Electrogravimetric transfer functions

Electrogravimetric transfer functions Am/A (o>) and AmlAq associated with the electrochemical impedance, A /A/(a>) were determined for the anodic dissolution of Fe in sulfuric acid. This gave the unique possibility of discriminating between the change in mass due to metal dissolution and the relaxation of the film thickness on the basis of their individual frequency responses [35, 36]. 

Figure 14.8 Experimental device for the measurement of the electrogravimetric transfer function.

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. 

The two loops that appear in both partial electrogravimetric transfer functions indicate the simultaneous transport of anions, cations and solvent molecules. A conclusion has been drawn that when anions are inserted, cations and solvent molecules are ejqrelled i.e., the positive charges created ditring the oxidation of the polymer ate compensated for in a rather complex way. (See also Sect. 6.2.)... 

Fig. 3.17 Electrogravimetric transfer function for a PANI electrode at 0.2 V vs. SCE. Electrolyte 1 moldm HCIO4. (From [243], reproduced with the permission of Elsevier Ltd.)...

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].

S. Bourkane, C. Gabrielli, and M. Keddam, Investigation of gold oxidation in sulphuric medium. 11. Electrogravimetric transfer function technique, Electrochim. Acta 38 1827 (1993). 

For electroactive thin films, the electrochemical impedance technique alone is not able to discriminate among the various models which have been proposed in the literature. So the measurement of an electrogravimetric transfer function, Am/AE, by using a fast QCM, in parallel to measurement of the impedance has been proposed to test these various models and to obtain a complete description of the ionic and solvent exchanges between the film and the solution. So far, two groups, one in Korea and the other one in France, have used this technique. 

Kwak et al. have considered that only two types of species may be involved in the charge compensation process cations and anions, which can be solvated or not. They considered the electrochemical capacitance, Aq/AE, and the electrogravimetric transfer function (which they called electrogravimetric capacitance ), which can be separated into two parts ... 

Then, when only one ion is involved in the ion transport, the electrogravimetric transfer function is... 

Figure 7. Electrogravimetric transfer function (AM/AE) plots for Zd in the case in which (a) ion transport is cation-specific, C ) 0, Cd = 0, (b) ion transport is anion-specific, = 0, C ) 0, (c) and (d) cation transport is faster than anion transport, (e) and (f) anion transport is faster than cation transport. From Yang et al. ...

In the same way, if the cation contribution is eliminated in the mass change, Aw/A 3, by using (130) and (108), the second partial electrogravimetric transfer function, Arties/AEs, which takes into account only the mass change of anions and solvent, is... 

From the plot of the cation-solvent, Ames/AEs, and anion-solvent, Amas/AEs, partial electrogravimetric transfer functions, a diagnostic criterion can be proposed. 

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. 

Figure 19a shows the variation of the low-frequency limit of the electrogravimetric transfer function Aw/A (apparent mass of the inserted cation allows one to determine the percentage of potassium and hydronium ions and hence the relative participation of these ions in the redox process. As a result of integration of the curves given in Fig. 19a, Fig. 19b shows the change of the concentrations of K+ and HsO" " in the Prussian blue film when the... 

These results clearly show that the charge compensation process occurring during the oxidation or reduction of the PPY film involves insertion and expulsion of cations and anions. However, it is difficult to separate the various processes. The coupling of the measurement of the electrochemical impedance and the electrogravimetric transfer function will enlighten these points. 

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. 

Finally, the plot of the partial electrogravimetric transfer function, Anias/ AE(oS), obtained by eliminating the cation contribution, is related to the anion and solvent alone (see Fig. 13). By taking nic as the atomic mass of Na+ -I- H20, where n is the number of... 

This identification is obtained by using the electrogravimetric transfer function. Am/AE co) (Fig. 25c). The high-frequency loop in the third quadrant is related to the potassium ion. Indeed, by keeping the constants Ki and G, calculated before, we can estimate the molecular mass of the ionic species and for the cation a mass of 39gmoP was found most of the time the cation was attached to some water molecules. To our knowledge, this technique is the only way to estimate the number n of water molecules attached to the... 

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