A universal strategy towards self-healing materials via dynamic interfacial liquid metal coordination

Domain: neuroscience
Published: 2026-02-16
Editorial outcome: major_revision

Abstract
Self-healing polymer materials, capable of autonomously repairing physical damage, have been broadly applied in modern technologies. In various self-healing systems, metal–ligand coordination bonds have been extensively utilized for their advantages of rich metal–ligand species and functionalities. However, common metal-ligand coordination either has excessively stable bond strengths or is too weak to construct self-healing materials. This work introduces coordination metals into liquid metals (LMs) to form multi-component LMs (mLMs), which creatively leverage the inherent fluidity of mLMs to convert common metal-ligand coordination (e.g., silver-sulfur and zinc/copper-imidazole systems) into reversible interfacial coordination. Such dynamic coordination successfully offers the fantastic self-healing efficiency over 90% for general polymers. Considering the ultra-high thermal conductivity of mLMs, self-healable thermal interface materials (TIMs) are obtained, which successfully address the long-standing challenge of the irreversible damage in long-term used TIMs. The self-healable TIMs can lower the peak temperature of the central processing unit (CPU) by 20oC under extreme conditions for long time (accumulated 16 hours thermal shock, −10oC to 100oC). This work provides a universal strategy for self-healing materials and greatly broadens the investigations of self-healing, coordination chemistry, liquid metal science, soft electronics, and thermal management materials.

Introduction
Self-healing polymer materials, owing to their inherent capacity for autonomous damage remediation, have emerged as indispensable constituents of modern intelligent material systems, such as wearable technologies, energy materials, and intelligent medical devices1,2. The current dominant strategy for achieving polymer self-healing properties involves introducing reversible covalent bonds (e.g., Diels-Alder reactions3, disulfide bonds4,5), non-covalent bonds (e.g., hydrogen bonds6–8, ionic bonds9, host-guest interactions10,11, coordination bonds12–14), and physical interactions (e.g., phase separation15, magnetic force16, shape memory effect17). These reversible interactions enable the fabrication of materials with high healing efficiency, spontaneous healing without external conditions, and functional capabilities18,19. In these self-healing systems, metal-ligand coordination bonds have been successfully and broadly used in self-healing polymer materials with the advantages of rich metal-ligand species20,21, selectable and adjustable coordination bond strengths (25–95% of covalent bonding)22, as well as functionalities of different coordination systems (stimulation correspondence, shape memory, and luminescence, etc.)23.

However, the vast majority of metal-ligand coordination bonds either have excessively stable bond strengths or are too weak to be suitable for constructing self-healing polymer materials24. To address these challenges, researchers have developed innovative strategies targeting the synthesis of new ligands and polymers, aiming to achieve metal-coordinated polymer materials with self-healing properties25,26. However, incorporating ligands into polymer systems often involves elaborate chemical synthesis, leading to greatly elevated costs and difficulties in industrial application compared to hydrogen and ionic systems. Additionally, the metal-coordinated polymer materials frequently lack ultra-high electrical conductivity (>1.0×10⁵S·m⁻¹) and thermal conductivity (>2W/m·K), which significantly restricts their applications in modern technologies27,28.

Liquid metals (LMs) have drawn considerable interest in the fields of flexible electronics and wearable devices owing to their fluidity at room temperature and exceptional thermal/electrical conductivity29–33. However, gallium (Ga)-based liquid metals exhibit weak coordination ability with common ligands and, like aluminum (Al) metals, have thus been rarely studied in metal-coordination systems34,35. In recent years, dissolving other metals in liquid metals to create functionalized multi-component LMs (mLMs) has gained significant attention. For instance, dissolving palladium in Ga can result in new catalytic materials with fluidity36. Mixing metallic iron with Ga builds a magnetic metal with high mobility37. Our team has also successfully dissolved metals such as bismuth and indium in liquid Ga to prepare phase change materials with high thermal conductivity for electronic heat dissipation and packaging38. Therefore, coordination-active metals such as silver (Ag) and zinc (Zn) are introduced into LMs to endow the resulting mLMs with coordination capabilities. The fluidic interfaces of mLMs microdroplets enable regeneration of coordination sites through interfacial atomic migration, thereby expanding the dynamic coordination unit from molecular to microscopic dimensions. This mLMs-based dynamic interfacial strategy can derive its reversibility from the self-renewing fluidic interface, rather than being constrained by the strength of coordination bonds. In contrast, existing reversible coordination systems rely on weak bonding interactions at the molecular dimensions, where the irreversible behavior remains confined by the inherent strength of the coordination bonds.

In this work, through the mLMs interfacial coordination bonds, we creatively leverage the inherent fluidity of mLMs to convert classical metal-ligand coordination into reversible interfacial interactions and endow general polymers with self-healing capabilities. This work introduces a wider range of metal-coordinated bonds into self-healing polymer systems. It thereby overcomes a critical limitation of conventional systems, where the bonds are either too strong or too weak to enable complete and autonomous healing. In this work, silver-sulfur coordination is fully investigated as a representative mLMs system and successfully achieved reversible coordination behaviors at the mLMs interfaces, offering the self-healing properties for natural rubber (NR). The coordination composites show excellent self-healing efficiencies of over 90% under room temperature. More importantly, such mLMs strategy can be applied to common metal-ligand coordination bonds and is suitable for general polymers. For example, zinc and copper-imidazole coordination are also introduced into liquid metal systems to achieve the surprisingly self-healing feature for general acrylic polymers with self-healing efficiency over 90%. Molecular dynamics (MD) simulations, Materials Studio (MS) calculations, mechanical evaluations, and X-ray photoelectron spectroscopy (XPS) analysis strongly demonstrated the dynamic interfacial characteristics of mLMs surface atoms and their ligand coordination capability. Considering the thermal performance of mLMs, self-healable thermal interface materials (TIMs) are obtained with high thermal conductivity (6.8W/m·K). The self-healable TIMs successfully address the long-standing challenge of irreversible damage in long-term used high-performance TIMs, which can lower the peak temperature of the central processing unit (CPU) by 20°C under extreme conditions for long time (accumulated 16h thermal shock from −10°C to 100°C). This work creatively combines LMs and metal coordination chemistry, which provides a universal and powerful strategy for the next generation of functional self-healable materials.

Results
Gallium is not suitable for use in metal-ligand coordination based self-healing polymers because of its weak metal coordination ability. Interestingly, liquid metal Ga acts as a metal solvent. This property allows the synthesis of coordination-active mLMs through the incorporation of metals such as silver (Ag), copper (Cu), and zinc (Zn). As shown in Fig. 1A, the introduction of mLMs into the polymer system resulted in successful interfacial coordination between the active metal atoms on the surface of the mLMs and the ligands on the polymer chains. Unlike a common metal-ligand coordination system, this interfacial coordination occurs exclusively around the active metal atoms on the surface of the fluidic mLMs. The fluidity of mLMs plays a critical role in the reversible interfacial coordination for self-healing involving mLMs and polymer materials. Figure 1B illustrates the self-healing process of interfacial coordination. Firstly, interfacial coordination is formed between the active metal atoms on the surface of mLMs and ligands (Fig. 1B1). When damaged by external force, defective regions are generated on the surface of mLMs, and the interfacial coordination formed between mLMs and ligands is simultaneously damaged (Fig. 1B2). Then, due to the fluidity of mLMs, the newly generated active metal atoms and Ga in the defective region migrate to the surface and heal the defects. The healed mLMs surface re-engages with the ligands on the polymer chains, thereby enabling the self-healing features (Fig. 1B3). In contrast, realizing the self-healing capability by common strong metal coordination systems (such as Ag-S) is challenging, as demonstrated in Fig. 1C. Owing to the abundant active sites on Ag powder, strong Ag-S coordination bonds form between the powder and sulfur ligands in natural rubber (NR), creating a rigid network. The permanent and irreversible nature of the coordination bond at the interface makes it difficult for the composite to exhibit self-healing properties.

