Flexible and printable composite ink for thermal management of soft electronics

Abstract

The current invention relates to an ink formulation for additive manufacturing, comprising a polymeric binder material, a dispersant, a thinner, nanoparticles of eutectic gallium indium (EGaIn), and silver flakes. The current invention also relates to a thermal management material comprising a substrate and a sintered layer of the ink formulation. The current invention further discloses a method of forming the thermal management material. Also, the current invention relates to an electrical device comprising at least one component that draws electrical energy attached to the thermal management material.

Description

[0001] FLEXIBLE AND PRINTABLE COMPOSITE INK FOR THERMAL MANAGEMENT OF SOFT ELECTRONICS

[0002] Field of Invention

[0003] The current invention relates to an ink formulation for additive manufacturing, a thermal management material, a method of forming the thermal management material, and an electrical device.

[0004] Background

[0005] The listing or discussion of a prior-published document in this specification should not necessarily be taken as an acknowledgement that the document is part of the state of the art or is common general knowledge.

[0006] With the emerging highly integrated hybrid electronic devices and circuit electronic devices, immense power consumption has inevitably generated excessive heat. However, this heat generation causes the device failure and performance deterioration (Solid-State Electronics 1990, 33, 553; IEEE Transactions on Electron Devices 1966, ED-13, 763). Thus, thermal management in electronic devices is of significant importance for enhancing device durability and for sustainable device performance.

[0007] For thermal management in electronic devices, such as central processing units (CPU) or light-emitting diodes (LED), and more recently for applications on electric vehicles, the conventional solution has employed a heat sink (or heat spreader) and thermal interface material (TIM). Typically, the heat sink is composed of a high thermally conductive metal such as copper (Cu) or aluminum-based material (Advanced Engineering Materials 2008, 10, 400; Engineering Science and Technology, an International Journal 2022, 27, 101019). These materials have performed good heat dissipation of structural standardized devices. Since thermal conductivities (K) of CU and aluminum (Al) are 401 and 429 W / mK (Journal of Physical and Chemical Reference Data 1972, 1, 279), respectively, heat can transport in the heat sink rapidly. Although the heat sink has high K, the rough interfaces on metal cause inefficient heat transfer due to air pockets between an electronic device and the heat sink. TIM has been employed to reduce thermal resistance between the electronic device and the heat sink to overcome the issue. Especially, considering the recent development of highly integrated electronic devices with sub 10 nm scale (IEEE Journal of the Electron Devices Society 2013, 1, 66), the role of TIM is crucial for thermal management in packaging the highly integrated electronic chip or heterogeneous integration. However, owing to the rigid structure of the heat sink and the leakage issue of TIM by mechanical stress, the conventional thermal management materials are hard to apply onto devices of various form factor such as foldable, wearable, and rollable devices. Especially in contrast to the traditional process of fabrication on a rigid substrate, such as a silicon (Si) wafer, flexible or wearable devices are fabricated on a soft substrate, such as a polyimide substrate. Thus, the design of thermal management materials, which require high heat dissipation performance under various mechanical stress, is essential.

[0008] To tackle these challenges, intensive efforts have been dedicated to polymer-based composite. A recent solution for these issues is employing thermally conductive filler / polymer composite. Fillers such as metal particles, carbon-based low dimensional materials, including graphene or carbon nanotube, liquid metal and hexagonal boron nitride provide a thermal transport path in polymer matrix (Scientific Reports 2020, 10, 14926; Journal of Applied Polymer Science 2012, 124, 669; Advanced Energy Materials 2021 , 11, 2101387; ACS Applied Materials & Interfaces 2018, 10, 34311 ; Advanced Materials 2022, 34, 2205120). The conventional composite has been prepared by the dispersion of thermally conductive fillers, such as aluminum oxide, aluminum nitride, silicon carbide, zinc oxide, or copper in a polymer matrix (Industrial & Engineering Chemistry Research 2018, 57, 3255; Polymers 2021 , 13, 3259; Materials 2020, 13, 1893; IEEE Transactions on Components, Hybrids, and Manufacturing Technology 1990, 13, 713; Journal of Applied Polymer Science 2003, 89, 2397; Journal of Applied Polymer Science 2012, 124, 669), and the K of these composites reaches ~7 W / mK. Although the higher filler contents provide the high thermal conductivity, the brittleness issue of the composite remains. Also, the drying issue with grease-type materials and low K has posed serious limitations to their thermal management in high-power electronic devices. Typically, the fillers used in these composites are low dimensional materials, which have high-aspect ratio, such as carbon nanotubes, graphene, and hexagonal boron nitride. However, due to their few micron-size dimension (in length or area) with one or a few atomthickness, the high anisotropy of K, ~10'1W / mK of through-plane K and ~103W / mK of in-plane K (Advanced Functional Materials 2015, 25, 4664; Advanced Materials 2014, 26, 4521 ; Carbon 2015, 94, 494; Journal of Materials Chemistry A 2014, 2, 16563; Nat. Mater. 2011 , 10, 569) is inevitable.

[0009] Recently, the vertical alignment of low-dimensional materials has been adopted to dissipate heat fluxing in through-plane direction. For example, various methods, such as magnetic field- assisted alignment (Advanced Materials 2022, 34, 2205120), freeze drying-assisted alignment (ACS Applied Materials & Interfaces 2017, 9, 13544), and mechanical machining process (ACS Nano 2019, 13, 11561), have been employed to align low-dimensional fillers, enhancing through-plane K. The complicated fabrication process and the requirement of external triggers for the alignment remain to be key limitations.

[0010] Since liquid metals have K ~30 W / mK and good processability with polymer via surface modification method (Chemical Science 2021 , 12, 2760; Applied Science and Manufacturing 2022, 163, 107216), liquid metal-based polymer composites have shown the potential in the thermal management of soft electronics. For example, eutectic gallium indium (EGaln) / polydimethylsiloxane (PDMS) composite was employed for heat dissipation of wearable LED (Proceedings of the National Academy of Sciences 2017, 114, 2143). Due to the deformability of the composite, the thermal transport of the composite was sustained under mechanical stress. However, the leakage of EGain under mechanical stress is an issue, which can be circumvented by the surface modified EGain nanoparticle elastomer (SMEE) composite as a thermal interface material (Advanced Energy Materials 2021 , 11, 2101387).

[0011] In addition, EGain can be utilized as an anchor role for thermal transport. Owing to the infinite deformation under mechanical stress and high electrical conductivity (a), liquid metals showed potential as an anchor role between metal flakes in the polymer composite, resulting in sustainable a (Advanced Materials 2018, 30, 1706157; Advanced Materials 2019, 31, 1805536; Nature Communications 2019, 10, 2158). For example, Cu particles and EGain composite was used as thermal interface materials for the thermal management of central processing unit (CPU) (Advanced Materials 2021, 33, 2103104). In the research, 3- chloropropyltriethoxysilane functionalization on Cu particles were employed for the effective thermal transport linker between Cu and EGain, resulting in 65.9 W / mK of K. Considering that the K is the sum of lattice K (Kiatuce) and electronic K (Keiectron) as determined by Eq. 1

[0012] K— Klatt ice"*" Keiectron” K|attice"*"LoT (Eq. 1), where L, o, and T are Lorenz number, electrical conductivity, and absolute temperature, respectively (Nano Letters 2020, 20, 989), liquid metal contained materials can contribute to higher Keiectron, due to the high o of liquid metals. However, since bulk liquid metal has noncrystalline structure (Advanced Functional Materials 2021 , 31, 2106397), there is a limit for higher K with liquid metal-contained materials because of lower Kiattice- Thus, improving lattice of liquid metal-contained material should be addressed for effective thermal management.

[0013] Paste or ink type composite can be an alternative for thermal management. Typically, the paste ink is composed of high electrically conductive inorganic materials such as silver (Ag) and organic binder. The ink has been utilized as an electrode material. In the case of conductive inks such as Ag pastes, the ink is mostly composed of metal filler and organic (or polymeric) binder. There have been several research utilizing silver paste as thermal interface material in electronic chip packaging (Journal of Electronic Materials 2007, 36, 1333). Since the silver has high thermal conductivity (-429 W / mK) (Journal of Physical and Chemical Reference Data 1972, 1, 279), the silver paste can be a good thermal interface material. Even though silver has high thermal conductivity, there are several obstacles when applied in deformable devices. As the o of the inks is -106S / m, the total K of the printed ink can be contributed by the Keiectron. However, owing to the low lattice of the non-crystalline structure of the binder (Acta Physica Academiae Scientiarum Hungaricae 1981 , 50, 321), the total K may be sacrificed. In practical, the Ag filler / epoxy composite inks showed the potential in thermal management (Advanced Materials 2023, 35, 2211100; Mechanics of Materials 2009, 41, 1116; Journal of Applied Physics 2012, 111, 104310). However, due to the limited thermal transport network in the composite, the K was restricted (-27 W / mK).

[0014] To circumvent the issue, the binder-free Ag paste after the hot pressing or sintering process was adopted, and it has high K ( -240 W / mK) (ACS Applied Materials & Interfaces 2015, 7, 9157; Materials Letters 2022, 311, 131603). However, the microporous Ag structure is formed during sintering process (Journal of Alloys and Compounds 2016, 687, 486; Materials Science and Engineering: A 2016, 669, 379). Based on the numerical calculation, the K of 50% porosity of sintered Ag showed about 50% of K compared to that of 0% porosity of sintered Ag (IEEE Transactions on Electron Devices 2023, 70, 702). Since the porosity is thermally insulative, the low K caused. Besides, binding-free materials are brittle and difficult to use in soft electronics.

