Flexible rubber with metal-like thermal conductivity achieved via hydrogen bonding engineering

Domain: biology
Published: 2026-03-24
Editorial outcome: major_revision

Abstract
The ideal electronics packaging for next-generation wearable devices and integrated circuits would be a flexible material with high thermal conductivity of a metal. We report a liquid-metal polyurethane composite (LiMPuC) with a thermal conductivity of 23.42 W m-1 K-1 while retaining extreme stretchability. The performance arises from interfacial-chemistry–guided ordering of the polyurethane matrix and improved liquid-metal wetting. By modulating hydrogen-bond donor/acceptor densities in the thermoplastic polyurethane and grafting –NH groups onto eutectic gallium–indium (EGaIn) droplets, we create anchored, reconfigurable interfaces that (i) increase matrix chain alignment and intrinsic heat transport and (ii) promote stable, strain-tolerant thermal near-percolation of the liquid metal. Under large tensile strain, these coupled effects preserve high conductivity and deliver a flexibility figure of merit > 100. This chemistry-to-microstructure pathway, linking hydrogen-bond engineering with LM surface functionalization, provides a general strategy for designing flexible, high-𝜅 composites for advanced thermal management in emerging electronics.

Introduction
The rapid advancement of flexible technologies, such as artificial intelligence (AI) robots1,2 and wearable electronics3-5, is driving an urgent need for advanced thermal management materials that seamlessly combine high thermal conductivity with mechanical flexibility. Effective heat dissipation is critical in these devices, especially under dynamic and variable conditions where both flexibility and thermal performance are paramount6-8. For instance, wearable devices require materials that can conform to diverse shapes and withstand continuous movement while efficiently dissipating heat. Flexible thermal bridges, made from soft, stretchable substrates, are ideally suited for these applications, ensuring both user comfort and device reliability. Similarly, in advanced integrated circuits, flexible thermal conduits are employed to transfer heat between different sections of electronic devices, accommodating mechanical deformation and thermal expansion while maintaining efficient thermal conductivity.

Despite these growing demands, integrating superior thermal conductivity and exceptional flexibility within a material remains a significant challenge (Fig. 1a). Conventional polymeric materials like rubbers are inherently flexible, for example, polydimethylsiloxane (PDMS) exhibits a flexibility figure of merit (f )9 greater than 1. Despite their mechanical advantages, these materials are typically thermal insulators FoM with thermal conductivity (𝜅) values less than 0.3 W m-1 K-1.10 In contrast, metals and ceramics offer excellent thermal conductivity (𝜅 >1 5 W m-1 K-1 for materials like stainless steel) but are rigid, with f FoM values less than 0.0111. This stark contrast highlights a fundamental trade-off between flexibility and thermal conductivity in existing materials.

To bridge this gap, significant efforts have been devoted to create composites by incorporating rigid, thermally conductive microparticles, such as metals12,13, ceramics14-16, and carbon-based materials17-19, into flexible polymer matrices. While this strategy enhances thermal conductivity, it often compromises mechanical flexibility, particularly when the filler content exceeds the percolation threshold necessary for effective heat transfer20-22. Liquid metals (LMs), such as eutectic gallium-indium (EGaIn), present a promising solution. LMs combine high thermal conductivity (EGaIn:~26.6 W m-1 K-1, Galinstan:~16.5 W m-1 K-1)23 and fluidity23-25, which allows them to conform to deformable microstructures within polymeric matrices, potentially maintaining the composite's flexibility26-28. This concept was pioneered by Bartlett et al29, who demonstrated stretch-activated thermal conduction in PDMS/EGaIn composites (𝜅 = 9.8 W m-1 K-1 at 400% strain and ~50 volume fraction (vol%) LM loading). Building on this foundation, subsequent studies by Haque30, Bark31, and Herbert32 have systematically improved thermal performance by engineering droplet morphology, introducing covalent anchoring strategies, and applying post-stretch annealing. Most recently, Yu et al33 reported a record-high 𝜅 of 27.1 W m-1 K-1 at 300% strain and ~80 % vol% LM loading, by percolating bulk gallium through a porous elastomer scaffold. In short, current LM-thermosetting polymer composites achieve thermal conductivities of approximately 10 W m-1 K-1 (under strain) with a f of approximately 1, representing a significant advancement over rigid particle FoM embedded polymers with similar thermal conductivity but much lower flexibility34-37.

Despite these promising developments, existing materials still fall short of the demanding requirements for high-performance wearable devices and next-generation advanced integrated circuits electronics. These applications demand materials that combine the thermal conductivity of metals (e.g., exceeding 20 W m-1 K-1) with the flexibility of rubber (e.g., f FoM over 10, as seen in materials like EcoflexTM)38,39. The key limitation in current LM composites is the lack of strong interactions between particles, and the existence of chemically crosslinked polymer networks that "lock" LM particles in place. This chemically inert oxide layer does not actively participate in polymer network crosslinking, resulting in weak interfacial adhesion and mechanical confinement. As a result, LM particles exist like isolated islands within the matrix (Fig. 1b left), preventing the formation of effective percolation networks at low concentrations. To achieve effective heat transfer, LM content must be increased significantly, such as reaching 60 % volume fraction (vol%). At this concentration, the thermal conductivity improves to around 11 W m⁻¹ K⁻¹, but the flexibility deteriorates, resulting in a low f of only 0.237. Alternatively, to FoM maintain a higher f (e.g. ~50), the LM content must be reduced to approximately 44 vol%, but this FoM sacrifice in LM content results in ineffective percolation, with thermal conductivity reaching only 1.2 W m-1 K-1 in the natural state and 2.6 W m-1 K-1 under strain31.

In this study, we present an approach that fundamentally overcomes these limitations by optimizing interfacial chemistry to enhance the interactions between the polymer matrix and the LM particles. By leveraging non-covalent interactions, specifically hydrogen bonding, we promote a connectivity-approaching (near-percolation) droplet arrangement under deformation, reminiscent of a “pearl-necklace” morphology (Fig. 1b, right). Importantly, we use the term near-percolation to describe a state of increased droplet connectivity and reduced inter-droplet spacing, rather than classical hard-contact percolation. At the same time, the dynamic nature of hydrogen bonding reinforces mechanically reconfigurable interfaces, enabling high thermal transport while retaining stretchability. Through this strategy, at only 46 vol% LM incorporation, we have developed a composite material exhibiting an unprecedented thermal conductivity of 23.42 W m-1 K-1, almost double that of current stae-of-the-art LM embedded polymer composites, which achieve 13 W m-1 K-1 at 70 vol% LM loading30. Equally striking, this composite achieves a f exceeding 100, surpassing performance limits of pristine rubbers and establishing FoM benchmark for flexible materials. This approach not only resolves the longstanding trade-off between flexibility and thermal conductivity but also paves the way for the development of advanced thermal management materials for high-performance wearable devices, integrated circuits, and other flexible electronic applications.