Interestingly, the mLMs strategy can make common metal coordination (e.g., the above Ag-S coordination) into dynamic interfacial coordination and provide self-healing properties for general polymers. As shown in Fig. 1D and Fig. S1, the stretchable mLMs-NR composites containing 30wt.% Ag0.1 LMs dispersed in NR are prepared by shear mixing, designated as Ag0.1 LMs-NR-30. Here, mLMs-Polymer-y is used to represent the composition of the sample in this work. m is the active metal in the LM, x is the weight ratio between the m and LM, y is the weight percentage of the m and LM in the composites, and polymer is the base material. The interfacial coordination of Ag0.1 LMs endows Ag0.1 LMs-NR-30 with fantastic self-healing capability. As shown in Fig. 1E, the damaged area of the composite completely heals after 180min at room temperature, with the healed material maintaining tensile properties comparable to the original state (Fig. 1E1, 2).

Based on the dynamic interfacial coordination formed between mLMs and ligands, the autonomous healing capability of mLMs composites is further demonstrated. As shown in Fig. 2A, the damaged Ag0.1 LMs-NR-30 achieved successful self-healing performance within 180min at room temperature. Uniaxial tensile experiments further show that the self-healed samples retained tensile capacity under large strains (0, 300, and 450%). This phenomenon can be attributed to the reversible interfacial coordination between polysulfide ligands and surface atoms and their ligand coordination capability. Upon mechanical damage, the fluidity of Ag0.1 LMs facilitates interfacial diffusion and reformation of coordination bonds, enabling self-healing capability while maintaining mechanical performance. In addition, DSC analysis of Ag0.1 LMs-NR-30 shows no melting peak (Fig. S2A), confirming the liquid state of Ag0.1 LMs from 0 to 80°C. This fluidity is maintained due to the supercooling effect of micro-sized LM droplets in the composite matrix (Fig. S2B)39. In addition, the self-healing properties of the Ag0.1 LMs-NR-y composites with different filler mass fractions (y = 0, 10, 30, and 50) are systematically investigated. As shown in Fig. S3, when Ag0.1 LMs are in excess (y > 50), it reduces the mechanical strength of the material due to the agglomeration of mLMs in composites. In contrast, at low loading (y < 30), the interfacial coordination network is defective due to insufficient coordination density. This results in decreased self-healing efficiency. The incorporation of Ag0.1 LMs with liquidity interfaces dramatically improves the autonomous healing performance of the Ag0.1 LMs-NR-30 (Fig. 2B). Ag0.1 LMs-NR-30 exhibits almost the same mechanical behaviors with the original sample after 180min of self-healing (Fig. 2B), indicating effective self-healing properties. Furthermore, 3D microscopy images (Fig. 2B, inset) reveal that the microcrack interfaces at the fracture surface are progressively repaired as healing time increases (Fig. S4), directly confirming the self-healing capability of Ag0.1 LMs-NR-30 composite. Notably, pure NR polymer exhibits an extremely low self-healing efficiency of 2.4% (Fig. S5), whereas NR polymer with 30wt.% Ag0.1 LMs (Ag0.1 LMs-NR-30) significantly enhances self-healing efficiency to 90.5%. Furthermore, as demonstrated in Fig. 2C, when pure Ga is composited with NR, Ga-NR-30 (the weight fraction of Ga in the composite is 30wt.%) has a self-healing efficiency of only 11.3%, confirming the critical role of coordination interactions at the interface. In contrast, Ag-NR-3 (3.0wt.% Ag) displays negligible self-healing efficiency (0.8%), which originates solely from polymer chain diffusion (Figs. 2C and S5). This system represents a traditional strong metal coordination system that lacks interfacial liquidity. Upon increasing the Ag mass fraction to 30%, the resulting Ag-NR-30 exhibits poor moldability. This is attributed to the fact that the excess Ag coordinates with sulfide bonds, which shows too heavy crosslinking to impair the molding process (Fig. S5). The mechanism of the self-healing ability can be further elucidated by microstructural analyses. The SEM images and element mapping in Fig. 2D show that the damaged region is enriched with coordination-active Ag and liquid Ga. Importantly, the fluidic Ga transports Ag to the damaged area, reconstructing an interface capable of coordinating with ligands in the polymer matrix and thereby enabling self-healing (Fig. S6). Figure 2E demonstrates that the healing efficiency of Ag0.1 LMs-NR-30 exhibits a time-dependent enhancement, reaching 90.5% after 180min of healing under room temperature. In addition, the Ag0.1 LMs-NR-30 has excellent self-healing stability with healing efficiency over 86% in five fracture-healing cycle tests (Fig. S7). The self-healing rate of composites is ultimately limited by polymer chain mobility. As shown in Fig. S8, with identical Ag0.1 LMs content, the low molecular weight NR composite (Ag0.1 LMs-L-NR-30) reaches 90% healing efficiency in just 120min. The relatively higher molecular weight NR composite (Ag0.1 LMs-NR-30) is 60min slower to complete self-healing. This marked difference confirms that chain migration and rearrangement kinetics govern macroscopic healing behavior. The hysteresis curves from mechanical cycling can effectively characterize the interfacial healing processes within the materials40. As shown in Fig. 2F, the cyclic tensile curve of Ag0.1 LMs-NR-30 after healing (strain: 200%) almost completely overlaps with that of the original sample, indicating significant recovery of its elastic properties. Notably, during the cycling tests, the hysteresis curve of Ag0.1 LMs-NR-30 gradually decreases with increasing tensile cycles but fully recovers to its initial state after 30min of rest (Fig. S9). This phenomenon is attributed to the rupture-reconstruction mechanism of the dynamic interfacial coordination between Ag0.1 LMs and sulfide bonds, which not only recovers the elastic properties but also ensures exceptional stability under repeated loading. In contrast, the hysteresis curve of Ag-NR-3 remains unaffected by increasing cycle numbers (Fig. S10), which is closely related to its highly stable crosslinked network within the polymer. The strong coordination interactions significantly suppress relative sliding between molecular chains, yet limit the ability of the material to self-heal. However, Ga-NR-30 exhibits high residual strain even after 30 minutes of rest following 200% strain stretching, demonstrating irreversible structural damage (Fig. S10). Further insight into the interfacial dynamics comes from rheological analysis. As shown in Fig. S11, the Ag0.1 LMs-NR-30 composite exhibits simultaneously decreasing storage and loss moduli with temperature, characteristic of a dynamic network enabled by interfacial fluidity. In contrast, the Ag-NR-3 composite shows constant moduli, reflecting a static, irreversible network. These results further confirm the critical role of the dynamic interfacial coordination in self-healing performance.

