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Electrochemical study of the properties of iron ions in ZnCl2 + 2NaCl melt at 450°C
ELSEVIER
Journal of Electroanalytical
Chemistry
397 (1995) 139- 147
Electrochemical study of the properties of iron ions in ZnCl, + 2NaCl melt at 450°C ‘, A.M. Martinez a, M. Vega a, E. Barrado ‘, G. Picard b
Y. Castrillejo ’ Deptrrtanzmto h Labomtoire
de Quinzica Analiticu, d’Electrochinzie
Facultud
Analytiyue
de Ciencias, et Appliqube.
Uniwrsidcrd
de Valladolid.
Ecole Nationale
Superieure
Pmdo de In Mqdolencl de Chinlie de Paris,
S/II.
47005
Volltrdohd,
I I rue Pierre et Mrwir
Spun
Curie.
75231 Paris Cedex 05, Frunce
Received 8 December
1994; in revised form 10 May 199.5
Abstract The electrochemical properties of Fe(II) in the ZnCI, + 2NaCI melt at 450°C have been studied using a glassy carbon electrode. Iron oxidation states II and III have been shown to exist in the mixture and the stability of metallic iron has been confirmed. The kinetics of the electrodeposition and electrocrystallization of iron were studied finding that the process is quasi-reversible. In the same way, the Fe(III)/Fe(lI) exchange was found to be quasi-reversible. The values of the kinetic parameters, k” and cy for both reactions were obtained. Mass transport towards the electrode is a simple diffusion process. The diffusion coefficient was found (I .3 _t 0.4) x IO-’ cm’ s-1. Potential step measurements indicate instantaneous nucleation and growth of iron (I against r ‘I’> followed by diffusion control (Cottrell equation). Keywords~
Molten salts; Fe(H); Glossy carbon electrode
1. Introduction
Among the main applications of molten salts, one of the most promising is their use as reaction media for extractive metallurgy purposes. Fused salts can be employed at working temperatures ranging from the high temperatures corresponding to pyrometallurgy to the low temperatures used in the classical hydrometallurgy. Thus molten salt metallurgy combines the main advantages of pyrometallurgy, i.e. high kinetics of chemical reactions and the possibility of manufacturing reactive metals and materials, and that of hydrometallurgy, which is applying solution chemistry to increase the selectivity of a given process [l-7]. Molten salts are known as suitable media for metal electrowinning and electrorefining [8,9], the metallurgical properties of the deposit strongly being dependent on the operating conditions. In order to reach a better understanding and control of the deposition processes, accurate knowledge of the electrochemical deposition mechanism is essential. In this way, electrocrystallization studies are very important. Nucleation and growth in metal deposition depend to a great extent on the substrate onto which the electrochemical reduction is performed, because of not only its chemical nature, but also its structural state. The nucleation process is closely related to the active sites 0022-0728/95/$09.50
0
SSDI 0022.0728(95)04151-6
1995 Elsevier
Science S.A. All rights reserved
existing on the substrate. Thus, with the same bath and the same experimental conditions, different deposits can be obtained by using various substrates. This study is part of a systematic research [lo-121 concerning: (i) the possibility of using mixtures of ZnC1, with alkali chlorides for the electrolytic production of zinc; (ii) the effect of impurities present in the cell feed; (iii) the possibility of using these mixtures for the treatment and recuperation of metals, such as iron, contained in ores and industrial wastes of zinc. There have been many electrochemical studies of iron ions in molten salts. More of them have been carried out in molten alkali and alkaline-earth chlorides than in any other halide system. In this way the eutectic LiCl + KCI [13-I 71, the equimolar mixture of KC1 + NaCl [ 181, MgCl 2 + KC1 and MgCl, + NaCl + KCI mixtures [ 19,201, and the AlCI, + NaCl [21-231 (in which the Fe(II), Fe(II1) and Fe(O) oxidation states are known to be stable) have been investigated. In an early study using AlCl, + NaCl melts at 3OO”C, Delimarskii et al. [22] obtained two electrochemical reduction waves for Fe(II1) ions, presumably related to Fe(I1) and Fe metal, respectively, whereas Laitinen and Pankey [13], working with LiCl + KC1 and platinum electrode at 4OO”C, did not observe an electrochemical reduction wave for the step Fe(II1) + e-e Fe(II), which was
140
Y. Cmtrillejo
et al. /Joumni
of Electronnd~ticcd Chemistry 397 (1995) 139-147
explained in terms of the chemical reduction of Fe(I1) ions by platinum. Most authors have investigated the kinetics of the Fe(H) electrochemical reduction in molten chlorides, finding that the process was controlled by the mass transfer rate of F&I) ions to the electrode surface and that the electronic exchange was reversible. The present study is related to the electrochemical properties of iron in ZnCl, + 2NaCl melt. The stability of the different oxidation states was first investigated. The properties of the Fe(III)/Fe(II) and Fe(II)/Fe(O) exchanges were studied and the kinetic parameters for both systems were calculated, using different electrochemical techniques with glassy carbon as working electrode. In addition, electrocrystallization of iron on glassy carbon was examined.
