Quiet solutions

The understanding of the nature of transient current after the imposition of a potential pulse is fundamental to the development of voltammetry and its analytical applications. Consider the same reaction, O+ne- = R, taking place in a quiet solution at a potential such that the reaction is diffusion controlled. Figure 18b.6a shows the pulse and Fig. 18b.6b shows the concentration gradient O as a function of time and distance from the electrode surface. 

Chronoamperometry is a technique in which a potential step is applied to the working electrode in a quiet solution at t = 0 (Figure 3). Initially [t < 0), the electrode attains r. For f > 0, a potential is selected, which drives the desired electrode reaction. Often, but not necessarily (see, e.g. References [23-25]) the latter is in the... 

In these techniques, the concentrations at the electrode do not immediately attain their extreme values after the start of the experiment. Rather, they change with E ox t according to equation (1). While the steepness of the concentration profiles increases with E (forward scan), simultaneously 8 increases in the quiet solution. The latter effect slows down the increase of i with E, and finally (close to the limiting current region) leads to the formation of a peak with a characterishc asymmetric shape. On the reverse scan (after switching the scan direction ad. Ef), products formed in the forward scan can be detected (B, in the case discussed). 

Chronopotentiometry is a transient constant-current technique in which the potential of the electrode is followed, as a function of time, in a quiet solution (Figure 6). Double-step applications [30], as well as programmed current experiments [31] have been described. 

We should note from this figure that a voltammogram obtained at an RDE looks wholly different from a voltammogram (of the same analyte) obtained under diffusion control (cf. Figure 6.13). We should also appreciate that the voltammetric currents obtained at an RDE are much larger than the corresponding currents obtained in a quiet solution this reflects the relative efficiencies of the different modes of mass transport (see Section 2.2 and the discussion above). 

It can be seen from the relative rate constants shown in Sch. 1 that the products formed will depend on the reaction conditions [26]. The production of formate, as shown by the right-hand reaction in Sch. 1, will be enhanced in protic solvents or in more acidic solutions. In water, formic acid is the main product. The production of CO, as shown by the left-hand reaction in Sch. 1, will be enhanced in rapidly stirred solutions in which locally high concentrations of the "C02 radical anion cannot buildup. This will decrease the probability of a bimolecular reaction between 02 radical anions. In quiet solutions and high current densities, the C02 radical anion concentration should be high in the diffusion layer, favoring formation of oxalate. 

Comparable or larger errors are introduced by unwanted convective mass transport. Convection is caused by physical motion of the solution, sometimes purposefully introduced for techniques such as rotating electrode voltammetry. When a quiet solution is desired, however, convective errors may arise at longer experiment times (slow scan rates) from mechanical vibrations of the solution. Convection is a particular problem for cells inside inert-atmosphere boxes, on which fans and vacuum pumps may be operative. Convection raises the current... 

In order to undergo a redox process, the reactant must be present within the electrode-reaction layer, in an amount limited by the rate of mass transport of Yg, to the electrode surface. In electrolyte media, four types of mass-transport control, namely convection, diffusion, adsorption and chemical-reaction kinetics, must be considered. The details of the voltammetric procedure, e.g., whether the solution is stirred or quiet, tell whether convection is possible. In a quiet solution, the maximum currents of simple electrode processes may be governed by diffusion. Adsorption of either reactant or product on the electrode may complicate the electrode process and, unless adsorption, crystallization or related surface effects are being studied, it is to be avoided, typically... 

The hydrodynamic flow in convective solutions is difficult to treat theoretically to develop quantitative expressions for expected plateau-current values. An exception is the rotated-disk electrode (RDE). The RDE is a flat disk sealed onto an inert shaft that is rotated with minimum wobble in an otherwise quiet solution. From the hydrodynamics is derived the expression of the limiting plateau current, i ... 

Figure 2. Cyclic Voltammetry at 3 V min in a quiet solution saturated with N2 or CO2 of a) a carbon rod electrode or b) a Ru electroplated electrode.

Amperometric electrodes made on a microscale, on the order of 5 to 30 /rm diameter possess a number of advantages. The electrode is smaller than the diffusion layer thickness. This results in enhanced mass transport that is independent of flow, and an increased signal-to-noise ratio, and electrochemical measurements can be made in high-resistance media, such as nonaqueous solvents. An S-shaped sigmoid current-voltage curve is recorded in a quiet solution instead of a peak shaped curve because of the independence on the diffusion layer. The hmiting current, q, of such microelectrodes is given by... 

This section treats the theory of homogeneous mediated bioelectrocatalysis in a quiet solution. An empirical equation explaining the catalytic current is presented, which is conveniently used for the determination of kinetic parameters of the enzyme reaction. A novel method of protein redox potential measurements is also described using a mediated continuous-flow column electrolytic spectroelectrochemical technique. 

A. Theory of Homogeneous Mediated Bioelectrocatalysis in Quiet Solution... 

Usual conditions for LSV or CV experiments require a quiet solution in order to allow undisturbed development of the diffusion layer at the electrode. Some groups, however, have purposely used the interplay between diffusion and convection in electrolytes flowing in a channel or similar devices [23]. In these experiments (see also Chapter 2.4), mass transport to the electrode surface is dramatically enhanced. A steady state develops [54] with a diffusion layer of constant thickness. Thus, such conditions are in some way similar to the use of ultramicroelectrodes. Hydro-dynamic voltammetry is advantageous in studying processes (heterogeneous electron transfer, homogeneous kinetics) that are faster than mass transport under usual CV or LSV conditions. A recent review provides several examples [22]. 

Kolev SD, Chow CWK, Davey DE, and Mulcahy DE (1998) Mathematical modelling of potentiometric stripping analysis. Chemical stripping in quiet solutions. Analytica Chimica Acta 377 13-19. 

Let us first examine the quiet solution case, which is depicted at the top of Fig. 1. In the time increment electroactive species from the... 

This section will explore the quantitative behavior of current-potential curves (voltammetry) and steady-state current measurements in flowing solution prior to considering liquid chromatographic assays. A similar examination of quiet solutions is reserved for the section on in vivo measurements. (In this and all subsequent voltammetry discussions, only oxidation reactions are treated, not because reductions are unimportant, but because there are to date few, if any, neurochemical applications.)... 

This is the quiet-solution experiment discussed in Section 1.2 with the current response shown in Fig. 2A. App is instantaneously switched from an initial value (open circuit or a value at which no electrolysis is occurring) to slightly past p, held constant for a fixed time, then normally switched off or back to E. If material diffuses to a planar electrode surface in only one direction (linear diffusion), then the exact description of the current-time curve is given by the Cottrell equation ... 

Quiet-Solution Behavior of Very Small Electrodes... 

Fig. 15. Electrode designs used in quiet-solution studies. (A) Strict linear diffusion style IS—insulating shield of glass or Teflon, etc. IM—extension of shield to make protective mantle (B) practical electrode type—active electrode surface diameter ca. 1-50 mm (C) typical in vivo electrode IS—glass capillary is insulating shield solid arrows—linear diffusion contributions dotted arrows—spherical-type diffusion contributions.

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