Breaking Thermal Conductivity–Electrical Resistivity Trade‐Off in Liquid Metal–Based Thermal Interface Materials via Interface Engineering

ABSTRACT

Liquid metal–based thermal interface materials offer superior thermal conductivity and fluidity but are limited in practical applications by their inherently low electrical resistivity. Here, we present an interface engineering strategy that overcomes this fundamental trade‐off, enabling the synthesis of GaIn‐B featuring a bimodal particle size distribution. This structure simultaneously exhibits a non‐contact network feature that effectively prevents electrical percolation while maintaining efficient thermal transport. GaIn‐B exhibits a significant thermal conductivity of approximately 16 W m⁻¹ K⁻¹ and an electrical resistivity exceeding 10¹¹ ohm cm. We developed a phenomenological model based on effective medium theory to quantitatively describe and predict the critical conditions for breaking the thermal–electrical trade‐off. The simplicity and scalability of the GaIn‐B synthesis process enable kilogram‐scale production, making it highly suitable for industrial applications.

An interfacially stabilized, electrically insulated bimodal architecture is established in a liquid‐state gallium–indium composite through ultrathin polysiloxane regulation. The design simultaneously delivers a thermal conductivity of ∼16 W m⁻¹ K⁻¹ and an electrical resistivity exceeding 10¹¹ Ω·cm, decoupling the long‐standing thermal–electrical trade‐off in liquid‐metal thermal interface materials and enabling scalable thermal management for advanced electronics.

1. Introduction

Energy consumption by data centers and robotic systems is projected to exceed 1000 TWh by 2026, driven by the rapid growth of Artificial Intelligence Big Data Models (AI BDM) [1]. Approximately 40% of this energy is consumed by cooling systems, which use nearly as much power as the IT equipment they cool [2, 3]. Efficient thermal management has thus become a critical global challenge, with thermal interface materials (TIMs) playing a pivotal role in dissipating heat from electronic components [4, 5]. Current TIM solutions, primarily composed of conductive metal or ceramic fillers (e.g., Al, Zn, Al₂O₃, ZnO, AlN) in insulating polymer matrices, are nearing their performance limits [6, 7, 8, 9, 10, 11, 12]. Leading commercial TIMs, such as Henkel's BERGQUIST LIQUI FORM TLF 10000 [13] and Laird's Tputty 910 [14], offer thermal conductivities (TC_com) of only around 10 W m⁻¹ K⁻¹, insufficient for next‐generation systems. Moreover, achieving high TC_com alone is inadequate; additional critical properties such as electrical insulation and material flowability must also be optimized. Solid particle–filled TIMs are increasingly struggling to meet the multifaceted needs of future thermal management [6, 15, 16, 17, 18].

Liquid metal–based TIMs (LM‐TIMs) are emerging as a promising alternative [19, 20, 21, 22]. LM offers superior TC_com (∼26.4 W m⁻¹ K⁻¹) and fluidity [21, 23, 24], allowing them to conform to irregular surfaces—an essential trait for advanced applications like AI‐driven robotics and flexible electronics [25], where conventional TIMs often fall short. Despite these advantages, LM‐TIMs face significant challenges, notably the trade‐off between TC_com and electrical insulation. LMs conduct heat primarily via free electron movement, which imparts high electrical conductivity [26, 27, 28, 29]. In LM‐TIMs, as the LM content increases to enhance heat transfer, electrical resistivity (ER_com) decreases sharply [17], increasing the risk of electrical failure and short circuits. Previous research has struggled to balance these conflicting requirements. The state‐of‐the‐art solutions have achieved TC_com around 6.70 W m⁻¹ K⁻¹ but at the cost of maintaining relatively low ERs on the order of 6.76 × 10⁹ ohm cm [15]. Recent advancements employing non‐percolation densification techniques have marked a significant breakthrough in ER_com, reaching 10¹⁷ ohm cm [30]. However, this achievement came at the expense of TC_com, which was limited to 4.20 W m⁻¹ K⁻¹, far below the performance required for advanced thermal management applications. These findings suggest that delivering both high TC_com and robust ER_com in LM‐based composites remains extremely challenging.

Here, we introduce a simple yet effective interface engineering strategy that overcomes the long‐standing trade‐off between TC_com and insulating property in LM‐TIMs (Figure 1a,e). By precisely regulating the interfacial tension of LM particles, we synthesized an LM‐TIM with a unique bimodal particle size distribution, designated as GaIn‐B (Figure 1b). This material architecture allows small LM particles to efficiently fill the gaps between larger ones while remaining electrically insulated, forming a non‐contact network that effectively prevents electrical percolation while maintaining efficient thermal transport.

FIGURE 1.

