(Invited) Transmission Line Modelling of Thin Film Graphene Electrodes: Capacitance of Chemically-Derived Graphene in Monolayer State
Authors: Sugimoto Wataru , Lei Zhongwei , Mitsui Takahiro , Itagaki Masayuki 
Published: February 2020

Graphene has been studied as a candidate for electrochemical capacitor electrodes owing to its good electronic conductivity and theoretically high specific surface area. Chemically-derived graphene, or reduced graphite oxide (rGO) nanosheets, have advantages including moderate surface area, high volumetric density and scalability. In order to fully take advantage of the 2D nanostructure, the complex pore structure and fundamental capacitive behavior particularly in a monolayer state needs to be better understood. In this study, a series of thin films with 1 to 10 mono-layers of rGO were were fabricated by layer-by-layer deposition as simplified model electrodes with well-defined, countable graphene layers.[1] Electrochemical impedance spectroscopy (EIS) and cyclic voltammetry were conducted in neutral and acidic electrolytes in order to investigate the (pseudo)capacitive behavior of chemical graphene. A transmission line model (TLM) was adopted to simulate the electrochemical impedance data. The model structure is composed of layers of rGO with slit pores with lateral size the same as the gold substrate (1×1 cm) (Fig. 1). The equivalent circuit inside the interlayer gaps can be expressed as Z
TLM (Fig. 2), which has a total impedance according to the de Levie model,
-Equation 1-
where X is the length of the slit pore along the ion penetration direction, Z* is the impedance per unit length in the slit pores, Z** is the impedance per unit area, l is the total length of perimeter of cross-section of the slit pores, j is the imaginary unit and, ω (=2πf, where f is frequency) is the angular frequency. The length of the slit pore along the ion penetration direction for all samples is equal to the geometric size of the electrode (X=1 cm) and the perimeter of the slit pores is l =2 cm × n layers.

C
TLM and R*TLM were obtained from TLM-simulation of (PDDA/rGO)10 reduced either by gas phase H2 or chemical reduction with N2H4. In Na2SO4, the frequency response will reflect only the electric double- layer capacitive behavior with no contribution from pseudo-capacitance. (PDDA/rGO)10-H2 shows a C
TLM of ~25 μF/cm2 at 0.2-1.0 V and ~10 μF/cm2 at 1.2 V. (PDDA/rGO)10-N2H4 shows C
TLM of 12-20 μF/cm2 between 0.2-1.2 V. R*TLM was higher for the N2H4-reduced (O/C=0.10) film compared to the H2-reduced counterpart (O/C=0.21). Samples with lower O/C have lower ionic conductivity due to lower hydrophobicity and higher electronic conductivity. Thus, R*TLM is suggested to be dominated by ionic conductivity. (PDDA/rGO)10-H2, with higher O/C and lower electronic conductivity, has higher C
TLM and lower R
TLM. These results imply that leaving a certain amount of surface functionalities seems to be advantageous for non-Faradaic electric double layer charging, which can be due to better wettability of the surface. R*TLM is higher in Na2SO4 compared to that in H2SO4, which can be attributed to the lower ionic conductivity of the electrolyte in the slit pores. In H2SO4, R*TLM for the H2-reduced samples (O/C=0.21) shows slightly higher values compared to the N2H4-reduced counterparts (O/C=0.10). From the results, we conclude that R*TLM is influenced more by ionic conductivity in Na2SO4, and more by the electronic conductivity of rGO in H2SO4.
[1] Z. Lei, T. Mitsui, H. Nakafuji, M. Itagaki, and W. Sugimoto, J. Phys. Chem. C, 118(13), 6624–6630 (2014).

Figure 1