The appeal of liquid metals begins with a basic physical paradox. Conventional stretchable conductors rely on rigid fillers, such as silver flakes or carbon particles, embedded in an elastic matrix. Increasing the filler loading improves conductivity but stiffens the composite and accelerates fatigue under repeated strain; reducing the loading preserves softness but degrades electrical performance. This conductivity–softness trade-off has constrained generations of wearable and implantable devices. Liquid metals, most notably eutectic gallium–indium alloys that remain molten at room temperature, sidestep the problem entirely because the conductive phase is itself a fluid. Droplets of the alloy can be suspended in elastomers, where they deform, elongate and reconfigure with the surrounding polymer rather than resisting it, maintaining metallic properties across large strains.

The review emphasizes that liquid metal composites deliver far more than stretchable wiring. When droplets are dispersed through a soft polymer, they enhance not only electrical conductivity but also dielectric and thermal properties. Elongated liquid metal inclusions, for example, have been shown to raise the thermal conductivity of elastomers dramatically, enabling soft materials that can dissipate heat, and liquid metal inclusions have been used to create high-permittivity dielectric elastomers for capacitive and actuating applications. In one striking demonstration highlighted in the review, an electrically insulating liquid metal silicone compound combined electromagnetic interference shielding with direct electronic potting and thermal management, showing that a single soft composite can perform multiple functions once reserved for rigid metal housings.

Yet the same fluidity that gives liquid metals their conformability creates their greatest engineering headaches. A liquid conductor can leak, smear, delaminate or migrate within a device, destroying pattern fidelity and reliability. The authors argue that the decisive design variable is not the liquid metal itself but the interfaces it forms, both between liquid metal and the surrounding polymer and between liquid metal inks and the substrates and components they must connect. Interface engineering, they contend, is essential for mitigating leakage, delamination and functional degradation under deformation, and tailored interfacial design is what converts a promising ink into a robust, integrated device.

A rich toolkit of surface chemistry has emerged to control these interfaces. Gallium-based alloys spontaneously form a thin native oxide skin that dramatically alters their interfacial energy, lowering surface tension enough to allow the metal to be shaped, printed and stabilized as droplets. Researchers have exploited this oxide, and chemical modifications of it, to stabilize particles, tune wettability and promote adhesion. Polyphenol-induced adhesives have produced liquid metal inks that write directly on nearly any substrate, while thiol coordination chemistry has been used to soften liquid metal particles and switch their conductivity on demand. Hydrogen-doped viscoplastic microparticles have enabled stretchable printed metal lines, and finite-gel strategies have produced highly concentrated inks suitable for direct writing.

Patterning at high resolution remains one of the field’s defining challenges, and the review surveys how recent advances in droplet stabilization and ink formulation are addressing it. Ultrasonic sintering has been used to assemble liquid metal particles within polymers into elastic printed circuit boards, in which pressing or sonicating the particles ruptures their oxide shells and merges them into continuous, leakage-resistant traces. Laser sintering of liquid metal nanoparticles offers a scalable route to soft, flexible electronics, and projection lithography has enabled rapid printing of highly stretchable circuits. Meniscus-guided printing has produced stable semi-solid microgranular particles for soft electronics, while high internal phase emulsion inks have allowed direct-ink-writing of three-dimensional liquid metal structures. One recent metalgel formulation maintained a conductivity of three million siemens per metre through a million stretching cycles, a durability benchmark that would have seemed unattainable for a fluid conductor only a decade ago.

The applications catalogued in the review span the full breadth of soft electronics. In wearable healthcare, liquid metal electrodes and sensors have been fashioned into electronic tattoos, electromyography patches for tendon localization and muscle injury prevention, and pressure sensors for health monitoring. In implantable and bioelectronic systems, liquid metal microelectrodes have been wafer-patterned for chronic biocompatibility, printed directly on the cranium for soft neural probes, and formed into three-dimensional microelectrode arrays integrated with ultrathin retinal prostheses for vision restoration; liquid metal neuro-interfaces have even been used to stimulate and record from human hippocampal organoids. Phase-transition behavior adds another dimension: temperature-responsive intravenous needles that irreversibly soften on insertion, and biphasic microfibers for minimally invasive implantable electronics, exploit alloys that are rigid at room temperature and compliant at body temperature.

Soft robotics and integrated systems feature prominently as well. Liquid metal–elastomer composites have demonstrated autonomous electrical self-healing, in which damaged circuits reconnect themselves as the liquid metal flows back together, and liquid metal inclusions have enabled shape-morphing elastomers that couple thermal transport with programmable actuation. Stretchable Arduinos embedded in soft robots, octopus-inspired sensorized arms, and stretchable core–shell cables that are patternable, recyclable and noise-resistant all illustrate how liquid metals can bridge soft and rigid electronic domains. Liquid crystal elastomer composites actuated by induction heating point toward untethered, programmable soft machines, while liquid metal antennas exploit fluidic deformability for reconfigurable radio-frequency devices.

