Nanowire-assisted freestanding liquid metal thin-film patterns for highly stretchable electrodes on 3D surfaces

Stretchable electronics is playing an integral role in fields such as wearable electronics and soft robots. Among soft conductive materials, liquid metal is drawing intense attention as an electrode material due to its liquid nature at room temperature. However, the merits of liquid metal conductor are limited by the presence of substrates or enclosed microchannels from physical disturbances by the underlying substrate when applying it to 3D surface and modifying complex circuit. To overcome this limitation, we develop freestanding patterned liquid metal thin-film conductor (FS-GaIn). FS-GaIn was achieved by introducing metal nanowires to liquid metal and subsequent sequential selective laser processing and etching of directly patterned traces. FS-GaIn can be applied directly to nonflat surface without substrates. When incorporated into electrical circuits, FS-GaIn shows high electrical conductivity, stretchability, and stability. The concept of freestanding liquid metal can open a functionality to the conventional liquid metal electronics.


INTRODUCTION
Stretchable and soft electronics are drawing attention in various emerging fields, such as wearable electronics [1][2][3][4] , bio-medical devices 5 , flexible optical devices 6 , and soft robots 7,8 . Within these fields, the stretchable conductive material represents an important and fundamental component, and remains the focus of intense research. Studies regarding stretchable conductor have been widely reported as follow; conductive elastomer 9-11 , metal nanowire 9,12 , and deterministically patterned metal thin-film conductor 1 . While highly promising for many applications, these approaches to stretchable circuit functionality have limitations that can interfere with their use in certain cases. For example, conductive elastomer and metal nanowire conductor can be limited in their functionality due to some combination of low volumetric conductivity, high electromechanical coupling, or poor elasticity. Likewise, deterministic architectures typically require advanced manufacturing techniques for patterning of wavy or serpentine traces of thin-film conductors. At the same time, they have limited stretchability and low areal density due to nonstraight pattern.
Stretchable conductors composed of liquid metal (LM) at room temperature have been widely reported in order to address the aforementioned limitations 13 . LM has appropriate properties for stretchable conductors such as high conductivity, extreme stretchability, patternability, and compliance that stems from inherent liquid-nature [14][15][16] . LM-based conductors have resolved the necessary capabilities for stretchable conductors. For instance, Tavakoli et al. introduced 3D hydrographic printing of inkjet printed AgNP-EGaIn on a tattoo paper that could be directly transferred to a highly curved surface 14 . Liu et al. presented biphasic gallium-indium fabricated by a heated furnace at 900°C that had stretchability over 1200% with stable electromechanical property 15 . Choi et al. has developed a fabrication method of 3-D electronics based on predistorted pattern generation for precise patterning on complicated 3-D surfaces 16 . Lucy et al. has achieved high resolution of LM pattern by applying it on the pre-deposited gold 17 . Kim et al. has developed a stretchable printed circuit board platform by realizing universal leak-free liquid metal interconnection with AgNW and LM 18 .
Despite great researches that have been conducted so far, the merits of liquid metal conductors are still largely limited by the presence of a substrate or an enclosed microchannel. A circuit with a substrate inevitably suffers from an unsolvable dilemma that the substrate and the circuit always go in couples; the substrate below the fabricated circuit inevitably hinders movement, attachment, repair and modification of the patterned circuit restricting the applicability of it. For this reason, researchers are actively developing thin and compliable substrates to minimize the negative effects caused by the substrate 12,19 . Nevertheless, the presence of substrate inevitably causes the aforementioned disturbances to the conductor, and it is impossible to completely exclude those problems without removing the substrate thoroughly. In order to overcome the limitations provoked by substrate and extend the applicability of stretchable conductor, an emergence of freestanding, or substrate-free conductor with superior electromechanical property is required.
Here, we introduce a freestanding patterned liquid metal thinfilm conductor (FS-GaIn) that is able to stand alone in substratefree state and be directly applied to irregular surfaces. FS-GaIn is fabricated by introducing metal nanowires to the liquid metal, and subsequent sequential selective laser processing and selective etching in maskless and room temperature condition. The laserassisted fabrication facilitates ultrafast patterning (laser scanning speed of 100 mm s −1 ) and rapid prototyping. When incorporated to electrical circuits, FS-GaIn withstands extreme strain with a small change in resistance without encapsulation, forms stable electrical contact with a rigid component with no post-processing, and is capable of making conformal contact with uneven 3-D surfaces. A modified circuit by FS-GaIn also shows great stability. FS-GaIn is an exceptional metal-based hyper-stretchable thin-film conductor that can be applied to bumpy 3-D surfaces or utilized for in situ circuit modification, extending the field of soft and stretchable electronics with the feature of substrate-free thin-film liquid metal conductor.

