Precuring Matrix Viscosity Controls Thermal Conductivity of Elastomeric Composites with Compression‐Activated Liquid and Solid Metallic Filler Networks

Polymer matrix composites with liquid metal droplet and solid particle fillers are promising candidates for thermal interface materials (TIMs) used in electronics thermal management. To achieve good thermal transport, the particle and droplet fillers must be interconnected to form thermally conductive percolation pathways in the polymer matrix. This in turn requires displacement of the polymer between fillers as well as rupture of the oxide shell on the liquid metal droplets. This study demonstrates a multipronged strategy to achieve extensive filler bridging and a high thermal conductivity polymer TIM pad. The strategy synergistically employs reactive solid and liquid microscale fillers, a polymer matrix with tuned precure viscosity, and mechanical compression during thermal curing of the composite. The data demonstrate that the viscosity of the precursor polymer solution prior to curing plays a major role in the resulting thermal conductivity. More specifically, samples made with low viscosity ≈100 cSt solutions achieve a high thermal conductivity of ≈15 W m−1 K−1 at a curing pressure of 2 MPa. This thermal conductivity is double that achieved with high viscosity ≈2300 cSt solutions. Since many polymer systems employed in industry and research have a high precure viscosity, this insight has important implications for next‐generation TIMs.


Precuring Matrix Viscosity Controls Thermal Conductivity of Elastomeric Composites with Compression-Activated Liquid and Solid Metallic Filler Networks
high-performance electronic devices, soft robotics, and flexible electronics. These materials ensure that devices reliably function by reducing thermal resistance between the heat-generating components and the cooling solutions. [1][2][3][4][5] Specifically, the inherent microroughness and imperfect contact at component interfaces leads to large thermal resistances. In order to function, TIMs need high thermal conductivity and good wettability to remove heat. TIMs also need to be mechanically compliant to overcome dynamic warpage of the mating surfaces. [6,7] This dynamic warpage arises due to the combined effects of thermal cycling and mismatches in thermal expansion of adjacent components. This temperature-induced dynamic warpage causes fluid-phase TIMs (e.g., silicone greases), to pump out of the interface, which in turn leads to a high thermal resistance and overheating. The inability to pump out of an interface is one of the advantages of solid-phase TIMs. Crosslinked polymers offer appropriate mechanical properties for solid-phase TIMs, but have a low thermal conductivity of 0.2-0.3 W m −1 K −1 . [8][9][10] To overcome this problem, high thermal conductivity rigid filler materials (alumina, copper, graphene, boron nitride, etc.) [11][12][13][14][15][16] are incorporated into the precursor polymer solution prior to crosslinking. A curing process is then used to crosslink the precursor polymer solution and create a solid polymer composite TIM pad. A high volume fraction of rigid filler particles substantially enhances the composite thermal conductivity by creating multiple percolation paths, but also causes detrimental stiffening of the polymer. [7] In addition, curing polymers with very high solid additive content results in pads that "crumble" and are not suitable for TIM applications. [6,17,18] In contrast, liquid fillers can be incorporated into polymer composites as microdroplets at high volume fractions without degrading the mechanical properties. [19][20][21] Liquid metals (LMs) based on Ga (e.g., elemental Ga, eutectic GaIn, and eutectic GaInSn) have sufficient thermal conductivity and mechanical compliance to function as TIMs, but present other challenges due to their reactive/corrosive properties. Consequently, LMs are typically used as fillers within polymer composites such that the polymer functions as a physical barrier that prevents corrosion between the TIM and Polymer matrix composites with liquid metal droplet and solid particle fillers are promising candidates for thermal interface materials (TIMs) used in electronics thermal management. To achieve good thermal transport, the particle and droplet fillers must be interconnected to form thermally conductive percolation pathways in the polymer matrix. This in turn requires displacement of the polymer between fillers as well as rupture of the oxide shell on the liquid metal droplets. This study demonstrates a multipronged strategy to achieve extensive filler bridging and a high thermal conductivity polymer TIM pad. The strategy synergistically employs reactive solid and liquid microscale fillers, a polymer matrix with tuned precure viscosity, and mechanical compression during thermal curing of the composite. The data demonstrate that the viscosity of the precursor polymer solution prior to curing plays a major role in the resulting thermal conductivity. More specifically, samples made with low viscosity ≈100 cSt solutions achieve a high thermal conductivity of ≈15 W m −1 K −1 at a curing pressure of 2 MPa. This thermal conductivity is double that achieved with high viscosity ≈2300 cSt solutions. Since many polymer systems employed in industry and research have a high precure viscosity, this insight has important implications for next-generation TIMs.