Properties and comparison of LM‐TIMs. (a) Comparative analysis showcasing applied thermal resistance (R _eff), contact thermal resistance (R _c), bulk thermal resistance (R _b), breakdown strength, thixotropy and TC_com, among GaIn‐B, commercial Tputty 910, GaIn‐U and Henkel TLF 6000. (b) Schematic illustration of the bimodal structure of GaIn‐B. (c) Schematic illustration of the unimodal structure of GaIn‐U. (d) The bond line thickness (BLT) of GaIn‐B, commercial Tputty 910, GaIn‐U, and Henkel TLF 6000 were evaluated. Here, R _b (unit: K m² W⁻¹) represents the theoretical thermal resistance of the TIM under a specified pressure, calculated as R _b = BLT/TC_com, where BLT is the bond line thickness at a given pressure and temperature. The contact thermal resistance (R _c) was obtained as the difference between the applied thermal resistance (R _eff) and R _b, with R _eff measured using a thermal resistance tester in accordance with ASTM D5470. All measurements were conducted under a pressure of 20 psi and a hot‐side temperature of 60°C. (e) Cross‐comparison of TC_com and ER_com of GaIn‐B and GaIn‐U with previously reported benchmarks. The numeric identifiers in the image correspond to those in Table S2.

As a result, GaIn‐B exhibits a substantial TC_com exceeding 15.83 W m⁻¹ K⁻¹, a remarkable 300% improvement over conventional LM‐TIMs with uniform dispersion, designated as GaIn‐U (Figure 1c). Due to the superior flowability, GaIn‐B also exhibits excellent thixotropy (Figure 1a and Figure S1) and a reduced bond line thickness (BLT, Figure 1d), ultralow applied thermal resistance (R _eff, Figure 1a) and high effective thermal interface conductance (TIC_eff, Table S1), even compared to state‐of‐the‐art commercial thermal grease like Tputty 910. Furthermore, GaIn‐B exhibits an ER_com greater than 10¹¹ ohm cm, exceeding conventional high‐TC_com TIMs containing conductive fillers by more than two orders of magnitude (Figure 1e and Table S2). This enables GaIn‐B to maintain a dielectric breakdown strength of 5.03 kV mm⁻¹ (Figure 1a and Figure S2).

2. Results and Discussion

2.1. Interfacial Tension‐Driven Formation of GaIn‐B With Bimodal Particle Size Distribution

The GaIn‐B TIM features a bimodal particle size distribution and an insulating isolated stacking structure, achieved by regulating the interfacial tension of LM droplets with a surface‐modifying agent during synthesis.

In synthesizing GaIn‐B, we began by mixing Ga‐based LM (eutectic gallium‐indium alloy, EGaIn) with 3‐mercaptopropyl trimethoxysilane (trade name: KH 590) under magnetic stirring. Fourier‐transform infrared (FTIR) (Figure S3a,b) and Raman spectroscopy (Figure S3c) confirmed that KH 590 effectively bonds to the naturally oxidized LM surface, forming a polysiloxane wrapping layer around the LM particles (Figure 2a,c,i and Figure S4). Subsequent addition of silicone oil (SO) under continued stirring led to a dynamic rearrangement of LM particles and the polysiloxane layer, driven by changes in interfacial tension. Specifically, the interfacial tension between the polysiloxane‐coated LM surfaces and SO was measured at only 32 ± 1 mN m⁻¹ (Figure S5a–e), promoting the formation of small LM particles (referred to as SLMs). In contrast, the interfacial tension between pristine LM surfaces and SO was significantly higher at 442 ± 47 mN m⁻¹ (Figure S7f,g and Table S3), favoring the formation of large LM particles (referred to as LLMs). The self‐assembly process, governed by the large interfacial tension difference and surfactant dynamics during synthesis, gives rise to the bimodal particle size distribution observed in the system. The mixture was then left undisturbed for 21 days at 25°C to enable unreacted KH 590 to further react with the LM, forming an SH‐polysiloxane encapsulated structure for both SLMs and LLMs. Simultaneously, the free KH590 was also polymerized into sulfhydryl‐polyhedral oligomeric silsesquioxanes (SH‐POSS) structure between LM particles, which further enhanced the electrical insulation properties of GaIn‐B. A detailed description of the evolving thermal and electrical characteristics with respect to reaction time can be found in Text S1. This reaction was evidenced by x‐ray photoelectron spectroscopy (XPS) (Figure 2b), which showed shifts in binding energies indicative of polysiloxane formation. In addition, nuclear magnetic resonance (NMR) [31] (Figure 2c), small‐angle x‐ray scattering (SAXS), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA) confirmed the presence and structural stability of the polysiloxane layers with a typical thickness of approximately 5.23 nm (Figures S6 and S7). This encapsulation layer acts as a critical insulating barrier, facilitating the formation of the desired non‐contact network.

FIGURE 2.