Results
2.1 Design and synthesis of thermoplastic polyurethane (PU) matrix with tunable hydrogen-bonding density

To engineer the H-bonding network within PU elastomers and their composites with LM, a series of PU elastomers was synthesized with precisely tailored H-bonding capacity. The synthesized PU samples are labelled according to their actual hydrogen bonding density (HEBD). For instance, PU2.90 indicates that the HBD in this pristine PU sample is 2.90 mmol cm-3. The synthesis strategy involved selecting components that balanced functionality, segmental mobility, and mechanical performance.

Polytetramethylene ether glycol (PTMEG), with varying molecular weights (M = 1000, 850, 650, and w 250 g mol-1), served as the soft segment. By decreasing M w of PTMEG, we increased the density of hydrogen bond donors and acceptors (see Supplementary Note 1, Supplementary Table 5 and 6 for detail), thereby enhancing the potential for H-bonding. This strategy allowed precise control over the HBD and ensured tunable mechanical properties. Isophorone diisocyanate (IPDI) acted as the hard segment, forming carbamate (–NHCOO–) bonds that function as both H-bonding donors and acceptors. Additionally, 2,6-pyridinedimethanol (PDM) was employed as a chain extender, introducing extra carbamate bonds and increasing segmental mobility by creating free volume for chain movement40. The molar ratio of IPDI:PDM:PTMEG was fixed at 1: 0.63: 0.37 to ensure the complete reaction of all functional groups (Fig. 2a).

Fourier-transform infrared (FT-IR) spectroscopy confirmed the successful synthesis of the PU elastomers (Fig. 2b). The disappearance of isocyanate (–N=C=O) and hydroxyl (–OH) peaks indicated the completion of polymerization, while the appearance of carbamate (–NHCOO–) and ether (–C–O–C–) peaks confirmed the formation of the PU network41. With synthesis confirmed, the focus shifted to controlling the H-bonding interactions within the PU matrix. In this system, only the amine hydrogen (–NH–) from IPDI served as the H-bonding donor, while multiple acceptors, including carbonyl (–C=O), imine (–C=N), and ether (–C–O–C–) groups, participated in H-bonding interactions (Supplementary Figure 4, Tables 7-9). Note that, FTIR analysis of these interactions revealed shifts in vibrational peaks corresponding to H-bonding, providing bulk-averaged measurements of bonding populations rather than localized interfacial values.42. For instance, the –C=O stretching peak of the free carbonyl group, typically observed near 1720 cm-1, shifted to lower wavenumbers upon forming hydrogen bonds with the –NH group. This red shift produced two distinct –C=O stretching bands: one at 1699 cm-1, corresponding to disordered hydrogen bonds, and one at 1667 cm-1, associated with more ordered hydrogen bonds (as illustrated in Fig. 2c)43. The pyridine ring within the chain extender (PDM) also contributed to hydrogen bonding interactions. When the –C=N group of the pyridine ring acted as a hydrogen bond acceptor, its stretching peak shifted to a higher wavenumber (around 1555 cm-1), compared to the non-hydrogen-bonded state at around 1532 cm-1.44 Similarly, the ether (–C–O–C–) groups from both PDM and PTMEG participated in hydrogen bonding. The C–O stretching peak shifted to a higher wavenumber when the ether group acted as a hydrogen bond acceptor45. For free ether groups, peaks were observed at 1102 cm-1 (for PDM) and 1025 cm-1 (for PTMEG), whereas hydrogen-bonded ether groups exhibited peaks at 1149 cm-1 (for PDM) and 1051 cm-1 (for PTMEG)46.

By fine-tuning the M of PTMEG, we precisely controlled the density of H-bonding sites, thus modulating w the PU's microstructure and molecular interactions. The HBD in the PU, varied from 2.9 mmol cm-3 to 5.0 mmol cm-3 (Fig. 2f, see Supplementary Table 10 and Supplementary Note 2 for detail). Higher HBD values corresponded to increased densities of available H-bonding donors and acceptors, indicating active participation in hydrogen bonding. For example, using PTMEG with an M of 1000 g mol-1 resulted in w hydrogen bond acceptor and donor densities of 7.31 and 3.16 mmol cm-3, yielding a HBD of 2.9 mmol cm-3. In contrast, using PTMEG with an M of 250 g mol-1 gave acceptor and donor densities of 12.39 w and 5.35 mmol cm-3, respectively, resulting in a HBD of 5.0 mmol cm-3. This controlled modulation of HBD is crucial for optimizing the composite's mechanical and thermal properties, as it directly influences the structural organization of the polymer network and its interactions with the embedded LM.

X-ray diffraction (XRD) patterns (Fig. 2d) and differential scanning calorimetry (DSC) analysis revealed significant changes in the microstructure with increasing HBD. XRD analysis of PU samples with varying HBD showed distinct changes in their crystallization behavior. For low HBD values (e.g., PU2.90 with a HBD of 2.9 mmol cm-3), only a broad peak at around 19.7° was observed, corresponding to an interplanar spacing of approximately 0.458 nm. This broad peak is indicative of amorphous clusters with short-range order. As the HBD increased, sharp diffraction peaks emerged at 28.6°, 32.1°, and 40.9°, corresponding to interplanar spacings of 0.311 nm, 0.279 nm, and 0.221 nm, respectively. The intensities of these peaks increased with higher HBD values, suggesting the formation of well-ordered crystalline structures within the hard domains of the PU samples. This enhancement can be attributed to strengthened H-bonding interactions that promote organized packing of polymer chains47. Complementary DSC analysis (Fig. 2e) further substantiated these observations. The PU sample with a HBD of 5.0 mmol cm-3 (PU5.0) exhibited a distinct glass transition temperature (T ) around 110 ℃. This transition signifies a shift from an g amorphous elastomeric state to a more semicrystalline plastic state as HBD increases. The presence of a clear T at higher HBD indicates restricted chain mobility due to stronger intermolecular interactions g facilitated by hydrogen bonds48. The concurrent evidence from XRD and DSC analyses underscores the pivotal role of H-bonding in dictating the thermal and microstructural properties of the PU samples. By fine-tuning the HBD through controlled variation of the soft segment molecular weight, it is possible to significantly alter the polymer's microstructure—from amorphous to semicrystalline—thereby influencing its mechanical and thermal behavior. In particular, the development of more ordered microstructures enhances phonon transport, resulting in a significant increase in thermal conductivity, from approximately 0.26 W m-1 K-1 to 0.69 W m-1 K-1 as the HEBD increases (Supplementary Figure 9). These results are consistent with prior studies49, which demonstrate that strengthening interchain interactions via hydrogen bonding can substantially improve the intrinsic thermal conductivity of polymers. Together, these findings underscore the critical role of hydrogen bonding in regulating polymer microstructure and thermal transport. Moreover, we establish a foundational strategy for enhancing the performance of PU-based composites, which will be further explored in subsequent sections.

