EHD impedance

Deslouis C, Maurin G, Pebere N, Tribollet B (1988) Investigation of tellurium electrocrystal-Uzation by EHD impedance technique. J Appl Electrochem 18 745-750 Yagi I, Nakabayashi S, Uosaki K (1998) In situ optical second harmonic rotational anisotropy measurements of an Au(l 11) electrode during electrochemical deposition of tellurium. J Phys Chem B 102 2677-2683... 

The fact of modulating the square root of Q was naturally supported by the results of the Levich theory in steady-state conditions [8]. With the increasing development of impedance techniques, aided by a sophisticated instrumentation [2], the authors of the present work promoted the use of impedance concept for this type of perturbation and introduced the so-called electrohydrodynamic (EHD) impedance [9, 10]. A parallel approach has been also investigated by use of velocity steps in both theoretical and experimental studies [5, 11, 12]. More recently, Schwartz et al. considered the case of hydrodynamic modulations of large amplitude for increasing the sensitivity of the current response and also for studying additional terms arisen with non linearities [13-15],... 

It is, of course, impossible to provide an exhaustive catalog containing the EHD impedance expressions with all possible mechanisms. We will, only, in the next section illustrate the general procedure to follow, by some examples. 

The EHD impedance appears clearly as the product of three transfer fonctions hydrodynamical ZHD, mass transport Zc and kinetic ZD/Zac [1 + ia>CD(/ t+ZD)]. 

It is worth noting that even in a situation where the interface overpotential U is zero, the EHD impedance IF/Q contains the relaxation effect of adsorbed species X. 

Uniform accessibility and reactivity of the electrode interface are the main hypotheses for developing the EHD impedance theory. However, in many cases a real interface deviates from this ideal picture due for example either to incomplete monolayer adsorption leading to the concept of partial blocking (2D adsorption) or to the formation of layers of finite thickness (3 D phenomena). 

Before presenting some applications of practical interest, the theoretical EHD impedance for partially blocked electrodes and for electrodes coated by a porous layer will be analyzed. 

In some applications where adsorption is involved, the blocking ratio V can depend on the overpotential. The EHD impedance technique under potentiostatic conditions seems therefore the most appropriate technique. 

The electrode arrangement and dimensions are displayed in Fig. 5-4. The two rotating electric contacts (disk and microelectrode) are ensured by two mercury contactors [58], allowing the EHD impedance to be measured under satisfactory signal-to-noise conditions. The system Fe(CN)g /Fe(CN)ft in the reduction direction was used. 

The general aspect of these EHD impedance diagrams reproduces the theoretical variations depicted in Fig. 5-3. By applying the p /pX criterion (Eq. 5-5), one finds a value of the microelectrode diameter which falls within the range of 100-150 pm. This gives a reasonable estimate of the actual diameter value of 105 pm. 

Fig. 5-5. Experimental EHD impedance in Bode coordinates for the microelectrode shown in Fig. 5-4. ( ) Isolated microelectrode, (+) controlled microelectrode, (o) disk electrode.

The EHD impedances corresponding to a constant concentration (c, (0) = 0) were simulated and the results were compared to those valid for a bare electrode. 

Fig. 5-7. From Eq. (5-17), EHD impedance versus the dimensionless frequency p for different rotation speeds (------10.47rd-s 1,-----------65.4rd-s l,. 262rd-s ).

It follows from the Section 3-1 that the potentiostatic EHD impedance I/Q is depending only on pScl/3 with an additional Schmidt number correction. Even, in the range Sc 1000 this correction is necessary because the error on Sc is approximately three times that on Sc1/3 directly measured. 

Fig. 6-3. Magnitude (left scale) and phase (right scale) of EHD impedance (at 400 rpm and 0.0 V/SCE) vs. log frequency. The dots are the measured values, and the curve is the best theoretical fit of Eq. (3-16). From [62],...

