome this issue. The\npermanently trapped entanglements stiffen the hydrogels but do not significantly\ncompromise their toughness, following the scaling Γ ~ σ⁻1.52. Transiently entangled\nhydrogels, however, show minimal strength-toughness conflict, with a scaling of Γ ~\nσ⁻0.61. Notably, even with nearly an order of magnitude increase in the σ value, the Γ\nvalue only changes slightly, indicating that transient entanglements effectively enhance\nstrength without leading to brittleness (Fig. 3d and Supplementary Fig. 12).\nFig. 3 ∣ Characterization of mechanical properties. d) Two families of the three types\nof hydrogels plotted in the strength-toughness (fracture energy) plane.\nSupplementary Figure 12\nTwo families of the three types of hydrogels plotted in the yield strength (σ ) versus\ny\ntoughness (Γ, fracture energy) plane. This relationship is described as Γ ~ σ ⁻3.26 for\ny\nregular hydrogels; Γ ~ σ ⁻2.58 for permanently entangled hydrogels; and Γ ~ σ ⁻0.07 for\ny y\ntransiently entangled hydrogels. The nearly two-order-of-magnitude increase in the σ\ny\nvalue did not reduce the Γ value, indicating that transient entanglement can effectively\nstrengthen the materials without causing brittleness.\nIn addition, during revising the Fig.3d, we noticed an inconsistency in the x-axis\ndefinition of Fig. 3c. In the original version, the plotted range inadvertently\ncorresponded to 𝑚 defined as the mass ratio of LMC crosslinker to (AAm + LMC\naqueous solution), whereas throughout the manuscript 𝑚 is consistently defined as the\nmass ratio of LMC crosslinker to AAm monomer. We have corrected Fig. 3c\naccordingly so that the x-axis definition and range are fully consistent with the\nmanuscript notation. This correction is purely a labeling/definition consistency fix and\ndoes not change any raw experimental data or the conclusions. We sincerely thank you\nfor giving us the opportunity to correct this mistake and make this point clear."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I cannot recommend acceptance of this manuscript in its current form. The inappropriate citations undermine the scientific\nrigor of the work. If the authors believe their conductivity originates from residual ions, they must provide experimental\nevidence, not fabricated literature support.\nThe sensing application requires either proper validation or removal.\n1. The authors claim (page 2 of rebuttal)\"Similar levels of conductivity from residual initiator ions have been reported for\nneutral PAAm hydrogels (Adv. Mater. 2023, 2210021; ACS Appl. Mater. Interfaces 2019, 11, 7405).\" This reference does\nNOT support the authors' claim about conductivity from residual ions. The authors cannot claim literature support when the\ncited papers do not address the topic (A paper about electronic conductivity in CNT composites).\n2. The claimed conductivity (σ = 1.5 × 10⁻² S/m) remains unvalidated. While typical residual initiator concentrations is very\nlow, the claimed conductivity is comparable to the intentionally added salt system of higher concentration. The authors need\nto perform quantifying K⁺/SO₄²⁻ concentrations with ICP-MS or a control experiment by removing remaining initiators.", "reviewer_2": "Now, the paper can be accepted by Nature Communications.", "reviewer_3": "Compared with the previous manuscript, the authors have made substantial efforts to revise the work and have addressed\nmost of the controversial points. However, several issues still need to be resolved:\n1. The authors propose an “transient entanglement” mechanism. If this is the case, the time-dependent mechanical\nperformance—such as fracture and fatigue resistance—must be evaluated. Testing at different loading rates (1 mm/min, 10\nmm/min, 100 mm/min, and 1000 mm/min) should clearly demonstrate the effectiveness of the transient-entanglement\nstrategy.\n2. The definition of a double-network hydrogel remains problematic. The authors emphasize that their material is a single-\nnetwork system. However, if the physical crosslinking network (formed by noncovalent, weak interactions) is considered as\nanother network, the system is in fact a multi-network structure. For example, even a single PVA network can exhibit a\nfatigue threshold as high as 10,500 J/m² (“Strong tough hydrogels via the synergy of freeze-casting and salting out”).\nTherefore, we believe the authors should not insist on claiming a single-network design. In addition, in Figure 3f, a complete\nAshby plot should be provided for comparison, rather than a selective comparison.\n3. In the notched sample images in Figure 1g, the crack tip does not appear sufficiently sharp. This can lead to significant\ndeviations in fracture and fatigue measurements.\n4. Although the authors have revised the description and now emphasize the strength–toughness trade-off, Figure 3d still\npresents modulus–toughness data. We recommend that the authors provide strength–toughness data instead, as this is\ncentral to the main claim of the paper."}, "author_response": "Point-by-point response to the reviewers’ comments\nReviewer #1 (Remarks to the Author)\nI recommend ACCEPTANCE. The authors have provided rigorous experimental validation (IC, ICP-MS, EDS)\ndemonstrating that residual ions quantitatively account for the observed conductivity, removed all inappropriate citations,\nand refocused the manuscript on its excellent core contribution.\nAuthors’ response: We sincerely thank the reviewer #1 for the positive\nrecommendation and for the careful and rigorous evaluation throughout the review\nprocess. Your constructive feedback greatly improved the rigor and clarity of the work.\nReviewer #3 (Remarks to the Author)\nIt is evident that the editor strongly supports the publication of this manuscript and has provided multiple opportunities for\nrevisions.Although there are still controversies surrounding some of the responses, the manuscript has basically met the\npublishing requirements.I don't have any further questions.\nAuthors’ response: We sincerely thank the reviewer #3 for the careful assessment of\nour revised manuscript and for acknowledging the substantial improvements made\nduring revision. We appreciate your constructive critiques and suggestions throughout\nthe review process, which helped us strengthen the experimental rigor, clarify the\nmechanistic interpretation, and improve the overall presentation. We are grateful for\nyour time and consideration, and we are pleased that you have no further questions."}, {"round": 3, "reviewer_comments": {"reviewer_1": "I recommend ACCEPTANCE. The authors have provided rigorous experimental validation (IC, ICP-MS, EDS)\ndemonstrating that residual ions quantitatively account for the observed conductivity, removed all inappropriate citations,\nand refocused the manuscript on its excellent core contribution.", "reviewer_3": "It is evident that the editor strongly supports the publication of this manuscript and has provided multiple opportunities for\nrevisions.Although there are still controversies surrounding some of the responses, the manuscript has basically met the\npublishing requirements.I don't have any further questions."}, "author_response": ""}]

Decision letter