A flexible and highly electrically conductive liquid metal adhesive for hybrid electronics

Abstract

Concepts directed to a conductive adhesive for coupling functional components of circuits formed in rigid, flexible, and stretchable substrates are described. In one example, a conductive adhesive includes an elastomeric epoxy network. The conductive adhesive further includes liquid metal elements disposed in the elastomeric epoxy network. The conductive adhesive further includes silver elements coupled to the liquid metal elements to form a conductive percolated network in the elastomeric epoxy network.

Description

A FLEXIBLE AND HIGHLY ELECTRICALLY CONDUCTIVE LIQUID METAL ADHESIVE FOR HYBRID ELECTRONICSSTATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0001] This invention was made with government support under grant number N000142112699, awarded by the Office of Naval Research (ONR). The government has certain rights in the invention.CROSS REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of and priority to U.S. Provisional Application Serial No. 63 / 535,930, filed August 31, 2023, titled “A FLEXIBLE AND HIGHLY ELECTRICALLY CONDUCTIVE LIQUID METAL ADHESIVE FOR HYBRID ELECTRONICS,” the entire contents of which are hereby incorporated herein by reference.BACKGROUND

[0003] Flexible circuits are an emerging technology with promising applications in modem consumer electronics, wearable health-monitoring devices, and soft robotics. Traditionally, electronic components have been soldered to rigid printed circuit boards (PCBs) either manually or through the use of automated systems such as reflow ovens and wave solder machines. In recent years, polymer-based electrically conductive adhesives have been more widely used as interconnects in deformable systems. Compliant, conductive adhesives are critical in flexible and hybrid electronics for the integration of rigid integrated circuits (ICs) with flexible circuits.SUMMARY

[0004] Described herein is an electrically conductive adhesive (ECA) which is extremely flexible, highly electrically conductive (e.g., up to 3.25xl(P S m'1) without sintering or high temperature post-processing and is strongly adhesive to various materials common to flexible circuits (e.g., cohesive fracture energy 350 < Gc< 700 J m'2). In one example, the ECA of the present disclosure is embodied as a multiphase soft composite of an elastomeric epoxy network and liquid metal droplets to maintain flexibility which are bridged by silver flakes to form aconductive percolated network. In one example, the ECA can be embodied and implemented as an ink that can be processed through masked deposition and direct ink writing at room temperature. This enables robust integration of rigid components onto flexible substrates for next generation hybrid electronic systems.

[0005] According to one example embodiment, a conductive adhesive includes an elastomeric epoxy network. The conductive adhesive further includes liquid metal elements disposed in the elastomeric epoxy network. The conductive adhesive further includes silver elements coupled to the liquid metal elements to form a conductive percolated network in the elastomeric epoxy network.

[0006] According to another example embodiment, a device includes a substrate and a conductive adhesive coupled to the substrate. The conductive adhesive includes an elastomeric epoxy network. The conductive adhesive further includes liquid metal elements disposed in the elastomeric epoxy network. The conductive adhesive further includes silver elements coupled to the liquid metal elements to form a conductive percolated network in the elastomeric epoxy network.BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Many aspects of the present disclosure can be better understood with reference to the following figures. The components in the figures are not necessarily to scale, with emphasis instead being placed upon clearly illustrating the concepts of the disclosure. Moreover, repeated use of reference characters or numerals in the figures is intended to represent the same or analogous features, elements, or operations across different figures. Repeated description of such repeated reference characters or numerals is omitted for brevity.

[0008] FIG. 1A illustrates a perspective view of an example conductive adhesive according to various aspects and embodiments of the present disclosure.

[0009] FIG. IB illustrates a top view of an example surface microstructure of the example conductive adhesive of FIG. 1A according to various aspects and embodiments of the present disclosure.

[0010] FIG. 1C illustrates a cross-sectional view of a region of an example conductive percolated network (CPN) formed in the example conductive adhesive of FIG. 1A according to various aspects and embodiments of the present disclosure.

[0011] FIG. 2 illustrates a perspective view of an example device according to various aspects and embodiments of the present disclosure.

[0012] FIG. 3 illustrates a perspective view of another example device according to various aspects and embodiments of the present disclosure.

[0013] FIG. 4 illustrates a top view of another example device according to various aspects and embodiments of the present disclosure.

[0014] FIG. 5 illustrates a top view of another example device according to various aspects and embodiments of the present disclosure.

[0015] FIG. 6 A illustrates a bar chart of conductivity data for two example material formulations of the example conductive adhesive of FIG. 1 A according to at least one embodiment of the present disclosure.

[0016] FIG. 6B illustrates a bar chart of adhesion data for two example material formulations of the example conductive adhesive of FIG. 1 A according to at least one embodiment of the present disclosure.

[0017] FIG. 7A illustrates a bar chart showing a comparison of conductivity of the example conductive adhesive of FIG. 1 A with and without LM according to at least one embodiment of the present disclosure.

[0018] FIG. 7B illustrates a plot of resistance vs. length measurements across example conductive traces and corresponding linear fits according to at least one embodiment of the present disclosure.

[0019] FIG. 7C illustrates a plot of current-voltage curves up to 0.5 volts (V) for example conductive traces according to at least one embodiment of the present disclosure.

[0020] FIG. 7D illustrates a plot of normalized resistance data for example conductive traces under cyclic bending with inset detailing cyclic behavior according to at least one embodiment of the present disclosure.

[0021] FIG. 8A illustrates a schematic of a 90-degree peel test of the example conductive adhesive of FIG. I A according to at least one embodiment of the present disclosure.

[0022] FIG. 8B illustrates an isometric view of another peel test of the example conductive adhesive of FIG. 1A showing steady-state cohesive fracture according to at least one embodiment of the present disclosure.

[0023] FIG. 8C illustrates an enlarged front view of a crack front during peeling of the example conductive adhesive of FIG. 1 A with encircled bridging LM droplets according to at least one embodiment of the present disclosure.

[0024] FIG. 8D illustrates a plot of peel curves for the example conductive adhesive of FIG. 1A scaled to Gcby normalizing a peel force by w = 5 mm according to at least one embodiment of the present disclosure.

[0025] FIG. 8E illustrates a bar chart of Gcvalues obtained with two example formulations of the example conductive adhesive of FIG. 1A on different substrates according to at least one embodiment of the present disclosure.DETAILED DESCRIPTION

[0026] Flexible circuits are an emerging technology with promising applications in modem consumer electronics, wearable health-monitoring devices, and soft robotics. Traditionally, electronic components have been soldered to rigid printed circuit boards (PCBs) either manually or through the use of automated systems such as reflow ovens and wave solder machines. However, utilizing these techniques to attach components to flexible substrates such as flexible polymeric substrates is a challenge, as flexible polymeric substrates and circuits cannot withstand the high temperatures used in traditional electronic processing. For example, typical tin-lead solders have melting temperatures that are often in excess of the glass transition temperature of polymeric substrates commonly used for flexible circuits, which can lead to thermal expansion or damage.