[0015] In this perspective, nanoparticle decoration on Ag particles / poly vinyl butyral (PVB) binder composite ink can be a viable solution. EGain nanoparticles can be a candidate for filling the voids, due to a convenient processability from bulk EGain into EGain nanoparticles (ultrasonic process). Besides, the electrochemical reactivity (galvanic replacement) between EGain nanoparticles and metals, which can form the alloy, can help anchor the Ag particles, forming an interconnected pathway as thermal transport junction. Since PVB binder is useful for bonding to metal or ceramic materials (Journal of the European Ceramic Society 2000, 20, 1375; Journal of The Electrochemical Society 2019, 166, A5275), a highly bindable PVB serves to provide the mechanical stability. Summary of Invention

[0016] It has been surprisingly found that an ink composition suitable for additive manufacture can be prepared that comprises thermal management components. The ink composition may be printed onto a substrate (e.g. a soft / flexible substrate, though rigid substrates may also be sued) and sintered to form a thermal management layer on the substrate for high heat dissipation performance. The resulting thermal management layer has a high thermal conductivity, it is also electrically conductive as well as being mechanically stable.

[0017] In summary, we successfully fabricated thermally and electrically conductive ink for soft electronics. Ag flake and EGain nanoparticle were employed as fillers, and PVBwas employed as the binder in the ink (FIG. 1). In detail, since the standard reduction potentials of Ga3+ / Ga, I n3+ / l n, and Ag+ / Ag are -0.56, -0.34, and 0.7996 V Journal of the American Chemical Society 2020, 142, 19283; Journal of the American Chemical Society 1936, 58, 2647), respectively, EGain nanoparticles can be attached to the surface of metal which higher reduction potential. The EGain nanoparticles were decorated on the Ag flakes via the galvanic replacement, resulting in the bimetallic formation on the surface of Ag flakes, such as Ag-Ga and Ag-ln alloy. Notably, the glass transition temperature of invented ink (Tg) was lower than that of Ag flake.

[0018] The prepared ink was readily printed on the substrate, such as polyimide or PDMS base elastomer. The sintering process of the printed samples result in enhanced thermal and electrical conductivity. The thermal transport junctions between the decorated Ag flakes results in a high thermal conductivity (-140 W / mK). In addition, owing to the well-connected metal fillers, the high electrical conductivity (-106S / m) has be obtained.

[0019] Since the PVB, which has a good adhesion property on a substrate such as SiO2, polydimethylsiloxane (PDMS), or polyimide, played as a binder role in the composite, the printed ink has good adhesion on these substrates. Especially, due to the PVB binder, the printed ink exhibited good mechanical stability. Thus, the thermal conductivity and electrical conductivity of the invented material were sustainable under cyclic bending. When the cyclic bending test of the printed composite was conducted up to 104cycles, there was no physical damage on the printed composite and significant loss of thermal and electrical conductivity.

[0020] By employing the invented material, the heat dissipation of various form factor devices such as wearable, rollable, and bendable devices is practical. Traditionally, the heat dissipation of electronic devices has been conducted by heat sink and thermal paste. However, these components are not suitable in deformable devices. Since the invented material is printable and has high thermal conductivity and mechanical stability, the heat dissipation layer on soft and free standing substrate can be printed.

[0021] One of the practical application of the invention is LED heat dissipation. Benefiting from the thermal conductivity, electrical conductivity, and mechanical stability of the developed ink, we demonstrated the thermal management of LED devices with the developed ink. When the LED heat dissipation performance with the invention was conducted, a better heat dissipation performance was shown compared to that of commercial thermal paste and conductive Ag paste. When we surveyed the temperature change of the LED installed on printed ink, the temperature was saturated at approximately 343 K, and the temperature was lower than that of commercial materials, such as Ag and thermal paste. In addition, when the invented ink was printed on the the thermally conductive PDMS based elastomer composite substate, the good heat dissipation performance of LED was shown. Especially, the invented ink can serve as an additional thermal transport layer and an electron transport line on the thermally conductive elastomer, which is electrically insulative. This invention showed better LED heat dissipation performance than the Al-based rigid heat sink. Accordingly, the invention is critically essential for the next generation thermal management of deformable electronic devices, as demonstrated successfully.

[0022] In addition, we showed the flexible thermal management solution with thermally conductive elastomer and the developed ink. Employing this thermal management solution, we showed the generated heat from LED was dissipated under deformation. Notably, the thermal management solution enhanced the lifetime of the LED compared to the lifetime of the LED with the Al plate. We anticipate that our strategy provides an effective strategy for thermal management in soft electronics.

[0023] Aspects and embodiments of the invention will now be discussed by Reference to the following numbered clauses.

[0024] 1. An ink formulation for additive manufacturing comprising: a polymeric binder material; a dispersant; a thinner; nanoparticles of eutectic gallium indium (EGain); and silver flakes. 2. The ink formulation according to Clause 1, wherein a surface of the silver flakes is decorated with EGain nanoparticles.

[0025] 3. The ink formulation according to Clause 2, wherein the surface of the silver flakes further comprises crystalline regions of Ag2ln and crystalline regions of AgsGa2.

[0026] 4. The ink formulation according to any one of the preceding clauses, wherein: the polymeric binder material is present in an amount of from 2 to 10 wt%; the thinner is present in an amount of from 1 to 8 wt%; the dispersant is present in an amount of from 0.1 to 1 wt% the EGain nanoparticles are present in an amount of from 5 to 50 wt%; the silver flakes are present in an amount of from 40 to 91.9 wt%.

[0027] 5. The ink formulation according to Clause 4, wherein: the polymeric binder material is present in an amount of from 4 to 6 wt%; the thinner is present in an amount of from 2 to 4 wt%; the dispersant is present in an amount of from 0.2 to 0.6 wt% the EGain nanoparticles are present in an amount of from 10 to 45 wt%; the silver flakes are present in an amount of from 45 to 83.8 wt%.

[0028] 6. The ink formulation according to Clause 5, wherein one or more of the following apply:

[0029] (a) the polymeric binder material is present in an amount of about 5.56 wt%;

[0030] (b) the thinner is present in an amount of about 3.94 wt%;

[0031] (c) the dispersant is present in an amount of about 0.5 wt%

[0032] (d) the EGain nanoparticles are present in an amount of from 10 to 45 wt%, such as from

[0033] 10 to 30 wt%, such as about 20 wt%; and

[0034] (e) the silver flakes are present in an amount of from 45 to 83.8 wt%, such as from 60 to 80 wt%, such as about 70 wt%.

[0035] 7. The ink formulation according to any one of the preceding clauses, wherein one or more of the following apply:

[0036] (ai) the polymeric binder material is polyvinyl butyral (PVB);

[0037] (aii) the thinner is terpineol;

[0038] (aiii) the dispersant is acrylic acid.

[0039] 8. The ink formulation according to any one of the preceding clauses, wherein the ink formulation is formed from: 5.56 wt% of PVB as polymeric binder material;

[0040] 3.94 wt% of terpineol as thinner;

[0041] 0.5 wt% of acrylic acid as dispersant; and one of:

[0042] (bi) 20 wt% of EGain nanoparticles and 70 wt% of silver flakes;

[0043] (bii) 10 wt% of EGain nanoparticles and 80 wt% of silver flakes;

[0044] (bii) 30 wt% of EGain nanoparticles and 60 wt% of silver flakes; and

[0045] (bii) 45 wt% of EGain nanoparticles and 45 wt% of silver flakes.

[0046] 9. The ink formulation according to any one of the preceding clauses, wherein after additive manufacture printing and sintering of the printed material, the sintered material displays one or more of:

[0047] (ci) an in-plane thermal conductivity of from 30 to 160 W / mK;

[0048] (cii) a through plane thermal conductivity of from 4 to 10 W / mK; and

[0049] (ciii) a conductivity of greater than 105S / m, such as greater than 106S / m.

[0050] 10. A thermal management material, comprising: a substrate; and a sintered layer of the ink formulation as described in any one of Clauses 1 to 9 on the substrate.

[0051] 11. The thermal management material according to Clause 10, wherein the substrate is formed from glass, a silicone polymer or a polyimide.

[0052] 12. The thermal management material according to Clause 10 or Clause 11 , wherein the thermal management material is a flexible thermal management material (e.g. the substrate is a silicone or a polyimide).

[0053] 13. A method of forming a thermal management material as described in any one of Clauses 10 to 12, the method comprising the steps of:

[0054] (i) providing an unsintered material comprising: a substrate; and an unsintered layer of the ink formulation as described in any one of Clauses 1 to 9 on the substrate; and

[0055] (ii) sintering the unsintered material at an elevated temperature for a period of time under an inert atmosphere. 14. The method according to Clause 13, wherein the unsintered material is obtained by applying the ink formulation onto the substrate by an additive manufacturing process.

[0056] 15. The method according to Clause 13 or Clause 14, wherein one or more of the following apply:

[0057] (di) the period of time is from 10 minutes to 2 hours, such as about 30 minutes;

[0058] (dii) the inert atmosphere is argon; and

[0059] (dii) the temperature is from 350 to 600 K, such as from 450 to 580 K, such as about 573 K.

[0060] 16. An electrical device, comprising at least one component that draws electrical energy attached to a thermal management material as described in any one of Clauses 10 to 12.

[0061] 17. The electrical device according to Clause 16, wherein the at least one component that draws electrical energy is a light emitting diode.

[0062] Drawings

[0063] FIG. 1 depicts the schematic illustration of preparation of the EGain nanoparticle decorated Ag flake / PVB composite ink.

[0064] FIG. 2 depicts the schematic illustration of fabrication process of EGain nanoparticle decorated Ag flake / PVB composite ink for flexible thermal management.

[0065] FIG. 3 depicts the size distribution histogram of EGain nanoparticles.

[0066] FIG. 4 depicts the energy-dispersive X-ray spectroscopy (EDS) mapping with transmission electron microscopy (TEM) of Ag70LM20 (scale bar: 200 nm).

[0067] FIG. 5 depicts the cross sectional Scanning Electron Microscopy (SEM) images of Ag80Lm10, Ag70LM20, Ag60LM40, and Ag45LM45.