2. Experimental 2.1. Prepurutiorl
and purification
of the melt
The ZnCl, + 2NaCl melt (analytical grade Merck products) was contained in a 100 cm3 Pyrex crucible placed in a Pyrex cell. The temperature was maintained constant within +2”C by means of a Taner furnace and a West 3200 programmable device. The mixture was fused under vacuum, purified by bubbling hydrogen chloride and then kept under a dry argon atmosphere, a procedure used previously [I I].
concentrations the solutions became dark red-brown. After long experiments (aproximately 4-5 days) some volatilised material was found on the cooler parts of the cell.
3. Results
and discussion
3.1. Stable oxidation
states
After the purification of the ZnCl, + 2NaCl melt and using a glassy carbon electrode, the electrochemical window of the melt was 1.885 V, extending from 1.885 V (chlorine evolution) to 0 V (zinc deposition) with respect to the Zn(II)/Zn reference electrode (Fig. l(a)). Fig. l(b) shows a typical linear sweep voltammogram for the reduction of a Fe(I1) solution. In the potential range 0.6 to 0 V (zone 1). a cathodic peak, A, and one sharp anodic stripping peak, A’, are evident. The shape of the voltammogram, the break corresponding to the beginning of the Fe(I1) reduction (characteristic of the formation and the reoxidation of a constant activity product). and the peak potential values are typical of those expected for the
-__I
i
O.l-
0.05. s
2.2. Electrochemical
apparatus
The emf measurements were carried out with a high impedance voltmeter (Crison 2002). Cyclic voltammetry and pulse techniques were performed with a PAR (Princeton Applied Research) Model 273A potentiostat/ galvanostat controlled with the M270 software package. The simulated voltammograms were recorded with M271 COOL kinetic analysis software. A glassy carbon rod (3 mm diameter) was used as working electrode, while a graphite rod served as the counter electrode. The reference electrode consisted of a Pyrex glass tube filled with liquid zinc and covered with molten ZnCl 2 + 2NaCl. A tungsten wire was inmersed into the liquid zinc to ensure electrical connection with the reference electrode (Zn(II>/Zn(liq) redox couple).
0
1
-0.2
0
I
0.2
*
0.4
1
0.6
-
0.8
8
3
1
I
8
1
1.2
1.4
1.6
1.8
0.8 1 E/V
1.2
1.4
1.6
1.B
Elv
s c(
2.3. General features 20n.1-
The Fe(I1) ions were prepared in situ by anodic dissolution of the metal (Aldrich Chem. Co. iron wire, 1 mm diameter) at constant current. The amount of iron ions generated can be calculated by means of Faraday’s law (0.01866, 0.02801, 0.03850 and 0.02550 mol kg-‘). The presence of Fe(I1) in the purified melts produced, at low concentration, pale yellow solutions, whilst at higher
0.02 -0.2
0
0.2
0.4 0.6
(b)
Fig. 1. (a) Linear sweep voltammogram obtained at a glassy carbon electrode in a pure ZnCI, + 2NaCI melt (sweep rate 0.2 V s- ’; electrode area 0.45 5 0.01 cm*). (b) Typical linear sweep voltammogram for the reduction of iron chloride (0.01866 mol kg-’ ) on a glassy carbon electrode (sweep rate 0.2 V s- ’).
