Double-layer effects

For a metal/solution interface, the pcz is as informative as the electron work function is for a metal/vacuum interface.6,15 It is a property of the nature of the metal and of its surface structure (see later discussion) it is sensitive to the presence of impurities. Its value can be used to check the cleanliness and perfection of a metal surface. Its position determines the potential ranges of ionic and nonionic adsorption, and the region where double-layer effects are possible in electrode kinetics.8,10,16... 

Bjerrum and coworkers have assigned the three rate maxima shown in Figs. 10.7 and 10.8 to (starting from the negative potential) (a) destruction of vanadium polymeric chains (b) electric double layer effect at gold working electrode (c) stabilization of V (V) vs V (IV). These explanations are very plausible. 

On the basis of experimental findings Heinze et al. propose the formation of a particularly stable, previously unknown tertiary structure between the charged chain segments and the solvated counterions in the polymer during galvanostatic or potentiostatic polymerization. During the discharging scan this structure is irreversibly altered. The absence of typical capacitive currents for the oxidized polymer film leads them to surmise that the postulated double layer effects are considerably smaller than previously assumed and that the broad current plateau is caused at least in part by faradaic redox processes. 

ELECTRIC DOUBLE-LAYER EFFECTS ON THE ELEMENTARY ACT OF ELECTRON TRANSFER... 

The effect of the phospholipids on the rate of ion transfer has been controversial over the last years. While the early studies found a retardation effect [6-8], more recent ones reported that the rate of ion transfer is either not retarded [9,10] or even enhanced due to the presence of the monolayer [11 14]. Furthermore, the theoretical efforts to explain this effect were unsatisfactory. The retardation observed in the early studies was explained in terms of the blocking of the interfacial area by the phospholipids, and therefore was related to the size of the transferring ion and the state of the monolayer [8,15]. The enhancement observed in the following years was attributed to electrical double layer effects, but a Frumkin-type correction to the Butler Volmer (BV) equation was found unsuitable to explain the observations [11,16]. Recently, Manzanares et al. showed that the enhancement can be described by an electrical double layer correction provided that an accurate picture of the electrical double layer structure is used [17]. This theoretical approach will be the subject of Section III.C. 

Of interest here is the question relating to the value for the slope coefficient, k, from equation (1), when surfactant structures incorporating both ionic (say sulphonate) and nonionic moieties are included together. The Ghanges in electric double layer effects imparted from salt addition might dominate the packing constraints and therefore the phase inversion process, or perhaps oxyethylene dehydration effects from the presence of toluene could also play a role. 

In the expressions of the driving force above, E is, strictly speaking, the potential difference between the electrode and the reaction site. It is usually not exactly the same as the potential difference between the electrode and the solution as illustrated by the potential profile across the double layer represented in Figure 1.6. In other words, E = M — (j)rs rather than E = (f>M, thus resulting in a double-layer effect on the electron transfer kinetics10 that ought to be taken into account. The reaction site is... 

Similarly, double-layer effects on the MHL law may be expressed through the same work terms ... 

Maximal rate constant values (uncorrected from double-layer effects) are on the order of 3 cm s 1. The preceding equation indicates that scan rates of not less than 50,000 V/s are required to reach such values, and are indeed accessible thanks to the use of small electrodes, as discussed in Section 1.3. 

In all preceding cases, the double-layer effect on electron transfer kinetics has not been taken into account explicitly. Doing so requires that we replace... 

FIGURE 1.22. Solvent reorganization energies derived from the standard rate constants of the electrochemical reduction of aromatic hydrocarbons in DMF (with n-Bu4N+ as the cation of the supporting electrolyte) uncorrected from double-layer effects. Variation with the equivalent hard-sphere radii. Dotted line, Hush s prediction. Adapted from Figure 4 in reference 13, with permission from the American Chemical Society. 

Double-layer charging current and ohmic drop are likely to interfere at high scan rates. The procedures for extracting the Faradaic component of the current and correcting the potential axis from the effect of ohmic drop described earlier (see Sections 1.3.2 and 1.4.3) should then be applied. The same is true for the double-layer effect on the electron transfer kinetics (Section 1.4.2). 