Introduction of FS-GaIn
FS-GaIn is fabricated by direct laser patterning of a vacuumfiltrated LM-Ag nanowire (LM-AgNW) thin-film with continuous visible laser and subsequent selective etching (Fig. 1a). A scanning electron microscope (SEM) image in Fig. 1a-i shows the FS-GaIn (Pattern resolution in Supplementary Fig. 1). It possesses high electrical conductivity of 5.79 × 10 5 S m −1 with thickness of around 12 μm ( Supplementary Fig. 2). SEM images in Fig. 1a-ii, a-iii demonstrate the thin-film after and before laser exposure, respectively. Exposing the laser to the thin-film induces multiphase sintering of LM and AgNW, which eventually generates FS-GaIn after an etching process. Figure. 1b demonstrates an image of FS-GaIn that is raised by tweezers. Since FS-GaIn can exist without any substrate, it is possible to be raised solely. Moreover, as shown in Fig. 1c, it can be applied to an irregular 3-D surface such as an ear model or attached to a rigid component to form a stable connection with mild pressure 15 (Fig. 1c inset). Figure 1d demonstrates a tree-patterned FS-GaIn by direct laser writing with computer-aided design ( Supplementary Fig. 3) and subsequent selective etching. FS-GaIn's property of substrate-free has great potential by granting a circuit an ability of in situ modification. As shown in Fig. 1e-i, an FS-GaIn with an LED is off due to the disconnection of the circuit. An FS-GaIn repair patch is attached to the disconnected area with gentle pressure, and the LED is turned on (Fig. 1e-ii). Moreover, the repaired circuit with the LED and the repair patch can be elongated without any disconnection indicated by the brightly shining LED (Fig. 1e-iii and Video S1). Figure 2a shows the laser processed LM-AgNW thin-film in a crosssectional view (SEM images in Supplementary Fig. 4). The apricot arrow in Fig. 2a-i exhibits the region where laser is scanned. The laser process allows localized heat treatment to the film inducing multiphase sintering of LM and AgNW, and further oxidation of LM surface 15,20 (Blue box in Fig. 2a-i). In previous studies, laser sintering is generally defined as a junction connection between Ag nanowires due to the heat concentration by a plasmonic effect 21 or an aggregation of LM particles due to a rupture of the gallium oxide shell, respectively 20 . However, in this research, these two processes happen simultaneously due to the coexistence of LM particles and AgNWs in the laser-scanned region. This phenomenon is defined as multiphase sintering in this research article. As the laser is exposed to the composite film of LM and AgNW, LM undergoes small explosion and the liquid core covers the AgNW due to the capillary force and the metallic binding force between them 22 , where other LM coalesces together. These results of coalescence between the two with enhanced interaction can be seen as gross coalescing in Fig 23 . This difference allows the non-sintered portion of the film to be etched away using a 0.2 M aqueous solution of sodium hydroxide (NaOH). Not only that, in order to create FS-GaIn, the localized heat from laser should only affect the surface of the film so that the film is divided into the laser-induced sintered region (Blue box in Fig. 2a-i) and non-sintered region (Green box in Fig.  2a-i) in-depth as well as in-plane. This in-depth division is realized by fast laser scanning speed (100 mm s −1 ). When the etching process is conducted, the multiphase sintered region (Blue box in Fig. 2a-i) becomes FS-GaIn. Figure 2b demonstrates the steps where laser sintering and solvent etching is used to create patterned FS-GaIn in perspective view, cross-section view, and real image, respectively (Video S2 for the fabrication of FS-GaIn). First, an LM-AgNW thin-film is synthesized using the vacuum filtration process (described in Supplementary Fig. 8 and Supplementary Note 2 of the Supporting Information and Methods section). Then, the desired pattern is drawn using CAD-assisted direct laser writing in maskless and room temperature condition ( Fig. 2b-i). Next, an etchant (0.2 M NaOH) is applied to remove the non-sintered region. In this step, a separation between the sintered region (Blue box and region in Fig. 2a, b-ii, respectively) and the non-sintered region (Green box and region in Fig. 2a, b-ii, respectively) occurs. Finally, only the sintered FS-GaIn remains as shown in Fig. 2b-iii.

