The Modern Student laboratory Using Electrochemical Principles
Determination of Ionic Mobilities by Thin-Layer Electrodeposition Alexander Kuhn and Franqoise Argoul Centre de Recherche Paul Pascal, Avenue Schweitzer, F-33600 Pessac Thin-layer electrodeposition of metals has been fascinating the scientific community for the last decade from an aesthetic point of view (1, 2) a s well a s under more theoretical aspects because of their sometimes fractal character. Some authors studied the variation of the morphology (3-7) and found that it depends strongly on the kind and the concentration of the metal salt, the applied voltage, the purity of the solution, and the geometry of the cell. The dynamical evolution of the growth in space and time has been examined by several groups (8-10 and references therein) and finally a n innumerable quantity of simulations have been undertaken in order to compare the experimental results with theoretical predictions (11,12). Our goal here is quite different. We use the results of a recent publication, describing the high sensitivity of the electmde~ositionorocess toward "imnurities" like oween .., or alkali s;llt.i ,7,, to dcvelop a new method for the dc~crmination ofionic rnobilit~es.This determination is uoss~ble.bemuse the alkali cations generate a well-defined morpholdgical transition of the deposit. A great advantage of the measurement described below is the simple experimental set-up, that allows its demonstration, for instance in the framework of the student's practical training in ionic conductivity. ~
~~~
Theoretical Considerations The deposit resulting from the experiment is generated by the cathodic reduction of a metal salt M"+ +n e- + M
The transport of the cations is essentially done by migration because of a relatively high electric field. The depletion of the neighborhood of the cathode in metal ions causes an instability of the electrode and quasi two-dimensional structures invade the thin layer in direction to the anode. The experiment can be done with any metal, whose morphology is
sensitive to interfacial perturbations. In the following, however, we will consider zinc as the ideal system, because the effect of impurities is here the most evident. In the case of pure zinc salt solutions, the generic structure, observed over a wide range of concentration and current density is dendritic like in Figure la. However, when adding wellknown quantities of alkali salts to the electrolyte, more disordered structures are obtained. This continuous transition from ordered to amorphous structures, partially shown in Figure 1, occurs because the impurities, also migrating under the influence of the electric field, destroy the crystal lattice of the metal. This effect can be used to generate deposits that are growing with a quite smooth front, as shown in Figure Ic. The maximum growth speed is determined by the migration velocity of the anions, as has been proposed by Flenry et al. (131,because the deposit follows the anion front, migrating toward the anode, in order to avoid the formation of a too large space charge region V h
=P
hE
= Udepos,t
(1)
where u h is the migration velocity, p h the anionic mobility, and E the electric field. The zinc ions are regenerated a t the zinc anode a t the same rate that they are consumed by the deposition on the outgrowing cathode; whereas, intentionally added alkali ions cannot be renewed during the experiment. This means that their concentration, which a t the beginning is equal everywhere in the cell, starts to decrease from the anode. This region of low alkali concentration invades the cell in direction to the cathode with the migration speed of the alkali cations: ~AI=VAIE
(2)
As a consequence, the growth meets a t some characteristic distance 1, from the initial cathode a region containing no more alkali ions and a transition from the former disordered
Figure 1. Evolution of the morphology with Increasing sodium content of the electrolyte. (0.1 M ZnSOa solution, L = 2 crn, W = 5 cm, d = 0.25 rnm, j = 60 m~crn-2)(a)Withoutsodium. (b) 1.25 x lo4 M Na2S04, and (c) 1.25 x 104M NazS04. Volume 71
Number 11 November 1994
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The Modern Student laboratory This length scales with the total distance between cathode and anode, in other words, the transition always takes place a t the s a k e percentage of the whole length orthe cell for a given alkali ion, whatever the current density j. I t is, therefore, possible, knowing the mobility of the anion, to estimate the absolute mobility of a n unknown cation from the position of the morphological transition. The higher the initial distance between anode and cathode, the more accurate the measurement.