2.2 Preparation and characterization of liquid metal-polyurethane composite

To fabricate the LiMPuC, EGaIn droplets were incorporated at a fixed volume fraction of 46% into a PU matrix. Prior to embedding, the droplet surfaces were functionalized with 3-aminopropyltriethoxysilane (APTES), introducing –NH groups on the native Ga O surface (Fig. 3a). These –NH moieties serve as 2 2 3 2 hydrogen-bonding donors that strengthen interfacial adhesion and wetting between the LM droplets and PU. As a result, the droplets are more effectively stabilized against interfacial debonding and maintain small inter-droplet separations under strain, which facilitates the formation of high-connectivity thermal transport pathways during deformation.

The successful grafting of APTES onto the LM surface was confirmed by the characteristic Ga–O–Si vibration at 457 cm-1 (Supplementary Figure 3)50, resulting in robust interfacial adhesion between LM droplets and the PU matrix. The introduction of LM droplets profoundly reconfigured the internal H-bonding landscape of the composite, as evidenced by FTIR spectra (Fig. 3b-f). In particular, key acceptor peaks of the PU matrix shifted upon LM incorporation. For example, the –C=O···H stretching vibration redshifted from 1667 cm-1 in pristine PU to 1662 cm-1 in LiMPuC, while the –C=N···H vibration associated with pyridine rings was redshifted by ~10 cm-1 relative to the neat PU (Fig. 3c). These shifts are attributed to the formation of stable, double H-bond interactions—enabled by the higher binding energy of –NH groups (5–10 kcal mol-1) compared to the original –NH donors (2–4 kcal mol-1)51— 2 between the polymer’s carbonyl and pyridinic nitrogen sites and the incorporated LM interface.

Quantitative deconvolution of the FTIR data (Supplementary Figures 5-6 and Table 10) revealed that the total H-bond density (HBD ) in LiMPuC could be systematically tuned via the M of the PU’s soft total w segment (PTMEG) (Fig. 3h). As the PTMEG M decreased, HBD increased from 1.46 to 2.38 mmol w total cm-3, following a trend established in the pure PU matrix. While the HBD among polymer chains (HBD PU- ) increased monotonically with decreasing M of the soft segment, the HBD at the LM-polymer PU w interface (HBD ) displayed a non-linear behavior. For samples with moderately low M (850–1000 LM-PU S w g mol-1), HBD remained around 0.6 mmol cm-3. However, further reducing the soft segment M LM-PU w below 650 g mol-1 led to a sharp drop in HBD to ~ 0.3 mmol cm-3. This substantial decrease is LM-PU attributed primarily to intensified steric hindrance from closely packed hard segments52 rather than interactions involving the nitrogen lone pair electrons, which provide weaker and less accessible hydrogen-bond acceptor sites53. Although functionalized LM particles could theoretically form hydrogen bonds among themselves, their dispersion and encapsulation within the rigid polymer matrix severely restrict direct particle–particle interactions, making this mechanism negligible in our system.

X-ray diffraction (XRD) further corroborated the interfacial and hard-domain structural features of the composite. Upon incorporation of LM, a broad diffraction feature centered at ~35.2° with a weak shoulder near 41.9° emerged (Fig. 3g). Importantly, these reflections do not indicate any atomic-scale ordering of the liquid metal droplets. Instead, they are attributed to the native nanocrystalline gallium oxide (Ga O ) 2 3 skin naturally formed on the EGaIn surface. Specifically, the features at 35.2° and 41.9° are consistent with the (002) and (−402) planes of 𝛽-Ga O (ICDD PDF# 41-1103), respectively. The pronounced peak 2 3 broadening is expected for an ultrathin oxide shell with nanoscale thickness and limited crystallinity. Meanwhile, a broad peak at ~19.6°, also present in pristine PU, arises from the intrinsic short-range packing correlations of the amorphous PU matrix. The persistence of this amorphous feature after LM incorporation indicates that the polymer bulk remains largely amorphous. Any structural modulation is therefore localized primarily within hydrogen-bond-stabilized hard domains and the polymer interphase adjacent to the LM interface, rather than within the liquid metal phase.

A key finding of this study is the strong correlation between interfacial HBD (HBD ) and the LM-PU composite’s thermal properties. Increasing HBD enhanced both thermal diffusivity and heat LM-PU capacity, thereby improving thermal conductivity (Fig. 3i). At the LM–PU interface, higher hydrogen-bond density enables more effective interfacial energy storage by allowing reversible bond dissociation and reformation, which raises the thermal energy required to elevate the material's temperature. In addition, increased interfacial HBD enhances molecular coupling between the LM droplets and the polymer matrix, restricting local chain mobility and possibly promoting low-frequency vibrational modes. These combined effects facilitate the formation of more efficient thermal transport pathways. As a result, LiMPuC3.41—with an HBD of 0.64 mmol cm-3—achieved a remarkable thermal conductivity of 4 LM-PU W m-1 K-1 at just 46 vol% LM loading. This thermal performance significantly exceeds previously reported values for materials with comparable LM loading (e.g., 1.3 W m-1 K-1 at 50 vol% LM)29.

The mechanical properties were similarly governed by the H-bonding network. In particular, the composites’ elongation at break is dominated by the H-bonding interactions among the PU matrices. As the HBD increased, the composites transitioned from ductile regime (elongation at break > 700%) to PU-PU brittle regime (elongation at break < 10%) once HBD exceeded 2.1 mmol cm-3. By contrast, the PPU-PU introduction of well-engineered H-bonding interactions between the PU and LM markedly boosted the toughness, measured as the area under the stress–strain curve54. This toughness reached a maximum of 9.97 MJ m-3 at HBD ≈ 0.65 mmol cm-3 (LiMPuC3.41). This high toughness reflects superior LM-PU interfacial load transfer arising from robust LM-PU interfacial H-bonding (Fig. 3j).

Notably, the synergy between mechanical toughness and filler-mediated thermal enhancement, quantified by the composite’s thermal conductivity per LM volume fraction (𝜙), underscores a unique mechano-thermal coupling in these composites (Fig. 3k). By strategically tuning the H-bonding network, we achieved exceptionally high thermal conductivity at comparatively low filler loadings while maintaining elevated toughness. This outcome suggests that robust interfacial H-bonding can both enhance energy dissipation mechanisms under load and foster continuous, percolated heat transfer networks.

