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2-4-4 Microelectrodes

Electrodes of micrometer dimensions were little used in electrochemical research before 1980, but interest in them has increased exponentially during the past decade. A microelectrode may be defined as an electrode with properties that depend on its size, typically with dimensions comparable to the thickness of the diffusion layer [53].

2-4-4-1 Characteristic features

Owing to its micrometer size, the edge effect of a microelectrode become significant, even at a planar surface. Fig 2-4-9 schematically describes diffusion fluxes to microelectrodes. The diffusion flux at a microelectrode is convergent to the surface of electrode, so that compared with the equation {2-4-7} for a large and effectively infinite planar electrode, Fick's second law for a microelectrode becomes

1dCj

- {2-4-16}

where r is the distance from the centre of the electrode in the plane of its surface, and z is the perpendicular distance from the electrode surface. As the result of reduction in size of an electrode, three major consequences arise: (1) mass transport rates to and from the electrode are increased because of nonplanar diffusion; (2) the double-layer capacitance is reduced due to the reduction in surface area; and (3) ohmic drop, which is the product of electrode current and solution resistance, is reduced due to the diminished current. These properties provide a starting point for the application of microelectrodes to electrode kinetics, electroanalytical chemistry and others. The following is going to focus on the third characteristic of the microelectrode which makes it possible to carry out electrochemical studies in highly resistive media .

\ I /

a b c d

Fig 2-4-9 Convergent flux to small sphere (a), disk (b), ring (c) and band (d) electrodes. Top: side view; bottom: plane view of the microelectrodes.

2-4-4-2 ÎR drop at a microelectrode

The electrical resistance of a microelectrode system includes two contributions: the resistance of the body of a microelectrode itself (R^) and the resistance in solution between the microelectrode tip and a secondary electrode (Rg). In general Rg is greater than Rjn- One can calculate Rg from the (specific) conductivity of the electrolyte, K . For

a microscopic hemispherical electrode, the contribution to the resistance dRg by an element of area 47Cr^ and thickness dr is given by

If the second electrode is placed at a large and effectively infinite distance from the microelectrode, the resistance Rg is obtained by integration between r^ and œ

R s = j 2 = — {2-4-18}

•''■o

27VKr iTcicr.

Although the resistance Rg is undoubtedly high and increases as the radius of the microelectrode is made smaller, the value of Rg per unit area of electroactive surface is low and lowers with decreasing radius of the microelectrode, as shown in Table 2-4-1 which presents the values of Rg and the products of Rg and the geometric surface area A for Pt electrodes with various radii immersed in 0.1 M KNO3 solution.

In a conventional three-electrode cell, the electrical contact between working electrode and reference electrode is often made through a Luggin capillary so as to reduce the effects of electrolyte resistance on the controlled potential. In order to eliminate the solution resistance, the tip of the Luggin capillary is better close to the working electrode. For practical reasons and to avoid deformation of the electric field near the working electrode, however, the tip of the Luggin capillary is nevertheless at a significant distance from the electrode. Thus an uncompensated resistance is present which introduces an error into the value of the controlled potential, proportional to the current passing through the call. This is called iR drop and usually needs compensating

through the electronic circuit [34, 53]. By contrast, the use of microelectrodes can make iR drop negligible. Table 2-4-1 presents an example. Since iR drop can be neglected, it is possible to use a two-electrode cell based on a microelectrode but without the interferences of iR drop on the potential of the micro-working electrode. In this type of two electrode cell, the second electrode (i.e. counter electrode) usually has a much larger area so that the current density passing through it can reduce further. As a result, the electrode maintains at equilibrium with the electrolytic solution, acting like a reference electrode in a three electrode cell. This is the basis of studying the electrochemistry of organic solvents alone without deliberately addition of a supporting electrolyte by using a microelectrode in a two-electrode cell.

Table 2-4-1 Resistance of Hemispherical Pt microelectrodes immersed in aqueous 0.1 M ICNO3 solution (quoted from [53]).

to (flm) Rg (kD)^ 103rA (ncm2)C - - 6.90'’ 50 0.135 2.20 0.345 25 0.542 4.39 0.172 10 339 11.0 0.0690 5 13.5 223 0.0345 1 339 110 0.00692

® Microwire of length 1 cm, with Opj = 9.4 X 10"^ cm’k I* For hemisphere, with k ~ 0,0145 cm'k

^ Product of R and geometric surface area.

Planar electrode with Luggin tip 1 mm from the surface.

2-5 B attery studies

2-5-1 Basic concepts

A battery is a device which can store chemical energy and, on demand, convert it into electrical energy to drive an external circuit [54]. The transformation between chemical energy and electrical energy follows the equation {2-1-1}. A battery consists of a single cell or several cells which are connected in parallel or series [55]. The basic elements of a cell which can act as a power source are shown in Fig 2-5-1. As indicated above, oxidation occurs at the anode and reduction at cathode. In a battery as opposed to an electrolysis cell, the anode is the negative electrode and the cathode the positive electrode because the former releases electrons (by oxidation), while the latter collects electrons from the external circuit (by reduction). The charging process is just opposite to the above.

e

anode load + cathode

. • ■ • electrolyte •

R'-ne G . . .solution . . O-H ne -^ R Fig 2-5-1 A schematic cell and electrode reactions at cathode and anode, respectively.

2-5-2 Battery characteristics; cell voltage, capacity, energy density and discharge rate

The energy stored in a battery is often measured by discharging the battery at an given current. The energy in Watt-hour (Wh) is the product of average operating voltage in volt (V) and discharge capacity in ampere-hour (Ah). Thus the major characteristics of a battery are cell voltage (intensive quantity) and cell capacity (extensive quantity).

Cell voltage is equal to the potential difference between the two electrodes and conventionally this is taken as the potential of the positive electrode minus the potential of the negative electrode