Cross potential

The original ideas of Evans and Polanyi [1] to explain such a Hnear relation between activation energy and reaction energy can be illustrated through a two-dimensional analysis of two crossing potential energy curves. 

Figure 1.4 Two-dimensional curve-crossing potential energy diagram of reacting system with similar potential energies before and after reaction (schematic).

Tsai, R.-S. El Tayar N. Carrupt, R-A. Testa, B., Physicochemical properties and transport behavior of piribedil Considerations on its membrane-crossing potential, Int. J. Pharm. 80, 39 49 (1992). 

This efficient conversion of substantial electronic energy to translation requires crossed potential curves. The process has a large cross-section and therefore... 

Another important point of the I-E curve is the crossing potential or equilibrium potential for which the current takes a null value,/pl i"e = 0 (see Fig. 2.4a). By inserting this condition in Eq. (2.27),... 

In the first case, when only species O is initially present in the electrolytic solution (Fig. 2.13a), it is observed that the amalgamation of species R leads to a shift of the wave to more negative potential values, and this shift is greater the more spherical the electrode, i.e., when the duration of the experiment increases or the electrode radius decreases. In the second case (Fig. 2.13b), both species are initially present in the system so we can study the anodic-cathodic wave. In the anodic branch of the wave, the amalgamation produces a decrease in the absolute value of the current. As is to be expected, the null current potential, crossing potential, or equilibrium potential ( Eq) is not affected by the diffusion rates (D0 and Z)R), by the electrolysis time, by the electrode geometry (rs), nor by the behavior of species R... 

From Eq. (4.67), it is possible to obtain an expression for the cross potential (null current potential) of the RPV curve valid for any electrode geometry... 

By equating Eq. (4.104) to zero, the expression of the cross potential is immediately deduced,... 

In Fig. 4.18, the influence of the kinetic parameters (k°, a) on the ADDPV curves is modeled at a spherical microelectrode l /Dr /r, = 0.2). In general terms, the peak currents decrease and the crossing and peak potentials shift toward more negative values as the electrode processes are more sluggish (see Fig. 4.18a). For quasireversible systems (k° 10-2 — 10 4 cm s ). the peak currents are very sensitive to the value of the heterogeneous rate constant (k°) whereas the variation of the crossing potential is less apparent. On the other hand, for totally irreversible... 

In Fig. 4.18b, the effects of the electron transfer coefficient (a) on the ADDPV curves is shown. A decrease of a leads to the decrease of the peak currents together with the shift of the peak and crossing potentials toward more negative values. The ratio of the peak currents (l/ he// hel) also varies with a, and the greater the a value, the greater the l/ he//j, ll llL ratio. It is worth highlighting the anomalous... 

The dimensionless theoretical ADDPV curves for a reversible EE mechanism at a disc electrode of radius rd = 50 pm, with a pulse amplitude A = 50 mV and different values of the difference between the formal potentials of both electrochemical steps, can be seen in Fig. 4.22. In all cases, ADDPV curves have a center of symmetry at the crossing potential, s given by Eq. (4.186). So, the determination of this point helps to extract the formal potentials accurately. Besides being easier to measure than the potential or width of a peak, the s, value is independent of the pulse amplitude, the electrode size and shape, and the difference between the formal potentials, so this diagnosis criterion is very general. 

The extreme crossing potentials c>1 and Ec2 do depend on the difference between the formal potentials (through K) and the pulse amplitude employed (through A) and they move apart when K decreases. When the ADDPV curve shows three crossing points, the values of the formal potentials can be easily and accurately extracted from the analysis of the c>1, s, and Ec2 values. For very... 