Electromechanical characteristic of FS-GaIn
We have measured the electromechanical properties of FS-GaIn in order to investigate its applicability as a stretchable thin-film electrode. Most previous LM studies required encapsulation of the liquid metal with elastomer in order to prevent leaking, smearing, or marking of the fluid and maintain material integrity. In this study, we placed the patterned film on VHB tape (3 M) but did not apply an encapsulating sealing layer. Figure 3a shows the electromechanical behavior from the pristine state to the most stretched state prior to failure. FS-GaIn endures up to 1358 % strain and a corresponding resistance change of about ten times its initial resistance value (i.e., ΔR/R 0~1 0). While 1358 % was the maximum measurement, most samples fractured at around 1000% strain (Supplementary Fig. 9 in Supporting Information). The value of maximum strain and the corresponding resistance change can be considered as remarkable compared to other thinfilm conductor that researchers have studied, as shown in Fig. 3c. At relatively low-strains (100%), the gauge factor (ΔR/R 0 )/(ΔL/L 0 ) is around 0.2 as shown in the Fig. 3a inset, well below that would be predicted by Pouillet's law for a stretchable conductor. This is comparable to other LM-based electrode that other researchers have previously shown 15,24 . The repeatability of FS-Gain is investigated through cyclic 100 % strain tests (Fig. 3b). Over 10,000 loading cycles, a stable resistance value is measured after initial loading cycle. The maximum resistance value relative to the initial resistance is sustained around 1.3 (i.e., R/R 0~1 .3) with steady ups and downs corresponding to the applied strain. The stability of FS-GaIn presents it can be used for a strain sensor in wearable electronics as well as stretchable electrode. (Supplementary Fig.  10 in Supporting Information for FS-GaIn sensor.) Figure 3d demonstrates SEM images of FS-GaIn in stretching condition in top view for both laser-treated side and not-treated side. The laser-treated side of FS-GaIn film is initially composed of agglomerations of LM-AgNW nanomaterials that are uniformly aligned along the laser scanning direction (Fig. 3d-i). At the same time, the laser-not-treated side is composed of multiphase sintered LM and AgNW though not forming an agglomeration (Fig. 3d-ii). According to the images in Fig. 3d-iii, d-iv, the agglomerations on laser-treated side and the sintered LMs and AgNWs on the other side are being stretched simultaneously allowing negligible resistance change.
The negligible resistance change with extreme stretchability can be understood by explaining three main factors. These three factors are surface reconciliation, wettability between LM and AgNW, and highly tortuous serpentine conductive path. FS-GaIn has a core-shell structure that consists of LM and AgNW core, and laser-induced beta gallium oxide shell. Before FS-GaIn is attached to an arbitrary substrate, it can maintain its structure while being held due to robust laser-induced beta gallium oxide shell. However, it does not possess stretchability because there is no place for liquid metal in the core to smear when the oxide shell ruptures. Therefore, FS-GaIn gains stretchability after it is attached to any arbitrary surface. (Supplementary Fig. 11 in Supporting Information) In this process, surface reconciliation becomes an important factor 25 . When the substrate and FS-GaIn adhere to each other with high affinity, it possesses high stretchability and small gauge factor. As shown in Supplementary Fig. 12, the reconciliated surface between FS-GaIn and substrate can be thought as anchoring sites. When FS-GaIn and the substrate are stretched, the anchoring sites of FS-GaIn firmly adhere to the substrate which subsequently results in downward net-force for other parts of FS-GaIn. This causes continuous electrical path of FS-GaIn in the subsequent stretching resulting in ultra-high stretchability without electrical failure. Besides, the stretching out of FS-GaIn barely changes the end-to-end conductance due to the highly tortuous serpentine conductive path composed of LM particles whose length and cross-sectional area does not change much when stretched as depicted in Supplementary Fig. 13 26 . This geometrical characteristic contributes to negligible resistance change. Moreover, the extreme stretchability of FS-GaIn is also intensified by the wettability between LM particles and AgNWs. When FS-GaIn is extremely stretched, the superior wettability between LM and AgNW induces a continuous and highly conductive electrical path, preventing the formation of electrically isolated liquid droplets that disconnects an electrical path 14,15 . Both the structure and interaction between LM and AgNW realize extreme stretchability with negligible resistance change.

