**4. Conclusions**

Different symmetric supercapacitors (EDLC and PC) were used as "model systems" to apply a robust impedance model to understand the influence of disordered electrode materials on the transport anomalies occurring in the ionic and electronic conductors. For the first time, deviations from Fick's law were identified and quantified during the charge storage process in SCs using the electrochemical impedance spectroscopy (EIS) technique. The use of an impedance model containing two time constants was adequate to represent normal and anomalous charge transports in the different channels (phases) in intimate contact.

Abnormal charge transport in the ionic and electronic conductors was quantified by the dispersive parameters (*n* and *s*) extracted from the different time constants. The anomaly degree verified for the ionic transport inside the narrow pores was pronounced for the EDLC system (*n* = 0.42). In contrast, in the case of the NiO@CNF (composite) system, the ionic transport was practically regular (*n* = 0.92). At the same time, the electronic transport was nearly regular (*s* ≥ 0.98) for the different solid-state conductors. The analysis of the exponent (*β*) representing the capacitance and pseudocapacitance dispersions revealed a low degree of deviation (*β* ≈ 0.95) for the different electrode materials compared to the ideal case (*β* = 1).

It was verified that the specific capacitance increased from 2.62 to 536 F g<sup>−</sup><sup>1</sup> after decorating the carbon substrate (CNF—carbon nanofibers) using NiO nanoparticles. These findings support the occurrence of a strong synergism in the composite, where the porous electrode structure of CNFs propitiates a fast ionic transport towards the hydrated oxide structure (NiO·*<sup>x</sup>*H2O) where the solid-state pseudocapacitance is localized. In addition, CNFs act as localized current collectors that promote a rapid capture of the electrons that originated from the solid-state redox reaction. Voltammetric and galvanostatic studies corroborated the very good capacitance and pseudocapacitance behaviors exhibited by the different symmetric coin cells, i.e., the presence of rectangular voltammetric profiles in conjunction with the triangular galvanostatic charge–discharge curves confirmed the strong capacitive behavior observed in the EIS study. Obviously, charge transport anomalies can only be identified using the impedance technique.

**Author Contributions:** Conceptualization, L.M.D.S., W.G.N. and H.Z.; data curation, A.M.P., L.G.D.S., D.V.F. and B.F.; methodology, W.G.N., H.Z. and L.M.D.S.; writing – original draft preparation, L.M.D.S., H.Z. and W.G.N.; review & editing, L.M.D.S. and W.G.N.; project administration, H.Z.; funding acquisition, H.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Fundação de Amparo à Pesquisa do Estado de São Paulo gran<sup>t</sup> number 2014/02163-7 and 2017/11958-1.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data is available on reasonable request from the corresponding author.

**Acknowledgments:** The authors are grateful to LNNano/CNPEM for SEM and XPS support and to the Brazilian funding agencies CNPq (301486/2016-6) and FAPESP (2014/02163-7, 2017/11958-1, 2018/20756-6) for financial support. L.M. Da Silva wishes to thank FAPEMIG (financial support for the LMMA/UFVJM Laboratory) and CNPq (PQ-2 grant: Process 301095/2018-3). The authors gratefully acknowledge support from Shell and the strategic importance of the support given by ANP (Brazil's National Oil, Natural Gas, and Biofuels Agency) through the R&D levy regulation.

**Conflicts of Interest:** The authors declare no conflict of interest.