[0068] FIG. 6 depicts the X-ray diffraction (XRD) spectra of Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, and Ag45LM45 after the sintering process.

[0069] FIG. 7 depicts the X-ray photoelectron spectroscopy (XPS) spectra of (a) Ag 3d region of Ag90LM0(top), Ag70LM20 before the sintering process (middle), and Ag70LM20 after the sintering process (bottom); (b) Ga 2p region of EGain nanoparticles (top), Ag70LM20 before the sintering process (middle), and Ag70LM20 after the sintering process (bottom); and (c) In 3d region of EGain nanoparticles (top), Ag70LM20 before the sintering process (middle), and Ag70LM20 after the sintering process (bottom).

[0070] FIG. 8 depicts (a) the schematic illustration of in-plane thermal diffusivity characterization, and (b) measured temperature wave of Ag90LM0.

[0071] FIG. 9 depicts (a) the schematic illustration of through-plane thermal conductivity; and (b) the position dependent temperature of Ag90LM0 before the sintering process (T 1 : temperature of Cu block at 5 mm from hot side, T2: temperature of Cu block at 15 mm from hot side, T3: temperature of Cu block at 15 mm from cold side, and T4: temperature of Cu block at 5 mm from cold side).

[0072] FIG. 10 depicts (a) the in-plane thermal conductivity and (b) the through-plane thermal conductivity of Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, Ag45LM45, Ag0LM90, and AgOLMO (PVB); and (c) electrical conductivity of Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, and Ag45LM45.

[0073] FIG. 11 depicts the cross sectional SEM images of (a) Ag90LM0, (b) Ag80LM10, (c) Ag70LM20, (d) Ag60LM30, (e) Ag45LM45, and (f) Ag0LM90 after the sintering process. All scale bars indicate 20 pm.

[0074] FIG. 12 depicts the XRD spectra of (top) Ag70LM20 before the sintering process and (bottom) Ag70LM20 after the sintering process.

[0075] FIG. 13 depicts (a) the optical photo image of Ag70LM20 printed polyimide film (left: before bending; right: after 10,000 cycle bending); and (b) the optical photo images of bending test.

[0076] FIG. 14 depicts bending cycle dependent (a) in-plane thermal conductivity, (b) sheet resistance, and (c) normalised sheet resistance and thermal conductivity of printed Ag70LM20 on the polyimide substrate.

[0077] FIG. 15 depicts (a) the as prepared printed Ag70LM20 on a polyimide substrate (sample on the top left figure), 10000 times cyclic bending tested Ag70LM20 on the polyimide substrate (sample on the top right figure) (scale bar: 2 cm), and LED installed film (bottom); and (b) optical and schematic images of cyclic bending test. FIG. 16 depicts (a) the time dependent temperature of LED with Ag70LM20, commercial Ag paste, and commercial thermal paste printed polyimide films, and (b) the infrared (IR) images of LED temperature change with Ag70LM20, commercial Ag paste, and commercial thermal paste printed polyimide films as a function of time.

[0078] FIG. 17 depicts the optical image of surface modified EGain nanoparticle elastomer (SMEE) (left) and Ag70LM20 printed SMEE (SMEE / Ag70LM20)(right). (Scale bar: 2 cm)

[0079] FIG. 18 depicts (a) the time-dependent LED temperature change with SMEE, SMEE / Ag70LM20, Al heat sink, and VHB film; and (b) the IR images of LED temperature change with SMEE, SMEE / Ag70LM20, Al heat sink, and VHB film.

[0080] FIG. 19 depicts the optical image of electron transport line (Ag70LM20) printed SMEE / Ag70LM20. (scale bar: 1cm)

[0081] FIG. 20 depicts (a) optical images of LED with SMEE, SMEE / Ag70LM20, Al plate, and VHB film (scale bar: 2 cm); and (b) time dependent infrared images of LED with SMEE, SMEE / Ag70LM20, Al plate, and VHB film (scale bar: 2 cm).

[0082] FIG. 21 depicts the lifetime simulated result of LED with SMEE, SMEE / Ag70LM20, Al plate, and VHB film.

[0083] FIG. 22 depicts the normalized lifetime divided by LED’s lifetime with Al plate of LED with SMEE, SMEE / Ag70LM20, Al plate, and VHB film (A: SMEE / Ag70LM20, B: SMEE, C: Al plate, and D: VHB film)

[0084] FIG. 23 depicts the optical images of flexible LED array with SMEE / Ag70LM20 on cylinder feature and the infrared image during the operation (scale bar: 2 cm).

[0085] FIG. 24 depicts the optical image of LED array on SMEE / Ag70LM20 (left) and schematic image of LED array configuration.

[0086] Description

[0087] In this invention, high thermal conductive, electrically conductive, mechanically stable, and printable ink composite was successfully fabricated. Notably, by employing galvanic replacement mechanism, liquid metal particles were decorated on silver flakes. After sintering process, the decorated particles formed thermal transport junction between large domains of Ag flakes, resulting in high thermal conductivity. Besides, owing to the included polymer binder, the printed ink showed good adhesion properties on various substrates, including glass, polyimide, and polydimethylsiloxane based composite, and exhibited mechanical stability under cyclic bending.

[0088] In a first aspect of the invention, there is provided an ink formulation for additive manufacturing comprising: a polymeric binder material; a dispersant; a thinner; nanoparticles of eutectic gallium indium (EGain); and silver flakes.

[0089] In embodiments herein, the word “comprising” may be interpreted as requiring the features mentioned, but not limiting the presence of other features. Alternatively, the word “comprising” may also relate to the situation where only the components / features listed are intended to be present (e.g. the word “comprising” may be replaced by the phrases “consists of” or “consists essentially of”). It is explicitly contemplated that both the broader and narrower interpretations can be applied to all aspects and embodiments of the present invention. In other words, the word “comprising” and synonyms thereof may be replaced by the phrase “consisting of’ or the phrase “consists essentially of’ or synonyms thereof and vice versa.

[0090] The phrase, “consists essentially of’ and its pseudonyms may be interpreted herein to refer to a material where minor impurities may be present. For example, the material may be greater than or equal to 90% pure, such as greater than 95% pure, such as greater than 97% pure, such as greater than 99% pure, such as greater than 99.9% pure, such as greater than 99.99% pure, such as greater than 99.999% pure, such as 100% pure.

[0091] As used herein, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a composition” includes mixtures of two or more such compositions, reference to “the catalyst” includes mixtures of two or more such catalysts, and the like.

[0092] The term “thinner” as used herein refers to its chemical use. That is a thinner is a volatile solvent that is used as a diluent and may help to provide an ink formulation with a suitable viscosity for use in additive manufacturing (e.g. screen printing). Any suitable material may be used herein as a thinner. For example, the thinner may be a terpineol.

[0093] In embodiments of the invention, the EGain nanoparticles may decorate a surface of the silver flakes. Without wishing to be bound by theory, the decoration of the surface of the silver flakes may result in the formation of hybrid crystalline regions. As such, in embodiments of the invention, the surface of the silver flakes may further comprise crystalline regions of Ag2ln and crystalline regions of AgsGa2.

[0094] In embodiments of the invention, the ink formulation may be one in which: the polymeric binder material is present in an amount of from 2 to 10 wt%; the thinner is present in an amount of from 1 to 8 wt%; the dispersant is present in an amount of from 0.1 to 1 wt% the EGain nanoparticles are present in an amount of from 5 to 50 wt%; and the silver flakes are present in an amount of from 40 to 91.9 wt%.

[0095] In embodiments of the invention, the ink formulation may be one in which: the polymeric binder material is present in an amount of from 4 to 6 wt%; the thinner is present in an amount of from 2 to 4 wt%; the dispersant is present in an amount of from 0.2 to 0.6 wt% the EGain nanoparticles are present in an amount of from 10 to 45 wt%; and the silver flakes are present in an amount of from 45 to 83.8 wt%.

[0096] In embodiments of the invention, the ink formulation may be one in which:

[0097] (a) the polymeric binder material is present in an amount of about 5.56 wt%;

[0098] (b) the thinner is present in an amount of about 3.94 wt%;

[0099] (c) the dispersant is present in an amount of about 0.5 wt%

[0100] (d) the EGain nanoparticles are present in an amount of from 10 to 45 wt%, such as from 10 to 30 wt%, such as about 20 wt%; and

[0101] (e) the silver flakes are present in an amount of from 45 to 83.8 wt%, such as from 60 to 80 wt%, such as about 70 wt%.

[0102] Any suitable polymeric binder material may be used in the ink formulations described herein. As will be appreciated, the binder forms a polymeric matrix following additive manufacture printing and forms the bulk of the ink formulation. As such, the binder may provide mechanical stability. It may be selected from any suitable polymeric material that can be subjected to formulation to provide an ink suitable for additive manufacture and which can then be subjected to sintering to provide a desired end product. A suitable binder material that may be mentioned herein, is polyvinyl butyral (PVB), though other materials may be used in its place, provided that said material has similar properties. For example, other polymeric binder materials that may be mentioned herein include, but are not limited to a polymeric material that contains hydroxyl groups, such as a polyvinyl alcohol (P A) and PVA-copolymers.

[0103] As noted above, the thinner may be chosen to be one suitable to act as a diluent and which may assist in providing the ink with a viscosity that enables additive manufacture. A suitable thinner that may be mentioned herein may be terpineol. This may be a specific isomer of terpineol or a mixture of said isomers.

[0104] The term “dispersant” when used herein refers to a material that is intended to improve the separation of particles within the ink formulation and prevent their settling or clumping together. A suitable dispersant that may be mentioned herein may be acrylic acid, though any material that can achieve a similar function may be used herein.