Applications of FS-GaIn
FS-GaIn has many advantages over conventional substrate-based stretchable thin-film conductors. For instance, it is not possible to modify or repair traditional printed circuits without replacing or soldering damaged material. Likewise, typical circuits require soldering or other forms of post processing in order to mount rigid components. In contrast, FS-GaIn exhibits a substrate-free feature that allows for in situ circuit modification and repairs. It also possesses liquid-like property that enables an integration with rigid components without the need for a post-processing step 15 . Figure 4a compares the electromechanical response between a pristine FS-GaIn circuit and a repaired one. In order to fabricate the repaired FS-GaIn circuit, a pristine FS-GaIn (Fig. 4a-i) is erased in the middle (Fig. 4a-ii). The erased FS-GaIn is reconnected by simply placing a circle-patterned FS-GaIn repair patch onto it with a gentle push to make electrical contact. (Fig. 4a-iii) This repaired circuit can be stretched up to nearly the same amount (1202%) compared to the pristine one (Fig. 4a). Furthermore, the gauge factor at 100% strain is also comparable to the pristine FS-GaIn, 0.76 (Fig. 4a inset). It is confirmed that not only the pristine circuit, but also the repaired one can be used as a stable stretchable circuit.
FS-GaIn's electromechanical behavior when connected with a rigid component is shown in Fig. 4b. The length of a rigid component-in this case a zero-ohm resistor-is about 3 mm, and the length of the FS-GaIn traces on each side of it is 3 mm. The electrical contact becomes disconnected when the sample is stretched to about 30 mm. This suggests that the circuit fails when the FS-GaIn electrodes (6 mm total) undergo over 500% strain, assuming that the length of the zero-ohm resistor (3 mm) remains fixed. This result shows that FS-GaIn can operate firmly when connected to rigid components with having stable contact. Figure 4c demonstrates the in situ circuit manipulation with FS-GaIn. At first, FS-GaIn is connected to an LED with stable electrical contact shown by the brightly illuminating LED. Then, a newly patterned FS-GaIn circuit (blue color in Fig. 4c left bottom inset) is simply added above the original circuit (red color in Fig. 4c left bottom inset) extending from the circuit with one LED to the circuit with two LEDs (Fig. 4c-ii). Stable contact is easily made on account of the FS-GaIn's fluidity as shown in the SEM image 27 (Fig.  4c left bottom inset). Moreover, when the circuit is erased or worn out (Fig. 4c-iii), simply laying a newly made FS-GaIn repair patch onto it can easily reconnect the circuit indicated by two bright LEDs (Fig. 4c-iv). The magnified view of the connection of the circuit can be seen in the right top inset in Fig. 4c with pseudocolors.
There may be situations where conventional circuits cannot be installed due to many reasons, such as disturbance by an underlying substrate, a limitation in the pattern resolution, various physical obstacles, or inapplicability because of an irregular 3-D target surface. Among these restrictions, Fig. 4d demonstrates four representative circumstances where each circumstance is overcome owing to FS-GaIn's properties of substrate-free feature, patternability, and shape-adaptability. In Fig. 4d-i, there is a cubeshaped obstacle in the way. By patterning the FS-GaIn circuit with the shape of a detouring path, an LED can be lit. As shown in Fig.  4d-ii, two cube-shaped obstacles are closely space and allow for only a narrow path to connect the circuit (slightly over 100 μm). A 100 μm thick FS-GaIn is made and connected to an LED thanks to the high pattern resolution and substrate-free feature of FS-GaIn. FS-GaIn can also be folded at a right angle (90°) without any failure owing to its liquid-like deformability. FS-GaIn is folded and conformally attached to a cube in Fig. 4d-iii. An illuminated LED in the figure indicates a stable and continuous folded electrical path. Figure 4d-iv demonstrates that FS-GaIn is directly attached to a miniaturized mountain model with high curvature and rough surface presenting its shape-adaptability and substrate-free property.