Structural and compositional analysis of the bimodal isolated stacking structure in GaIn‐B. (a) Schematic representation of the synthesis process of GaIn‐B. (b) XPS analysis of GaIn‐B and KH 590. (c) ²⁹Si NMR characterization of GaIn‐B, showing two distinct peaks at −68.5 and −58.3 ppm with an approximate 1:1 ratio, corresponding to the SH‐polysiloxane network and SH‐POSS. (d) Comparison of mean particle sizes derived from interfacial tension by using Kolmogorov's theory at various KH 590 ratios with those measured via SEM and Nano‐CT for GaIn‐B. (e) Particle size distribution of LLM and SLM in GaIn‐B (ratio of KH 590 = 6 vol%), with inset showing Nano‐CT imaging (scale bar: 50 µm). (f) Temperature‐dependent TC_com of GaIn‐B and GaIn‐U. (g) Arrhenius analysis of the temperature‐dependent ER_com of GaIn‐B and GaIn‐U. (h) EDX spectrum of GaIn‐U showing a distinct unimodal distribution (LM spheres: blue; scale bar: 7.5 µm). (i) EDX spectrum of GaIn‐B, revealing a bimodal distribution of particles (large spheres: yellow; small spheres: purple; polysiloxane matrix: cyan; scale bar: 7.5 µm). (j) SEM and EDX mapping of GaIn‐B (scale bar: 200 µm).

According to Kolmogorov theory [32, 33], during the droplet breakup process in the dispersion of immiscible liquids, dispersed droplets deform under flow‐induced stresses, and breakup occurs only when the disruptive viscous or inertial forces overcome the restoring force provided by interfacial tension. Lower interfacial tension reduces the energy barrier required for breakup, thereby promoting the formation of smaller droplets. Therefore, Shinnar [34] proposed that the average droplet size (d _mean) under viscous stress‐dominated conditions is controlled by the interfacial tension between immiscible liquids and the dynamic viscosity of the continuous phase:

$$d_{\mathrm{mean}}=\frac{d_{\max }}{C}{A}_2{\epsilon }^{-\frac{1}{2}}{{\mu }_c}^{-\frac{1}{2}}\sigma {{\rho }_c}^{-\frac{1}{2}}$$ (1)

where d _max is the maximum stable droplet diameter, C is a dimensionless constant, A ₂ is a proportionality constant, ε is the energy dissipation rate per unit mass, μ _c is the dynamic viscosity of the continuous phase, σ is the interfacial tension between the dispersed and continuous phases, and ρ _c is the density of the continuous phase (detailed parameters are provided in Table S4).

By adjusting the concentration of KH 590, we were able to control the viscosity of the continuous matrix phase and, consequently, the particle sizes of SLM and LLM (Figure 2d). The SLM sizes derived from the bimodal particle distribution model (BPDM) (Figure S8a) and the LLM sizes measured by scanning electron microscopy (SEM) (Figure 2d and Figure S8b) were consistent with the theoretical predictions based on interfacial tension data, as described by Kolmogorov theory. Specifically, GaIn‐B samples were synthesized with KH 590 volume fraction of 2, 4, 6, 8, and 10 vol%, while maintaining a constant volume ratio of LM to SO(LM:SO in volume ratio = 5.86:1). As the KH 590 concentration increased, the dynamic viscosity of the continuous phase decreased from 284.90 to 16.37 mPa s (Figure 2d and Figure S9), inversely correlating with the particle sizes after dispersion. Consequently, the LLM particle sizes increased from 6.79 to 80.63 µm with higher KH 590 concentrations (Figure S10 and S11). In addition, SEM analysis confirmed the presence of SLM.

To measure the SLM size distribution and gain further insights into the microstructure of GaIn‐B, we conducted nano‐computed tomography (Nano‐CT) (Figure 2d,e; Figure S8a and S12) on samples containing 6 vol% and 10 vol% KH 590. The average size of the LLM particles was 22.50 ± 8.79 µm, while the SLM particles averaged 3.60 ± 1.14 µm, confirming a clear bimodal distribution where the smaller SLMs homogeneously fill the interstitial spaces between the larger LLMs (Figure 2e and Figure S13a–f). This unique architecture effectively reduces the thickness of the low TC_com insulating layer between LLM particles, thereby optimizing the thermal transport properties of GaIn‐B.

