J. Phys. Chem. 1993,97, 4871-4876
4871
Oscillations and Pattern Formation during Electrodeposition of Lead Metal in Batch and Flow Reactors R. P. Rastogi Central Drug Research Institute, Lucknow 226 003, India
Ishwar Das,’ Anal Pushkama, and Sudha Chand Department of Chemistry, University of Gorakhpur, Gorakhpur 273009, India Received: September 8, 1992; In Final Form: January 13, 1993
Cathode potential changes with time during the process of electrodeposition of lead metal from its aqueous solutions in batch reactor as well as in a continuously stirred tank reactor (CSTR) have been reported. Growth kinetics at constant current/potential has been studied for correlation. Influence of electrolyte concentration, applied current and certain polymer additives on morphologies, and oscillatory characteristics have been investigated.
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Introduction In recent years, there has been a tremendous increase in the number of experimental and theoretical studies of oscillations and spatial pattern formation. The study of morphological stability of growing bodies, crystal growth, development of chemical waves, and rhythmic crystallization in gel media offers the possibility for investigating nonequilibrium structures in physicochemicaland biologicalsystems.’ Oscillationsoccur only when the system is far away from thermodynamic equilibrium achieved by imposing some sort of external force, such as concentration gradient, electrical field, imposed light, and others. Many examplesof biochemical and cellular oscillationsare known and have been extensively studied. Systematicstudieson sustained potential oscillations in an artificial membrane were carried out by Teorell,2 who discussed the possible physicochemical model for the action potential in neurons. One can explore a wide variety of morphologies during electrochemical deposition’-l2 by varying the concentration of metal ions, the conductivity of the electrolyte, and the applied constant current or voltage. Suter and WonglO exhibited periodic oscillations during electrochemical growth of zinc dendrites. Oscillations were observed due to the side branching nature of dendrites. In most of the measurements oscillationswere coherent over many cycles. Argoul et al.I3have reported on spatiotemporal chaos in diffusionlimited growth phenomena. They have explored a wide variety of morphologies, namely dendritic, hybrid DLA, and DLA-like fractal patterns during electrodeposition of zinc metal. Fleury et al.I4 proposed a model of fluid flow for the electric field and for the concentration map around the branches during electrodeposition. According to them, the morphology of deposit depends on the current density J . A forestlike deposit grows on the cathode for J > j , 1 mA/cm2. The ‘trees” look tortuous and “fractal” for J < 40 mA/cm2 and look parallel and vertical for J > 40 mA/cm2. In the present paper, new results on the morphology and cathode potential changes during electrochemical deposition under different experimental conditions in a batch reactor as well as in CSTR have been reported.
Experimental Section Materials. Lead acetate (AR, BDH),agar-agar (S.Merck), and poly(viny1 alcohol) (LR, Appex) were used as such without purification. To whom all correspondence should be addressed.
0022-3654/93/2091-487 1$04.00/0
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Figure 1. Experimental setup of a batch reactor to monitor potential changes during electrochemical deposition of lead metal.
Procedure. The experimental setup of a batch reactor shown in Figure 1 was employed to monitor the potential changes at the cathode during electrochemical deposition of lead metal at an air-water interface. The experiment was conducted in a porcelain dish containing 45 mL of solution. A microslide was put in the dish containing solution of lead acetate in such a manner that smallvolumeof the solution was just above the slide. Two identical platinum electrodes PI, P2 were inserted in the solution 50 mm apart. The anode was extended below the surface of the solution and attached to the side of the dish while the lower end of the cathode was put at the surface of the solution as shown in Figure 1. During the experiment, the current was maintained constant with the help of a potential divider, a milliammeter, and a galvanometer. A calomel electrode was inserted in the solution and attached with a digital multimeter. Potential changesduring electrochemicaldeposition of lead metal was monitored with the help of platinum electrode coupled with a calomel electrode (C). The entire assembly was kept in a thermostat which was maintained at constant temperature accurately to k0.1 OC.A typical microphotograph of electrodeposited lead metal is shown in Figure 2. All experiments were performed three times and typical results are shown here. Potential changes during the electrodeposition of l q d metal at various electrolvte concentrations and amlied current were noted as a functiod of time. Results are sh&n in Figures 3 and 4. Variation of conductancewith time was also monitored during the electrodeposition. Results are shown in Figure 5. Influence of Certain Polymers on Cathode Potential, Morphology, and Growth Velocity. Influence of certain polymer 0 1993 American Chemical Society
4872 The Journal of Physical Chemistry, Vol. 97, No. 18, 1993
.Rastogi et al.
