A Temperature and Electrochemical Impedance Spectroscopy

Dynamique des Transferts aux Interfaces, CNRS UMR 6107, UniVersite´ de Reims, BP ... electrocrystallization from a Watts-type solution, it has been p...
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J. Phys. Chem. B 2001, 105, 7205-7210


A Temperature and Electrochemical Impedance Spectroscopy Analysis of Nickel Electrocrystallization from a Watts Solution O. Aaboubi, J. Amblard, J.-P. Chopart, and A. Olivier* Dynamique des Transferts aux Interfaces, CNRS UMR 6107, UniVersite´ de Reims, BP 1039, 51687 REIMS Cedex 2, France ReceiVed: February 28, 2001; In Final Form: May 13, 2001

Through the use of temperature as an investigational tool to elucidate the still-debated mechanism of Ni electrocrystallization from a Watts-type solution, it has been possible to determine the whole set of parameters governing the process. Starting from the simplest model capable of depicting the general form of the stationary I-E curves, i.e., a two-monoelectronic-step mechanism involving an intermediately adsorbed species, we have shown that the model may also be used for the analysis of electrochemical impedance spectroscopy (EIS) data. Both kinds of measurements, stationary and dynamic, lead to one and the same set of parameters: transfer coefficients (R1 ) 0.72 ( 0.02; R2 ) 0.44 ( 0.02), intrinsic rate constants, and activation energies [Ea1 ) (85 ( 3) kJ mol-1; Ea2 ) (68 ( 5) kJ mol-1]. The excellent accordance found in the temperature range explored (293-333 K) between experimental results and those calculated from the model demonstrates the consistency of the whole procedure.

1. Introduction

2. Experimental Section

Since the very first Ni electrodeposit, more than 150 years ago,1 a great amount of work has been devoted to the subject, with some 10 000 references. They most often deal with the properties of Ni deposits, which, according to Brenner et al.,2 dramatically depend on the bath composition. To keep to the Watts bath that was first introduced in 1916 for industrial purpose3 and is still widely used, several thousands of references are now available. Despite this abundant literature, very few papers tackle the rather complex problem of the Ni electrocrystallization mechanism. The models proposed so far are somewhat controversial, even though they agree to consider a multistep cathodic process that involves at least one intermediately adsorbed species, a two-step reduction,4-8 and no mass-transport control, except for inhibiting species.5-7 It has to be stressed that none of them has used temperature as an additional tool to decipher the Ni electrocrystallization mechanism. As a matter of fact, only few papers deal with the effects of temperature on nickel deposition,9-11 most often for seeking deposits exhibiting better properties. Nevertheless, temperature is capable of exerting dramatic effects on most physicochemical phenomena, e.g., on processes taking place at the electrode/electrolyte interface. Dramatic alterations of Faradaic currents can be observed as temperature varies, whatever the kind of cell used, isothermal or not.12 For the particular case of mass-transport-controlled systems, a strong growth of limiting currents has thus been reported.12,13 The aim of the present work is to resume the study of the Ni electrocrystallization mechanism for temperatures varying within the 20-60 °C range to determine unambiguously from steady-state current density-potential curves and electrochemical impedance spectroscopy (EIS) measurements the whole set of kinetic parameters.

Experiments have been carried out with a classical threeelectrode setup: a 6 mm diameter Ni disk as the working electrode, a SCE reference, and another Ni rod of greater area (5 cm2) as counter electrode so as to minimize the Ni2+ impoverishment of the electrolytic solution. Prior to each experiment, the working electrode was mechanically polished first with emery paper (Struers P 4000) and then with alumina (grain size 1 µm), rinsed with distilled water, and dried. A nickel predeposit of ≈2 µm was then plated at a potential Ep of -0.825 V/SCE. The solution was a classical Watts-type bath containing 300 g L-1 of NiSO4‚7H2O, 35 g L-1 of NiCl2‚6H2O, and 40 g L-1 of boric acid, H3BO3. Its pH was adjusted to 4.5 by adding a few drops of concentrated aqueous NH3. The solution temperature was controlled and made constant with a circulating water thermostat (Bioblock Scientific). The working electrode potential was potentiostatically controlled, and the impedance measurement was realized through a transfer function analyzer. E. Merienne made both devices in our laboratory.

* To whom correspondence may be addressed. E-mail: alain.olivier@ univ-reims.fr.

