An Exploration of Graphene-Water Interface Electrochemical Circuit Model
Authors: Lin Cheng-Yu , Lu Yu-Xuan , Tsai Ming Hsiu , Lin Chih-Ting 
Published: September 2023

Graphene has been considered a good candidate for sensor material due to its large surface-to-volume ratio and high conductivity. For instance, high-sensitivity solvent sensors can be achieved through liquid-gated graphene field effect transistors (GFET). In such kind of sensors, ions and other molecules in the test solution will be chemically adsorbed by the graphene sheet. It results in changes of the channel surface potential and conductance. However, the measured potential difference are affected by electrical double-layer capacitance in solution, and quantum capacitance in graphene. Studies have reported the quantum capacitance of graphene in an ionic or aqueous liquid, while the interface between graphene and deionized (DI) water hasn’t been fully explored yet. To address this point, in this work, we measured the electrochemical impedance spectroscopy (EIS) of graphene electrodes in deionized water and proposed an electrical circuit model for the electrochemical cell. The meaning of each element of the circuit model was also discussed.

In our experiment, single-layer graphene was grown by chemical vapor deposition (CVD) on copper foil and transferred to Si/SiO2 substrate with gold contacts. Our test solution, DI water, was confined on the graphene sensing layer by polydimethylsiloxane (PDMS). This electrochemical cell was measured with BioLogic SP-150 potentiostat by 2-probe EIS method, with graphene as working electrode (WE) and Ag/AgCl electrode placed in DI water as counter electrode (CE). Another electrochemical cell with gold pad WE was also prepared as the control group.

The electrochemical impedance of the water-graphene cell was plotted in a Nyquist plot and showed two semicircles. This observation is different from a regular electrochemical cell, whose impedance shows a semicircle, corresponding to the interface RC impedance, and a low-frequency 45° straight line, corresponding to molecular mass transport limitation. The two semicircles in our water-graphene cell impedance indicate that the equivalent circuit model is based on two parallel RC circuits, corresponding to the interface and solution impedance. By modifying the biasing potential and adding supporting electrolyte, we observed the response of the impedance and identified that the high-frequency semicircle is related to solution impedance, and the low-frequency semicircle is related to interface impedance, which is consistent with the reaction rate of both parts. To make more precise fittings, an additional Warburg element was introduced into the circuit model for the effect of mass-transfer limitation. We proposed a model based on an RC parallel circuit in series with a Randles circuit. Comparing with the 2-RC model, the fitting residual of the proposed model improved by 13%. The RWC parallel circuit was fitted to the high-frequency semicircle, which corresponds to the solution impedance. This is different from the commonly used Randles model, where the Warburg element is included in interface impedance. This difference arises from the lack of supporting electrolytes. When there are supporting electrolytes in an electrochemical cell, the double-layer capacitor at the electrode-solution interface is mainly contributed by supporting electrolytes. While using DI water as the solution in our case, the charged species contributes to both faradic current and non-faradic current, which means that the mass-transport limitation affects both the charge transfer resistor and the double-layer capacitor. Hence, the Warburg element for mass-transport limitation can be extracted from the interface RC parallel circuit and put into the solution impedance when there is no supporting electrolyte.

After the circuit model was decided and the elements were identified, we fit the electrochemical impedance curves of both the water-graphene cell and the control group, whose WE was replaced by a gold pad. The fitting result shows that the bulk resistor and capacitor, Rb and Cb, values are unrelated to the WE material, which again supports our circuit model. While the WE surface capacitance Cs of the graphene-water electrochemical cell is 0.0606 F/m2, which is 1/65 of that of the control group. To verify the reason for the capacitance difference, we considered the effect of the graphene quantum capacitance. The theoretic value of the quantum capacitance in single-layer graphene was found to be 0.0752 F/m2 under our setup, which is only 18.8% smaller than our experimental value. Hence, we concluded that SLG surface capacitance was dominated by quantum capacitance.

Figure 1