Half-Wave Potentials measurement

It is certain that, in the first reduction step in aprotic solvents, an electron is accepted by the LUMO of the organic compound. However, it was fortunate that this conclusion was deduced from studies that either ignored the influence of solvation energies or used the results in different solvents. Recently, Shalev and Evans [55] estimated the values of AG V(Q/Q ) for 22 substituted nitrobenzenes and nine quinones from the half-wave potentials measured by cyclic voltammetry. For quinones and some substituted nitrobenzenes, the values of AG V(Q/Q ) in a given solvent were almost independent of the EA values. Similar results had been observed for other aromatic hydrocarbons in AN (Section 8.3.2) [56]. If AG V(Q/ Q ) does not vary with EA, there should be a linear relation of unit slope between El/2 and EA. Shalev and Evans [55], moreover, obtained a near-linear relation between AG V(Q/Q ) and EA for some other substituted nitrobenzenes. Here again, the Ey2-EA relation should be linear, although the slope deviates from unity.8)... 

Figure 11.15 (from Stone, 1987) illustrates that the rate of oxidation of various substituted phenols by Mn02 can be correlated with the half-wave potentials, of these phenols. The half-wave potentials, measure the tendency of the anode to oxidize the phenols. The half-wave potential corresponds in first approximation to the redox potential of the phenol and its one-electron oxidation product. Figure 11.15 implies that the thermodynamic tendency of an electrode to oxidize a certain phenol relates to the kinetic tendency of Mn02 to oxidize this phenol. 

The half-wave potentials measured by this method include the amalgamation potential of the metal-mercury reaction. The potential for the overall process for Fm, i.e. 

From the preceding it follows that the half-wave potential measured in DCP will only in rare cases approximately equal the standard potential. The requirements for this are (i) no side reactions (equilibria) of the reduced or oxidized form (esp. no protonation reactions), (ii) no amalgamation, or a dissolution in mercury with negligible Gibbs free energy of amalgamation, and (iii) no strong deviation of the activity coefficient ratio from unity. 

The polarographic half-wave potentials of dissolved cations shift in the more negative direction with an increase in the stabilities of the complexes, including solvate complexes, whereas with anions stronger solvation results in a shift of the half-wave potential in the more positive direction [Ko 57]. However, the comparison of half-wave potentials measured in different solvents is accompanied by extreme difficulties because of the large solvent dependence of the potential of the reference electrode [Sc 55]. 

The effect of the potential applied to the electrode on velocity of fluid motion was investigated by using a solution of 0.1 mM prepared by chemical oxidation of a solution of II with ca. 1.5 equivalents of Fe. The onset of the motion of fluid occurred between 0.2 and 0.1 V, which spans the half-wave potential measured for oxidation of II" to (0.17 V vs. SCE). The velocity of fluid motion increased with increasingly negative (reducing) potentials up to ca. — 0.2 V where the velocity reached a plateau. Above — 0.2 V, mass transport of the surfactant to the working electrode plausibly limits the rate of generation of surfactant and thereby limits the velocity of fluid motion. 

The basic condition to be fulfilled by a reference electrode for half-wave potential measurements is the constancy of its potential over the whole course of measurement. The reproducibility of the potential of the reference electrode is of secondary importance. 

The materials tested, and the half-wave potentials measured, are given in Table 4. If the final polarographic analysis of the pyrolysis products and the corresponding nitro-compounds is carried out in three different buffered solutions, this interesting method would gain additional selectivity. 

The examination of the voltanunetric response at carbon fiber UMEs as a function of miCTOvial volume was undertaken by Clark et al. (89). The experimental volume was varied from about 4 nL to as little as 1 pL. For a 5 pm diameter electrode, the volammograms of ferrocenecarboxylic acid did not vary as a function of sample volume. The shape of the voltammograms was sigmoidal which is expected for disk microelectrodes scanned at slow rates (1-1000 mV/sec) under steady-state conditions (102). The half wave potential measured in the microvials was identical to that of ferrocenecarboxylic acid in bulk solution and the current value also matched the expected value. In addition, Clark et al. performed voltammetry with a 1 pm diameter flame etched carbon fiber electrode in a 1 pL vial however, no deviation from bulk solution behavior was apparent. 

The systematic application of modern electrochemical methodology proved in a first instance to be a very useful tool to gather thermodynamic information, as Gibbs energies of transfer from half-wave potential measurements. Then, in 1981, Samec et al used convolution linear sweep voltammetry to address experimentally the fundamental aspects of ion transfer reactions. The main advantage of this technique when studying charge trans-... 

Inspection of the data in Table 7.1 reveals significant differences between the reversible half wave potentials measured for different fullerenes. They cannot be accounted for by solvent and/or background electrolyte effects (see below) and they reflect the unique electronic properties of each fullerene. The first simple explanation of the different electrochemistry of C o and C70 in toluene/dichloromethane mixtures was given by Cox et al. [28]. They found that the first and second reduction potentials were almost identieal for both fullerenes, whereas the third one was around 80 mV more negative for C6o- The difference in the third reduction potential was explained in terms of a simple charge separation, delocalization model. The larger C70 would more easily accommodate three additional electrons than the smaller Ceo- Almost identical first and second reduction potentials for C60 and C70 have... 