[0027] Low- temperature solders, which incorporate low -melting point metals such as bismuth and indium, can be used to prevent damage to substrates. However, a vast majority of solder alloys, regardless of their melting temperature, tend to be brittle in their solid state. Consequently, bending strains in flexible systems can cause brittle fracture or delamination of the solder, which demands extra design considerations to allow for deformation with integrated components. Such considerations can severely limit the types of geometries that flexible circuits can conform to. As a result, there is an increasing need for materials that have high flexibility, exceptional electrical conductivity, strong adhesion, and processibility at low temperature, as these properties are essential to component integration in flexible electronic systems.

[0028] In recent years, polymer-based electrically conductive adhesives (ECAs) have been more widely used as interconnects in deformable systems. However, their fabrication andintegration into these systems has proven to be difficult. For example, intrinsically conductive polymers have been used as EC As, but these typically have lower values of conductivity (e.g., 102< o < 103S m'1) and poor adhesion strength (e.g. , < 1 kPa in shear), and various chemical processes are required to enhance these properties. Another method to enhance electrical conductivity and adhesion is to put fillers such as conductive ceramics, carbon-based fillers, and metals into naturally adhesive polymers such as epoxies. However, most epoxies do not have the desired mechanical properties to function as a flexible interconnect, as they are typically rigid (e.g., E > 1 GPa) and thus do not easily interface with flexible substrates. Additionally, rigid fillers can further increase the modulus of the composite system, which is highly detrimental in deformable applications. It therefore remains a challenge to create solder-like materials with optimal combinations of flexibility, conductivity, and adhesion for integrated hybrid systems such as flexible electronics with rigid components.

[0029] The present disclosure is directed to highly flexible and electrically conductive epoxyadhesives which are conductive to address the aforementioned problems. The electrically conductive adhesives can be relied upon to incorporate electrical components into flexible or stretchable substrates in general and with respect to existing ECA approaches. No sintering or other processes are required to create a highly conductive networks using the approaches described herein. The ECA material may be embodied through the incorporation and interaction of soft liquid metal (LM) droplets (e.g., gallium-indium droplets or eutectic gallium-indium (EGain) droplets) and silver (Ag) flakes in a flexible and adhesive epoxy matrix. As such, the ECA material described herein is referred to as an “Electrically Conductive Adhesive with Silver and EGain” material (or an “E-CASE” material), which highlights its ease of fabrication and integration into hybrid systems.

[0030] The E-CASE material described herein provides numerous technical advantages and benefits. For example, in the uncured state, the E-CASE material can be manually stenciled or automatically deposited through direct ink write (DIW) printing, allowing for versatility in manufacturing techniques and a high degree of precision when needed. Curing can take place between room temperature and 100 °C to allow for low-temperature processing for heat-sensitive components, but accelerated curing is also an option when higher temperatures are not problematic. Once cured, the E-CASE material robustly adheres to a substrate and any integrated functional component (e.g., an electrically conductive element such as alight emitting diode). The E-CASE material can be used as both a soft wiring as well as an interconnect for contact pads.

[0031] The E-CASE material was DIW-printed into two traces which contact solder pads of a light-emitting diode (LED) on a polyethylene terephthalate (PET) substrate in one embodiment. The E-CASE material was stenciled as contact pads onto a flex circuit (e.g., etched copper traces on polyimide) in another embodiment, and stretchable elastomeric substrates such as Styrene- Isoprene-Styrene (SIS) copolymers in another embodiment. After an LED was coupled to a PET substrate by way of the E-CASE material, the resulting assembly was cured and subsequently deformed in various ways while the LED remained adhered and functional. The E-CASE material is also capable of maintaining a very low bending radius. A flexible circuit including an LED coupled to a substrate by way of the E-CASE material in one example was wrapped around a pen with a diameter of approximately 8 millimeters (mm).

[0032] By varying the silver (Ag) content within the E-CASE material, it can be seen that the electrical and adhesive properties of the E-CASE material have an inverse relationship. In one embodiment including a relatively lower amount of Ag the E-CASE material, the material was found to have an electrical conductivity of 3.75x 104S nT1and a cohesive fracture energy up to 675 J m'2In another embodiment including a relatively higher amount of Ag the E-CASE material was found to have a conductivity of 3.25 x 105S m'1with a fracture energy up to 380 J tn'2These values of conductivity are among the highest to date compared to other epoxy-based ECAs, and for those that have achieved slightly higher conductivity and / or adhesion, flexibility is lacking due to the use of only rigid fillers with a high-modulus matrix. The findings described herein in accordance with various embodiments promote the use of the E-CASE material in integrated systems in which rigid functional components are adhered to flexible substrates.

[0033] Turning now to the figures, FIG. 1A illustrates a perspective view of an example conductive adhesive 100 according to various aspects and embodiments of the present disclosure. FIG. IB illustrates a top view of an example surface microstructure of the example conductive adhesive 100 of FIG. 1A according to various aspects and embodiments of the present disclosure. FIG. 1C illustrates a cross-sectional view of a region of an example conductive percolated network (CPN) formed in the example conductive adhesive 100 of FIG. 1A according to various aspects and embodiments of the present disclosure.

[0034] The conductive adhesive 100 is an example embodiment of a flexible (e.g., bendable, twistable), stretchable (e.g., elastic), and electrically and thermally conductive adhesive described herein. The conductive adhesive 100 is an example embodiment of the E-CASE material of the present disclosure. The conductive adhesive 100 can be embedded in and / or formed on a surfaceof at least one of a rigid, flexible, stretchable, or elastic substrate. The conductive adhesive 100 can be embodied and implemented as at least one of an electrode, an electrical trace, an electrical contact pad, an electrical interconnect, or another electrically conductive element. The conductive adhesive 100 is embodied as at least one of an electrically conductive electrode, trace, or interconnect in the example shown. The conductive adhesive 100 can be embedded in and / or formed on a surface of at least one of a rigid, flexible, stretchable, or elastic substrate to couple one or more conductive elements (e.g., LEDs) to the substrate in some examples or to couple multiple conductive elements (e.g., LEDs) to one another in other examples.

[0035] Referring among FIGS. lAto 1 C, the conductive adhesive 100 includes an elastomeric epoxy network 1 10. The elastomeric epoxy network 110 includes liquid metal elements 120 and silver elements 130. Only a single silver element 130 is denoted in each of FIGS. IB and 1C, and only a single liquid metal element 120 is denoted in FIG. 1C for clarity. Subsets of the silver elements 130 shown in FIGS. 1 A and IB that are positioned at or near an edge of the elastomeric epoxy network 110 are coupled (e.g., electrically, mechanically, thermally) to one another and at least partly form an outer surface of the conductive adhesive 100. Such subsets of the silver elements 130 are also coupled (e.g., electrically, mechanically, thermally) to and at least partly encase individual liquid metal elements 120 positioned at or near the edge of the elastomeric epoxy network 110. Other subsets of the silver elements 130 shown in FIG. 1C are coupled (e.g., electrically, mechanically, thermally) to and at least partly encase individual liquid metal elements 120 positioned within and throughout the elastomeric epoxy network 110. The silver elements 130 of each of the aforementioned subsets are also coupled (e.g., electrically, mechanically, thermally) to one another and to silver elements 130 of other such subsets throughout the conductive adhesive 100.