DISCUSSION
In this work, we have introduced FS-GaIn that has high electrical conductivity (5.79 × 10 5 S m −1 ) with small resistance change over 1350% strain, cyclic stability over 10,000 cycles of 100% strain, and stable contact with a rigid component when stretched. The exceptional electromechanical property of FS-GaIn stems from three major factors which are surface reconciliation, highly tortuous serpentine structure, and wettability between LM and AgNW. A circuit repaired by applying an FS-GaIn patch also demonstrates stable contact and the ability to withstand over 1000% strain without electrical disconnection. The facile fabrication method of FS-GaIn using a combination of direct laser writing and etching enables the rapid fabrication of appropriately patterned FS-GaIn in maskless and room temperature condition. The fabrication of FS-GaIn is realized by fully utilizing the differentiated etching behavior between multiphase sintered region and not sintered region. The features of FS-GaIn also make it possible to perform in situ circuit modification, attachment to 3-D surfaces with sharp contours, and installation of a circuit in constrained circumstances. It is expected that applying FS-GaIn to wearable electronics, flexible optical devices, and soft robots will open up the next-generation stretchable electronics surmounting inevitable limitations with conventional thin-film conductors.

Preparation of Ag nanowires
Ag nanowires were synthesized relatively long (100 μm or less in length with 1000:1 aspect ratio) using a modified polyol process. For convenient synthesis, all reagents are blended into a triangular flask simultaneously as the one-pot process 28 . In 50 ml of ethylene glycol (EG), 0.4 g of polyvinylpyrrolidone (Mw ≈ 360,000) and 0.5 g of silver nitrate (AgNO 3 ) were successively dissolved using a magnetic stirrer. After all reagent chemicals were comprehensively dissolved, the magnetic stirrer was delicately removed from the mixture solution. Next, 800 μL of copper(II) chloride dihydrate solution (CuCl 2 ·2H 2 O, 3.3 mM dilution with EG) was swiftly injected into the mixture solution and then stirred moderately. Lastly, the triangular flask with the mixture solution was located in a 130°C silicone oil bath for 3 h to grow Ag nanowires. After the desired growth was accomplished, the solution containing synthesized Ag nanowires was cleaned using acetone and ethanol with centrifugation of 3000 rpm for 10 min to eliminate the residual chemicals. The previous cleaning step was repeated three times. In the end, the prepared Ag nanowires were kept in ethanol for use.

Liquid metal particles
In this study, eutectic gallium-indium alloy (EGaIn) was selected to be utilized among several room temperature liquid metals. Gallium (Ga, 99.99%) and indium ingot (In, 99.99%) were purchased from ROTOMETALS. 75.5 wt% of gallium (Ga) and 24.5 wt% of indium (In) were put together in a beaker and heated at 200°C with 200 rpm of magnetic stirring for 24 h to make EGaIn. After fabricating EGaIn, a tip sonicator (UH-1200Z with Φ13 mm probe, Fangke Technology (Shanghai) Co., LTD.) was used to break liquid metal into microparticles. The tip sonicator was operated for a total of 15 min (1 min operation, 1 minute rest, 8 times repetition, power setting with 95%) to sonicate 80 ml of ethanol and 8 ml of EGaIn mixture in a beaker, where the beaker was immersed in an ice-water bath.

