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

	Type of analysis	Parameters extracted
Imaging techniques	Tomographic analysis	MorphologyPorosityTortuosityPore dimensions
FIB-SEM tomography	PorosityTortuosityPore dimensions
Non-imaging techniques	Electrochemical analysis
Linear sweep voltammetry and cyclic voltammetry	Electrochemical stability
Electrochemical impedance spectroscopy	Mac Mullin number via bulk electrolyte conductivity σ and effective electrolyte conductivity σsepTransport parameters (Diffusion coefficient, ion mobility, viscosity)
Potentiostatic polarization combined with electrochemical impedance spectroscopy	Lithium-ion transference number according to Bruce–Vincent method
Spectroscopic and diffractive methods (OR may be considered basic characterizations)
NMR	Transport propertiesDiffusion coefficientsConductivityTransference number
X-ray diffraction	Structural compositionDegree of crystallinityCrystallite size/interchain separation
Thermomechanical analysis
Compressive loading	Effective membrane moduliYoung’s modulusFlow stress
Thermo-gravimetric analysis and differential scanning calorimetry	Brittleness and stabilityDuctile-to-brittle transition temperatureMelting temperatureGlass transition temperatureCrystallinity

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 ∫idV 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 ΔV 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 (Δt) 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 ΔV 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 ΔV

(3.5)

Here ΔVIR 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_d and t_c are 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, Δt 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)

Here I is the discharging current, Δt is the discharge time, ΔV is the potential drop during discharge, and m is the total mass of the active electrode materials in the both (+ ve, - ve) electrode.

Energy Density & Power Density

(3.11)

(3.12)

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.