2.2. Breaking the Thermal–Electrical Trade‐Off in LM‐TIMs

Energy‐dispersive x‐ray (EDX) mapping demonstrates that in GaIn‐B, the LM particles are uniformly encapsulated within a polysiloxane layer. Silicon enrichment is observed in association with the LM particle surfaces (Figure 2i,j). In addition, sulfur‐containing species are identified in the interfacial/grain‐boundary regions, as shown in Figure S13g. The encapsulation likely results from the non‐covalent interaction between the ─SH groups and Ga₂O₃ [35] on LM particle surfaces, which effectively isolates the LM particles. This isolation prevents the formation of electrical percolation pathways, thereby reducing the risk of dielectric breakdown. In contrast, GaIn‐U lacks this encapsulation (Figure 2h), leading to inadequate coverage of polysiloxanes on the LM particle surfaces. As a result, there is an elevated risk of ohmic contact and coalescence between particles in GaIn‐U. The bimodal size distribution facilitates the formation of a non‐contact thermally conductive network, effectively separating electrically conductive pathways while maintaining efficient thermal transport [36]. At an LM loading of 80.30 vol%, this arrangement significantly reduces the thickness of the SO insulative layer (SO layer, d _SO) to 0.15 µm (Figure 3d and Figure S13c). Compared with GaIn‐U (d _SO = 0.42 µm), this reduction decreases the low‐thermal‐conductivity transport path length by about 65%, greatly enhancing the thermal transport efficiency of GaIn‐B. As a result, GaIn‐B achieves a composite interfacial thermal resistivity (R _i) as low as 0.29 K m W⁻¹, compared to 2.16 K m W⁻¹ in GaIn‐U (Figure 1b,c and Figure S14).

FIGURE 3.

A phenomenological model for predicting TC_com and ER_com of nonpercolation TIMs with a bimodal particle distribution structure. (a) Simulated distribution of LM droplets within GaIn‐B, illustrating the dispersed SLM situated between LLM particles, thereby preventing direct contact between any LM droplets. (b) Measured TC_com and ER_com of GaIn‐B across various KH 590 ratios. (c) Calculated d _SLM and vol_SLM at different KH 590 ratios, derived from solutions obtained through the BPDM model. (d) Calculated results of d _SO corresponding to different KH 590 ratios obtained from the BPDM model. (e) Comparison between the experimentally measured TC_com and ER_com of GaIn‐B (comprising 6 vol% KH 590, 13.70 vol% SO, and 80.30 vol% LM) and the corresponding theoretical values calculated by the BPDM model. (f) Comparison of experimental measured TC_com and (g) ER_com of GaIn‐B with predictions from the BPDM, Bruggeman, MG, Series, and Parallel Models.

The formation of the bimodal particle size distribution and the insulating polysiloxane encapsulation are critical for breaking the thermal–electrical trade‐off in LM‐TIMs. The smaller SLM particles fill the interstitial spaces between the larger LLM particles, effectively reducing the thickness of the low‐thermal‐conductivity layer and enhancing heat transfer pathways [37]. Simultaneously, the polysiloxane layer prevents direct contact between LM particles, avoiding the formation of electrically conductive pathways and thus maintaining high ER_com. It should be noted that the microstructural parameters (particle size and volume fraction) do not affect TC_com and ER_com independently in a simple one‐parameter manner. Instead, their combined effect is mainly reflected in the effective insulating‐layer thickness (d _SO) and the geometry of the interface region. A smaller d _SO shortens the low‐conductivity heat‐transport path and thus increases TC_com, but simultaneously reduces the electrical separation between particles, which tends to decrease ER_com. Therefore, the balance between TC_com and ER_com is governed by the collective structural outcome of particle size, volume fraction, and interface‐region configuration. The design strategy enables GaIn‐B to achieve exceptionally high TC_com, approximately 16 W m⁻¹ K⁻¹, representing a 300% enhancement compared with conventional LM‐TIMs, and this value further increases to 18.44 W m⁻¹ K⁻¹ when the temperature rises to 155°C. The temperature‐dependent increase in TC_com can be attributed to the reduction in the thermal resistivity of the interfacial region within the composite with increasing temperature (Figure 2f and Figure S14).

Meanwhile, to analyze the temperature‐dependent insulating behavior of GaIn‐B and GaIn‐U, an Arrhenius‐type relationship was used for qualitative analysis of their ER_com–T responses. The log ER_com–1000/T curves show that the ER_com of both samples decreases with increasing temperature, indicating typical thermally activated conduction behavior. Compared with GaIn‐U, GaIn‐B maintains a higher ER_com over the entire temperature range and exhibits a more pronounced linear relationship, suggesting that its charge transport is mainly governed by interfacial barriers. The KH 590‐derived polysiloxane insulating layer increases the electron transport barrier between EGaIn particles and suppresses the formation of thermally activated leakage pathways. Therefore, GaIn‐B exhibits superior high‐temperature insulation retention capability (Figure 2g).

These results demonstrate that by carefully controlling interfacial tension and dynamic viscosity during synthesis, it is possible to engineer the microstructure of LM‐TIMs to optimize both thermal and electrical properties, effectively breaking the traditional thermal–electrical trade‐off.