2.3 Exceptional thermal conductivity of LiMPuC under strain

To investigate the strain-dependent thermal behaviour of the LiMPuC, we developed a custom in situ experimental platform combining uniaxial tensile loading with steady-state in-plane thermal conductivity measurements55, in accordance with ASTM-D5470 (Fig. 4a, See Supplementary Note 3.2 for detail). The reliability of this setup was verified against benchmark materials: quartz (𝜅 = 1.47 W m-1 K-1), 304 stainless steels (𝜅 = 15.3 W m-1 K-1), and copper (𝜅 = 380 W m-1 K-1). Measured thermal conductivities deviated by less than 10% from standard values (Supplementary Figure 12), confirming the accuracy of our apparatus. In addition, we cross-validated the setup by comparing its results with those obtained by laser flash analysis (LFA) on the composite samples without stretching (Fig. 3i and Supplementary Table 20), which yielded an average deviation of 4.8%, further corroborating the measurement fidelity.

Under tensile deformation, ductile LiMPuC samples exhibited a marked increase in thermal conductivity along the stretching direction. Particularly striking was LiMPuC3.41, which reached a thermal conductivity of 23.42 W m-1 K-1 at 400% strain—an approximate six-fold enhancement over its unstressed state (Fig. 4b). Under identical strain conditions (e.g., 400% strain), samples with higher HBD demonstrate enhanced thermal conductivity (Fig. 4c) under the same filler concentration. This remarkable LM-PU improvement stems from the synergy between the deformable EGaIn droplets and the stretchable PU matrix (Fig. 4d).

To elucidate the underlying mechanism, the investigation commenced with characterizing the mechanical response of the PU3.41. Progressive tensile deformation promotes increased chain orientation and hard-segment packing coherence in PU, as evidenced by XRD. With increasing strain, the initially broad scattering evolves into a more distinct diffraction feature that shifts from ~28.07° to ~29.24°. We attribute this evolution to strain-induced ordering/packing of hydrogen-bond-stabilized hard segments (often described as quasi-crystalline or mesophase-like ordering), rather than the formation of fully developed lamellar crystallites in the polymer backbone. The peak sharpening and shift to higher 2θ suggest increased packing density and orientational coherence of hard domains under the strain-fixed protocol.56,57 (Supplementary Figure 15a). Concurrently, FTIR analysis revealed an increase in ordered hydrogen bonding, specifically carbonyl-acceptor interactions, from 0.67 to 0.87 mmol cm-3 between 0% and 400% strain (Supplementary Figure 15b and Supplementary Table 21). This improved ordering substantially elevated the PU3.41 thermal conductivity from 0.32 W m-1 K-1 to 1.09 W m-1 K-1, highlighting a direct quantitative relationship between hydrogen bond ordering and thermal transport (Supplementary Figure 15c, d). Thermal conductivity accelerated markedly as ordered HBD exceeded 0.80 mmol cm-3, approaching approximately 1.1 W m-1 K-1 at 0.87 mmol cm-3.

Direct in situ measurement of the matrix thermal conductivity during composite stretching was experimentally challenging. Therefore, FTIR spectroscopy was employed to quantify ordered HBD density in LiMPuC3.41 (46 vol% LM) at each strain level. Due to robust interactions between liquid metal droplets and the PU matrix, the ordered HBD significantly increased from 0.98 mmol cm-3 to 1.32 mmol cm-3 over the strain range of 0% to 400%, strongly implying significantly enhanced thermal conductivity of the PU3.41 matrix within the composite. The strain-induced reorganization of hydrogen bonds at APTES-functionalized LM interfaces increases donor/acceptor matching, enhances wetting, and anchors chain segments that transmit load and orientation into the surrounding matrix. The resulting reduction of inter- and intra-chain scattering, together with improved LM connectivity, elevates the bulk 𝜅 composite while preserving stretchability. This ordering-driven enhancement is consistent with the broader literature on highly oriented polymers, where extreme drawing yields conductivities from tens to >100 W m-1 K-1 (e.g., polyethylene (PE) nanofibers and drawn films) despite isotropic PE being ~0.2 W m-1 K-1.58,59

Incorporating –NH functionalized LM droplets into the PU matrix strengthens interfacial wetting and 2 adhesion through hydrogen bonding. These interactions stabilize the droplet–matrix interface and maintain reduced inter-droplet spacing and high local connectivity, thereby forming a percolation-like conductive structure within the composite. As tensile strain increases, droplets progressively elongate into spindle-like morphologies and preferentially align along the tensile direction, producing an anisotropic microstructure that supports directional, high-conductance heat-transport routes.

Crucially, the dynamic hydrogen-bond network acts as a reversible “binder” that suppresses interfacial debonding and prevents droplet isolation, preserving the percolation-like interconnected structure even under large deformation. This stabilizes the strain-induced droplet reshaping and alignment, and thereby increases the number and effectiveness of continuous thermal pathways at the mesoscale, leading to a pronounced enhancement of the effective thermal conductivity (Fig. 4e).

We note that droplet deformability can be limited below a critical size, where Laplace pressure may inhibit elongation even with improved wetting. In addition, at sufficiently high strain, rupture of the oxide skin and associated electrical percolation may occur in some formulations, consistent with our preliminary observation of LM extrusion beyond 400% strain in a subset of samples (e.g., LiMPuC2.90). A systematic, size- and strain-dependent study of these electrical effects will be pursued in future work.

Taking LiMPuC3.41 as an example, we demonstrate its remarkable softness and deformability (Fig. 5a), exemplified by its ability to bend to a radius of 1.5 mm. Fig. 5b further illustrates LiMPuC’s thermal performance under torsional twisting between two thermal sources (52 ℃ hot end and 23 ℃ cold end). Even in this deformed state, LiMPuC effectively transfers heat across the twisted junction, exhibiting temperatures approximately 10 ℃ higher than those measured for PDMS under similar conditions. Infrared imaging (Fig. 5c) provides additional evidence of LiMPuC3.41’s superior thermal conduction: when stretched, it surpasses stainless steel, PDMS, and its own unstretched state. These results highlight the capacity of LiMPuC to maintain efficient heat dissipation even under significant mechanical stress, thereby meeting the stringent demands of flexible thermal management applications. Collectively, these findings confirm that the hydrogen bonding within LiMPuC not only imparts mechanical adaptability but also preserves robust thermal pathways, making it an exceptional candidate for next-generation flexible heat-dissipation technologies.

Methods
4.1 Materials.
Polytetramethylene Ether Glycol (PTMEG, M = 1000, 850, 650, 250 g mol−1), 2,6-pyridinedimethanol w (PDM), isophorone diisocyanate (IPDI, 99%), 3-aminopropyltriethoxysilane (APTES) was purchased from Adams, Dibutyltin dilaurate (DBTDL) catalyst, N, N-Dimethylformamide (DMF), were purchased from Macklin. Toluene was offered by Aladdin. Eutectic gallium indium (EGaIn, 75% Ga:25% In) was purchased from Zhenjiang Asian Electronic Technology Co., Ltd.

