Designing functional filler networks via in situ silver nanoparticles through barrier tuning and volume exclusion

Domain: physics
Published: 2025-12-12
Editorial outcome: minor_revision

Abstract
The fabrication of high-performance functional polymer composites requires delicate balance between functionalities, filler content and overall performance, and preparation route is urgently needed. Guided by Simmons theory, a PDMS-based stretchable conductor with metal-level conductivity is realized through a strategy by combining silver nanoparticle in-situ formation, optimized barrier height and volume excluding effect. Firstly, a universal matrix-independent etching-reduction method generates uniform Ag nanoparticles (~9.7 nm), shortening tunneling distances. Then, tunneling barrier height is minimized to 0.06 eV by aligning energy levels of surface-treated silver nanoflakes and PDMS, reducing electron scattering. Finally, silver-plated PDMS microspheres act as volume-excluding phase, compressing tunneling widths below the critical threshold (<10 nm). This integrated approach yields exceptional electrical conductivity (29429 S/cm) at 50 wt% Ag loading. Such tunneling networks retain 53% conductivity at 100% strain, while thermal conductivity increases from 4.3 to 24.3 W/m·K. This work demonstrates rational quantum tunneling barrier control to overcome performance trade-offs, providing a design framework for advanced conductive composites.

Introduction
High-performance functional polymer composites require robust percolating filler networks for electrical/thermal conductivity and stretchability1–3. Physical connections between fillers critically influence functionality by reducing interfacial contact resistance4. Minimizing inter-filler distance is quite important. However, increasing filler concentration beyond the percolation threshold to cut down electron tunneling distance compromises elasticity and processability due to aggregation and restricted polymer mobility5,6. A delicate balance between functionalities, filler content and overall performance is often needed. Advanced strategies have been proposed to decouple functionality from mechanical degradation, including filler welding7, aspect ratios optimization8, spatial alignment9, dispersion control10, and hierarchical structuring11, and incorporating minor auxiliary fillers like metallic nanowires12, carbon nanotubes (CNTs)13 or low-aspect-ratio metallic nanoparticles14–17 to bridge discontinuous domains. Among them, the generation of uniform silver nanoparticles (AgNPs) surrounding silver nanoflakes (AgFs) shows an order-of-magnitude improvement in electrical conductivity18,19. However, diffusion-dominated Ag⁺ migration causes uncontrolled AgNPs concentration, hindered in viscous polymers18, and requires matrix reducing groups, failing in silicone elastomers20, despite their wide range of applications. Thus, a universal Ag NPs in situ synthesis strategy remains a challenge.

Meanwhile, preparing strain-insensitive conductivity in stretchable conductors is equally critical and challenging, which demands preserved network integrity under tensile strain21. Conventional conductive composites exhibit strain-dependent resistance increases due to disrupted filler connections22. Strategies accommodate deformation via controlled percolation pathways8 or microstructural modulation11, exemplified by locally bundled Ag nanowires (AgNWs) assemblies23, ternary self-organization AgNWs/AgFs/AgNPs hybrids8, and metal nanowires porous architectures11, which allows further optimization via engineered structural designs24. Meanwhile, largely kept conductivity under strain and filler self-alignment has been observed in AgFs20 and AuNPs based high performance stretchable conductors25 under specific conditions. However, the mechanism is still unclear, and it lacks reproducibility and general applicability. Overall, a generalizable, scalable network modulation strategy has not yet been realized.

Furthermore, high-performance conductive elastomers require understanding electron transport and rational network design. Transport primarily occurs via quantum tunneling across sub-10-nm interparticle gaps26,27. Simmons' theory dictates exponential scaling of tunneling resistance with barrier width (interparticle distance) and is sensitive to barrier height (energy-level mismatch)17,28. While most studies modulate barrier width, systematic co-optimization of both parameters remains unexplored despite being essential for efficient networks. Herein, we propose a Simmons theory-guided strategy by combining silver nanoparticle in situ formation, optimized barrier height and volume excluding effect. Surface-treated AgFs enhance electron affinity and intrinsic conductance. Kelvin probe force microscopy (KPFM) indicates PDMS as the optimal matrix, aligning work functions with AgFs for minimal barrier height (0.06 eV). Subsequently, a universal chemical etching-reduction method generates uniform AgNPs (~9.7 nm) within PDMS, reducing tunneling distances to ~19.2 nm. Then, incorporating silver-coated PDMS (PAg) microspheres as a volume-excluding phase compresses tunneling widths below the critical cut-off (9.6 nm). This yields a stretchable composite with exceptional conductivity (29429 S/cm) at 50 wt% Ag loading. Meanwhile, the thermal conductivity increases from 4.3 to 24.3 W/m·K thanks to efficient carrier transport. Uniform AgNPs (1.29 vol%) and optimized tunneling enabled 53% conductivity retention at 100% strain. This demonstrates that such a strategy can overcome intractable performance trade-offs. By elucidating the interplay between filler architecture, matrix properties, and electron transport physics, our strategy provides a guideline for high-performance functional nanocomposites containing silver.

Results
Characterization of PAg microspheres and AgFs
Micron-sized PDMS microspheres are synthesized via suspension polymerization and subsequently coated with a conductive Ag layer to form PAg microspheres. Scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) (Fig. 1a) reveal that the PAg microspheres exhibit a uniform spherical morphology, with each microsphere uniformly coated with a metallic Ag layer. The particle size distribution (Fig. S1) indicates an average diameter of ~28 μm. Elemental mapping (Fig. 1b) demonstrates distinct distributions of Si and Ag, with the surface dominated by Ag, forming a continuous conductive layer approximately 132 nm thick. X-ray diffraction (XRD) analysis (Fig. S2) displays prominent characteristic peaks at 2θ values of 38.1°, 44.3°, 64.5°, 77.4° and 81.5°, corresponding to the (111), (200), (220), (311) and (222) crystal planes of Ag29, confirming a face-centered cubic structure. The Ag content is quantified using thermogravimetric analysis (TGA) (Fig. S3). Based on the residual weight of PAg (44.4 wt%) and that of pure PDMS (13.8 wt%), the Ag content is calculated to be 64.5 wt%30.

To endow composites with high conductivity, AgFs are employed as the primary conductive filler due to their moderate aspect ratio and intrinsic high conductivity. However, the as-received AgFs are coated with a thin layer of surfactant, typically long-chain unsaturated fatty acids, which can increase inter-flake contact resistance and impair conductivity31. To address this, the AgFs are subjected to multiple washing cycles in boiling ethanol to remove the surfactant. X-ray photoelectron spectroscopy (XPS) analysis (Fig. 1c) reveals distinct C1s and O1s peaks for the unwashed AgFs (0 cycle). After 4 washing cycles, the C1s peak intensity markedly decreases, while the O1s peak remains. This is because ethanol dissolves the fatty acids, eliminating the associated C1s signal, whereas the persistent O1s peak originates from a native oxide layer on AgFs. The ratios of C1s/Ag3d and O1s/Ag3d peak areas, derived from the XPS spectra, are compared in Fig. S4. After washing, the C1s/Ag3d ratio drops from 0.207 to 0.043, confirming the effective removal of physisorbed fatty acids. The residual carbon likely stems from trace amounts of chemically bonded surfactant31 (Fig. S5a). In contrast, the O1s/Ag3d ratio decreases less markedly, from 0.097 to 0.074.

The fine surface structure of the untreated AgFs is obscured by the surfactant coating (Fig. 1d). After surfactant removal, however, the AgFs display a clear surface morphology with well-defined grain boundaries and sharp edges. Additional physical and chemical evidence further supports the effective removal of surfactants (Fig. S5). Consequently, the intrinsic conductivity of AgFs increases from 127540 S/cm to 341438 S/cm, representing a ~3-fold enhancement (Fig. 1e). This substantial improvement in conductivity is highly beneficial for constructing highly conductive composites.

Preparation and electrical properties of PDMS-AgFs-PAg conductor
The fabrication process of PDMS-AgFs-PAg conductive composite is illustrated in Fig. 2a. First, a PDMS precursor mixture is prepared by combining PDMS base, a crosslinking agent (10:1, w/w), and 10 wt% glycerol (Gly). The abundance of electron-donating hydroxyl (-OH) groups in Gly enables it to act as a reducing agent, facilitating the reduction of Ag⁺ to elemental Ag through a redox reaction20. Gly also modifies the mechanical properties of the PDMS matrix (Fig. S6). Next, AgFs and a specific amount of formic acid are incorporated into the matrix. The formic acid removes surface oxides from the AgFs through in situ etching, forming Ag formate (Fig. S7)32. Then, PAg microspheres are added as a volume-excluding phase. The final step involves the chemical crosslinking of the PDMS matrix at 160 °C to form the PDMS-AgFs-PAg conductor. Such high temperature accelerates the decomposition of Ag formate and the redox reactions between Ag+ and the –OH groups of Gly, promoting the formation of Ag nanoparticles (Ag NPs) (Fig. S8). This method enables flexible control over Ag NPs concentration with matrix independence, a capability not yet achieved in other reported systems10,15,20, as discussed in subsequent sections.

