Limiting current measurements

Fig. 6. Comparison between mass transfer correlations and results of limiting current measurements [14, 22],...

B. Electrochemical Reactions Used in Limiting-Current Measurements. 219... 

The conceptual development of limiting-current measurement was advanced substantially by Agar and Bowden (A2), who investigated the current-overpotential relationship for oxygen evolution at nickel electrodes in fused sodium hydroxide. Here water transport is the limiting step ... 

In 1971 Mizushina (M9) reviewed the limiting-current method with particular emphasis upon shear-stress and fluid-velocity measurements. Mass-transfer measurements, that is, limiting-current measurements in the original more restricted sense, are documented fairly extensively. The electrochemical analysis of limiting-current measurements is touched upon, but not elaborated. 

The total overpotential in limiting-current measurements is therefore represented as the sum of these three components ... 

The ohmic contribution to the overpotential can be minimized by suitable placement of the reference electrode, but the surface overpotential cannot be reduced similarly. In making limiting-current measurements, the surface overpotential, or rather its rate of increase with current density, should be low enough to permit observation of a long, clearly defined limiting-current plateau. 

In limiting-current measurements, the counterelectrode is sometimes used as a reference electrode. In that case, the surface overpotential of the counterelectrode contributes to the recorded overpotential that is, the potential of the reference electrode is now current dependent. Unless precautions are taken (e.g., the area of the counterelectrode is much larger than that of the working electrode), a properly defined limiting-current plateau may not be obtained. 

Potentiostatic current sources, which allow application of a controlled overpotential to the working electrode, are used widely by electrochemists in surface kinetic studies and find increasing use in limiting-current measurements. A decrease in the reactant concentration at the electrode is directly related to the concentration overpotential, rj0 (Eq. 6), which, in principle, can be established directly by means of a potentiostat. However, the controlled overpotential is made up of several contributions, as indicated in Section III,C, and hence, the concentration overpotential is by no means defined when a given overpotential is applied its fraction of the total overpotential varies with the current in a complicated way. Only if the surface overpotential and ohmic potential drop are known to be negligible at the limiting current density can one assume that the reactant concentration at the electrode is controlled by the applied potential according to Eq. (6). 

In many limiting-current measurements the expected current distribution is only moderately nonuniform, and a single unsegmented electrode will yield well-defined limiting-current plateaus. The various techniques by which the limiting current at a single electrode can be generated are discussed in the next section. 

The type of electrode reaction employed, the cell geometry, and the manner in which the limiting-current measurement is carried out determine the shape of the current versus electrode-potential curve. Often the ideal horizontal inflection in such curves is absent, making the determination of true limiting current problematical if not impossible. Characteristics of satisfactory limiting current plateaus are as follows ... 

Mass-transfer rates from limiting-current measurements in well-supported solutions should invariably be correlated with ionic and not with molecular diffusivities. The former can be calculated from limiting-current measurements, for example, at a rotating-disk electrode. 

The effective diffusivities determined from limiting-current measurements appear at first applicable only to the particular flow cell in which they were measured. However, it can be argued plausibly that, for example, rotating-disk effective diffusivities are also applicable to laminar forced-convection mass transfer in general, provided the same bulk electrolyte composition is used (H8). Furthermore, the effective diffusivities characteristic for laminar free convection at vertical or inclined electrodes are presumably not significantly different from the forced-convection diffusivities. 

The validity of Eq. (12) for correlations of limiting-current measurements was first questioned by Arvia et al. (A5), and later by Wragg and Ross (W13a). The latter found that limiting currents in an annular flow cell could be correlated in better agreement with the Leveque mass-transfer theory if a lower mobility (Stokes-Einstein) product were employed, such as... 

This value is based on Cu2+ diffusivities calculated Arvia et al. (A5) from limiting-current measurements at a rotating-disk electrode by, with CuS04 concentrations below 0.1 M. In practical applications (e.g., copper refining or electrowinning) higher Cu2+ concentrations are often required, as is also the case in free-convection limiting-current measurements. 

Limiting currents measured for a deposition reaction may be excessively high due to surface roughness formation near the limiting current. Rough deposits in the case of copper deposition have been mentioned several times in previous sections, since this reaction is one commonly used in limiting-current measurements. However, many other metals form dendritic or powdery deposits under limiting-current conditions, for example, zinc (N lb) and silver. Processes of electrolytic metal powder formation have been reviewed by Ibl (12). 

Certain conditions that adversely affect the precision of limiting current measurements can be avoided rather easily. These include . ... 

Changes in bulk reactant concentration during the limiting current measurement, due, for example, to variations in gas pressure (oxygen reduction) or to the presence of other species susceptible to reduction at the... 

As discussed in Section IV,E, it is necessary, as well as convenient, in studies such as these to divide the electrode into several insulated sections in order to make accurate limiting-current measurements otherwise the limiting current may be obscured. A limiting-current curve is then obtained for each insulated section. This technique, first introduced by Fenech and Tobias (F3), requires that the potential be kept equal on the various sections as limiting current is approached. Sectional currents are therefore measured by means of potential drop through low-ohmic precision resistors. 

By substituting the well-known Blasius relation for the friction factor, Eq. (45) in Table VII results. Van Shaw et al. (V2) tested this relation by limiting-current measurements on short pipe sections, and found that the Re and (L/d) dependences were in accord with theory. The mass-transfer rates obtained averaged 7% lower than predicted, but in a later publication this was traced to incorrect flow rate calibration. Iribame et al. (110) showed that the Leveque relation is also valid for turbulent mass transfer in falling films, as long as the developing mass-transfer condition is fulfilled (generally expressed as L+ < 103) while Re > 103. The fundamental importance of the Leveque equation for the interpretation of microelectrode measurements is discussed at an earlier point. 

The limiting-current method has been used widely for studies in packed and fluidized beds (see Table VII, Part H). Limiting current measurements in these systems overlap in part with the design and analysis of packed-bed and fluidized-bed electrochemical reactors in particular the potential distribution in, and the effectiveness of, such reactors (for example, for metal removal from waste streams) is an extensive area of research, which cannot be covered in this review. For a complete discussion of porous flow-through electrodes the reader is referred to Newman and Tiedemann (N8d). 

In Table VII, Section H, some limiting current measurements on or in packed beds are represented. These measurements were initiated by Sioda (S12a d) and others (V6, W13b) in cells with stacked grids or spheres. 

This expression has been satisfactorily confirmed by limiting current measurements. 

In this chapter the theory and practice of limiting-current technique for the measurement of mass-transport coefficients have been described. The selective discussion and tabular compilation of results of investigations that used limiting-current measurements should be indicative of the widespread use of this relatively novel method. 

Fig. 9 Temperature dependence of the hole mobility of a polyfluorene copolymer inferred from space-charge-limited current measurements on samples of thicknesses 122 nm, 1 pm, and 10 pm. The full curve is an extrapolation to the low carrier density limit using the extended Gaussian disorder model. From [90] with permission. Copyright (2008) by the American Institute of Physics...

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