Y. Castrillejo
et al. /Journal
~~~Electmanulytical
(b)
Fe
Chemistry
397 (1995)
139-147
141
iron wire in different solutions containing Fe2’ in concentrations between 10e2 and 10-l mol kg-‘. A plot of the cell emf versus the logarithm of the Fe(I1) concentration was linear with a slope of 0.070 V (decade)-‘, which is in agreement with the theoretical value for a two-electron process at 450°C (0.072 V (decade)-‘). We found that E&,~,I~,Fe~is 0.341 f 0.001 V (molality scale). The experimental problems related to the low solubility and the hygroscopic characteristics of FeCl, prevented direct measurement of the standard potential of the Fe(III)/ Fe(B) re d ox system. Nevertheless, it was possible to estimate it from voltammetric measurements by applyE,,, = (Ei + Ei)/2 (where Ei and ing the relationship: EE are the anodic and the cathodic peak potentials respectively), assuming that the Fe(II1) and Fe(I1) diffusion coefficients are so similar that the standard potential of the Fe(III)/Fe(II) system can be taken equal to the half-wave potential of the Fe(I1) oxidation, E,,,. The average value obtained was E&l,,~,Fe~,,~ = 1.403 i 0.002 V. 3.2. Fe(H) / Fe(O) exchange
L
2
As shown in Fig. l(b), the cathodic peak corresponding to the electroreduction of Fe(B) ions presents a steep rise and slow decay, and the anodic peak has the expected characteristics of a stripping peak, decay steeper than rise. The ratios of the forward-to-reverse current peaks (,,“/I%> are typical of a process leading to an insoluble product. A more significant and less arbitrary parameter is the ratio Qa/Qc3 anodic charge/ total cathodic charge, including that after sweep reversal. This remains approximately constant and equal to unity with increasing sweep rate, which indicates that all deposited material on the electrode is electrochemically removed during the positive sweep and also that there are no chemical reactions coupled to the primary electrochemical process.
R
e CC”)
Fig. 2. (a) SEM micrograph of an iron deposit. (b) ED analysis deposit shown in (a). (c) X-ray diffraction of the deposit formed.
for the
deposition and reoxidation of an insoluble product. This was confirmed by deposition of the metal under potentiostatic conditions (150 mV). The deposit obtained consisted of pure metallic iron (determined by energy dispersive X-ray analysis with the scanning microscope and by X-ray diffraction) (Fig. 2(a-c)). We will therefore assume that the reaction along cathodic peak A is Fe(H) + 2e- ti Fe(O). Moreover, Fig. l(b) shows an anodic wave B’ associated with the cathodic wave B in the potential range 1.0 to 1.8 V (zone 2). The shape of the B/B’ system was characteristic of a soluble-soluble exchange related to the Fe(III)/ Fe(I1) couple. The standard potential of the Fe(II)/Fe system was determined by measuring the equilibrium potential of an
3.2. I. Reuersibilit_v study Voltammograms yield more information about the iron deposition process. The study of the voltammetric curves recorded at different potential sweep rates (Fig. 3(a)) clearly shows that the cathodic as well as the anodic peak potentials shifted with increasing sweep rate, suggesting that the deposition is not a reversible process. In Fig. 3(b) Ei is plotted vs. log 0, giving AE,/Alogu = 84 mV. For a two-electron irreversible reaction with a transfer coefficient, cr, equal to 0.40, the variation 2,3RT/2anF is equal to 90 mV at 450°C. This criterion proves that the Fe(II)/ Fe(O) exchange is quasi-reversible [24,25] with a first approximation of the transfer coefficient equal to 0.43. The number of electrons transferred during the reduction process can be calculated from the half-peak width. For a reversible deposition of an insoluble product [26], the half-peak width is: E, - Ep/Z = -0.77RT/nF