2.3. Universal Rule to Manipulate Thermal–Electrical Trade‐Off for Functional Composites

To understand the simultaneous achievement of high TC_com and ER_com in GaIn‐B, we developed the BPDM model within the framework of effective medium theory [38] (Figure 3a and Figure S15). In this model, GaIn‐B is considered to comprise two distinct regions: Bulk regions containing LLM and interface regions surrounding the LLM particles, consisting of SLM and the matrix. The bulk and interface regions are connected in series, and within the interface region, the SLM particles and matrix are also connected in series.

The overall composite thermal conductivity (TC_com) and the overall composite electrical resistivity (ER_com) of the composite are determined by the following equations (see Text S2 for detailed derivations):

$$\mathrm{T}{\mathrm{C}}_{\mathrm{com}}=\frac{d_{\mathrm{LLM}}+d_{\mathrm{INTER}}}{\frac{d_{\mathrm{LLM}}}{\mathrm{T}{\mathrm{C}}_{\mathrm{LM}}}+\frac{d_{\mathrm{SLM}}}{\mathrm{T}{\mathrm{C}}_{\mathrm{LM}}}+\frac{d_{\mathrm{INTER}}-d_{\mathrm{SLM}}}{\mathrm{T}{\mathrm{C}}_{\mathrm{SO}}}}$$ (2)

$$\mathrm{E}{\mathrm{R}}_{\mathrm{com}}=\frac{d_{\mathrm{LLM}}\times \mathrm{E}{\mathrm{R}}_{\mathrm{LM}}+d_{\mathrm{SLM}}\times \mathrm{E}{\mathrm{R}}_{\mathrm{LM}}+\left(d_{\mathrm{INTER}}+d_{\mathrm{SLM}}\right)\times \mathrm{E}{\mathrm{R}}_{\mathrm{SO}}}{d_{\mathrm{LLM}}+d_{\mathrm{INTER}}}$$ (3)

$$d_{\mathrm{INTER}}=d_{\mathrm{SO}}+d_{\mathrm{SLM}}=\frac{d_{\mathrm{LLM}}\times \left(1-\mathrm{vo}{\mathrm{l}}_{\mathrm{LLM}}\right)}{3\times \mathrm{vo}{\mathrm{l}}_{\mathrm{LLM}}}$$ (4)

Here, d _LLM is the average diameter of the LLM particles, d _SLM is the average diameter of the SLMs, d _INTER is the effective thickness of the interface region between neighboring LLM particles, including both the SO insulating layer and the SLMs, TC_LM and ER_LM are the intrinsic thermal conductivity and electrical resistivity of bulk LM, and TC_so and ER_so are the intrinsic thermal conductivity and electrical resistivity of the SO matrix containing the polysiloxane layer. Given the total volume fraction of the LM phase (vol_LM), we have vol_LM = vol_LLM + vol_SLM. By inputting the measured values of d _LLM (Figure S11), TC_com, and ER_com (Figure 3b), we solve Equations (2) and (3) to determine d _SLM and vol_SLM (Figure 3c). For the optimized GaIn‐B composition (6 vol% KH 590, 13.70 vol% SO, and 80.30 vol% LM), our model predicts an average small LM particle size d _SLM of 2.74 µm and a volume fraction (vol_SLM) of 7.30%. These calculated values reasonably agree with the experimental results, which measured d _SLM as 3.60 µm. Despite minor discrepancies due to experimental uncertainties and model assumptions, this close agreement validates the predictive capability of the BPDM model in estimating particle size distribution and volume fractions. By fixing vol_LM and d _LLM at measured values, we simulate TC_com and ER_com over a range of d _SLM and vol_SLM. The results (Figure 3e and Figure S16a) show that the optimized TC_com reaches approximately 16 W m⁻¹ K⁻¹, while maintaining ER_com well above 10¹⁰ ohm cm. By tuning KH 590 concentration to modulate d _LLM and d _SLM, we obtained TC_com and ER_com values approaching theoretical limits. For example, in the optimized GaIn‐B sample with 6 vol% KH 590, the material exhibits an ER_com of 1.59 × 10¹¹ ohm cm and a TC_com of 15.83 W m⁻¹ K⁻¹. This high performance benefits from the optimized interface region, within which the average size of SLM particles is 2.74 µm with a volume fraction of 7.3 vol%. The ER_INTER reaches 1.33 × 10¹² ohm cm (Figure S17a), while the TC_INTER attains 3.47 W m⁻¹ K⁻¹ (Figure S17b). Compared with the series, parallel, Bruggeman, and Maxwell–Garnett (MG) models, the BPDM model shows closer agreement with experimentally measured TC_com and ER_com results (Figure 3f,g).

