Soft dielectric materials typically exhibit poor heat transfer properties due to the dynamics of phonon transport, which constrain thermal conductivity (k) to decrease monotonically with decreasing elastic modulus (E). This thermal−mechanical trade-off is limiting for wearable computing, soft robotics, and other emerging applications that require materials with both high thermal conductivity and low mechanical stiffness. Here, we overcome this constraint with an electrically insulating composite that exhibits an unprecedented combination of metal-like thermal conductivity, an elastic compliance similar to soft biological tissue (Young's modulus < 100 kPa), and the capability to undergo extreme deformations (>600% strain). By incorporating liquid metal (LM) microdroplets into a soft elastomer, we achieve a ∼25× increase in thermal conductivity (4.7 ± 0.2 W·m ) under stress-free conditions and a ∼50× increase (9.8 ± 0.8 W·m) when strained. This exceptional combination of thermal and mechanical properties is enabled by a unique thermal−mechanical coupling that exploits the deformability of the LM inclusions to create thermally conductive pathways in situ. Moreover, these materials offer possibilities for passive heat exchange in stretchable electronics and bioinspired robotics, which we demonstrate through the rapid heat dissipation of an elastomer-mounted extreme high-power LED lamp and a swimming soft robot.liquid metal | thermal conductivity | soft materials | soft robotics | stretchable electronics

An all-soft-matter composite with exceptional electro-elasto properties is demonstrated by embedding liquid-metal inclusions in an elastomer matrix. This material exhibits a unique combination of high dielectric constant, low stiffness, and large strain limit (ca. 600% strain). The elasticity, electrostatics, and electromechanical coupling of the composite are investigated, and strong agreement with predictions from effective medium theory is found.

Binary mixtures of liquid metal (LM) or low-melting-point alloy (LMPA) in an elastomeric or fluidic carrier medium can exhibit unique combinations of electrical, thermal, and mechanical properties. This emerging class of soft multifunctional composites have potential applications in wearable computing, bio-inspired robotics, and shape-programmable architectures. The dispersion phase can range from dilute droplets to connected networks that support electrical conductivity. In contrast to deterministically patterned LM microfluidics, LMPA- and LM-embedded elastomer (LMEE) composites are statistically homogenous and exhibit effective bulk properties. Eutectic Ga-In (EGaIn) and Ga-In-Sn (Galinstan) alloys are typically used due to their high conductivity, low viscosity, negligible nontoxicity, and ability to wet to nonmetallic materials. Because they are liquid-phase, these alloys can alter the electrical and thermal properties of the composite while preserving the mechanics of the surrounding medium. For composites with LMPA inclusions (e.g., Field's metal, Pb-based solder), mechanical rigidity can be actively tuned with external heating or electrical activation. This progress report, reviews recent experimental and theoretical studies of this emerging class of soft material architectures and identifies current technical challenges and opportunities for further advancement.

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Soft and tough materials are critical for engineering applications in medical devices, stretchable and wearable electronics, and soft robotics. Toughness in synthetic materials is mostly accomplished by increasing energy dissipation near the crack tip with various energy dissipation techniques. However, bio-materials exhibit extreme toughness by combining multi-scale energy dissipation with the ability to deflect and blunt an advancing crack tip. Here, we demonstrate a synthetic materials architecture that also exhibits multi-modal toughening, whereby embedding a suspension of micron sized and highly deformable liquid metal (LM) droplets inside a soft elastomer, the fracture energy dramatically increases by up to 50x (from 250 ± 50 J m to 11,900 ± 2600 J m ) over an unfilled polymer. For some LM-embedded elastomer (LMEE) compositions, the toughness is measured to be 33,500 ± 4300 J m , which far exceeds the highest value previously reported for a soft elastic material. This extreme toughening is achieved by (i) increasing energy dissipation, (ii) adaptive crack movement, and (iii) effective elimination of the crack tip. Such properties arise from the deformability of the LM inclusions during loading, providing a new mechanism to not only prevent crack initiation, but also resist the propagation of existing tears for ultra tough, soft materials.