Introduction
Thermal interface materials (TIMs) are critical enablers in developing an efficient thermal management system to support www.advmatinterfaces.de adjacent components. LM volumetric fill fractions up to 80% are readily achievable in a variety of polymers. However, even at these extreme volume fractions, the composite thermal conductivity [19][20][21] is only around ≈5 W m −1 K −1 due to poor thermal contact between filler particles (i.e., filler-filler contacts). In particular, the interfacial resistance between adjacent filler particles/droplets is high due to a nanoscale oxide shell [22] on the LM surface and the presence of an interstitial polymer matrix that is often viscous. [23] Thus, to increase the composite thermal conductivity substantially above 5 W m −1 K −1 , more effective thermal bridging between the solid and/or liquid microadditives into percolation pathways must be achieved. Several strategies have been attempted to this end, including particle alignment through vacuum-assisted filtration, [24] chemical vapor deposition, [25] application of magnetic [26][27][28] and electrical fields, [29,30] as well as sample straining, [31,32] hot pressing, [33] press-rolling, [34] and mechanical cutting. [35] However, only a few of these strategies have been employed on LM-based composites, and at most yielded materials with thermal conductivity of ≈2 to 10 W m −1 K −1 in the cross-plane direction (≈1.7 W m −1 K −1 by vacuum-assisted infiltration, [36] 4 W m −1 K −1 by magnetic alignment, [27] 4.8 W m −1 K −1 by adopting sacrificial templating, [37] and ≈10 W m −1 K −1 by a mechanical mixing fabrication technique [16] ).
Using LM-fillers typically results in electrically conductive polymer composites, which can be good or bad depending on the specific TIM application. In a typical electronics package, there are three different types of interface materials, "underfill," "TIM1," and "TIM2," and these are described in various review articles. [38,39] Underfill is co-located with the signalcarrying electrical interconnects to the silicon chip, and hence must be electrically insulating (i.e., LM-based materials should not be used for underfill). However, both TIM1 and TIM2 are located away from the electrical interconnects, and these TIMs do not need to be electrically insulating (i.e., TIM1 is located on the backside of the silicon die and the heat spreader; TIM2 is between the heat spreader and heat sink, respectively). Furthermore, in other TIM applications (e.g., energy-harvesting devices, soft electronic systems, wearable/flexible devices, sensors, etc.), enhanced electrical properties are desirable, [40] and hence the electrical conductivity of an LM-based TIM is attractive.
In this work, we introduce a multipronged strategy to generate polymer TIM pads with thermal conductivities up to ≈15 W m −1 K −1 . This strategy employs reactive solid and liquid microscale fillers, a polymer matrix with tuned precure viscosity, and mechanical compression during sample curing. This approach builds on our prior insights that the oxide shell of LM droplets ruptures easily for droplets that are microscale and freshly fabricated, [22] and that thermal bridging across filler particles is substantially facilitated by the addition of solid Ag particles that react with Ga. [23] More specifically, Ag and Ga spontaneously react with each other to form intermetallic alloys. These intermetallic alloys crystallize into high aspectratio solids (i.e., nanoneedles) that improve thermal percolation. In addition, our recent work on uncured silicone greases (fluid-phase TIMs) showed that a low viscosity (≈100 cSt) silicone oil matrix enhances thermal conductivity by facilitating oil displacement from in-between particles during compression. [23] Conversely, silicone oils with viscosities above 1000 cSt inhibit filler-filler contact within a compressed grease and result in a lower thermal conductivity. This factor is important because many of the precursor polymer solutions that are commonly used for solid-phase TIM pads (e.g., Sylgard 184 and Ecoflexes [41,42] ) have an even higher precure viscosity of around 2000-5000 cSt. [43] To understand whether the thermally beneficial features of low viscosity oils can be preserved within a cured solid-phase TIM pad, we use a tailored silicone polymer precursor solution system that can have precure viscosities of ≈100 and ≈2300 cSt. Employing these two silicones, we systematically study the impact of the precure viscosity, the filler type (LM-only or LM-Ag), and compressive pressure during curing on the thermal conductivity of the polymer TIM pads.

