Behavior, Nemstian

The general theoretical treatment of ion-selective membranes assumes a homogeneous membrane phase and thermodynamic equilibrium at the phase boundaries. Obvious deviations from a Nemstian behavior are explained by an additional diffusion potential inside the membrane. However, allowing stationary state conditions in which the thermodynamic equilibrium is not established some hitherto difficult to explain facts (e.g., super-Nemstian slope, dependence of the selectivity of ion-transport upon the availability of co-ions, etc.) can be understood more easily. 

Thus, the peak separation can be used to determine the number of electrons transferred, and as a criterion for a Nemstian behavior. Accordingly, a fast one-electron process exhibits a AEp of about 59 mV Both the cathodic and anodic peak potentials are independent of die scan rate. It is possible to relate the half-peak potential (Ep/2. where the current is half of the peak current) to the polarographic half-wave potential, El/2 ... 

Recall that Nemstian behavior of diffusing species yields a r1 /2 dependence, hi practice, the ideal behavior is approached for relatively slow scan rates, and for an adsorbed layer that shows no intermolecular interactions and fast electron transfers. 

Thin-film ideal or Nemstian behavior is the starting point to explain the voltammetric behavior of polyelectrolyte-modified electrodes. This condition is fulfilled when (i) the timescale of the experiment is slower than the characteristic timescale for charge transport (fjD pp, with Ithe film thickness) in the film, that is all redox within the film are in electrochemical equibbrium at any time, (ii) the activity of redox sites is equal to their concentration and (iii) all couples have the same redox potential. For these conditions, anodic and cathodic current-potential waves are mirror images (zero peak splitting) and current is proportional to the scan rate [121]. Under this regime, there exists an analytical expression for the current-potential curve ... 

For a le couple, the Nemstian behavior predicts a peak full width at half-height (FWHH) of 90.6 mV. Real peak FWHH usually differs from that value. This... 

An internal electrochemical mechanism was proposed long ago for deposition on certain metal substrates, since the rate of deposition sometimes depended on the nature of the substrate [11].) The standard potential of Reaction (5.3) is -l- 0.08 V, considerably more positive than the rednction potential of S to (-0.45 V). Free sulphide, if formed, would be in a very low concentration, since it will be removed continually by precipitation of PbS this will move the S rednction potential strongly positive according to the Nemst equation [Eq. (1.32)]. This positive shift will be even greater than normal because of the non-Nemstian behavior of the S /S couple when [S] > [S ] (at least in alkaline solntion) [12]. In opposition to this, the solubility of S in the (slightly acidic) aqneons solntions is very low, which will move the potential in the opposite direction. Add to this the very small concentration of S in acid solution [Eq. (1.15)], and it becomes clear that it is not trivial to estimate the feasibility of the formation of PbS by free snlphide. The non-Nemstian behavior of the sulphur-rich S /S couple and the lack of knowledge of the solnbility of free S in the deposition solntion are the two factors that complicate what would have been a tractable thermodynamic calcnlation. 

As reported by Chung-Chiun Liu et al. (Science, 207, 188-189, 1980), a palladium-palladium oxide miniature pH electrode has been developed for pTl measurement. The miniature wire-form electrode exhibits a snper-Nemstian behavior and gives a mean pH response of 71.4 mV per [pH] (standard deviation, 5.3 mV). The electrode may find applications in biological, medical, and clinical studies. 

There are many examples of reversible (or nemstian) behavior.1 For example, the redox conversions of a great number of metallic complexes such as Ferrocene, Ru(NH3)g+, or metallic cations like Tl+ (see Eq. (2.1) for the redox reactions in detail2). It is important to highlight that the reversible behavior can also be obtained in many cases by acting on suitable experimental parameters in the particular electrochemical technique used. Under the appropriate experimental conditions, the characterization of these types of processes can be applied to many systems. 

Moreover, if nemstian behavior for the charge transfer reaction is assumed, the following condition holds ... 

In practice, ideal Nemstian behavior often cannot be attained in the presence of interfering ions. The degree of interference caused by other cations is determined by the selectivity of the ion receptor for the primary ion, by the partition coefficients of the different ions over the membrane and aqueous phase, and by the relative activities of the ions in the sample solution. This imposes a second important role to the ion receptor for obtaining ion selectivity in the membrane. By selective complexation of the primary ions i, other cations j are largely excluded from the membrane, with the result that the primary ion becomes the potential determining species. When interfering ions are not completely excluded from the membrane, their contribution to the membrane potential can be treated in terms of an apparent increase of the activity of the primary ion. This is expressed in the semi-empirical Nickolsky-Eisemnan equation (Equation 4) ... 

Mendybaev R. A., Beckett J. R., Stolper E., and Grossman L. (1998) Measurement of oxygen fugacities under reducing conditions non-Nemstian behavior of Y203-doped zirconia oxygen sensors. Geochim. Cosmochim. Acta 62, 3131-3139. 

Figure 9.20. Relationship between pH, surface potential, (or Coulombic term, log P, or Coulombic free energy, AGcoui) and surface charge density, o (or surface protonation), for various ionic strengths of a 1 1 electrolyte for a hydrous ferric oxide surface [P = exp(--Fi/ // 7 )]. (a) Dependence of the Coulombic term and surface potential on solution pH note the near-Nemstian behavior at low ionic strength, (b) xp versus or these curves correspond to the Gouy-Chapman theory, (c) o versus pH these are the curves obtained experimentally. (From Dzombak and Morel, 1990.)...

As the operating temperature increased, the Nemstian behavior of the sensor based on the Al203-Zr02-Y203 eutectic became more predominant. The reproducibility of the measured em/at temperatures higher than 480°C was reasonably good... 

Nemstian behavior, diffusion equations, and boundary conditions were assumed... 

Note that this relation could also have been derived under the conditions Cq= 0 and Cr = 0 without requiring nemstian behavior. It therefore holds also for irreversible systems, provided large enough potential steps are employed. 

When reaction 12.3.42 is reversible, the overall process is denoted as ErCrEj., and the observed voltammetric behavior depends upon both K and A = RT Fv) kf + k y). The zone diagram for this case is shown in Figure 12.3.34 (57, 58). When K is large, species B is always favored and a simple one-electron process is observed (region DO). At the opposite limit, when K is such that conversion of B to C takes place and A is large, nemstian behavior is again found, but with a two-electron wave seen for the overall reaction... 

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