Electrical and Electronic Devices, Circuits, and Materials

The suitability of the prepared polymer electrolyte as an electrolyte in the supercapacitor cell is examined by evaluating the characteristic parameter. These parameters play a significant role and are specific capacitance, resistance (bulk, charge transfer), energy density, power density, capacity retention, and coulombic efficiency. The important techniques are complex impedance spectroscopy (CIS), cyclic voltammetry (CV), and galvanostatic charge/discharge (GCD).

The overall capacitance of the cell is (F) as obtained from impedance spectroscopy using equation 3.1

(3.1)

Table 3.3Selected separator characterization techniques with examples for extracted parameters [Reprinted with permission from Ref. [31], © Springer Nature 2019].

Here, where f is the frequency in Hz and Z″ is the imaginary part of the complex impedance in Ohm. The single electrode specific capacitance of cell is (F/g) by multiplying the overall capacitance by a factor of 2 and divided by the mass of the active electrode material in g [32].

The specific capacitance of the supercapacitors from cyclic voltammetry (CV) has been calculated using the following equation 3.2[33]

(3.2)

Where ∫ id V is the integrated area of the CV curve, m is the single electrode mass of active material (activated carbon) in g, S is the scan rate and Δ V is cell voltage range.

The galvanostatic charge/discharge (GCD) is important technique to evaluate the capacitance of device and cyclic stability by measuring the discharge time (Δ t ) and current applied (i) (equations 3.3– 3.5). The overall capacitance of the cells ( F / g ) is calculated from the discharge curves using the relation

(3.3)

Where, i = discharge current, Δt = discharge time, m= mass of active material and Δ V is cell voltage. For a symmetrical cell system, the specific capacitance referred to a single electrode is related to the overall capacitance of the cells by the following relation [34].

(3.4)

The equivalent series resistance (ESR) of the cell is obtained from GCD Δ V

(3.5)

Here Δ VIR is an internal Ohmic voltage drop and i is the applied discharge current.

The Coulombic efficiency is calculated using the following relation

(3.6)

Here t dand t care discharging and charging times respectively obtained from the charge-discharge curve.

The various electrochemical parameters are obtained from the GCD using the formulas given below [35].

(i) For two-electrode (symmetric cell configuration)

Specific Capacitance

(3.7)

Here, I is the discharging current, Δ t is the discharge time, ΔV is the potential window, and m is the mass of active material in the single electrode

Energy density & Power density

(3.8)

(3.9)

Here, E (Wh/kg), C, ΔV, P (W/kg) and Δt are the specific energy, specific capacitance, potential window, specific power, and discharge time, respectively.

(ii) For two-electrode (asymmetric cell configuration)

Specific Capacitance

(3.10)