Fig. 2b (insert) presents digital photographs of uncured, grease-like PDMS-AgFs-PAg mixture. After crosslinking the PDMS matrix, a stretchable conductor with a smooth surface and a golden hue was obtained. SEM images reveal that PAg microspheres are uniformly dispersed within PDMS-AgFs. Magnified view (20k×) identifies several large AgNPs, and higher-magnification imaging (200k×) further shows numerous uniformly dispersed AgNPs throughout the PDMS matrix, which are expected to enhance conductivity.

Maximizing electrical conductivity requires the complete removal of the Ag₂O surface layer from AgFs. XRD spectra (Fig. S9a) confirm the presence of an oxide layer, in situ etching and conversion to silver formate (Ag(HCOO)), and the subsequent reduction to metallic Ag33. To investigate its effect on AgFs microstructure and conductor properties, the formic acid content is systematically varied from 10 to 40 μL/g. At 40 μL/g, the completed disappearance of Ag₂O peaks (Fig. S9b) indicates thorough etching and reduction. TEM images and derived O/Ag signal ratio (Fig. S10) reveal that the O signal decreases from 3.6% in untreated AgFs to 0.2% at 40 μL/g. Furthermore, numerous Ag NPs are observed around the treated AgFs. The crystal structure of the etched AgFs (Fig. S11) further validates the complete removal and conversion of the Ag₂O layer. SEM images (Fig. 2c) show AgNPs populated among adjacent AgFs, which serve as electron bridges to enhance electron hopping within the matrix.

The formic acid concentration critically modulates the chemical etching and in situ reduction process, directly determining the ultimate electrical conductivity. The control composite without formic acid treatment (0 μL/g) contains only AgFs (Fig. S12a). In contrast, treated composites exhibit secondary conductive Ag NPs between AgFs, with their abundance increasing with formic acid concentration. Dynamic light scattering (DLS) (Fig. S12b) results further show two distinct peaks corresponding to AgFs and in situ formed Ag NPs, respectively. Figure 2d compares the conductivity of PDMS-AgFs-PAg composites (45 wt% AgFs, 10 wt% PAg) at different formic acid concentrations. Without etching, conductivity is merely 3.6 S/cm, escalating to 1483 S/cm at 40 μL/g. Beyond this concentration, conductivity decreases due to excessive etching-induced defects in AgFs. Therefore, 40 μL/g is selected for subsequent analyses. The proposed strategy uniquely leverages Ag₂O layers-eliminating their insulating barriers while converting them into functional Ag NPs (Fig. 2e). Moreover, this dual optimization allows controllable Ag NPs synthesis, distinguishing it from methods that consume pristine AgFs to generate AgNPs17,34,35.

Percolation modulation based on the simmons theory
Electron transport in conductive composites occurs via the quantum tunneling effect, whereby electrons tunnel through a thin insulating layer between adjacent conductive fillers36. As illustrated in Fig. 3a, in the PDMS-AgFs-PAg composite, neighboring AgFs serve as electrodes separated by PDMS. The tunneling barrier width (d) equates to inter-filler distance, while the barrier height (λB) is governed by the difference between the work function of AgFs (φAg) and the electron affinity of PDMS matrix (χPDMS)28. Simmons theory quantifies the electron tunneling current density (J) at low applied voltages (V) as a function of d and λB:

J = 3(2meλB)1/2 / h d exp(-4π d (2meλB)1/2 / h) V (1)

where me is the electron mass, h is Planck’s constant, and e is the electronic charge. Adjusting the distance between conductive fillers varies the tunneling barrier width, while selecting polymer matrices with different electron affinities tunes the barrier height.

The distribution of conductive fillers within PDMS-AgFs-PAg composite is systematically analyzed (Fig. 3b). Compared to the untreated composite, a substantial number of AgNPs are synthesized and uniformly dispersed within the PDMS matrix, effectively reducing the inter-particle tunneling distance. As depicted in Fig. 3c, the AgNPs exhibit a size distribution ranging from 1.8 to 12 nm, with an average size (s) of 9.8 nm and an estimated concentration of 1.29 vol% (Fig. S14). The resulting tunneling distance distribution in PDMS-AgFs-PAg composite ranges from 2.1 to 47.6 nm, with an average value of 19.2 nm. In contrast, the composite without Ag NPs shows a much larger tunneling distance (>500 nm). This effective percolation modulation strongly promotes high conductance, as predicted by Simmons' theory. Moreover, the tunneling distance overlaps with the tunneling cut-off distance (10 nm), which facilitates efficient electron transport.

The work function of AgFs (φAg) and the electron affinity of PDMS matrix (χPDMS) are measured using KPFM (Fig. S15a). The values of φAg and χPDMS are extracted from the surface potential distribution images. Surface potential can be influenced by factors such as surface chemical adsorption, surface roughness, and chemical purity37,38, leading to a broad potential distribution (Fig. S15b). Based on these results, the energy level distributions of PDMS and AgFs are calculated (Fig. 3d). The surface potential of PDMS corresponds to an electron affinity of 4.76 eV, showing significant overlap with the work function of AgFs (4.70 eV). This close alignment yields a negligible barrier height (λB = 0.06 eV), which greatly facilitates charge transport and contributes to the composite’s high conductance.

Using AgFs as conductive filler, the barrier height (λB) can be modulated by selecting polymer matrices with varying electron affinities39. To validate the rationale for choosing PDMS, several elastomers, including styrene-butadiene-styrene copolymer (SBS), thermoplastic polyurethane elastomer (TPU), and thermoplastic polyester elastomer (TPAE), are investigated (Fig. 3e). Their electron affinities differ significantly from φAg, resulting in increased barrier heights of 0.13 eV (SBS), 0.51 eV (TPU), and 0.86 eV (TPAE). This increase correlates with a clear decline in conductivity (Fig. 3f). At a fixed Ag loading (45 wt%, 10 wt% PAg), conductivity drops from 1483 S/cm (PDMS) to 1037 S/cm (SBS), 829 S/cm (TPU), and 472 S/cm (TPAE). Since barrier widths, AgNPs sizes and conductive fillers (AgFs, PAg) dispersion state remain identical across systems (Figs. S16, S17), the reduced conductivity is primarily attributed to the increased barrier heights. These findings confirm the universality of the proposed in situ AgNPs generation strategy, which is independent of the type of polymer matrix, providing a versatile and effective method for optimizing the electrical performance of conductive composites.

According to Simmons' theory, large barrier height amplifies the resistance change under strain, resulting in high strain sensitivity14. As shown in Fig. 3g, the PDMS-AgFs-PAg composite (45 wt%, 10 wt% PAg) exhibits the lowest strain sensitivity. This behavior stems from a negligible barrier height (λB ~ 0.06 eV), which permits electrons to tunnel efficiently through the PDMS conduction band. Moreover, the short travel distance (19.2 nm) between AgNPs minimizes stretch-induced electron scattering. In summary, by precisely modulating the tunneling distance and matching the energy levels of polymer-filler, we realized a highly conductive PDMS-AgFs-PAg conductor that maintains excellent conductivity retention under strain.

Volume-excluding-induced network formation
Subsequently, the tunneling distance is further minimized by tailoring the PAg content. Owing to the volume excluding effect, a higher PAg content confines the conductive fillers (AgFs, AgNPs) into a smaller matrix volume, promoting the formation of localized, efficient conductive pathways. As shown in Fig. 4a, the incorporation of 10 wt% PAg microspheres boosts the conductivity by ~4 orders of magnitude compared to the PAg-free composite (total Ag content: 45 wt%). Such dramatic enhancement stems from the localized densification of the conductive network, as schematized in Fig. 4b. Although the PAg-free composite (PDMS-AgFs) generates numerous AgNPs, the interparticle distance remains insufficient for efficient conduction. In contrast, the PAg microspheres act as a passive filler that compresses the available space, effectively ‘squeezing’ the AgFs and AgNPs phases. This selective distribution increases their local concentration and drastically reduces the tunneling distance, thereby accounting for the substantial conductivity increase.

To further demonstrate the superiority of PAg in enhancing electrical percolation, the percolation curves of PDMS-AgFs-PAg composites without and with PAg, as well as AgFs-filled PDMS without AgNPs, are presented (Fig. S18). The PAg-containing composite exhibits markedly higher conductivity, particularly within the critical 35–55 wt% filler range. To gain deeper insights into the conductive mechanisms, we analyzed the data using the power-law equation from percolation theory40, which describes the conductivity as follows:

σ = σ0 (V - Vc)t (2)

where σ is the composite conductivity, σ0 is a proportionality factor related to the filler conductivity, V and Vc represent the filler volume fraction and percolation threshold, respectively, and t is the critical exponent.