Why do double-layer effects cause a longer time delay in the current trace than in the potential trace ... 

The analytical sensitivity of classical polarographic or voltammetric methods is usually quite good at about 5 x 10 mol dm . At the lowest concentrations of analyte, however, the currents caused by double-layer effects or other non-faradaic sources causes the accuracy to be unacceptably low. Pulse methods were first developed in the 1950s to improve the sensitivity of the polarographic measurements made by pharmaceutical companies. At present, two pulse methods dominate the analytical field, i.e. normal pulse and differential pulse . Square-wave methods are also growing steadily in popularity. 

Specifically, Figure 16 shows that the current density in a cell with dry cathode gas feed drops nearly instantaneously once the cell voltage is relaxed from 0.6 to 0.7 V due to the fact that the electrochemical double-layer effect has a negligibly small time constant. Further, there exists undershoot in the current density as the oxygen concentration inside the cathode catalyst layer still remains low due to the larger consumption rate under 0.6 V. As the... 

Nernst Diffusion-Layer Model This model assumes that the concentration of Ox has a bulk concentration up to a distance 8 from the electrode surface and then falls off linearly to Ox x = 0) at the electrode (neglecting the double-layer effect). The Nernst diffusion-layer model is illustrated in Figure 6.11. 

The electrochemical rate constants of the Zn(II)/Zn(Hg) system obtained in propylene carbonate (PC), acetonitrile (AN), and HMPA with different concentrations of tetraethylammonium perchlorate (TEAP) decreased with increasing concentration of the electrolyte and were always lower in AN than in PC solution [72]. The mechanism of Zn(II) electroreduction was proposed in PC and AN the electroreduction process proceeds in one step. In HMPA, the Zn(II) electroreduction on the mercury electrode is very slow and proceeds according to the mechanism in which a chemical reaction was followed by charge transfer in two steps (CEE). The linear dependence of logarithm of heterogeneous standard rate constant on solvent DN was observed only for values corrected for the double-layer effect. 

The catalytic effect of N,N -dia -kylthioureas on Zn(II) electroreduction was also observed by Dalmata [81], In this case, the rate constant of the first electron transfer increased with increasing concentration of M,Al -dialkylthioureas, whereas the rate constant of the second electron transfer was largely dependent on the double-layer effect. 

In mixed (0.8 - a ) M NaCl04 + x M NaF supporting electrolyte the electroreduction of Cd(II) was also studied by Saakes etal. [25]. The kinetic parameters were analyzed using CEE mechanism. The obtained chemical rate constants at both steps, kg 1 and kg 2, decreased with increasing NaF concentration. The data were corrected for nonspecific double-layer effect (Frumldn correction). The interpretation of CEE mechanism with parallel pathways connected with coexisting cadmium complexes was presented. 

Fig. 4 Dependence of the logarithm of standard rate constant corrected for the double-layer effect of the Cd(ll)/Cd(Hg) system on donor number of the solvents [66].

The double-layer effect in the electrode kinetics of the amalgam formation reactions was discussed [67]. The dependences on the potential of two reduction (EE) mechanisms of divalent cations at mercury electrode, and ion transfer-adsorption (lA) were compared. It was suggested that a study of temperature dependence of the course of these reactions would be helpful to differentiate these two mechanisms. 

Under specific conditions, the potential of zero charge does not appear to be constant during electrochemical experiment, which makes the double-layer effect more complex. For example, the shift of the potential of zero charge during electroreduction of S20g , combined with the Frumldn-type double-layer effect, has been proposed [26] as an explanation for the oscillatory reduction of peroxodisulfate on Au(llO) in diluted solutions of NaF. 

It is known that double-layer effects are the most pronounced in the reaction of multivalent ions in a dilute solution. According to the calculation of Grahame, d°HP A3 potential region far from the pzc. Evaluate the cathodic and anodic Tafel slope values for the reaction... 

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