(‘1
142
Y. Crtstrillejo
et cd. /Journal
of Electronnnlytical
where E, is the peak potential, E,,,z the half-peak potential and II the number of electrons transferred in the rate-determining step. R, T and F have the usual meanings. The average value of n calculated for the voltammograms recorded under conditions where any nucleation phenomenon does not occur by means of the above equation is unsatisfactory, which can be explained by the quasi-reversibility of the iron deposition. A further study of the electrochemical behaviour of iron ion reduction was made using chronopotentiometry. The plots of the electrode potentials vs. log [l - (Z/T>‘/‘] were linear, but the slope of the linear part of the curve (0.089 V (decade)-‘) is slightly different from the theoretical value for a two-electron reversible exchange process (0.072 V (decade)-‘> at 450°C. Taken together, these results show that the Fe(II)/ Fe(O) exchange dots not have a typical reversible behaviour and suggest that it is a quasi-reversible process. 3.2.2. Electrochemical nucleation The voltammogram presented in Fig. 4 suggests the presence of the nucleation process. A cross-over (hysteresis) of the cathodic peak after potential reversal may be
0 - 0.002 - 0.004 : H
-0.006 - O.OO& I-0.01
(a) Xi
o.i5
011
0:2
0
E/V
-I .4
-1.2
-I
-0.8 log
-0.6
-0.4
-0.2
0
cv/vs-‘)
Fig. 3 (a) Voltammetric reduction of iron chloride. FeCl? concentration 0 01 X66 mol kg ' ; electrode area 0.45 + 0.01 cm*; sweep rates: (1) 0.05 (2) 0.075 (7) 0. I V s ’ (b) Variation of the cathodic potential peak with the logarithm of the sweep rate.
Chemistry
397
(I 9951
139-
147
o.w0.030.02-
s
O.Ol0--
P -o.Ol-0.02-0.03~
0
* 1 I 0.05 0.1 0.15 0.2 0.25 03
0.35
1
0.4
1
0.45
0.5
EN Fig. 4. Linear sweep voltammogram obtained at a glassy carbon electrode (0.45 kO.01 cm*) in ZnCI, +2NaCI at 450°C. Sweep rate 0.7 V s- ‘. FeCl 2 concentration 0.0 I866 mol kg- ’
observed. This phenomenon indicates a phase formation and growth. The current-time transients obtained were particularly sensitive to nucleation and growth phenomena. In this potentiostatic step or pulse method, the potential of the working electrode is stepped from a potential slightly positive of the metal deposition potential to a potential in the range where the deposition occurs (this potential step is named overpotential, though it is not a departure from a well-defined potential in the thermodynamic sense>. If the metal is deposited on a foreign substrate, the initial response of the current yields information about the nucleation behaviour of the metal on the substrate in question. Usually, the transient is compared with expressions from nucleation theory [27-301, which are valid for basic types of nucleation and growth. Fig. 5(a) shows typical I - t transients for the deposition of iron on a foreign surface (glassy carbon). As the applied potentials were between 180 mV and 100 mV, a significant change in the usual habit of l-t transients took place. After the initial double layer charging, the current dropped to a minimum and then rose with time. At even more negative potentials the current still passed through a minimum, and then a maximum, before finally decaying in the usual way with time. The appearance of the I-t transients indicated that nucleation and growth phenomena play a part in the overall deposition process. After every run the deposited iron was removed from the surface by polarizing the working electrode anodically. The most interesting part of the cathodic I-t transients is the rising portion of the curve which corresponds to the current before overlapping of the first monolayer of the growing nuclei and therefore it can be used to determine the kinetics of nuclei growth. The time corresponding to the maximum current, t,,,, is