This experiment describes the determination of the stability (cumulative formation) constant for the formation of Pb(OH)3 by measuring the shift in the half-wave potential for the reduction of Pb + as a function of the concentration of OH . The influence of ionic strength is also considered, and results are extrapolated to zero ionic strength to determine the thermodynamic formation constant. 

Determine the half-wave potential from the current-voltage curve as described in Section 16.6 the value in 1M potassium chloride should be about — 0.60 vs S.C.E. Measure the maximum height of the diffusion wave after correction has been made for the residual current this is the diffusion current Id, and is proportional to the total concentration of cadmium ions in the solution. 

The half-wave potentials of these steps are approximately — 0.1 and — 0.9 V (versus the saturated calomel electrode). Hie exact stoichiometry of these steps is dependent on the medium. Hie large background current accruing from this stepwise oxygen reduction interferes with the measurement of many reducible analytes. In addition, the products of the oxygen reduction may affect the electrochemical process under investigation. 

Capacitance and interfacial tension measurements were used to study the interface between Hg and mixtures of acetone + nitromethane.330 The potential was measured against an SCEin H20 and corrected for the liquid junction potential by measuring the half-wave potential of the ferrocene-... 

The electron transfer series W(R2fi ic)4° W(R2tfic)4 -> W(R2rfic)4 was detected by voltametric measurements (37), the half wave potentials are 0.24 and 0.36 V lower than the corresponding values of the molybdenum compounds. Both transfers obey the Taft relation with a low value of p, which points to a rather small contribution of the ligand orbitals into the redox orbitals. 

The electron transfer Au(R2voltametric measurements 163). The half-wave potentials of the quasi-reversible process depends on the substituent R according to the Taft relation, as was described for Mo, W and Mn 37). The value of p decreases in the series Au > Mn > Mo = W, which indicates that in this sequence the mixing of ligand orbitals into the redox orbital decreases. The dominant ligand character of the unpaired electron MO in Au(R2dtc)2 relative to those in copper and silver compounds is found from Extended Hiickel MO calculations, as will be discussed later on. 

Figure 4 illustrates the dependence of on Aq for the case when r = 1 at several different values of [Fig. 4(a)] and when = 0.5 and at several different values of r [Fig. 4(b)]. From Fig. 4(a), one can see that takes a maximum around y = 0, i.e., Aq The volume ratio affects strongly the value of as shown in Fig. 4(b), which is ascribed to the dependence of the equilibrium concentration on r through Eq. (25). This simple example illustrates the necessity of taking into account the variation of the phase-boundary potential, and hence the adsorption of i, when one tries to measure the adsorption properties of a certain ionic species in the oil-water two-phase systems by changing the concentration of i in one of the phases. A similar situation exists also in voltammetric measurements of the transfer of surface-active ions across the polarized O/W interface. In this case, the time-varying thickness of the diffusion layers plays the role of the fixed volume in the above partition example. The adsorption of surface-active ions is hence expected to reach a maximum around the half-wave potential of the ion transfer. 

FIG. 19 Dependence of the half-wave potentials for Fc (curve 1) and ZnPor (curve 2) oxidation in benzene on CIO7 concentration in the aqueous phase. In these measurements, half-wave potentials were extracted from reversible steady-state voltammograms obtained at a 25 pm diameter Pt UME. The benzene phase contained 0.25 M tetra-w-hexylammonium perchlorate (THAP) and either 5 mM Fc or 1 mM ZnPor. All potentials were measured with respect to an Ag/AgCl reference electrode in the aqueous phase. (Reprinted from Ref. 48. Copyright 1996 American Chemical Society.)... 

The ET reaction between aqueous Fe(CN)g and the neutral species, TCNQ, has been investigated extensively with SECM, in parallel with microelectrochemical measurements at expanding droplets (MEMED) [84], which are discussed in Chapter 13. In the SECM studies, a Pt UME in the aqueous phase generated Fe(CN)g by reduction of Fe(CN)g. TCNQ was selected as the organic electron acceptor, because the half-wave potential for TCNQ ion transfer from DCE to water is 0.2 V more positive than that for ET from Fe(CN)g to TCNQ [85]. This meant that the measured kinetics were not compromised by TCNQ transfer from DCE to the aqueous phase within the potential window of these experiments. 

The theory has been verified by voltammetric measurements using different hole diameters and by electrochemical simulations [13,15]. The plot of the half-wave potential versus log[(4d/7rr)-I-1] yielded a straight line with a slope of 60 mV (Fig. 3), but the experimental points deviated from the theory for small radii. Equations (3) to (5) show that the half-wave potential depends on the hole radius, the film thickness, the interface position within the hole, and the diffusion coefficient values. When d is rather large or the diffusion coefficient in the organic phase is very low, steady-state diffusion in the organic phase cannot be achieved because of the linear diffusion field within the microcylinder [Fig. 2(c)]. Although no analytical solution has been reported for non-steady-state IT across the microhole, the simulations reported in Ref. 13 showed that the diffusion field is asymmetrical, and concentration profiles are similar to those in micropipettes (see... 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

Some divalent transition and post-transition metal ions, Co", Nr, Cu", Zm, and Cd, have been studied in the same way, but these systems need a pH-control in order to avoid any precipitation. Although measurements have not been completed yet, a pair of waves has been observed only in the Cu system that is somewhat irreversible (—100 to —50 mV of the half-wave potential). In the other systems, any waves except ambiguous broad ones could not be obtained. While analyzing some waves, Cu seems to be facili-... 

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