4.2 The Synthesis of PU.
We maintained a fixed molar ratio of IPDI: PDM: PTMEG at 1: 0.63: 0.37, To remove residual moisture, PTMEG was added in a dried glass vessel equipped with a mechanical stirrer. It was heated by an electrical heating jacket at 120 ℃ under vacuum for 1 hour. After cooling down to 80 ℃, IPDI (100 mmol, 22 g) was added into the vessel and stirred for 1 hour under argon atmosphere. Then, catalyst DBTAL was dissolved in anhydrous toluene and added into the above system. The chemical reaction was continued for another 3 hours. Afterward, anhydrous toluene was added to adjust the viscosity, followed by employing PDM (63 mmol, 8.75 g) powder as the chain extender to the system to complete the reaction at 80 ℃. It took about 10 hours until the –NCO peak in the FTIR spectrum disappeared. Detailed information concerning the composition and quantitative content of each component is provided in the Supplementary Table 4. Finally, the mixture in the vessel was transferred into a rectangular mold and brought to vaporize the solvent in a fume hood at ambient conditions for 24 hours. The product was dried at 80 ℃ for another 24 hours in an air-circulating oven, followed by removing residual solvent at 80 ℃ for 24 hours in a vacuum oven.

4.3 Surface modification of liquid metal.
The surface modification of the liquid metal was carried out using APTES, which was pretreated by adding 10 mL of dimethylethanolamine (DMEA) to 110 mL of APTES to achieve an alkaline pH. 1.57 mL (10 g) of liquid metal was mixed with DMEA modified APTES (0.46 mL, 0.44 g) and DMF (1 mL, 0.95 g) to regulate the suspension’s viscosity. The resulting dispersion was subjected to magnetic agitation at 1200 rpm for 4 minutes at ambient temperature, whereby the bulk metal was comminuted into droplets with an average diameter of ≈10 µm. Subsequently, the stirring speed was reduced to 300 rpm and maintained for 2 hours, during which APTES hydrolysis proceeded and the silane was covalently grafted onto the droplet surfaces. The specific content of each component is provided in the Supplementary Table 11. The liquid metal suspension was then placed in a water bath ultrasonic device for 30 minutes to further reduce the droplet diameter to 1.52 m ± 1.17 m (Supplementary Figure 32).

4.4 Preparation of LiMPuC.
A separately, 1.68 g of PU was added to 5.07 g of DMF and stirred magnetically at 80 ℃ for 4 hours until completely dissolved. The PU/DMF solution was combined with the liquid metal/APTES suspension and stirred using a planetary mixer at 1600 rpm for 10 minutes. The liquid metal droplets were reduced to approximately 1 m by treating the mixture with an ultrasonic device in a water bath for 30 minutes. The mixture was then poured into molds pre-sprayed with release agent and dried at 80 ℃ for 24 hours.