The authors are candid about what stands between laboratory demonstrations and real-world deployment. Long-term interface durability and manufacturing precision remain the key translation challenges: devices must survive millions of deformation cycles in wet, biological environments without leaking, delaminating or drifting in performance, and patterning methods must reach the resolution and throughput that industrial electronics demand. Questions of biocompatibility are being actively studied, with gallium’s known antimicrobial activity offering intriguing therapeutic possibilities even as toxicity profiles continue to be mapped. The review’s central message is nonetheless one of momentum: by treating the liquid metal–material interface as the primary design object, rather than an afterthought, researchers now have a coherent strategy for building soft electronics that no longer force a choice between how well a device performs and how gracefully it bends. If that strategy matures, the circuits of the future may not merely sit on the body but move with it, heal with it and, in the case of implants, dissolve the boundary between machine and tissue altogether.

Subject of Research: Design strategies for liquid metal-based soft and stretchable electronics

Article Title: Design strategies for liquid metal-based soft electronics

Article References: Pan, C., Zhang, C., Wang, J., Han, M., CHIU, W. Y. P., Zhao, P., & Dickey, M. D. (2026). Design strategies for liquid metal-based soft electronics. Nature Reviews Electrical Engineering. https://doi.org/10.1038/s44287-026-00335-1

Image Credits: AI Generated

DOI: 10.1038/s44287-026-00335-1

Keywords: liquid metals, stretchable electronics, soft electronics, gallium alloys, interface engineering, wearable devices, implantable bioelectronics, soft robotics, elastomer composites, self-healing materials, printed electronics, dielectric elastomers

The appeal of Dzugutov’s scheme lies in its microscopic foundation. Rather than reducing transport coefficients by macroscopic parameters such as number density and temperature, as Yosenfeld’s earlier excess-entropy scaling did in 1977, Dzugutov used microscopic reduction parameters: an effective hard-sphere diameter for length and the Enskog collision frequency for inverse time. The hard-sphere picture rests on two propositions. First, at high densities, the transfer of momentum and energy between atoms is dominated by short-range repulsive interactions, which behave essentially like binary collisions of billiard-ball-like hard spheres. Second, the frequency of local structural relaxation—the rate at which atoms escape the transient cages formed by their neighbors—can be calculated from Enskog kinetic theory for hard spheres. The result is a remarkably compact formula in which the normalized diffusivity equals 0.049 times the exponential of the excess entropy, expressed in units of the Boltzmann constant.

The excess entropy itself is a subtle quantity. Defined as the total thermodynamic entropy minus the ideal gas entropy, it can be expanded as a series of contributions from pairs of particles, triplets, and higher-order correlations. The leading two-body term, which depends directly on the pair distribution function, is known to contribute more than 85 percent of the excess entropy across most thermodynamic states, and as much as 95 percent near the triple point of simple liquids. Crucially, the pair distribution function can be obtained from x-ray or neutron diffraction experiments or from computer simulations, making Dzugutov’s scaling unusually practical: it connects atomic dynamics to structure and thermodynamics using quantities that are actually measurable. Later work by Jakse and Pasturel showed that an excess entropy derived from the Carnahan-Starling equation of state—the best analytical description of hard-sphere thermodynamics—can also justify the scaling, provided the temperature dependence of the effective hard-sphere diameter is properly accounted for.

What has been missing, the authors argue, is a systematic test for alloys rather than pure metals. Although Yokoyama and colleagues applied the scaling law to binary alloys in 2007, their analysis was restricted to equiatomic compositions. The new study therefore examines cobalt-iron (CoxFe1−x) and nickel-iron (NixFe1−x) alloys across the full concentration range, from iron-rich to cobalt-rich or nickel-rich, at a temperature of 1833 Kelvin. Iron-based transition metal alloys are not an arbitrary choice: they underpin structural steels, magnetic materials, and even models of planetary cores, and their liquid-state transport properties remain poorly constrained by experiment because of the extreme conditions involved.

On the theoretical side, the team combined the Bretonnet-Silbert pseudopotential—a model specifically designed for liquid transition metals that accounts for both s-p and d band contributions, including the sp-d hybridization that simpler pseudopotentials miss—with linearized Weeks-Chandler-Andersen perturbation theory. The latter provides the effective hard-sphere diameters by solving a transcendental equation that equates the Helmholtz free energy of the real interacting system with that of a hard-sphere reference system. Two different local field correction functions, due to Ichimaru-Utsumi and Vashishta-Singwi, were used to screen the electron-ion interaction, allowing the authors to assess which treatment of electron correlation better describes these dense metallic liquids. This combination of Bretonnet-Silbert potential and LWCA theory had never before been applied to calculate diffusion and viscosity in transition metal alloys.