[0036] Respective clusters of the silver elements 130 shown in FIG. 1C are coupled to individual liquid metal elements 120. These respective clusters of coupled silver elements 130 and liquid metal elements 120 are also coupled to one another to collectively form a conductive percolated network (CPN) in the elastomeric epoxy network 110. The silver elements 130 of such respective clusters are coupled to one another and further coupled to and shroud individual liquid metal elements 120 in the elastomeric epoxy network 110 to collectively form the conductive percolated network and at least one conductive pathway (e.g., multiple conductive pathways) in and through the conductive percolated network. The conductive pathway or pathways extend through the conductive percolated network from a first end (e.g., first distal end) to a second end(e.g., second distal end) of the conductive percolated network to facilitate continuous conductivity (e.g., electrical, thermal) from the first end to the second end of the conductive percolated network.

[0037] The conductive percolated network is embodied as a continuous, flexible, stretchable, and electrically and thermally conductive percolated metal structure formed in the elastomeric epoxy network 1 10 as a collection of respective clusters of silver elements 130 coupled to one another and further to individual liquid metal elements 120 (e.g., as illustrated in FIG. 1C). Each of the liquid metal elements 120 and the silver elements 130 is embodied as a flexible, stretchable, and electrically and thermally conductive metal element. When the conductive adhesive 100 is embedded in or deposited on a surface of a flexible or stretchable substrate to form an electronic device, the conductive percolated network of coupled liquid metal elements 120 and silver elements 130 formed in the elastomeric epoxy network 110 of the conductive adhesive 100 allows for the entire resulting electronic device to have at least one of flexible or stretchable properties.

[0038] The conductive adhesive 100 can be formed to a variety of geometries and dimensions. The conductive adhesive 100 is formed to an approximately rectangular shape in the example shown. The conductive adhesive 100 can have a width that is greater than or equal to approximately 10 micrometers (pm) and is less than or equal to approximately 5 millimeters (mm) in various embodiments. The conductive adhesive 100 can have a height that is greater than or equal to approximately 10 pm and is less than or equal to approximately 5 mm in other embodiments. The conductive adhesive 100 has a width of approximately 1 mm and a height of approximately 480 pm in the example shown, although another dimension for either or both of the width or height may be relied upon in some cases.

[0039] The elastomeric epoxy network 110 can include various volume percentages of the liquid metal elements 120 and the silver elements 130. The elastomeric epoxy network 110 can include 58.8 percent by volume of the liquid metal elements 120 and 9.3 percent by volume of the silver elements 130 in one example. The elastomeric epoxy network 110 can include 50.0 percent by volume of the liquid metal elements 120 and 23. 1 percent by volume of the silver elements 130 in another example. The liquid metal elements 120 can individually include an alloy of gallium and indium. The liquid metal elements 120 can be individually embodied as a micro-scale liquid metal element (e.g., a micro-sized liquid metal particle or droplet). The liquid metal elements 120 can be individually embodied as a eutectic gallium-indium liquid metal element. The liquid metal elements 120 can be individually embodied as a eutectic gallium-indium liquid metal element having a gallium to indium mass ratio of 3: 1. The liquid metal elements 120 in the example shownare individually embodied as a micro-scale eutectic gallium-indium liquid metal element (e.g., a micro-sized liquid metal particle or droplet) having a gallium to indium mass ration of 3: 1. The silver elements 130 can be individually embodied as a silver flake. The silver elements 130 in the example shown are individually embodied as a micron-sized silver flake.

[0040] The conductive adhesive 100 can be applied as a manually stenciled ink in some examples. The conductive adhesive 100 can be applied as an automatically deposited direct ink write printing ink in other examples. The conductive adhesive 100 can also be embedded in, deposited on, or embedded in and deposited on a surface of a substrate in other cases. The conductive adhesive 100 is curable at an ambient temperature ranging between 20 °C and 100 °C, and other temperatures can be relied upon in some cases.

[0041] The electrical and adhesive properties of the conductive adhesive 100 have an inverse relationship. The conductive adhesive 100 has an electrical conductivity7of up to 3.25x 105 S m’1in one example. The conductive adhesive 100 has a cohesive fracture energy between 350 J m’2and 700 J m’2in another example. The conductive adhesive 100 has an electrical resistance that increases as a function of length and at least one of diameter, width, or height of the conductive adhesive 100. An electrical resistance of the conductive adhesive 100 increases approximately 0.06 Ohms per centimeter length up to a diameter of 40 millimeters in one example. An electrical resistance of the conductive adhesive 100 increases approximately 0.75 Ohms per centimeter length up to a diameter of 40 millimeters in another example. Thus, the electrical resistance of the conductive adhesive 100 can range.

[0042] FIG. 2 illustrates a perspective view of an example device 200 according to various aspects and embodiments of the present disclosure. The device 200 is an example embodiment of an electronic device or other device described herein that includes a flexible, stretchable, electrically and thermally conductive adhesive embedded in and / or formed on a surface of a substrate to couple conductive elements to one another and / or to the substrate.

[0043] The device 200 includes a substrate 201, a conductive element 250, and the conductive adhesive 100 coupled (e.g., electrically, mechanically, thermally) to the substrate 201 and the conductive element 250. The conductive adhesive 100 is embodied as at least one of an electrically conductive electrode, trace, or interconnect in the example shown. The conductive adhesive 100 is formed on a surface of the substrate 201 and couples (e.g., electrically, mechanically, thermally) the conductive element 250 to the substrate 201.

[0044] The substrate 201 is embodied as a rigid substrate in the example shown, although the substrate 201 may be embodied as another type of substrate in some cases. The substrate 201 can be embodied as a silicon substrate in one example. The substrate 201 can be embodied as a crystalline silicon substrate in another example. The substrate 201 can be embodied as a silicon- on-insulator (SOI) substrate in yet another example. The conductive element 250 is embodied as an LED in the example shown, although the conductive element 250 may be embodied as another type of conductive element in other examples. The conductive element 250 can be embodied as at least one of an electrode, a Hall effect sensor, a passive component, a resistor, a capacitor, an inductor, a sensor, a transformer, an integrated circuit (IC), or another conductive element.

[0045] FIG. 3 illustrates a perspective view of another example device 300 according to various aspects and embodiments of the present disclosure. The device 300 is an example embodiment of an electronic device or other device described herein that includes a flexible, stretchable, electrically and thermally conductive adhesive embedded in and / or formed on a surface of a substrate to couple conductive elements to one another and / or to the substrate. The device 300 is an example alternative embodiment of the device 200 described herein and illustrated in FIG. 2. A difference between the devices 200, 300 is that the device 300 includes at least one of a flexible or stretchable substrate rather than a rigid substrate.