More importantly, the reversible interfacial coordination strategy establishes a universal approach for coordination-mediated self-healing, enabling the construction of high-performance self-healing materials by common coordination bonds. As shown in Fig. 2G, the introduction of the interfacial coordination system of Zn-imidazole into polymer materials can also obtain excellent self-healing composites. When mechanical damage occurs, interfacial fracture develops within the composite. The Zn0.2 LMs at the fracture interfaces spontaneously coordinate with imidazole ligands on polymer chains, driving reconstruction of coordination networks that eliminate cracks and enabling self-healing of composites. To demonstrate the healing mechanism, polymers containing imidazole ligands are synthesized through a facile one-pot free radical polymerization method. The monomers (n-butyl acrylate (nBA), 1-vinylimidazole (Vim), and methyl methacrylate (MMA)) are selected to copolymerize to obtain PBVM copolymer (P(nBA-co-Vim-co-MMA)) (the synthetic procedure is shown in Fig. S12). The 1H NMR spectrum and Fourier infrared (FT-IR) results indicate successful copolymerization (Fig. S13- S14). The obtained PBVM is solvent-blended with Zn0.2 LMs to form the Zn0.2 LMs-PBVM-12 composite. As shown in Fig. 2H, the cut sample of Zn0.2 LMs-PBVM-12 (0.2g) achieves self-healing and supports a 200g load, demonstrating its high load-bearing capacity and structural stability. Optical microscopy observations reveal that microcracks disappear completely after 18h of healing. Furthermore, mechanical tensile tests reveal a 91.9% self-healing efficiency for the Zn0.2 LMs-PBVM-12 after 18h at room temperature (Fig. 2I). In addition, the self-healing capability of Zn0.2 LMs-PBVM-12 originates from Zn0.2 LMs-driven coordination interactions. As a result, pure PBVM materials do not show self-healing properties (Fig. S15). Similarly, Zn-PBVM-2.4 (without Ga) and Ga-PBVM-12 (without Zn) are also unable to self-heal. These control experiments confirm that both fluidic character and coordination ability are indispensable for achieving self-healing. In addition, similar self-healing behaviors are also observed for the copper-imidazole system. With the same PBVM polymer, Cu0.05 LMs-PBVM-6 showed the self-healing efficiency near 90% (Fig. S16), indicating the broad applicability of the reversible interfacial coordination strategy for common metal-ligand systems.

The fabrication process of mLMs is shown in Fig. 3A, the mLMs are obtained by doping Ag or Zn reactive metal particles in Ga matrix at high temperature (~250°C). Ag or Zn active metals are uniformly dispersed as atoms or atomic clusters within the mLMs. Notably, the obtained mLMs are also fluidic metals near room temperature, which is verified by dynamic scanning calorimetry (DSC) with melting temperatures at 33.4°C and 29.4°C, respectively (Fig. S17 and S18). The self-healing process of mLMs is illustrated in Fig. 3A2. When mLMs are damaged, their intrinsic mobility enables the atoms to migrate to the damaged surface, thereby forming the renewable surface character for mLMs. The fluidity of mLMs allows coordination-active atoms to migrate between adjacent droplets. EDS analysis in Fig. S19 shows that Ag atoms transferred through the liquid Ga matrix from Ag-rich to Ag-poor droplets until reaching compositional equilibrium. This inter-droplet mobility enables network redistribution of Ag atoms, significantly enhancing the efficiency of the self-healing process. To investigate the dispersion state of Ag in the Ag0.1 LMs matrix, molecular dynamics (MD) simulations are performed using the LAMMPS software under canonical ensemble system (NVT) conditions at a temperature of 537.15 K, for a duration of 100 ps with a timestep of 1 fs, and a mixing potential truncation radius of 10.0 Å, constructing an Ag0.1 LMs model system composed of 2304 Ga atoms and 256 Ag atoms (Fig. S20). Figure 3B demonstrates the RDF of the atoms of the Ag0.1 LMs bulk region, which shows that the radial distances of the different atom pairs in the system are Ag-Ag (2.7 Å), Ga-Ga (2.8 Å), and Ag-Ga (3.5 Å), respectively. Atomic configuration analysis confirms that Ag atoms are uniformly dispersed as isolated atoms or small clusters within the Ag0.1 LMs model, with no significant aggregation observed. The distribution of Ag atoms at the interface is consistent with that in the bulk region (Fig. S21A). Additionally, the atomic density distribution along the Z-direction reveal that Ag atoms are uniformly distributed in the Ag0.1 LMs model, with a slight shift toward the interface (Fig. S21B). SEM and elemental mapping reveal that Ag0.1 LMs form spherical droplets with smooth surfaces (Fig. 3C). Surface analysis detects both Ga and Ag, confirming the presence of active Ag atoms at the liquid interface. The green area corresponds to regions enriched with Ga, whereas the red areas indicate Ag atoms distributed on the surface of Ag0.1 LMs particles, confirming the presence of Ag atoms at the liquid interface. Zn atoms are also identified on the surface of Zn0.2 LMs (Fig. S22). Similarly, as shown in Fig. 3D, the XRD spectra of Ag0.1 LMs exhibit characteristic peaks corresponding to Ag and Ga, along with distinct Ag-Ga phase peaks detected at approximately 23.6°, 40°, and 47.7°. It is noteworthy that similar phase formation and elemental dispersion behavior are observed in the Zn0.2 LMs (Fig. S23).

Based on the atomic distribution characteristics of mLMs, the active Ag atoms uniformly distributed at the mLMs interface can form active sites capable of coordination with functional ligands. Interestingly, coupled with the inherent fluidity, the interfacial active region in mLMs also exhibits fluidity and thus shows damage-reconstruction, endowing a renewable interfacial coordination feature for mLMs after surface damage. XPS analyses further confirmed the atomic structure features of the mLMs interface. As shown in Fig. 3E, the characteristic peaks of Ga 2p and Ag 3d are observed simultaneously on the surface of Ag0.1 LMs. Notably, the characteristic peaks of Ga 2p and Ag 3d are still observed on the newly exposed surface after interfacial damage with consistent peak positions and intensities. This result clearly demonstrates the distinctive liquid-like interfacial self-healing of Ag0.1 LMs. The mechanism relies on their inherent fluidity, which enables spontaneous reorganization after interfacial damage. More importantly, as shown in Fig. S24, the Ag 3d peak of Ag0.1 LMs shifts to a higher binding energy (0.6 eV) compared to conventional Ag powder. The higher binding energy indicates the polarization of Ag atoms, and similar results are observed in previous reports36. The Ag atoms on the surface of Ag0.1 LMs are polarized by the local environment in liquid metal Ga, leading to partial positive electroneutrality of Ag atoms. Similar to previous work41,42, these polarized metal atoms provided anchor points for coordination at the interface with the polymer, and the entire polymer chain interacts with the Ag0.1 LMs by coordination adsorption, providing the basis for material self-healing. The surface atomic activity of mLMs plays a crucial role in the renewable interfacial coordination. As shown in Fig. 3F, the Linear Scanning Voltammogram (LSV) polarization curves of Ga, Ag0.1 LMs, and Zn0.2 LMs are presented. The results indicate that the overpotentials for Ag0.1 LMs and Zn0.2 LMs are significantly lower than those of Ga at current densities of 20 mA·cm⁻² and 50 mA·cm⁻². As previously reported43, the lower overpotentials suggested that the reaction kinetics of the mLMs are faster (Fig. S25), which further highlights the high reactivity of Ag and Zn atoms located on the surface of mLMs. Materials Studio (MS) calculations demonstrate significant differences in the interaction of Ag, Ga, and Ag0.1 LMs with sulfur (Fig. S26). As shown in Fig. 3G, the strong Ag-S binding energy results from coordination bonding. This creates a rigid interfacial structure that prevents self-healing. In contrast, Ga exhibits a lower binding energy with S, only 61% of the binding energy of Ag to S, making it challenging for Ga surfaces to effectively anchor S atoms. For Ag0.1 LMs, the binding energy is intermediate between pure Ag and Ga compared to pure Ag-S coordination. The Ag0.1 LMs weakened the binding between Ag and S by reducing the exposure of Ag bulk atoms, which is favorable for the renewable interfacial coordination. Furthermore, the XPS spectrum of Fig. S27 shows a characteristic peak of Ag-S coordination bonding in the S 2p spectrum of Ag0.1 LMs-NR-30. In contrast, no similar peak is observed for Ga-NR-30. These results further supported the existence of Ag-S coordination at the interface for Ag0.1 LMs. In addition, the significantly weaker Ag-S peak in Ag0.1 LMs-NR-30 compared to Ag-NR-3 further confirm that Ag atoms are diluted in the Ga matrix, resulting in fewer effectively exposed atoms at the interface and demonstrating the dynamic nature of the liquid Ga interface (Fig. S27C, D). For the Zn-imidazole coordination system, the ability of Zn0.2 LMs and Ga to coordinate with the imidazole ligand is evaluated by sedimentation experiments. As shown in Fig. 3H, in the PBVM solution with dichloromethane as the solvent (50 mg/mL), Zn0.2 LMs remained well dispersed in the PBVM solution for 24h, whereas Ga exhibited significant sedimentation as early as 12 hours. This difference demonstrates the coordination between the imidazole groups in the PBVM solution and Zn0.2 LMs. Additionally, the XPS characterization (Fig. 3I) further confirms the mechanism of interfacial coordination. In the N 1s spectrum, the imidazole functional group (C-N=) in Zn0.2 LMs-PBVM-12 shows a 0.12 eV shift toward lower energy compared to PBVM (Fig. S28). In contrast, the same functional group in the pure Ga system does not exhibit an obvious shift.