The weight fraction of Ag from Fig. S18 is converted to volume fraction for analysis (Fig. 4c). According to the best-fit results (Fig. 4d), a percolation threshold (Vc) of 5.1 vol% is determined for PDMS-AgFs-PAg composite, which is 1.1 vol% lower than that of PDMS-AgFs (6.2 vol%). This reduction is attributed to the volume-excluding effect of PAg microspheres. Furthermore, the conductivity-filler content relationship for PDMS composites filled solely with AgFs is calculated. As shown in Fig. 4c, d (blue curves), these composites exhibit a higher Vc of 9.4 vol%, indicating that the in situ growth of Ag NPs effectively reduces Vc from 9.4 vol% to 6.2 vol%. Together, these findings highlight the synergistic effect of in situ AgNPs formation and volume-excluding effect in regulating the percolation behavior of composites, enabling high conductivity at low filler contents.

The conductivity of PDMS-AgFs-PAg composite is further optimized by increasing the PAg microsphere content (Fig. 4e). Across the 30–60 wt% filler range, a higher PAg content substantially enhances conductivity. For instance, at a fixed 40 wt% total Ag loading, the conductivity escalates from 2.8×10−4 S/cm (0 wt% PAg) to 0.3 S/cm (10 wt% PAg) and ultimately 6544 S/cm (50 wt% PAg), representing an increase of ~7 orders of magnitude. Notably, at 50 wt% Ag content, the composite with 50 wt% PAg achieves a metal-like conductivity of 29429 S/cm. Once a dense conductive network forms, further increases in Ag content yield diminishing returns. To visualize this volume-exclusion effect, we examined the composite’s microstructure (Figs. 4f, S19). The introduction of PAg continuously increases the local concentration of AgFs and Ag NPs, drastically reducing the interparticle distance. With 10 wt% PAg, the composite shows a broad tunneling distance distribution (1.2–48.3 nm) and an average of 20.7 nm (Fig. 4g). This distance is effectively reduced to 15.5 nm and 9.6 nm at 30 wt% and 50 wt% PAg, respectively. The shortened tunneling distance facilitates efficient electron transport, underpinning the dramatic conductivity enhancement.

Generally, enhancing composite conductivity often compromises stretchability41. Interestingly, our PDMS-AgFs-PAg composites simultaneously improves both properties at PAg contents between 0 and 30 wt% (Fig. 5a). The conductivity increases monotonically with PAg content, reaching 29429 S/cm at 50 wt%. Conversely, stretchability first increases, peaks at 30 wt% PAg, and then decreases, defining an optimal balance. Thus, application-specific selection of PAg content is essential to effectively harness the resultant conductivity-stretchability trade-off. This optimal PAg content also enables robust conductivity retention under strain (Fig. 5b). In contrast to the PAg-free composite, which fails mechanically below 150% strain, PAg-containing counterparts maintain high conductivity within the 0–150% strain range. Notably, the composite with 30 wt% PAg retains high conductivity even at 222% strain. The diminished strain tolerance beyond this optimal content is likely due to crack formation induced by the heavily loaded rigid filler.

For practical applications, maintaining effective conductivity under various external perturbations is as crucial as achieving high conductivity over a wide strain range. The mechanical robustness of the conductor was evaluated through cyclic stretching (Fig. S20). Remarkably, it shows negligible fatigue, with minimal degradation in conductivity after 1000 cycles. Furthermore, the temperature dependence of conductivity was investigated (Fig. 5c). As the temperature increases from 25 °C to 200 °C, the conductivity of the composite displays a unique V-shaped trend. The initial decrease is attributable to the thermal expansion of the PDMS matrix, which dilutes the filler concentration, while the subsequent increase at higher temperatures is likely due to thermal welding between adjacent AgFs35. The composite also exhibits efficient thermal stability, demonstrated by a minimal resistance deviation of only 0.8% over 20 heating-cooling cycles (Fig. 5d). Finally, a two-week reliability test was conducted (Fig. S21). After the damp heat aging process, the internal Ag NPs showed unobservable migration or aggregation, which effectively preserved the electrical conductivity.

Previous stretchable conductors typically require conductive filler contents exceeding 80 wt% to achieve conductivities above 10000 S/cm29,42,43. In contrast, the present work achieves a high conductivity of 29429 S/cm at a markedly lower Ag content (Fig. 5e). Additionally, due to the narrow barrier width and negligible barrier height, the composites exhibit exceptional conductivity retention under large strains. As shown in Fig. 5f, which compares the normalized conductivity (σ/σ₀) at 100% strain, the PDMS-AgFs-PAg composite simultaneously delivers high conductivity and superior electromechanical stability.

Thermal conductivity of PDMS-AgFs-PAg composites
According to the Wiedemann-Franz law, the electrical conductivity (σ) and thermal conductivity (k) of a composite are related as follows44:

L = k / σT = π2 / 3 (κB / e)2 (3)

where κB is the Boltzmann constant, e is the electronic charge, T is the temperature in Kelvin (K), and L is the Lorenz number (2.44 × 10−8 W Ω/K for free electrons). Since the ratio k/σ is constant, the high electrical conductivity of PDMS-AgFs-PAg suggests that the composite may also exhibit satisfactory thermal conductivity.

At a fixed total Ag loading (50 wt%), the thermal conductivity of composites with varying PAg content (10–50 wt%) is investigated (Fig. 6a, Table S3). Both in-plane and out-of-plane thermal conductivity increased monotonically with PAg content, rising from 9.7 to 24.3 W/(m·K) and from 7.7 to 11.9 W/(m·K), respectively. This monotonic increase is attributed to the formation of additional thermally conductive pathways45–47, while the observed anisotropy stems from the preferential in-plane orientation of AgFs48,49. To elucidate the contributing factors, three systems at identical Ag content are compared (Fig. 6b): (i) AgFs only, (ii) AgFs with in situ Ag NPs, and (iii) the synergistic combination of Ag NPs and volume-excluding effect from PAg. The in situ formation of Ag NPs enhanced the in-plane (out-of-plane) thermal conductivity from 4.8 (4.3) to 9.7 (7.7) W/(m·K). A more substantial improvement is induced by the volume-excluding effect, elevating conductivity to 24.3 (11.9) W/(m·K). Meanwhile, the enhancement in thermal conductivity is accompanied by a progressive intensification of anisotropic behavior, which arises from the increasingly aligned orientation of AgFs (Fig. S22). Using Eq. (3), the electron-contributed thermal conductivity (ke) is quantified (Fig. 6c). Due to the significant enhancement in electrical conductivity, ke increases sharply with PAg content, surging from 4.16 (10 wt% PAg) to 21.4 W/(m·K) (50 wt% PAg). Consequently, the relative contribution of electrons to the total thermal conductivity increased from 42.9% to 86.3%.

To evaluate the efficacy of the proposed percolation modulation strategy, the thermal conductivity enhancement (TCE) of PDMS-AgFs-PAg is compared with recently reported metal-polymer composites. TCE is defined as49:

TCE = (kc - kp) / kp × 100% (4)

where kc and kp represent the thermal conductivity of PDMS-AgFs-PAg and PDMS, respectively. As shown in Fig. 6d, the TCE values achieved in this work significantly outperform those in the literature. This exceptional performance primarily stems from two mechanistic factors: (i) optimized energy-level alignment between the AgFs and PDMS matrix, which minimizes electron scattering, and (ii) a modulated tunneling barrier width that enhances the probability of electron hopping between adjacent conductive particles. The advantage of our strategy is further underscored in Fig. S23, where the TCE per 1 vol% filler content for PDMS-AgFs-PAg (8.7 vol% Ag) is compared against other metal-filled composites, demonstrating the superior efficiency in enhancing the thermal conductivity of PDMS.

Methods
Raw materials
Sylgard 184 PDMS elastomer kit was produced by Dow Corning Corporation. Silver nanoflakes (AgFs) was kindly provided by Bohuas Nanotechnology (Ningbo, China) Co., Ltd. Glycerol (AR, ≥99.7%) was purchased from Titan Technology (Shanghai, China) Co., Ltd. Anhydrous ethanol (AR, ≥ 99%), formic acid (AR, ≥ 99%), tin chloride dehydrate (SnCl2·2H2O, AR, ≥99%), silver nitrate (AgNO3, 1M), ammonia (NH3·H2O, 7M) and potassium sodium tartrate (AR, ≥99%) were obtained from Sigma-Aldrich.