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Figure 3. Qualitative behavior of potential oscillations during electrochemical deposition of lead. Conditions: Applied current across the electrodes = 4.0 mA; [lead acetate] = 0.1 M (a), 0.5 M (b), 1.0 M (c), and saturated solution (d).
additives such as agar-agar and poly(viny1 alcohol) (PVA) on cathode potential during electrochemical deposition and growth behavior have been studied. Influence of polymer materials on the growth behavior during electrochemical deposition is clearly indicated in Figure 6, whereas Figure 7 shows the changes in cathode potential with time during the process of electrochemical deposition. To study the growth rate of electrodepositedlead metal leaves, we have used a different experimental setup as shown in Figure 8. Two platinum electrodeswere placed horizontally. At constant applied current, length of the metal leaves at varioustime intervals was noted with the help of a traveling microscope. Results are
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Figure 5. Variation of conductance with time during the process of electrochemical deposition: [lead acetate] = 1.0 M; applied current = 4.0 mA (a), 8.0 mA (b), and 10.0 mA (c).
shown in Figures 9 and 10. The experiment was also performed at constant potential and varying the other experimental conditions. ElectrocbemicalDeposition Experimentsin a CSTR. In a batch reactor, the concentration of the solution may decrease continuously during electrochemical deposition. As the electrodesurface is continuously growing, it may not allow enough time for the
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 4873
Pattern Formation during Electrodeposition
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Figure 7. Influence of polymer additives on potential changes during electrochemicaldeposition process when (a) aqueous lead acetate (1 M), (b) lead acetate (1 M) containing 0.022%PVA, (c) lead acetate (1 M) containing 0.022%agar-agar were used at 35.0 f 0.1 O C ; appliedcurrent = 8.0 mA.
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Figure 6. Growth behavior of electrochemical deposited metal cluster at the tip of the cathode from (a) aqueous lead acetate solution ( 1 .O M), (b) solution a containing 0.022% PVA, and (c) solution a containing 0.022%agar-agar at 35.0 f 0.1 OC, applied current = 8.0 mA.
concentration to equilibrate. Thus, in order to maintain the electrolyte concentration constant throughout the experiment, we have designed a continuously stirred tank reactor as shown in Figure 11. It consists of a flat bottom petri dish having an outlet nozzle (0)at the corner. A glass slide AA' was put in the dish containing a solution of lead acetate in such a manner that only a small volume of the solution (thickness 1 mm) was just above the slide. The slide was supported by two glass pieces. The concentration and level of the solution were maintained constant with the help of a reservoir (BJ connected with a buret (B2). Electrolyte solution was influxed at a flow rate of 0.25 mL/min. Remaining part of the experimental setup was the same as described in the case of the batch reactor. Such an arrangement permitted maintenance of constant concentration around the electrodes. Results are shown in Figures 12 and 13.
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Results and Discussion Pattem formation and growth behavior during electrochemical deposition of lead from its aqueous solution have been studied by employing the experimental setup shown in Figure 1. On account of the instability, after some induction period different types of strucures appear at the cathode. From the electrochemical point of view the recording of the potential of the cathode is a classical
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Figure 8. Experimental setup to study the growth velocity during electrochemical depositionof lead: PI, Pz,platinumelectrodes; R, potential divider; B, dc battery; m, milliammeter; G, galvanometer.
way to get qualitative information on the local kinetics. Therefore, potential changes with time were also noted during the process of electrochemical deposition. Figure 2 shows a close view of a typical dendritic growth of lead metal. Dependence of oscillatory characteristics and growth morphologies during electrochemical deposition on the current density, concentration of the electrolyte and presence of colloidal materials such as agar-agar gel and PVA have been studied. Figure 3 shows the potential changes with time during electrochemical deposition of lead from its aqueous solutions of different concentrations ranging from dilute solution (0.1 M)to saturated solutions and keeping the current across the electrodes constant (4.0 mA). It has been observed that cathode potential oscillates with time (Figure 3a-c), but no such oscillation could be observed when saturated solution was used (Figure 3d), indicating that at high concentration, dendritic growth is more controlled and hence potential does not fluctuate. Results shown in Figure 4 indicate that amplitude of the potential increases with the applied current. However, on turning off the applied current, potential did not change with time (Figure 4a). Efforts have been made to characterize the nature of oscillations using next amplitude plots (Figures 14-16). At+,, the amplitude of
4874 The Journal of Physical Chemistry, Vol. 97, No. 18, 1993
Rastogi et al.