[0105] In particular embodiments of the invention that may be mentioned herein, the ink formulation may be formed from:

[0106] 5.56 wt% of PVB as polymeric binder material;

[0107] 3.94 wt% of terpineol as thinner;

[0108] 0.5 wt% of acrylic acid as dispersant; and one of:

[0109] (bi) 20 wt% of EGain nanoparticles and 70 wt% of silver flakes;

[0110] (bii) 10 wt% of EGain nanoparticles and 80 wt% of silver flakes;

[0111] (bii) 30 wt% of EGain nanoparticles and 60 wt% of silver flakes; and

[0112] (bii) 45 wt% of EGain nanoparticles and 45 wt% of silver flakes.

[0113] The ink formulation disclosed herein is intended for additive manufacture and the resulting additive manufactured article may then be subjected to sintering in order to provide a final product. The term “sintering” in this context may refer to subjecting the additive manufactured article to an elevated temperature (e.g. 573 K or 300 °C) for a suitable period of time (e.g. 30 minutes). This sintering process may help improve the electrical and thermal conductivity of the additive manufactured article. Thus, after additive manufacture printing and sintering of the printed material, the sintered material may display one or more of:

[0114] (ci) an in-plane thermal conductivity of from 30 to 160 W / mK;

[0115] (cii) a through plane thermal conductivity of from 4 to 10 W / mK; and (ciii) a conductivity of greater than 105S / m, such as greater than 106S / m.

[0116] In a second aspect of the invention, there is provided a thermal management material, comprising: a substrate; and a sintered layer of the ink formulation as described herein on the substrate.

[0117] The substrate may be any suitable substrate material. As will be appreciated, it should be a material that can withstand the sintering conditions that are intended to be applied to the ink formulation following additive manufacture printing. Suitable substrates include, but are not limited to, glass, a silicone polymer or a polyimide. It will be noted that it may be preferred to make use of flexible substrate materials, so as to allow for the use of the thermal management material in a flexible electronic device, but it will be equally appreciated that the ink may be printed on any suitable substrate for a range of applications using rigid substrates too. Nevertheless, in certain embodiments of the invention, the thermal management material may be a flexible thermal management material (e.g. the substrate is a silicone or a polyimide).

[0118] In a further aspect of the invention, there is provided a method of forming a thermal management material as described herein, the method comprising the steps of:

[0119] (i) providing an unsintered material comprising: a substrate; and an unsintered layer of the ink formulation as described hereinbefore on the substrate; and

[0120] (ii) sintering the unsintered material at an elevated temperature for a period of time under an inert atmosphere.

[0121] As will be appreciated, the unsintered material of step (i) may be obtained by applying the ink formulation onto the substrate by an additive manufacturing process.

[0122] The sintering process may make use of any suitable period of time, any suitable temperature and any suitable inert atmosphere. In certain embodiments of the invention, one or more of the following may apply:

[0123] (di) the period of time is from 10 minutes to 2 hours, such as about 30 minutes;

[0124] (dii) the inert atmosphere is argon; and

[0125] (dii) the temperature is from 350 to 600 K, such as from 450 to 580 K, such as about 573 K. In yet a further aspect of the invention, there is provided an electrical device, comprising at least one component that draws electrical energy attached to a thermal management material as described hereinbefore. This may be any suitable component or components and examples of these are provided in the examples section below. As an example, the at least one component that draws electrical energy may be a light emitting diode.

[0126] In particular embodiments of the invention, the ink composition may be one that comprises polyvinyl butyral (PVB), acrylic acid, terpineol, ethanol, eutectic gallium indium (EGain) and silver (Ag) flakes.

[0127] A thermal management material may be formed from the ink composition following additive manufacture and sintering. The thermal management material may be one that comprises: a) a thermal management layer on a flexible substrate (polyimide); and b) the thermal management layer comprises PVB, EGain particles on Ag flakes.

[0128] Also disclosed herein is a method to prepare an ink composition, comprising the steps of: c) dissolving polyvinyl butyral and acrylic acid in ethanol at 333 K for 10 min to form a solution and cooling the solution to 300 K; d) adding EGain nanoparticles (liquid phase) into the solution to form mixture (A) and subjecting mixture (A) to ultrasonication at 300 W for 60 min; and e) adding Ag flakes and terpineol into mixture (A) to form mixture (B), and subjecting mixture (B) to ultrasonication at 300 W for 60 min.

[0129] A method to fabricate a thermal management material, comprising the steps of: f) subjecting the ink composition of features (c) - (e) to evaporation to remove most of the ethanol to obtain a viscous ink; g) printing the ink composition onto a substrate to form an ink-coated substrate; and h) subjecting the ink-coated substrate to a sintering process at 573 K for 30 min in Argon atmosphere to form the thermal management material.

[0130] PVB (as a binder), may have a good adhesion property on a substrate such as SiC>2, polydimethylsiloxane (PDMS), or polyimide.

[0131] After the sintering process, the decorated EGain particles may form a thermal transport junction between large domains of Ag flakes, resulting in high thermal conductivity. Besides, owing to the included polymer binder (e.g. PVB), the printed ink may show good adhesion properties on various substrates, including glass, polyimide, and polydimethylsiloxane-based composites, and exhibit mechanical stability under cyclic bending. While EGain particles are mainly formed on the Ag flakes, there may be presence of intermetallic AgGa and Agin alloys formed at the interface between the interface of the thermal management layer and the substrate.

[0132] Some advantages of the current invention may include one or more of the following.

[0133] 1. Owing to the ink-liked properties of the invented material, it is possible to make customized patterning of thermal management layer by methods of printing (e.g. screen-printing).

[0134] 2. The EGain nanoparticle can be decorated on metal flakes by galvanic replacement mechanism, and the nanoparticles can be a thermal transport junction between Ag flakes with a further sintering process in an inert atmosphere.

[0135] 3. Since the composite ink contains a binder (e.g. PVB), the ink can be printed on various substrates, and printed ink is good adhesive on the substrate.

[0136] 4. When the invented material is printed on the free-standing thermally conductive elastomer, the synergetic heat dissipation performance can be obtained.

[0137] 5. When mechanical stress such as cyclic bending was applied, there is no significant sacrificing of thermal conductivity and electrical conductivity. Thus, the heat dissipation with various form factor devices is possible.

[0138] The current invention can be applied in heat dissipation of electronic devices. Emerging devices with various form-factors such as wearable, foldable, and rollable devices demand mechanically stable thermal management materials. Since the various form factor devices are subjected to mechanical stress, the mechanically stable heat dissipation layer is required. Thus, the invention can be used in foldable mobile or packaging of deformable electronic devices. Especially, since the invention can be printed on various substrates such as glass, polyimide, and elastomer composite, printing on the thermally conductive substrate can provide the synergetic effect of heat dissipation. In addition, owing to the high electrical conductivity, the invention can be utilized in electromagnetic interference (EMI) shielding or radio frequency (RF) power transmission. Notably, due to the high thermal conductivity, thermal manageable EMI shielding or RF power transmission can be practical with the invention.

[0139] Owing to the nanoparticles chemically anchored and formed alloys on the surface of Ag flakes, the effective thermal transport junctions between Ag flakes were formed, resulting in high inplane K (-142 W / mK), and high electrical conductivity of the printed ink (-10® S / m). In addition, incorporating polymer binders (PVB) helped enhance the printed ink's mechanical stability and adhesion on a substrate, such as polyimide. When the cyclic bending test of the printed ink on a polyimide substrate was conducted up to 104times, the thermal and electrical resistance were sustainable. The prepared ink showed the good heat dissipation performance of LED device. The comparative heat dissipation test between our printed ink and commercial Ag paste / thermal paste, showed better performance of our printed ink for heat dissipation of LED during the operation. Notably, the flexibility of the flexible bilayer heat sink composed of the developed ink and thermally conductive elastomer exhibited long-lifetime of the LED device. This validates that this invention can be utilized in the thermal management of various form factor devices. The current approach provides the solution for thermal management in next-generation soft electronics.

[0140] Further aspects and embodiments of the invention will now be described by reference to the following non-limiting examples.

[0141] Examples

[0142] The following examples are provided for easier understanding of the present invention. For example, eutectic gallium indium alloy, silver flake, polyvinyl butyral, terpineol, and acrylic acid have been employed for the preparation of thermal management ink. However, the contents of the present invention are no limited thereto.

[0143] Materials

[0144] EGain was purchased from Smart Memories Pte. Ltd., Singapore. Silver (Ag) flake (~10 pm ), polyvinyl butyral (PVB), terpineol, and acrylic acid (99%) were purchased from Sigma-Aldrich. Commercial thermal paste (TC-5121) was purchased from Dow Corning. Commercial Ag paste (PELCO Conductive Silver paint) was purchased from TED PELLA, Inc.

[0145] Example 1. Preparation of Ink and Screen Printing Process

[0146] FIG. 2 illustrates the schematic approach of the preparation of the thermally and electrically conductive ink. As an example of such preparation, Ag flake and EGain nanoparticle were selected as metal fillers. Owing to the high electrical (6 x 107S / m) and thermal conductivity (430 W / mK) of Ag (Journal of Physical and Chemical Reference Data 1972, 1, 279; Journal of Physical and Chemical Reference Data 1979, 8, 1147), Ag flake (~10 pm) was adopted for the large domain filler in the composite. Also, the EGain nanoparticle was employed for the additive filler due to the influential role as anchor between metal flakes, such as Ag and Ni flakes. The prepared ink can then be printed on a substrate via the screen-printing method.

[0147] Preparation of EGain Nanoparticle Decorated Ag Flake Ink

[0148] The ink was composed of EGain (Smart Memories Pte. Ltd., Singapore) nanoparticle, Ag flake (Sigma-Aldrich, ~10 pm), polymer binder (polyvinyl butyral, PVB, Sigma-Aldrich), thinner (terpineol, Sigma-Aldrich), and dispersant (acrylic acid, Sigma-Aldrich).

[0149] The weight ratio of the ink was 90 (metal filler (EGain and Ag flake)), 5.56 (polymer binder (PVB)), 3.94 (thinner (terpineol)), and 0.5 (dispersant (acrylic acid)) wt%. The weight ratio between Ag flake and EGain was further tuned.