Fabrication of Composites with Tuned Precure Matrix Viscosity
Our TIM pad fabrication process consists of preparing reactive solid and LM microscale fillers, formulation of a precursor polymer solution, sequential mixing of co-fillers, and subsequent thermal curing under applied load. We prepared Ga LM droplets with controlled size distribution through ultrasonication and selective sedimentation. [22,23] To promote facile rupture of the LM oxide shell on the droplets, we adjusted the ultrasonication and sedimentation time to obtain LM droplets with a diameter of 8.2 ± 4.2 µm (68% confidence interval). [22] We used commercially available Ag powder (Alfa Aesar, APS 4-7 µm particle size) as the solid metal additive. Scanning electron microscope (SEM) images illustrating the size and shape of the Ga and Ag fillers is available in Figure S1 of the Supporting Information.
We used a vinyl terminated polydimethylsiloxane (V-PDMS) elastomer system available from Gelest Inc. to create the polymer matrices with precure viscosities of ≈100 and ≈2300 cSt. This elastomer system uses five components (adjustable base polymer, crosslinker, inhibitor, catalyst, and chain extender) that can be chosen to vary the resultant properties. We process this V-PDMS elastomer system using procedures outlined in various review articles. [41,44] More specifically, we create a "part A" mixture consisting of base polymer, inhibitor, and catalyst and a "part B" mixture consisting of crosslinker and chain extender. With the exception of the base polymer choice, we keep all procedures identical when preparing our samples. The base polymer is available in various viscosities (which is achieved by varying polymer length as opposed to chemical composition). We utilized the DMS-V21 and DMS-V33 base polymers to prepare our samples with precure viscosities of ≈100 and ≈2300 cSt, respectively. Detailed procedures are contained in the Experimental Section as well as the Supporting Information Section S2.
It is important to note that we mixed the V-PDMS formulation sequentially in parts. We sequentially mixed the Ga LM and Ag fillers into the V-PDMS formulations (see schematic in Figure 1) to minimize premature alloying between the LM and Ag prior to sample curing under applied load. Specifically, we www.advmatinterfaces.de first gently mixed newly fabricated LM droplets into the "part A" of the V-PDMS. This covers the LM droplets in a precursor polymer solution coating that decreases direct contact, and hence alloying, between the LM and any subsequently added Ag filler particles. For composites with combined LM and solid particles additives, we next stirred Ag particles into "part A" of the V-PDMS. We next added "part B" to the precursor polymer solution (see Experimental Section and Supporting Information Section S2). We note that some contact and alloying between the LM and Ag [23] occurs during the mixing process and that the extent of this contact is higher in the lower viscosity matrix. However, in either matrix, the degree of alloying during the mixing process is minimal compared to the alloying induced by compression during curing. This is evidenced by a significant increase in thermal conductivity for samples with applied curing pressure relative to those without applied curing pressure (see Sections 2.2 and 2.4). We also note that this mixing process is done at room temperature and this helps ensure that premature curing of the polymer matrix does not occur prior to the application of curing pressure.
We apply pressure during curing by directly placing the uncured sample within our variable-pressure thermal conductivity measurement system. Our thermal conductivity measurement system is a custom stepped bar apparatus (SBA) [45] that is based on a modified ASTM D5470 standard. [46] The sample is loaded into the system by placing it in between upper and lower copper reference bars with known cross-sectional area. [47][48][49] The copper reference bars are equipped with a linear encoder and load cell that determine sample thickness and applied pressure. The copper bars are also equipped with a heater and thermocouples to apply heat flow and measure temperature.