The above studies demonstrate the notable benefits of mLMs-polymer composites for self-healing properties. Given the excellent thermal conductivity of mLMs, the self-healable mLMs-polymer composites will be excellent TIMs for modern electronics. The central processing unit (CPU), as the data processing center in a computer, generates significant heat and becomes a key high-temperature component on the motherboard (Fig. S29). To address this challenge, we fabricate Ag0.1 LMs-NR films (70wt.% filler) that combine the high thermal conductivity of Ag0.1 LMs with the flexibility of NR, yielding excellent thermal dissipation. These films are applied as TIMs between the CPU and the heatsink. As shown in Fig. 4A, the Ag0.1 LMs-NR-70 film covers the CPU surface, and the flexibility of the Ag0.1 LMs-NR-70 film makes it to conform closely to the CPU surface, effectively eliminating air gaps and thereby improving heat dissipation efficiency. As shown in Fig. 4B, the thermal conductivity of Ag0.1 LMs-NR-70 films increases significantly with increasing Ag0.1 LMs filler loading. At 70wt.% Ag0.1 LMs filler content, Ag0.1 LMs-NR-70 exhibits a thermal conductivity of 3.2 W/m·K. When the filler content is increased to 90wt.%, the thermal conductivity rose to 6.8 W/m·K, a 20-fold enhancement over pure NR. Further, at the same filler mass fraction, the thermal conductivity of Ag0.1 LMs-NR-70 is increased by 33.3% compared to Ga-NR-70, indicating that the Ag atoms in Ag0.1 LMs form coordination with the sulfur atoms in the molecular chain of NR, thereby lowering the interfacial thermal resistance and significantly enhancing the thermal conductivity (Fig. S30). The prepared Ag0.1 LMs-NR-70 films demonstrated high thermal conductivity and outperformed most reported Ga-based thermally conductive composites fabricated via the simple shear-mixing method (Table S1). In addition, due to polymer barrier effect, the Ag0.1 LMs-NR-70 films exhibit excellent electrical insulation properties and prevent leakage of Ag0.1 LMs, even at a high filler content of 70wt.% (Fig. S31). Flexible and highly thermally conductive Ag0.1 LMs-NR-70 films are utilized as advanced TIMs to be further evaluated by a CPU. Figure 4C and S32 present the infrared thermography and temperature-time curves with the CPU running at 100% power loading. The CPU covered with NR film exhibited a significant increase in temperature during operation, reaching an operating temperature of approximately 100°C in 120s. In contrast, the CPU covered with Ag0.1 LMs-NR-70 films exhibited a gradual increase in temperature from 40°C to 64°C during the first 60s, then stabilized at approximately 68°C at 120s. The Ag0.1 LMs-NR-70 demonstrated a significant reduction in CPU operating temperature, achieving a decrease of 32°C compared to NR films without Ag0.1 LMs. Additionally, as a control, the CPU covered with Ga-NR film operated at a temperature approximately 4°C higher than that of the Ag0.1 LMs-NR-70 films, which was stabilized at about 72°C. The results demonstrated that Ag0.1 LMs-NR-70 and Ga-NR-70 films were able to effectively reduce the rate of temperature rise and peak temperature during CPU operation.

Although Ga-NR-70 and Ag0.1 LMs-NR-70 possess similar thermal conductivity, the self-healing property of Ag0.1 LMs-NR-70 ensures its long-term thermal management efficiency. As shown in Fig. 4D, the damages created by the blade-scratching on Ag0.1 LMs-NR-70 surface gradually disappeared over time and fully healed after 6h under near room temperature. In contrast, the scratches on the Ga-NR-70 surface under the same conditions did not show obvious changes after 6h (Fig. S33). The self-healing properties of Ag0.1 LMs-NR-70 films enable them to maintain efficient thermal management. As shown in Fig. 4E, interfacial damage in the Ag0.1 LMs-NR-70 films reduced their heat transfer efficiency, which in turn raised the maximum CPU temperature by 6°C compared to the initial state. However, after 6h of self-healing, the thermal performance of the healed Ag0.1 LMs-NR was effectively restored, with the maximum CPU temperature dropping to about 68°C, which was similar as the intact Ag0.1 LMs-NR-70.

The self-healable TIMs in this work will successfully address the long-standing industrial challenge44–46 of the irreversible damage in long-term used TIMs. Figure 4F evaluates the long-term stability of Ag0.1 LMs-NR-70 and Ga-NR-70 under extreme conditions. Ag0.1 LMs-NR-70 and Ga-NR-70 films were treated with harsh thermal shocks from −10°C to 100°C for different cycles (0–500 times, accumulative 16h, see supplementary information for detailed thermal shock experiment). The treated TIMs were covered on the working CPU (100% power loading), and the real-time temperature of the CPU was monitored. During the long-term 500 cycles of harsh thermal shocks, CPUs with Ag0.1 LMs-NR-70 TIMs exhibited nearly constant working temperature at an initial 68°C to a final 73°C (Fig. 4F). In sharp contrast, after 16 hours intensive thermal shock treatment, the temperature of the CPU covered with Ga-NR-70 TIMs increased from 72°C to 93°C in about 250 cycles of the extreme thermal shocks. The surface changes of the films during the extreme thermal shocks were further observed by SEM images (Fig. 4F, insets). Initially, the surface of Ga-NR-70 was smooth and defect-free, exhibiting no visible defects or cracks. In contrast, Ga-NR-70 developed surface irregularities, voids, and cracks after the 16h thermal shock treatment. These defects hindered heat transfer and compromised the material’s performance. However, the Ag0.1 LMs-NR-70 TIM exhibits no obvious change on its surface due to the self-healing capability to heal the surface micro-cracks to maintain its thermal conductivity at 2.9 W/m·K (Fig. S34). Finally, Fig. 4G presents the real-time maximum CPU temperature for the thermally shocked Ga-NR-70 TIM. The temperature rise to 93°C after 120s of operation. In contrast, the CPU covered with the Ag0.1 LMs-NR-70 treated with the same extreme conditions showed much better heat dissipation performance by stabilizing the temperature at about 73°C after 120s. The above results indicate that the dynamic interfacial LM coordination strategy could be a highly promising route to address the long-standing industrial challenge for the long-term stability of high-performance TIMs.