Y. Castrillejo
et al. /Journal
of Electroancclytical
related to the time at which full coalescence of the crystallites occursThere are two types of nucleation [28] described by: (= nFS~(2D)‘/2c3/2M1/2No for instantaneous at the beginning I = (4/3)nF%(
p-‘/2t’/2
1/2ANot”/2
I
1 E
I
4
6
-0.004
T l-l
\
-0.006
\
165
mV
160 mV
-0.007 -0.008 155 mV -0.009*
0.2
0.4
0.6
0.8
coefficients
(b)
I
1.2
obtained by different techniques
Technique
IO’ D/cm’ 5-l from Fe(II)/Fe system values
IO’ D/cm2 s-’ from Fe(III)/Fe(II) system values
Voltammetry Semi-integral Chronopotentiometry Chronoamperometry
_
I.3 * 0.I I .4 + 0.2 I.2 & 0.2
I .2 * 0.4 I.3 i_0.3 I .6 & 0.4
_
mechanisms [28,29]. The products of current and time at the current maxima were evaluated. The product (I,, t,,,) was found to decrease rapidly with increasing overpotential, while the product (Ii . t,,,) showed a stable value. This indicates growth of three-dimensional centers randomly nucleated. 3.2.3. The diffusion coefficient of Fe(ll) The diffusion coefficients, DFeC,,), given in Table 1, were calculated from different electrochemical techniques by applying the appropriate equations. It has to be indicated that although a glassy carbon rod was used as working electrode, all the formulas used are relevant to the plane semi-infinite diffusion because under the experimental conditions, the corrections related to cylindrical geometry can be neglected [3 l-341. We can obtain the diffusion coefficient of Fe(B) from the boundary semi-integral values by means of the relationship: m’ = t~FscD’/~, where m* is the limiting value of the convoluted current, c the bulk concentration of the electroactive species, D its diffusion coefficient and S the electrode surface area. Chronopotentiometrical studies of the reduction of Fe(B) obeyed Sand’s law: [ri/2
(a)
-0.003
-0.005
Table I Iron (II) diffusion
143
139-147
(3)
for progressive nucleation in which the nuclei are continuously formed during the crystal growth. In the equations, M represents the mol mass, N, the number of nucleation sites at t = 0, p the density and A the nucleation rate constant. The analysis of the rising part of the cathodic l-t transients obtained (Fig. 5(a)), obeyed an I against t’/’ linear relationship according to Eq. (2) (Fig. 5(b)). Therefore, the initial stages at the surface of the substrate of electrochemical deposition of iron on the glassy carbon electrode can be explained in terms of a model involving instantaneous nucleation. Several diagnostic criteria have been developed for testing current transients with respect to the nucleation
- 0.002
397 (1995)
(2)
nucleation in which the nuclei are formed of the pulse; and D)3’2c”‘2M”~-
Chemistry
I:4I
tl/2,Sl/2
Fig. 5. (a) Potentiostatic current transients for electrochemical deposition of iron on a glassy carbon electrode in ZnCl, + 2NaCI at 450°C. [FeCI? 1 = 0.01866 mol kg-‘; electrode area 0.45 cm’. The applied potentials are: (1) 170, (2) 165, (3) 160, (4) 155, (5) 145 and (6) 130 mV. (b) Cathodic current against square root of time for the rising part of the potentiostatic current transient. The applied potentials are indicated on the curves.