4.5 Materials characterizations
1H Nuclear Magnetic Resonance Spectroscopy (1H NMR) was recorded at room temperature using a 500 MHz NMR spectrometer (AVANCE Ⅲ, Bruker, U.S.) with dichloromethane-D as the solvent. 2 Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) spectra were acquired on a Vertex 70 spectrometer (Bruker, U.S.) equipped with a diamond ATR crystal. The wavenumber range was set from 4000 to 400 cm-1, with 64 scans collected at a resolution of 4 cm-1. X-ray diffraction (XRD) patterns were obtained using a D8 Advance diffractometer (Miniflex 600, Rigaku, Japan) with Cu Kα radiation (𝜆 = 0.1541 nm). Scanning electron microscopy (SEM) was performed on a field-emission scanning electron microscope (SU8010, Hitachi, Japan) at an acceleration voltage of 14 kV to analyze the sample morphology. Differential scanning calorimetry (DSC) curves were measured using a DSC25 analyzer (DSC25, TA Instruments, U.S.) under a dry nitrogen atmosphere, with a temperature range of 20–200 ℃ and a heating rate of 10 °C min-1. Modulated Differential Scanning Calorimetry (MDSC) was employed to determine the heat capacity at room temperature, with a heating rate of 2 ℃ min-1 across a temperature range of 17–30 ℃. The thermal conductivity of the samples in the unstretched state was measured at room temperature using a laser flash apparatus (LFA 467, NETZSCH, Germany) equipped with an out-of-plane fixture. For samples under tensile strain, measurements were performed using a steady-state thermal conductivity testing apparatus.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript reports a LM droplet-dopted elastomer composite. The authors claim that they achieve a streatching-enabled high thermal conductivity of 23.4 W/mK@400% for ϕ_EGaIn=46 vol% LM concentration, which violates the theoretical value of the parallel rule for the effective thermal conductivity: K_eff =ϕE_GaIn*K_EGaIn + (1-ϕ_EGaIn)*K_PL≈0.46*28+0.54*0.2=13W/mK (EGaIn is used here K_EGaIn= 28W/mK). The authores have no explanation about this unpredictable performance. Therefore, I cannot recommend this work publication in Nature Communications. The detailed issues including:\n1) The authors should focus more attention on the thermal conduction mechanisms of the composites. The authors also lack an understanding of the latest research developments in this field. The LM droplet-dopted elastomer composite can achieve a streatching-enabled high thermal conductivity, which has been reported for the first time by Majidi group (PNAS 2017(114): 2143-48), K_eff=9.8W/mK@400% for ϕ_LM=50%(EGaIn is used here KEGaIn= 28W/mK). Another strategy is to design porous LM-based lastomer composite reported by He group (Nature Communications 2024(15):1179), K_eff=21.2W/mK@0% ϕ_Ga=81.4% (here pure gallium LM is used, K_Ga= 33.4W/mK) and K_eff=27.1W/mK@300% which approaches the limit of the parallel rule (27.2W/mK). The results reported previously do not violate the parallel rule. In this manuscript, the authors prepared LM droplet-dopted elastomer composite, which is similar to the work of Majidi group. They claim that unpredictable thermal conductivitiy of 23.4 W/mK@400% (exceeding the theoretical value of 13W/mK for ϕ_EGaIn=46%) arises from a hydrogen-bonding network that enhances liquid metal particle wetting by modulating hydrogen-bond donor/acceptor densities in the thermoplastic polyurethane. This explanation is unreasonable. The interface enhancement can improve the thermal conduction while cannot make it exceeding the theoretical value.\n2) Based on the preparation of LM-based elastomer composites and the measurement of their thermal conductivity, it is hypothesized that the high thermal conductivity value of 23.4 W/mK at 400% strain may not correspond to the bulk composite material's thermal conductivity but instead reflects the thermal conduction characteristics of the surface layer. In the Method section of the manuscript, the authors claim “The mixture was then poured into molds pre-sprayed with release agent and dried at 80 ℃ for 24 hours”, which may lead to the sedimentation of the LM droplets, thereby forming a dense layer of LM with a high-volume content. This is easily validated by providing the cross-sectional microstructure SEM. In addition, a superhigh thermal conductivity value of 23.4 W/mK at 400% strain was obtained by measuring the surface temperature using an infrared camera. This method cannot accurately reflect the internal heat transfer characteristics of the layered sample.\n3) The streatching can incarese the thermal conductivity of LM-based elastomer composite along the streatching direction, while it would lead to decrease in the perpendicular direction. The author should add relevant experimental tests.", "reviewer_2": "In this work, the authors have explored the strategy of introducing hydrogen bonding and leverage them for improving thermal percolation to achieve high thermal conductivity of the liquid metal composites. The strategy looks reasonable and the authors have provided the relevant results. Prior to considering for publication, the authors may need to address some issues.\n1. Page 2, line 46, please check the unit of thermal conductivity.\n2. Page 4, lines 78-80, can this context be explained in terms of non participation of the oxide layer chemically in the crosslinking process of the polymeric chains?\n3. Page 5, line 122, please check the mentioned ratio.\n4. Page 9, lines 217-224, the scenerio is nit clear. At very low molecular weight (100g/mol) soft segment, the hard segments' increased proximity might isolate the LMs from acheveing H bonding with the interface. But at 650 g/mol, too the HBD value seems similar. Can't the functionalized LM particles form hydrogen bond among themselves? Or, at this molecular weight, spatial arrangement is such that the effective hindrance from the lone pair electrons of N are contributing negatively towards H bond formation?\n5. In Figure 3j, especially for elongation at break values, how many times they have been repeated? Because samples 3.41 and 3.74 are having break values in closed proximity and toughness seems being calculated from the reported single graph. Are the tensile graphs the best from experiment? As seen in the graph, the toughness for sample 3.41 is almost thrice that of sample 3.74. These values may change if elongation at break values are not consistent.\n6. The conclusion in Figure 4 is interesting.By stretching the composite, the authors have obtained metallic like thermal conductivity in polymer. The presence and absence of hydrogen bonding between LM and PU is also going to manipulate it's interfacial tension. And also, beyond a certain downsized LM particle size, the effect of stretching might not influence the entrapped LM's geometry, depending on this interfacial tension. Can the authors explain from this point of view. Also, due to strong interaction between the polymer and LM, beyond a certain strain value, electrical percolation might occur due to oxide rupture. The authors should report this finding.\n7. Where are the parameters for calculating flexibility figure of merit? Please mention the youngs modulus and yield stress of the composites in a separate table.\n8. How to realize practical utility of these composites? As the thermal conductivity is anisotropic in nature here, is it possible to slice and arrange them to achieve large area through plane thermally conductive composite? (https://doi.org/10.1021/acsami.7b08061) Such strategies can be useful for fabricating soft heat sinks for wearable electronics. Also, the author has referred to the material as ductile in many places, but can they attain permanent plastic deformation? If not, can their microstructures be preserved through annealing? (https://doi.org/10.1002/adfm.202000832)\n9. Page 36, Supporting Information, S3.2, what is the tone frame within which the IR imaging is conducted? Similarly, for the thermograms in Figure 5, what are the time frames?\n10. Page 4, line 70, Supporting information, please provide a particle size distribution data in terms of major- minor axes or aspect ratio to ascertain the average diameter value. The microscopic image in Figure 4d clearly does not depict a homogeneous distribution\n11. Higher diameter particles around 50-100μm might have contributed more to the thermal conductivity. Was 1 μm chosen for increased area for H bond interaction? Also, larger particles might have deformed more under strain to contribute to thermal conductivity. What is the compliance level of the 1μm particles with respect to external stretching for the mentioned HBD? The inset images in Figure 4 d are not very clear.\n12. All composites have high thermal conductivity (~23 W/m-K) under strain conditions, not under un-stretched one (4 W/m-K). Usually, TIM’s are not used under permanent stretched conditions. Though mechanical deformation may occur randomly. If we use it under permanent stretch condition to leverage its high thermal conductivity, due to constant applied stress, creep failure may occur.