For high values of the chemical rate constant, i.e., under conditions of a diffusive-kinetic steady state (d[Pg.308]

For an electrode process followed up by an irreversible homogeneous chemical reaction (K = 0, Fig. 4.31b), the peak currents are independent of the chemical kinetics whereas the peak potential takes more positive values as xi increases because the chemical reaction facilitates the reduction process by removal of species B. In all cases plotted in this figure, the value of the crossing potential can be evaluated with good accuracy from Eq. (4.255) (error smaller than 3 mV for X2 > 102). With respect to the E mechanism of species A, in the EC response both peak currents are smaller, and this effect is especially noticeable in the minimum which is more affected by the follow-up reaction. 

The quantitative determination of the homogeneous rate constants can be easily carried out from the values of the peak currents and the crossing potential of the ADDPV curves [78]. The use of the crossing potential is very helpful since this parameter does not depend on the pulse height (AE) employed and so can be measured with good accuracy from several ADDPV curves obtained with different AE values. In addition, for fast kinetics the simple analytical expressions that are available for cross (Eqs. (4.254) and (4.255)) allow a direct determination of the rate constants of the chemical reaction. 

In the case of surface-bound molecules, due to the characteristics of the current obtained when a sequence of potential pulses is applied (see Sect. 6.4.1.2), the use of DSCVC is only recommended for the analysis of non-reversible electrochemical reactions, since for very fast electrochemical reactions (i.e., for values of the dimensionless rate constant which fulfill log( 0r) >0.5), the current becomes negligible, in accordance with Eq. (6.132). The response obtained in DSCVC when non-reversible electrochemical reactions are considered presents two peaks, one maximum positive fV dscvc) an(J one minimum negative (v Sdscvc) which appear for values of the applied potentials EMax and Emin, respectively (with i// >scvc = / >scvc/The cross potential value, at which dscvc = 0,... 

When the electrochemical reaction can be considered as fully irreversible, it is possible to deduce analytical expressions for the maximum, minimum, and cross potentials. By taking into account equation (6.134) for the dimensionless current under these conditions, we obtain [73] ... 

In this case, the cross potential or null current potential is... 

This equation indicates that the peak potential is located at more negative values than E 1 and it moves toward the formal potential as Esw increases. When high values of the square wave pulse amplitude are used, the Q — E curves show a broad plateau which is centered at a potential E Et° — (RT/(2F)) n + c). Another interesting characteristic of the Q, — E curve is the cross potential for which the converted charge is null. For reversible conditions, it is given by (see... 

The criteria for SHAC voltammograms to yield reversible potentials are that the zero-current crossing potentials must be both frequency- and phase-independent. In practice one measures the in phase (/) and quadrature (Q) components of the second harmonic a.c. current by means of a phase-sensitive detector or lock-in amplifier. The response is illustrated in Figs 10-12 obtained during measurements on the oxidation of 9,10-diphenylanthracene (DPA) in acetonitrile (Fig. 10) and in acetonitrile containing pyridine (Figs... 

Fig. 7. (a, d) Evolution of the 200th dihedral angle of the united atom 400-mer over a 500 ps thermostatted simulation without (a)/with(d) REPSWA. (b,e) Histogram of the number of dihedral angles crossing potential barriers a given number of times without (b)/with(e) REPSWA. (c), (f) Evolution of the end-to-end distance without(c)/with(f) REPSWA... 

Molecular dynamics calculation is solving Newton s equation of motion using a hybrid target function between empirical force fields and experimental data. The degrees of freedom are the Cartesian coordinates of the atoms. The dynamics aim to cross potential barriers caused by inappropriately folded structures. This can reduce the problem of being trapped in local minima more than the torsion angle space minimization. Usually, a... 

From the previous discussion it became clear that the description of inelastic atom-molecule collisions on crossing potential surfaces is a very difficult problem. Moreover trajectories on such surfaces are critically dependent on details of the surfaces and, in contrast with two particle collisions, the crossing region may be passed several times. In the next few paragraphs we will give a brief discussion of several methods which have been proposed to simplify this task. 

For near-degenerate vibrational levels of any two crossing potential curves, the i -centroid has the convenient property of being nearly equal to Rc, the F-value where the two curves cross (Schamps, 1977). Thus,... 

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