Macroelectrodes and Microelectrodes

As already given in Chap. 1, the most frequently used form of the cathodic polarization curve equation for flat or large spherical electrode of massive metal is given by  

The electrochemical processes on microelectrodes in bulk solution can be under activation control at overpotentials which correspond to the limiting diffusion current density plateau of the macroelectrode. The cathodic limiting diffusion current density for steady-state spherical diffusion, /l,sphere is given by  

An electrode around which the hydrodynamic diffusion layer can be established, being considerably lower than dimensions of it, could be considered as a macroelectrode. An electrode, mainly spherical, whose diffusion layer is equal to the radius of it, satisfying 

Simultaneously, the cathodic current density on the spherical microelectrode, spher, is given by  

This means that the process on the microelectrode in the bulk solution can be under complete activation control at the same overpotential at which the same process on the macroelectrode is simultaneously under full diffusion control. 

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The different behavior of macroelectrodes and microelectrodes under the same conditions of electrodeposition causes the disperse deposit formation. 

Ammann, D., Pretsch, E., Simon, W., Lindner, E., Bezegh, A., Pungor, E., Lipophilic salts as membrane additives and their inflnence on the properties of macroelectrodes and microelectrodes based on neutral carriers. Ana/ Ghim Acta 1985, 171(May), 119-129. 

The microelectrode is a class of working electrodes that has increased in popularity since the 1980s and is used mainly by electroanalytical chemists. These electrodes have improved time resolution for electrochemical reactions, and can function in higher resistance solutions. Diffusion is treated as hemispherical as the electrode surface area is more like a point than a plane as is the case with macroelectrodes. Typically microelectrodes are difficult to construct and have cross sections on the order of 5 J,m. 

The current density on the tip of a protrusion, /tip, is determined by k, hence by the shape of the protrusion. If A —>- 0, y)ip — j (see (7)) and if k -> oo, jt p -> j0(fc - fa) > j. The electrochemical process on the tip of a sharp needle-like protrusion can be under pure activation control outside the diffusion layer of the macroelectrode. Inside it, the process on the tip of a protrusion is under mixed control, regardless it is under complete diffusion control on the flat part of the electrode for k -> 0. If k = 1, hence for hemispherical protrusion, y tip will be somewhat larger than j, but the kind of control will not be changed. It is important to note that the current density to the tip of hemispherical protrusion does not depend on the size of it if k = 1. This makes a substantional difference between spherical microelectrodes in bulk solution and microelectrodes inside diffusion layer of the macroelectrode.16 In the first case, the limiting diffusion current density depends strongly on the radius of the microelectrode. 

A mathematical model can be derived under the assumption that the electrochemical process on the microelectrodes inside the diffusion layer of a partially covered inert macroelectrode is under activation control, despite the overall rate being controlled by the diffusion layer of the macroelectrode. The process on the microelectrodes decreases the concentration of the electrochemically active ions on the surfaces of the microelectrodes inside the diffusion layer of the macroelectrode, and the zones of decreased concentration around them overlap, giving way to linear mass transfer to an effectively planar surface.15 Assuming that the surface concentration is the same on the total area of the electrode surface, under steady-state conditions, the current density on the whole electrode surface, j, is given by ... 

Dr. Archer conrmented that mass transport to spherical microelectrodes was much more efficient than semi-infinite linear diffusion to planar macroelectrodes, and asked whether this advantage was lost if the microparticles were embedded in a polymer matrix, as described in one part of Professor Bard s talk. Professor Bard replied that this was the case, and added that mass transport to and from, and within, polymer matrix films is now the limiting factor controlling reaction rates in such systems. It will probably be necessary to imitate photobiological systems in the use of ultra-thin membranes to avoid these mass-transport limitations. 

A simple electrochemical cell consists of a minimum of two elements in series, that is, a double-layer capacitance and an ionic resistance. The time constant of a cell is the product of capacitance and the resistance, and it represents the required timescale for building the double layer when polarizing an electrode. The time constant of a cell is very important because it determines the timescale over which an electrochemical process cannot be smdied. The double-layer capacitance is proportional to the surface area of the electrode, regardless of its dimensions. At a macroelectrode, the ionic resistance of the solution is proportional to the inverse of the area. As a result, the time constant is not dependent on the size of the electrode for flat macroelectrodes. At microelectrodes, the ionic resistance is proportional to the inverse of the electrode radius. Therefore, the time constant is proportional to the electrode radius for microelectrodes. In practice, it means that one is able to study faster reactions by decreasing the size of the microelectrode. 

From Macroelectrodes to Microelectrodes Theory and Electrode Properties... 

From Macroelectrodes to Microelectrodes Theory and Electrode Properties Table 15.4 Mass transfer coefficient for some microelectrodes of different geometry... 

Microelectrodes have attracted much attention recently in electrochemistry due to their superior properties, which enable them to outperform conventional macroelectrodes and extend the experimental range to several new fields, such as fast-scan measurements and analysis in poorly conducting media [1-4]. The history of microelectrodes actually started more than 60 years ago, when 1942, Davies and Brink [5] reported the use of platinum microdisk electrodes for the measurement of oxygen in muscle tissues. In their work, microelectrodes were used to minimize the damage to the muscle, and to limit the current flowing through the electrode. Since then, several reviews [6-8] and books [9,10] about microelectrodes have been published. 

Comparison experiments were performed using a bare platinum microelectrode, A Pt deposited diamond macroelectrode, and a bare Pt macroelectrode. The s/b values for each electrode taken for 1 mM H2O2 in 0.1 M PBS are summarized in Fig 18.9. 

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. 

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