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Figure 11. Experimental setup of a continuously stirred tank reactor to monitor the potentialchanges with timeduringelectrochemicaldeposition of lead metal. 2.7i
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Figure 9. Characteristics morphologies observed during electrochemical deposition of lead with experimental setup shown in Figure 8: dendritic growth (a); tree type structure (b); continuous wave (c). Conditions: [lead acetate] = 0.55 M,(b) and (c) also contain 0.022% agar-agar and PVA polymer, respectively. Temperature = 35.0 f 0.1 OC, applied current = 8.0 mA, when the distance between the electrodes was 50 mm.
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TIME (min) Figure 10. Plots of length of lead metal leaf as a function of time, Conditions: [lead acetate] = 0.55 M,(b) and (c) also contain 0.022% agar-agar and PVA, respectively. Applied current = 8.0 mA at 35.0 i 0.1 OC.
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oscillation at any time t 1 (seconds) were plotted against A,, the amplitude of oscillation at time t (seconds) from the data recorded in corresponding potential-time plots. The oscillations in potential at higher applied current (8.0 mA) become more like
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random noise (Figure 14a). However, at relatively low current, the fluctuations in potential appear to be periodic (Figure 14b,c). As structure grows on the surface of the cathode, potential and conductance were expected to vary with time at constant applied current and concentration. Variation in conductance with time was monitored with the help of a digital conductivity meter (century, India). Influence of applied current on a conductance-
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The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 4875
Pattern Formation during Electrodeposition 1,9~
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Figure 13. Potential changes as a function of time during electrochemical deposition of lead in (a) a batch reactor (Figure 1) and (b) a continuously stirred tank reactor (Figure 11). Conditions: [lead acetate] = 1.0 M, applied current = 8.0 mA.
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Figure 14. Plots of A,+Iversus A, for corresponding values recorded in Figure 4.
time plot was also studied. Conductivity was found to oscillate and gradually increase with time in each case (Figure 5 ) . It has been observed that polymer additives influence the oscillatory and growth behavior during electrochemicaldeposition of the metal. We have performed experiments with aqueous lead acetate solution (1 .O M) as well as with solutionscontaining PVA
and agar-agar gel under identical experimental conditions, viz. temperature, applied current, and volume of the solution. Patterns shown in Figure 6 clearly indicate that the morphology changes on addition of minute quantities of these polymer additives. The dendritic growth was observed when aqueous lead acetate was used whereas a DLA/fractal type structure was observed when PVA was added in this solution. We observe a hybrid dendritiw DLA morphology when agar-agar was added instead of PVA. Besides the changes in morphology, changes in oscillatory behavior
4876 The Journal of Physical Chemistry, Vol. 97, No. 18. 1993
Rastogi et al.
