Linearly Increasing Current

Chronopotentiometry — is a controlled-current technique (- dynamic technique) in which the - potential variation with time is measured following a current step (also cyclic, or current reversals, or linearly increasing currents are used). For a - nernstian electrode process,... 

One advantage of amperometric titrations is that the substance titrated does not have to be electroactive if an appropriate titrant with electrolytic properties is used. For example, sulfate ion can be determined by titration with Pb +. In this case, an essentially constant residual current flows until there is excess titrant in the test solution. After the endpoint a linearly increasing current appears which is proportional to the concentration of the excess titrant. The amperometric titration curve will have a shape the reverse of that shown in Figure 3.19B —/-shaped, or reverse L-shaped. ... 

Fig. 8. Limiting-current curve for low concentration of the reacting ion in free convection at a horizontal electrode, recorded by linear increase of applied potential. [From Fenech (F2).]... 

Experimental data relative to unsteady-state mass transfer as a result of a concentration step at the electrode surface are not available. However, for a linear increase of the current to parallel-plate electrodes under laminar flow, Hickman (H3) found that steady-state limiting-current readings were obtained only if the time to reach the limiting current at the trailing edge of the plate (see Section IV,E), expressed in the dimensionless form of Eq. (18), is... 

The growth of an anodic alumina film, at a constant current, is characterized by a virtually linear increase of the electrode potential with time, exemplified by Fig. 10, with a more or less notable curvature (or an intercept of the extrapolated straight line) at the beginning of anodization.73 This reflects the constant rate of increase of the film thickness. Indeed, a linear relationship was found experimentally between the potential and the inverse capacitance78 (the latter reflecting the thickness in a model of a parallel-plate capacitor under the assumption of a constant dielectric permittivity). This is foreseen by applying Eq. (38) to Eq. (35). It is a consequence of the need for a constant electric field on the film in order to transport constant ionic current, as required by Eqs. (39)-(43). 

When aluminum is anodically dissolved in halide solutions, the rate of hydrogen evolution linearly increases with increasing current density as shown in Fig. 25. This phenomenon is historically, and somewhat misleadingly, termed the negative difference effect 124 (NDE). It is contrary to what one would normally expect, for hydrogen evolution should subside with the potential going positive (as indeed is observed in alkaline solutions) or at least stay constant at a constant-potential plateau. 

This phenomenon, however, is not difficult to understand in view of the mechanism of dissolution under such conditions. Since the number of active sites increases linearly with current density and these sites are characterized by a film structure (or thickness or both) different from that at the OCP, one could expect corresponding increases in the corrosion rate. However, as was mentioned earlier, the active surface area in the pits increases with time, and hence one should expect the corrosion rate to increase correspondingly. Therefore, since the effect is not time dependent, one... 

Figure 43 illustrates the possible current transients during thermal treatment of Al-anodic Al203-Au structures at linearly increasing temperature (a) and during isothermal annealing (b). The first case is characterized by a TSC maximum at —400 K followed by a change in current direction and a second maximum (Fig. 43a). In the case of isothermal treatment, jTSC follows a t n dependence, where n is close to unity. These findings are usually interpreted in terms of a release from deep traps of those electrons that were initially captured there in the process of anodization. There are no clear ideas as to the physical nature of these traps. Parkhutik and Shershulskii249 have postulated that traps are associ-...

Amino acids enhance the oxidation peak of Cu(0) obtained with a carbon paste electrode incorporating Cu(II) cyclohexylbutyrate. The increased current is proportional to the amino acid concentration at trace levels in the pM range373. The behavior of such electrodes was investigated for cysteine (115). On scanning potentials in the positive direction, the amino acid is accumulated on the electrode as the Cu(I) complex at +0.90 V vs a standard calomel electrode (SCE), in acetate buffer at pH 4.5 linear range is 2 x 10 9 to 1 x 10-7 M, 1 min accumulation, RSD 3% (n = 5)374,375. 

The voltage output from an MCFC is reduced by ohmic, activation, and concentration losses that increase with increasing current density. The major loss over the range of current densities of interest is the linear iR loss. The magnitude of this loss (iR) can be described by the following equations (64,85,86) ... 

Bange S, Schubert M, Neher D (2010) Charge mobility determination by current extraction under linear increasing voltages case of nonequilibrium charges and field-dependent mobilities. Phys Rev B 81 035209... 

The corresponding injection currents for sensitized hole generation are almost independent of the applied voltage. The remaining increase in the quantum efficiency (holes per incident photon) with rising external field strength (Fig. 27) corresponds to a relative linear increase of the current with a coefficient of 10-6... 

During a CV experiment a linearly increasing potential difference is applied between the working and counter electrodes until a certain potential difference is reached, and the difference is then decreased, usually at the same speed, the sweep rate v the cycle may be repeated. The current i is recorded as a function of the potential E and in the case of an ideal, reversible electrode reaction the resulting curve from a reduction-reoxidation reaction assumes a shape as shown in Fig. 1. The shape of the curve may be understood from the following qualitative description. 

Approximately 0.7-pm diameter MIP beads with hydroquinone recognition sites have been prepared using similar one-step precipitation polymerization (Table 6) [183], These beads were immobilized in an agarose gel film deposited on GCE. The resulting MIP-modified electrode has been used as a chronoamperometric chemosensor for determination of hydroquinone. The current response of the chemosensor linearly increased with the hydroquinone concentration in the range of 2-100 pM and LOD for hydroquinone was 1 pM. 

Electrical-current signal in differential pulse voltammetry with (a) the DC-current signal due to applied and linearly increasing DC ramp and (b) the signal due to the application of potential pulses. 

The current situation in bioinformatics is characterized by an avalanche of DNA sequences from the human genome project and similar programs and, consequently, an exponential increase in DNA sequences but only a linear increase in protein 3D structures. While multitudes of putative genes have been annotated, up to 90% of all known DNA sequences have no assigned, i.e., experimentally proven, function. From this situation arise the need for interpretation of DNA sequences by information technology, and moreover, analysis of functional genomics and proteomics (see Chapter 15). 

The variation of the peak current in the presence of a coupled catalytic reaction differs from the above behavior due to the catalytic contribution. Thus, as the chemical rate constant increases and the frequency decreases, that is, as the catalytic component becomes more apparent, there is a deviation from the linear increase of / d sc>Pcak wjth f/2. This deviation is only significant for kx > 10s 1. When steady-state conditions are achieved (very small frequencies and/or large kinetic constants), the peak current becomes independent of the frequency, as shown in Fig. 7.37 for k = 100s-1 and f1 2 < 5 s-1/2. 

The more accurate relationships obtained from the underlying microscopic current equations are discussed below (see Section III.3.iii). There we will see that the impedance that describes the stoichiometry polarization is composed of a so-called Warburg behavior (linear increase with a slope of 45° followed by a semicircular behavior, see Figure 39). Figure 37 shows an experimental example that comes close to the ideal situation. The detailed behavior around the maximum is also in accord with the precise treatment (see Section III.3.iii). 

The kind of voltammetry described in Sect. 4.2. is of the single-sweep type, ie., only one current-potential sweep is recorded, normally at a fairly low scan rate (0.1-0.5 V/min), or by taking points manually. Cyclic voltammetry is a very useful extension of the voltammetric technique. In this method, the potential is varied in a cyclic fashion, in most cases by a linear increase in electrode potential with time in either direction, followed by a reversal of the scan direction and a linear decrease of potential with time at the same scan rate (triangular wave voltammetry). The resulting current-voltage curve is recorded on an XY-recorder,... 

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