Methods
Materials: Gallium (Ga, 99.999%, melting point: 29.8°C) was purchased from Changge Shuochen Metal Co., Ltd. Silver powder (Φ: 25μm, 99.9995%, melting point: 961.8°C) was purchased from Nangong Xindun Alloy Welding Spraying Co., Ltd. Zinc powder (Φ: 20 μm, 99.99%, melting point: 419.5°C), copper powder (Φ: 22μm, 99.99%, melting point: 1083.4°C), Sulfur (S8, AR, 99.5%), other rubber additives (zinc oxide, ZnO, AR, 99%, stearic acid, Sta, GC, 95%; N-cyclohexyl benzothiazole-2-sulfenamide, CZ, HPLC, 98%) and methyl methacrylate (MMA, GC, 99.0%) were purchased from Shanghai Aladdin Bio-Chem Technology Co., Ltd. Natural rubber (NR, complex viscosity η*=454 kPas, 100°C) was purchased from Hainan Rubber Industrial Co., Ltd, China, Low molecular weight rubber (L-NR, complex viscosity η*=155 kPas, 100°C) was purchased from Hong Manli Rubber Products Co., Ltd. 1-Vinylimidazole (VIM, 99%), n-butyl acrylate (BA, CP, 98%), dichloromethane (DCM, AR, 99.5%), and 2-hydroxy-2-methylpropiophenone (HMPP, 99%) were purchased from Shanghai McLean Biochemical Technology Co. Ltd.

Preparation of metal-polymer composite: (1) Ag0.1 LMs: The metals Ga (18g), Ag (2g) (mass ratio of Ga:Ag = 9:1) were put in a 10mL round-bottom flask. The mixtures were then heated in an electric heater above 250°C (melting point of Ga: 29.8°C, Ag: 961.8°C) under a nitrogen atmosphere until all metals were melted. After a slight cooling (about 100°C), the melt was mechanically stirred at 500 rpm to ensure homogeneity. Finally, the Ag0.1 LMs were obtained by moving the flask out of the electric heater and cooling the mixture at room temperature for 30 min. (2) The Zn0.2 LMs (Ga: Zn mass ratio 8:2, 16g Ga and 4g Zn) and Cu0.05 LMs (Ga: Cu mass ratio 19:1, 19g Ga and 1g Cu) were prepared in the same way as Ag0.1 LMs. (3) Ag0.1 LMs-NR-y: The preparation of Ag0.1 LMs-NR-y composites with 15% mass fraction was taken as an example. NR (10g), rubber additives (ZnO (0.5g), SA (0.2g), CZ (0.12g)), Sulfur (0.12g), and Ag0.1 LMs (4.7g) were sequentially added to an open mill (STD-2KL) and shear-mixed at 60°C at 30 rpm for 15 min to ensure uniform dispersion of the filler. The 0.5-mm-thick Ag0.1 LMs-NR-30 composite was fabricated by hot-pressing the mixture at 150°C under 20-ton pressure for 16 min with a dumbbell-shaped mold and a melt-compounder (AP2113, AUPLEX). Other samples with different filler contents were prepared using the method described above. (4) PBVM: in a typical free-radical co-polymerization procedure, VIM (1.37g, 14.6 mmol), BA (5.23g, 40.9 mmol), MMA (0.29g, 2.9 mmol) and Photoinitiator HMPP (0.048g, 0.292 mmol) (mole ratio of VIM: BA: MMA = 5:14:1) were placed into a bottle equipped with a magnetic stirrer, and irradiated under UV light (365 nm) for 10 min, PBVM had been obtained. (5) Zn0.2 LMs-PBVM-y: PBVM (1g) was dissolved in dichloromethane (20 mL) and stirred at 400 rpm for 12 h at 45 oC to ensure completed dissolution, forming a viscous PBVM solution. Following this, Zn0.2 LMs (0.12g) was added to the solution and manually ground with a pestle at room temperature until Zn0.2 LMs was uniformly dispersed in the solution. The mixture was then transferred to a vial and stirred at 400 rpm at 45°C for 24 h. Finally, the mixture was poured into a polytetrafluoroethylene mold, left to evaporate at room temperature for 4h, and subsequently dried in an oven at 80°C for 12h to obtain the Zn0.2 LMs-PBVM-12 composite. Comparative samples were prepared using the same procedure.