3. Results Steady-State Regime. For a given temperature, the currentpotential curve was measured by applying successive 10-mVpotential steps and waiting for the current to be stabilized after each step. The analysis of the current density-potential curves plotted in a semilogarithmic scale, corrected for the ohmic drop [ln(-J) ) f(-E)], for different solution temperature values (Figure 1) clearly shows a strong increase of the Faradaic currents as temperature increases. Because Ni electrocrystallization kinetics from a Watts solution is known to be mainly governed by the charge transfer, this current increase stems from an increase of the reaction rates through the modification of the rate constants for the different steps governing the system. Moreover, the representation given in Figure 1 shows two distinct Tafel components. Such behavior is similar to the literature results that prove the existence of at least two electrochemical steps in the reaction mechanism.5,8

10.1021/jp010769d CCC: $20.00 © 2001 American Chemical Society Published on Web 07/07/2001

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Aaboubi et al.

Figure 3. Evolution with temperature of the solution resistance, Rs. Figure 1. Tafel plot of the current density-potential curves after ohmic drop correction for various temperatures: (b) 293 K; ([) 312.5 K; (4) 323.5 K; (/) 333 K.

Figure 2. Nyquist plot of EIS measurements at a potential Ep ) -900 mV/SCE for various temperatures: (b) 299 K; (0) 305 K; ([) 312 K; (4) 325 K; (/) 333 K.

Electrochemical Impedance Spectroscopy. The EIS studies have been made at a given potential and various solution temperature values between 20 and 60 °C. Figure 2 gives as a Nyquist plot the EIS curves, corrected for the solution resistance, in the frequency range from 10 kHz to 10 mHz, for a potential Ep ) -0.9 V/SCE. The diagrams are composed of a highfrequency capacitive loop followed at low frequency by an inductive loop typical for the existence of an adsorption process. The existence of two distinct relaxation processes emerges from the diagrams of Figure 2, a slow kinetic step and an adsorption step, which is in agreement with the results of studies in the literature. As temperature varies, the amplitudes of the loops are dramatically modified in the whole frequency domain explored. One must notice particularly that the polarization resistance, which corresponds to the zero frequency impedance, is consistent with the evolution of the steady-state currents. By means of a fitting procedure, the values of the different parametersssolution resistance, Rs, double-layer capacity, Cd, and charge-transfer resistance, Rtshave been determined for each temperature and for the different polarization potentials explored. Figure 3 shows the temperature variation of Rs. One can note a fall in solution resistance as temperature increases due to higher solution conductivity. Figure 4 shows the potential variation of Cd. One can also notice a slight decrease of Cd, either as temperature increases or as the potential becomes more cathodic, but the order of magnitude of the average value corresponds to the values quoted in the literature.5,14 From the values of the charge-transfer resistance, Rt, and the steady-state current, I, the product RtI is derived. Its evolution

Figure 4. Evolution with potential of the double layer capacity, Cd, for various temperatures. Symbols are the same as those in Figure 2.

Figure 5. Evolution with the cathodic potential of the product RtI for various temperatures. Symbols are the same as those in Figure 2.

with the polarization potential is shown in Figure 5 for various temperatures. The product RtI is fairly constant over a 100-mV range, particularly for high temperatures. Its value is somewhat weaker than the values quoted in the literature. It highly depends on the quality of the EIS measurements and the numeric treatment chosen for its determination. 4. Theoretical Considerations Steady-State Current. To analyze the effects of temperature on the Ni cathodic process, we have chosen the simplest mechanism that is suggested as well by the above results as by most of the available references.8,15-20 Thus, we consider a mechanism composed of two monoelectronic steps, which seems far more reasonable than considering multielectronic steps that would involve two7 or three5 electrons exchanged in one single

Temperature and EIS Analysis of Ni

J. Phys. Chem. B, Vol. 105, No. 30, 2001 7207

step. Moreover, we have checked that the three-electron adsorption step proposed by Wiart5 did not allow us to account for our steady-state and EIS results simultaneously, namely the RtI value. Therefore, the mechanism could be written as k1

