Electron tunneling of hierarchically structured silver nanosatellite particles for highly conductive healable nanocomposites

Healable conductive materials have received considerable attention. However, their practical applications are impeded by low electrical conductivity and irreversible degradation after breaking/healing cycles. Here we report a highly conductive completely reversible electron tunneling-assisted percolation network of silver nanosatellite particles for putty-like moldable and healable nanocomposites. The densely and uniformly distributed silver nanosatellite particles with a bimodal size distribution are generated by the radical and reactive oxygen species-mediated vigorous etching and reduction reaction of silver flakes using tetrahydrofuran peroxide in a silicone rubber matrix. The close work function match between silicone and silver enables electron tunneling between nanosatellite particles, increasing electrical conductivity by ~5 orders of magnitude (1.02×103 Scm−1) without coalescence of fillers. This results in ~100% electrical healing efficiency after 1000 breaking/healing cycles and stability under water immersion and 6-month exposure to ambient air. The highly conductive moldable nanocomposite may find applications in improvising and healing electrical parts.

vol%, THF peroxide = 15 mL) nanocomposite (7.5 × 7.5 × 1.0 mm 3 ) was used for the electrical conductivity (σ) measurement. The  was measured by the four-point probe in-line method using a current source (Keithley 6221) and a nanovoltmeter (Keithley 2182A) [2]. The distance between tungsten probes was 1 mm. The σ was calculated by the following equation.

=
where I is the supplied current, V is the measured voltage, and G is the geometric factor of the specimen.
A detailed description about the geometry calibration is provided elsewhere [2,3].
14 Supplementary Figure 13 The electrical conductivity of the AgNS-AgFL-SR nanocomposites. a The data from multiple batches. b The data from multiple specimens from the same batch.
Supplementary Figure 14 The density of the AgNS-AgFL-SR nanocomposite. The density was measured by the Archimedes method as a function of the THF peroxide amount in the initial mixture.
The error bars represent the standard deviation of the data.

16
Supplementary Figure 15 The cyclic voltammetry analysis. a THF peroxide electrolyte. b H2O2 electrolyte. The scan rate was 10 mV s −1 . The concentration of the THF peroxide and H2O2 was identical (0.068 M). The AgFLs deposited on a glassy carbon electrode, Ag/AgCl electrode, and platinum wire were used as the working, reference, and counter electrodes, respectively. The oxidation peak was marked using a circular symbol. The oxidation peak was observed at a higher bias potential (0.44 V) for the H2O2 electrolyte, compared with that (0.29 V) for the THF peroxide electrolyte.
The H2SO4 facilitated an acidic environment required for the liberation of I2 while ammonium molybdate acted as a catalyst for the oxidation of THF peroxide [21]. where I is the integrated peak area of 1 H NMR spectrum, N is the number of hydrogen atoms contributing to the peak, and C is the molar concentration. NTHF peroxide and NDimethyl sulfone was 1 and 6, respectively.
The Supplementary Figure 8d shows the 1 H NMR spectrum after the reaction of THF peroxide with AgFLs (AgNS-AgFL). The spectrum of pure THF peroxide before the reaction is also shown for comparison. The residual THF peroxide peak was negligible after the AgNS particle generating reaction (AgNS-AgFL).

Supplementary Note 3 Finite element analysis of the AgNS-AgFL-SR nanocomposite
Finite element analysis (FEA, ABAQUS, SIMULIA) [24] was conducted to simulate the effect of AgNS particles on the mechanical property of the AgNS-AgFL-SR nanocomposite. The AgNS-AgFL-SR nanocomposite was modeled as a unit cube (side length = 0.4 µm). The unit cube was made up of one million C3D8R elements (100 elements each in X, Y, and Z directions), and the size of each element was 4 nm. The size of element was determined considering the average size of small AgNS particles (Fig. 2c). The AgNS-AgFL-SR nanocomposite was considered to be composed of two parts. The AgFLs and SR matrix constituted one part while the AgNS particles comprised the other part. Here after, the first part containing AgFLs and SR was referred to as the reference matrix for clarity. The stress-strain characteristic of the reference matrix was assumed to be the same as that of the AgFL-SR nanocomposite, and the compressive modulus of the AgFL-SR nanocomposite was directly obtained from experiments ( Fig. 6a). A definite volume fraction of nanoparticle elements, representing AgNS particles, was introduced into the reference matrix to simulate the mechanical property of the AgNS-AgFL-SR nanocomposite (Ag = 44 vol%). Supplementary Figure 25 shows four AgNS-AgFL-SR nanocomposite models. The AgNS particle volume fractions were 3, 6, 9, and 12 vol%, respectively. The experimentally measured stress-strain data of the AgFL-SR nanocomposites with Ag volume fractions of 41, 38, 35, and 32% (Fig. 6a) were used for the mechanical properties of the reference matrix, respectively. The total Ag filler fraction was fixed at 44 vol% (e.g., AgNS 3 vol% + AgFL 41 vol %) since the AgNS particles were formed by the in-situ etching and reduction reaction of Ag flakes in the SR matrix. The AgNS particles were randomly placed in the cube to theoretically simulate the mechanical properties of the AgNS-AgFL-SR nanocomposite.