Synthesis of PAg microspheres
The synthesis procedure for PAg microspheres is as follows: PDMS crosslinker and matrix in a volume ratio of 1:10 were mixed in a planetary mixer (AR100, Thinky) for 5 min to obtain 22 mL PDMS precursor mixture. Then, the PDMS mixture was loaded in a syringe (10 G) and slowly injected into 300 mL DI water. Simultaneously, an emulsification disperser (IKA Magic Lab) was utilized to apply high-speed shear (15000 rpm) at 80 °C. After 1 h, a crosslinked PDMS microsphere suspension was synthesized. Further, PDMS microspheres were separated from water by vacuum filtration, which was followed by drying at 60 °C for collection. Meanwhile, a 500 mL SnCl2 aqueous solution at a concentration of 5 mg/mL was formulated. Then, 10 g dried PDMS microspheres, 100 mL silver ammonia solution (14 mg/mL), and 100 mL potassium sodium tartrate aqueous solution (20 mg/mL) were uniformly dispersed in the above solution. This Ag-plating ink was stirred at room temperature for 2 h (500 rpm). Finally, the obtained Ag-coated PDMS (PAg) microspheres were collected by vacuum filtration and dried thoroughly at 60 °C for further use.

Surface pretreatment of AgFs
First, AgFs (20 g) were added to a flask containing 200 mL ethanol, and the dispersion was stirred at 70 °C for 10 min (500 rpm). Then, the dispersion was allowed to stand for 1 h, and the settled AgFs at the bottom were collected. Next, the collected AgFs were redispersed in fresh ethanol, and the above operation was cycled 4 times. Finally, the treated AgFs were separated and dried under vacuum for 12 h to obtain surface-treated AgFs.

Preparation of PDMS-AgFs-PAg composites
First, PDMS matrix and crosslinker in a volume ratio of 10:1 were uniformly mixed. Then, 10 wt% glycerol (Gly), an appropriate amount of AgFs, and formic acid were added to the PDMS mixture (Note that for composites without removing the Ag oxide layer, formic acid was not introduced, while other experimental parameters maintain unchanged). After homogeneously mixing, the mixture was allowed to stand at room temperature for 24 h to ensure thoroughly reaction between formic acid and the surface oxide layer of AgFs. The volume fraction of AgFs is 25–60 wt%, and the content of formic acid is 0–40 μL (per gram of AgFs). Further, PAg microspheres were homogeneously blended into the above composite. The mass fraction of PAg is 0–50 wt%, and the amount of AgFs was adjusted appropriately according to the content changes of each component, ensuring the total Ag content remains constant (the mass fraction of Ag in PAg is 64.5 wt%). Finally, the obtained blends were cast onto a PDMS substrate and thermally crosslinked at 160 °C for 2 h to obtain a stretchable PDMS-AgFs-PAg conductor.

Preparation of PDMS-AgFs-PAg composites without AgNPs
First, purified AgFs were uniformly mixed with formic acid (40 μL/g) to etch the surface Ag2O layer. The etching process lasted for 12 h at 25 °C and then repeatedly rinsed with ethanol to completely remove the exfoliated Ag formate particles, which is followed by drying in a vacuum oven (60 °C, 8 h). Next, the etched AgFs were uniformly mixed with PDMS (containing 10 wt% Gly) matrix and PAg to elaborate a composite mixture (for the cases of AgFs-filled PDMS composites without AgNPs, PAg was not introduced). Finally, the mixture was cast onto the PDMS substrate and cured at 160 °C for 2 h to obtain PDMS-AgFs-PAg composites without AgNPs.

