A majority of efforts are focussed towards the positive electrodes for supercapacitors, based on metal oxides, sulphides and selenides. However, only limited options are available for the negative electrodes. Fe₂O₃ is popular among metal oxides as negative electrode. It provides a broad potential window, high theoretical specific capacitance of ∼3600 F g^-1 and is also economically viable. However, Fe₂O₃ suffers from poor electrical conductivity, limiting its application. Its performance can be improved by tuning its morphology to provide enhanced density of accessible surface sites for ionic interactions. Fractal-like structures have gained significant attention in various areas of research involving active surface site driven applications like catalysis, solar energy, life science etc. However, such fractal-like structures have been relatively less explored for supercapacitor applications.

In the present study, Fe₂O₃ fractal-like structures are synthesized via hydrothermal route synthesis. Various morphologies viz. fern leaf shaped fractal-like structures (FR), snowflake structures (FS), nano-microspindles (NS) and microspheres (MS) are synthesized from different precursors. The FR morphology synthesized from K₃[Fe(CN)₆] showed promising performance upon being supported by Ni foam as a current collector. Among all the morphologies, the Ni-foam-supported FR (FR@NF) negative electrode exhibits a superior specific capacitance (C_sp) of ∼484 and ∼406 F g^–1 at 1 and 10 A g^–1, respectively. It is also stable up to at least 5000 cycles at 10 A g^–1 with ∼91.4% capacitance retention.

Fractal dimensions (FD) of the morphologies are estimated to study their effect on the electrochemical performance of these morphologies. The geometrical FD_Geom is estimated through voxel counting method using 3D-converted images from scanning electron microscopy. The FD_Geom for FR, FS, NS and MS are 2.48, 2.37, 2.31 and 2.28, respectively. Fractal dimension is also estimated through electrochemical impedance spectroscopy (EIS) and termed as FD_EIS. The Nyquist plots are modelled with an equivalent circuit consisting of solution resistance connected in series with a parallel arrangement of constant phase element (CPE) with a series connected charge-transfer and Warburg elements. The CPE coefficient viz. n is used to estimate the FD_EIS = (1+n)/n. The estimated FD_EIS for FR, FS, NS and MS are 2.40, 2.35, 2.28 and 2.19, respectively. The FD_EIS values are lower than the corresponding FD_Geom due to the difficulty in the adsorbing ions accessing the geometrical surface of these morphologies, as expected.

The estimated C_sp increases with (geometrical) fractal dimension as seen in Fig. 1. The enhanced performance at higher FD_Geom is attributed to the presence of higher density of active sites present in the form of grooves and troughs etc. These active surface sites render decreased resistances for charge transfer and, coincidentally, for the bulk solution with an increase in the FD.