Current time curve

Current-time curve for controlled-potential coulometry. 

Minimizing Electrolysis Time The current-time curve for controlled-potential coulometry in Figure 11.20 shows that the current decreases continuously throughout electrolysis. An exhaustive electrolysis, therefore, may require a long time. Since time is an important consideration in choosing and designing analytical methods, the factors that determine the analysis time need to be considered. 

Charge-time curve obtained by integrating the current-time curve in Figure 11.20. 

A second approach to coulometry is to use a constant current in place of a constant potential (Figure 11.23). Controlled-current coulometry, also known as amperostatic coulometry or coulometric titrimetry, has two advantages over controlled-potential coulometry. First, using a constant current makes for a more rapid analysis since the current does not decrease over time. Thus, a typical analysis time for controlled-current coulometry is less than 10 min, as opposed to approximately 30-60 min for controlled-potential coulometry. Second, with a constant current the total charge is simply the product of current and time (equation 11.24). A method for integrating the current-time curve, therefore, is not necessary. 

Figure 1.4 (A) Current-time curves for Au wires etched in a mixture of HChethanol (1 Iv/v) at different voltages. (B) SEM images ofthe etched Au tips. A 2.1 V, B 2.2 V, C 2.4 V. Reprinted with permission from Xi Wang, Applied Physics Letters, 91, 101105 (2007). Copyright 2007, American Institute of Physics.

For controlled-potential coulometry the voltage drop over a standard resistor is measured as a function of time by means of a voltage-to-frequency converter the output signal consists of a time-variant and integrally increasing number of counts (e.g., 10 counts mV-1), which by means of an operational amplifier-capacitor yields the current-time curve and integral158. 

Figure 3.31 Current/time curve for methanol adsorption. The methanol concentration was 0.5 M. Adsorption occurred after holding the potential at -I- 1.55 V for 20 ms, and then stepping the potential to 0.37 V. The step from 1.55 V to 0.37 V takes place 40 ms in from the right-hand edge. The x-nxis scale is 200 ms cm the y-axis scale is 3.33pAcm. After Bciglcr and Koch...

If the nonlinear character of the kinetic law is more pronounced, and/or if more data points than merely the peak are to be used, the following approach, illustrated in Figure 1.18, may be used. The current-time curves are first integrated so as to obtain the surface concentrations of the two reactants. The current and the surface concentrations are then combined to derive the forward and backward rate constants as functions of the electrode potential. Following this strategy, the form of the dependence of the rate constants on the potential need not be known a priori. It is rather an outcome of the cyclic voltammetric experiments and of their treatment. There is therefore no compulsory need, as often believed, to use for this purpose electrochemical techniques in which the electrode potential is independent of time, or nearly independent of time, as in potential step chronoamperometry and impedance measurements. This is another illustration of the equivalence of the various electrochemical techniques, provided that they are used in comparable time windows. 

Clearly, for times tpotential step response. In this time interval (/Cottrell equation therefore, the cathodic current is expressed by the relationship ... 

Figure 11 Unnatural amino acids to probe the inactivation mechanism of ion channel Kv1.4. OMeTyr or dansylalanine extends the side chain length of tyrosine, which impedes the inactivation peptide from threading through the side portal of the ion channel and abolishes the fast inactivation, as shown in the current-time curve in the bottom panel.

Fig. 15 (a) Schematic illustration of the potential-controlled STM measurement, (b) Cyclic voltammetry of the Cgo-modified substrate in a 0.1 M TBAPFs DMF solution, (c) Representative current-time curves upon potential sweep for the bare gold surface trans-2-C Q in a 0.1 M TB APFg DMF solution. (Reprinted with permission from [107])... 

Recently flow coulometry, which uses a column electrode for rapid electrolysis, has become popular [21]. In this method, as shown in Fig. 5.34, the cell has a columnar working electrode that is filled with a carbon fiber or carbon powder and the solution of the supporting electrolyte flows through it. If an analyte is injected from the sample inlet, it enters the column and is quantitatively electrolyzed during its stay in the column. From the peak that appears in the current-time curve, the quantity of electricity is measured to determine the analyte. Because the electrolysis in the column electrode is complete in less than 1 s, this method is convenient for repeated measurements and is often used in coulometric detection in liquid chromatography and flow injection analyses. Besides its use in flow coulometry, the column electrode is very versatile. This versatility can be expanded even more by connecting two (or more) of the column electrodes in series or in parallel. The column electrodes are used in a variety of ways in non-aqueous solutions, as described in Chapter 9. 

