THE POLARIZED CELL

5.2 THE POLARIZED CELL

Consider a cell made up of zinc in ZnSO 4 solution and copper in CuSO 4 solution (the Daniell cell), the electrodes of which are connected to a variable resistance R , voltmeter V , and ammeter A , as shown in Fig. 5.1 . The potential difference (emf) of zinc and copper electrodes of the cell without current fl ow is about 1 V. If a small current is allowed to fl ow through the external resistance, the measured potential difference falls below 1 V because both electrodes polarize. The voltage continues to fall as the current increases. On complete short - circuiting (very small external resistance), maximum current fl ows and the potential difference of copper and zinc electrodes becomes almost zero.

Figure 5.1. Polarized copper – zinc cell.

THE POL ARIZED CELL

Figure 5.2. Polarization diagram for

copper – zinc cell.

The effect of net current fl ow on voltage of the Daniell cell can be repre- sented by plotting a polarization diagram — that is, a graph showing potential, φ, of copper and zinc electrodes (as described in Section 5.3 , “ How Polarization Is Measured ” ) with total current, I , as shown in Fig. 5.2 . The thermodynamic poten- tials (no current fl ow through the cell) are given by φ Zn and φ Cu .

In Fig. 5.2 , the zinc electrode polarizes along curve abc , and the copper electrode polarizes along curve def . At a value of current through the ammeter equal to I 1 , the polarization of zinc in volts is given by the difference between the actual potential of zinc at b and the thermodynamic value a or φ Zn . Similarly, the polarization of copper is given by the difference of potential e – d . The

potential difference of the polarized electrodes, b – e , is equal to the current i 1 multiplied by the total resistance of both the external metallic resistance R m and the internal electrolytic resistance, R e , in series, or I 1 (R e m + R ). On short - circuiting, the current becomes maximum, I max . Then R m can be neglected, and the potential difference of both electrodes decreases to a minimum equal to max I e R . The maximum current is equivalent to (65.38/2) I max / F grams zinc corrod- ing per second, where I max is in amperes, F is equal to 96,500 C/eq, and 65.38/2 is the equivalent weight of zinc.

The cathodic reaction corresponds to the identical chemical equivalents of copper depositing per second on the cathode. The corrosion rate of zinc can exceed the indicated equivalent corrosion rate, I max , only if a method is introduced for reducing the polarization of zinc or copper, or both, thereby reducing the slopes of abc or def , causing an approach to intersection at a larger value of I . Similarly, any factor tending to increase polarization will decrease current through the cell and decrease the corresponding corrosion rate of zinc. Obviously, the polarization curves can never actually intersect, although they can approach each other very closely if anodes and cathodes are closely spaced in media of moderate

56 KINETICS: POL ARIZATION AND CORROSION R ATES

to good conductivity. There will always be a fi nite potential difference accompa- nying an observed fl ow of current.

Electrolytic cells that account for the corrosion of metals are analogous to the short - circuited cell. The measured potential of a corroding metal, the mixed potential of both polarized anodes and cathodes, is also referred to as the corro- sion potential, φ corr . The value, I max , is known as the corrosion current, I corr . By

Faraday ’ s law, the corrosion rate of anodic areas on a metal surface is propor- tional to I corr , and hence the corrosion rate per unit area can always be expressed as a current density. For zinc, a corrosion rate of 1 gmd is equivalent to 0.0342 A/

m 2 . For Fe corroding to Fe 2+ , the corresponding value is 0.0400 A/m 2 . Values for other metals are listed in the Appendix (Section 29.8.2 ). Referring to Fig. 5.2 , we can calculate the corrosion rate of a metal if data are available for the corrosion potential and for the polarization behavior and thermodynamic potential of either anode or cathode. In general, the relative anode – cathode area ratio for the corroding metal must also be known, since polarization data are usually obtained under conditions where the electrode surface is all anode or all cathode.