Characterization
The morphologies of PAg microspheres, AgFs, and PDMS-AgFs-PAg composites were characterized using a Field Emission Scanning Electron Microscope (FEI-SEM, Quanta 650 ESEM, Thermo Fisher Scientific, Inc.) equipped with an Energy Dispersive Spectrometer (EDS, OXFORD Xplore 30). The surface potentials of PDMS and AgFs were measured using Kelvin Probe Force Microscopy (KPFM, Bruker, Icon, USA) with a gold-coated silicon AFM tip. Prior to measurement, KPFM was calibrated based on the contact potential difference between the tip and highly oriented pyrolytic graphite with a known work function (4.6 eV). The microstructure of AgFs and composites, as well as the thickness of AgFs, were characterized using an Atomic Force Microscope (AFM, Bruker, Icon, USA). The lattice structure and surface elements of AgFs were analyzed using a Scanning Transmission Electron Microscope (STEM, Talos F200i, Thermo Scientific). When analyzing the conductive network in PDMS-AgFs-PAg composites, the composites were sliced using Focused Ion Beam (FIB) technology before characterization. The chemical composition and bonding type analysis of surfactant on AgFs were conducted on an FTIR (Nicolet 6700, Thermo Scientific, USA) within a scanning wavenumber range of 400–4000 cm−1, with 32 scans performed. X-ray Photoelectron Spectroscopy (XPS) tests were conducted on a Thermo ESCALAB 250 XPS spectrometer under a pressure of 2.0×10−7 Pa, using Al Kα (hv= 1486.6 eV) as the X-rays source. Thermal gravimetric analysis (TGA) was conducted using a TGA instrument (Q500, TA, USA). The test was performed under a nitrogen (N2) atmosphere within a temperature range of 25–800 °C, with a heating rate of 10 °C/min. Differential Scanning Calorimetry (DSC) of AgFs was collected using a DSC 8000 (PerkinElmer), heated from room temperature to 800 °C at a rate of 10 °C/min under an N2 atmosphere. The thermal diffusivity (α) and specific heat capacity (Cp) of the composites were determined using the laser flash method with an LFA 467 analyzer (NETZSCH, Germany). Thermal conductivity (k) was further calculated according to: k=α×Cp×ρ, where the composite density (ρ) was measured using Archimedes’ Law method. For each sample, the final reported value represents the average of at least five independent measurements. The mechanical properties of PDMS film were tested on a universal tensile testing machine (SANS CMT40000) at a temperature of 25 °C and a relative humidity of approximately 60%, using a sensor with a load of 100 N. The conductivities of PDMS-AgFs-PAg composites and AgFs were measured using the four-probe method (JCY3100, Xi’an Hechuang Electronic Technology Co., Ltd.), with the average of five measurements taken as the result. Resistance changes under strain were obtained using the two-point method with a JK2512B DC low resistance tester (Jinko, China), equipped with a universal tensile testing machine (SANS CMT40000) to apply synchronous strain. Prior to testing, both ends of the specimen were coated with a uniform layer of conductive silver paint to minimize contact resistance. The composition and crystal structure of PAg, AgFs, and PDMS-AgFs-PAg composites were characterized using XRD (Bruker D8). The Cu-Kα X-rays source was used with a voltage of 40 kV, a current of 40 mA, a scanning range of 10–90°, and a scanning speed of 10°/min. Particle size and particle size distribution were obtained using Dynamic Light Scattering (DLS, ZetaPALS 190 Plus, Brookhaven). The intrinsic conductivity of AgFs was measured using a four-point probe method. Prior to the measurement, an appropriate mass of AgFs was pressed into a pellet with a thickness of 100 μm under a pressure of 100 MPa.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this study, the authors demonstrate an AgFs-based composite with high electrical/thermal conductivity, and excellent\nelectrical conductivity retention under strain. This was achieved through the synergistic modulation of both the barrier height\nand width of electron tunneling within the composite. Unlike traditional methods for in-situ generation of Ag NPs, the authors\npropose a universal chemical etching-in-situ reduction strategy. This strategy allows the controllable generation of uniformly\ndistributed Ag NPs within any matrix, significantly enhancing electron tunneling capability. Furthermore, by determining the\nenergy levels of the matrices, the authors screened polymer matrices to modulate the barrier height, thereby ensuring\nefficient electron transport within the composite. The presented percolation modulation strategy facilitates the realization of\nhigh-performance composites with low AgFs loading, providing an efficient conductive network modulation method and\nshowing potential commercial value. In summary, the research features a novel concept, comprehensive data, and thorough\ncharacterization, resulting in composites with outstanding performance. I recommend this study for publication in Nature\nCommunications after resolving the following concerns.\n1. Page 10, Line 244: The work function of AgFs is described as 4.70 eV, which is consistent with the calculated results in\nFigure 3d. However, in Figure 3e, χAg is described as 4.71 eV. Please confirm and unify the results.\n2. The authors conclude that using PDMS as elastic matrix lowers the electron tunneling barrier, enabling the fabrication of\nAgFs composite with optimal conductivity. However, this explanation cannot fully account for the conductivity differences\nobserved among the various composites shown in the Figure 3f. The most apparent flaw in this conclusion is that it\noverlooks the differences in AgFs arrangement structure within each elastic matrix, resulting from interfacial energy\ndifferences between AgFs and the matrices. Specifically, the distribution of AgFs may vary across different matrices.\n3. Figures 3d-g: The authors measured the work functions of different elastic matrices using KPFM and demonstrated that\nPDMS achieves optimal energy level match with AgFs, leading to highly conductive composites with efficient conductivity\nretention under strain. However, this approach only allows for the passive screening of matrixes. Is there any method to\nactively tune the energy levels of a matrix, enabling energy level to be well-matched with any metallic filler?\n4. Could the in-situ generated Ag NPs (lacking surface ligand protection) experience oxidation, migration, and\nagglomeration during long-term service? This would compromise the practical utility of the composite.\n5. Experimental Section (Page 21, Line 508): When preparing the PDMS-AgFs-PAg composite without Ag NPs, the authors\nstate that after etching AgFs, the generated silver formate particles were separated. However, completely separating\nnanoparticles from nanosheets is challenging. Were the etched silver formate particles totally removed? If yes, how was this\nachieved?\n6. The author should read the entire manuscript carefully to correct some obvious formatting and spelling errors. For\nexample, “…Chuanhuan Technology Co. Ltd,” should be “…Chuanhuan Technology Co., Ltd.”", "reviewer_2": "In this study, the authors propose a novel strategy grounded in Simmons tunneling theory, which leverages the in-situ\nformation of silver nanoparticles, optimization of tunneling barrier height, and a volume exclusion effect to construct high-\nperformance conductive networks. The work demonstrates that rational control of the tunneling barrier offers a versatile\ndesign principle for developing high-performance and multifunctional conductive elastomers. While the results are\nimpressive, several issues require discussion and minor revisions prior to publication:\n1. The authors employed different concentrations of formic acid to etch the oxide layer on the surface of AgFs, thereby\ngenerating Ag NPs for enhanced electrical conductivity. Could the thickness of this surface oxide layer be actively\ncontrolled? Such control may further reduce the tunneling distance after etching-in-situ Ag NPs generation, thereby\nimproving electrical conductivity and its retention under strain.\n2. Electrical conductivity was measured using a four-probe method, whereas strain testing utilized a two-probe setup. The\npotential influence of contact resistance on the results should be addressed and clarified.\n3. Figure 5a visually illustrates the enhancement in electrical performance resulting from varying degrees of volume\nexclusion. However, the effect of this strategy on stretchability appears more complex. It would be valuable to identify the\noptimal PAg content that achieves the best balance between conductivity and stretchability for applications in stretchable\nconductors.\n4. There is an inconsistency between Figures 5a and 5e regarding the total silver content (50 wt% or 60 wt%). This\ndiscrepancy should be verified and corrected.\n5. Several data plots (e.g.: thermal conductivity) lack error bars. Uncertainties should be included.\n6. The manuscript requires significant condensation. Streamlining the focus toward key performance metrics and polishing\nthe language for clarity and impact is recommended.", "reviewer_3": "This manuscript reports a study on the fabrication of high performance functional polymer composites by innovatively\ncombing silver nanoparticle in-situ formation, optimized barrier height and volume excluding effect. An etching-reduction\nmethod was used to generate Ag nanoparticles with a diameter around 9.7nm from micro-meter scale Ag flakes, so that,\nlocal conductive network can be constructed between Ag flakes to cut down tunneling distance. Meanwhile, Ag coated\nPDMS microspheres were introduced into the system to further reduce the inter-particle distance through volume excluding\neffect. Furthermore, PDMS was found to have the minimum tunneling barrier height, thus, electron scattering is reduced to\nobtain high electrical conductivity. The combination of above three methods results in exceptional high electrical\nconductivity around 29000 S/cm at merely 50wt.% Ag content. Thermal conductivity also increases from 4.3 to 24.3 W/m·K.\nComparing with results in literature, lower filler content can be used to build even better functional network, achieving more\neffective contribution for these functional fillers in the composites. It provides an interesting and potentially useful method to\nprepare highly functional polymer composites. Overall, this paper is well prepared. I think it can be published after some\nminor corrections.\n1. In Fig 1b, the Ag shell layer seems like a collection of individual Ag particles, please try to discuss the mechanism\nresponsible for this particular morphology.\n2. Fig 1d, it should be “2 cycles”, “4 cycles”; the same for Fig 1c.\n3. Regarding the barrier height difference between different polymers: PDMS, SBS, TPU, TPAE. Indeed, these polymers\nshould have different barrier height due to their difference in chemical structure, thus, different final electrical properties were\nobtained. Nevertheless, filler dispersion could also have important influence on the final electrical property. Please discuss\nthe influence of filler dispersion on the final conductivity.\n4. In Fig 4b, the volume-excluding effect of PAg microspheres is considered to significantly compress tunneling distances.