examined by thermogravimetric analysis and differential scanning calorimetry. The characterizations are summarized in Table 3.3.
Performance Parameters for Supercapacitors
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
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
The specific capacitance
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
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
(3.4)
The equivalent series resistance (ESR) of the cell is obtained from GCD ΔV
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 td and tc 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