\n13. After multiple cycles of stretch-release, there may be possibility of mechanical sintering of LM particles which may increase thermal conductivity of composites?", "reviewer_3": "Soft materials, such as plastics and elastomers, are typically characterized by low thermal conductivity, while stiff materials, such as ceramics and metals, tend to exhibit high thermal conductivity. This manuscript introduces a liquid-metal/polyurethane composite LiMPuC that demonstrates an impressive thermal conductivity of 23.4 W m-1 K-1 at a tensile strain of 400%, while maintaining a flexibility figure of merit greater than 100. By delivering metal-like heat transport within a rubbery matrix at a moderate filler fraction of 46 vol%, this composite surpasses the existing performance plateau (10-13 W m-1 K-1) observed in liquid metal composites. The authors propose a hydrogen-bond–mediated interfacial design that simultaneously enhances LM percolation and strengthens the polymer network, thus overcoming the traditional stiffness–conductivity trade-off. This work represents a timely and significant contribution to both the thermal-management and soft-materials communities. I recommend publication after minor revisions to address the following points.\nDetailed comments:\n1. In Fig. 3i, LiMPuC 3.74 and 5.00 show an abrupt increase in volumetric heat capacity relative to LiMPuC 2.90 and 3.41. Please clarify the underlying mechanism, e.g. enhanced polymer crystallinity, higher hydrogen-bond density, or confinement of LM droplets? Supporting DSC or modulated-DSC data would strengthen the explanation.\n2. Contact resistance issue in the in house measurement set up adhere to ASTM-D5470 standard. The in-situ fixture is well validated, yet the manuscript does not quantify the contribution of contact resistance (Rc) to the “apparent” thermal conductivity defined by ASTM-D5470. Please (i) report typical Rc values (e.g. via thickness extrapolation) or (ii) present a sensitivity analysis showing that Rc remains ≤ 10 % of the total thermal resistance across the strain range.\n3. As illustrated in Fig. 4a, how does the testing apparatus based on the ASTM-D5470 standard monitor thermal conductivity under different strain conditions? The Materials characterizations part should be enhanced.\n4. Upper-limit strain in strain dependent thermal conductivity tests (Fig. 4b). The composites endure > 500 % elongation (Fig. 3j), but thermal conductivity is reported only up to 400 % strain. Was sample integrity or fixture alignment compromised beyond this point? If higher-strain data are available, even for a subset of samples, please include them; otherwise, briefly justify the 400 % ceiling.\n5. Strain-rate dependence. State the tensile strain rate used during in-situ thermal conductivity measurements and discuss its influence on hydrogen-bond reconfiguration and resulting thermal conductivity.\n6. Definition of the flexibility figure of merit. Introduce flexibility figure of merit formally in the main text where it first appears, including its mathematical definition and rationale.\n7. Does liquid metal leak out of the material when stretched or compressed?\n8. Some recent studies regarding liquid metal-based thermal conductors may be useful to enhance the manuscript, e.g. Nature Nanotechnology 20, 104–111 (2025), Proceedings of the National Academy of Sciences, 114, 2143-2148 (2017), Science, 379, 488-493 (2023), Device 3, 100576 (2025), and position the present advance relative to these reports."}, "author_response": "We extend our sincere gratitude to the reviewers for their thorough and insightful review of our manuscript. The detailed feedback has prompted us to make substantial revisions to enhance the clarity and depth of our research findings. We have carefully reviewed all the reviewers’ feedback and revised our manuscript accordingly (highlighted in yellow). Here are our detailed responses to individual comments."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I appreciate the authors’ effort to address my previous concerns. However, I cannot agree with their explanation regarding my key concern, the unreasonable value of thermal conductivity (23.4 W/mK at 400% strain for an LM concentration of ϕEGaIn = 46 vol%).\nThe reported effective thermal conductivity of 23.4 W/mK at 400% strain for LM concentration of ϕEGaIn=46vol% indeed exceeds the Voigt upper bound. According to the parallel rule for the effective thermal conductivity: K_eff =ϕEGaInKEGaIn + (1-ϕEGaIn)KPL, K_eff=23.4 W/mK means KPL ≈19.48W/mK for polymer matrix of Pu3.41. However, KPL=1.2W/mK is for Pu3.41 at 400% strain (see Extended Data Figure 1 (b)). In addition, the data for the theoretical upper bound of composite thermal conductivity presented in Extended Data Figure 1(d) appear inconsistent; therefore, the corresponding formulation should be provided for clarification.", "reviewer_2": "The authors have well addressed most my comments, however, I still have a few queries that the authors may need to address.\nresponse to comment 5: I think the toughness calculation technique is still discrepant. Because, ideally calculating the toughness values from the best curves followed by calculation of the mean value of toughness will be quite different from the reported single value of the median curve. Also, though I agree with the author's statement that the shapes of the graphs are evident, it is to be noted that the reported graphs are the median graphs and thus calculations can vary by margins.\nresponse to comment 6: Can the authors provide a few experimental evidence as to the possible minimum LM size beyond which the LM particles would not undergo stretching? As the interfacial tension values in such systems are difficult to calculate, experimental evidence would be helpful to the readers.\nresponse to comment 13: it is advisable to report thermal conductivities of a few samples after cyclic tests to support the claim. The evidence of non percolation state can be also proved by other conventional techniques, e.g. measuring dielectric constant of the composites.", "reviewer_3": "Liu and colleagues have provided a thorough and thoughtful response to the reviewers’ comments. Despite the breadth of the questions raised, the authors conducted a substantial number of additional experiments and characterizations to support their conclusions. They also incorporated relevant discussions to address the concerns. I am satisfied with the revised manuscript and support the publication of these research findings."}, "author_response": "We sincerely thank the reviewers for their thorough and insightful evaluation of our manuscript. Their detailed feedback has been invaluable in helping us improve the clarity, depth, and overall quality of our work. In response, we have carefully considered every comment and made substantial revisions to the manuscript, which are highlighted in yellow for ease of reference. Below, we provide a detailed point-by-point response to each of the reviewers’ comments."}, {"round": 3, "reviewer_comments": {"reviewer_1": "I have thoroughly examined the authors' response to my concerns, as well as the revised manuscript. To address my primary concern regarding the reported thermal conductivity of 23.4 W/mK at a strain of 400% for a LM concentration of 46 vol%, the authors claim that the elastomer polymer demonstrates an exceptionally high thermal conductivity with K_matrix = 48.01 W/m/K, which is even higher than thermal conductivity of LM (~28W/m/K). If this report is accurate, it represents a significant discovery, as most polymers exhibit low thermal conductivity in the range of approximately 0.1 to 0.5 W/m/K. However, this claim lacks rigorous justification and contains numerous contradictory statements. Therefore, the authors are unable to address my concerns while introducing new issues.\n1) The authors claim K_matrix=48.01W/m/K (this value should be 47.85W/m/K) estimated by Eq.(R1) for ordered HBD=1.32, and does not represent an experimental measurement. One of the key issues is whether the Eq.(R1) is appropriate for large ordered HBD. For example, for ordered HBD=1.4, Eq.(R1) gives K_matrix=81.40W/m/K. This value is remarkably high and may seem difficult to accept. If K_matrix=48.01W/m/K is indeed accurate, the main text (including abstract and conclusion) needs be rewritten to highlight this value.\n2) Another key issue is the impact of LM on the ordered HBD of the polymer matrix. For pristine PU3.41, a strain of 400% results in an ordered HBD of 0.87, whereas for LiMPuC3.41 at 400% strain, the matrix exhibits an ordered HBD of approximately 1.32. It is important to note that the LM droplet only influences the contacted polymer and not its bulk properties. It is important to consider whether it is reasonable to utilize FTIR for the accurate measurement of the ordered HDB value.", "reviewer_2": "The authors have well addressed the prior concerns. The revised manuscript can be considered to get published.", "reviewer_3": "I would like to raise comments regarding whether the reported thermal conductivity (23.4 W/mK) at 400% strain is reasonable.\nUsing the Voigt (parallel) model, the theoretical upper bound appears to be around 19.48 W/mK, assuming the thermal conductivity of the polymer matrix is 1.2 W W/mK at 400% strain. However, the authors provided data (Figure R2-1a and c) showing that at 400% strain, the ordered hydrogen bonding densities (HBDs) differ significantly between pure PU and PU/LM composites. Since the thermal conductivity of the PU matrix is strongly dependent on the degree of ordered HBD, the PU matrix within the composites at 400% strain is likely to have a value higher than 1.2 W/mK. This explanation is reasonable and quite interesting. Gallium-based liquid metals are known to oxidize easily under ambient conditions, and the polar oxygen-containing functional groups at the LM surface may indeed promote the formation of ordered hydrogen bonding in PU macromolecules during uniaxial stretching.