Instruments: mLMs were mixed by LED Digital Overhead Stirrer (DLAB 8033100200 OS20-S) and heated by electric heater mantle (PTHW250ML). The mLMs and natural rubber (NR) were mixed by an open mill (STD-2KL) and a melt-compounder (AP2113, AUPLEX) to obtain mLMs-NR composites. Oven (DZF-6020) was used to control the temperature and maintain an isothermal condition. An oven (DZF-6020) was used to control the temperature and remove solvents from the mLMs-PBVM composites. The surface structure of the mLMs-polymer composite was observed by a digital microscope (Leica DVM6). The mechanical and self-healing performance of mLMs-polymer composites was performed on a universal testing machine (MTS E42). The microstructure and healing process of mLMs and mLMs-NR composites were characterized by a Field Emission Scanning Electron Microscope (FEI Inspect F50). The Energy-dispersive X-ray spectroscopy (EDS) of mLMs-NR composites was used to characterize the element distributions. The chemical compositions of samples were characterized by the X-ray photoemission spectrometer (XPS, ESCALAB 250Xi) with Al Kα radiation (λ = 1486.6 eV). X-ray diffraction (XRD) was measured with Ultima IV. The mLMs were loaded onto quartz glass for measurement. Scanning range: 5°–110°, scanning speed: 5°/min, optical grating: 5 mm. Gel Permeation Chromatography (GPC) The PL-GPC 220 (Polymer Laboratories) was operated to measure samples at 40°C with DMF as mobile phase. The functional group components of PBVM were characterized by using Fourier transform infrared spectroscopy (FT-IR) Characterization. 1H nuclear magnetic resonance (1H NMR) spectroscopy was performed on the Avance III HD 600 MHz 300 MHz spectrometer. Differential scanning calorimetry (DSC) characterization was carried out using the DSC 25 thermal analyzers (TA instruments) to characterize thermal transitions. The samples (5–10 mg) were loaded into DSC pans, then quenched to −50°C and subsequently heated to 60°C at a rate of 5°C/min. The thermal conductivity of NR, Ga-NR, and Ag0.1 LMs-NR films was measured on a thermal conductivity tester (XIATECH TC3000E). It should be noted that the measured value of thermal conductivity was the apparent thermal conductivity. The general tests were performed at room temperature. The rheology data of the samples were collected by a rheometer, Discover HR20, TA Instruments. All the samples were fabricated into a small round sheet (Φ = 20±0.5 mm, H = 2±1 mm). The temperature sweep was in oscillation mode from 30 to 200°C with 10°C/min at 10 rad/s, 3.0% strain.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript presents an innovative strategy for designing self-healing materials by introducing reversible interfacial coordination between multi-component liquid metals (mLMs) and polymers. Several aspects require further clarification and discussion before the manuscript can be considered for publication\n1. While the introduction provides a comprehensive overview of self-healing materials, the distinction between the proposed “dynamic interfacial coordination” and existing reversible coordination systems is not sufficiently highlighted.\n2. Please explicitly emphasize how the liquid–solid interfacial coordination fundamentally differs from conventional solid–solid coordination in terms of kinetics, reversibility, and healing efficiency\n3. Although MD simulations and XPS analyses support the proposed mechanism, quantitative evidence linking atomic migration at the mLM interface to observed self-healing rates is limited.\n4. It is suggested that a horizontal comparison with the existing TIMs (Business or literature reports) be added in the discussion section or table\n5. Streamlining some long sentences would also improve readability.\n6. Ensure that all supplementary figures (S1–S30) referenced in the text are clearly mentioned in the appropriate context.", "reviewer_2": "The present manuscript entitled “A Universal Strategy towards Self-Healing Materials via Dynamic Interfacial Liquid Metal Coordination” by Z. Li et al. describes the fabrication of polymer composites based on liquid metals. The polymers featured ligand containing side chains, which formed a network with the incorporated liquid metal nanoparticles / droplets. These composites featured excellent self-healing ability.\nThe authors studied two polymer composites: i) natural rubber crosslinked with sulfur and ii) poly(vinylimidazole-co-MMA-co-BA). The LMs have been adjusted using silver for the sulfur containing polymers and Zn and Cu for the imidazole polymers. Different ratios of the Lms have been introduced.\nThe mechanical properties of the polymers were studied in detail using tensile tests. The self-healing has been studied in the tensile tests as well as in scratch healing experiments. For the best compositions excellent healing efficiencies could be obtained. Moreover, the composition of the LMs was studied in detail, also considering the distribution of the metals being able to coordinate with the polymers. Finally, the authors could demonstrate the usage of the polymers composites as thermal interface materials on a CPU, since these materials featured also excellent thermal conductivity, while showing no electric conductivity.\nOverall the study is very interesting and sound. There are only some open questions:\nFigure 2 D: It is hard to see the silver (yellow) in the images. Therefore, the claim that in the crack there is a lot of Ga and Ag is hard to understand. For me it looks more greenish and the yellow seems to be missing.\nThe above fact brings me to another aspect. The authors proposed a healing mechanism based on the coordination of the metals with the ligands and their reversible binding. Based on the reversible nature of the LMs (as the authors described their ability to replace surface atoms) one could also consider that the silver is exchanged between different particles, i.e. the silver with the sulfur would “leave” one particle and would be taken by the next particle.\nMinor comments:\n- Page 3: It is a bit unclear what the others mean with coordination metals.\nSI:\nFigure S9: The SEC curve looks strange. Why is the baseline rising?\nFigure S10: Why is the methyl group of the MMA repeating unit not assigned in the NMR spectrum?\nFigure S14: Are the phase diagrams based on reported diagrams from the literature?\nFigure S23: “This reduction was attributed to the dynamic interface of Ag0.1LMs, which weakened the force between Ag-S.”\n– Might the lower Ag-S content relate to the lower silver content in the LMs compared to the pure silver nanoparticles?"}, "author_response": "Reviewer #1:\n1. While the introduction provides a comprehensive overview of self-healing\nmaterials, the distinction between the proposed \"dynamic interfacial coordination\"\nand existing reversible coordination systems is not sufficiently highlighted.\nResponse: Thank you for your insightful comments. We fully agree that clarifying the\nfundamental novelty of our \"dynamic interfacial coordination\" is crucial. Therefore,\nwe have added new content to the introduction to clarify the distinction between the\n\"dynamic interface coordination\" studied in this work and the existing concept of\n\"reversible coordination\" systems. The main modifications are as follows:\nTherefore, coordination-active metals such as silver (Ag) and zinc (Zn) are introduced\ninto liquid metals (LMs) to endow the resulting multi-component liquid metals\n(mLMs) with coordination capabilities. The fluidic interfaces of mLMs microdroplets\nenable regeneration of coordination sites through interfacial atomic migration, thereby\nexpanding the dynamic coordination unit from molecular to microscopic dimensions.\nThis mLMs-based dynamic interfacial strategy can derive its reversibility from the\nself-renewing fluidic interface, rather than being constrained by the strength of\ncoordination bonds. In contrast, existing reversible coordination systems rely on weak\nbonding interactions at the molecular dimensions, where their reversible behavior\nremains confined by the inherent strength of the coordination bonds.\nThe aforementioned content has been revised in the manuscript's introduction and\nhighlighted in bright yellow throughout the text. These revisions enhance the\n2\ninnovative interpretation and elaboration of \" dynamic interface coordination\" in this\nwork.\n2. Please explicitly emphasize how the liquid-solid interfacial coordination\nfundamentally differs from conventional solid-solid coordination in terms of kinetics,\nreversibility, and healing efficiency.\nResponse: Thank the reviewer for this insightful comment. We systematically\ncompare the liquid-solid interfacial coordination with conventional solid-solid\ncoordination through detailed investigations, including rheological temperature\nsweeps and time-dependent healing efficiency tests.\nAs shown in Fig. S11, rheological temperature sweeps are performed on Ag-NR-3 and\nAg LMs-NR-30 under identical conditions (3% fixed strain, 10 rad/s angular\n0.1\nfrequency, and these two samples have the equivalent Ag weight percentage (3.0 wt.