**5. Discussion**

The proposed model can effectively describe the dynamic behavior of UC without the usage of PDEs. This model describes the concentration of ions by an electrical potential, charge diffusive motion by electric current, and diffusion coefficient by electrical resistance. Therefore, the exact physical nature of electrolyte is considered in the proposed mathematical model. The infinite r–C chain-based equivalent circuit exactly describes the behavior of ion movement in the electrolyte and porous electrodes. Moreover, we succeeded in finding a rigorous analytical solution of this model in the closed form. The symmetric double layer UCs are purely electrostatic devices. Hence, no electrochemical (Faradaic) reactions occur on electrodes instead of asymmetrical UCs, where the electrochemical reactions occur in the one compartment of UC. Therefore, the voltage-dependent term (pseudo-capacitance related to Faradaic reactions) is not considered in the model. Some previous studies have considered the voltage-dependent capacitance term for the modeling [33,43]. Rafik et al. claimed that consideration of the voltage-dependent term could improve the modeling precision by 10% more than that of constant term approximation [33]. If the voltage and current deviations are significantly large, then the parameters should be adjusted accordingly. Future works will consider the incorporation of voltage-dependent capacitance term in the infinite r–C chain equivalent circuit. More importantly, this study also approved the principle possibility of applying the reverse Fourier transform on the frequency domain for the description of dynamic behavior. We also want to mention that the finite analytical representation of the Fourier transform cannot be applied for every mathematical expression. Hence, the proposed model was analyzed using simulation software to study the dynamic behavior of UC. The experimental and calculated charge-discharge characteristics displayed good agreement with a relative error of 5–8%. During the modeling, it was noted that a higher number of r–C chains led to higher accuracy in the impedance representation. Last but not least, we want to mention that this article strengthens the usefulness and advantages of the infinite r–C chains-based equivalent circuit.