Ni(II) + e- 98 Ni(I)ad



Ni(I)ad + e- 98 Ni


where k1 and k2 are rate constants per surface unit that will be assumed to be exponential functions of the electrode potential E (i.e., Ep after ohmic drop correction):

k1 ) k°1 exp(b1E) and k2 ) k°2 exp(b2E)


and the formation/destruction rate of Ni(I)ad is expressed by


dθ ) k1C(1 - θ) - k2Γθ dt

k1Ck2Γ -I ) 2FA k1C + k2Γ


Electrochemical Impedance. As a weak amplitude sineshaped potential perturbation is superimposed to the steadystate potential value, sine-shaped modulations of θ and I are produced. Given that the mass-transport plays a minor part, which is actually the case for Ni electrocrystallization from a Watts solution,5,6 the Faradaic admittance is given by

∂I ∂I ∆θ ∆I ) + ∆E ∂E θ ∂θ ∆E

( ) ( ) K1K2



τ (s)

0.8 0.815 0.827 0.843 0.863

23.0 16.7 12.7 9.59 6.54

193 134 125 109 77.3

0.154 0.135 0.143 0.123 0.139

with K1 ) k1C and K2 ) k2Γ. Taking into account the solution resistance, Rs, and the double layer capacity, Cd, the electrochemical impedance measured will be

Z ) Rs +





ZF-1 ) R0-1 +




R1-1 1 + jωτ


K1K2 R0-1 ) Rt-1 ) FA(b1 + b2) K1 + K2


K1K2 R1-1 ) FA(b1 - b2)(K2 - K1) (K1 + K2)2



Γ K 1 + K2


Determination of the Kinetic Parameters. Through comparison of the experimental results with the theoretical expression giving the electrochemical impedance, the values of the parameters R0, R1, and τ (Table 1) may be derived. From the parameters given therein and from the current values, we can then deduce the values of b1, b2, K1, and K2. To achieve this determination, we followed a two-step procedure. 1. Determination of R1 and R2. Taking account of eq 6 giving the expression of the steady-state current and of eq 13 giving the charge-transfer resistance, a relation may be established that gives access to the sum (b1 + b2) that is fairly constant in the potential range explored (see Figure 5) and hence to (R1 + R2):

-2 2RT ) b1 + b2 (R1 + R2)F


Now, if we let K ) K2/K1, eq 14 may be written under the form

I K-1 (b - b2) 2K+1 1


Combining the latter with eq 16, we get


K1K2(b1 - b2) ZF-1 ) Rt-1 + FA(K2 - K1) (K1 + K2)(jωΓ + K1 + K2) (10)



R1-1 )

(∂θ∂I ) ) FA(K - K )

ZF 1 + jωCdZF

Equation 10 giving the Faradaic impedance may be written under the form

R0I ) RtI )

(∂E∂I ) ) FAK + K (b + b ) θ

R1 (Ω)


From eqs 5-7, we get

Rt-1 )

R0 (Ω)


At the steady state, the above term must be zero. Hence, the current is given by

ZF-1 )

-[Ep - RsI] (V/SCE)


In eq 3, k°1 and k°2 are the rate constants, b1 ) -R1F/(RT) and b2 ) -R2F/(RT) are the Tafel slopes, R1 and R2 are the transfer coefficients, F is the Faraday constant (96 500 C mol-1), R is the ideal gas law constant (8.314 J mol-1 K-1), and T is the temperature (K). Let us now assume that the Ni(I)ad species is identically adsorbed on the available surface sites according to a Langmuir type isotherm. The surface ratio covered by Ni(I)ad is θ, Γ is the maximum number of available surface sites per surface unit, and C is the bulk concentration of Ni(II) ions. Then, the Faradaic current, I, is given by

-I ) FA[k1C(1 - θ) + k2Γθ]

TABLE 1: Values of Parameters R0, R1, and τ for T ) 325 K and Various Cathodic Potentials (E ) Ep - RsI)


R1-1 + R0-1 - Ib2 R1-1 - R0-1 - Ib2

Keeping in mind that ln K can be written as


7208 J. Phys. Chem. B, Vol. 105, No. 30, 2001

ln K ) ln

[ ]

Aaboubi et al.