Using this phenomenological model, we can readily determine the optimal particle sizes and volume fractions to achieve desired thermal and electrical properties in TIMs. To validate the general applicability of our model, we prepared a copper thermal grease containing 57.51 vol% large particles (LCu, average size of 25 µm) and 14.37 vol% small particles (SCu, average size of 1 µm). The measured TC_com and ER_com were 2.14 W m⁻¹ K⁻¹ and 4.65 × 10¹¹ ohm cm, respectively, reasonably consistent with the model‐predicted values from our model of 1.21 W m⁻¹ K⁻¹ and 8.08 × 10¹¹ ohm cm (Figure S16b,c). An aluminum thermal grease containing 55.63 vol% large particles (LAl, average size of 25 µm) and 14.37 vol% small particles (SAl, average size of 1 µm) verifies the reliability of the model as well (Figure S16b,c). Note that the difference between experimental and theoretical values can arise due to partial percolation within the composite material. This phenomenon manifests as lower ER_com and higher TC_com than predicted, as partial percolation facilitates enhanced conductive pathways that are not fully accounted for in the theoretical model.

It is noteworthy that, theoretically, increasing the filler concentrations could enhance the TC_com of copper/SO composites (e.g., achieving over 30 W m⁻¹ K⁻¹ at 85 vol% total filler concentration), as shown in Figure S18, while keeping the ER_com well above 10¹⁰ ohm cm. However, in practice, the maximum achievable filler concentration is limited to 71.88 vol% (57.51 vol% large particles and 14.37 vol% small particles), beyond which the composite becomes powder‐like and loses flowability due to the rigidity of the solid copper filler (Figure S19). In contrast, employing LM filler allows us to increase the filler concentration to even 83.71 vol% (e.g., the composition of 2 vol% KH 590, 14.29 vol% SO, and 83.71 vol% LM) while maintaining excellent flowability, fully demonstrating the advantages of LM over traditional solid fillers.

2.4. Scalable Production and Performance of GaIn‐B

The simplicity and scalability of GaIn‐B synthesis allow for kilogram‐scale production even in laboratory conditions, making it highly suitable for industrial applications. For example, a single batch of GaIn‐B weighing 2.5 kg, demonstrated consistent performance similar to that of a smaller batch (Figure S20), can effectively meet the thermal management needs of 15 000 units of 5 W LED (Figure S21) modules, 5000 smartphones, or 50 sets of 1000 W searchlights (Figure 4a). Notably, GaIn‐B exhibits excellent thixotropy across a wide range of shear rates (10⁻¹ to 10² s⁻¹), allowing it to be easily processed in high‐throughput manufacturing environments (Figure S22a). With increasing KH 590 content, the storage modulus (G′) and yield stress of GaIn‐B decrease significantly, resulting in enhanced fluidity. These characteristics make GaIn‐B particularly suitable for industrial‐scale manufacturing [39] (Figure S22b). Utilizing direct ink writing (DIW) technology, GaIn‐B can be patterned onto various substrates, including printed circuit boards (PCBs), chips, and heat sinks. The precision of this technique was confirmed by ultra‐depth microscopy, which revealed uniform dot matrix units with an average height of ∼800 µm (Figure 4b). This consistency across large‐scale arrays demonstrates the excellent processing stability and suitability of GaIn‐B for advanced manufacturing techniques.

FIGURE 4.

Applications of GaIn‐B (ratio of KH 590 = 6 vol%) as a TIM. (a) GaIn‐B is mass‐produced in 2500 g batches, facilitating single‐use in 15000 LED units, 5000 smartphones, or 50 high‐power searchlights; (b) Printing capabilities of GaIn‐B (scale bar: 1.5 cm): A 5 mm diameter GaIn‐B dot matrix demonstrating a uniform distribution thickness of less than 1000 µm; (c) Schematic representation of thermal management in an LED array, and GaIn‐B underwent 10000 temperature cycling tests (1 min on, 2 min off) in a 6587 W m⁻² LED array; (d) Photo and infrared imaging of pure silicone rubber (right) and GaIn‐B incorporated into silicone rubber (left) to enhance TC_com (scale bar: 7.5 cm; histogram equalization color distribution); (e) The conformability and adhesion of GaIn‐B (Left, scale bar: 1.5 mm, Scale bar of left panel: 400 µm; Scale bar of right panel: 150 µm). The shear stress‐strain curves of GaIn‐B and GaIn‐U (right); (f) The infrared thermal images of the motherboard with and without GaIn‐B encapsulation during operation; (g) GaIn‐B is highly suitable for extensive application in the thermal management of IGBT on high‐power inverters; (h) Infrared imaging of IGBT on inverter using GaIn‐B compared to cTIM (Laird Tputty 910) at a total power of 20672.0 W and power density of 287.1 W cm⁻²; (i) Internal chip junction temperatures in high‐power IGBT on inverter using GaIn‐B compared to cTIM (Laird Tputty 910) at a total power of 20672.0 W and power density of 287.1 W cm⁻².

