Nemstian conditions, concentration

The above description of the redox reaction for Fe(CN)64- -/3 is a textbook example because the system nicely obeys Nemstian conditions and many cycles can be repeated without distortion of the voltammogram (we call this a reversible system) electron transfer is rapid and reversible at the electrode surface and complete concentration polarization is achieved under conditions of 1 m KNO3. We know this is a reversible system because ipa/ /pc 1. For a rigorous check on this condition, a plot of ip vs vl,/2 should be linear (where v — scan rate), equation (4.5). 

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 ... 

Surface condition (3.9) indicates that the surface concentrations of species O and R, Cq and cj(, are not only functions of variable, v[> (i O, R), as in the case of Nemstian charge transfer processes, but also time dependent, since their corresponding derivatives at s = 0 are too. 

Equation (5.62) for the current-potential response in CV has been deduced by assuming that the diffusion coefficients of species O and R fulfill the condition Do = >r = D. If this assumption cannot be fulfilled, this equation is not valid since in this case the surface concentrations are not constant and it has not been possible to obtain an explicit solution. Under these conditions, the CV curves corresponding to Nemstian processes have to be obtained by using numerical procedures to solve the diffusion differential equations (finite differences, Crank-Nicholson methods, etc. see Appendix I and ([28])3. 

Under concentration control, the reversible hydrogen electrode exhibits Nemstian reversibility. This provides for a potential shift of 29.75 mV at room temperature, which translates to a shift of 46.8 mV at 200 °C for each decade of change in hydrogen concentration. Under fuel-cell operating conditions with highly dispersed electrocatalysts, it is possible to approach the kinetic rate determined by the dual-site dissociation of the hydrogen molecule, viz. ... 

The review finds it difficult to assess this paper as experimental conditions and primary data are lacking. There can be no doubt that the authors have used concentrations instead of activities in their calculations. The activity of water was set equal to 1 despite the high concentration of solutes and any liquid junction potentials have been neglected. It appears fortuitous that Nemstian slopes were observed. The large concen-... 

We mentioned that selectivity coefficients determined using the Nicolsky equation often vary, depending on relative concentrations and measurement conditions, and the equation does not dpply if the response is non-Nemstian (often the case with secondary ions). The matched potential method is an attempt to deal with this. Bakker and co-workers introduced a new formulism that provides a.clear interpretation of the matched potential method, elegantly deriving an equation based on ion exchange in which the last term in Equation 13.49 becomes where... 

A solution of volume 50 cm contains 2.0 X 10 M Fe and 1.0 X 10 M in 1 M HCl. This solution is examined by voltammetry at a rotating platinum disk electrode of area 0.30 cm. At the rotation rate employed, both Fe and have mass-transfer coefficients, m, of 10 cm/s. (a) Calculate the limiting current for the reduction of Fe under these conditions, (b) A current-potential scan is taken from +1.3 to —0.40 V vs. NHE. Make a labeled, quantitatively correct, sketch of the i-E curve that would be obtained. Assume that no changes in the bulk concentrations of Fe and Sn " occur during this scan and that all electrode reactions are nemstian. 

Let us now consider the prototypical case in which the electrode reaction O ne R exhibits reversible kinetics and the solution contains O, but not R, in the bulk. The solution has been homogenized and the initial potential E is chosen well positive of, so that the concentration profiles are uniform as the SWV scan begins. The experiment is fast enough to confine behavior to semi-infinite linear diffusion at most electrodes, and we assume its applicability here. These circumstances imply that we can invoke Pick s second law for both O and R, the usual initial and semi-infinite conditions, and the flux balance at the electrode surface, exactly as in (5.4.2)-(5.4.5). The final boundary condition needed to solve the problem comes from the potential waveform, which is linked to the concentration profile through the nemstian balance at the electrode. It is convenient to consider the waveform as consisting of a series of half cycles with index m beginning from the first forward pulse, which has m = 1. Then,... 

Stationary values of the potential are measured, the concentrations at the electrode surface and in the bulk being not equal, and stationary diffusion fluxes of electroactive species being available in the system. Since the species at the surface are in equilibrium and the Nemst equation is still valid, we can denote such conditions as Nemstian. 

Thus, there is effectively a gradient in the concentration of neutral species across the cell, and therefore we must include in the total potential difference a Nemstian term which is equal to the potential difference that would exist immediately after the interruption of current flow but before the reestablishment of uniform concentration profiles. The other contribution to the potential difference, that which is due to the flow of current itself, is a term arising from the gradient in conductivity due to the variations in concentration. This of conrse arises from differences in the mobility of the two species. It must be distinguished from the ohmic term present at very short times (high frequencies) due to the initially uniform conductivity of the electrolyte. The concentration polarization is therefore the additional polarization which is present due to concentration gradients caused by the current flow this is compared to the ohmic polarization that would be present if the current flow (and distribution) were the same bnt the concentration gradients were absent Substitution of the condition (144) into the flux equation for cations... 

Very frequently the Ag AgCl electrode is connected with the electrolytic cell by a porous plug. However, such connection brings difficulties, because of the contributions to the measured emf from the liquid junction. It is difficult to control it, because of the continuous nature of the diffusion in the plug [47]. These contributions may be calculated using a proper model however, the assumption on the linear change of concentrations may be not exactly obeyed [48, 49] and under some conditions the emf of the cell deviated from the Nemstian behavior. Because of such influences, sometimes it is not possible to say whether changes of... 

Electrodes modified only with porphyrins or porphyrins associated with other species were explored as potentiometric detectors for different applications. A manganese(lll) porphyrin was utilized as the main component of recovered glassy carbon electrodes used as potentiometric detector of thiocyanate in urine. This sensor was coupled to a FIA system to optimize parameters such as membrane composition, pH, and flow injection parameters. Under the best conditions, a Nemstian response with 58.0 mV per decade of thiocyanate concentration was recorded. The new sensor presented a linear response in the 4.2 x to... 

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