%)\nin the composites). For the Ag-NR-3 composites (solid-solid coordination system),\nboth the storage modulus (G′) and loss modulus (G″) remained nearly constant with\nincreasing temperature. This behavior reflects a static network structure where\ncoordination sites are immobilized on solid surfaces, preventing dynamic\nreorganization and resulting in an irreversible network. In contrast, the\nAg LMs-NR-30 composites (liquid-solid coordination system) exhibits a\n0.1\nsimultaneous decrease in both storage G′ and G″ with increasing temperature. This\nbehavior originates from the inherent fluidity of the Ag LMs interface under\n0.1\ndynamic polymer deformation, which enables the renewable coordination sites and\nthe dynamic network undergoes ongoing rearrangement. This structural difference\nalso determines the self-healing performance. As shown in Fig. 1, the healing\n3\nefficiency of Ag LMs-NR-30 composites increases over time, reaching 90% within\n0.1\n180 minutes. The Ag-NR-3 composites consistently exhibits negligible healing\nefficiency (<1%) without significant change over time. The solid-solid system lacks\nsuch fluidity, making it difficult to effectively restore broken coordination bonds and\nresulting in severely limited healing capability.\nAccording to the suggestions, we have incorporated these experimental findings into\nthe manuscript and marked the revisions with yellow highlighting.\nFig. S11. Rheological temperature sweeps characteristic curves of Ag-NR-3 and\nAg LMs-NR-30 composites, with a heating rate of 10 °C/min, temperature range of\n0.1\n30 °C - 200 °C, fixed strain of 3%, and angular frequency of 10 rad/s. The storage\nmodulus (G′) and loss modulus (G″) of Ag LMs-NR-30 decrease with increasing\n0.1\ntemperature, indicating a dynamic polymer network. The G′ of Ag-NR-3 remains\nstable throughout the temperature range, demonstrating a rigid static network\nstructure.\n0.1\ntemperature as a function of fixation time (30, 90, 180 min).\n3. Although MD simulations and XPS analyses support the proposed mechanism,\nquantitative evidence linking atomic migration at the mLM interface to observed\nself-healing rates is limited.\nResponse: We sincerely thank the reviewer for raising this important question. The\nquantitative relationship between atomic migration rates and macroscopic self-healing\nefficiency is indeed a critical aspect of this work. To clarify this relationship, we\ndesigned experiments to directly observe atomic migration behavior in mLMs and to\nindependently assess the influence of polymers with different molecular weights on\nhealing efficiency.\nTo directly visualize the migration of Ag atoms in the liquid metal Ga, we placed a\nsilver foil on the surface of a Ga droplet and monitored the dissolution and diffusion\nprocess in real time using optical microscopy. As shown in Fig. 1, the silver foil (0.4\n5\nmg) underwent instantaneous dissolution upon contact with the Ga surface. The Ag\natoms subsequently migrated rapidly within the Ga matrix, with initial diffusion\nachieved within 10 seconds and complete incorporation into a homogeneous alloy\nafter 10 minutes. Further, the rapid migration process of Ag atoms at the microscopic\nscale is also elucidated via scanning electron microscopy (SEM). Two mLMs droplets\nwith different initial silver concentrations (10.0 wt.% and 1.0 wt.%) are brought into\ncontact. As shown in Fig. S19, EDS analysis before and after contact clearly revealed\nthe migration of Ag atoms through the Ga matrix from the Ag-rich droplet to the\nAg-poor one, with the two droplets reaching compositional equilibrium after 10\nminutes of contact. The migration of Ag atoms can be more clearly observed at the\nmicroscopic scale to occur on a timescale of minutes. This result confirms that Ag\natom migration within liquid Ga is a quick process, occurring on a timescale of\nseconds. This rate far surpasses that required for macroscopic damage repairing of the\npolymer composites (usually asks for 1 to 2 hours for self-healing). This means that\nthe self-healing rate is heavily determined by the polymer chain relaxation instead of\nthe metal atom migration.\nIn addition, to verify the above conclusion, a low molecular weight natural rubber\n(L-NR, complex viscosity η* = 155 kPa·s, 100 oC) was selected as a comparative\nmatrix. Composites with identical Ag LMs filler content were prepared, allowing a\n0.1\nsystematic comparison of the self-healing efficiency between matrices of different\nmolecular weights. As shown in Fig. S8, although both Ag LMs-NR-30 and\n0.1\nAg LMs-L-NR-30 composites eventually reach a similar healing efficiency of\n0.1\napproximately 90%, Ag LMs-L-NR-30 (low-molecular-weight system) attains this\n0.1\nlevel within only 120 min, compared to 180 min for Ag LMs-NR-30\n0.1\n(high-molecular-weight, complex viscosity η* = 454 kPa·s, 100 oC) counterpart. This\n6\nmarked difference in healing time demonstrates that, when the supply of active atoms\nis sufficient and identical, the migration and rearrangement kinetics of the polymer\nchains become the determining factor for the macroscopic healing behavior.\nBased on the experimental results described above, the migration of active atoms\nwithin mLMs occurred rapidly (seconds to minutes), whereas the macroscopic\nself-healing process-which relies on polymer chain motion to achieve the final\nreconstruction of the damaged interface-proceeds slowly (hours). Thus, the overall\nhealing rate in this system is limited not by the metal atoms migration, but by the\nmigration rate and dynamic mobility of the polymer chains themselves. These results\nestablish a clear understanding about the atomic migration at the mLMs interface and\nthe macroscopic self-healing kinetics, directly addressing the reviewer's insightful\nquestion. We have provided the detailed explanation in the manuscript as you\nrequired.\nFig. 1. Optical microscope images of the dissolution and migration process of silver\nfoil in liquid metal Ga interface. Experimental conditions: Ga droplets were pretreated\nwith 1 mol/L HCl to remove surface oxide layers, experiments conducted at room\n7\ntemperature. (A) Initial Ga droplet; (B) Silver foil (0.4 mg) contacting gallium surface;\n(C) Rapid silver diffusion after 10 s of contact; (D) Complete silver dissolution\nforming a homogeneous alloy after 10 min of contact.\nFig. S19. Surface scanning electron microscope (SEM) images and energy-dispersive\nX-ray spectroscopy (EDS) elemental distribution maps of mLMs with different silver\ncontents (10 wt.%, 1.0 wt.%). (A ) SEM image of droplets with different initial silver\n1\ncontents before contact; (A ) Ga element distribution and (A ) silver element\n2 3\ndistribution. (B ) SEM image of droplets with different silver contents after 10 min of\n1\ncontact; (B ) Ga element distribution and (B ) Ag element distribution.\n2 3\nFig. S8. Effect of polymer chain mobility on self-healing kinetics. (A) Stress-strain\ncurves of low molecular weight natural rubber (L-NR, complex viscosity η* = 155\n8\nkPa·s, 100 oC) matrix composite (Ag LMs-L-NR-30) at different healing times (30,\n0.1\n90, 120 min). (B) Comparison of healing efficiency over time for Ag LMs-L-NR-30\n0.1\nand Ag LMs-NR-30 composites (NR, complex viscosity η* = 454 kPa·s, 100 oC).\n0.1\nAg LMs-L-NR-30 achieved 90% healing efficiency within 120 min, significantly\n0.1\nfaster than Ag LMs-NR-30. The high mobility of chain segments in low molecular\n0.1\nweight NR is a key factor responsible for the accelerated macroscopic healing\nefficiency.\n4. It is suggested that a horizontal comparison with the existing TIMs (Business or\nliterature reports) be added in the discussion section or table.\nResponse: We thank you for this valuable suggestion. Following your comment, we\nhave added a systematic comparison of our Ag LMs-NR-70 films with recently\n0.1\nreported advanced TIMs via the same shear-mixing preparation method. Based on the\nliterature, our literature-based research indicates that the material exhibits high\nthermal conductivity and significant self-healing capability at low metal content.\nThese results are included in the Table S1 in Supplementary Materials, and marked\nthe revisions with yellow highlighting.\n0.1\nother LM-based composites fabricated via the same simple shear mixing.\nFiller Thermal\nReferences\nReferences Filler types contents conductivity\nmark\n(vol%) (W/m·K)\nProc. Natl. Acad. Sci. U.S.A.\n2017, 114, 2143-2148\nAdv. Energy Mater. 2021, 11,\n2101387\nAdv. Funct. Mater. 2023, 33,\n2210553\nAdv. Funct. Mater. 2020, 30,\n2000832\nCompos. B Eng. 2022, 239,\n109961\nACS Appl. Mater. Interfaces 30% Ga\n9 50 1.12\n2023, 15, 3534–3542 +20%Cu\nJ. Mater. Chem. C 2021, 9,\n2904-2911\n112462.\nThis work Ag LMs 32.5 3.20\n0.1\n10\n5. Streamlining some long sentences would also improve readability.\nResponse: We thank the reviewer for this helpful suggestion. The manuscript has\nbeen carefully revised to improve readability, with overly long sentences restructured\nor split into shorter, clearer statements. We have incorporated all of the above\nmodifications into the manuscript and marked them in yellow.\n6. Ensure that all supplementary figures (S1–S30) referenced in the text are clearly\nmentioned in the appropriate context.\nResponse: We thank the reviewer for this careful reminder. We have thoroughly\nchecked the manuscript and ensured that all supplementary figures are now explicitly\nreferenced in their appropriate contexts.\n1. Figure 2 D: It is hard to see the silver (yellow) in the images. Therefore, the claim\nthat in the crack there is a lot of Ga and Ag is hard to understand. For me it looks\nmore greenish and the yellow seems to be missing.\nResponse: We thank the reviewer for this critical observation regarding the elemental\nmapping in Figure 2D. The attenuated Ag signal is primarily due to the significant\nheight variations (~40 μm) within the fracture zone, as shown in Fig. S4. This surface\nstructure hinders EDS focusing, thereby reducing Ag signal intensity. The relatively\nlow Ag content (3.0 wt.%) in the composite further contributes to this signal\nattenuation.