Fig. 6-4. Reduced amplitude A/A(0) and phase shift 6 of the EHD impedance I/Q as functions of...

This method, first proposed by Smyrl [65] to determine the Schmidt number from ac impedance measurements, was furtherly extended by Tribollet et al. [66] to the EHD impedance. By taking a Taylor expansion of W to the first order, they showed d (Re (IV))... 

Very early, Miller and Bruckenstein [6] had felt that for an electrochemical system under mixed kinetic control, HMRDE was able to derive information about the kinetic parameters and give more valuable interpretation than by conventional RDE technique. At that time, they developed a theoretical analysis, restricted to quasi steady state, and which is now presented in a more quantitative way and over a large frequency domain with the formalism of EHD impedance (see Chapter 4). 

However, their simplified analysis offers the interest of a fast criterion about the kinetics control. They considered a Butler-Volmer equation such as Eq. (4-5) where Q and the limiting currents explicitly appear, and expressed the derivative of this steady current with respect to Q (which represents, in fact, the zero frequency limit of the EHD impedance). 

One of the earlier application of the EHD impedance method was aimed at finding the mechanisms of corrosion and in particular to evaluate the role of developing layers of insoluble corrosion products which are known to be formed at neutral pH. 

Theory of EHD Impedances for a Mediated Reaction on a Redox Polymer Modified Electrode [85]... 

ZEHd, p is the EHD impedance of the substrate under potentiostatic conditions, i.e. when E2 = 0, and measured without polymer layer. 

The EHD impedance, defined in Eq. (6-29), takes a very simple form when the steady-state current /s is diffusion-controlled, i.e. at the diffusion plateau, and is generally analyzed under those conditions when possible. 

On both Pt and polyaniline-coated electrodes, diffusion-limited currents are observed at <250 mV for Fe(CN)500 mV for Fe(CN)g- oxidation. Potentiostatic EHD impedance was measured on both diffusion plateaux (50 mV and 550 mV), using Pt electrodes coated with polyaniline films of various thickness 50 and 130nm. As an example, the results obtained on the cathodic plateau are shown in Fig. 6-13 those observed on the anodic plateau were very similar [93]. 

Table 6-1. Potentiostatic EHD impedance experiments on diffusion plateaux. From [93].

EHD impedances have been measured on the diffusion plateau at 0.7 V/SCE. The mass transport time constant of the redox couple in solution, which is one of the terms implied in the impedance expression is independent of the interface nature. The Schmidt number Sc was first determined on a bare electrode, and this value of 1540 is further used as a fixed parameter in the analysis of the diagrams obtained on pECBZ films at different Q (Fig. 6-14). The different diagrams are analyzed in the light of the theoretical model predicted by expression (6-34). 

Fig. 6-14. Potentiostatic EHD impedance plots, in Bode representation (reduced amplitude A(pSc /3)/A(0) and phase shift, versus dimensionless frequency pSc / ) for the oxidation of hydroquinone on a 360 nm thick poly(TV-ethylcarbazole) film at E - 0.7 V (diffusion plateau).

Table 6-2. Potentiostatic EHD impedance results at E = 0.7 V (diffusion plateau). Sc was fixed at 1540. From [94],...

The experimental set-up is shown in Fig. 7-1 an electrochemical interface with low level noise and a transfer function analyzer (TFA) were used for measurements of the EHD impedance. A matched two-channels 24 db/octave low pass filter (F) was used to remove HF noise and the ripple due to electric network supply, this analog filtering allows the TFA to operate with an increased sensitivity. These instruments were controlled by a computer, which recorded the data. 

In EHD impedance studies, the relaxation times for the different transport processes are obtained by variation of the modulation frequency of the flow. The utility of the technique relies on being able to separate out individual transport relaxation times. This is possible because, with EHD, each relaxation time will have a different functional dependence upon the perturbation. The theory and methodology were first developed for sinusoidal modulation of the flow velocity in a tube [20, 22]. The results... 

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