[0150] This viscous ink prepared by the protocol below is denoted as Ag70LM20, which is 70 and 20 wt% of Ag flake and EGain, respectively. Similarly, Ag80LM10, Ag60LM30, and Ag45LM45 were prepared by following the same protocol. When the ink composed of Ag flakes without liquid metal, it is denoted as Ag90LM0.

[0151] 0.278 g of PVB and 25 mg of acrylic acid were dissolved in 25 ml of ethanol at 333 K for 10 min. After cool down to 300 K, 1 g of EGain was added to the solution, followed by probe ultrasonic process at 300 W for 60 min. In this process, the bulk EGain was split into EGain nanoparticles.

[0152] Next, 3.5 g of Ag flakes and 0.197 g of terpineol were added to the mixture, and the probe ultrasonic process was repeated at 300 W for 60 min. Then, most of the ethanol in the mixture was evaporated by rotary evaporation to afford a viscous ink This viscous ink is Ag70LM20, which is 70 wt% of Ag flake and 20 wt% of EGain. Similary, Ag80LM10, Ag60LM30, and Ag45LM45 were prepared by same protocol.

[0153] Printing Process

[0154] The viscous ink was printed on substrates such as glass, polyimide film, or surface modified EGain elastomer, which is illustrated in our previous research (Advanced Energy Materials 2021 , 11, 2101387). During the printing process, a spacer with 50 pm of thickness was used, and the thickness of printed ink was approximately 25 pm. After printing, the sintering process was conducted at 573 K for 30 min in Ar atmosphere. Determination of Size Distribution of Particles by Dynamic Light Scattering (DLS)

[0155] The size distribution of EGain particles was measured by the dynamic light scattering method (SZ-100, HORIBA).

[0156] Results and Discussions

[0157] The incorporation of metal fillers with polyvinyl butyral (PVB) binder was employed. In the ink composite, the metal fillers provide the thermal and electrical transport paths, and the PVB provides the mechanical stability of the printed ink composite. The viscosity of the prepared inks was about ~104cP, (Table 1). The prepared ink composite can be printed on substrates such as SiC>2, polydimethylsiloxane (PDMS) composite, or polyimide (PI). The printed ink achieves higher electrical and thermal conductivity upon sintering.

[0158] Table 1. Viscosity of Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, Ag45LM45, and Ag0LM90 at shear rate of 1 s’1.

[0159] Sample Ag90LM0 Ag80LM10 Ag70LM20 Ag60LM30 Ag45LM45 Ag0LM90

[0160] Viscosity

[0161] 19543 24414 12237 28486 19676 61444

[0162] (cP)

[0163] We conducted two step ultrasonic process for dispersion of metal fillers. The first step is the preparation of the EGain nanoparticles. Typically, the ultrasonic process is known as an effective way to split bulk EGain into colloidal EGain nanoparticles (Advanced Materials 2015, 27, 2355). In ethanol containing PVB, acrylic acid, and terpineol, the EGain nanoparticles were dispersed. The average size of EGain nanoparticles obtained was approximately 250 nm, and the size distribution was confirmed by dynamic light scattering method (FIG. 3).

[0164] The second step of ultrasonic process was conducted with incorporation of Ag flakes. In the second ultrasonic process, the galvanic replacement between Ag flake and EGain nanoparticle occurred, resulting in the decoration of EGain nanoparticles on Ag flakes. The galvanic replacement is an electrochemical reaction for alloy preparation, and the driving force of the galvanic replacement is the different standard reduction potential between metals (Chemical Reviews 2021 , 121, 736). In detail, the standard reduction potentials of -0.529 V (Ga3+ / G°) , -0.340 V (ln3+ / ln°), and 0.799 V (Ag+ / Ag°) were considered in this reaction (Journal of the American Chemical Society 2017 , 139, 1464; Standard Potentials in Aqueous Solution, CRC Press, New York 1985). Typically, dissolved oxygen in reaction media made the Ag flakes partially oxidized as Ag2O (Materials Today Advances 2020, 5, 100037), and the Ag+in the Ag2O can be released readily during the ultrasonic process (Langmuir 2012, 28, 15929). Thus, the redox reaction between Ga (or In) and Ag+can occur as represented respectively by Eq. 2 or Eq. 3.

[0165] Ga°+3Ag+->• Ga3++3Ag° (Eq. 2)

[0166] Ag++ln° — 3Ag°+ln3+(Eq. 3)

[0167] Due to the reaction, alloys such as Ag-Ga and Ag-ln can be obtained.

[0168] After the second step, most of the solvent was evaporated for the viscous ink, and the prepared ink can be printed on a substrate via the screen-printing method. After printing, the sintering process was carried out at 573 K for 30 min in Ar atmosphere.

[0169] In this example, we fixed filler contents (Ag flake and EGain nanoparticle) as 90 wt%. We prepared different weight ratios between EGain nanoparticle and Ag flake for Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, Ag45LM45, and Ag0LM90 (Table 2), which indicate 90 wt% of Ag flake (0 wt% of EGain nanoparticle), 80 wt% of Ag flake (10 wt% of EGain nanoparticle), 70 wt% of Ag flake (20 wt% of EGain nanoparticle), 60 wt% of Ag flake (30 wt% of EGain nanoparticle), and 45 wt% of Ag flake (45 wt% of EGain nanoparticle), respectively.

[0170] Table 2. Weight ratio between EGain nanoparticle and Ag flake for Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, Ag45LM45, and Ag0LM90.

[0171] Sample Ag90LM0 Ag80LM10 Ag70LM20 Ag60LM30 Ag45LM45 Ag0LM90

[0172] Ag Flake

[0173] 90 80 70 60 45 0

[0174] (wt%)

[0175] EGain 0 10 20 30 45 90

[0176] (wt%)

[0177] Example 2. Morphology and Crystalinty of the EGain Decorated Ag Flakes

[0178] Here, we investigated the morphology of the EGain nanoparticle decorated Ag flake.

[0179] Scanning Electron Microscopy (SEM)

[0180] Scanning electron microscopy was characterized by FESEM 7600F (JEOL).

[0181] Transmission Electron Microscopy (TEM)

[0182] The transmission electron microscopy (TEM) images were obtained by the JEOL 21 OOF. Energy Dispersive X-Ray Spectroscopy (EDS)

[0183] To investigate the crystallinity of the printed ink, X-ray diffraction (XRD, D8 Discover, Broker) was employed.

[0184] X-ray photoelectron spectroscopy (XPS)

[0185] The X-ray photoelectron spectroscopy (XPS, AXIS Supra+, Shimadzu) was used for investigation of chemical bonding state of the printed ink.

[0186] X-ray diffraction (XRD)

[0187] To investigate the crystallinity of the printed ink, X-ray diffraction (XRD, D8 Discover, Bruker) was employed.

[0188] Rheology Test for Viscosity Determination

[0189] Rheology test (viscosity) was conducted by rheometer. (MCR 302e, Anton Paar)

[0190] Results and Discussions

[0191] To investigate morphologies of the printed composite without sintering, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) were employed. FIG. 4 shows the energy-dispersive X-ray spectroscopy (EDS) mapping with transmission electron microscopy (TEM) of Ag70LM20. The large flake shape was composed of Ag. Some nanoparticles were detected on the surface of the Ag flake, the particles were composed of Ga and In, which indicate that the particles are EGain nanoparticles and / or related compounds. It is shown that EGain nanoparticles were decorated on the Ag flake. From the Energy Dispersive X-Ray Spectroscopy (EDS) mapping analyses, the particles on Ag flake were mostly composed of Ga and several In. Ga and In were found on the surface of Ag flake. In SEM images (FIG. 5), the cross sectional images of the printed composite showed that the EGain nanoparticles were decorated on the Ag flakes.

[0192] After the decoration of EGain nanoparticles, the crystallines of Ag2ln and Ag3Ga2were detected by X-ray diffraction (XRD) (FIG. 6). shows the X-ray diffraction of the prepared samples after the sintering process. In the case of Ag flake, four strong peaks were detected at 38.5°, 44.2°, 64.4°, and 77.3°, which correspond to (1 1 1), (2 0 0), (2 2 0), and (3 1 1), respectively. The crystallinity of the Ag flake is good agreement with literature (Journal of Radiation Research and Applied Sciences 2016, 9, 217; Angewandte Chemie International Edition 2009, 48, 3806). After decoration of EGain nanoparticles on Ag flakes followed by the sintering process, several new peaks at 29.7° (Agin (3 1 1)), 31.1° (AgGa (0 0 1)), 36.1 ° (Agin (4 0 0)), 39.6° (Agin (3 3 1)), 43.3° (Agin (2 0 0)), 47.7° (AgGa (2 1 1)), and 48.6° (AgGa (3 1 0)) were detected, and new peaks are mostly related to Ag-Ga and Ag-ln alloys. The detected peaks were analyzed using the ICDD databases PDF4 (2023).