To cure the sample under applied load, we fit a sliding sample mold around the lower copper reference bar in the SBA and transfer the uncured sample into the mold. We then apply sealant between the sliding sample mold and the copper bar to reduce leakage of the precursor polymer mixture as it is cured under applied compression. A flat "pad" is formed by squeezing the uncured mixture between the upper and lower bars during curing ( Figure 1b). The samples were cured by setting the copper bars to 50 °C and maintaining this temperature and the desired applied load for a curing time of 3 h. We note that the compression was applied within 1 min of placing the sample in the curing setup. Whereas the effect of curing happens over a 3 h curing time, the effect of compression is relatively instantaneous. Hence, the process of compression-induced bridging of fillers effectively occurs prior to polymer curing. We chose the 50 °C curing temperature to balance competing effects between curing time and resultant mechanical/thermal properties (see results in Supporting Information Section S4). The applied load during this curing process was set as a process variable and ranged from 0 to 4.5 MPa. We denote the pressure during curing as the "curing pressure," and report this value as the initial applied pressure during curing (i.e., we observe a small amount of pressure relaxation during the curing process). Additionally, we note that the curing pressure is distinct from the applied pressure during thermal conductivity measurements, which we denote as the "measurement pressure." Unless otherwise stated, we used a measurement pressure of ≈0.2 to 0.3 MPa during thermal conductivity measurements. Importantly, Figure S2 in the Supporting Information shows that the thermal conductivity of cured composites is insensitive to measurement pressure. This means that thermal conductivity The applied pressure during curing displaces the uncured precursor polymer from in-between filler particles. Upon direct contact, the Ag and Ga fillers react to form intermetallic alloy particles with a needle-like shape. Also illustrated is a photograph of an ≈1 cm × 1 cm cured pad.
www.advmatinterfaces.de enhancements that arise from applied curing pressure are preserved even if the mechanical load is removed after curing.
We fabricated all of the composites with a total filler volume fraction of 50%, which is known to be above the percolation threshold for spherical particles. [10,[50][51][52] For composites with both solid and liquid fillers, we based our selection of the LM:Ag ratio on the Ga atomic percentage (at%) that yields the highest thermal conductivity in silicone greases. [48] Specifically, the ratio was fixed at 70 at% Ga, which translates to a composite of Ga:Ag:silicone elastomer volumetric ratio of 37:13:50 [23] (corresponding to 0.7 g Ga fillers, 0.46 g Ag particles, and 0.16 g of precursor polymer solution). The final thickness of the cured composites depends on the curing pressures (0 to 4.5 MPa), with larger curing pressures leading to smaller thicknesses. To ensure that sample thickness did not affect our data interpretation, we collected an additional data set of the 100 cSt samples where the final thickness was kept constant. This was done by scaling the volume of the uncured/uncompressed sample in such a way that the final thickness of the cured composite resulted in a thickness of ≈1.5 mm (see the Experimental Section and Supporting Information Table S1). Next, we describe the thermal properties and microscopic morphology of the resulting composite pads with LM fillers as well as pads with combined LM and Ag co-fillers. for 50% LM volume fraction [16,19,21,53] ). Curiously, applying ≈0.4 MPa compressive pressure during curing of the LM-only composite pads only increases the thermal conductivity of the 100 cSt matrix composite. When cured under load, the conductivity increases ≈20% to 1.6 W m −1 K −1 for the lower viscosity matrix but is equal to 1.26 W m −1 K −1 for the 2300 cSt matrix (i.e., effectively equivalent to that without load).

V-PDMS Composites with LM Fillers
The electron micrographs of the composite pad cross-sections revealed the underlying physical reasons for these different responses to applied curing pressure (see Figure 3). Regardless of the matrix precure viscosity, LM-only composite pads cured without a load consist primarily of separate and nearly spherical liquid microdroplets (see Figure 3a,c). LM fillers embedded in the compressed higher viscosity matrix elongate in the direction perpendicular to the load applied during curing (see Figure 3b). This feature is preserved by the curing process and implies that the 2300 cSt viscosity precursor polymer solution does not easily displace from in-between the fillers. The nondisplaced precursor polymer matrix solution and unruptured oxide shells keep the encapsulated droplets isolated from the neighboring droplets. This microstructural feature of the higher viscosity sample prevents the formation of thermal percolation paths with interconnected features and thus yields a lower thermal conductivity.
