Nernstian relationships

Since neutral ionophores essentially render the membrane differentially permeable to a positive charge (the charge carried by M ) and since electrical potentials are actively maintained across the membranes of virtually all cells, two factors determine the thermodynamic gradient governing net transport of M by neutral ionophores (1) the magnitude of the membrane potential, i.e. AEmAB, and (2) the concentration gradient of the permeable ion M across the membrane. In terms of experimentally measurable parameters, a Nernstian relationship is established ... 

From Eq. (37), remembering that the initial value of Fxj is zero, we can write the Nernstian relationship ... 

In general, the bio-sensors of the above sandwich constmction type exhibit a nearly Nernstian relationship between the substrate concentration and the EMF. The response times of constructions of this sort are influenced by many different factors [182] The enzyme reaction itself procedes at a finite rate which depends upon the initial substrate concentration and the Michaelis constant. The product of this reaction must then diffuse to and from the surface of the indicator electrode as its concentration changes. 

Useful experimental parameters in cyclic voltammetry are (i) the value of the separation of the potentials at which the anodic and cathodic peak currents occur, A = Pia — PiC, and (ii) the half wave potential, 1/2, the potential mid-way between the peak potentials. A value of AE of c. 0.057 V at 25°C is diagnostic of a Nernstian response, such as that shown in Figure 2.87. More generally, if n electrons are transferred from R, then the separation will be 0.057/n V. It should be noted that the expected value for AE of 0.57/nV has no relationship to the usual Nernstian slope of RT/nF = 0.059/n V at 25UC. 

This linear approximation is certainly valid about the pHZpC, and valid over a much wider domain if the surface potential-pH relationship is nearly Nernstian, that is, if the value of a defined in Equation 25 remains small over a wide domain. 

Comparison of Methods. The use of Method I for interpretation of data has resulted in the conclusions that, for a great number of oxides, the value of is small, the relationship between and In aH+ is significantly sub-Nernstian, and the value of C is relatively large. 

Fig. 2 Plot illustrating the relatively linear relationship between the Cu"/ L redox potential and logarithmic value of the Cu" L stability constant, Cu"L- The line drawn has the Nernstian slope (0.059) and represents a Cu L stability constant value of 10 All complexes represented involve uncharged ligands (see Table 4).

A significant feature of NPSV analysis is that linear relationships were observed when theoretical data for Nernstian charge transfer were taken as the X axis and theoretical data for various electrode mechanisms were taken as the Y axis. The slopes of the resulting straight lines are indications of the mechanisms of the electrode processes. Some of the slopes are included in Table 25. 

In this case, the Nernstian condition given in Eq. (H.5) must be replaced by the following relationship [in which a Butler-Volmer kinetics formalism has been assumed see Eq. (1.101)] ... 

For an ideal Nernstian reaction where the adsorbates do not interact laterally, or at least where the interactions are independent of the surface coverage, a surface-confined species will follow the following relationships ... 

The relationship between the concentration ratio of the oxidised to reduced form of the protein and the absorbance readings has been demonstrated in Section 2.3.1 and can be used to create a Nernst plot using eqn (2.3) (Figure 2.5). ° The result is a well-behaved Nernstian plot as evidenced by its slope ( / mV ) corresponding to a single electron-transfer process n= 1). The reduction is expected to facilitate the dissociation of the reduced Fe because of its increased lability and lower affinity for the protein. In the presence of a mediator, the equilibria involved in the OTTLF cell can be as follows,... 

The redox potential (ORP) for a single redox couple is related to the activities of species in solution through the Nernst equation (7) which has the limitations inherent in any thermodynamic relationship. If a measured ORP (corrected to the standard hydrogen electrode, SHE) corresponds to one computed from the experimental activities of a particular redox couple, electrode behavior is said to be nernstian with respect to that couple. 

Such electrode reactions are often called reversible or nernstian, because the principal species obey thermodynamic relationships at the electrode surface. Since mass transfer plays a big role in electrochemical dynamics, we review here its three modes and begin a consideration of mathematical methods for treating them. 

Fig. 2.5 The relationship between the reflectance of an electrode covered with an electroactive thin organic film and the potential modulation. The solid line represents Eq. (9) with a Nernstian equilibrium ...

