Switch potential

An alternative way to eliminate discontinuities in the energy and force equations is to use a switching function. A switching function is a polynomial ftmction of the distance by which the potential energy function is multiplied. Thus the switched potential o (r) is related to the true potential t> r) by v r) = v(r)S(r). Some switching functions are applied to the entire range of the potential up to the cutoff point. One such function is ... 

Example For two atoms having point charges of 0.616 and -0.504 e and a constant dielectric function, the energy curve shows a switching function turned on (Ron) at a nonbonded distance of 10 A and off (Roff) at a distance of 14 A. Compare the switched potential with the abruptly truncated potential. 

Fig. 3-5 Switching potential measurements for lead (1,2) and steel (3) in soil solution ...

Additional information on the rates of these (and other) coupled chemical reactions can be achieved by changing the scan rate (i.e., adjusting the experimental time scale). In particular, the scan rate controls the tune spent between the switching potential and the peak potential (during which the chemical reaction occurs). Hence, as illustrated in Figure 2-6, i is the ratio of the rate constant (of the chemical step) to die scan rate, which controls the peak ratio. Most useful information is obtained when the reaction time lies within the experimental tune scale. For scan rates between 0.02 and 200 V s-1 (common with conventional electrodes), the accessible... 

Fig. 1. Multisweep cyclic volt-ammograms for the polymerization of Af-phenyl-carbazole (C = 1.7xl0-2mol/l)in CHjNOa/TBAPFe, Pt working electrode. The switching potential in the upper diagram is 50 mV less positive than in the lower...

Figure 14. Cyclic voltammograms of /<2c-Re(bpy)(CO)3Cl in acetonitrile-0.1 M Bu4NPF6 at a Pt electrode.144 Scan rate 0.2 V/s. The lower voltammograms show the switching potential characteristics A and F, reversible one-electron wave B and D, redox couple due to a dimer of the complex C, the second metal-based wave. The upper curves show the effect of C02 on the voltammogram. See also Figure 15.

Figure 3,55 Cyclic vollammograms of Re(Bipy)(CO)3CI in CH3CN/0.l M letrabutylammonium hexafluorophosphate as supporting electrolyte at a button Pt electrode, and with a sweep rate of 200 mV s (a) The switching potential characteristics of the coupled chemical reactions in the ahsence of C02. The lettered redox processes are discussed in the text. (b> The effect of saturating the solution with C02. From Sullivan et al. (1985).

During cyclic voltammetry, the potential is similarly ramped from an initial potential E but, at the end of its linear sweep, the direction of the potential scan is reversed, usually stopping at the initial potential E (or it may commence an additional cycle). The potential at which the reverse occurs is known as the switch potential ( >.) Almost universally, the scan rate between E and Ex is the same as that between Ex and E. Values of the scan rates Vforwani and Ubackward are always written as positive numbers. 

Cyclic voltammogram (CV) A plot of current (as y ) against potential (as x ) obtained during a voltammetric experiment in which the potential is ramped twice, once forward to the switch potential and then back again. 

Linear-svreep voltammogram A normal voltammogram, in which the voltage ramp stops at the switch potential (in contrast to a cyclic voltammogram, in which it does not). 

Switch potential, Ex, In cyclic voltammetry, the potential at which the voltage ramp changes direction. 

Depending on the time variation of the applied potential, several types of voltammetry can be distinguished. Among them, the most widely used are linear and cyclic voltammetries. Here, the excitation signal is a linear potential scan that is swept between two extreme values, and in cyclic voltammetry the potential is swept up and down between the two values (or switching potentials) with the same absolute scan rate (v, usually expressed in mV/s), although it has the opposite sign [79]. 

Initially, at potentials between -0.25 and about +0.1 V, a rather low current is recorded due to double-layer charging. Later, when the potential is sufficiently positive to oxidized [Fe(CN)g]" to [Fe(CN)g] , the anodic current increases rapidly until the concentration of [Fe(CN)g]" at the electrode surface is substantially diminished. Then, the (anodic) current increases dramatically until a maximum value is reached, thus defining a (anodic) voltammetric peak with the peak potential pa and the peak current fpa. The correct peak current must be measured in relation to the background current, which can be extrapolated from the starting region. After the peak, the current decreases slowly as the electrode is depleted of [Fe(CN)g] due to its electrochemical conversion into [Fe(CN)g] . When the (anodic) switching potential Ex is attained, the potential scan reverses its direction. In the subsequent cathodic scan, a similar cathodic peak is measured, defining a cathodic peak potential pc and a cathodic peak current Then, the current reaches a maximum and subsequently decays. 

The general problem of determining the relative amounts of oxidized and reduced forms of an electroactive species in solution was faced theoretically by Scholz and Hermes [203] for the cyclic voltammetry of an electrochemically reversible process controlled by diffusion. These authors used the currents at the larger and lower potential limits (anodic and cathodic switching potentials, respectively) rep-... 

The cyclic voltammogram for reaction (2) is shown in Fig. 3. The first half of the cycle, which involves a potential sweep from Ex to Ex, called the switching potential, is identical to the corresponding LSV wave (Fig. 

The peak potertial on the reverse scan of a CV depends upon the switching potential, Ex, which results in some variation of the peak potential separation AEp. Some values are tabulated in Table 2. These, along with the peak current ratio, (/p)r/(/p)f, where the subscripts refer to the reverse (r) and forward (f) scans, provide additional criteria for the reversible charge transfer. 

Note There is a slight dependence of AEp on switching potential. Values given are for switching potential 112.5/n mV beyond Ep. Other conditions a = 0.5 T = 298 K. 

Figure 23.18 Experimental CV scans to two different switching potentials for a complex reducing by the ECE mechanism of Eq. 23.24-23.26 with a rapid chemical reaction (Eq. 23.25). The system is [Fe(CN)5NO]2- in CH2C12 (Eq. 23.27-23.29), and the anodic feature at approximately -1.0 V arises from a product not referred to in Eq. 23.27-23.29. v = 0.08 V/s. Reprinted from Ref. 23 with permission.

Concerning the peak potential and peak current of the reverse (second) scan, it is important to take into account that the shape of the reverse current depends on the switching potential (i.e., the last potential of the first scan, finai)- This especially affects the measurement of the reverse peak current, for which different criteria have been reported [9]. It should be noted that these criteria are ambiguous and it is... 

There is another characteristic point in the voltammogram known as the isopoint [25, 26]. At the isopoint, the current is zero regardless of the scan rate (see black dot in Fig. 5.4). In reference [26], the following numerical expression was reported to determine the difference between the peak potential of the forward scan, FpeXf, ar,d the potential of the isopoint, F 1 6, in terms of the switching potential Ffinai ... 

---