In contrast, the cross-sectional micrograph of the 100 cSt LM-only composite pad cured under load reveals many interconnected droplets (see Figure 3d). This observation confirms that within the 100 cSt matrix, the applied load displaces the precursor polymer solution between fillers, ruptures the Ga oxide shell on the LM droplets, and produces a higher degree of connectivity between the fillers. However, this approach for LM-only composites is limited by the overall fluidity of the LM-polymer mixture. Specifically, despite the tightly applied sample mold, the LM-polymer mixture leaks even under the mild 0.4 MPa pressure, which results in thin pads (0.7 mm for 100 cSt and 0.8 mm for 2300 cSt samples, see Figure 2a). Further increasing the pressure, results in leakage of the majority of the sample with only a small amount of residual sample left www.advmatinterfaces.de on the bars (i.e., a suitable pad is not formed). As we discuss below, the addition of solid particles resolves this issue. Figure 2b illustrates the thermal impact of the precure viscosity of the precursor polymer solution (≈100 cSt vs ≈2300 cSt) as well as the curing pressure (no pressure vs 0.4 MPa) on composite pads with both Ag and LM co-fillers. The thermal conductivity enhancement in these composite pads relative to LM-only composites is evident even for samples cured without applied load. We measure thermal conductivities of 2.6 and 3.5 W m −1 K −1 for the 2300 and 100 cSt matrices, respectively (vs 1.24 and 1.3 W m −1 K −1 for the LM-only composite pads described in Section 2.2). As explained in Section 2.1, some alloying between the Ag and LM fillers occurs even during mixing prior to sample casting. The higher thermal conductivity of the 100 cSt matrix sample stems from the lower precure viscosity solution promoting a higher degree of contact and alloying of fillers during mixing than the 2300 cSt matrix (evidenced by the amount of visible alloy nanoneedle formation observed in the electron micrographs of Figure 3e,g).

V-PDMS Composites with Ag and LM Co-Fillers
The combined benefits of applied curing pressure, lower precure viscosity, and combined LM and Ag co-fillers are evident through the thermal conductivity and thickness data in Figure 2b. Applying 0.4 MPa of curing pressure approximately doubles the composite pad thermal conductivity relative to no applied pressure. In addition, the lower precure matrix viscosity promotes increased Ag-Ga alloy formation and reaches a value  Figure S8). www.advmatinterfaces.de of 7.6 W m −1 K −1 . Notably, the addition of the solid Ag particles inhibits leakage of the polymer precursor mixture during curing and addresses the issue described at the end of Section 2.2. The thickness of cured composites with and without applied curing pressure is similar as in Figure 2b, whereas a large drop in thickness is seen in Figure 2a.
The cross-sectional electron micrographs in Figure 3e-h illustrate a high degree of LM droplet "smudging" and nanoneedle formation in all of the samples. Thus, as we expected, the alloying process increases the fillers' interconnectivity and enhances the composite's thermal conductivity. The thermal data indicates that the process is promoted by lowering the precure viscosity of the polymer matrix and applying the compressive load during the thermal curing process. While the focus of this work is primarily on thermal properties, we also note that all of the LM-Ag-based cured polymer pads were electrically conductive and had low electrical resistances of ≈5-10 Ω (see Supporting Information Section S7). In simple terms, both of these factors allow more direct contact between solid and liquid particles, while the applied load also facilitates the rupture of the oxide shell. The application of curing pressure is critical because only limited alloying occurs when Ag is gently mixed with Ga (evident from cross-sectional electron micrographs in Figure 3e,g). The magnitude of the curing pressure impacts these microscopic mechanisms and we systematically explore this parameter below. Figure 4 illustrates the effect of varying curing pressure on the thermal conductivity and thickness of low and high precure matrix viscosity samples with solid and liquid co-fillers. In agreement with the above results, thermal conductivity increases as curing pressure is increased and/or precure viscosity is decreased. For samples with the 100 cSt precursor polymer formation, this increase is approximately linear up to ≈2 MPa and reaches a thermal conductivity of ≈15 W m −1 K −1 . The thermal conductivity of the lower viscosity matrix samples is less sensitive to curing pressures in the ≈2 to 4.5 MPa range and spans the 15 to 20 W m −1 K −1 range. The composites with the 100 cSt precursor polymer solution have a noticeably higher thermal conductivity than the 2300 cSt samples throughout the entire curing pressure range.

Impact of Curing Pressure on V-PDMS Composites with Ag and LM Co-Fillers
Increasing the curing pressure ruptures the LM fillers and forms thermally conductive bridges within the low viscosity polymer matrix as shown in the cross-sectional electron micrograph in Figure 4c. This increased connectivity within the matrix enhances the thermal conductivity of the composite as the curing pressure is increased. The presence of unruptured LM fillers in the higher viscosity polymer pads shows a decrease in filler connectivity relative to the lower viscosity polymer pads (Figure 4c,d). Upon increasing the curing pressure, enhanced

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alloying is observed between the LM and Ag fillers, but the presence of unruptured LM fillers explains the smaller increase in the thermal conductivity for the samples that used the precursor solution with higher viscosity.