If the special conditions (e.g., nernstian behavior or diffusion limiting current) are not valid, the solution of the differential equations are more difficult. In electro-analytical chemistry, techniques are used where the current-potential relationship is relatively simple consequently, the evaluation of the data is straightforward. This means that the current is directly proportional to the concentration (quantitative analysis) or the characteristic potential (peak potential, half-wave potential, etc.) values can easily and unambiguously be determined (qualitative analysis). In most cases, the experimental conditions can be varied in such a way that the desirable situation is realized. 

Ruzic " has derived a general theory of multistep electron transfer for cases in which electron transfer is reversible and the rate of electron transfer is sufficient to maintain Nernstian conditions. This theory was derived for dc polarography, but it is applicable to normal-pulse polarography. The current-potential relationship is... 

In their early studies, Caruana et al. measured the potential difference in a single flame between two dissimilar metal electrodes (chosen from Ti, Mo, Nb, Hf, Ta, and W, because of their high melting points and low ionization potentials) [15], Consequently, stable, reproducible potentials were observed and it was possible also to demonstrate a Nernstian-like relationship between the potential and the composition of a Pt/Rh alloy electrode. Preliminary voltammetric studies were also carried out at a Pt working electrode, using a three-electrode configuration for flames containing iron and copper ions. The results of these initial experiments confirmed fhaf fhe flame acts rather like an electrolyte solution and can be used as a medium for electrochemistry. 

This study is also a good example of how EIS provides additional data to what can be obtained from chronoamperometry or CV. As the data can be fit to a circuit, parameters such as charge transfer resistance and diffusion lengths can be obtained from the fitting. In this case, charge transfer resistance was used to validate the Nernstian-based model used to fit the j-V relationship. Also, Dominguez-Benetton and Sevda [37]... 

V, the relationship between Eq, and [Py ] needs to be defined only over this narrow potential region. While the Nernst equation should, in principle, define this relationship, these films are non-Nernstian (see Figure 6). Therefore, the relationship between Eqc and [Py ] was determined empirically using a coulometric titration procedure (58-60). This procedure is described in detail in reference (30). 

Equations similar in form lo Equation 22-11 are described as nemstun relationships electrodes and seasors whose behavior can be described by the Nernst equation are said to exhibit nernstian behaxior, and RTnF (2.303 ftr- rif when base 10 logarithms are used) is often called the nerns-lian facuir. 

This means that the linear relationship exists between the electrode potential and the pH. Therefore, if we can find an electrode that shows Nernstian response to hydrogen ion activity, then measuring the E value and having reliable calibration data we can get the hydrogen ion activity and the pH of the tested solution. If and E are the electrode potentials in calibrating the standard and the sample, and pjjj and pjj are the pH of the standard and that of the sample, respectively, then we can easily get pjj, the unknown p of the sample solution. 

Now what other information can be obtained from the data One obvious relationship to explore is the plot of E as function of log For ventricle the results are unambiguous. A least squares linear regression plot yields a slope between 56 and 57 mv, which is not significantly different than 58 mv. The correlation coefficient is 0.91. Atrium and sinus venosus presented a rather disquieting picture in that the slopes of the straight lines are about one half Nernstian. The correlation coefficient for atrium is lower, 0.72, but for sinus venosus the correlation coefficient is again 0.91. From these data it appears that the relation is a linear one but with only one half Nernstian slopes. 

Spectroelectrochemical studies refer to the measurement of variables which are related individually to the concentrations of the oxidized and reduced species and then relating these measured variables to electrochemical relationships like the Nernst equation. Because of the large number of bands in vibrational spectra, it should be relatively easy to find SERS bands which are proportional to oxidized and reduced species surface concentrations. If the surface concentrations are related to bulk concentrations by a Langmuir isotherm, it can be shown for a reversible (Nernstian) redox process involving adsorbed species that... 

This section describes the various calibration and evaluation methods which can be used with ion-selective electrodes. The specific procedure chosen determines whether the activity or concentration of the indicated ion is obtained as a result of the measurement Fundamental to all analytical methods is the Nernst equation. We have seen in Chap. 1.2 that the Nernst equation is a theoretically derived relationship. In practice it is usually the case that an electrode deviates somewhat from the Nernst equation. As long as this deviation is reproducible, the electrode can still be used for analytical applications. Testing an electrochemical cell for exact Nernstian behavior is quite painstaking, and is often impossible. Standard solutions of precisely known activities are needed. This, in turn, requires the individual activity coefficients of the corresponding measured ions, and these are not always known with sufficient accuracy. Instead, one usually uses an empirical form of the Nernst equation for analytical applications ... 

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