Radio-frequency linear absorption coefficient of carbon materials, its dependence on the thickness and its independence on the carbon structure

This work provides the first explicit report of the linear absorption coefficient α of materials in the radio frequency regime (0.1-1.5 GHz). The coefficient decreases with increasing carbon thickness. The highest α (940 mm−1) is provided by the smallest carbon thickness (7 μm). The lowest α (38 mm−1) is provided by the largest carbon thickness (460 μm). For carbon thicknesses that are much larger than the skin depth, α is essentially independent of the thickness. For any frequency, α depends negligibly on the carbon structure, as its values for carbon fiber, carbon nanofiber and flexible graphite fall on the same curve of α vs. carbon thickness. This is expected from the wavelength being long (30 cm at 1 GHz) compared to the carbon microstructural dimensions. At frequencies ≥0.3 GHz, the decrease of α with the carbon thickness is approximately exponential, with the exponent related to the inverse of the skin depth. At 0.1 GHz, α tends to be below the value based on the exponential function. An absorption edge (with α increasing with increasing frequency) occurs at 0.5-1.0 GHz, as shown for carbon fiber mat.

Decrease of the linear absorption coefficient α with increasing carbon thickness, with the experimental data points for carbon fiber (●), carbon nanofiber (○) and flexible graphite (Δ) falling on the same curve (not shown). The solid curve is the theoretical exponential curve for carbon fiber resistivity 1.2 × 10−3 Ω cm; the dashed curve is the theoretical exponential curve for flexible graphite resistivity 7.5 × 10−4 Ω cm. The frequency is 1 GHz.90