Macroelectrodes

In all actual electrochemical converters, the electrodes are three-dimensional, porous structures, the pores of which contain the catalyst material to and from which electric charge transfer occurs.14 

The electrodic catalyst consists of active nanoparticles. The distribution of the active material on the surface inside the pores is very 

Mass transfer in a porous structure strongly depends on macro-geometric parameters, but the electrochemical properties of the surface of the solid phase depend on the mutual relation of the active particles on it, being independent of the macrogeometry of the system. 

In spite of some specific characteristics of nanoparticles, this can also be treated as the case of an inert substrate modified with active grains in general. Naturally, for the sake of simplicity, this analysis can be performed for planar electrodes. 

According to Scharifker and Hills,15 in systems where the charge transfer is fast, the rates of growth of nuclei are well described in terms of control by mass transfer of the electrodepositing ions to the growth centers. 

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The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

FIGURE 4-29 Cottrell plot of the chronoamperometric response for 1 x 1(T3M Ru(NH3)63 + at a Kel-F/gold composite electrode. Points are experimental data, the solid line is the least-squares fit to theory. Dashed lines are theoretical Cottrell plots for a macroelectrode with active area equal to the active area of the composite (curve a) and to the geometric area of the composite (curve b). (Reproduced with permission from reference 87.)... 

Sonovoltametric measurement of the rates of electrode processes with fast coupled homogeneous kinetics making macroelectrodes behave like microelectrodes Compton RG, Marken F, Rebbitt TO (1996) Chem Commun 1017-1018... 

Preparation and Electrochemical Behavior of Macroelectrodes Modified with Polv(I). The electrochemical behavior of 2 was investigated in CH3CN/0.I 1 [11-BU4N]PF via cyclic voltammetry at a Pt electrode. 

Electrochemistry at electrodes with microscopic dimensions (e.g., a disk of 10 j,m diameter) and nanoscopic dimensions (e.g., a disk of <100 nm diameter) constitutes one of the most important frontiers in modern electrochemical science [25]. Such micro- and nanoscopic electrodes allow for electrochemical experiments that are impossible at electrodes of macroscopic dimensions (e.g., disks of mm diameter we call such electrodes macroelectrodes ). Examples of unique opportunities afforded by micro- and nanoscopic electrodes include the possibility of doing electrochemistry in highly resistive media and the possibility of investigating the kinetics of redox processes that are too fast to study at electrodes of conventional dimensions (both are discussed in detail below). In addition, microscopic electrodes have proven extremely useful for in vivo electrochemistry [62]. 

In order to explore the effects of small electrode size, we have used the template method to prepare ensembles of disk-shaped nanoelectrodes with diameters as small as 10 nm. We have shown that these nanoelectrode ensembles (NEEs) demonstrate dramatically lower electroanalytical detection limits compared to analogous macroelectrodes. The experimental methods used to prepare these ensembles and some recent results are reviewed below. 

FIG. 7. Simulated (dotted curves) and experimental (solid curves) voltammograms at 100 mV s at a lONEE (0.079 cm geometric area) in 5 pM TMAFc+ and 0.5 mM sodium nitrate. Simulation assumes the total overlap limiting case (i.e., a macroelectrode with area = 0.079 cm ). 

So far we have discussed only the reversible case. The equivalence of the net Faradaic current at the NEE and at a macroelectrode of the same geometric area (Fig. 7) means that the flux at the individual elements of the NEE are many orders of magnitude larger than the flux at the macroelectrode. Indeed, the experimentally determined fractional electrode areas (Table 1) indicate that, for the reversible case, the flux at the elements of a... 

The simplest way to think about this situation is that for any redox couple, the quasireversible case can be observed at a NEE at much lower scan rates than at a macroelectrode. Indeed, because flux is related to the square root of scan rate, the 10 -fold enhancement in flux at the lONEE means that one would have to scan a macroelectrode at a scan rate 10 times higher in order to obtain the same kinetic information obtainable at the NEE. That is, if for a particular redox couple one observed quasireversible voltammetry at the lONEE at scan rates above 1 V s , one would have to scan at rates above 10 V s to achieve the quasireversible case for this couple at a macroelectrode. This ability to obtain kinetic information at dramatically lower scan rates is an important advantage of a NEE. 

AEpij 59 mV) at the lowest scan rates shown, but the voltammograms become quasireversible at scan rates above 0.01 V s . Therefore, as expected, the transition to quasireversible behavior is observed at dramatically lower scan rates at the 30NEE than would be observed at a macroelectrode. It is again important to emphasize that the increase in AEp observed is not due to uncompensated solution resistance [25]. 

Voltammograms for various low concentrations of TMAFc at a lONEE are shown in Fig. 9B. While the voltammograms look nearly identical to those obtained at the macroelectrode, the concentrations are 3 orders of magnitude lower. Using the same criterion for the detection limit, we obtain a detection limit at the lONEE that is 3 orders of magnitude lower (1.6 nM) than at the macroelectrode. This experimentally observed enhancement in detection limit at the NEE is exactly as would be predicted from the fractional electrode area data in Table 1. 