[0193] Additionally, X-ray photoelectron spectroscopy (XPS) was conducted to show the chemical bonding formation. FIG. 7a shows the Ag 3d region of Ag flake (top), Ag70LM20 before sintering (middle), and Ag70LM20 sintering at 537 K (bottom). All samples showed two main peaks near approximately 368 and 374 eV, which corresponds to Ag 3d3 / 2 and Ag 3du2, respectively. Elaborating further, the Ag flake (FIG. 7a, top figure) showed two deconvolution peaks at 374.7 and 374.2 eV detected in Ag 3cfa / 2, which are assigned to Ag° (metal) and Ag+, respectively. Another two deconvolution peaks at 368.7 and 368.2 eV were detected in Ag 3^5 / 2 region can be assigned to Ag° (metal) and Ag+, respectively. These results show that the Ag flake was composed of Ag metal and Ag2O formation, and the A 2O formation is attributed to the native oxide layer formation on the surface (Scientific Reports 2016, 6, 37192). After decoration of EGain nanoparticles on the Ag flake, the main peaks of Ag 3d and Ag 3cf5 / 2were shifted to 373.6 and 367.6 eV, respectively. The peak shifting to lower binding energy was caused by electronic occupation change in alloy structure (Physical Review B 1991 , 43, 4659). Such peak shift has been found in bimetallic structure such as Pd-Ag or Pd-Au (Applied Surface Science 1990, 45, 319; Faraday Discussions 2018, 208, 255). Accordingly, the shift of Ag 3d peaks after decoration of EGain nanoparticles implies that the bimetallic formation between Ag and Ga (or In) by galvanic replacement occurred. Additionally, the XPS spectra of Ga 2p3 / 2 and In 3d was investigated as shown in FIG. 7b-c. In the case of EGain nanoparticles, the Ga 2p3 / 2 of EGain nanoparticle was composed of three peaks; Ga° (metal), Ga+, and Ga3+were assigned to 1116.7, 1117.8, and 1118.8 eV, respectively. (FIG. 7b, top figure). Two main peaks in In 3d of EGain nanoparticle were observed at -444.4 (In 3cfc / 2) and -451 .9 eV (In 3cfe / 2). The XPS spectra of EGain nanoparticle at Ga 2ps / 2 and In 3d regions are good agreement with literature (Physical Chemistry Chemical Physics 2021 , 23, 13458). After decoration of EGain nanoparticle on Ag flakes, peak shifting of Ga 2p3 / 2 and In 3d was also observed. (FIG. 7b, middle and bottom figures, and FIG. 7c, middle and bottom figures) Similar to the peak shifting of EGain nanoparticle decorated Ag flakes in the Ag 3d, the redistribution of electrons after the galvanic replacement contributed to the peak shifting in Ga 2p3 / 2 region. The sintering process provided further peak shifting, which indicates the Ga-based alloy formation, such as Ag-Ga.

[0194] Example 3. Thermal Conductivity and Electrical Conductivity of Screen Printed EGain Nanoparticle Decorated Ag Flake In this example, the thermal conductivity of the ink was characterized depending on the ratio between EGain nanoparticles and Ag flakes. In the case of thermal conductivity, two methods were employed for the in-plane and through-plane thermal conductivity. Thermal conductivity of the screen printed samples was characterized by ASTM 5470-06 (through-plane thermal conductivity) and Angstrom method (in-plane thermal conductivity). The schematic illustration of thermal conductivity measurement and examples are depicted in this example (FIG. 8a and FIG. 9a).

[0195] ASTM 5470-06 (through-plane thermal conductivity)

[0196] In the case of through-plane thermal conductivity, ASTM D5470 method was employed ("Design, assembly and commissioning of a test apparatus for characterizing thermal interface materials", presented at ITherm 2002. Eighth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (Cat. No.02CH37258), 30 May-1 June 2002, 2002). Two copper blocks (10 mm *10 mm x 20 mm, width x length x height) were prepared, and the printed ink was located between copper blocks. (FIG. 9a) After then, heat flux was generated from one side of copper block to the other copper block. The temperature of copper blocks depending on the position was measured by T-type thermocouples and recorded by data logger (DAQ6510, Keithley). (FIG. 9b) Based on the position dependent temperature, the thermal resistance of the sample was obtained by Eq. 4:

[0197] Rsample = ^^ (Eq. 4), where Rsampie, ATSamPie, and Q are thermal resistance of sample, temperature difference from hot side to cold side of the sample, and heat flux, respectively. The thermal resistance was converted into thermal conductivity using Eq. 5: ksample= ^^ (Eq. 5), are thermal conductivity of the sample, thickness of the sample, and area of the sample, respectively. The heat flux (Q) was calculated by Eq. 6: where QH, Qc, kcu, and A are heat flux from hot side to sample, heat flux from sample to cold side, thermal conductivity of copper, and area of copper block, respectively. Angstrom Method (in-plane thermal conductivity)

[0198] The in-plane thermal conductivity (Km) was characterized by Kin=Cpxainxd, where Cp, am, and d are specific heat, in-plane thermal diffusivity, and density, respectively. The specific heat was characterized by differential scanning calorimeter (DSC, Q10, TA instruments). For the in-plane thermal diffusivity, the Angstrom method was employed (International Journal of Heat and Mass Transfer 2016, 92, 784). The strip type of the printed sample (5 mm x 30 mm x 0.1 mm, width x length x thickness) was prepared. Sinusoidal heat source at the one side of the prepared strip was generated on a commercial Peltier device as illustrated in FIG. 8a, and the Peltier device was controlled by power supply (2280S-32-6, Keithley). T-type thermocouples were located on the middle part of the strip and the distance between the thermocouples was 8 mm. The time dependent temperature change was recorded by data logger (DAQ6510, Keithley). Based on the set up, the thermal diffusivity was obtained by Eq. 7 where L, dt, M, and N are length between thermocouples, time difference between peak temperature at near heat source and far heat source, amplitude of the temperature wave at near heat source, and amplitude of the temperature wave at far heat source, respectively. (FIG. 8b)

[0199] Measurement of Electrical Conductivity by 4-Point Probe Method

[0200] The electrical conductivity was characterized by 4-point probe method was used (HPS2524, HELPASS, China). The 4-point probe was arranged with 2 mm distance between probes for use in testing.

[0201] Results and Discussions

[0202] After sintering process, the screen printed composite showed higher in-plane thermal conductivity, as illustrated in FIG. 10a-b. Also, electrical conductivity of the screen printed composite was characterized by the 4-point probe method. All the printed ink showed >105S / m of electrical conductivity.

[0203] FIG. 10a-b illustrate the in-plane and through-plane thermal conductivities (K) of prepared ink composites, respectively. The in-plane thermal conductivity (Kin) was examined by Angstrom method, and through-plane thermal conductivity (Keough) was examined by ASTM 5470. The measurement of thermal conductivities was conducted at 298 K of temperature and 48% of humidity.

[0204] FIG. 10a shows the Kin of various printed inks. The Kin of AgOLMO (pure PVB) and Ag90LM0 before sintering was approximately 0.4 and 23 W / mK, respectively. When the EGain nanoparticles were decorated on Ag flakes, the Kin was decreased as a function of EGain nanoparticle concentration. The sample Ag80LM10, Ag70LM20, Ag60LM30, Ag45LM45, and Ag0LM90 before the sintering process was at 9.1 , 8.5, 7.7, 5.6, and 4.1 W / mK, respectively. After the sintering process, the Kin of all printed inks was increased, and that of Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, Ag45LM45, and Ag0LM90 after the sintering process was 53.7, 61.9, 142.4, 34.0, 31.8, and 4.8 W / mK, respectively. In the case of Kthrough (FIG. 10b, Kthrough Of AgOLMO, Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, Ag45LM45, and Ag0LM90 before the sintering process was 0.4, 3.1 , 5.3, 3.1, 4.8, 2.5, and 2.0 W / mK, respectively. After the sintering process, Kthrough of Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, Ag45LM45, and Ag0LM90 was 5.6, 8.2, 5.8, 9.4, 5.9, and 2.2 W / mK, respectively. Generally, all printed inks showed the anisotropic K (high Kin). The higher Kin is attributed to the lateral alignment of the micro-sized Ag flakes, during the screen-printing process. Since the anisotropic fillers induced higher thermal transport with the lateral direction of the fillers, the Kinwas higher than the Kthrough- Notably, with the EGain nanoparticle decorated on Ag flakes, the Kinof printed inks (before sintering) reduced with increasing contents of EGain nanoparticles. Typically, the EGain nanoparticle / silicone-based composite with high contents of EGain nanoparticle has -10° W / mK of K (Advanced Energy Materials 2021 , 11, 2101387; RSC Advances 2018, 8, 16232). Thus, the K of printed ink before the sintering process was dominated by that of EGain nanoparticles. Interestingly, after the sintering process, the K of all printed inks was enhanced. In the case of Ag90LM0, owing to the diffusion of Ag atoms at the interfaces between Ag flakes during the sintering process (ACS Applied Electronic Materials 2021 , 3, 5365), the sintered boundaries provided further thermal transport junction, resulting in more than twice higher Kin compared to that of Ag90LM0 before the sintering process. After decoration of EGain nanoparticles, the Kin of Ag80LM10 and Ag70LM20 after the sintering process was higher than that of Ag90LM0 after the sintering process. In the case of micro-sized metal filler, the gaps between micro-sized metal fillers cause the low K (Applied Physics Letters 2011 , 98, 182906). Thus, filling the gaps between micro-sized fillers is important to enhance the K.

[0205] As showed in FIG. 11 , the cross-sectional scanning electron microscope (SEM) images of Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, Ag45LM45, and Ag0LM90 after the sintering process showed that the decoration of EGain nanoparticles on Ag flakes assisted in the gap fill. Since the decorated EGain nanoparticle on Ag flakes provided a dense composite, the effective thermal transport path between micro-sized Ag flakes was formed. However, it seems that dominated EGain nanoparticles in Ag60LM30, Ag45LM45, and Ag0LM90 caused the lower K. Besides, due to the improvement of the crystalline of the Ag-Ga or Ag-ln alloy formation by the sintering process, the higher K was obtained. When the XRD spectra of Ag70LM20 after the sintering process was compared to that of Ag70LM20 before the sintering process, the intensity of Ag-Ga and Ag-ln alloy formation of Ag70LM20 after the sintering process was stronger than that of Ag70LM20 before the sintering process as shown in FIG. 12. A numerical calculation had demonstrated that the higher degree of ordering in a binary alloy has higher K (Journal of Heat Transfer 2011 , 134, 014501). Thus, the decorated EGain nanoparticle on Ag flakes provided the effective thermal transport junctions between microsized Ag flakes, resulting in the higher K of Ag80LM10 and Ag70LM20 after the sintering process. However, the samples of Ag60LM30 and Ag45LM45 have lower Kinthan that of Ag90LM0. Owing to the phonon scattering effect at the interfaces of the nanostructured materials (Advanced Materials 2007, 19, 1043; Phys. Rev. Lett. 2006, 96, 4), the higher contents of EGain nanoparticles on the surface of Ag flakes caused the low Kin.

