W. H. Reinrnuth Columbia University New York City
Three-Dimensional Representation of Electrodeposition
Three-dimensional models have been used successfully to illustrate the principles of electrometric and voltammetric proce~ses.'.~Their value as teaching aids lies in the fact that they present the relationships between parameters of interest in a graphical rather than in an algebraic form. This seems to lead to easier assimilation by the student. Moreover, several techniques can often he represented using the same model. Thus the common basis of the techniques and their differences become immediately apparent. These factors make the graphical approach particularly advantageous in the discussion of electrodeposition. Some instructors in instrumental analysis follow the historical development of the field and present electrodeposition very early in the discussion of electrochemical methods. However, in our experience, the student is in a much better position to appreciate the subtleties of the methods after he has been exposed to polarography. REILLEY, C. N., COOICE, W. D., AND FURMAN, N. H., Anal. C h m . , 23, 1226 (1951). REINMUTH, W. H., Anal. Chem., 32, 1509 (1960).
The discussion begins with the observation that the conditions prevailing in a cell during electrolysis are similar at, any time to those in a polarographic cell. In stirred solution, the relation between deposition current and electrode potential is the same as in the polarographic one. For reversible deposition, this takes the form
where E is the electrode potential measured with respect to an unpolarized reference potential; En' is the formal standard potential for the couple; i,, the limiting current controlled by the rate of mass transfer; i, the current at potential E; n, the number of electrons involved in the reduction; 0, the mass transfer coefficient dependent on the rate of stirring, cell and electrode geometries, diffusion coefficient of the reducible species, and the like; R, T, and F have their usual thermodynamic significance. The difference between the polarographic and deposition processes lies in the fact that in the latter case
Volume 38, Number
3, March 196 1 / 149
the currents are large enough to change the concentration of metal ion in solution. The current-potential relationship therefore changes with time and instead of a two-dimensional line becomes a three-dimensional surface of the type depicted in Figure 1. As the concentration of metal ion in solution decreases so also does the limiting current plateau. The decomposition potential (potential at which current is zero) simultaneously shifts to more cathodic values. The system during deposition can be represented by a point constrained to move on the surface of Figure 1. For purposes of discussion it is helpful to inclcde the plane ABC in the figure. This plane represents the onset of a second electrode process such as plating of a second metal or decomposition of the solvent.
A
Figure 2. 8,
B
C
Models of vorious types of deposition: A, constant currenb C, pote,,,i.~.
general, however, it is difficult to avoid the second reaction and still have the first proceed a t a reasonable rate. This is the major disadvantage of the constant current method. Constant voltage electrolysis. At this point it is necessary to divide the total voltage applied to the cell into its component parts. Part of the applied voltage is opposed by the back-electromotive force a t the electrodes, the remainder by the ohmic potential drop due to the passage of current through the resistance represented by the cell plus external circuitry, that is, V=E-iR
P>TsrlTIPL
Figure 1 . Current-potential-conceefr(~tion surface for deposllion of insoluble metal obeying the Nernrt equation (units of axes arbitrary).
In principle, the system can be forced to move over the surface in any random fashion. In practice, however, it is fruitful to consider three simple possibilities: electrolysis a t constant current, constant applied voltage, and constant electrode potential. The tendency in texts has been to suggest only two possibilities: "constant current" and constant potential. Unfortunately, the case often termed constant current is in fact generally the case of constant applied voltage. Comtant current electrolysis. As the name implies, the current is invariant with time. The technique can be represented by the intersection of the system surface with a plane parallel to the base (zero current) plane. Figure 2a depicts the situation. The system moves along the intersection between plane and surface. At some point during the electrolysis the potential becomes sufficiently cathodic that the second electrode process can occur. From this point on an increasing fraction of the current is devoted to the second process. In the particular case represented in Figure 2a the second process begins when deposition is only fifty per cent complete (at point X). If this is undesirable, the situation can be alleviated in several ways: one of these is to increase the rate of mass transfer to the electrode by more vigorous stirring; a second is to decrease the current; a third is to increase the electrode area. All of these procedures in effect bring the intersecting plane closer to the zero current plane. I n 150
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Journal o f Chemical Educafion
where V is the applied voltage, E the electrode potential, and i, the current. When the current is zero, the potential is equal to the applied voltage. However as the current increases, the cell potential becomes less cathodic. If the voltage be held constant, the electrolysis process can be represented by the intersection of the system surface with a slanted plane. The intersection of the plane with the zero current plane is on the line V = E and its slope is the resistance of the circuit. There are two sub-cases, one in which the applied voltage is greater than the potential required for the second electrode process and the other in which it is less. The former case is depicted in Figure 26, and the behavior of the system is seen to be qualitatively similar to that at constant current. I n the latter case, the second reaction does not occur but this advantage is achieved a t the cost of diminished current a t any time and hence longer time for complete electrolysis. Constant potential electrolysis. If the cathode potential is maintained a t a constant value, the process is represented by the intersection of the system surface with a plane parallel to the zero potential plane, as in Figure 2c. Under these conditions the deposition process reaches maximum efficiency. Firstly, the reaction occurs a t its maximum rate, i.e., the system point is always on the limiting current plateau. Secondly, the potential can be maintained a t a low enough value that the second reaction cannot occur. This efficiency is achieved only a t the cost of complicated instrumentation or continuous manual adjustment of the applied potential. It should be pointed out that these possibilities are the ideal ones. I n actual electrolyses there are many complicating factors: the anode potential, cell resistance, activity coefficients, and the like may change with time; the apparatus may not give constant potential, voltage or current. However, with the simplest possibilities and their interrelations firmly in mind, the student is in a position to appreciate the effects of the complications.
