## 3 Results
### Device Performance Metrics
The wavelengths at which the transmittance was measured and the switching pulse sequence are labeled on each panel. where, \(l\), is the sample optical depth (cm), \(\varepsilon_{+}\), and \(dc_{+}(t)\) are the molar extinction coefficient (dm\({}^{3}\) mol\({}^{-1}\) cm\({}^{-1}\)) and the infinitesimal change in the concentration of the radical cation species. Integration of Equation (2) gives the change in the optical density of the sample at time \(t\):  
\[\Delta OD(t)=l\,\varepsilon_{+}[c_{+}(t)-c_{+}(0)]=l\,\varepsilon_{+}c_{+}(t) \tag{6}\]  
being \(c_{+}(0)=0\). It follows that:  
\[\Delta OD(t)=l\,\varepsilon_{+}c_{+}(t)=\eta_{+}Q_{i} \tag{7}\]  
Equation (7) tells us that the coloration efficiency is a function of the molar extinction coefficient of the active electrochromic species (the radical cation in our case) and of its concentration at time \(t\). The molar extinction coefficient of the two species are \(1.9\times 10^{5}\) mol\({}^{-1}\) dm\({}^{3}\) cm\({}^{-1}\) and \(1.2\times 10^{4}\) mol\({}^{-1}\) dm\({}^{3}\) cm\({}^{-1}\) respectively for the TV\({}^{\bullet+}\) and FD\({}^{\bullet+}\). In order to estimate the concentration of the radical cation at time \(t\) in the device, we can assume that the heterogeneous electron transfer reactions at the ITO electrode are of first order with rate coefficients \(k_{e}\). The rate of change of \(c_{+}(t)\) is therefore expressed as  
\[\frac{d}{dt}c_{+}(t)=k_{e}c_{p}(t)=k_{e}[c_{p}(0)-c_{+}(t)] \tag{8}\]  
where, \(c_{p}(t)\) is the concentration of the precursor species (the dication state for TV and the neutral state for FD) at time \(t\). Integration of the differential Equation (8) leads to the desired equation that expresses the concentration of the radical cation species as a function of time:  
\[c_{+}(t)=c_{p}(0)\Big{[}1-e^{k_{e}t}\Big{]} \tag{9}\]  
Equation (9) shows that the concentration of the monocation species is an exponential growing function of time with characteristic time \(k_{e}^{-1}(s)\) and depends on the initial concentration of the precursor species \(c_{p}(0)\). The higher is the kinetic constant of the heterogeneous electron transfer process, the faster is the coloration kinetics. Figure 4 displays the optical density change of the devices at the two wavelengths investigated, as a function of time. It clearly shows the exponential growth of the OD with time that can be very well fitted by the Equations (6) and (9) (R\({}^{2}\) > 0.99). The fitting results are summarized in Table 1.  
Figure 4: Optical density changes vs. time at 670 nm and 1430 nm of the devices with TV/Fc and TV/FD, respectively. The continuous lines are the best fitting curves obtained by the Equation (6). It is interesting to note that the rate coefficient \(k_{e}\) for the reduction of the thienoviologen dication is almost 8 times larger than that for the oxidation of the neutral diarylamine species at the ITO electrode surface. This should be expected due to the charged nature of the first species which can migrate more rapidly toward the cathode surface upon application of the DC bias. The difference in the CE observed for the two bands can then be rationalized on the basis of the Equation (4) rearranged as follows and the coloration kinetics data:  
\[dA(t)=l\,\varepsilon_{+}dc_{+}(t) \tag{5}\]0  
It is clear from the Equation (10) that the faster is the kinetics of coloration and the higher is the extinction coefficient, the larger is the coloration efficiency, being the same the thickness of the absorbing layer (l) and the injected/ejected surface charge, as is the case for the thienoviologen compared to the arylamine.