Nernstian behavior

The explicit mathematical treatment for such stationary-state situations at certain ion-selective membranes was performed by Iljuschenko and Mirkin 106). As the publication is in Russian and in a not widely distributed journal, their work will be cited in the appendix. The authors obtain an equation (s. (34) on page 28) similar to the one developed by Eisenman et al. 6) for glass membranes using the three-segment potential approach. However, the mobilities used in the stationary-state treatment are those which describe the ion migration in an electric field through a diffusion layer at the phase boundary. A diffusion process through the entire membrane with constant ion mobilities does not have to be assumed. The non-Nernstian behavior of extremely thin layers (i.e., ISFET) can therefore also be described, as well as the role of an electron transfer at solid-state membranes. 

NADH, 121, 122, 180 Nafion coating, 118, 123, 124, 126 Nanometer electrodes, 116, 128 Nernst equation, 3, 15, 80 Nernstian behavior, 143 Nernst Planck equation, 5 Neuronal sensors, 188 Neurotransmitters, 40, 116, 124 Neutral carrier electrodes, 154 Nickel, 123... 

The simulation of other electrochemical experiments will require different electrode boundary conditions. The simulation of potential-step Nernstian behavior will require that the ratio of reactant and product concentrations at the electrode surface be a fixed function of electrode potential. In the simulation of voltammetry, this ratio is no longer fixed it is a function of time. Chrono-potentiometry may be simulated by fixing the slope of the concentration profile in the vicinity of the electrode surface according to the magnitude of the constant current passed. These other techniques are discussed later a model for diffusion-limited semi-infinite linear diffusion is developed immediately. 

Assuming Nernstian behavior for both processes of the EE reaction scheme, symmetrically shaped waves arise that are relatively easy to interpret. If E2° is well negative of E° (E2° E° ), two separate waves are observed, in which ipc j is measured from extrapolation of the current from i (see Fig. 23.8). Each individual wave obeys the diagnostics listed in Section IV. A for the simple E mechanism. 

At the same time, the response deviates more from the theoretical value the fewer proton-binding sites are present. On the other hand, both the adsorption effects and the sub-Nernstian behavior vanish if the thickness of the hydrated layer is allowed to increase up to 800 nm (Fig. 6.24). It is seen from this model that as the thickness of the hydrated layer exceeds the thickness of the space the adsorption effects and the sub-Nernstian behavior disappear. 

Calix[4]arene-crown-6 derivatives MC7, MC8, and MC10 in the 1,3-alternate conformation, incorporated in polyvinylchloride) membranes of CHEMFETs, exhibit high Cs+ selectivity and Nernstian behavior. The selectivity Cs+ over Na+, given by logX ° Na = 3.3, is slightly better than that observed for bis(18-crown-6) derivatives, logX ° Na = 3.0. The CHEMFETs display a sub-Nernstian response in the presence of K+ and NH4+ behavior, which can be explained, respectively, by the small difference between the stability constants of the Cs+ and K+ complexes and by the high ratio of NH4+ in favor of the membrane phase.76... 

Thus, the peak separation can be used to determine the number of electrons transferred, and as a criterion for a Nernstian behavior. Accordingly, a fast one-electron process exhibits a AEp of about 59 mV. Both the cathodic and... 

Recall that a Nernstian behavior of diffusing species yields a vm dependence. In 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. 

In the absence of suitable scavengers, recombination occurs within a few nanoseconds (19). Valence band holes (h+(vb)) have been shown to be powerful oxidants (20-231 whereas conduction band electrons (e (cb)) can act as reductants (24,251. The redox potentials of both, e and h+, are determined by the relative position of the conduction and valence band, respectively. Bandgap positions are material constants which have been determined for a wide variety of semiconductors (26). Most materials show "Nernstian" behavior which results in a shift of the surface potential by 59 mV in the negative direction with a pH increase of ApH = 1. Consequently electrons are better reductants in alkaline solutions while holes have a higher oxidation potential in the acid pH-range (26). Thus, with the right choice of semiconductor and pH, the redox potential of the e (cb) can be varied from +0.5 to -1.5 V (vs. NHE) and that of the h+(vb) from +1.0 to more than +3.5 V. This sufficiently covers the full range of redox chemistry of the H20/02 system (271. 

In fact, at equilibrium, not only are electrons transferred across the interface, but ions also cross the <3 1% interface. Taking into account this additional transfer yields non-Nernstian behavior. In the simple case of polarons being the predominant species, one obtains [8]. 

A reference electrode which can directly be dipped in the organic phase is not available, except the AgPh4B/Ag electrode [44]. It is customary to use a nonpolarized liquid-liquid interface, i.e., a reference ITIES. The potential drop across this interface is primarily determined by an ionic species distributed commonly in both aqueous and organic phases. There are two points to be taken into account in using this reference ITIES the deviation from nernstian behavior and limited reversibility. 

If the various eonstants are known, the potential ean be determined. Brown [134] has made this determination and the results are shown for two iron coneentrations in Figure 38. The redox potential between pH 4 and 6 is 117 mV (NHE) and is sueh that a bleach made with this oxidizing agent can immediately follow a developer with little risk of the developer being oxidized and subsequently forming unwanted dye. For example, CD3 has a half-wave potential of 0.399 V (NHE) at pH 5. Assuming Nernstian behavior, it can be shown that the proportion of developer oxidized in the bleaeh is governed by Eq. (96). 

The usefulness of a number of metal/metal-oxide (e.g. Ir/IrC>2, Zr/ZrC>2, W/WO2, etc.) electrodes and the glass electrode has been tested over a wide range of temperatures. However, the existence of the Nernstian behavior has not been well demonstrated yet. The glass electrode can probably be employed at temperatures up to about 200 °C but was found to be impractical owing to an inconvenient design for high-temperature subcritical and supercritical aqueous solutions. 

In practice, a glass electrode is almost always used in place of the Pt(H2) electrode. A glass electrode has a deviation from the H+ (aq) ion response function (non-Nernstian behavior) and, therefore, should be calibrated using a set of the standard (buffer) solutions. 

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

Cyt c adsorbed at a DNA-modified metal electrode showed voltage-dependent orientation resulting in non-Nernstian behavior at high electrode potentials. 

Real systems deviate frequently from ideal behavior due to large uncompensated electrolyte resistance, slow kinetics of electron transfer, and site-to-site interactions (Ilangovan and Chandrasekara Pillai, 1997). Such deviations from Nernstian behavior can be expressed by an interaction term, r, which can be estimated from the variation of peak potential with potential scan rate ... 

In the single-phase region, the OCV decreases with decreasing value of X in Na2S c- The OCV-composition plot is much too steep to reflect the Nernstian behavior of the simple... 

---