Growth of isolated nuclei at an electrode surface is eventually limited when they start to coalesce due to their number and size and the size of the electrode area. Analysis of the overlap problem can be performed by use of the Avrami theorem [152] and leads to maxima in the current—time curves at constant potential. Potentiostatic conditions are convenient for the study of these phenomena because electrochemical rate coefficients and surface concentration conditions are well controlled. 

Figure 3.30 (A) Current-time curves illustrating the sampling sequence for current-sampled polarography if, diffusion-controlled faradaic current id), double-layer charging current it = if + idl. (B) Current-sampled polarogram.

Additional improvement may be noted if the simulated current-time curve is rendered more exact through the judicious selection of DMA. This may be done by noting that unit relative concentration of A exists in the second volume element at the start of the second time iteration. Therefore, Z(2) as calculated in the simulation will be jLDMA. This may be set equal to L[QC(2) - Qc(l)], as obtained from Equation 20.35 and solved for DMA. Thus... 

Figure 21.9 (Left) Anodic-cathodic current-time curve for 2,2,5,7,8-pentamethyl-6-hydroxychroman (lb) showing the method of current and time measurements for the double-potential-step chronoamperometric method. The xr/xf ratio shown here is 0.3. (Right) Plot of kxf vs. xf for the ring opening of lib in 75 vol% water-25 vol% acetonitrile pH 3.99 0.5 M chloroacetic acid, 0.5 M sodium chloroacetate. (From Ref. 6, reprinted with permission.]...

Figure 28.12 Current-time curves observed with time-delayed potentiostatic analysis. x, x2, and x3 refer to three different delay times used for three different experiments. [From Ref. 67.]...

Fig. 6.14 The voltammogram in Fig. 6.9 plotted as the current-time curve (left) and the differentiated current-time curve (right).

Current-Time Curves (Chronoamperometry) and Current-Potential Curves... 

Note that the reversible l(E, t) response is expressed as a product of a potential-dependent function ((c 0 - c Rt l)/( + ye 1)) and a time-dependent function (FA sjDo/(nt)). This behavior is characteristic of reversible electrode processes. In the next sections the current-time curves at fixed potential (Chronoamperograms) and current-potential curves at a fixed time (Voltammograms) will be analyzed. 

Fig. 2.3 Experimental current-time curve (a) and logarithmic curves (b) for the application of a constant potential to a graphite disc electrode of radius 0.5 mm (planar electrode) for the reduction of Fe(CN)g. ...

In Fig. 2.12, the analytical current-time curves under anodic and cathodic limiting current conditions calculated from Eq. (2.137) (Fig. 2.12a and b, respectively) when species R is soluble in the electrolytic solution (solid curves) and when species R is amalgamated in the electrode (dotted lines) are plotted. In Fig. 2.12a, the amalgamation effect on the anodic limiting current has been analyzed. As expected, when species R is soluble in the electrolytic solution, the absolute value of the current density increases when the electrode radius decreases because of the enhancement of... 

Fig. 2.12 Influence of the electrode radius on the current-time curves under anodic (a) and cathodic (b) limiting conditions (Eq. 2.137) when species R is soluble in the electrolytic solution (solid curves) and when it is amalgamated in the electrode (dashed curves). The electrode radius values (in cm) are rs = 5 x 1CT2 (red curves), rs = 1CT2 (blue curves), and rs = 5 x 10-3 (green curves). c 0 = c R= 1 mM, D0 = Dr = 1CT5 cm2 s-1. (The dashed green curve has been calculated numerically for t > 0.5 s). Reproduced with permission [52]...

Fig. 2.15 (Solid line) Current-time curves for the application of a constant potential to a spherical electrode calculated from Eq. (2.142). D0 = Dr = 10-5 cm2 s 1, co = cr = 1 mM, rs = 0.001 cm, (E — E ) = -0.2 V, 7=298 K. (Dashed line) Current-time curves for the application of a constant potential to a planar electrode of the same area as the spherical one calculated from Eq. (2.28). (Dotted line) Steady-state limiting current for a spherical electrode calculated from Eq. (2.148). The inner figure corresponds to the plot of the current of the spherical electrode versus j ft...

The analysis of the current-time curves at electrodes or microelectrodes of different geometries has also a great interest in detecting the presence of small particles or nanoparticles at its surface or even single nanoparticles events through the current due to the electro-oxidation (or reduction) of the particles (see Fig. 2.18) or to a electrocatalytic reaction on the nanoparticle surface when this comes into contact with the electrode and transiently sticks to it [62-65]. 

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