[0046] The device 300 includes a substrate 301, the conductive element 250, and the conductive adhesive 100 coupled to the substrate 301 and the conductive element 250. The conductive adhesive 100 is embodied as at least one of an electrically conductive electrode, trace, or interconnect in the example shown. The conductive adhesive 100 is at least partly embedded in the substrate 301 and couples the conductive element 250 to the substrate 301. The conductive element 250 is embodied as an LED in the example shown, although the conductive element 250 may be embodied as another type of conductive element in other examples. The conductive element 250 can be embodied at least one of an electrode, a Hall effect sensor, a passive component, a resistor, a capacitor, an inductor, a sensor, a transformer, an integrated circuit (IC), or another conductive element.

[0047] The substrate 301 is embodied as at least one of a flexible or stretchable substrate in the example shown, although the substrate 301 may be embodied as another type of substrate in some cases. The substrate 301 can be embodied as a polyethylene terephthalate (PET) substrate in one example. The substrate 301 can be embodied as an indium tin oxide (ITO) film in anotherexample. The substrate 301 can be embodied as a styrene-isoprene-styrene (SIS) elastomer substrate in still another example.

[0048] FIG. 4 illustrates a top view of another example device 400 according to various aspects and embodiments of the present disclosure. The device 400 is an example embodiment of an electronic device or other device described herein that includes a flexible, stretchable, electrically and thermally conductive adhesive embedded in and / or formed on a surface of a substrate to couple conductive elements to one another and / or to the substrate. The device 400 is an example alternative embodiment of each of the devices 200, 300 described herein and respectively illustrated in FIGS. 2 and 3. A difference between the device 400 and the devices 200, 300 is that the device 400 includes several electrical traces and contact pads formed from the conductive adhesive 100.

[0049] The device 400 includes a substrate 401 as well as electrical traces 403a, 403b, 403c, 403d. 403e, 403f (or “the traces 403”) and electrical contact pads 405a, 405b, 405c, 405d, 405e, 405f (or “contact pads 405”) at least partly embedded in and / or formed on the substrate 401. Only a single trace 403a and a single contact pad 405a are denoted in FIG. 4 for clarity. The electrical traces 403a, 403b, 403c, 403d, 403e, 403f are respectively coupled to and formed with a corresponding electrical contact pad 405a, 405b, 405c, 405d, 405e, 405f from the conductive adhesive 100. Each of the traces 403 and contact pads 405 is an example embodiment of and is formed from the conductive adhesive 100.

[0050] The traces 403 and the contact pads 405 are at least partly embedded in and / or formed on a surface of the substrate 401. The traces 403 and the contact pads 405 are at least partly embedded in and / or formed on a surface of the substrate 401 in a defined integrated circuit pattern in this example. The defined integrated circuit pattern includes electrical contact pad regions that are at least partly defined by the traces 403 and the contact pads 405. The electrical contact pad regions and the contact pads 405 can have defined sizes and can be spaced apart from one another at defined spacings. Each of the electrical contact pad regions and contact pads 405 in the example shown has a width and a length of approximately 1.5 mm, although another width or length may be relied upon for any or all of the contact pads 405 in some cases.

[0051] The contact pads 405 are spaced approximately 2.5 mm or more from one another in this example, although another spacing distance may be used in other examples. The traces 403 can have defined sizes and can be spaced apart from one another at defined spacings. Each of the traces 403 in the example shown has a width of approximately 390 pm or more, although anotherwidth may be relied upon for any or all of the traces 403 in some cases. The traces 403 are spaced approximately 220 pm or more from one another in this example, although another spacing distance may be used in other examples. The contact pads 405 in the example shown are arranged on the substrate 401 such that they align with one or more electrodes or contact pads of an external electronic device (e.g.. a surface mount device) or another electrically conductive component.

[0052] The substrate 401 can be embodied as at least one of a rigid, flexible (e g., bendable, twistable), or stretchable (e.g., elastomeric) substrate. The substrate 401 can be embodied as at least one of silicon substrate, a crystalline silicon substrate, a silicon-on-insulator (SOI) substrate, or another rigid substrate in some examples. The substrate 401 can be embodied as a polyethylene terephthalate (PET) substrate, an indium tin oxide (ITO) fdm, or a styrene-isoprene-styrene (SIS) elastomer substrate in other examples.

[0053] FIG. 5 illustrates a top view of another example device 500 according to various aspects and embodiments of the present disclosure. The device 500 is an example embodiment of an electronic device or other device described herein that includes a flexible, stretchable, electrically and thermally conductive adhesive embedded in and / or formed on a surface of a substrate to couple conductive elements to one another and / or to the substrate. The device 500 is an example alternative embodiment of the device 400 described herein and illustrated in FIG. 4. A difference between the devices 400. 500 is that the device 500 includes several electrodes formed from the conductive adhesive 100 rather than traces and contact pads.

[0054] The device 500 includes the substrate 401 and electrodes 505a, 505b, 505c, 505d, 505e, 505f, 505g. 505h, 505i, 505j (or ‘‘electrodes 505”) at least partly embedded in and / or formed on a surface of the substrate 401. Only a single electrode 505a is denoted in FIG. 5 for clarity. Each of the electrodes 505 is an example embodiment of and is formed from the conductive adhesive 100. The electrodes 505 are at least partly embedded in and / or formed on a surface of the substrate 401 in a defined integrated circuit pattern in this example. The defined integrated circuit pattern includes electrode regions that are at least partly defined by the electrodes 505. The electrodes 505 can have defined sizes and can be spaced apart from one another at defined spacings. Each of the electrodes 505 in the example shown has a width of approximately 356 pm and a length of approximately 794 pm, although another width and / or length may be relied upon for any or all of the electrodes 505 in some cases. The electrodes 505 are spaced approximately 400 pm or more from one another in this example, although another spacing distance may be used in other examples. The electrodes 505 in the example shown are arranged on the substrate 401such that they align with one or more electrodes or contact pads of an external electronic device (e.g., a surface mount device) or another electrically conductive component.

[0055] FIG. 6A illustrates a bar chart of conductivity data for two example material formulations of the conductive adhesive 100 according to at least one embodiment of the present disclosure. Error bars in FIG. 6A represent the standard deviation for N = 3 measurements. FIG. 6B illustrates a bar chart of adhesion data (e g., cohesive fracture energy Gcunder peel) for two example material formulations of the conductive adhesive 100 according to at least one embodiment of the present disclosure. Error bars in FIG. 6B represent the standard deviation for N= 9 measurements based on cross-sectional area.

