Mass Transport and Current Response

Well-defined hydrodynamic conditions, with high rate of mass transport, are essential for a successful use of electrochemical detectors. According to the Nernst approximate approach, the thickness of the diffusion layer (8) is empirically related to the solution flow rate (U) via 

A more rigorous treatment takes into account the hydrodynamic characteristics of the flowing solution. Hence, expressions for the limiting currents (under steady-state conditions) have been derived for various electrode geometries by solving the three-dimensional convective diffusion equation  

The resulting equations, arrived at by setting appropriate initial and boundary conditions (depending on the particular electrode), are given in Table 3.4. 

TABLE 3.4 Limiting-Current Response of Various Flow-Through Electrodes  

A generalized equation for the limiting current response of different detectors, based on the dimensionless Reynolds (Re) and Schmidt (Sc) numbers, has been derived by Hanekamp and coworkers (84) 

FIGURE 3-24 Electrophoretic separation of catechols with end-column detection. Detection potential, -1-0.8 V separation capillary, 20 kV The peaks correspond to 4.6 fmol dopamine (1), 4.1 fmol isoproterenol (2), and 2.7 fmol catechol (3). (Reproduced with permission from reference 60.) 

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We will now discuss how the relationship between potential, mass transport and current manifests itself experimentally in some situations typically met in electroanalytical chemistry. In Sections 6.7.1-6.7.3, we discuss the response curves for two families of electroanalytical methods that are conducted under conditions where linear semi-infinite diffusion to/from planar working electrodes prevail. These are chronoamperometry and double... 

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

For small K, i.e., K = 0.5 in Fig. 17, the response of the equilibrium to the depletion of species Red] in phase 1 is slow compared to diffusional mass transport, and consequently the current-time response and mass transport characteristics are close to those predicted for hindered diffusion with an inert interface. As K is increased, the interfacial process responds more rapidly to the electrochemical perturbation in phase 1. The transfer of the target species across the interface generates an enhanced flux to the UME, causing... 

The analysis of the kinetics of the charge transfer is presented in Sect. 1.7 for the Butler-Volmer and Marcus-Hush formalisms, and in the latter, the extension to the Marcus-Hush-Chidsey model and a discussion on the adiabatic character of the charge transfer process are also included. The presence of mass transport and its influence on the current-potential response are discussed in Sect. 1.8. 

When the surface concentration of species Csoi cannot be considered as constant the analysis of the electrochemical response that arises from reaction scheme (6.X) becomes much more complex since the process is of second order and the value of the surface concentration of Csoi will be a function of the kinetics of the catalytic reaction and also of the mass transport (and therefore of the electrode geometry). Due to this higher complexity, only the current-potential response in CV will be treated with the additional simplification of fast surface charge transfer. 

The limiting or mass transport limited current As soon as the potential is reached when [A]j,=o = 0, the current reaches a fixed limiting current value that is determined by the mass transport of material to the electrode surface. Under these conditions, material is continuously replenished at the electrode surface by convection, in contrast to the situation in a CV where depletion occurs and a peak-shaped response is observed. Table 5 gives the analytically derived expressions for the limiting currents obtained at the three electrode types discussed in this section. 

The concentration changes at the electrode surface due to mass transport limitations are responsible for the concentration overvoltages. When a reduction process takes place (e.g. Zn + + 2e Zn), a concentration of the oxidized species at the electrode surface (Cox,e) lower than that in the bulk makes the current, at a given potential, lower than that in the absence of an ion diffusion limitation, and to achieve the same current value an overvoltage (concentration overvoltage) must be imposed. This concentration (or diffusion) overvoltage can be calculated from Eq. (16) ... 

Response to Catechols in the Presence of Ascorbic Acid. In addition to the enhanced response for most catechol compounds, the voltammetric signals due to species in solution that are not complexed by the polymer are often diminished. Because the solvent-swollen polymer occupies space near the electrode surface, it effectively decreases the concentration of uncomplexed solution species. Furthermore, the polymer hinders diffusion of all species to the electrode surface. In the case of catechols, the increase in concentration in the film offsets this effect, but for species that do not bind with the polymer (e.g. ascorbic acid), the rate of mass transport (and subsequently the oxidation current monitored) is attenuated. This effect can be very useful when determining catechol in biological samples. 

As the rate of the electron transfer process increases it must eventually be fast compared with the maximum rate of mass transport and the surface concentration will then become zero. Diffusion is then the rate-determining step (of sequence (1.16)—(1.18)) and the current becomes independent of potential with the value given by equation (1.53). A similar argument applies to the oxidation reaction although the limiting current is about one-third of the plateau reduction current because of the ratio Cp /Cr employed. Figure 1.10 shows the I-E curves for both the reversible and the irreversible cases. In the former, the I-E response arises directly from equation (1.20) while for an irreversible couple we need an overpotential to drive both the oxidation and reduction processes, see equations (1.35) and (1.37). 

Chronoamperometry Chronoamperometry involves the study of the variation of the current response with time under potentiostatic control. Generally the working electrode is stepped from a potential at which there is no electrode reaction to one corresponding to the mass-transport-limited current, and the resulting current-time transient is recorded. In double-step chronoamperometry, a second step inverts the electrode reaction and this method is useful in analysing cases where the product of the initial electrode reaction is consumed in solution by a coupled homogeneous chemical reaction. 

A key feature of SECMID (and related methods) is that mass transport and the interfacial processes of interest are well defined so that the tip current response can be calculated readily and compared with experiment to obtain interfacial kinetic data. It is beyond the scope of this chapter to provide a complete overview of the theoretical treatment of SECM problems, but some discussion of the elements involved in the formulation of this particular SECM problem is useful to aid understanding of the method and analysis. Furthermore, the basic theoretical principles and results apply to many of the other modes that are considered subsequently in this chapter and, indeed, in many of the other chapters. 

The effects of ultrasound-enlianced mass transport have been investigated by several authors [73, 74, 75 and 76]. Empirically, it was found that, in the presence of ultrasound, the limiting current for a simple reversible electrode reaction exhibits quasi-steady-state characteristics with intensities considerably higher in magnitude compared to the peak current of the response obtained under silent conditions. The current density can be... 

The chronoamperometric technique illustrates the principle that analytically useful current responses depend critically on the efficiency of analyte mass transport within the solution. The analyte mass transport in turn depends on the efficiency with which an appHed voltage can maintain the surface concentrations of oxidized and reduced species at values specified by the Nemst equation. It is generally the case in chronoamperometry that the bulk concentration of one of the species is zero whereas the surface concentration of the other species is forced to zero by the appHed potential, but this is not always so. 

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