[0206] Generally, since the Ag filler based composite inks can be utilized as electrodes, the electrical conductivity (o) of printed inks was investigated. The electrical conductivity of the printed composites was enhanced by sintering process. FIG. 10c shows the o of Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, and Ag45LM45. Generally, the o of Ag90LM0, Ag80LM10, Ag70LM20, Ag60LM30, and Ag45LM45 was over 105S / m, and the sintering process enhanced the o of all printed inks. The o of Ag90LM0 before the sintering process was about 6.5 x 10sS / m, and that of Ag90LM0 after the sintering process was increased to 9.6 x 106S / m. After the decoration of EGain nanoparticle on Ag flakes, the o of Ag80LM10, Ag70LM20, Ag60LM30, and Ag45LM45 before the sintering process was 4.4 x 105, 3.0 x 105, 2.0 x 105, and 1.5 x 10sS / m, respectively, and that of Ag80LM10, Ag70LM20, Ag60LM30, and Ag45LM45 after the sintering process was 3.0 x 106, 2.4 x 106, 1.8 x 106, and 6.2 x 10sS / m, respectively. When the contents of EGain nanoparticles were increased, the a was decreased. In the case of Ag-based alloy, the electronic structure of alloy formation, such as AgGaTe, AglnSe, AgAu, and AgGe, differs from that of pure Ag, resulting in a lower o than that of pure Ag flake (Advanced Functional Materials 2019, 29, 1806534; Inorganic Chemistry Frontiers 2019, 6, 3545; Physical Review 1967, 157, 564). Thus, the alloy formation on the Ag flakes caused the slightly lower o as a function of the EGain nanoparticle. In the case of Ag0LM90, there was no o of Ag90LM0 before / after the sintering process, owing to the polymer encapsulation and oxide layer on EGain nanoparticles (Advanced Energy Materials 2021 , 11, 2101387, npj Flexible Electronics 2021 , 5, 11). Example 4. Adhesion and Cyclic Bending Test

[0207] One advantage of the prepared ink is the mechanical stability. To show the mechanical stability, a cyclic bending test was conducted. Ag70LM20 ink was printed on a polyimide substrate and the Ag70LM20 printed sample was employed for the test.

[0208] Cyclic Bending Test

[0209] A cyclic bending test was conducted by moving one side of the polyimide substrate, and the diameter of the bent semicylinder substrate was 5 mm. The bending test was repeated 10000 times.

[0210] Sheet Resistance and Thermal Conductivity

[0211] The sheet resistance and in-plane thermal conductivity was measure at stress-free state.

[0212] Results and Discussions

[0213] As illustrated in FIG. 13a (sample on the left), the Ag70LM20 ink was printed on a polyimide substrate. The printed and sintered Ag70LM20 showed good adhesion on polyimide film (FIG. 13a (sample on the left)). After the sintering process, the cyclic bending was conducted with moving one side of the gripped part of the polyimide film with printed Ag70LM20 to show mechanical stability (FIG. 13b). During the bending test, the diameter of the bent semicylinder film was 5 mm, and the bending test was repeated 10,000 times. The distance between gripped parts before bending was 20 mm and the distance was 5 mm after bending (5 mm of bending diameter). The speed of cyclic bending test was 1000 mm / min, as shown in FIG. 13b. After 10000 times of bending cycle, there was no significant damage on the printed Ag70LM20, and the printed ink showed the good adhesion properties on the substrate (FIG. 13a (sample on the right)).

[0214] Also, the sheet resistance and thermal conductivity were characterized as a function of bending cycle (FIG. 14a-b). Elaborating further, we examined the sheet resistance (Rsq) and Kin of Ag70LM20 after the sintering process at 1 , 100, 1000, and 10000 times of bending cycles. The RSq and Kin were characterized at a stress-free state after cyclic bending. The normalized value of sheet resistance was increased to about 5 % after 10,000 times of bending, whereas that of thermal conductivity was decreased to about 4 % after 10,000 times of bending (FIG. 14c) . The Rsqof Ag70LM20 after the sintering process was 0.363, 0.373, 0.384, and 0.381 Q / sq at 1 , 100, 1000, and 10000 times of bending cycles, respectively as shown in FIG. 14a. The Kin of Ag70LM20 after the sintering process was 143.7, 141.0, 138.3, and 138.5 W / mK at 1, 100, 1000, and 10000 times of bending cycles, respectively (FIG. 14b. When the Rsqand K were normalized by each value at 1 time of bending cycle, the Rsqwas changed 1 to 1.05, whereas the Kjnwas changed from 1 to 0.96, as a function of bending cycles as depicted in FIG. 14c. The PVB polymer contributed to the mechanical stability of the printed ink. Owing to the good ductility and adhesion properties of PVB with a substrate such as glass substrate, the PVB has been utilized as an interlayer for the laminated glass (Construction and Building Materials 2015, 93, 404). With these properties, the printed Ag70LM20 after the sintering process showed good mechanical stability. This mechanically stable composite ink is significantly important in soft electronics. Since enforced mechanical stress on soft electronics is inevitable, thermal management and electrical transport functions with mechanical stability are crucial. Thus, the developed ink can play a key role in the related field.

[0215] Example 5. LED Heat Dissipation Test

[0216] To demonstrate the heat dissipation performance of the prepared ink, heat dissipation performance of a light-emitting diode (LED) was investigated. In this example, to show the heat dissipation performance, a white light-emitting diode (LED) was employed as a thermal or heat source. The LED was attached on the polyimide film using three different thermal paste: commercial thermal paste (TC-5121 , Dow Corning), commercial Ag paste (PELCO Conductive Silver paint, TED PELLA, Inc.), and Ag70LM20. (FIG. 15) 4V of potential was applied onto the LED using power supply. The time dependent temperature change of LED (dot box part in FIG. 15b was examined by IR camera (Ti200, Fluke).

[0217] Determination of Heat Dissipation Performance

[0218] In order to demonstrate heat dissipation performance, 1210 / 3528 SMD / SMT white lightemitting diode (LED) was used. For the comparison test between the Ag70LM20 ink and commercial Ag paste and thermal paste, each ink was printed on the polyimide substrate with a spacer having 50 pm of thickness. The LED was installed on the printed layer, and 4 V of potential was applied at the LED. To show the five LED array assemble on SMEE / Ag70LM20 substrate, SMEE was prepared by same protocol as illustrated in our previous research (Advanced Energy Materials 2021, 11, 2101387). In this case, Ag70LM20 was used as not only thermal management layer but also electron transport line for operation of the LED. To operate the device, a series connection between the LED and 100 ohms of the resistor was composed, and the series connected couples (LED + resistor) were configurated by parallel connection. During the operation of the LED, time dependent infrared (IR) image was obtained by I camera (Ti200, Fluke), and the average area temperature was obtained by the software provided from Fluke. Results and Discussions

[0219] As illustrated in FIG. 15a, we prepared screen printed Ag70LM20, commercial Ag paste (PELCO), and commercial thermal paste (Dow corning) on polyimide substrates. The white LED was installed on each printed layer, and the heat dissipation test was conducted (FIG. 15c). To operate the LED, 4 V of potential was applied in the LED, and the temperature change of LED was measured by infrared (IR) camera.

[0220] FIG. 16 shows the temperature change of LED with Ag70LM20, commercial Ag paste (PELCO), and commercial thermal paste (Dow corning) layers as a function of time. The time dependent IR images of printed Ag70LM20, commercial Ag paste (PELCO), and commercial thermal paste (Dow corning) on polyimide substrates are illustrated in FIG. 16b. Generally, the temperature of LEDs with Ag70LM20, commercial Ag paste (PELCO), and commercial thermal paste (Dow corning) layers were dramatically increased at the initial state and saturated after 50 s. However, the saturated temperature of LEDs was different depending on the layers. The temperature of LED with Ag70LM20 was saturated at approximately 343 K, whereas that with commercial Ag paste (PELCO) and commercial thermal paste (Dow corning) layers were saturated at around 349 and 351 K, respectively. The lower saturated temperature indicates that the generated heat from LED was dissipated more effectively through Ag70LM20 layer, compared to two other commercial ink.

[0221] As illustrated in Table 3, the K of Ag70LM20 was higher than that of commercial Ag paste (PELCO), and commercial thermal paste (Dow corning). Notably, the higher Km of Ag70LM20 is helpful for the heat dissipation. The generated heat from the LED was induced to the lateral direction of the printed layer.

[0222] Table 3. Thermal conductivity of Ag70LM, commercial Ag paste, and commercial thermal paste.

[0223] Sample Kin(W / mK) Keough (W / mK)

[0224] Ag70LM20 142.39 5.82

[0225] Commercial Ag paste 32.45 1.23

[0226] (PELCO)

[0227] Commercial thermal paste

[0228] 4.09

[0229] (Dow) Example 6. Flexible Heat Sink and Heat Dissipation Performance

[0230] Furthermore, we designed flexible heat sink for the thermal management of soft electronics using a bilayer approach. In this example, the utilization of Ag70LM20 as a flexible heat sink was demonstrated.

[0231] In order to prepare flexible heat sink, the surface modified EGain nanoparticle elastomer composite (SMEE) was employed as thermally conductive, flexible, and free-standing substrate. The based layer consists of electrically insulative printed composite made of surface modified EGain nanoparticle embedded in elastomer (SMEE) which was reported previously (Advanced Energy Materials 2021 , 11, 2101387). The top layer is made of the printed Ag70LM20 (without sintering) for electrical conduction and heat dissipation.

[0232] To show the heat dissipation performance, the time dependent temperature change of LED was examined with same protocol in Example 5.