\nAre there quantitative structural characterizations (e.g., 3D tomography, small-angle scattering) that can directly confirm\nchanges in filler spatial distribution.\n5. In Fig 5 e and f, the results in literature should be divided into difference groups, they should vary in terms of filler,\npolymer matrix, etc. So that, it is more clear to the audience.\n6. In Fig 6b, the different in thermal conductivity between in-plane and out-of-plane in these specimens becomes more and\nmore obvious from left to right, please discuss this phenomenon and explain the mechanism.\n7. In Fig 6, the enhancement of thermal conductivity is mainly attributed to electronic contribution. Has the role of phonon\ntransport and interfacial phonon scattering been considered, especially under high-temperature conditions where phonon\ntransport might become limiting.\n8. Compared with other high-conductivity composite systems (e.g., liquid metals, CNT networks), what advantages does the\nproposed strategy offer in terms of cost, recyclability, or compatibility with flexible device integration."}, "author_response": "Response to Reviewer #1:\nComments: In this study, the authors demonstrate an AgFs-based composite with high\nelectrical/thermal conductivity, and excellent electrical conductivity retention under\nstrain. This was achieved through the synergistic modulation of both the barrier height\nand width of electron tunneling within the composite. Unlike traditional methods for\nin-situ generation of Ag NPs, the authors propose a universal chemical etching-in-situ\nreduction strategy. This strategy allows the controllable generation of uniformly\ndistributed Ag NPs within any matrix, significantly enhancing electron tunneling\ncapability. Furthermore, by determining the energy levels of the matrices, the authors\nscreened polymer matrices to modulate the barrier height, thereby ensuring efficient\nelectron transport within the composite. The presented percolation modulation strategy\nfacilitates the realization of high-performance composites with low AgFs loading,\nproviding an efficient conductive network modulation method and showing potential\ncommercial value. In summary, the research features a novel concept, comprehensive\ndata, and thorough characterization, resulting in composites with outstanding\nperformance. I recommend this study for publication in Nature Communications after\nresolving the following concerns.\nQ1. Page 10, Line 244: The work function of AgFs is described as 4.70 eV, which is\nconsistent with the calculated results in Figure 3d. However, in Figure 3e, χAg is\ndescribed as 4.71 eV. Please confirm and unify the results.\nA1. Very appreciate to you for the kind reminder. The energy level of AgFs in Figure\n3e has been corrected to 4.70 eV.\nQ2. The authors conclude that using PDMS as elastic matrix lowers the electron\ntunneling barrier, enabling the fabrication of AgFs composite with optimal conductivity.\nHowever, this explanation cannot fully account for the conductivity differences\nobserved among the various composites shown in the Figure 3f. The most apparent flaw\nin this conclusion is that it overlooks the differences in AgFs arrangement structure\nwithin each elastic matrix, resulting from interfacial energy differences between AgFs\nand the matrices. Specifically, the distribution of AgFs may vary across different\nmatrices.\nA2. Thanks for your good question. The energy level difference between the filler and\nmatrix may influence the distribution structure of the filler. However, in this study, the\npre-composite solution process ensured thorough mixing and dispersion of all\ncomponents, while the phase isolation effect of PAg promoted the formation of a\nuniform, high-density conductive network by AgFs within the matrix. Consequently, as\nshown in Figure R1, the arrangement of AgFs exhibits no significant variation across\ndifferent matrixes. Based on this, the disparity in electrical conductivity can be\nreasonably attributed to the energy level difference. Similar findings have been\ndocumented in other study (Adv Sci. 2024, 11, 2409337). The latest experimental\nevidence and relevant discussions have been incorporated into the revised manuscript.\n(See Figure S17 and Page 11, Line 249-251)\nFigure R1. The corresponding SEM images of different composites in Figure 3f\n(revised manuscript), clearly revealing a random and uniform distribution of conductive\nfillers within the matrixes (scale bar: 20 μm).\nQ3. Figures 3d-g: The authors measured the work functions of different elastic matrices\nusing KPFM and demonstrated that PDMS achieves optimal energy level match with\nAgFs, leading to highly conductive composites with efficient conductivity retention\nunder strain. However, this approach only allows for the passive screening of matrixes.\nIs there any method to actively tune the energy levels of a matrix, enabling energy level\nto be well-matched with any metallic filler?\nA3. Thank you for raising this insightful question. The energy levels of polymers can\nbe tuned through strategic molecular design. The most effective method involves\nengineering the polymer backbone, particularly by creating a donor-acceptor structure\nwhere electron-rich and electron-deficient units are alternated to systematically narrow\nthe bandgap and shift the orbitals (Prog Polym Sci. 2011, 36, 1326). Further fine-tuning\ncan be achieved via side-chain engineering, such as attaching electron-withdrawing\ngroups like fluorine to lower the HOMO level for enhanced stability, or using bulky\nsubstituents to induce backbone twisting and widen the gap (Sci China Chem. 2015, 58,\n192). Finally, post-processing techniques like thermal or solvent vapor annealing can\noptimize morphology, leading to minor yet crucial energetic adjustments for enhanced\nperformance (Polymers 2020, 12, 2627).\nRegarding silicone rubber elastomers, the type and concentration of crosslinking\nagents influence their energy levels, which subsequently affects the electrical properties\nof conductive composites (Adv Sci. 2024, 11, 2409337). We are currently conducting\nrelevant research to proactively achieve polymer-filler energy level matching through\nmolecular structure engineering, with the goal of maximizing electrical conductivity.\nThese findings will be reported in our subsequent work.\nQ4. Could the in-situ generated Ag NPs (lacking surface ligand protection) experience\noxidation, migration, and agglomeration during long-term service? This would\ncompromise the practical utility of the composite.\nA4. Thanks for your good question. Compared with other metallic materials (such as\ncopper and iron), Ag exhibits relatively superior stability in air (Adv Funct Mater 2023,\n33, 2308799). To demonstrate the long-term service capability of the composite, we\nconducted hygrothermal aging tests at 85°C and 85% relative humidity. As shown in\nFigure R2a, after two weeks of accelerated aging, the distribution of Ag NPs within the\nPDMS matrix remained unchanged. Furthermore, the electrical conductivity of\ncomposite shows no degradation after aging (Figure R2b), which further confirms the\nabsence of significant oxidation in Ag NPs. This stability can be attributed not only to\nthe inherent corrosion resistance of Ag, but also to the inherent hydrophobicity and\ncross-linked structure of PDMS, which collectively contribute to the preservation of\nelectrical conductivity. The relevant experimental evidence and discussion pertaining\nto this issue have been incorporated into the revised manuscript, as suggested (please\nsee Page 16, Line 356-359 and Figure S21).\nFigure R2. a) TEM images and b) conductivity changes of PDMS-AgFs-PAg composite\n(50 wt% PAg) in Figure 5 (revised manuscript) before and after aging.\nQ5. Experimental Section (Page 21, Line 508): When preparing the PDMS-AgFs-PAg\ncomposite without Ag NPs, the authors state that after etching AgFs, the generated\nsilver formate particles were separated. However, completely separating nanoparticles\nfrom nanosheets is challenging. Were the etched silver formate particles totally\nremoved? If yes, how was this achieved?\nA5. Thanks for your good question. As shown in Figure R3, the etched dispersion\ncontains both AgFs and uniformly distributed Ag formate particle (Figure R3a). Upon\ncessation of stirring and allowing the dispersion to stand, AgFs rapidly float to the\nsurface, while Ag formate particle remain dispersed in the aqueous phase (Figure R3b).\nThe floated AgFs can then be collected to obtain the etched product (Figure R3c). This\nmethodology enables complete separation of the two nanomaterials (Figure R3d).\nFigure R3. a) SEM image of AgFs/Ag formate particle mixture obtained after formic\nacid etching. b) Optical image of the separation of AgFs/Ag formate particle mixture in\nwater, along with c, d) the corresponding SEM images from outlined regions,\ndemonstrating the complete segregation of the two nanomaterials.\nQ6. The author should read the entire manuscript carefully to correct some obvious\nformatting and spelling errors. For example, “…Chuanhuan Technology Co. Ltd,”\nshould be “…Chuanhuan Technology Co., Ltd.”\nA6. Sorry for our carelessness. The error has been corrected and similar errors have\nbeen corrected to the best of our ability.\nResponse to Reviewer #2:\nComments: In this study, the authors propose a novel strategy grounded in Simmons\ntunneling theory, which leverages the in-situ formation of silver nanoparticles,\noptimization of tunneling barrier height, and a volume exclusion effect to construct\nhigh-performance conductive networks. The work demonstrates that rational control of\nthe tunneling barrier offers a versatile design principle for developing high-\nperformance and multifunctional conductive elastomers. While the results are\nimpressive, several issues require discussion and minor revisions prior to publication:\nQ1. The authors employed different concentrations of formic acid to etch the oxide\nlayer on the surface of AgFs, thereby generating Ag NPs for enhanced electrical\nconductivity. Could the thickness of this surface oxide layer be actively controlled?\nSuch control may further reduce the tunneling distance after etching-in-situ Ag NPs\ngeneration, thereby improving electrical conductivity and its retention under strain.\nA1. We fully acknowledge the values of your concerns. This study strategically utilizes\nthe native oxide layer on AgFs by in situ converting Ag O into Ag NPs, thereby\n2\nachieving precise modulation of tunneling distances and ultimately maximizing the\nelectrical conductivity of composites. Consequently, as you rightly pointed out,\nenhancing the surface oxide content holds significant promise for further improving\nelectrical performance.\nAt the current stage, we attempted to accelerate oxidation of AgFs through thermal\ntreatment in air. However, their high specific surface area induces a depressed melting\npoint, leading to structural deformation upon heating (Figure R1). Furthermore, the\nrelatively stable nature of Ag limits the efficacy of thermal oxidation (J Porous Mater.