We also performed experiments with commercial "offthe-shelf" two-part silicone polymer kits that are commonly employed by researchers, and found that these did not replicate the results of the five-part V-PDMS kit. More specifically, we worked with Sylgard-184, Ecoflex 00-20, and Smooth-on OOMOO-25 kits. These polymer kits have viscosities on the order of several thousand cSt, and so one might expect them to behave similarly to our 2300 cSt V-PDMS samples, but this was not the case. We found that the Sylgard-184 and Ecoflex 00-20 kits did not consistently cure with applied load (see Supporting Information Section S5). OOMOO-25 did consistently cure with applied load and so those results are included in Figure 4a,b. While the thickness of the OOMOO-25 samples trended similarly with curing pressure to the 2300 cSt V-PDMS data, the thermal conductivity data trended quite differently. The thermal conductivity of the OOMOO-25 samples was consistently lower than the 2300 cSt V-PDMS data and was insensitive to curing pressure. One possible reason for this thermal conductivity difference could be the presence of silica particles in the polymer solution that were originally put in place by the manufacturer (see Supporting Information Section S6). The presence of these silica particles could disrupt the formation of a metallic percolation network. In addition, the pot life of the OOMOO-25 kit is only 15 min and this short amount of processing time could affect the ability to rupture the LM oxide shell and achieve good filler-filler contact. The collective results in this paragraph indicate that the polymer matrix for these composites must be carefully selected.
We also performed experiments to confirm that sample thickness and/or thermal contact resistance is not affecting our data interpretation. More specifically, the thermal conductivity measured by our system is an effective property that includes the thermal resistance of the sample itself as well as the thermal contact resistance between the sample and the SBA bars. The thinnest 100 cSt V-PDMS samples were ≈1 mm thick, and this is much larger than the sub-10 µm particle sizes for the LM and Ag filler particles. Consequently, the true thermal conductivity of the sample should not be affected by sample thickness. Thermal contact resistance between our measurement system and the sample could also affect the measurement results, and we performed several experiments that indicate this effect is small. One of these experimental sets is illustrated in Figure 4a,b and is labeled "constant thickness 100 cSt V-PDMS." In this experimental set, we prepared a set of samples that had a final constant thickness of ≈1.5 mm regardless of the applied curing pressure. The measured thermal conductivity of these constant thickness samples overlaps with the variable thickness samples (Figure 4a) and this indicates that thermal contact resistance does not play an important role in our measurements (or that this effect is at least smaller than the thermal conductivity uncertainty resulting from sampleto-sample variations). Additional experiments confirming the small-to-minimal effect of thermal contact resistance on our data interpretation are included in Section S3 of the Supporting Information.
Finally, we qualitatively discuss the intercoupling between curing pressure, viscosity of the precursor polymer solution, and composite mechanical characteristics. We observed that the lower viscosity polymer composite pads were less compliant and more brittle than the higher viscosity polymer composite pads throughout the entire curing pressure range of 0-4.5 MPa (see Supporting Information Section S7). We believe this decreased compliance is a result of two main effects. First, the lower viscosity polymer composite pads exhibit more alloying between the Ag and Ga fillers and this process should stiffen the composite. Second, at higher curing pressures (e.g., ≳1.7 MPa for the precursor polymer solution with lower viscosity), the composite began to noticeably leak outside of the sample mold. Since the Ag and Ga fillers have solidified into a stiff alloy network, we suspect this leakage is primarily uncured precursor polymer solution and that the 50 vol% fraction of polymer matrix is no longer maintained at these elevated curing pressures (i.e., a decrease in soft polymer content leads to a more brittle composite). In contrast to the lower viscosity polymer pads, the higher viscosity polymer pads maintained mechanical compliance throughout the entire range of curing pressures. We believe this maintained compliance originates from the absence of a stiff alloy network formation between the Ag and Ga fillers. In addition, at higher curing pressures when leakage began to noticeably occur (e.g., ≳0.8 MPa for the precursor polymer solution with higher viscosity), that leakage was likely not selective and consisted of precursor polymer solution, Ag filler, and Ga filler. This means that the 50 vol% fraction of polymer matrix in these composites would be roughly maintained and so would the corresponding mechanical compliance. We also observe that when applying curing pressure, the lower viscosity polymer composite pad is thicker than the higher viscosity polymer composite pad (Figures 2b and 4b). We attribute this to the presence of the stiff Ag-Ga network in the samples that used the precursor polymer solution with lower viscosity, which likely inhibits sample leakage while curing under compression. The qualitative observations in this paragraph highlight that increasing curing pressure beyond a certain point has diminishing benefits and that further research will be necessary to balance the materials composition, thermal properties, mechanical properties, and curing pressure of these solid-phase polymer TIMs.