A key challenge with gallium‐based LM is its susceptibility to dealloying in aqueous environments, resulting in volumetric expansion and fracture during operation and consequently increasing contact thermal resistance [40]. The released gallium aggressively corrodes metals such as aluminum, tin, and copper, posing significant safety risks in real‐world applications [41, 42, 43]. In contrast, the encapsulated polysiloxane layer in GaIn‐B inhibits the diffusion of gallium [44], substantially mitigating this issue. To evaluate the corrosion resistance of GaIn‐B, we coated it onto aluminum plates and exposed them to an environment of 85°C and 85% relative humidity for 240 h, after which GaIn‐B was removed and the Al plates were tested. EDX analysis showed no signs of gallium diffusion or corrosion after this prolonged exposure (Figure S23a,b). In contrast, LM exhibited pronounced corrosiveness under the same conditions, as evidenced by EDX analysis showing gallium and indium peaks at 1.12 and 3.29 keV, respectively, along with visible corrosion marks. In practical applications, GaIn‐B was applied to CPU surfaces operated alongside cooling fans for over 240 h without any detected corrosion or significant residues upon cleaning (Figure S23c).

GaIn‐B maintained stable thermal resistance and electrical resistivity after 1000 h of evaluation under 125°C high‐temperature conditions, further verifying its operational reliability under harsh thermal environments (Figure S24). GaIn‐B exhibited stable thermal management capability even after more than 10 000 thermal shock cycles (1 min on, 2 min off), indicating excellent long‐term performance (Figure 4c). Passive heat dissipation performance was comparatively evaluated on high‐power MOSFET module (2.95 W cm⁻²) coated with either GaIn‐B or commercial thermal greases (cTIMs). Infrared thermography revealed that the average case temperatures of the MOSFET modules coated with GaIn‐B were 8.2°C and 8.0°C lower, respectively, than those of the modules treated with two cTIMs (Figure S25a), demonstrating the superior thermal performance of GaIn‐B.

Furthermore, GaIn‐B exhibits significant potential for thermal management in flexible electronics (Figure S25b). By injecting GaIn‐B into Ecoflex silicone rubber, we fabricated a twisted strip subjected to a constant 130°C heat source at one end. Infrared imaging showed efficient heat diffusion along the GaIn‐B‐filled strip, in contrast to the pure silicone rubber strip, which demonstrated heat accumulation and poor thermal performance (Figure 4d). This highlights the applicability of GaIn‐B in flexible and wearable electronics, where effective thermal management is crucial but often challenging [45].

Excellent confinement integrity of GaIn‐B for LM droplets in sub‐100 µm channels was validated by conformally bonding meshing tooth‐type substrates. KH 590 functionalization enabled enhanced interfacial adhesion forces over pristine LM in GaIn‐U (Figure 4e). The superior encapsulation properties of GaIn‐B enable its direct integration onto electronic motherboards, lowering the operating temperature of heat‐generating components from 53.5°C to 46.1°C, and demonstrating excellent potential for electrical insulation applications (Figure 4f).

The high TC_com of GaIn‐B makes it suitable for thermal management in high‐power electronic devices. In experiments with an inverter module (trade name: NVF2G‐22/TS4), both GaIn‐B and commercial Laird Tputty 910 grease (9.1 W m⁻¹ K⁻¹) were applied between the module and the heatsink under a fixed torque of 0.29 N m (Figure 4g). With an input of 380 V and 54.4 A (total power: 20672 W, power density: 287.1 W cm⁻²), the module was operated for 30 min. The junction temperature of the IGBT chip cooled with GaIn‐B stabilized at 70.0°C, while that of the chip set cooled with cTIM stabilized at 74.0°C (Figure 4h,i). This significant temperature reduction demonstrates the superior heat dissipation capability of GaIn‐B, enabling more efficient thermal management for high‐power electronic devices under limited heat exchange conditions with potential benefits for energy‐efficient thermal management.

3. Conclusion

This study presents a significant advancement in the field of TIMs by overcoming the longstanding trade‐off between TC_com and electrical insulation in LM‐TIMs. We synthesized GaIn‐B, a material featuring a bimodal particle size distribution of large and small particles. GaIn‐B exhibits a substantial TC_com of about 16 W m⁻¹ K⁻¹ and an ER_com greater than 10¹¹ ohm cm simultaneously. This remarkable performance stems from the precise regulation of LM interfacial tension and encapsulation within a polysiloxane layer, preventing electrical percolation without compromising TC_com.