\n2014, 21, 467). While chemical synthesis of Ag O is straightforward, achieving\n2\ncontrolled surface oxidation on pre-formed AgFs remains challenging (Mater Res\nExpress 2017, 4, 105406; Asian J. Chem 2013, 25, 3405). Several alternative methods\nfor converting Ag to Ag O have been reported, including the use of ozone or strong\n2\noxidizing agents in alkaline environments (Poiyhedmn 1982, 1, 183436; J Electrochem\nSoc. 2005, 152, A996). These approaches are currently under active attempts in our\nlaboratory, and the latest findings will be detailed in a forthcoming publication.\nFigure R1. SEM images of AgFs a) before and b) after 12 hours of heat treatment at\n100 ° C in an air atmosphere (scale bar: 10 μm).\nQ2. Electrical conductivity was measured using a four-probe method, whereas strain\ntesting utilized a two-probe setup. The potential influence of contact resistance on the\nresults should be addressed and clarified.\nA2. We thank the reviewer for this important comment. We agree that the potential\ninfluence of contact resistance is a critical consideration when using a two-probe setup\nfor strain-dependent resistance measurements. The four-point probe method was\nexclusively used for determining the DC electrical conductivity, as it is a well-\nestablished technique for eliminating errors associated with contact resistance. For the\nstrain testing, we applied a high-conductivity silver paste to both ends of the specimen\nto minimize the influence of contact resistance on the measurement results. The two-\nprobe setup was employed due to its simpler integration with our mechanical straining\napparatus.\nWe have revised the manuscript to clarify this point (See Methods-\nCharacterization Section, revised manuscript). We believe this clarification strengthens\nthe manuscript and thank the reviewer for the opportunity to improve it.\nQ3. Figure 5a visually illustrates the enhancement in electrical performance resulting\nfrom varying degrees of volume exclusion. However, the effect of this strategy on\nstretchability appears more complex. It would be valuable to identify the optimal PAg\ncontent that achieves the best balance between conductivity and stretchability for\napplications in stretchable conductors.\nA3. In conventional conductive elastomers, an increase in conductive filler content\ntypically leads to a significant decline in stretchability (Nat Mater. 2017, 16, 834; Nat\nNanotech. 2018, 13, 1048). In contrast, this study demonstrates a concurrent\nenhancement in both electrical conductivity and stretchability through rational design\nof the conductive network architecture. The optimal PAg content is application-\ndependent and requires careful consideration of specific performance requirements. For\ninstance, a PAg content of 30 wt% is suitable for applications prioritizing high\nstretchability, whereas a higher PAg loading is preferable when superior electrical\nconductivity is desired. Remarkably, the optimized trade-off between conductivity and\nstretchability achieved in this work surpasses that of most reported PDMS-based\nstretchable conductors (Chem Soc Rev. 2019, 48, 1566; Chem Soc Rev. 2019, 48, 2946).\nRelated discussion has been added into the manuscript (see Page 15, Line 337-338)\nQ4. There is an inconsistency between Figures 5a and 5e regarding the total silver\ncontent (50 wt% or 60 wt%). This discrepancy should be verified and corrected.\nA4. Thank you for pointing this out. The total silver content in Figure 5a has been\ncorrected to 50 wt%.\nQ5. Several data plots (e.g.: thermal conductivity) lack error bars. Uncertainties should\nbe included.\nA5. Thank you for pointing this out. The data points in Figure 6b and 6c have been\nupdated accordingly. The values now represent the average of at least five independent\nmeasurements per sample, which we believe enhances the reliability of our results.\nQ6. The manuscript requires significant condensation. Streamlining the focus toward\nkey performance metrics and polishing the language for clarity and impact is\nrecommended.\nA6. Thank you for your suggestions. We have done our utmost to refine the content of\nthe manuscript, polishing the sentences and expressions as much as possible. We hope\nthe revised version will better meet the journal's requirements.\nResponse to Reviewer #3:\nComments: This manuscript reports a study on the fabrication of high performance\nfunctional polymer composites by innovatively combing silver nanoparticle in-situ\nformation, optimized barrier height and volume excluding effect. An etching-reduction\nmethod was used to generate Ag nanoparticles with a diameter around 9.7nm from\nmicro-meter scale Ag flakes, so that, local conductive network can be constructed\nbetween Ag flakes to cut down tunneling distance. Meanwhile, Ag coated PDMS\nmicrospheres were introduced into the system to further reduce the inter-particle\ndistance through volume excluding effect. Furthermore, PDMS was found to have the\nminimum tunneling barrier height, thus, electron scattering is reduced to obtain high\nelectrical conductivity. The combination of above three methods results in exceptional\nhigh electrical conductivity around 29000 S/cm at merely 50wt.% Ag content. Thermal\nconductivity also increases from 4.3 to 24.3 W/m·K. Comparing with results in\nliterature, lower filler content can be used to build even better functional network,\nachieving more effective contribution for these functional fillers in the composites. It\nprovides an interesting and potentially useful method to prepare highly functional\npolymer composites. Overall, this paper is well prepared. I think it can be published\nafter some minor corrections.\nQ1. In Fig 1b, the Ag shell layer seems like a collection of individual Ag particles,\nplease try to discuss the mechanism responsible for this particular morphology.\nA1. The deposited Ag layer forms as a polycrystalline aggregate of grains primarily due\nto the Volmer-Weber (island) growth mechanism (J Appl Phys. 2001, 89, 4886). This\nmode is dictated by the fact that the cohesive energy between Ag adatoms exceeds their\nadhesive energy to the foreign substrate. Consequently, incoming Ag atoms\npreferentially nucleate and form three-dimensional clusters to minimize energy, rather\nthan wetting the surface in a two-dimensional layer. These initial islands subsequently\ngrow and coalesce into a continuous Ag shell, whose final microstructure-including\ngrain size, morphology, and density-is further governed by deposition parameters such\nas temperature, rate, and the use of chemical additives. There have been many reports\non the Ag coating of polymer microspheres via chemical methods. Similar findings are\navailable at Chem Eng J. 2023, 472, 144934; Appl Surf Sci. 2020, 513, 145857; Adv\nFunct Mater. 2023, 33, 2308799.\nQ2. Fig 1d, it should be “2 cycles”, “4 cycles”; the same for Fig 1c.\nA2. We appreciate you pointing out the error. Both Figures have been updated as\nsuggested.\nQ3. Regarding the barrier height difference between different polymers: PDMS, SBS,\nTPU, TPAE. Indeed, these polymers should have different barrier height due to their\ndifference in chemical structure, thus, different final electrical properties were\nobtained. Nevertheless, filler dispersion could also have important influence on the final electrical\nproperty. Please discuss the influence of filler dispersion on the final conductivity.\nFigure R1. SEM images of composite conductors with PDMS, SBS, TPU and TPAE as\nmatrix (scale bar: 20 μm), clearly revealing a random and uniform distribution of\nconductive fillers within the matrixes.\nA3. We fully concur with your perspective. In electrically conductive composites, the\ndispersion and distribution state of conductive fillers indeed have a critical impact on\nthe electrical properties (Prog Polym Sci. 2014, 39, 627). Generally, achieving a\nuniform distribution of fillers within the matrix through appropriate compounding\nmethods can lead to higher conductivity at the same filler loading (Nano-Micro Lett\n2022, 14, 35). In this work, we employed a solution-based method to mix the\ncomponents, which effectively facilitates the dispersion of fillers. Furthermore, the\nfillers used (AgFs, PAg) are both low-aspect-ratio micro-particles/flakes (unlike high-\naspect-ratio nanomaterials, e.g., CNTs, Ag NWs), which also makes them easier to\ndisperse. Consequently, as shown in Figure R1, the fillers exhibit a homogeneous\ndistribution across all matrices. Therefore, combined with the TEM results in Figure\nS17, the differences in conductivity observed in Figure 2 (revised manuscript) can be\nentirely attributed to variations in the tunneling barrier height. The latest\ncharacterization and the corresponding discussion have been incorporated into the\nrevised manuscript and can be found on Page 11, Line 249-251 and Figure S17.\nQ4. In Fig 4b, the volume-excluding effect of PAg microspheres is considered to\nsignificantly compress tunneling distances. Are there quantitative structural\ncharacterizations (e.g., 3D tomography, small-angle scattering) that can directly\nconfirm changes in filler spatial distribution.\nFigure R2. a) 3D micro-CT scanning of PAg filled PDMS composite.\nA4. The characterization methods you recommended are indeed valuable for\nquantifying or visualizing the spatial distribution of fillers. For instance, microcomputer\ntomography (micro-CT) and 3D X-ray computed tomography (3D XCT) scanning can\nbe employed to examine the 3D distribution of fillers (ACS Nano 2019, 13, 6531; Adv\nMater. 2023, 35, 2211100). However, these techniques are generally limited to micron-\nscale resolution, making them unsuitable for observing the distribution of Ag NPs or\nfor calculating tunneling distances. As shown in Figure R2, we attempted to\ncharacterize PAg (~ 28 µm) filled PDMS composite, but the structure of PAg could not\nbe clearly observed even at the maximum magnification. Introducing smaller AgFs (~\n7 µm) further complicates the observation, and it is reasonable to infer that AgFs would\nbe even more challenging to detect. Therefore, it is difficult to use a single\ncharacterization method to simultaneously capture the multi-scale conductive network\n(nanometers to tens of micrometers) within PDMS-AgFs-PAg composite.\nFigure R3. a) 2D SAXS patterns of PDMS-AgFs-PAg composites with increased PAg\ncontent and b) the corresponding SAXS diffraction curves.\nSmall-angle X-ray scattering (SAXS) enables quantitative characterization of\nfiller distribution within a matrix, proving particularly effective for determining filler\nalignment and inter-filler distance (Nature 2013, 500, 59; Sci Adv. 2019, 5, eaaw1879;\nMacromolecules 2014, 47, 5365). On this basis, SAXS analysis was performed on 3\ncomposite film specimens (Figure R3). As illustrated in Figure R3a, the 2D scattering\npatterns of composites exhibit isotropic scattering geometry, indicating random filler\ndispersion within the matrix without preferential alignment. The scattering profiles\n(Figure R3b) further corroborate that the spatial distribution of fillers follows a Poisson\ndistribution pattern (J. Mater. Sci. 1996, 31, 281).\nSubsequently, we attempted to fit the scattering curves to directly extract inter-\nfiller distances according to the equations deduced in Macromolecules 2014, 47, 5365.