\nNevertheless, I suggest that the authors delete the data in Figure R2-1b and d, and revise Table R2-2 accordingly. In the revised manuscript, they used a fitting extrapolation method to predict the thermal conductivity of PU at high degrees of ordered HBD. Although the exponential model fits the data well at low HBD order, it likely loses accuracy at higher levels. For instance, in Figure R2-1d, the predicted thermal conductivity of PU with an HBD order of 1.3 exceeds 20 W W/mK, which is unrealistic.\nOverall, I believe that the main issues raised by the reviewers have been addressed satisfactorily. After minor and reasonable revisions, I recommend the manuscript for publication in Nature Communications."}, "author_response": "We sincerely thank the reviewers for their thorough and insightful evaluation of our manuscript. Their detailed feedback has been invaluable in helping us improve the clarity, depth, and overall quality of our work. In response, we have carefully considered every comment and made substantial revisions to the manuscript, which are highlighted in yellow for ease of reference. Below, we provide a detailed point-by-point response to each of the reviewers’ comments."}, {"round": 4, "reviewer_comments": {"reviewer_1": "I cannot recommend this work publish in Nature Communications due to the contradictory results it presents. The key finding of \"thermal conductivity of 23.4 W/mK at a strain of 400% for a LM concentration of 46 vol%\" lacks supporting data and theoretical framework for interpretation. As I highlighted in my initial round of review comments, the method employed for testing thermal conductivity exhibits considerable errors when the concentration of liquid metal is relatively high. This discrepancy may be attributed to the coalescence of liquid metal droplets during the stretching process. The authors claim K_matrix=48.01W/m/K for ordered HBD=1.32, which is higher than thermal conductivity of LM (~28W/m/K). So, it is unreasonable to assert that the incorporation of a low thermal conductivity liquid metal into a high thermal conductivity elastic matrix can improve the overall thermal conductivity of the material system. If the thermal conductivity of the elastic matrix is lower than that of the liquid metal, according to the Voigt upper bound principle, the thermal conductivity of the resulting composite cannot attain a superhigh value of 23.4 W/mK for for a LM concentration of 46 vol%. Another contradiction lies in the author's overestimation of the impact of the interface effect between liquid metal and elastic matrix on bulk thermal conductivity, lacking both empirical evidence and theoretical support. In conclusion, the findings presented in this study lack rigorous scientific validation, and the exceptionally high thermal conductivity values reported are unlikely to be accepted by experts in the field of heat transfer.", "reviewer_4": "This work, describing the effect of modulating hydrogen bond density on mechanical and thermal properties of PU-LM composites is interesting and cites measurement of thermal conductivities significantly higher than those previously measured in literature. The method of modulating hydrogen bonding is straightforward and well described in the manuscript. My concern in the manuscript comes from the discussion of liquid metal participation in the hydrogen bonding particularly with respect to stretch and some of the experimental data (and corresponding assumptions) made in the document. The instrument that the authors created itself appears valid and the authors have included appropriate references and comparisons to standards to convince the reader that measurements are valid. The authors also state at what strain they start to external evidence of LM droplet rupture, which is a common problem with LM composites when measuring any kind of conductivity. My challenge with this work is that (1) the authors use measurements of XRD and FTIR under strain to justify claims of hydrogen bond rearrangement [the authors should make it abundantly clear in the manuscript that it is hydrogen bonds and not the liquid metal droplets themselves that are rearranging] however the methods for taking this measurement (i.e., how strain was applied and maintained and in what direction/orientation) are not described anywhere and (2) the only evidence provided by the authors of what is happening morphologically in the composite is in Figure 4d and Supp Figure 30, both of which are highly unconvincing.\nSurrounding the discussion of Figure 4, the authors use the word “percolation,” but classically the term percolation is when conductive elements are physically touching one another such that there is a clear pathway. That is not the case with LM droplets as at 46vol% the droplets are encapsulated with oxide and have a polymer barrier between them. There isn’t a real percolation threshold for liquid metal droplets in general, and for this system with the PU hydrogen bonding is a dominant force in the conduction percolation seems like an incorrect term. In Figure 4d the authors attempt to make the reader see the percolation by highlighting droplets in the PU system in red (I assume this is highlighting since the caption doesn’t describe why some droplets are red while others aren’t in either the PU or PDMS image). It isn’t clear why these droplets were chosen since they are not consistently in conductive contact or at least anymore obviously isolated than the droplets in the PDMS sample. The cartoon below the unstrained images is misleading since there are certainly droplets in the PDMS sample that seem as close in contact as the droplets in PU and there are many large gaps between the LM droplets in the PU just from the naked eye. I similarly don’t understand the strained image. The concentration of droplets seems to have significantly dropped in the strained PDMS image but not the PU image. Unless there is rupture of the LM composite and the loss of LM, and assuming that the magnification was maintained constant, there is no reason for there to be a sudden large gap between the strained LM in PDMS while the PU strained images appear more crowded.\nIn terms of organization that may promote thermal conductivity, the authors cite a peak that develops at 200% strain in XRD around 28/29o as crystallinity in the PU (the reference [55] does not highlight this peak, so I am not sure how the authors know that this peak related to crystalline PU). The authors also cite XRD of LM-PU composites that have a peak at 35o with the argument that these demonstrate short term order of the LM droplets. This is related to increase in thermal conductivity at the unstrained state. (1) I can’t understand how the LM droplets could show any kind of order on the level of 0.255nm and 0.224nm interplanar spacing. (2) SEM images indicate no order, and basically look like any other LM dispersion. If the “order” refers to PU directly adjacent to the LM interface this should be made very clear. I can understand that FTIR measures bulk which has interfacial measurements essentially baked into them, but even with the current revisions the authors need to refine their language about what the LM is inducing in the polymer, what happens in polymer bulk, and what is actually happening to the LM itself.\nI hesitate to suggest new experiments, but it would be of great use to the reader to understand what happens to one of these samples after the initial strain. Are all of these measurements (XRD, thermal behavior, FTIR, etc.) done under strain or when the material is relaxed? Are the increases in crystallinity and “rearrangement” of H bonds permanent (so that straining is essentially a manufacturing process) or does the material have to be under strain in order to achieve these results?\nIn sum, the authors comments to previous reviewers leads me to believe that the measurements as presented are credible and believable, but the authors description of the phenomenon that leads to the increase in thermal conductivity should be better described. As stated, the description of percolation as well as induced polymer changes that come with the inclusion of LM are confusing or seemingly inaccurate."}, "author_response": "We sincerely thank the reviewers for their thorough and insightful evaluation of our manuscript. Their detailed feedback has been invaluable in helping us improve the clarity, depth, and overall quality of our work. In response, we have carefully considered every comment and made substantial revisions to the manuscript, which are highlighted in yellow for ease of reference. Below, we provide a detailed point-by-point response to each of the reviewers’ comments."}, {"round": 5, "reviewer_comments": {"reviewer_4": "The authors have sufficiently addressed my comments and concerns about this manuscript, particularly related to denoting changes in the LM vs. oxide vs. bulk as well as concerns about the use of the word \"percolation,\" and I believe that manuscript in its current form is worthy of publication."}, "author_response": ""}]

Decision letter