Beyond the performance itself, the key conceptual advance lies in realizing a stable bimodal particle‐size distribution in a liquid‐state composite. Bidisperse and multimodal filler distributions are widely used in conventional solid‐state composites, where particle packing can be readily controlled and fixed within a solid matrix. In contrast, achieving such a distribution in a liquid‐state system is far more challenging because the dispersed phase remains mobile and can continuously deform, merge, and reorganize under interfacial forces. Here, we show that surface‐energy regulation provides an effective strategy to control this dynamic behavior and stabilize a bimodal distribution in a liquid‐metal composite. To the best of our knowledge, this is the first report of a deliberately engineered bidisperse liquid‐metal composite in the liquid state.

In addition, we established the BPDM model that quantitatively correlates particle size, volume fraction, and interfacial‐region parameters with the coupled evolution of TC_com and ER_com, providing a useful framework for the rational design of high‐performance TIMs. The simplicity and scalability of the GaIn‐B synthesis process enable kilogram‐scale production, making it highly suitable for industrial applications. GaIn‐B represents a promising approach to thermal management in advanced electronic systems, introducing a new approach where interface engineering and particle size distribution are leveraged to optimize multiple functional properties simultaneously. The ability to achieve both high TC_com and robust electrical insulation opens new avenues for designing functional composites tailored to the complex demands of next‐generation systems. Its potential extends beyond conventional electronics, with significant implications for emerging technologies such as AI‐driven robotics, flexible electronics, and wearable devices.

4. Experimental Section/Methods

4.1. Preparation of LM

The metallic gallium and metallic indium were mixed at volume fractions of 75.50 vol% and 24.50 vol%, followed by stirring with a magnetic stirrer (450 rpm, 90.0°C) for 6 h in an argon atmosphere glove box.

4.2. Preparation of GaIn‐B and GaIn‐U

(1) GaIn‐B: First, LM of 80.30 vol% was combined with KH 590 of 6 vol% and magnetically stirred at a speed of 900 rpm for 180 s. This stirring process facilitated the formation of larger LM particles with a KH 590‐modified surface. Next, an additional SO of 13.70 vol% was added to the mixture. The combined mixture was then magnetically stirred at an increased speed of 1200 rpm for 190 s. During this phase, the KH 590‐modified large LM particles were partially broken down, resulting in a mixture containing both KH 590‐modified LM particles and unmodified LM particles. (2) GaIn‐U: LM of 85.42 vol% was added to SO of 14.58 vol%. The mixture was then subjected to stirring at a high speed of 1200 rpm, which is essential to the uniform dispersion of the LM within the SO, optimizing the mixture's overall properties. The duration was set at 320 s in light of the requirement of thorough mixing and a full integration of components.

4.3. Materials Characterizations

The overall electrical resistivities (ER_com) of GaIn‐U and GaIn‐B were measured using a high‐resistance electrometer (Keithley 6517B) by loading GaIn‐U and GaIn‐B samples into customized sample cells with internal dimensions of 10 mm in length, 5 mm in width, and 5 mm in height, with two stainless steel electrodes connected along the length direction for sample resistance measurement, where ER_com was calculated from the measured resistance and sample geometry, and over three independently specimens were tested per data point. The temperature‐dependent ER_com was calculated using the data obtained from a series of temperature‐dependent resistance measurements conducted between 25°C and 155°C, performed using a vacuum oven in combination with a high‐resistance electrometer. GaIn‐B was sandwiched between two 0.5 mm‐thick stainless steel plates to test the breakdown voltage (refer to ASTM D149 method), and the breakdown strength was obtained by dividing the breakdown voltage by the thickness of the GaIn‐B sample. The mixture of LM and KH 590 was applied to KBr wafers and analyzed in‐situ within 14 days using the Nicolet iS50 infrared spectrometer in transmission mode, at a scan resolution of 4 cm⁻¹ and 64 scans. Steady‐state GaIn‐B was ground into powder, the excess LM droplets were removed, and a 400 MHz Bruker NMR instrument was used for solid‐state ²⁹Si NMR tests. The steady‐state infrared spectra were tested using the Nicolet iS50 infrared spectrometer with the KBr pellet method. Interactions between polysiloxane and the LM surface were characterized via Escalab 250Xi XPS and InVia Reflex confocal laser Raman spectrometers. The thickness of the KH 590 polymer layer was measured using SAXS. The element distribution of GaIn‐B, GaIn‐U, and the Al plates exposed to GaIn‐B or LM aging/corrosion for 240 h was scanned via a Bruker Quantax 200 XFlash energy spectrometer with a test voltage of 15 kV. The GaIn‐B crystal structure was measured with a Bruker D8 advance x‐ray diffractometer across a range of 10° ∼ 90°, with a step of 0.02° and a frequency of 0.10 step s⁻¹.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Supporting File: adma73894‐sup‐0001‐SuppMat.docx.

Data Availability Statement

The data that support the findings of this study are available in the supplementary material of this article.