[0056] Referring to FIGS. 1A to 6B collectively, the conductive adhesive 100 consists of a flexible epoxy matrix (e.g., 832FX, E ~ 1 MPa) which contains dispersed droplets of roomtemperature LM (e g., EGain, 3: 1 mass ratio of gallium and indium) and Ag flakes (e.g., SF94) in various examples. The LM and Ag were chosen as fillers in various examples described herein due to their contrasting, yet synergistic properties. EGain is mechanically soft and typically creates an electrically insulating composite when dispersed in a polymer matrix while Ag flakes are rigid and have been shown to be the most electrically conductive geometry compared to micro and nanoparticles, especially in deformable applications. By incorporating LM in addition to Ag in various examples, percolation and connection of the Ag flakes can be achieved at much lower loading. Furthermore, the lower loading of Ag in some examples along with the soft nature of the LM inclusions prevent the composite from being brittle and instead allow' it to remain flexible. The electrical and mechanical performance of two distinct formulations of the conductive adhesive 100 is described and evaluated in examples herein. The first example formulation of the conductive adhesive 100 had a total filler loading of 68 vol%, composed of 58.8 vol% LM and 9.3 vol% Ag. The second example formulation of the conductive adhesive 100 had a total filler loading of ~73 vol %, with 50 vol% LM and 23.1 vol% Ag. The two example formulations of the conductive adhesive 100 are denoted herein as low Ag and high Ag, respectively.

[0057] Microstructure and Electrical Performance.

[0058] FIG. 7A illustrates a bar chart showing a comparison of conductivity of the conductive adhesive 100 with and without LM according to at least one embodiment of the present disclosure. Error bars in FIG. 7A represent the standard deviation for N = 9 measurements based on cross- sectional area. FIG. 7B illustrates a plot of resistance vs. length measurements across example conductive traces and corresponding linear fits according to at least one embodiment of the presentdisclosure. Error bars in FIG. 7B represent the standard deviation for TV = 3 measurements. FIG. 7C illustrates a plot of current-voltage curves up to 0.5 V for example conductive traces according to at least one embodiment of the present disclosure. Shaded regions in FIG. 7C represent the standard deviation for N = 3 measurements. FIG. 7D illustrates a plot of normalized resistance data for example conductive traces under cyclic bending with inset detailing cyclic behavior according to at least one embodiment of the present disclosure.

[0059] To evaluate the microstructure of the conductive adhesive 100, optical microscopy, 3D profilometry, and SEM imaging were utilized in at least one example. Based on measuring the 3D profile of a stencil-deposited trace, it was observed that the cross-section of the conductive adhesive 100 has a generally rectangular shape in one example (e.g., FIG. 1A). Closer examination of the top surface under SEM revealed an abundance of micron-size Ag flakes in this example (e.g., FIG. IB). However, there was a lack of observable LM droplets at the surface of the conductive adhesive 100 in this example. This is due to the very low viscosity and low density of the uncured epoxy matrix that forms the elastomeric epoxy network 1 10 in comparison to the LM of the liquid metal elements 120. Since EGain is denser, the droplets tend to sink into the bulk in- situ during fabrication and thus are not seen on the surface after curing. Ag is also seen throughout the bulk; however, due to EGain's high surface tension, oxide shell, and low mixing speeds during fabrication in one example, the Ag did not penetrate the LM and instead shrouded the LM droplets (e.g., FIG. 1C). This mechanism allows for the creation of conductive pathways around the EGain LM elements in various examples described herein. As shown in FIG. 7 A, in one example where the LM was removed from the system, but the amount of Ag remained the same, the low Ag formulation was no longer conductive, and the high Ag formulation was an order of magnitude less conductive. These results highlight the benefit of the LM used as a conformal and spatial filler in many examples herein. Additionally, EGain is known to be a highly thermally conductive filler and can act alongside the Ag to dissipate heat generated throughout the material when applying a current or voltage.

[0060] The electrical behavior of the conductive adhesive 100 was further analyzed through quantifying resistance-length and current-voltage characteristics in several examples. It was found in one example that the resistance-length behavior follows a positive linear trend, which is typical of conductors (e.g., FIG. 7B). Linear least-squares fits were used in one example to predict an increase of ~0.75 Q per cm of trace length for the low Ag formulation of the conductive adhesive 100 and ~0.06 Q per cm for the high Ag formulation of the conductive adhesive 100. It should benoted that, for high Ag formulations, all resistance values up to d = 40 mm were less than 0.25 Q with d = 10 mm in particular having an extremely low value of 0.09 Q in one example. Additionally, the low Ag formulation in one example had a sub-ohm resistance of 0.55 Q at d = 10 mm. These results substantiate example uses of the conductive adhesive 100 as both an effective material for solder-like connections as well as a soft wiring for flexible PCBs.

[0061] Common components of interest for hybrid electronics are rigid surface mount components. These packages are typically on the scale of millimeters and include components such as pulse oximeters, time of flight sensors or heart-rate monitors for wearable technologies. To verify the feasibility of the conductive adhesive 100 on this type of package size, a set of connection pads with dimensions of 0.7 x 0.3 mm and a spacing of 0.4 mm was designed in one example (e.g., the device 500 shown FIG. 5) and a custom circuit pattern with a close spacing as small as 220 pm was designed in another example (e.g., the device 400 shown in FIG. 4) for the 1005 metric SMD package size. These example implementations of the conductive adhesive 100 were stencil printed using masks fabricated with a CO2 laser cutter. To further improve the resolution of the conductive adhesive 100 patterning, higher resolution masks could be used. Additionally, recent work has shown promising high resolution methods such as photo-patterning of LM materials that can be implemented to improve resolution.

[0062] FIG. 7C shows the current-voltage behavior observed in one example up to 0.5 V of applied voltage at a probing distance of d = 40 mm. In this example, the low Ag formulation of the conductive adhesive 100 demonstrates less current draw per voltage applied compared to the high Ag formulation, with maximum current draw for each around 0.25 A and 2.0 A, respectively. This result is consistent with the conductivities of each formulation of the conductive adhesive 100, as greater amounts of Ag allow for higher conductivity and thus more current flow in examples herein.

[0063] Cyclic resistance behavior of the conductive adhesive 100 was also evaluated in some examples to determine its robustness against repeated bending for flexible systems. This was accomplished in one example by bending a trace formed with the conductive adhesive 100 on a PET substrate to 1,000 cycles. Over the course of the test, the conductive adhesive 100 traces remained conductive and maintained conformal contact with the electrode in this example. It w as found in this example that the bulk resistance generally increases when bending, decreases when flattening, and decreases overall as the cycle count increases, eventually nearing a plateau (e.g., FIG. 7D). This is likely a result of LM droplet oxide layers breaking due to high bending stressesat the top peak, which in turn creates more conductive pathways in some cases. These findings further justify the use of the conductive adhesive 100 in deformable systems, as repeated bending of the conductive adhesive 100 seems to be beneficial to its overall function.

[0064] Adhesion Performance.

[0065] FIG. 8 A illustrates a schematic of a 90-degree peel test of the conductive adhesive 100 according to at least one embodiment of the present disclosure. FIG. 8B illustrates an isometric view of another peel test of the conductive adhesive 100 showing steady-state cohesive fracture according to at least one embodiment of the present disclosure. FIG. 8C illustrates an enlarged front view of a crack front during peeling of the conductive adhesive 100 with encircled bridging LM droplets according to at least one embodiment of the present disclosure. FIG. 8D illustrates a plot of peel curves for the conductive adhesive 100 scaled to Gcby normalizing a peel force by w = 5 mm according to at least one embodiment of the present disclosure. FIG. 8E illustrates a bar chart of Gc values obtained with two example formulations of the conductive adhesive 100 on different substrates according to at least one embodiment of the present disclosure.

