Dynamics in Electrochromic Windows Interpreted with an Extended Logistic Model

R Roldán,Y E Romanyuk

doi:10.1149/2.1371608jes

Abstract

Complete electrochromic (EC) devices based on tungsten oxide are characterized by the chronocoulometry technique in a wide range of applied voltage and time. An empirical model is proposed to approximate the recorded charge evolution over extended periods of time required for the full coloration transition. The model is described by an analytic expression based on the logistic population growth of tungsten bronzes that are responsible for the coloration upon ion intercalation into tungsten oxide, and just four parameters characterize the dynamics of the EC device. The model is verified by fitting experimental chronocoulograms recorded from two different commercial EC windows. It is discussed how the model can be used for the description of the coloration dynamics and estimation of the coloration efficiency.

Highlights

Laboratory for Thin Films and Photovoltaics, Empa - Swiss Federal Laboratories for Materials Science and Technology, 8600 Dubendorf, Switzerland
The coloring and bleaching processes of LixWO3 films were examined in short time ranges considering diffusion-limited process,[4] whereas the kinetics of electrochemical reactions in WO3 was found to be governed by the resistance that depends on the conductivity of electrolyte, reduced forms of WO3 and transparent conducting layers.[5]
In 1999, the so-called quadratic logistic differential equation was introduced by Torresi et al.[20] for the interpretation of electrointercalation processes in electroactive films in analogy to the power response of a fuel cell described by Gonzalez.[21]

Summary

Introduction

Laboratory for Thin Films and Photovoltaics, Empa - Swiss Federal Laboratories for Materials Science and Technology, 8600 Dubendorf, Switzerland. The diffusion flux of intercalated species at the electrode surface limited by the interfacial charge transfer kinetics was represented by the Butler-Volmer equation.[14] The kinetics limitations at the electrolyte/electrode interface as well as Ohmic drop effects were introduced in the diffusion model through a single dimensionless parameter,[15] and approximate expressions of the current transients were proposed.[16] The three main models used in the literature to fit experimental data for insertion/extraction processes under the potential step chronoamperometry technique were discussed and compared.[17]. The logistic model has been confirmed and elaborated later[22,23,24] and disputed by Sadkowski,[25] who stated that the logistic equations are rather limiting forms valid in the special case of linear potential scan of a fully (ir-)reversible process

Methods

Results

Conclusion