L Figure 2. Schematic representation of the electrochemical reactor. The top drawing represents the frontview, the bottom drawing shows the longitudinal section. C and A denote the position of the cathode and the anode, W the width of the cell, L the distance between the electrodes and d the depth of the cell. The two glass plates are fixed together with an inert thermoplastic polymer (hot glue). structure to a more dendritic morphology occurs. I t can be shown easily by a strai~htfonvardcalculation that the chararterist~fd&tance /:,r~~fi~rtmcsd tu the total distance bctween anode and cathode, is Oven by the following equation:
Experfmental Procedure The simplest electrochemical cell, well adapted to study morphological changes in electrodeposition experiments even on a n overhead oroiector. is shown in Firmre 2. I t is prepared in the followiigway. G o 0.25-mm diameter zinc wires with a l e n d h of 5 cm are saueezed between two thick glass plates. 6 e y are separated' by 2 cm, playing simultaneously the role of spacers and the role of cathode and anode. The glass plates and the electrodes are fxed together with an inert thermoplastic polymer (hot glue). The resulting volume is filled with the electrolyte with the help of a syringe. The experiment is done under galvanostatic conditions with a current density j of 20 mAcm', which means in this geometry, that a constant current of 2.5 mAis applied. I n the example shown in Figure 3 a, b, and c, 10 mL of a 0.05 M aqueous solution of ZnS04 have been mixed with 0.06 mL of 0.05 M alkali salt solutions, Li2S04,Na2SO&and &SO4, respectively. Prior to use, the mixture has been purified by bubbling nitrogen through for one hour, in order to eliminate molecular oxygen that could otherwise perturb the growth. Results The addition of such a small quantity (2.5 x 104mol) of either Li2S04,K2S04,or Na2S04 causes highly disordered structures, a t least a t a macroscopic scale. The points of transition, visible in Figure 3, are 65%, 56% and 45% for lithium, sodium, and potassium, respectively. Given ~ , & 3 lo4 cm2V-I s d we can estimate the corresponding mobilities from eq. 3. The experimental values are too high compared to the theoretical mohilities of standard tables a s can be seen from the table. This is due to the fact that we have used the anionic mobility a t infinite dilution to calculate them. However, taking into account that the anionic mobility is much lower a t finite concentrations, reasonable values of the cationic mohilities can be obtained: a rough approximation of pso, = 6 x 104 em2 V-I s-' for a 0.03 M solution can be calculated from the Debye-Huckel-Onalthoueh it is onlv saeer theorv (14). " rieorous a t verv low cmcentriltions I< 0.01 .\I,. The cationic mobilities, estimated this way, arc g v c n in the last ]in(: of the tnble. Working at a constant current, the transition also should be \.lslble in the evolution of the ccll potential. Figure 4 shours a record of the applied potentlal fnr thc thrcc experiments with lithium, sodium, and potassium. In a first stare the potential is dc:creasin~continuously, be. cause t h i deposit approaches the anobe, but a t themoment of the transition the voltage goes up due to a change in the reduction mechanism and the selection of some dendrites. The value of the E-field is known from the actual voltage and the cathode-anode distance and can be considered a s constant in a first approximation during the whole experiment. Taking the time delay of the reversion point in the potential curve together with the absolute distance
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Journal of Chemical Education
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Using Electrochemical Principles
Figure 3. Morphological transitions due to vanishing alkali ion concentration (0.05 M &SO4 solution, L = 2 cm, W = 5 cm, d = 0.25 mm, j = 20 m~cm-2)(a)2.5 x lo4 M Li,S04, (b) 2.5 x lo4 M Na2S04,and (c)2.5 x lo4 M K2S04
where the transition takes place, one can estimate the velocities uAl and u h . This offers another way to calculate the mobility of the "impurity" and of the anion by solving eq 2 and eq 1,respectively. We should emphasize here that the described experiment works for every kind of cation that is able to disturb the electrocrystallization of zinc or any other depositing metal sufficiently even a t low concentration. A great ad-
vantage of this determination is the simple experimental set-up. Needing only two glass plates, a piece of zinc wire, a constant current source and nonhazardous chemicals makes it a suitable student demonstration. A growth experiment with the above described geometry and current density takes about 15 min and is, therefore, a fast and low-cost possibility to get a rough idea of the cationic mobilities.
Volume 71
Number 11 November 1994
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The Modern Student loboratory Using Electrochemical Principles
time [s] Figure 4. Temporal evolution of the voltage (anodeversus cathode)for the three experiments shown in Figure 3.
Comparison of Standard Table Values for the Cationic Mobilities to the Results of the Described Method
Mobility cm2 V' s-' of
Li
Na
K
lo4 lo4
Theoretical Value
4.0 x 104
5.2 x 10"
7.6 x
Experimental value
4.3 x 104
6.2 x 10"
9.7 x
Experimental Value
3.2 x 10"
4.7 x 10"
7.3 x 10"
PA,,= 8 x 10-4
llnn=6x104
Acknowledgment We are very grateful to A. Arneodo and J. F. Muzy for stimulating discussions. This work has been supported by the Centre National des Etudes S ~ a t i a l e sunder contract No. 92lCNES!0225, NATO under &ant RGNo. 900685 and the DRET under m a n t No. 891196. The work of A. Kuhn was supported h y 5 ~ under c contract S!SC1*!915114 Literature Cited 1. Lieon. W.V.J Cham. Educ. 1987.61.1053. 2. siiveman, L. E J. c k m . E ~ Z C399%. . 68, 929. 3. G"er, D.: BenJamb, R.: Clarke. R.:Sander. L. M.Phvs. RPUL 4 t 1986.66.1264. 4. Sawads,Y.:Dough&% A,; Gollub, J. PPhrs. Re". ki.1986.56, 1260.
5. nlgueros, P. P;Claret, J.; Mas, F; Sagues, F. J Eledroonnl. Chem. 1991,312,219.
W.Y.:Chae..I..I.PhvaiolReuisulA l(*J1.45.4528 6. Tam. ~ ~ ~ ~
