# Setup for simultaneous electrochemical and color impedance measurements of electrochromic films: theory, assessment, and test measurement

## TL;DR

This paper introduces an experimental setup for simultaneous electrochemical and optical impedance measurements of electrochromic films, analyzing its uncertainty, response behavior, and effects of excitation voltage, demonstrated on amorphous WO3.

## Contribution

It presents a novel setup for combined electrochemical and color impedance measurements, including analysis of frequency-dependent variables and noise, with experimental validation on WO3 films.

## Key findings

- Complex differential coloration efficiency increases monotonically at low frequencies.
- Upper frequency limit for reliable measurements can be increased from 11.2 Hz to 125.9 Hz.
- Trade-off exists between signal-to-noise ratio and linearity of responses.

## Abstract

Combined frequency-resolved techniques are suitable to study electrochromic (EC) materials. We present an experimental setup for simultaneous electrochemical and color impedance studies of EC systems in transmission mode and estimate its frequency-dependent uncertainty by measuring the background noise. We define the frequency-dependent variables that are relevant to the combined measurement scheme, and a special emphasis is given to the complex optical capacitance and the complex differential coloration efficiency, which provide the relation between the electrical and optical responses. Results of a test measurement on amorphous $\mathrm{WO}_3$ with LED light sources of peak wavelengths of $470$, $530$, and $810~\mathrm{nm}$ are shown and discussed. In this case, the amplitude of the complex differential coloration efficiency presented a monotonous increase down to about $0.3~\mathrm{Hz}$ and was close to a constant value for lower frequencies. We study the effect of the excitation voltage amplitude on the linearity of the electrical and optical responses for the case of amorphous $\mathrm{WO}_3$ at $2.6~\mathrm{V}~\mathrm{vs.}~\mathrm{Li/Li}^+$, where a trade-off should be made between the signal-to-noise ratio (SNR) of the optical signal and the linearity of the system. For the studied case, it was possible to increase the upper accessible frequency of the combined techniques (defined in this work as the upper threshold of the frequency region for which the SNR of the optical signal is greater than $5$) from $11.2~\mathrm{Hz}$ to $125.9~\mathrm{Hz}$ while remaining in the linear regime with a tolerance of less than $5\%$.