Uncompensated resistance systems

Three or four-electrode systems together with the use, when appropriate, of a Luggin capillary solve most of the problems of uncompensated resistance in solution. However, at times positive feedback... 

In order to avoid the distortion caused by these two effects, the usual approach is to compensate the resistance Ru by a positive feedback loop (this is imperative in systems like plasticized membranes for which the uncompensated resistance can be of the order of megaohms [32-34]). Another possibility is to use microelectrodes, for which a decrease in the measured current is obtained which minimizes the ohmic drop and charging current distortion (see Sects. 2.7 and 5.4.1). 

Electrode geometry in controlled-potential electrolysis. When fast response and accuracy of potential control are desired, considerable attention must be paid to the design of the cell-potentiostat system, and several papers have discussed the critical parameters and made recommendations for optimum cell design.8"11 In general, to achieve stability and an optimum potentiostat rise time for a fast potential change, the total cell impedance should be as small as possible, and the uncompensated resistance should be adjusted to an optimum (nonzero) value that depends on the characteristics of the cell and potentiostat.9,12 The electrode geometry also should provide for a low-resistance reference electrode and a uniform current distribution over the surface of the... 

Dirichlet boundary condition — A Dirichlet boundary condition specifies the value of a function at a surface. In electrochemical systems that function is commonly the concentration of a redox species at the surface of an electrode. For reversible reactions in the absence of uncompensated resistance, complicating homogeneous kinetics or adsorption, Dirichlet boundary conditions of Ox and Red are specified by the applied potential, E, according to... 

The electrochemical cell is coupled to a three-electrode potentiostatted form of instrumentation. If a two-electrode (working and reference) system were to be used, the current would have to flow through the reference electrode, thus risking instability in the reference potential. Furthermore, in a two-electrode system, the IR drop could be substantial. In contrast, in the three-electrode potentiostatted system, the current is forced to flow through the counter electrode, thereby avoiding problems with the reference electrode. Additionally, much of the IR drop is compensated by the potentiostat circuitry (Macdonald, 1977), which drives the potential between the working and counter electrode to a value which compensates the majority of this potential loss. However, the use of a potentiostat does not remove all of the IRu drop, since uncompensated resistance remains due to solution resistance between the tip of the reference and working electrodes, and... 

The peak-potential difference A p depends mainly on the kinetic parameter i/t, as illustrated in Table 2. By measurement of A p as a function of v for a given system, k° can be estimated. However, great care should be exerted to ensure that uncompensated resistance does not contribute to the value of A p, since this would hamper the procedure. Clearly, the use of ultramicroelectrodes can be recommended for this kind of measurements, as the ohmic drop is much smaller here compared to microelectrodes of normal size. This is particularly true when high sweep rates are required for determining large values of k° (see Section 2.4)... 

Cyclic-voltammetry measurements of quasireversible systems yield more easily to interpretation. Both the cathodic and anodic peak potentials shift as a function of scan rate, resulting in an increasing AE as v increases. This dependence of AEp on electron-transfer rate is used to measure the k value of the system, but AE also increases monotonically with v from the effects of uncompensated resistance, and the two effects are difficult to separate. The absence of appreciable resistance effects must be insured when making these measurements. Many reported rate constants are erroneous because of improper attention to this problem ... 

This approach has been employed, for example, in determining the steady-state uncompensated resistance at an ultramicroelectrode (28) and the solution resistance between an ion-selective electrode tip and a surface in a scanning electrochemical microscope (29, 30). It also is sometimes possible to model the mass transport and kinetics in an electrochemical system by a network of electrical components (31, 32). Since there are a number of computer programs (e.g., SPICE) for the analysis of electric circuits, this approach can be convenient for certain electrochemical problems. 

In a system with spherical symmetry, which would apply approximately to any working electrode that is essentially a point with respect to the counter electrode, the uncompensated resistance is given by (47),... 

Fig. 20. (A) Thin-layer dectrochemical detector with external rererenceoompattment. (B) Condensed detector cell with internal reference electrode and negligible uncompensated resistance. In both schemes, the working electrode block is interchangeable to provide various dual-and single-electrode configurations. The condensed cell is directly suital Ibr mkrobore LC. Reproduced with permission from Bioanalytkal Systems Inc.. West Lafayette, Indiana.

The importance of knowing the exact value of the ohmic drop or uncompensated resistance in an electrochemical system has been pointed out by many workers. In studies of the kinetics of electrode processes by potentiostatic techniques, the ohmic potential drop produces a distortion of the steady state polarization curve which, if uncorrected, will yield erroneous values of the characteristic parameters (Tafel slope, reaction orders) of the electrode reactions (Fig. 6.2). 

When performing polarization measurements an error due to the ohmic drop over the uncompensated resistance will be included in the potential between the working and the reference electrode. The significance of this error is decided by the ratio between the value of the uncompensated resistance and the polarization resistance of the system. The uncompensated resistance can be minimized by careful design of the cell and the positioning of the electrodes. Several methods of instrumental compensation of the ohmic drop are available, of which the interrupt methods are the most versatile. Such methods are applied during the polarization measurements. 

It can be seen that cyclic voltammograms at low scan rate have peak-to-peak separations close to the value theoretically expected for a reversible process of A p = 2.218 X 7 r/ = 57 mV at 298 K [47] and the peak current increases with the square root of the scan rate. Under these conditions, the process is diffusion controlled and termed electrochemically reversible or Nernstian within the timescale applicable to the experiment under consideration. Hence, as with all reversible systems operating under thermodynamic rather than kinetic control, no information concerning the rate of electron transfer at the electrode surface or the mechanism of the process can be obtained from data obtained at slow scan rate. The increase of A p at faster scan rate may be indicative of the introduction of kinetic control on the shorter timescale now being applied (hence the rate constant could be calculated) or it may arise because of a small amount of uncompensated resistance. Considerable care is required to distinguish between these two possible origins of enhancement of A p. For example, repetition of the experiments in Table II.l.l at... 

Steady state SECM measurements are relatively immune to problems of uncompensated resistance and charging current, quantitative studies are therefore usually carried out under steady state conditions as long as the chemical nature of the system permits. The steady state theory is simpler than for transient techniques and several useftil analytical expressions suitable for least squares fitting of data are available. 

Cyclic voltammograms of quasi-reversible systems show more or less pronounced backward peaks [114]. The separation of anodic and cathodic (backward and forward) peak potentials, dEp, increases with decreasing values of the dimensionless parameter defined in Eq. (88a). Typical results are given in Table 3. This method for estimating k requires to minimize the uncompensated resistance, R. Extrapolation of the data in Table 3 leads to the conclusion that a totally irreversible... 

The cyclic voltammetric currents were normally not the main source of attention but rather the semi-integral Ij of the current was calculated from this the semi-differential or square root of time deconvolution dlj/dt. This dlj/dE were used for the clearest displays of results. The main difference in application of the latter pair depends on whether a potential ramp linear with time is applied at die working electrode surface i.e. hardware compensated at tte potentiostat if necessary for resistance between working counter electrodes. In this case using the linearly varying potential as an axis dlj/dt dl/dE are similar in shape either provides a suitable display. If uncompensated resistance remains then in Nernstian systems I is a function of the appropriate E (E ) suitable compensation via -i.R can be sqiplied post csqiture... 

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