[0066] Strong adhesive properties are critical to a well-functioning ECA. For flexible applications, the conductive adhesive 100 can withstand stresses induced by bending and twisting near integrated components. To analyze the adhesion performance of the conductive adhesive 100, 90-degree peel tests were utilized in one example in which the conductive adhesive 100 was cast between a rigid bottom substrate and a flexible top substrate (e.g., FIG. 8 A). Copper, polyimide (PI), and polyethylene terephthalate (PET) were chosen as substrate materials in this example due to their common use in flex circuit applications. At the onset of peeling, the crack front moved from the center of the thickness (e.g., pre-crack) towards the top substrate in this example. This behavior is due to the larger bending stiffness of the thick sample in this example compared to that of the thin top adherend, which causes the crack front to move up as it requires less energy to bend near the sample-adherend interface. Although the crack front relocated towards the interface in this example, the conductive adhesive 100 did not delaminate from the adherends. All samples of the conductive adhesive 100 tested in various examples exhibited cohesive fracture, as evidenced by a thin layer of material left on the top adherend after testing. An interesting aspect of the material fracture in some of these examples is highlighted through macro photography and highspeed imaging in FIGS. 8B and 8C. In FIGS. 8B and 8C droplets are shown actively bridging the crack front. Interestingly, no active liquid was left on the fracture surface after testing in the examples. Hence, the LM seemed to temporarily locate at the crack front in the examples, but thenbreak apart and again become surrounded by Ag flakes on both fracture surfaces. This liquidbridging phenomenon has not been seen in other systems and further highlights the unique properties of the conductive adhesive 100.

[0067] FIG. 8D shows representative peel data scaled to the cohesive fracture energy (Gc= Fw) of the system according to one example, where F is the peel force and w is the width of the sample. FIG. 8E shows a bar chart representation of G_ according to one example, where an average peel force has been taken across the plateau region. The low Ag formulation of the conductive adhesive 100 had greater values of fracture energy (up to 700 J m'2) on all low Ag formulations of the conductive adhesive 100 samples tested in various examples compared to its high Ag counterpart (up to 300 J m‘2). This is attributed to the high Ag formulation of the conductive adhesive 100 having less epoxy in various examples as a result of higher overall filler content, which effectively decreases the thickness of the epoxy layer surrounding each LM droplet or Ag flake, both in the bulk and near the surface where the material is adhered. Furthermore, the values of Gcwere found in at least one example to be relatively similar across materials within the same formulation. This is a result of consistency in the cohesive failure mechanism across all samples tested in several examples. Given the strong adhesive properties of the conductive adhesive 100 paired with its high flexibility and conductivity, it can be integrated into hybrid systems consisting of both rigid and flexible components.

[0068] Robust Flexible Electronics Demonstration.

[0069] To demonstrate the feasibility and multifunctionality of the conductive adhesive 100 in hybrid deformable systems, a flexible electronic sy stem was created in one example in which 19 LEDs were interfaced with the conductive adhesive 100 in series. The conductive adhesive 100 was stencil-printed in this example such that it formed the letters “VT” on a sheet of flexible, transparent PET. FIG. 3 shows a schematic representation of how the conductive adhesive 100 interfaces with one of such LEDs (e.g., the conductive element 250) and the substrate (e.g., the substrate 301) in this example. The system was folded long-ways twice in one example demonstration, and no LEDs delaminated from the substrate or shorted during the process. This highlights the multifunctionality of the conductive adhesive 100 as a soft wire and adhesive, as well as its robustness to bending and creasing.

[0070] In another example, the powered circuit (e.g., the device 300 embodied as a powered flexible electronic system) was laid on pavement and then subjected to extreme forces and pressure as a result of being driven over by a car tire. As this occurred, there was no delamination of theLEDs from the conductive adhesive 100, nor did the circuit fail at any point in this example. After the tire passed over the system, all 19 LEDs remained illuminated, and there were no signs of any shorts or broken conductive pathway s in the circuit in this example. This further demonstrates the strong adhesive properties of the conductive adhesive 100 as well as its ability to endure large amounts of stress. These results successfully demonstrate the use of the conductive adhesive 100 as both a soft wiring and a highly flexible interconnect for systems which incorporate both rigid and flexible functional components.

[0071] Methods and Fabrication.

[0072] Conductive adhesive 100. Low Ag samples of the conductive adhesive 100 were fabricated in one example by adding 58.8 vol% LM and 9.25 vol% Ag flakes to mixed, uncured epoxy and hand-mixing until homogeneous. For high Ag samples of the conductive adhesive 100, additional Ag was added in some examples to the base mixture to increase the volume loading to 23.13 vol%. In at least one example, approximately (~) 20 wt% acetone was used to reduce viscosity and the solution was hand-mixed again.

[0073] For conductive traces and interconnects formed from the conductive adhesive 100, stencils were fabricated in one example by laser cutting masks 55 mm in length, 1 mm in width, and 480 pm in height on stencil mask (A= 3 layers). In one example, the stencils were placed onto a 125 pm-thick PET substrate and the conductive adhesive 100 was deposited and leveled with a tongue depressor before removing the stencil mask layer by layer with tweezers. In another example, DIW prints were done by loading the conductive adhesive 100 into a syringe and then placing the syringe into an SDS-10 head on a 3D printer. The conductive adhesive 100 was extruded onto 125 pm PET at 2000-2500 pulses per microliter and head speeds of 600-800 mm / min in this example. LEDs were placed down using tweezers and assemblies were cured at 100 °C for 30 min in one example.

[0074] Indentation samples. Polymethylsiloxane (PDMS) molds (e.g., 10: 1 curing ratio) were fabricated in one example in the shape of a hollow square with dimensions of l5 x l5 x l9 mm. Molds were affixed to an acrylic substrate using a thin layer of silicone adhesive, and the epoxy was deposited into the mold in one example. A thin sheet of cured PDMS was laid on top of the mold to ensure a flat sample surface in one example. Samples were cured at 100 °C for 1 h in one example.

[0075] Quasi-static bending samples. Bending samples were fabricated in one example through stencil deposition using the same methods described above.

[0076] Peel specimens. PDMS molds (e.g., 10: 1 curing ratio) were prepared in one example by casting the uncured silicone into a large acrylic mold to create a stock sheet with a uniform thickness of 3.2 mm. The molds (e.g., 75 x 5 mm with a 5 mm wall thickness) were laser-cut from the stock and cleaned thoroughly in a container of isopropyl alcohol floating in a sonication bath in this example. Substrates (e.g., copper, PI, PET) were affixed to a supporting acrylic substrate using very high bond (VHB) tape in one example. The molds were sealed to the bottom substrate by applying a thin layer of Sil-Poxy in one example. Samples were cast into the molds and another substrate (e.g., 120 x 5 mm) was placed on top in one example. Specimens were cured at room temperature overnight and then at 100 °C for 30 min in one example. The molds were removed after curing and a 10 mm central pre-crack was cut into the conductive adhesive 100 prior to testing with a razor blade in one example.