LM-AgNW thin-film transfer
The LM-AgNW thin-film with uniform thickness was fabricated by the vacuum filtration process. 2000 μl of AgNW solution (density: 5.5 mg ml −1 ), 500 μl of liquid metal particle solution (density: 580 mg ml −1 ) and 9 ml of ethanol were mixed in a 20 ml vial glass. Then, nylon and PTFE film were sequentially placed on the funnel. The mixed solution was used for vacuum filtration with enough amount of ethanol. The LM-AgNW thin-film on PTFE film was transferred to a glass substrate.

FS-GaIn fabrication
The LM-AgNW thin-film on the glass was sintered by the CW 532 nm laser source (Sprout-G-5W, Lighthouse Photonics) with a Galvano-mirror (hurrySCAN II, Scanlab). Optimal laser power range (1.0 W~1.5 W) and laser scanning speed (100 mm s −1 ) for FS-GaIn sintering were found by the parametric study. After sintering was complete, the thin-film was placed in 0.2 M NaOH solution for 10 min for separation. The separated FS-GaIn in the base solution was delicately held by tweezers and moved to an ethanol solution to eliminate the peripheral base solution. And then, the cleaned FS-GaIn was dredged from the ethanol solution before (or after) applied to a target surface, and dried in an oven at 60°C for 1 min.

FS-GaIn sensor fabrication
FS-GaIn sensor was made by laying FS-GaIn over an index finger and contacting copper tape. It was encapsulated by VHB tape and the sensor signal was obtained.

Imaging and characterization
The digital images were taken by a smartphone (Galaxy S20, Samsung Electronics). An optical microscope (BX53M, Olympus) with Stream Basic software (version 2.2, Olympus) was utilized for high magnification optical images. SEM images were obtained from a field-emission scanning electronic microscopy (AURIGA, Carl Zeiss). Elemental composition and mapping images were acquired using energy dispersive X-ray spectroscopy (Flat-Quad, Bruker) equipped in the field-emission scanning electronic microscopy.

Electromechanical performance measurements
To quantify the electromechanical characterization, a rectangular sample (length 10 mm × width 0.5 mm) was prepared for the test. Initial conductivity of the FS-GaIn was calculated as 5.79 × 10 5 S m −1 from the conductivity equation σ = l/Rwt, where l, R, w, and t are length, resistance, width and thickness of FS-GaIn sample, respectively. After laying the FS-GaIn on VHB(3 M), a copper tape connected with an alligator clip was attached to the sample. To ensure the stability of contact between the FS-GaIn and the copper tape, a small amount of EGaIn was spread thinly on them. The sample was stretched from the initial gap of 3 mm with a uniform speed of 0.5 mm s −1 through a uniaxial tensile load system (Physik Instrumente). Real-time electrical resistance was measured by the PXIE hardware system with LabVIEW software. (National Instrument).
The durability of the FS-GaIn was measured under 100% mechanical strain with the same measuring instrument until 10,000 cycles. To investigate contact with a rigid component, a zero-ohm resistor bridged two FS-GaIn, where they had a gap of 1 mm. The resistor was softly pressed to ensure stable contact when the resistor connected between the two FS-GaIn lines. The electromechanical characteristic was measured in the same way; the sample was stretched with a uniform speed of 0.5 mm s −1 through a uniaxial tensile load system until failure. To verify the electromechanical behavior of the repaired circuit, a circular FS-GaIn repair patch was prepared in advance. The prepared patch simply covered the target area, which was intentionally created by erasing the previously existing FS-GaIn circuit line by scrubbing with NaOH solution-soaked tissue. The electromechanical performance was measured in the same manner as the preceding measure procedure.
All electromechanical performance evaluations were conducted without any encapsulation.

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon request.