[ ]

k°2Γ k°2Γ F + (b2 - b1)E ) ln - (R2 - R1)E k°1C k°1C RT (19)

it follows that



[ ]


k°2Γ F 1 ) ln K - 2 R2 + E k°1C RT R0I


For a given temperature, the first term should be constant whatever the cathodic potential E. Thus, it is mathematically possible to determine the value of R2 that leads to a constant value for the second term of eq 20. To give an example taken at a temperature of 333 K, we show in Figure 6 a plot of ln[k°2Γ/ (k°1C)] in different potential conditions, which has been obtained for a constant value of R2 (0.43). Once that value is determined, eq 16 allows the value of R1 to be readily calculated. The same computation process is repeated for each temperature explored. 2. Determination of k°1 and k°2. Equations 13 and 14 may give access to the values of k°1 and k°2. Let R ) R1/R0. Then, it follows that

1 + Rγ K 2 ) K1 Rγ - 1

Figure 6. Evolution of the term ln(k°2Γ/(k°1C)) for a temperature of 333 K and various cathodic potential values.



b1 - b2 R1 - R2 ) b1 + b2 R1 + R2


K1 )

Rγ I FA Rγ + 1


K2 )

Rγ I FA Rγ - 1


γ) It follows that

Figure 7. Synoptic representation of the values found for R1 (circles) and R2 (squares) for the various temperatures explored: dark symbols, steady-state data; open symbols, EIS data.


For given values of potential and temperature, the determination of γ leads to K1 and K2 and hence to k°1 and k°2. By means of the EIS measurements, the values of R1, R2, k°1, and k°2 can readily be obtained. It is now quite easy to test and further refine the values thus determined by means of the steady-state current density-potential curves: for each temperature explored, we seek the best values of the four parameters that allow the whole set of steady-state current density-potential curves to be restored. Discussion Coming up to our expectations, we have determined in a first step the value of R2 that verifies eq 20 from the values of R0, R1, and τ. Actually, as shown in Figure 7, the different values of R2 obtained are virtually temperature-independent. Their average value is 0.44. According to the calculation procedures given above, we get also a constant 0.72 value for R1 in the whole temperature domain explored. Note that both values are strikingly close to those that can be directly derived from the steady-state current density-potential curves. Both R1 and R2 being known, we have determined the values of k°1 and k°2 from eqs 23 and 24, taking also into account eq 3, the concentration, C, of Ni(II) ions (C ) 1.22 mol L-1 for the Watts solution), and an average value for Γ ) 5 × 10-4 mol m-2. The latter was calculated from eq 15 for each temperature and each polarization potential value. Such a value

Figure 8. Evolution with temperature of Γ. The vertical bars show its fluctuations according to the various cathodic potentials explored.

may appear somewhat greater than the values usually quoted (10-6-10-5), which may well correspond to an actual surface greater than the geometric area. The temperature evolution of Γ is shown in Figure 8, where the fluctuations of Γ with the potential are symbolized by vertical bars. These fluctuations show that the determination of Γ is far from being accurate. A confrontation may be found in Figure 9 where the J(E) curves calculated from eq 8 have been plotted, together with the experimental curves measured for several solution temperatures. The confrontation displays an excellent accordance between experimental and calculated curves: variations of both parameters R never exceed (0.02 with respect to the values deduced from the EIS data; k°1 and k°2 values are quite close to those calculated.

Temperature and EIS Analysis of Ni

Figure 9. Confrontation of the experimental current density-potential curves with those calculated from our theoretical approach for various temperatures: (b or O) 293 K; ([ or ]) 312 K; (9 or 0) 323.5 K; (2 or 4) 333 K. Dark symbols represent experimental data; open symbols represent calculated data.

J. Phys. Chem. B, Vol. 105, No. 30, 2001 7209

Figure 12. Arrhenius plot showing the temperature evolution of the two rate constants k°1 and k°2 deduced from both sets of experiments, steady-state (O or 0) and dynamic (b or 9) results. The circles refer to k°1 and the squares to k°2.

TABLE 2: Values of the Different Characteristic Parameters Obtained R1


Ea1 (kJ Ea2 (kJ mol-1) mol-1)



0.72 ( 0.02 0.44 ( 0.02 85 ( 3 68 ( 5 2.5 ( 1 18 ( 2

104Γ (mol m-2) 5(2

the validity of our model involving two monoelectronic steps for Ni electrocrystallization from a Watts solution. Now, starting either from steady-state or from dynamic results, the temperature variation of the intrinsic rate constants obtained for both steps may be analyzed according to an Arrhenius law: Figure 10. Confrontation of the experimental impedance results with those calculated from our theoretical approach at 325 K for various applied potentials: (9 or 0) -0.825 V/SCE; (2 or 4) -0.850 V/SCE; (b or O) -0.875 V/SCE; ([ or ]) -0.900 V/SCE; (× or +) -0.925 V/SCE. The first symbol refers to experimental data, the second to calculated data.