\nTo directly address this issue and unambiguously confirm the presence of Ag at the\ndamaged interface, we prepared a new sample of Ag LMs-NR-30 and by destroying\n0.1\nthe material to expose fresh cross-sections. The cross-sectional SEM images provide a\nclear view of the interfacial region, allowing the focusing on the region by EDS to\ndirect observation of elemental distribution at the contact interface. As shown in Fig.\nS6, the newly exposed cross-section clearly shows uniform distributions of Ga (green),\nS (purple), and Ag (yellow), confirming that the fracture interface is distribution with\nmLMs components.\nWe have included the additional experimental results in the manuscript as\nrecommended by the reviewers, with all changes highlighted in yellow for easy\nidentification.\n0.1\n(A) Schematic diagram of a composites fractured by external force (A ) and the\n1\nresulting cross-section after fracture (A ). (B) SEM image of the fracture interface\n2\nwith corresponding EDS elemental maps for (C) Ga (green), (D) S (purple), and (E)\nAg (yellow). Scale bar: 5 μm. The uniform distribution of all three elements across the\ninterface confirms the presence of mLMs components within the cross-section region.\n2. The above fact brings me to another aspect. The authors proposed a healing\nmechanism based on the coordination of the metals with the ligands and their\nreversible binding. Based on the reversible nature of the LMs (as the authors\ndescribed their ability to replace surface atoms) one could also consider that the silver\nis exchanged between different particles, i.e. the silver with the sulfur would “leave”\none particle and would be taken by the next particle.\nResponse: We are deeply grateful for your insightful suggestion. The possibility of\natomic exchange between droplets that you have pointed out reveals a more dynamic\n13\nmechanism in the healing process we proposed, and we fully acknowledge its\nsignificance.\nTo investigate this possibility, we conducted additional experiments by bringing two\nmLMs droplets with different Ag concentrations (10.0 wt.% and 1.0 wt.%) into\ncontact, and tracked the changes in silver content at the droplets to confirm the\noccurrence of Ag atomic exchange between droplets. As shown in Fig. S19, initially,\nthe EDS signal intensity of Ag in the two droplets are different. After 10 minutes of\ncontact, the distribution of silver elements tended to become uniform. EDS analysis\nclearly demonstrated the migration of Ag atoms through the liquid Ga matrix from the\nAg-rich droplet to the Ag-poor one until equilibrium was reached.\nThese findings confirm that Ag atoms possess high mobility not only on the surface of\nindividual droplets but also between different mLMs droplets via the Ga matrix. Such\ninter-droplet atomic exchange facilitates the redistribution of coordination-active\natoms during self-healing, thereby significantly improving the overall healing\nefficiency and material stability.\nBased on your suggestions, we have incorporated a discussion on the \"inter-droplet\natomic exchange\" mechanism into the revised manuscript and supplementary\nMaterials with all changes highlighted in yellow for easy identification. We sincerely\nthank the reviewers for helping us deepen our understanding of this research.\nX-ray spectroscopy (EDS) elemental distribution maps of mLMs with different silver\ncontents (10 wt.%, 1.0 wt.%). (A ) SEM image of droplets with different initial silver\n1\ncontents before contact; (A ) Ga element distribution and (A ) silver element\n2 3\ndistribution. (B ) SEM image of droplets with different silver contents after 10 min of\n1\ncontact; (B ) Ga element distribution and (B ) Ag element distribution.\n2 3\n3. - Page 3: It is a bit unclear what the others mean with coordination metals.\nResponse: We thank the reviewer for pointing out this lack of clarity in terminology.\nWe have revised the manuscript to provide a clearer definition. The original term\n\"coordination metals\" specifically referred to metal elements introduced into the\nliquid metal matrix that can form coordination bonds with ligands on polymer chains,\nsuch as silver (Ag), zinc (Zn), and copper (Cu), in contrast to the gallium (Ga) base\nwhich exhibits weak coordination capability.\nTo further clarify this distinction, we have replaced the aforementioned term with\n\"coordination-active metals\" and made corresponding revisions on the manuscript.\n15\n4. Figure S9: The SEC curve looks strange. Why is the baseline rising?\nResponse: We thank the reviewer for this careful observation. The rising baseline in\nthe original SEC curve (Revised Supplementary Materials Fig. S12) was indeed\ncaused by insufficient solubility of the copolymer in the Tetrahydrofuran (THF)\nmobile phase, which is a known issue for polymers containing polar comonomers. To\nresolve this, we repeated the SEC measurement using N, N-dimethylformamide\n(DMF) as the solvent, which provides better solvation for this copolymer system. The\nupdated SEC curve now shows a stable baseline and improved signal profile. This\ncorrected data has replaced the original Fig. S12 in the revised Supplementary\nMaterials.\nFig. S12. (A) The Zn LMs-PBVM-y composites were synthesized through a\n0.2\ntwo-step process. Initially, a copolymerization of butyl acrylate (BA),\n1-vinylimidazole (VIM), and methyl methacrylate (MMA) at a molar ratio of 14:5:1\nwas conducted under UV light irradiation (365 nm) at room temperature using\n16\n2-hydroxy-2-methylpropiophenone (HMPP) as a photoinitiator. The resulting poly\n(BA-co-VIM-co-MMA) (PBVM) was dissolved in dichloromethane (DCM) and\nsubsequently reacted with Zn LMs at 50°C for 24 h to obtain the final composites.\n0.2\n(B) Gel permeation chromatography (GPC) curves of PBVM. To run GPC, solution\nafter purification was rotary evaporated to collect polymers for GPC with N,\nN-dimethylformamide as the solvent.\n5. Figure S10: Why is the methyl group of the MMA repeating unit not assigned in\nthe NMR spectrum?\nResponse: We sincerely thank the reviewers for their meticulous review. In the\noriginal ¹H NMR spectrum (Revised Supplementary Materials Fig. S13), the methoxy\nsignal (-O-CH ) of the MMA unit partially overlaps that of the -O-CH - proton in the\n3 2\nnBA unit. The observed chemical shift agrees with values reported in the literature for\nsimilar polymer systems (Macromolecules 2023, 56, 23, 9626-9635; ACS Macro Lett.\n2022, 11, 10, 1217-1223).\nWe have now clearly labeled both characteristic peaks in the revised Supplementary.\nof PBVM, the peaks of the imidazole unit appear at 8.0 - 6.8 ppm, The methylene\n(-CH -O-) peak of butyl acrylate and the methyl (-CH -O-) peak of methyl\n2 3\nmethacrylate appear near 4.0 ppm and 3.70 ppm, respectively.\n18\n6. Figure S14: Are the phase diagrams based on reported diagrams from the literature?\nResponse: We thank the reviewer for raising this important point regarding the source\nof our phase diagrams. The phase diagrams presented in Fig. S14 (Revised\nSupplementary Materials Fig. S17) are indeed based on established data from the\nscientific literature, and not newly constructed by ourselves. In the revised manuscript,\nwe have now explicitly cited the original sources both in the figure caption of Fig.\nS14 (Revised Supplementary Materials Fig. S17) and in the reference list.\nThe specific references for the phase diagrams are as follows:\nThe phase diagram for the Ga-Ag system is adapted from reference (Science\n2022,378,1118-1124).\nThe phase diagram for the Ga-Zn system is adapted from reference (Adv. Funct. Mater.\n2024,34, 2304248).\n7. Figure S23: \"This reduction was attributed to the dynamic interface of Ag LMs,\n0.1\nwhich weakened the force between Ag-S.\" – Might the lower Ag-S content relate to\nthe lower silver content in the LMs compared to the pure silver nanoparticles?\nResponse: Thank you for raising this question regarding the reduced Ag-S peak\nintensity. We would like to clarify that both Ag-NR-3 and Ag LMs-NR-30 compared\n0.1\nin Fig. S23 (Revised Supplementary Materials Fig. S27) contain the same total Ag\ncontent (3.0 wt.%). The key difference lies in the silver distribution: in Ag-NR-3,\nsilver is presented as fully exposed particles, whereas in Ag LMs-NR-30, the Ag\n0.1\n19\natoms are uniformly dispersed within the Ga matrix. Only part of the Ag atoms is\navailable for the coordination on the surface of the Ga. This structural difference is the\ndirect cause of the significant disparity in Ag-S peak intensity between the two\nmaterials. In pure Ag nanoparticles, the surface comprises of static and Ag-rich atoms,\nproviding abundant fixed coordination sites that yield a strong Ag-S peak. In contrast,\nin Ag LMs, the Ag atoms are diluted and dynamically dispersed in the liquid Ga\n0.1\nmatrix. This leads to a considerably lower number of effectively exposed Ag atoms at\nthe surface available for sulfur coordination, thereby resulting in the attenuated Ag-S\npeak intensity.\nTherefore, the reduction in Ag-S peak is not merely due to the lower silver content,\nbut is fundamentally associated with the distinctive dynamic interface of Ag LMs.\n0.1\nWe have incorporated your suggestions into the revised manuscript, with all\nmodifications highlighted in yellow for easy identification.\n20"}, {"round": 2, "reviewer_comments": {"reviewer_2": "Thanks to the authors for preparing the comprehensive revision for their manuscript including several new experiments and measurements. The comments raised by the reviewers have been addressed. Also new insights could be gained with the new measurements."}, "author_response": ""}]

Decision letter