Introduction

Nanophase mixtures serve as building blocks for functional composites because they can potentially maximize synergistic effects by leveraging the strengths of each component without any compromise1,2,3,4. However, when combining materials that lack strong mutual interaction, thermodynamically driven phase separation hinders the blending of their chemical and physical properties5,6,7,8. This challenge is particularly pronounced in composites of metals and elastomers for stretchable conducting membranes8,9,10,11,12. Such membranes have long sought after properties that include metal-like conductivity, rubber-like elasticity, mechanical durability, and physicochemical resilience13,14,15,16,17. Nevertheless, creating conductive metal-elastomer nanophase mixtures is challenging, as the simple physical mixing of metal nanoparticles (or nanowires)13,14,18 with elastomer precursors or the in-situ reduction of metal nanostructures within the elastomer19,20,21,22 have proven to be insufficient, as they result in either low electrical conductance or reduced mechanical stretchability or elasticity23. Alternatively, intrinsically stretchable organic conductors24,25 or extrinsically configured structures, such as wrinkled/buckled15,26,27,28 and kirigami structures29,30, could solve such performance issues. However, we still expect true metal-elastomer nanophases to be a superior option, especially for usage in high-profit bioelectronic applications which require high-fidelity, long-term stable operation31 in demanding microcosms within the human body32. This is because tailored metal-elastomer nanophases should excel in electrical performance, mechanical durability, and environmental resilience, where each characteristic is inherited from the respective metal and elastomer components. Nanoscale blending forms large interfaces that enhance the adhesion strength between metal and polymerFull size image

The Raman data are consistent with the results obtained from finite element method (FEM) simulations based on hyper-elastic material models (Suppl. Note 4 and 5). Specifically, we used a hyperelastic Mooney-Rivlin material with parameters derived from uniaxial tensile tests (see Suppl. Fig. 12 and Suppl. Table 1 for the uniaxial tensile tests for the φ = 3.5 PDMS). For the plain Au layer and the Au-PDMS layer (an elastic rectangular block of dimensions of 24 µm × 24 µm × 20 µm in x-, y- and z-direction), we used two geometrically exact Cosserat shells as described in the literature55. To model the swelling ratio, we attached a swollen plain Au layer and a swollen Au-PDMS layer to a stretched-out plain PDMS layer. After releasing the stretch on the plain PDMS layer, a 3D microstructure formed due to the stress mismatch. For all simulations, we chose the same maximum penetration depth of Au atoms as in the HRTEM images (Fig. 2a). There was almost no dependence on the deposition thickness in the case of φ = 3.5, which corresponds to our experiments.

In our computational analysis, we explored the surface morphology using three key parameters: Young’s modulus (EY), the swelling ratio of the Au-PDMS nanophase layer (Q), and the thickness of the top plain Au layer (tAu). Among the various experimental conditions, in particular we focused on the effect of deposition thickness on the swelling and releasing behavior of gyrified structures. In our simulations, we assumed that that with an increase in the process time, tprocess, at a fixed deposition rate, both the swelling ratio of the Au-PDMS nanophase layer, Q, and Young’s modulus, EY, also increase (Fig. 3d). The calculated surface morphology after stress release closely matched the experimental data in many aspects, including the shape, feature size, and general trend with increasing tprocess. The transition from hexagonally arranged islands to a labyrinth pattern was confirmed when tAu is 80 nm, Q is 1.3, and EY is 10 GPa, aligning well with observations in the OM images. These results support our hypothesis that the spontaneous evolution of the 3D structure is initially driven by the compressive stresses of an Au-PDMS nanophase accumulated by excessive crosslinkers. However, it is important to note that the complete replication of gyrified experimental results with deep folds in simulations was challenging using this simplified FEM model, even when scanning all possible computational parameters. This is mainly because gyrification cannot be solely induced by compressive stresses with fixed force; rather, it involves a complex dynamic process that includes chemical migrations and changes in volume and compressive force vector over time.