To anchor the theory, the researchers performed classical molecular dynamics simulations with the LAMMPS code, using modified embedded atom method (MEAM) interatomic potentials that capture both many-body effects and the angular orientation of bonds—features essential for transition metals. Each simulation placed 30,000 atoms in a cubic box 70 angstroms on a side with periodic boundary conditions. The alloys were first equilibrated at 2500 Kelvin, above their melting points, in a constant-pressure ensemble, then cooled to 1833 Kelvin, and finally equilibrated for a full nanosecond at the target temperature. One thousand configurations were extracted from each run, and the pair correlation functions were computed with the OVITO visualization tool and averaged with a Python code. The team also verified that their results were independent of system size by repeating selected simulations with 20,000 and 40,000 atoms; the reduced diffusion coefficients and viscosities changed only in the second decimal place, consistent with the finite-size correction formula proposed by Khrapak.

The calculated structural quantities proved encouraging. Effective hard-sphere diameters obtained from theory and simulation were comparable and consistent with literature values for pure liquid iron, cobalt, and nickel, and the partial pair correlation functions reproduced the expected concentration trends: the peak height of like-atom pairs rises as that component becomes richer, while cross-pair correlations peak at mid-concentrations. When the reduced diffusion coefficients were plotted against excess entropy, however, a nuanced picture emerged. Simulated data followed Dzugutov’s universal scaling line fairly well across all concentrations of both alloy families. The theoretically calculated data, by contrast, obeyed the scaling only for mid-concentrated alloys, deviating systematically when a single component dominated the mixture. The culprit, the authors show, is the overestimated principal peak height of the calculated partial pair correlation functions in single-component-rich alloys, which inflates the two-body excess entropy.

Notably, the Carnahan-Starling excess entropy proved far more reliable than the two-body approximation, remaining stable across concentrations and closer to established values for pure liquid metals, even in single-component-rich compositions where the two-body entropy varied wildly. This suggests that the Bretonnet-Silbert potential combined with LWCA theory is a sound framework for mid-concentrated liquid transition metal alloys, even if the perturbative treatment of structure needs refinement at the compositional extremes. The Ichimaru-Utsumi local field correction consistently outperformed the Vashishta-Singwi alternative, yielding more reliable inter-diffusion coefficients and shear viscosities, which remained nearly constant across all concentrations and agreed reasonably with molecular dynamics results.

The transport coefficients themselves tell an industrially relevant story. Partial self-diffusion coefficients of cobalt or nickel decrease while those of iron increase as the minority component’s concentration grows, and the inter-diffusion coefficients—computed as concentration-weighted sums of the self-diffusivities—fall in the range of roughly 7 to 9 times 10⁻⁹ square meters per second, comparable to simulation data and to scattered theoretical and experimental values for the pure liquid metals. Shear viscosities derived from the Stokes-Einstein relation with slip boundary conditions, and from Yokoyama’s modified upper-bound formula, came out around 1.6 to 2.8 millipascal-seconds—smaller than experimental measurements, which run nearly twice as high, but closer to experiment than earlier theoretical estimates and consistent in trend with prior work on Fe-Co and Fe-Ni liquid alloys.

Perhaps the most striking result appears in the paper’s appendix, where the authors propose a new scaling law of their own. Because both alloy families deviated from Dzugutov’s line at single-component-rich compositions, they refitted the data with independent prefactor and exponential factors and found that both Co-Fe and Ni-Fe melts obey the same alternative relationship, with a reduced diffusion coefficient proportional to the exponential of minus 0.3 times the excess entropy and a much smaller prefactor of 0.005. Until more sophisticated theories or new experimental data for iron-based liquid alloys become available, the authors suggest, this proposed scheme offers young researchers a practical route to predicting atomic diffusion in these industrially vital melts—while the half-century-old interplay between entropy and atomic mobility continues to reveal fresh surprises in the liquid state.

Subject of Research: Testing Dzugutov's excess-entropy scaling law for atomic diffusion in liquid iron-based cobalt-iron and nickel-iron transition metal alloys using pseudopotential theory and molecular dynamics simulation.

Article Title: Test of scaling law for atomic diffusion of Fe based liquid transition metal alloys

Article References: Test of scaling law for atomic diffusion of Fe based liquid transition metal alloys. (n.d.). https://doi.org/10.1016/j.rinp.2026.108743

Image Credits: AI Generated

DOI: 10.1016/j.rinp.2026.108743

Keywords: atomic diffusion, liquid metals, transition metal alloys, excess entropy scaling, Dzugutov scaling law, molecular dynamics simulation, pseudopotential theory, iron-cobalt alloys, iron-nickel alloys, shear viscosity, hard-sphere model, LAMMPS