[0077] Flexible electronics demonstration sample. A circuit was fabricated using the conductive adhesive 100 in one example by laser-cutting a stencil mask with N = 2 layers. In this example. 2.5-mm breaks in the lines were periodically integrated for LEDs. The stencil was placed onto PET and the conductive adhesive 100 was manually deposited and leveled before removing the mask in this example. LEDs were also placed down using tweezers and the completed assembly was cured at 100 °C for 30 min in this example. After curing, the conductive adhesive 100 was spray-coated in this example with a thin layer of polyurethane.

[0078] Characterization of Mechanical, Electrical, and Optical Data.

[0079] Mechanical data for the conductive adhesive 100 were obtained using an Instron 5944 universal testing system in one example.

[0080] Modulus. Elastic modulus of the epoxy was measured for the conductive adhesive 100 in one example using an indentation setup in which a hemispherical indenter (N-BK7 half-ball lens, 3 mm diameter) indented to 1 mm below the surface of a l5 x l5 x l9 mm sample at 0.5 pm / s.

[0081] Quasi-static bending. Bending data were measured for the conductive adhesive 100 in one example using a three-point bend setup with a span length of 2 cm. Substrates were 4 cm long by 1 cm wide in one example. Substrate thicknesses were 125 pm for PET and 120 pm for copper on polyimide (H / l / 1 / 0) in one example.

[0082] Adhesion. Fracture energy data were obtained for the conductive adhesive 100 in one example from a 30 mm plateau region of the force-displacement curves of specimens 75 x 5 x 3.2 mm under 90-degree peel at 1 mm / s.

[0083] Resistance measurements. Resistance vs. length data were obtained for the conductive adhesive 100 in one example using a source measuring unit with a four-probe setup. To minimize contact resistance in one example, small drops of LM were dispensed onto the surface of a conductive trace formed from the conductive adhesive 100 at different points of interest and copper probes were used to make measurements. Linear least-squares fits were mapped to the data to obtain R-L relationships in one example.

[0084] IV Curves. Using the same setup described above, a step voltage from 0 to 0.5 V in intervals of 0.1 V was sent through conductive traces formed from the conductive adhesive 100 at a fixed probe distance of 40 mm in one example.

[0085] Conductivity. The formula G = L / RA was used to calculate conductivity for the conductive adhesive 100 in one example, where L'R is the inverse of the obtained linear leastsquares relationship, and A is an average cross-sectional area of a conductive trace formed from the conductive adhesive 100 that is found using the methods described below in some cases.

[0086] Cyclic resistance. Using methods described herein, conductive traces formed from the conductive adhesive 100 with dimensions 20 mm x 1 mm x 480 pm were stencil-deposited on 125 pm-thick PET atop extended copper leads (e.g., double-sided conductive copper foil tape, 3 mm width) in one example. The ends of the sample were secured with acry lic clamps onto a custom fixture with an integrated linear actuator and stepper motor in one example. The motor was connected to a motor controller stack, which was programmed to displace one clamp back and forth by 15 mm over 1,000 cycles in one example. Resulting electrical data was obtained in one example by connecting the extended copper leads (e.g., shown in FIG. 7D) on the sample to a source measuring unit with alligator clips.

[0087] Optical microscopy and profilometry. Optical images and profiles of the conductive adhesive 100 w ere obtained in one example on a 3D profiler using white light at 5x magnification and a laser at 10x magnification. Cross-sectional area measurements of the conductive adhesive 100 were calculated in one example using a slicing tool across a trace formed from the conductive adhesive 100 and manually adjusting the boundaries of the region to be considered.

[0088] Various embodiments of a multifunctional flexible and electrically conductive epoxybased adhesive (e.g., the conductive adhesive 100) are described herein and illustrated in the figures. By filling a low-modulus epoxy with LM and a relatively low fraction of Ag flakes in some examples, flexibility comparable to the neat polymer is maintained. Additionally, the shrouding of LM droplets by Ag flakes in the bulk of the conductive adhesive 100 in variousexamples allows for the creation of highly electrically conductive networks in interstitial spaces without sintering. The conductive adhesive 100 possesses very low values of bulk resistance across relatively large lengths in several examples, which makes it ideal for use as both a wire and an interconnect. Furthermore, the conductive adhesive 100 is highly robust to repeated bending at low radii and decreases in resistivity with each cycle until eventually reaching a plateau in various embodiments. Across tw o material formulations of the conductive adhesive 100, a trade-off is discovered in which conductivity7increases and adhesion decreases with greater Ag content in at least one example. Specifically, increasing the amount of Ag from 9.3 vol% to 23.1 vol% in one example increases the conductivity7by an order of magnitude (104to 105S m-1) but decreases the fracture energy by about half (~700 J m'2to ~350 J m’2). These values were found to be similar in several examples across three substrates due to a consistent cohesive failure mechanism under peel.

[0089] As the conductive adhesive 100 fractures, a unique liquid-bridging phenomenon is discovered in several examples in which LM spans the crack front across the top and bottom fracture surfaces. The unique combination of the conductive adhesive 100 properties including flexibility, conductivity, and adhesion in one example are highlighted through the fabrication of a hybrid rigid-flexible system in which magnetic field sensors are adhered to common electrical circuit materials using the conductive adhesive 100 in the forms of traces and solder-ty pe connections. The system remains functional and outputs data while deforming to extreme configurations in several examples, thus demonstrating the feasibility7of integrating the conductive adhesive 100 into complex systems in which resilience to deformation is important to performance. The embodiments of the conductive adhesive 100 described herein could inspire the future development of, and / or be used to implement, soft robotic and electronic systems, skin-mounted medical devices, and machines in yvhich reliable integration of rigid and deformable components is critical to system function.

[0090] Disjunctive language, such as the phrase “at least one of X, Y, or Z,” unless specifically stated otherwise, is to be understood w ith the context as used in general to present that an item, term, or the like, can be either X, Y, or Z, or any combination thereof (e.g., X, Y, and / or Z). Thus, such disjunctive language is not generally intended to, and should not, imply that certain embodiments require at least one of X, at least one of Y, or at least one of Z to be each present. As referenced herein in the context of quantity, the terms “a” or “an7’ are intended to mean “at least one” and are not intended to imply “one and only one.”