\nHowever, in the PDMS-AgFs-PAg composite, the coexistence of three distinct filler\ntypes (AgFs, PAg, and AgFs) introduces polydispersity in both size and density, thereby\nprecluding meaningful curve fitting. Actually, reliable quantification of filler\ndistribution via SAXS requires fulfillment of two essential criteria: (1) the filler\ndimensions must fall within the 1-200 nm range (unsuitable for microscale PAg and\nAgFs), as constrained by the scattering vector q (= 4π sinθ/λ), and (2) the system only\ncontain one type of filler, since structural parameters derived from fitting represent\nensemble-averaged quantities and become invalid in multi-component filler systems.\nConsequently, the multilevel conductive network architecture developed in this work is\nnot amenable to SAXS-based distribution analysis.\nTo characterize the structural evolution of conductive network across different\nscales, we have supplemented with SEM images under varying degrees of volume\nexcluding level. As illustrated in Fugure R4, with increased PAg content, enhanced\nvolume excluding results in a significantly higher local concentration of AgFs within\nthe PDMS phase. Combined with the results in Figure 4f (revised manuscript), these\nobservations clearly validate the proposed evolution of conductive network structure\n(Figure 4b, revise manuscript). These results and the associated discussion have been\nadded to the updated manuscript (See Page 14, Line 316-318, Figure S19).\nFigure R4. SEM images (scale bar: 25 μm) and zoom-in SEM images (scale bar: 10 μm)\nof PDMS-AgFs-PAg composites with intensified volume excluding effect,\ncorresponding to the samples in Figure 4f (revised manuscript).\nQ5. In Fig 5 e and f, the results in literature should be divided into difference groups,\nthey should vary in terms of filler, polymer matrix, etc. So that, it is more clear to the\naudience.\nA5. Yes, both the conductive fillers and the matrix influence the electrical properties of\ncomposite. In fact, when categorizing and discussing conductive polymer composites,\nthey are typically classified based on the type of filler used-such as carbon materials,\nmetallic nanomaterials, intrinsic conductive polymers, etc.-because the type and\nmorphology of conductive filler have a more pronounced impact on electrical\nperformance (Chem Soc Rev. 2019, 48, 1566; Susmat 2024, 4, e204.).\nAs shown in Figure 5e and 5f (revised manuscript), we have made revisions to\nmore clearly present the composition of composites corresponding to each data point.\nAs you can see, all the cited results in figures are based on Ag fillers, albeit with\ndifferent morphologies. In fact, among currently reported conductive elastomers, Ag\n(particularly AgFs) is the most widely used filler. This is because Ag exhibits higher\nintrinsic conductivity compared to other types of fillers (e.g., carbon nanomaterials).\nMoreover, it also holds an advantage in intrinsic conductivity over other metallic\nmaterials, while simultaneously offering benefits such as low cost (in the case of AgFs)\nand resistance to oxidation.\nQ6. In Fig 6b, the different in thermal conductivity between in-plane and out-of-plane\nin these specimens becomes more and more obvious from left to right, please discuss\nthis phenomenon and explain the mechanism.\nA6. Thank you for raising this insightful question. In composites filled with flake-like\nfillers, the orientation of these fillers during molding leads to anisotropic properties.\nAs illustrated in Figure 6b (revised manuscript), the three compared composites exhibit\nprogressively stronger anisotropy, which correlates directly with their increasing degree\nof AgFs alignment (Figure R5). This directional dependence arises because enhanced\norientation promotes more efficient construction of thermal conduction pathways\nwithin the planar direction, while simultaneously impeding the formation of effective\nnetworks in the out-of-plane direction (ACS Appl. Mater. Interfaces 2020, 12, 6503;\nAdv Mater. 2023, 35, 2211100). Consequently, the thermal conductivity contrast\nbetween these two directions becomes more pronounced. It should be noted that this\naligned microstructure develops under shear flow during composite processing, with\nthe extent of orientation being significantly influenced by both composite viscosity and\nfiller characteristics. This discussion has been incorporated into the revised manuscript\non Page 18, Line 396-398 and Figure S22.\nFigure R5. SEM images of AgFs filled PDMS, PDMS-AgFs composites and PDMS-\nAgFs-PAg composite (50 wt% PAg) at consistent Ag content (50 wt%), clearly\ndemonstrating a progressive increase in the planar orientation of AgFs. Scale bar: 50\nμm.\nQ7. In Fig 6, the enhancement of thermal conductivity is mainly attributed to electronic\ncontribution. Has the role of phonon transport and interfacial phonon scattering been\nconsidered, especially under high-temperature conditions where phonon transport\nmight become limiting.\nA7. In general, the thermal conductivity (k) of conductive composites is dominated by\nelectronic (k ) and phononic (k ) contributions. The total thermal conductivity can\ne ph\ntherefore be expressed as the sum of these two components. Further, electronic\ncontributed thermal conductivity can be expressed as k = LσT, where L is the Lorenz\ne\nnumber, σ is the electrical conductivity, and T is the absolute temperature (Nat Mater.\n2008, 7, 105).\nIn this study, enhanced volume excluding led to an increase in the electrical\nconductivity of composites and strengthened electron transport capability, thereby\nprogressively raising the electronic contribution to thermal conductivity\n(Macromolecules 2015, 48, 585). In contrast, the phononic contribution remained\nrelatively low and gradually decreased with intensified volume excluding effect (Table\nR1). This reduction may be attributed to the following factors:1) Electron-Phonon\nScattering: Conductive composites contain a high concentration of free electrons. The\nincreased conductivity enhances both the concentration and mobility of these electrons,\nwhich in turn intensifies scattering interactions with phonons, as supported by Adv\nMater. 2016, 28, 7220. 2) Interfacial Phonon Scattering Induced by PAg: A higher PAg\ncontent increases the number of internal interfaces within the composite. Due to\ndifferences in phonon density of states and mismatches in phonon spectra, phonons are\nscattered at the PDMS-Ag interfaces, thereby constraining efficient thermal transport\n(J Mater Chem. 2010, 20, 3579). 3) Microstructural Changes: Increased PAg content\nmay introduce additional voids and defects, which can act as scattering centers for\nphonons, further reducing the phonon mean free path and suppressing thermal\nconduction (Chem Eng J. 2022, 435, 135118). In fact, the reduction in thermal\nconductivity is not obvious because the relatively weak phonon scattering in Ag-based\nconductive composites (Chem Eng J. 2022, 446, 137319).\nTable R1. Thermal conductivity of PDMS-AgFs-PAg composites at different PAg\ncontents.\nPAg content (wt%) k (W/m·K) k (W/m·K) k (W/m·K)\ne ph\n10 4.46 4.74 9.2\n20 6.35 3.85 10.2\n30 9.19 3.31 12.5\n40 14 3.6 17.6\n50 21.1 3.4 24.3\nQ8. Compared with other high-conductivity composite systems (e.g., liquid metals,\nCNT networks), what advantages does the proposed strategy offer in terms of cost,\nrecyclability, or compatibility with flexible device integration.\nA8. Thank you for your insightful comments and for highlighting the comparison with\nother high-conductivity systems. We address your query as follows.\nWhen it comes to cost-effectiveness, the proposed strategy uses AgFs and PAg,\nwhich are less costly than liquid metals, such as gallium-based systems. Liquid metals\nare particularly costly due to their complex production methods and integration\nprocesses. Furthermore, the process of generating Ag NPs in situ within the PDMS\nmatrix is simpler and more cost-effective compared to the intricate procedures required\nfor liquid metal dispersion or carbon nanotubes (CNTs) alignment. This approach,\ntherefore, provides a more scalable and economically feasible solution for large-scale\napplications. The Ag components (AgFs and Ag NPs) offer significant advantages over\nliquid metals, particularly gallium, which is more challenging to recycle due to its\nreactivity. Although CNTs are recyclable, they require more energy-intensive processes\nto purify and reuse, making silver-based systems more attractive from a recycling\nperspective (Adv Mater. 2020, 32, 1902743; Chem Soc Rev. 2019, 48, 2946; Chem Soc\nRev. 2019, 48, 1566).\nThe composite in our study offers excellent mechanical flexibility, making it ideal\nfor stretchable and wearable electronics. Unlike liquid metals, which may face\nmechanical degradation and leakage risk under long-term strain, our Ag-based\ncomposite maintains excellent performance under significant strain. CNTs networks,\nwhile flexible, require more complex fabrication techniques to integrate them\nefficiently into flexible devices. In contrast, the proposed strategy is easier to integrate\ninto flexible substrates, providing a more straightforward and cost-effective solution for\nwearable and stretchable electronics (Chem Soc Rev. 2018, 47, 4073; Adv Mater. 2017,\n29, 1606425; Adv Mater. 2015, 27, 1606425).\nWhen liquid metal interconnects with rigid electronic components, it readily alloys\nwith various metal (e.g., Au, Cu, Ag, etc.) solder joints, potentially triggering\nelectrochemical corrosion that compromises long-term interfacial stability. In contrast,\nAg-containing composites leverage silver's inherent high electrical conductivity and\nlow migration barrier to form low-resistance, highly reliable ohmic contacts with\nmultiple metal electrodes, consequently demonstrating superior interfacial\ncompatibility and robust connectivity in integrated systems. Compared to their CNTs\ncounterparts, the proposed Ag-based conductive elastomers can form inherently low-\nresistance ohmic contacts with most metal electrodes (e.g., Au, Cu, Ni) without\nrequiring high processing pressures or temperatures, enabling direct and reliable\ninterconnects in complex assemblies. Moreover, the percolation network of\nAg achieves high conductivity at low filler loading, which facilitates micro-patterning\nvia standard printing or stencil techniques-crucial for high-density, miniaturized\nflexible systems (Adv. Mater. 2017, 29, 1606425; Nat Nanotech. 2010, 5, 853; Adv\nMater. 2018, 30, 1707035; Adv Mater. 2020, 33, 2002640).\nIn conclusion, our proposed Ag-based composite system provides significant\nadvantages in cost-effectiveness, recyclability, and compatibility with flexible/rigid\ndevice integration compared to other systems like liquid metals or CNTs networks. The\ncombination of in-situ generation of Ag NPs, volume excluding effect, and the flexible\nPDMS matrix ensures high conductivity retention under strain, ease of integration, and\nthe possibility for material recovery, making it a versatile and practical choice for high-\nperformance functional composites."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have revised the manuscript as the comments. It can be accepted without any revision now.", "reviewer_2": "[Editor's note: this reviewer left comments to the author indicating their comments have been addressed]", "reviewer_3": "now this paper can be accetped."}, "author_response": ""}]

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