Based on real-time OM observations (Suppl. Movie 1), together with HRTEM morphologies and FEM simulations, we conclude that the gyrification phenomenon is initially driven by accumulated compressive stress. However, it is further influenced by the subsequent self-swelling of uncross-linked, low-molecular-weight PDMS oligomers for a couple of hours. Macroscale expansion due to the self-swelling of oligomers was observed and quantified by measuring the change in a patterned deposition area (Suppl. Figs. 13 and 14). The different nanophases exhibited variations in expansion: the reticular nanophase displayed a roughly 10% change in measured area, while the particulate nanophase showed a change in area of approximately 3% (measured by the photolithographically defined gap between before and after gyrification, Suppl. Fig. 14). Another strong piece of evidence suggesting the self-swelling of PDMS oligomers can be found by etching out metal layers after gyrification. If the nanostructures collapse after the etching process, it indicates that there were no crosslinked PDMS nanostructures but only Au nanostructures with excessive crosslinkers. However, if they maintain their gyrified morphologies even after the etching process of Au, it indicates that the PDMS oligomers themselves migrated and crosslinked to form the nanophase structures. It was observed that the gyrified PDMS structures were maintained even without the Au layer (Fig. 3e), strongly suggesting the self-swelling of oligomers as well as their crosslinking into reticular nanophases during the gyrification processes.

Elastomer-like stretchability with metal-like conductivity

As mentioned earlier, the primary goal of forming a metal-elastomer nanophase is to achieve pure PDMS stretchability while maintaining Au electrical conductivity. We argue that our Au-PDMS nanophase materials demonstrate such characteristics. In a sample with optimized parameters (1.25 mm thick PDMS membrane, φ = 3.5, Au deposition rate of 2.5 Å s−1, and d of 100 nm), we observe a conductivity as high as 1.4 × 104 S cm−1 (Fig. 4). This initial conductivity obtained by four-point probe measurements did not change upon the application of uniaxial strain up to 150% (Fig. 4a, b, blue) or areal strain up to 156% (Fig. 4a, b, red). No mechanical failures, such as cracks or delamination, were observed during the stretching tests, confirming its rubber-like elasticity. Moreover, the initial conductivity remained constant even after 10,000 stretching–releasing cycles with uniaxial and areal strains in the same range (Fig. 4b). Additionally, it exhibits superior long-term stability, as the electrical performance remained virtually constant for more than 8 years of shelf life (Suppl. Fig. 15).

Fig. 4: Highly strain-invariant electrical conductivity achieved by the gyrified 3D structure.
figure 4

a Optical microscopy (lower) and photo images (upper) showing stress dissipation by the gyrified 3D structure coupled with internal Au–PDMS nanophase upon applied strain both at uniaxial (leftwards) and areal (rightwards) strains. Strain-released images (0% at the outermost right side) show reversibility. Scale bars in the photo images denote 1 cm. Scale bar denotes in the optical microscopy images 150 μm. b Electrical conductivity of >104 S cm−1 up to uniaxial 150% (left) and areal 156% (right) strain, along with cyclic stability over 10,000 cycles of each strain (insets). c A uniaxial strain-dependent relative resistance changes of the 3D structure of Au–PDMS nanophase strap pads with various initial widths (5, 4, 3, 2, and 1 mm). A cyan-colored ideal curve represents calculated relative resistance change. d An areal strain strain-dependent relative resistance changes of the 3D structure of Au–PDMS nanophase disc-shaped pad. A magenta-colored ideal curve represents calculated relative resistance change. e Confocal microscopy scan image of the 3D structure of Au–PDMS nanophase sample. Line profiles extracted at the dot line A and B show that the high specific surface area contributed to the strain-invariant conductivity.

Depending on the application, electrodes can generally be classified into two types: active and passive. Active electrodes are used to directly inject or extract currents into/from a system, while passive electrodes serve to carry currents between different components or parts of a circuit. Among these, strain-invariant electrical properties are especially important for passive bus lines, ensuring a stable and reliable conductive path within and between circuit elements. To address this importance and cater to practical applications, we studied the relative resistance of our 3D Au-PDMS nanophase samples by employing two-terminal measurements with electrode widths ranging from 1 to 5 mm (Fig. 4c).

The standout feature of our Au-PDMS nanophase is its invariance to strain, greatly surpassing other state-of-the-art materials (Suppl. Tables 2, 3, Suppl. Fig. 16)13,14,15,24,25,56. The “ideal elastic conductor” in Fig. 4c depicts a hypothetical sample with strain-invariant resistivity in two-terminal measurements, only portraying the geometric change in resistance that would come with stretching, including considerations regarding Poisson’s ratio (Suppl. Fig. 17). Under this condition, the calculated resistance increases by 2.5 times at 100% uniaxial strain (calculation details in Suppl. Note 6). Comparing this to the measured resistance changes of our Au-PDMS, we arrive at a compelling result: even up to 30% uniaxial strain, the resistance changes of our samples were significantly lower than those of an ideal elastic conductor. This intriguing behavior comes from the unfolding of the 3D gyrified structures upon stretching, effectively compensating for the increased resistance due to dimensional changes.