[0233] Print of Ag70LM20 ink on SMEE Substrate

[0234] Typically, the Ag70LM20 ink was printed on the as-prepared SMEE substrate, and the printed substrate was sintered at 573 K for 30 min in Ar atmosphere.

[0235] Results and Discussions

[0236] As illustrated in FIG. 17a, the Ag70LM20 printed SMEE, the thickness of SMEE and printed Ag70LM20 layer was 200 and 25 pm, respectively. The brighter grey layer (Ag70LM20) showed good adhesion on the SMEE substrate. Since the Ag70LM20 is electrically conductive, the Ag70LM20 was used as not only thermally conductive layer but also electron transport conductive line for LED operation (FIG. 17b) On the bilayer structure (SMEE / Ag70LM20), the white LED was installed, and the temperature of the LED was examined as a function of time.

[0237] FIG. 18 shows the time dependent temperature of LED and I images, respectively. With its high K and high o, the Ag70LM20 was used as an electron transport line for LED operation as illustrated in FIG. 19. VHB™ film from 3M was used as the polymer substrate to track the temperature of LED without heat dissipation. The temperature was increased to around 373 K.

[0238] The bilayer structure showed the effective heat dissipation of flexible LED device. When the substrate was Ag70LM20 printed SMEE, the temperature of LED can be lowered to approximately 319 K. Notably, the temperature of LED with Ag70LM20 / SMEE was lower than that with SMEE only (322 K) and Al heat sink (331 K). FIG. 18b and FIG. 20 show the IR images of temperature change of LED with SMEE, SMEE / Ag70LM20, VHB film, and aluminum (Al) plate. The thickness of the SMEE, SMEE / Ag70LM20, VHB film, and aluminum (Al) plate was 225, 200, 100, and 130 pm, respectively.

[0239] The time dependent temperature of LED with SMEE, SMEE / Ag70LM20, VHB film, and aluminum plate was plot as illustrated in FIG. 18a. In this test, 100 mA of current was applied in all LEDs, and the test was conducted for 400 hours. To show the LED temperature without heat dissipation, we prepared the LED with VHB film, which is an insulative film. Since the generated heat from LED was not dissipated to outside, the temperature of LED with VHB film was increased to approximately 363 K. However, the temperature of LED with SMEE / Ag70LM20 layer was saturated at around 334 K. Interestingly, the saturated temperature of LED with SMEE / Ag70LM20 was lower than that with Al plate (356 K), which indicates that the SMEE / Ag70LM20 layer showed higher heat dissipation performance. In the case of Al plate, the gap between Al heat sink and LED might cause the low heat dissipation. Whereas the thermally conductive elastomeric layer (SMEE) improved the contact with the LED, and the thermal energy was dissipated through the Ag70LM20 layer. In addition, when we surveyed the temperature of LED with SMEE layer, the saturated temperature was approximately 349 K, and the saturated temperature of LED with SMEE layer was higher than that with SMEE / Ag70LM20. The lower temperature of LED with SMEE / Ag70LM20 implies that the Ag70LM20 layer played an influential heat transport role for heat dissipation of the LED. The developed material can be a powerful solution for the longer lifetime of electronic devices and low power consumption. For example, the junction temperature of an LED is one of the influential factors for the lifetime of the LED. The high junction temperature of the LED causes thermal stress in the LED, and the thermal stress deteriorates the lifetime of the LED (Microelectronics Reliability 2012, 52, 1332). Accordingly, the effective heat dissipation from the LED junction to the substrate should be addressed. In this perspective, we simulated the lifetime of the LED with the developed material. To simulate the lifetime of the LED, the exponential decaying function was employed, and based on the function, the equation was used for the simulation of the lifetime as expressed by Eq. 8 where p, p, A, I, Ea, k, and Tj are pre-factor, percentages of lumen maintenance, model constant, current, activation energy, Boltzmann constant and junction temperature, respectively (Materials 2018, 11, 817). FIG. 21 shows the junction temperature dependent lifetime of the LED. In this simulation, the saturated temperature illustrated in FIG. 18a was regarded as the junction temperature, and the applied current was 100 mA. Based on the model, the lifetime of the LED with SMEE / Ag70LM20, which has 334 K of the junction temperature, was approximately 39500 hours, whereas that with SMEE, Al plate, and VHB film (no heat dissipation) was 24000, 18600, and 13200 hours, respectively. When the lifetime of the LED was normalized by the value of that with Al plate, a 112% longer lifetime of the LED with SMEE / Ag70LM20 was shown than the lifetime of the LED with Al plate. (FIG. 22) The simulated result reveals that the developed material significantly prolonged the long lifetime of the LED. The effective heat dissipation from the LED junction to SMEE / Ag70LM20 layer contributed to reducing the thermal stress in the LED, resulting in the longer lifetime.

[0240] Example 7. LED Array Assemble

[0241] Lastly, we fabricated the five LED array assemble on SMEE / Ag70LM20 substrate, as shown in FIG. 23. In this prototype, the Ag70LM20 was employed as heat dissipation layer as well as electron transport line for the LED operation.

[0242] To operate the device, a series connection between the LED and 100 ohms of the resistor was composed, and the series connected couples (LED+resistor) were configurated by parallel connection FIG. 24.

[0243] Results and Discussions

[0244] The assembled device was readily deformed on the curvature surface, such as the surface of a centrifugal tube (diameter: 28 mm) in FIG. 23. When the 6.5 V of potential was applied in the device, the temperature of LED was saturated at approximately 320 K. This result shows that the developed material played the thermal transport role under the deformed state of the device. Thus, the developed material can be a powerful solution for the thermal management of soft electronics.

Claims

Claims1. An ink formulation for additive manufacturing comprising: a polymeric binder material; a dispersant; a thinner; nanoparticles of eutectic gallium indium (EGain); and silver flakes.

2. The ink formulation according to Claim 1, wherein a surface of the silver flakes is decorated with EGain nanoparticles.

3. The ink formulation according to Claim 2, wherein the surface of the silver flakes further comprises crystalline regions of Ag2ln and crystalline regions of Ag3Ga2.

4. The ink formulation according to any one of the preceding claims, wherein: the polymeric binder material is present in an amount of from 2 to 10 wt%; the thinner is present in an amount of from 1 to 8 wt%; the dispersant is present in an amount of from 0.1 to 1 wt% the EGain nanoparticles are present in an amount of from 5 to 50 wt%; the silver flakes are present in an amount of from 40 to 91.9 wt%.

5. The ink formulation according to Claim 4, wherein: the polymeric binder material is present in an amount of from 4 to 6 wt%; the thinner is present in an amount of from 2 to 4 wt%; the dispersant is present in an amount of from 0.2 to 0.6 wt% the EGain nanoparticles are present in an amount of from 10 to 45 wt%; the silver flakes are present in an amount of from 45 to 83.8 wt%.

6. The ink formulation according to Claim 5, wherein one or more of the following apply:(a) the polymeric binder material is present in an amount of about 5.56 wt%;(b) the thinner is present in an amount of about 3.94 wt%;(c) the dispersant is present in an amount of about 0.5 wt%(d) the EGain nanoparticles are present in an amount of from 10 to 45 wt%, such as from 10 to 30 wt%, such as about 20 wt%; and(e) the silver flakes are present in an amount of from 45 to 83.8 wt%, such as from 60 to 80 wt%, such as about 70 wt%.

7. The ink formulation according to any one of the preceding claims, wherein one or more of the following apply:(ai) the polymeric binder material is polyvinyl butyral (PVB);(aii) the thinner is terpineol;(aiii) the dispersant is acrylic acid.

8. The ink formulation according to any one of the preceding claims, wherein the ink formulation is formed from:5.56 wt% of PVB as polymeric binder material;3.94 wt% of terpineol as thinner;0.5 wt% of acrylic acid as dispersant; and one of:(bi) 20 wt% of EGain nanoparticles and 70 wt% of silver flakes;(bii) 10 wt% of EGain nanoparticles and 80 wt% of silver flakes;(bii) 30 wt% of EGain nanoparticles and 60 wt% of silver flakes; and(bii) 45 wt% of EGain nanoparticles and 45 wt% of silver flakes.

9. The ink formulation according to any one of the preceding claims, wherein after additive manufacture printing and sintering of the printed material, the sintered material displays one or more of:(ci) an in-plane thermal conductivity of from 30 to 160 W / mK;(cii) a through plane thermal conductivity of from 4 to 10 W / mK; and(ciii) a conductivity of greater than 105S / m, such as greater than 106S / m.

10. A thermal management material, comprising: a substrate; and a sintered layer of the ink formulation as described in any one of Claims 1 to 9 on the substrate.

11. The thermal management material according to Claim 10, wherein the substrate is formed from glass, a silicone polymer or a polyimide.

12. The thermal management material according to Claim 10 or Claim 11 , wherein the thermal management material is a flexible thermal management material (e.g. the substrate is a silicone or a polyimide).

13. A method of forming a thermal management material as described in any one of Claims 10 to 12, the method comprising the steps of:(i) providing an unsintered material comprising: a substrate; and an unsintered layer of the ink formulation as described in any one of Claims 1 to 9 on the substrate; and(ii) sintering the unsintered material at an elevated temperature for a period of time under an inert atmosphere.

14. The method according to Claim 13, wherein the unsintered material is obtained by applying the ink formulation onto the substrate by an additive manufacturing process.

15. The method according to Claim 13 or Claim 14, wherein one or more of the following apply:(di) the period of time is from 10 minutes to 2 hours, such as about 30 minutes;(dii) the inert atmosphere is argon; and(dii) the temperature is from 350 to 600 K, such as from 450 to 580 K, such as about 573 K.

16. An electrical device, comprising at least one component that draws electrical energy attached to a thermal management material as described in any one of Claims 10 to 12.

17. The electrical device according to Claim 16, wherein the at least one component that draws electrical energy is a light emitting diode.

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