  The coloration mechanisms in electrochromic (EC) systems can be probed by
comparing the dynamics of the electrical and optical responses. In this paper,
the linear frequency-dependent electrical and optical responses of an amorphous
tungsten oxide thin film were measured simultaneously by a combination of two
techniques$\text{---}$that is, electrochemical impedance spectroscopy (EIS) and
the so-called color impedance spectroscopy (CIS). This was done at different
bias potentials, which can be associated with different intercalation levels.
Equivalent circuit fitting to the EIS spectra was used to extract the Faradaic
components participating in the total impedance response. The latter were
assigned to an intermediate adsorption step before the intercalation and to the
diffusion of the electron-ion couple in the film. A quantity denoted complex
optical capacitance is compared to the complex electrical
capacitance$\text{---}$in particular, their expressions are related to the
Faradaic processes. The coloration at low intercalation levels followed both
the adsorption and diffusion phenomena. Conversely, the diffusion contribution
was dominant at high intercalation levels and the adsorption one seemed to be
negligible in this case. For perfectly synchronized electrical and optical
responses, their complex spectra are expected to differ only by a multiplying
factor. This was the case at low intercalation levels, apart from small
deviations at high frequencies. A clear departure from this behavior was
observed as the intercalation level increased. A combination of
frequency-dependent techniques, as presented in this work, can help in the
understanding of the dynamics of the coloration mechanisms in EC materials at
various conditions$\text{---}$for example, at different intercalation levels
and optical wavelengths.