Conclusion
In this work, we introduced a multifaceted strategy to enhance the thermal conductivity of solid-phase polymer composites. This strategy synergistically combines three key characteristics: reactive solid and liquid fillers, a polymer matrix with low precure viscosity, and mechanical compression during thermal curing. Each of these characteristics plays a key role in creating the high thermal conductivity polymer composite. The low precure matrix viscosity and mechanical compression during thermal curing facilitates direct physical contact between the composite's co-filler materials (Ga LM droplets and solid Ag particles) and rupture of the oxide shell on droplet surface. Upon physical contact, the Ga and Ag react to form needlelike intermetallic alloy structures. These needle-like alloys in www.advmatinterfaces.de turn promote the formation of a percolated network of Ga, Ag, and Ag-Ga alloy. The end result of this multifaceted strategy is the achievement of a solid-phase polymer TIM pad with a high thermal conductivity of ≈15 W m −1 K −1 (for a curing pressure of 2 MPa). Importantly, this high thermal conductivity is maintained even after removal of the curing pressure, which means that these pads can be used in typical low-pressure TIM applications (0.2-0.3 MPa, i.e., less than 50 psi). One of the key discoveries in this work is that precure viscosity of the polymer matrix should be significantly smaller than that of typical two-part polymer kits (on the order of 10 2 cSt vs 10 3 cSt). This finding will have important implications on the development of next-generation solid-phase polymer TIMs.

Experimental Section
Materials: Pure Ga (99.99%) was purchased from Rotometals which was used to fabricate the LM fillers. Commercially available Ag powder (APS 4-7 µm, 99.9%) was purchased from Alfa Aesar and used as the metal co-filler (see Supporting Information Section S1 for further filler size distribution characterization). The different polymer matrices used in this work were low viscosity V-PDMS (≈100 cSt), high viscosity V-PDMS (≈2300 cSt), and OOMOO-25 (see Supporting Information Section S8 for measured viscosity). The components for V-PDMS polymer were purchased from Gelest. Specifically, base polymers with different viscosities, specifically DMS-V21 (100 cSt) and DMS-V33 (3500 cSt), catalyst SIP6830.3, inhibitor SIT7900.0, chain extender DMS-H21 (100 cSt), and crosslinker HMS-301 (25-35 cSt) were used for formulating the polymer. While the DMS-V33 base polymer had a viscosity of 3500 cSt, its mixture with the chain extender and crosslinker resulted in a viscosity of ≈2300 cSt (see Table S3 in the Supporting Information), and so this measured viscosity was instead referred throughout this work. The OOMOO-25 kit (tin cured silicone) from Smooth-On was used to fabricate polymer pads that used high viscosity commercially available silicone kits as the matrix. Ecoflex 00-20 kit (platinum cured silicone) from Smooth-On and Dow Corning 184 Sylgard polymer-curing agent set were also attempted as a composite matrix to formulate the pads under thermal curing load.
V-PDMS Elastomer System Formulation: The low viscosity V-PDMS was prepared using 100 cSt base polymer. The 100 cSt formulation "part A" was prepared by mixing 2 g DMS-V21 base polymer with 1 µL of SIP6830.3 catalyst and 3 µL SIT7900.0 inhibitor. "Part B" was prepared by mixing 0.13 g HMS-301 crosslinker with 0.58 g DMS-H21 chain extender. For the high viscosity polymer matrix (2300 cSt formulation), "part A" was prepared by mixing 6.62 g DMS-V33 base polymer with 0.5 µL of SIP6830.3 catalyst and 1.4 µL SIT7900.0 inhibitor. "Part B" was prepared by mixing 0.06 g HMS-301 crosslinker with 0.27 g DMS-H21 chain extender. An inhibitor was added to extend the time allowed for processing the premixes by inhibiting crosslinking between the hydride and vinyl groups and preventing a premature increase in viscosity. A chain extender was included to replace the long base polymer chains with shorter polymer chains, which then led to a lower viscosity. [41] For both formulations, molar ratios of crosslinker to chain extender and crosslinker to polymer base were maintained (0.56 and 0.78, respectively). Further, the molar ratio of the inhibitor to crosslinker was kept constant at 0.13 and the molar ratio of the catalyst to crosslinker was kept constant at 0.03 (see Supporting Information Section S2).
