# Observation of Complex Conjugate Roots and Resonant Behavior in Quasi-Solid Supercapacitors as an Indication of Its Electrochemical instability

## TL;DR

This paper shows that unstable electrochemical behavior in quasi-solid supercapacitors can be detected through complex conjugate roots and resonant peaks in impedance measurements.

## Contribution

The study introduces complex conjugate roots and resonant behavior as indicators of electrochemical instability in quasi-solid supercapacitors.

## Key findings

- Newly fabricated devices showed poor energy storage that improved with aging time.
- Resonant peaks and anticlockwise arcs in impedance plots were linked to electrochemical instability.
- Stability issues persisted in devices with longer electrolyte immersion times even after 28 days.

## Abstract

Quasi-solid supercapacitors are promising electrochemical
devices
for energy storage applications due to their high-power density, long
life cycle, and environmental benefits. However, their electrochemical
performance can change over time as a result of interactions between
the electrodes and electrolyte, as well as the fabrication process.
In this study, the electrochemical behavior of quasi-solid supercapacitors
with activated carbon electrodes immersed in 4 M H2SO4 poly(vinyl alcohol) electrolyte for periods of 10 min and
24 h were investigated. Initial measurements show a lack of energy
storing properties in newly fabricated devices, which improve with
the aging time, as observed in cyclic voltammetry and charge–discharge
cycles. Anticlockwise arcs and resonant peaks were observed in Nyquist
and Bode plots, respectively, and were modeled by introducing complex
conjugate roots and a damping factor ξ in the transfer function
of the electronic equivalent circuit. This unfavorable behavior disappeared
after 14 days in devices with shorter immersion times. On the other
hand, the effects persisted in devices with longer immersion times
even after 28 days. The stability of quasi-solid supercapacitors is
thus demonstrated to be linked to complex conjugate roots and resonant
behavior in impedance spectroscopy.