The experimental and calculated resistance changes under areal strain showed the same tendency, where the Au–PDMS 3D nanophase samples exhibited a smaller resistance change than an “ideal elastic conductor” with up to 156% areal strain (Fig. 4d, Suppl. Fig. 18). Note that areal strain, in this context, is different from biaxial strain, as areal strain involves 3D stretching using a sphere, while biaxial strain is limited to stretching within a 2D plane (Suppl. Table 3). The unprecedented characteristics of our Au-PDMS nanophase material is primarily attributed to both the inherent stretchability of the reticular nanophases as well as the auxetic nature of the extrinsically gyrified 3D morphology (Suppl. Fig. 19). The combination of these intrinsic and extrinsic properties provides the high adhesivity and the structural, electrical elasticity required to prevent delamination and deterioration of electrical conductance in composite materials. Our view is further supported by the high gyrification index of 1.75 calculated in our samples, which is defined as the ratio of the actual surface area to the projection area (Fig. 4e).

Environmental durability for soft electronics

Following the electrical and mechanical properties of our gyrified reticular Au-PDMS nanophase samples, we showcase their multifaceted performance for applications in environmentally resilient soft electronics. Our samples display excellent stability against pH, chemical, and thermal exposure, as well as mechanical abrasion (Fig. 5a and Suppl. Note 7). After immersion in various polar and non-polar solvents (water, ethanol, acetone, chlorobenzene, and toluene) for 1 day, the conductivity of the nanophase samples slightly decreased, especially in organic solvents. This is possibly because of the deformed conduction network that comes from the swelling of the PDMS matrix itself. However, after the nanophases were dried, the conductivity almost fully recovered to within a 5% margin of error. Meanwhile, the conductivity was preserved under harsh pH conditions (pH 2–13), demonstrating this material’s suitability for bioelectronics applications in the stomach (pH 1.3–3.5) as well as for use on skin wounds (pH 7.2–8.9) (Fig. 5b). The conductivity of the gyrified Au–PDMS reticular nanophases was also almost fully maintained during adhesive tape tests (ranging from 16 to 32 N cm−1) for 500 cycles (Fig. 5c). Even after an abrasion test using an eraser (Suppl. Fig. 20 and Suppl. Movie 3), the conductivity remained in the same order of magnitude (red in Fig. 5c). In contrast to other thermoplastic elastomer-based stretchable electrodes, the gyrified Au–PDMS nanophases also showed excellent thermal stability up to 250 °C for 2 h (Fig. 5d). This expands their potential use in interfacing with functional elements that require thermal annealing during fabrication and operation at elevated temperatures, such as thermoelectric and heater modules, or during hydrothermal sterilization processes (Suppl. Movie 4, and Suppl. Fig. 21).

Fig. 5: Multimodal stability of the 3D structure of Au–PDMS nanophases.
figure 5

a Durability performance of the 3D structure of Au–PDMS nanophases in various organic solvents (cyclobz. stands for cyclobenzene), (b) pH (pH 2–13), (c) eraser and adhesive tape test (red line from eraser test and other lines from tape test), and (d) thermal annealing up to 250 °C. e Patterning of the 3D structure of Au–PDMS nanophases using stencil mask lithography (black color scale bar is 1 cm and white color scale bar is 50 µm) and (f) conventional photolithography, which can be realized for patterning of stretchable electronics. g Washing test, displaying no degradation of electrical function under machine washing with detergent, as shown in Suppl. Movie 5.

Furthermore, we also verified the reliability of the standard lithography processes for the gyrified Au-PDMS nanophase (Fig. 5e, f). The chemical (organic solvents) and thermal (annealing processes for photoresists) durability of the Au–PDMS nanophase samples enabled microscale patterning down to a 20 μm feature size using conventional photolithography with complex circuit designs (Suppl. Figs. 22, 23). The Au–PDMS nanophase samples were also found to be washable in a laundry machine. The initial conductivity and stretchability showed almost no change even after 20 cycles of 15 min. washing with detergent (Fig. 5g, Suppl. Fig. 24, Suppl. Movie 5). These findings imply that this stretchable conducting membrane can be used to produce lithographically defined, functional devices intended for repeated use with reliable operation in the field of wearable electronics for virtual reality (Suppl. Note 8, Suppl. Figs. 25, 26, and Suppl. Movie 6), including educational and medical applications.

Our 3D structure of Au-PDMS nanophases holds considerable appeal as a stretchable conducting membrane for soft and bioelectronics applications and may find extensive use in various fields, including biomonitoring within the digestive tract, multimodal implantable devices like ocular prostheses, soft robotics employing mechanical strain-gated logic gates, and functional fabrics for space exploration.