Potential Electrogravimetric Transfer Function

The mass/potential transfer function is then defined by Aw, , ACi 

Another interesting quantity is the change of mass per unit charge, F Am/Aq), such as 

When only one charged species is involved in the redox switching, the latter function has the particular form 

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In fact, ac electrogravimetry is the combination of electrochemical impedance spectroscopy with a fast quartz crystal microbalance. The fluxes of all mobile species are considered, and the usual conditions and treatments of EIS are applied. Beside the electrochemical impedance, an electrogravimetric transfer function, Aw/A ((o), can be derived which contains the dependences of the fluxes of anions, cations and solvent molecules, respectively, on the small potential perturbation. The complex plane plot representations of electrogravimetric transfer functions for PANI are shown in Figs. 3.17 and 3.18. 

Figure 14. Electrogravimetric transfer function of iron in IMH2SO4, potential 0.5 V/SSE. Experimental a and nnmerically simulated b , with a model based on a relaxation of the charge carriers density in the passive film. Same set of parameters as for Figure 13a. From ref [139,140].

AC electrogravimetry consists in the simultaneous measurements of the electrochemical impedance and the mass/potential, or electro-gravimetric, transfer function. Impedance measurements are already well documented in the literature hence, in this text, only the electrogravimetric transfer function measurement will be described. It uses a fast QCM whose general concepts are first given below. 

Only the partial electrogravimetric transfer function allows identification of the ions. From (141), Arrias,/ AE co) was calculated and is presented in Fig. 17d, which corresponds to the elimination of a cation having a mass of 23 g. Here, this partial electrogravimetric function, Amas/AE co), is very small, showing that this is mainly a cation with an apparent molar mass of 23 g which is involved at 0.375 V This result implies that, according to the theory, the contributions of anions and water molecules are always negligible in this potential range. 

For this potential, the plot of the electrochemical capacitance Aq/AE(o)) (Fig. 21b) in the complex plane shows two loops. This demonstrates that two charged species are involved in the charge compensation process. For E = —0.55 V vs. SCE, the plot of Am Aq co) also shows two loops like in the simulation part (see Fig. 12). This demonstrates that the solvent is involved in the redox reaction in addition to anions and cations. Now, the plots of the partial electrogravimetric transfer function will help to identify the loop related to each species. 

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