First, 10 g of platy alumina powder (> 99.0%, 160SG, Merck, Germany) was added to 65 mL of N-Methyl-2-pyrrolidone (NMP, Daejung, Korea). Then, FLG powder (3 nm, SKU-NP, Graphene supermarket, USA) was added to the alumina slurry. To obtain a homogeneous suspension, the aqueous slurry was milled by a planetary mill (Pulverisette 5, Fritch, Germany) using alumina balls (ϕ = 3.0 mm) as a medium for 10 h with a speed of 250 rpm as shown in Fig. 1. The ball to powder weight ratio was 4:1. The milled slurry was dried in a vacuum oven at 200°C for 24 h. The dried powder was sintered by hot pressing (Hot press furnace, Thermotech, Korea) in an Ar flowing atmosphere. The sintering temperature was raised at a rate of 10°C/min and maintained at 1500°C for 1 h under a pressure of 30 MPa (Fig. 1).

The microstructure of the sintered samples was investigated using field-emission electron microscopy, FE-SEM (JSM-6710F, Jeol, Japan). The microstructure of the composites were investigated using transmission electron microscopy, TEM (JEM-4010, Jeol, Japan).

The volume resistivity was measured at a constant voltage of 1 V/mm with a source meter (617, Keithley, United states) using the guarded electrode method according to ASTM D257 association standards.

Recently, ball milling techniques employing higher mechanical energy such as planetary milling using a medium (DMF, CO₂, melamine, salt)^14-17) and stirred media milling using smaller media^18,19) has been found to be effective to produce graphenes. The high mechanical energy of planetary milling is favorable for the exfoliation of graphite, while its drawbacks are long processing time (several tens of hours) and a post-dispersing step using sonication due to low yield. To obtain the hybrid powders, we adopted a planetary milling technique to allow pulverization and uniform mixing of FLG powder (Fig. 2(a)) and platy alumina (Fig. 2(b)s) using NMP as a dispersing media. Then, the acquired powders were compacted into bulk composites by hot press, and we investigated the electrical and dielectric properties of the composites.

The anisotropic structure of the platy alumina/FLG composites was derived by using platy alumina instead of spherical alumina as a matrix. We fabricated self-assembled solids with a multilayer dielectric/graphene structure composed of platy alumina/FLG with enhanced permittivity. We synthesized multi-layered structures using platy alumina (thickness = 300 - 400 nm, lateral dimension > 10 μm) and FLG (thickness ~ 3 nm, lateral dimension > 5 μm). The final layer thickness values in the sintered platy alumina/FLG composites were determined by Field-emission Electron microscopy (FE-SEM) and Transmission Electron Microscopic (TEM) analysis. As shown in Figs. 2(c) and 2(d), the platy alumina layer thickness obtained by FE-SEM analysing was 0.3 - 1 μm, whereas the FLG layer thickness obtained by TEM analysis was 3 - 5 nm. The dielectric property in the direction parallel to the hot pressing pressure was measured by impedance spectroscopy.

The electrical resistivity values of the composites at room temperature are shown in Table 1. According to the resistivity versus FLG concentration, below ~ 0.75 vol.% of FLG, the resistivity decreased slowly with an increasing FLG concentration, while the resistivity abruptly decreased above ~ 0.75 vol.% of FLG (Fig. 3). This phenomena can be explained by the metal-insulator (MI) transition by the percolation theory.^5-7) In our composites, the percolation threshold was 0.7 - 0.8 vol.% and the MI transition occurred in this region, which enhanced the electrical conduction by several orders of magnitude. The percolation threshold of the FLG/ platy alumina composite was only 0.75 vol.%, which is comparable to the experimental values for GO/spherical alumina ( f_c = 0.38 vol.%)¹³⁾ and MWCNT/alumina ( f_c = 0.79 vol.%).²⁰⁾ This value is much lower than the GO/silica composite (~ 3.9 wt.%)²¹⁾ and FLG/spherical alumina ( f_c = 3.0 vol.%).¹²⁾ The calculated threshold value of the composite with ellipsoids and an aspect ratio of 100 - 1000 ranged from 1.3 to 0.13 vol.%;²²⁾ therefore, our threshold value for FLG with a thickness of < 5 nm and a lateral dimension of 2 - 3 μm was quite consistent with a well-dispersed disk-shaped filler (FLG) in a dielectric alumina matrix.

According to the percolation theory, the electrical conductivity of the composite material containing a metallic filler (M) in a dielectric matrix (D) is given by the power law as follows.²³⁾

where σ_D : the conductivity of the dielectric material, σ_M : the conductivity of the metallic filler, f : the volume fraction of the dielectric and conducting filler, q = the critical exponent before the percolation threshold, and t = the critical exponent after the percolation threshold.

For the plotting log (conductivity) vs. the log ( f -f_c) linearly, we calculate the σ_D, σ_M, t, and q values. The f is the volume fraction of the FLGs, f_c is the critical volume fraction or percolation threshold, and the exponent t reflects the dimensionality of the system. The fitted values according to equations (1) and (2) are quite consistent with the experimental values (Fig. 3). These parameters are given in Table 2. The fitted t value of 1.65 in the proposed system is similar to the reported values for mullite-molybdenum cermet (t = 1.6)⁷⁾ and alumina-FLG composites (t = 1.84).¹³⁾ In the percolation theory based on a discrete lattice-percolation network, the t values are 1.3 and 2.0 in 2D- and 3D-systems, respectively.²⁴⁾

The conductivity below the percolation threshold is also described by equation (2). We fitted this equation to the data for the composites and obtained a value of q = 0.929 (Fig. 3). This value is slightly lower than t = 1.1 - 1.3 for a 2D-system and comparable to q = 0.7 - 1.0 for a 3D-system. ²⁴⁾

In classical percolation theory, the conducting network is considered to be established by the connection between the neighboring conducting fillers. However, in some cases, the competition between percolative conduction and tunneling between conducting particles is suggested.^25,26) Although the conducting particles are not geometrically connected, electrical conduction occurs via tunneling. In such cases, a nonuniversal critical exponent t as high as 5 - 10 has been observed in percolative composites.^25,27) In our study, t and q values were intermediate between those for the 2D-systme and the 3D-system. This might be because of non-negligible quantum tunneling between neighboring graphenes. However, the graphenes are separated by at least > 1.0 mm by platy alumina partcles with regular thickness (Fig. 1) and, therefore, the interdistance distribution of the graphenes are not quite as broad as randomly distributed graphenes in previously reported polymer composites.