k°i ) Ai exp(-Eai/(RT)) exp(RiESCEF/(RT))


where Ai is a constant and Eai the activation energy for the step i. ESCE is the reference potential for which the temperature evolution has been taken into account.21 Therefore, the values of both parameters Ai and Eai are readily derived from the straight Arrhenius lines then obtained (Figure 12). The results, reported in Table 2, show that the activation energies lie in the 60-90 kJ mol-1 range with a value somewhat weaker for the second step. This is consistent with a comment of Wiart5 about the quite low value he found for R2 (according to his model R2 was 0.06), which originates from the fact that the second step requires less energy than the first one. Conclusion

Figure 11. Confrontation of the experimental impedance results with those calculated from our theoretical approach at 305 K for various potentials. Symbols are the same as those in Figure 10.

A similar conclusion may be drawn after the confrontation of the experimental EIS data with those recalculated from eqs 10 and 11. To illustrate this, the Nyquist plots of Figures 10 and 11 let the EIS measurements be compared to the calculated impedances for two different temperatures, 325 and 305 K, respectively. A striking accordance exists, frequency for frequency, in the whole range explored. This confirms, once again,

This work demonstrates the usefulness of temperature as an investigational tool for the analysis of an electrochemical mechanism. The evolution of our impedance measurements shows that a quite simple two-step process involving an adsorbed species well accounts for the whole set of results in a broad domain of potential and temperature. Moreover, it allowed us to determine all the parameters governing the mechanism. The validity of these determinations is further reinforced by the excellent accordance obtained through comparison of the dynamic results with the steady-state current density-potential curves. Nevertheless, one may note a lack of accuracy in the determination of a parameter such as Γ. This will lead us to resume the present study by means of another kind of dynamic technique that has been developed and validated for the case of an electrochemical system controlled by mass-transport: the

7210 J. Phys. Chem. B, Vol. 105, No. 30, 2001 thermoelectrochemical transfer function22 (or TEC), which could prove to be crucial too in the elucidation of a strongly temperature-dependent process involving short relaxation times. This is actually the case for adsorption. Using still another impedance technique based on the analysis of the magnetohydrodynamic (MHD) transfer function, we have clearly demonstrated the hydrogen discharge during Ni electrocrystallization.23 Another work, still in progress, will show what can be further extracted from the TEC transfer function in the case of Watts deposited nickel. References and Notes (1) (2) (3) (4) (5) (6) (7) (8) 557.

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Aaboubi et al. (9) Turner, D. R. J. Electrochem. Soc. 1953, 100, 15. (10) Schaus, O. O.; Gale, R. J.; Gauvin, W. H. Plating 1971, 58, 801. (11) Holm, M.; O’Keefe, T. J. J. Appl. Electrochem. 2000, 30, 1125. (12) Citti, I.; Aaboubi, O.; Chopart, J.-P.; Merienne, E.; Olivier, A. Electrochim. Acta 1996, 41, 2731. (13) Marchiano, S. L.; Arvia, A. J. Electrochim. Acta 1968, 13, 1657. (14) Devos, O.; Aaboubi, O.; Chopart, J-.P.; Olivier, A.; Gabrielli, C.; Tribollet, B. J. Phys. Chem. A 2000, 104, 1544. (15) Matlosz, M. J. Electrochem. Soc. 1993, 140, 2272. (16) Madore, C.; Matlosz, M.; Landolt, D. J. Electrochem. Soc. 1996, 143, 3927. (17) Madore, C.; Landolt, D. J. Electrochem. Soc. 1996, 143, 3936. (18) Baker, B. C.; West, A. C. J. Electrochem. Soc. 1997, 144, 164, 169. (19) Cheng, C. C.; West, A. C. J. Electrochem. Soc. 1997, 144, 3050. (20) Cheng, C. C.; West, A. C. J. Electrochem. Soc. 1998, 145, 560. (21) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and Applications; John Wiley and Sons: New York, 1980; Appendix 3. (22) Aaboubi, O.; Citti, I.; Chopart, J.-P.; Gabrielli, C.; Olivier, A.; Tribollet, B. J. Electrochem. Soc. 2000, 147, 3808. (23) Devos, O.; Aaboubi, O.; Chopart, J.-P.; Merienne, E.; Olivier, A.; Amblard, J. J. Electrochem. Soc. 1998, 145, 4135.