[0091] As referred to herein, the terms ‘’include,” '‘includes,” and “including” are intended to be inclusive in a manner similar to the term “comprising.” As referenced herein, the terms “or” and “and / or” are generally intended to be inclusive, that is (z.e.), “A or B” or “A and / or B” are each intended to mean “A or B or both.” As referred to herein, the terms “first,” “second,” “third,” and so on, can be used interchangeably to distinguish one component or entity from another and are not intended to signify location, functionality, or importance of the individual components or entities. As referenced herein, the terms “couple,” “couples,” “coupled,” and / or “coupling” refer to chemical coupling (e.g., chemical bonding), communicative coupling, electrical and / or electromagnetic coupling (e.g., capacitive coupling, inductive coupling, direct and / or connected coupling), mechanical coupling, operative coupling, optical coupling, and / or physical coupling.

[0092] It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications can be made to the abovedescribed embodiment(s) without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims.

Claims

CLAIMSTherefore, at least the following is claimed:

1. A conductive adhesive, comprising: an elastomeric epoxy network; liquid metal elements disposed in the elastomeric epoxy network; and silver elements coupled to the liquid metal elements to form a conductive percolated network in the elastomeric epoxy network.

2. The conductive adhesive of claim 1, wherein each of the conductive percolated network, the liquid metal elements, and the silver elements comprises at least one of a flexible, stretchable, electrically conductive, or thermally conductive metal element.

3. The conductive adhesive of claim 1. wherein individual ones of the liquid metal elements comprise an alloy of gallium and indium.

4. The conductive adhesive of claim 1 , wherein individual ones of the liquid metal elements comprise a eutectic gallium-indium liquid metal element having a gallium to indium mass ratio of 3: 1.

5. The conductive adhesive of claim 1, wherein individual ones of the silver elements comprise a silver flake.

6. The conductive adhesive of claim 1, wherein individual ones of the silver elements comprise a micron-sized silver flake.

7. The conductive adhesive of claim 1, wherein subsets of the silver elements are coupled to and shroud individual ones of the liquid metal elements in the elastomeric epoxy network to collectively form conductive pathways of the conductive percolated netw ork.

8. The conductive adhesive of claim 1, wherein the elastomeric epoxy network comprises 58.8 percent by volume of the liquid metal elements and 9.3 percent by volume of the silver elements.

9. The conductive adhesive of claim 1, wherein the elastomeric epoxy network comprises 50.0 percent by volume of the liquid metal elements and 23. 1 percent by volume of the silver elements.

10. The conductive adhesive of claim 1, wherein the conductive adhesive is applicable as a manually stenciled ink.

11. The conductive adhesive of claim 1 , wherein the conductive adhesive is applicable as an automatically deposited direct ink write printing ink.

12. The conductive adhesive of claim 1, wherein the conductive adhesive is curable at an ambient temperature ranging between 20 °C and 100 °C.

13. The conductive adhesive of claim 1, wherein electrical and adhesive properties of the conductive adhesive have an inverse relationship.

14. The conductive adhesive of claim 1, wherein the conductive adhesive has an electrical conductivity of up to 3.25xl05S m1.

15. The conductive adhesive of claim 1, wherein the conductive adhesive has a cohesive fracture energy between 350 J m'2and 700 J m'216. The conductive adhesive of claim 1, wherein an electrical resistance of the conductive adhesive increases approximately 0.06 Ohms per centimeter length up to a diameter of 40 millimeters.

17. The conductive adhesive of claim 1, wherein an electrical resistance of the conductive adhesive increases approximately 0.75 Ohms per centimeter length up to a diameter of40 millimeters.

18. A device, comprising: a substrate; and a conductive adhesive coupled to the substrate, the conductive adhesive comprising: an elastomeric epoxy network; liquid metal elements disposed in the elastomeric epoxy network; and silver elements coupled to the liquid metal elements to form a conductive percolated network in the elastomeric epoxy network.

19. The device of claim 18, wherein the substrate comprises a rigid substrate, a flexible substrate, a stretchable substrate, or an elastomeric substrate.

20. The device of claim 18, wherein the substrate comprises a polyethylene terephthalate substrate.

21. The device of claim 18, wherein the substrate comprises an indium tin oxide film.

22. The device of claim 18, wherein the substrate comprises a st rene-isoprene-styrene elastomer substrate.

23. The device of claim 18, wherein the conductive adhesive is at least one of embedded in the substrate or formed on a surface of the substrate.

24. The device of claim 18, wherein the conductive adhesive is at least one of embedded in the substrate or formed on a surface of the substrate as at least one of an electrode, an electrical trace, an electrical contact pad, or an electrical interconnect.

25. The device of claim 18, wherein the conductive adhesive is at least one of embedded in the substrate or formed on a surface of the substrate in a defined integrated circuitpatern, the defined integrated circuit patern comprising electrical contact pad regions having defined sizes and being spaced apart from one another at defined spacings.

26. The device of claim 18, wherein each of the conductive percolated network, the liquid metal elements, and the silver elements comprises at least one of a flexible, stretchable, electrically conductive, or thermally conductive metal element.

27. The device of claim 18, wherein individual ones of the liquid metal elements comprise an alloy of gallium and indium.

28. The device of claim 18, wherein individual ones of the liquid metal elements comprise a eutectic gallium-indium liquid metal element having a gallium to indium mass ratio of 3: 1.

29. The device of claim 18, wherein individual ones of the silver elements comprise a silver flake.

30. The device of claim 18, wherein individual ones of the silver elements comprise a micron-sized silver flake.

31. The device of claim 18, wherein subsets of the silver elements are coupled to and shroud individual ones of the liquid metal elements in the elastomeric epoxy network to collectively form conductive pathways of the conductive percolated network.

32. The device of claim 18, wherein the elastomeric epoxy network comprises 58.8 percent by volume of the liquid metal elements and 9.3 percent by volume of the silver elements.

33. The device of claim 18, wherein the elastomeric epoxy network comprises 50.0 percent by volume of the liquid metal elements and 23.1 percent by volume of the silver elements.

34. The device of claim 18, wherein the conductive adhesive is applicable as a manually stenciled ink.

35. The device of claim 18, wherein the conductive adhesive is applicable as an automatically deposited direct ink write printing ink.

36. The device of claim 18, wherein the conductive adhesive is curable at an ambient temperature ranging between 20 °C and 100 °C.

37. The device of claim 18, wherein electrical and adhesive properties of the conductive adhesive have an inverse relationship.

38. The device of claim 18, wherein the conductive adhesive has an electrical conductivity7of up to 3.25x105S m'1.

39. The device of claim 18, wherein the conductive adhesive has a cohesive fracture energy between 350 J m'2and 700 J tn'240. The device of claim 18, wherein an electrical resistance of the conductive adhesive increases approximately 0.06 Ohms per centimeter length up to a diameter of 40 millimeters.

41. The device of claim 18, wherein an electrical resistance of the conductive adhesive increases approximately 0.75 Ohms per centimeter length up to a diameter of 40 millimeters.

42. The device of claim 18, further comprising: a conductive element positioned in or on the substrate and coupled to the conductive adhesive.

43. The device of claim 18. further comprising: at least one of a light emitting diode, an electrode, a passive component, a resistor, a capacitor, an inductor, a sensor, a transformer, or an integrated circuit positioned in or on the substrate and coupled to the conductive adhesive.

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