Fabrication of Composite Pads with only LM-Fillers: For fabricating 100 cSt V-PDMS pads with LM fillers only (Ga:V-PDMS 100cSt 50:50 v/v), 1.93 g Ga fillers were weighed and added in 0.234 g "part A" of the 100 cSt formulation and mixed gently for 1 min until the Ga LM was dispersed in the matrix. 0.083 g of "part B" (100 cSt formulation) was then added to the Ga-Part A V-PDMS 100cSt mixture and further mixed for 1 min. A similar procedure was followed for the 2300 cSt V-PDMS pads with LM fillers. In this case, the weights of the 2300 cSt V-PDMS "part A" and "part B" were scaled to 0.302 and 0.015 g, respectively, to maintain the molar ratios used in the 100 cSt recipe (see Supporting Information Section S2). The resultant uncured composite was transferred to the bottom bar of the SBA setup using a mold that was sealed around the bars to decrease leakage of uncured composite during the application of the curing pressure. The top and bottom bar of SBA were heated to 50 °C prior to transferring the uncured composite to the lower bar. Pressure during thermal curing of the composite was applied through the top bar (0-4.5 MPa), and the sample was cured for 3 h.
Fabrication of Composite Pads with LM and Ag Co-Fillers: The composites with Ga and Ag fillers were fabricated in a similar manner to the LM-only composites. These pads were made with 50 vol% filler while maintaining 70 at% Ga. This translated to a Ga:Ag:polymer volumetric ratio of 37:13:50. For the 100 cSt V-PDMS polymer pads, 0.7 g Ga fillers were weighed and added to 0.116 g Part A V-PDMS 100cSt and mixed gently for 1 min, followed by the addition of 0.46 g Ag co-filler and an additional 1 min stirring. Next, 0.041 g Part B V-PDMS 100cSt was added and then stirred for another 1 min. The uncured composite was then transferred to the SBA for thermal curing under compression. The quantity of Ga and Ag fillers was kept the same for the 2300 cSt V-PDMS composite pads. To fabricate constant thickness samples at all curing pressures, the weight of all the components (fillers and polymer) was scaled such that the 70 at% Ga ratio between the Ga and Ag fillers was maintained. The polymer weight was adjusted to maintain 50 vol% fillers (see Supporting Information Section S2). The composite pads fabricated with the commercial silicone kit of OOMOO-25 were also fabricated using the same amount of Ga and Ag fillers and the same sequential mixing as adopted for the V-PDMS composite pads (see Supporting Information Section S2 for more details).
Thermal Characterization: The thermal characteristics and pressure of the samples were measured using a stepped-bar apparatus which is a steady-state thermal reference bar method following a modified ASTM D5470 standard. [16,48,49,54] After curing the samples, the temperatures of the top and bottom copper reference bars were adjusted to 95 and 30 °C, respectively, to perform the thermal conductivity measurement. During the measurements, the samples were subjected to a constant measurement pressure of ≈0.2-0.3 MPa, and the thermal resistance was measured for the corresponding thickness of the polymer pad. The uncertainties for an individual measurement were ≈4-6% for thermal conductivity, 0.1 MPa for pressure, and 10 µm for thickness (68% confidence interval). [16,48] Rheological Characterization: Viscosity was measured using a Discovery Hybrid Rheometer 2 (DHR2) from TA Instruments at 25 °C using a parallel plate geometry (25 mm stainless steel parallel plates). Using the parallel plate geometry in a rotational experiment to measure viscosity resulted in a shear rate that is a function of the radius. Therefore, viscosity measurements were repeated using the cone-andplate geometry and comparable results were obtained (see Supporting Information Figure S9). The detailed procedure can be found in Section S8 of the Supporting Information.
Microscopy: All electron micrographs were collected using an Amray 1910 FE-SEM with a 15 kV accelerating voltage. Energy-dispersive spectroscopy element graph of the commercial kit OOMOO-25 was collected using SEM/FIB Focused Ion Beam-Auriga (Zeiss). The optical images were collected with a Zeiss Axio Zoom.V16 microscope.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.