Carbon-Nanotube–Electrolyte Interface: Quantum and Electric Double Layer Capacitance

We present a comprehensive study of the electrochemical capacitance between a one-dimensional electronic material and an electrolyte. In contrast to a conventional, planar electrode, the nanoscale dimension of the electrode (with diameter smaller than the Debye length and approaching the size of the ions in solution) qualitatively changes the capacitance, which we measure and model herein. Furthermore, the finite density of states in these low dimensional electronic systems results in a quantum capacitance, which is comparable to the electrochemical capacitance. Using electrochemical impedance spectroscopy (EIS), we measure the ensemble average, complex, frequency dependent impedance (from 0.1 Hz to 1 MHz) between a purified (99.9%) semiconducting nanotube network and an aqueous electrolyte (KCl) at different concentrations between 10 mM and 1 M. The potential dependence of the capacitance is convoluted with the potential dependence of the in-plane conductance of the nanotube network, which we model using...