Cyclic voltammetry is generally considered to be of limited use in ultratrace electrochemical analysis. This is because the high double layercharging currents observed at a macroelectrode make the signal-to-back-ground ratio low. The voltammograms in Eig. 9B clearly show that at the NEEs, cyclic voltammetry can be a very powerful electroanalytical technique. There is, however, a caveat. Because the NEEs are more sensitive to electron transfer kinetics, the enhancement in detection limit that is, in principle, possible could be lost for couples with low values of the heterogeneous rate constant. This is because one effect of slow electron transfer kinetics at the NEE is to lower the measured Faradaic currents (e.g.. Fig. 8). 

We have demonstrated a new method for preparing electrodes with nano-scopic dimensions. We have used this method to prepare nanoelectrode ensembles with individual electrode element diameters as small as 10 nm. This method is simple, inexpensive, and highly reproducible. The reproducibility of this approach for preparing nanoelectrodes is illustrated by the fact that NEEs given to other groups yielded the same general electrochemical results as obtained in our laboratory [84]. These NEEs display cyclic voltammetric detection limits that are as much as 3 orders of magnitude lower than the detection limits achievable at a conventional macroelectrode. 

Here the construction of macroelectrodes and the possibility of replacing the internal ISE solution by a metallic contact will be discussed. The principal requirement is that the membrane completely separates the test solution from the electrode interior, because otherwise irregular deviations from the calibration dependence occur. 

Macroelectrodes with solid membranes contain homogeneous [142] or heterogeneous [25] membranes. The construction of an ISE of this type with an internal reference electrode is shown in fig. 4.1. For good functioning of an ISE it is necessary that the membrane be completely sealed in the electrode body, with no cracks leading to short-circuiting between the external and internal solutions. Cements based on Teflon, PVC or epoxy resin are used (170). 

Liquid-membrane macroelectrodes come in two completely different versions. The older type, no longer extensively used, contains a porous... 

The simplest measurement of the response time of macroelectrodes involves the determination of the time elapsed from the transfer of the ISE from the solution in which it was stored into the test solution. Data obtained in this way are only significant for response times of at least tens of seconds. For short response times, flow-through [44, 131] or injection [92] methods are suitable. For microelectrodes, a rapid immersion method [181], a flow-through [166] or an iontophoretic method [97] have given good results. In the last method... 

The most important application of the valinomycin macroelectrode is for the determination of potassium in serum [9, 126,141,174] and in whole blood [45, 71, 224]. This electrode with a polymeric membrane is a component of most automatic instruments for analysis of electrolytes in the serum. It has also been used for monitoring the K level during heart surgery [168]. The valinomycin ISE is also useful for determination of Rb [33]. 

The principles underlying the diffusion of molecules to a microelectrode are identical to those described earlier in this book for diffusion to macroelectrodes. A reaction occurring at the surface of the electrode produces a concentration gradient in solution in the vicinity of the electrode, which in turn gives rise to a diffusional flux. The diffusionally induced rate of change of concentration in solution is described, in general, by Fick s second law ... 

With macroelectrodes, the duration of an experiment in stationary solutions is determined by the onset of distortion due to solution convection. Even in... 

D. Transition from Microelectrode to Macroelectrode Diffusion Regimes... 

There are four general responses to the problem of solution resistance. First, if only qualitative information is sought in the experiment, a certain amount of iR error can be tolerated, perhaps 100 mV. Second, electronic compensation of solution resistance can be applied, and this is often quite successful and will allow accurate data to be obtained even with macroelectrodes. Nevertheless, problems of potentiostat stability and signal distortion must be addressed. 

There are other advantages of microelectrodes as compared to the macroelectrodes. Because the current is small, on the order of nA to pA, the voltage drop due to the electrical resistance of the medium is negligible. For this reason, it is possible to perform electrochemical experiments in media that would be otherwise unsuitable for macroelectrodes, such as resistive hydrocarbon solvents and solid electrolytes, without a potentiostat. Secondly, the double-layer capacitance is very small because the area of the electrode is small. This means that very fast modulation experiments... 

In Fig. 2.10, the boundary between the enzyme-containing layer and the transducer has been considered as having either a zero or a finite flux of chemical species. In this respect, amperometric enzyme sensors, which have a finite flux boundary, stand apart from other types of chemical enzymatic sensors. Although the enzyme kinetics are described by the same Michaelis-Menten scheme and by the same set of partial differential equations, the boundary and the initial conditions are different if one or more of the participating species can cross the enzyme layer/transducer boundary. Otherwise, the general diffusion-reaction equations apply to every species in the same manner as discussed in Section 2.3.1. Many amperometric enzyme sensors in the past have been built by adding an enzyme layer to a macroelectrode. However, the microelectrode geometry is preferable because such biosensors reach steady-state operation. 

The demand for reliability of the analyses, a long-life of the electrodes and their readiness to be used any time (for so-called Stat samples) directly dictated the design of ISSs/GSSs. Instead of macroelectrodes, a large variety of microelectrodes have been developed [26]. 

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