TABLE I: Growth Behavior and Values of Slope (m), Intercept (C), and Correlation Coefficient (R) Used in Equation d = mP C for Lead Metal Growth at Constant Applied Current Using the Experimental Setup Shown in Figure 8' exwrimental conditions ~~~
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Conditions: [lead acetate] = 0.55 M; applied current = 8.0 mA; distance between the electrodes = 50.0 mm; temperature = 35.0
were also observed (Figure 7). It was found that amplitude decreased by adding an additive. The change may be ascribed as due to appreciable increase in viscosity of the solution by adding a polymer material. The kinetics of the growth behavior have been studied using a different experimental setup shown in figure 8. After turning on the applied current, many lead trees emerge from the cathode after some induction period. Successively, most of them stop growing and cooperative phenomena such as the simultaneous extinction of several trees can be observed. Length of the growing metal leaf as a function of time was measured. Changes in morphology and growth rate on account of addition of agar-agar as well as PVA are shown in Figures 9 and 10, respectively. The data are best fitted by the relation d = mt2 C, where m and C are slope and intercept, respectively. The values of slope, intercept, and correlation coefficient values are recorded in Table I. Values of growth velocity (V) as evident by their respective slope follow the sequence
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TABLE Ik Values of Slope (m), Intercept (C), and Correlation Coefficient (R)Used in Equation d = mP + Cfor Lead Metal Growth at Different Experimental Conditions Using the Experimental Setup Shown in F i m e 8 applied field [lead acetatel/M intensity'/V cm-' 0.20 0.40 0.60
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VLA VLA+ agar-agar VLA+ PVA The decrease in amplitude of electrochemical oscillation and growth rate by adding agar-agar and PVA may be ascribed as due to the adsorption of these surface active substances on the crystal nuclei. In all the cases described earlier, experiments were performed at constant applied current. Besides the experiments performed at constant applied current, certain experiments have also been performed at constant field intensity (applied potential/distancebetweentheelectrodes). In thiscase, two types of experiments were performed: (i) the length of the dendritic metal leaf was noted as a function of time at constant applied field intensity and varying the electrolyte concentrations; (ii) length of the dendritic metal leaf was noted as a function of time at different field intensities keeping the electrolyte concentration constant. The salient feature of this investigation is that at constant applied current or at constant applied field intensity, in both the cases the data obey the same kinetic law d = mt* C. The values of the slope ( m ) and intercept (C) at different experimental conditions are summarized in Table 11. Slope m increases with concentration and field intensity. This clearly indicatesthat at constant field intensity,growthvelocity increases with concentration. Similarly, at fixed concentration, growth velocity increases with the field intensity. In the case of batch reactor the concentration of the solution decreases continuously as the structure grows. To maintain the constant electrolyte concentration, lead acetate solution was influxed continuously throughout the experiment using a reactor shown in Figure 11. Results obtained at various current are shown in Figure 12. It has been found that amplitude increased by increasing the applied current. The results of the batch and flow reactor experiments have been compared (Figure 13).
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correlation coefficient ( R ) 0.992 0.996 0.991 0.994 0.992 0.992 0.996 0.991
Ratioof theappliedpotentialand thedistance between theelectrodes.
Although there was no change in the morphology of the electrochemical deposition in the two cases, the lifetime was increased in the case of the flow reactor as compared to that observed in a batch reactor. Amplitudes of the oscillations are higher in the case of the batch reactor as compared to that observed in a flow reactor. A,+, versus A, plots shown in Figures 15 and 16 indicate that in the case of CSTR, fluctuations are periodic, whereas in a batch reactor oscillations are more like random noise when the applied current was 8.0 mA (Figure 16a).
Acknowledgment. The authors wish to thank Professor S. Giri, Head, Chemistry Department, for providing necessary facilities and C.S.I.R., New Delhi, for financial assistance. Thanks are also due to anonymous reviewers for critical suggestions. References and Notes (1) Henisch, H. K. Crysrals in Gels and Liesegang Rings; Cambridge University Press: New York, 1988. (2) Teorell, T. Exp. Cell. Res. Suppl. 1958, 5 , 83. (3) Brady, R. M.; Ball, R. C. Nature (London)1984, 309, 225. (4) Matsushita, M.; Hayakawa, Y.; Sawada, Y . Phys. Rev. A 1985,32, 3814. (5) Sawada, Y.;Doughterty, A.;Gollub., J. P. Phys. Reu. Letr. 1986,56, 1260. (6) Grier, D. G.; Ben-Jacob, E.;Clarke, R.; Sander, L. M. Phys. Reu. Lett. 1986, 56, 1264. (7) Grier, D. G.; Kessler, D. A.; Sander, L. M. Phys. Reu. Lett. 1987, 59, 2315. (8) Kahanda, G. L. M. K. S.; Tomkiewicz, M. J . Electrochem. SOC. 1989. 136. 1497. (9) Melrose, J. R.; Hibbert, D. B. Phys. Reu. A 1989, 40, 1727. (10) Suter, R. M.; Wong, P. Phys. Reo. B 1989, 39, 4536. (11) Grier, D. G.; Allen, K.;Goldman, R.S.; Sander, L. M.; Clarke, R. Phys. Reu. Lett. 1990, 64, 2152. (12) Sawada, Y.; Hyosu, H. Physica D 1989, 38, 299. (13) Argoul, F.; Arneodo, A.; Elezgaray, J.; Swinney, H. L. Personal communication. (14) Fleury, V.; Chazalviel, J. N.; Rosso, M. Phys. Reu. Lett. 1992, 68, 2492. ~
