Inversion of two-flux and four-flux radiative transfer models in WO3-NiO electrochromic devices

Intrinsic and extrinsic scattering and absorption coefficients (S&A-C) of four inorganic electrochromic device (ECD) samples were determined at their bleached-off optical state (BOOS, 0 V) and at their colored-on optical state (COOS, +3 V DC). The same inversion procedure previously applied to suspended particle device (SPD) and polymer-dispersed liquid crystal (PDLC) samples, approximated for a single layer sandwich structure, was used here for a third smart window technology, based on redox reactions. The four studied ECDs incorporated cathodic WO3 and anodic NiO layers corresponding to the four possible combinations of two thicknesses for each material —single (120 nm) and double (240 nm)— within their sandwich structures. The analysis of their S&A-C was performed in three stages. First, determination of optical constants using the collimated solutions of the four-flux model (4FM) from collimated transmittance and reflectance (T&R) measurements. Second, estimation of extrinsic S&A-C from the two-flux model (2FM) using total (collimated + diffuse) T&R data. Third, extraction of intrinsic S&A-C from the diffuse 4FM solutions by means of diffuse T&R data, employing the diffuse interface reflectance, an approximate average crossing parameter, and the forward scattering ratio. Although light scattering was found to be weak, absorption for the COOS showed a clear dependence on the WO₃–NiO active layers thicknesses: neutral gray ECD11 (single WO3–single NiO), brownish gray ECD12 (single WO3–double NiO), bluish gray ECD21 (double WO3–single NiO), and dark gray ECD22 (double WO3–double NiO). As expected, similar optical appearances were observed in the BOOS for the four ECDs. The values weighted by the CIE 1931 standard observer color matching function (ȳ) indicate that increasing the WO3 thickness twofold leads to a larger absorption coefficient increment than a twofold increase in the NiO thickness. The single-layer 4FM implementation adopted in this study provides reliable agreement in the 250–1500 nm wavelength range, while fitting inaccuracies appear beyond 1500 nm (i.e., in the 1500–2500 nm region) between the calculated and the measured diffuse transmittance at BOOS, for ECD11 and ECD22, and at COOS, for ECD11. No fitting inaccuracies were observed between the calculated and the measured diffuse reflectance. Concerning the 2FM study, an excellent agreement in fitting was observed between the calculated and the measured total T&R for the four ECD samples.