Characterization of Porous WO₃ Electrochromic Device by Electrochemical Impedance Spectroscopy

Table 1

Equilibrium circuits and mathematical results of real (𝑍_RE) and imaginary value (𝑍_IM) in porous WO₃ EC glass.

Equilibrium circuit	𝑍RE	𝑍IM
𝑅0+𝐿0	𝑅0	𝜔𝐿0
{𝐶1//[𝑅1+(𝐶2//𝑅2)]}	[(𝑅2+𝑅1)×(1−𝜔^2𝐶1𝐶2𝑅1𝑅2)+(𝜔𝐶2𝑅1𝑅2)×(𝜔𝐶2𝑅2+𝜔𝐶1𝑅2+𝜔𝐶1𝑅1(1−𝜔^2𝐶1𝐶2𝑅1𝑅2)^2+(𝜔𝐶2𝑅2+𝜔𝐶1𝑅2+𝜔𝐶1𝑅1)^2	[(𝜔𝐶2𝑅1𝑅2)×(1−𝜔^2𝐶1𝐶2𝑅1𝑅2)−(𝑅2+𝑅1)×(𝜔𝐶2𝑅2+𝜔𝐶1𝑅2+𝜔𝐶1𝑅1)(1−𝜔^2𝐶1𝐶2𝑅1𝑅2)^2+(𝜔𝐶2𝑅2+𝜔𝐶1𝑅2+𝜔𝐶1𝑅1)^2
[𝐶3//(𝑊+𝑅3)]	𝜎+𝑅3√𝜔√𝜔×(1+2𝜎𝐶3√𝜔+2𝜎^2𝜔𝐶^23+2𝜎𝜔^1.5𝐶^23𝑅3+𝜔^2𝐶^23𝑅^23)	−𝜎−2𝜎^2√𝜔𝐶3−2𝜎𝜔𝐶3𝑅3−𝜔^1.5𝐶3𝑅^23√𝜔×(1+2𝜎𝐶3√𝜔+2𝜎^2𝜔𝐶^23+2𝜎𝜔^1.5𝐶^23𝑅3+𝜔^2𝐶^23𝑅^23)
(𝐶4//𝑅4)	𝑅41+(𝜔𝑅4𝐶4)^2	−𝜔𝑅^24𝐶41+(𝜔𝑅4𝐶4)^2
(𝐶5//𝑅5)	𝑅51+(𝜔𝑅5𝐶5)^2	−𝜔𝑅^25𝐶51+(𝜔𝑅5𝐶5)^2