Dynamics in Electrochromic Windows Interpreted with an Extended Logistic Model

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. Switchable smart windows based on the electrochromic (EC) technology are becoming popular in the architectural sector as they offer potential energy savings and improved visual comfort.1 One of the key parameters of the EC device is its switching speed, i.e. time required to switch between the lightest and most intensive coloration. When compared to other "switchable" technologies like suspended particle devices (SPDs) or polymer dispersed liquid crystal devices, EC windows exhibit a relatively slow switching speed, on the order of 10 -20 min for the full color transition, which hinders a fast market penetration and still remains an important topic for research and development.An EC window contains typically tungsten oxide layer (WO 3 ) as the primary EC material, which changes its color due to the potentialinduced intercalation of protons or alkali ions into the WO 3 electrode resulting in the formation of so-called tungsten bronzes. Numerous approaches and models have been proposed to investigate electrointercalation into EC materials like WO 3 . Early studies focused on the bleaching and coloring of WO 3 electrodes immersed in various liquid electrolytes. The time dependence of the coloration of amorphous WO 3 at low voltages was described in terms of a barrier for current at the WO 3 -electrolyte interface.2,3 The coloring and bleaching processes of Li x WO 3 films were examined in short time ranges considering diffusion-limited process, 4 whereas the kinetics of electrochemical reactions in WO 3 was found to be governed by the resistance that depends on the conductivity of electrolyte, reduced forms of WO 3 and transparent conducting layers. 5 The ion transport in host electrodes was reviewed in Refs. 6-9, and rigorous models of diffusion phenomena often require sophisticated numerical calculations. 9-11The current transients for potential steps during the intercalation of Li-ions in Li 1−δ CoO 2 electrodes were found by Refs. 12,13 to deviate from the theoretical predictions. Their chronoamperometric data were interpreted in terms of the cell-impedance controlled diffusion of Li-ions. The diffusion flux of intercalated species at the electrode surface limited by the interfacial charge transfer kinetics ...

Electrochromic Infrared Light Modulation in Optical Waveguides

“…The temporal optical behavior of the ECD‐integrated optical waveguide based on the ionic insertion/deinsertion process can be analyzed using quadratic logistic equation and used to determine the number of electrochemically active sites …”