= I FScD’/*n’/2 211
(4)
which confirms that the electrochemical reaction is diffusion controlled. The dependence of I on I/T’/~ (see Fig. 6(a)) was found to be a straight line whose slope was used to determine the diffusion coefficient. It is also possible to calculate the diffusion coefficient from I-t transients. Chronoamperograms obtained exhibited a linear I against t-II2 relationship indicating that diffusion control took over shortly after the initial nucleation. The long time behaviour of the current transients approached the limiting behaviour for the diffusion control, i.e. the Cottrell equation: I = nFSDt12c( rt)
-“2
(5)
Thus, we calculated the diffusion coefficient value from the slope of the straight line obtained by plotting I vs. I/t’/’ (Fig. 6(b)). In the case of a quasi-reversible process, most of the authors consider that the Berzins-Delahay equation: I,, = 0.61 nFSc( nF/KT)“2u’/2D’/”
(6)
Y. Ca.strillejo
144
et al. /Journal
of Electroanalyt~cal
Clzemstry
397 (1995)
139-147
O-
for a reversible diffusion-controlled process can be used. We have calculated the value of the diffusion coefficient from the slope of the plot I, vs. u’/* (Fig. 6(c)), obtaining a value lower than the values obtained by other electrochemical techniques (0.9 X 10m5 cm2 s-‘1, which indi-
-0.002- 0.004-0.006-0.008a -O.Ol\ E - -0.012H -0.014-0.016-
0
-0.018-
(a
-0.02-
-5
-0.0221 0
0.05
0.1
0.15
0.2
0.25
C 3
-10
E/V
-z 6
is
Fig. 7. Linear sweep voltammogram of FeCI, reduction and its convoluted curve. Sweep rate 0.4 V SK’. [FeCI,] = 0.01866 mol kg-’ ; electrode area 0.45 f 0.01 cm’,
-IS
-20
-25
+
0
cates that in our conditions this equation.
( b)
-10
0
0.2
0.4
0.6 p,;m
0.0
1
1.2
it is not fully correct to apply
3.2.4. Determination of the charge-transfer kinetic parameters An alternative approach to the interpretation of the mechanism and the estimation of kinetic parameters that has proved to be very successful is the convolution [35,36] or semi-integration transform [37]. Fig. 7 shows a linear sweep voltammogram and its convoluted curve. The convolution transformation is readily performed on a small computer using numerical techniques. For non-reversible processes, it is possible to derive linear plots of logarithmic functions of convoluted current as a function of E to enable kinetic parameters to be determined. In the case of a quasi-reversible exchange with formation of an insoluble product, the expression obtained was (see Appendix): E=E”+
RT -Ink” anF
RT + -1nR anF
(7)
where: k” and a are the charge-transfer rate constant and the transfer coefficient, respectively, and E” is the standard potential of the Fe(II)/Fe(O) system. The electrode potential varies linearly with the logarithm of the function R, being: (m* -rn)D0
0.2
0.4
I r.~(Vi’~z
O-‘
l
Fig. 6. (a) Chronopotentiometric data for the reduction of 0.01866 mol kg- ’ FeCI,, S = 0.64+ 0.01 cm’. Verification of Sand’s law. (b) Current versus the inverse square root of time from chronoamperometry. [FeCI,] = 0.01866 mol kg-’ ; electrode area 0.45 50.01 cm’; &, = 90 mV. Verification of Cottrell’s law. (c) Variation of the cathodic current peak with the square root of the sweep rate. [FeCl,]= 0.01866 mol kg-‘; electrode area 0.45 & 0.01 cm2.
R=
‘I2 + nFSexp[ ( nF/RT)
( E - E”)]
I
(8) where m is the convoluted current. The slope of the linear part of the curve yields the transfer coefficient, CY, and from the intercept we can calculate the charge-transfer rate constant. The average values so obtained were: (Y= 0.45 & 0.10 and log(k”/cm s-l) = -4.44 k 0.50.
Y. Castrillejo et al./Journal
of Electroanalytical Chemistry 397 (1995) 139-147
145
All these characteristics indicate that under these conditions the electron transfer rate is significantly lower than that of mass transport [24]. Another reversibility test was performed by comparing the convoluted voltammograms. The convoluted curves were practically identical and independent of the sweep rate. However, the direct and reverse scans do not remain unchanged. The electrode potential varies linearly with log[ m/( m * - m)] and the slope of the linear part of this curve (0.211 V (decade)-‘) is different from that expected for a reversible exchange process (0.143 V (decade)-’ ). All these criteria indicate that the electrochemical Fe(III)/ Fe(I1) process is not fully reversible.
1.2
1.4
1.6
1.8
2
3.3.2. Diffusion coefficient of Fe(H) The diffusion coefficients summarized in Table 1 were calculated from the boundary semi-integral values (m * = nFSCD”*), and by applying the Sand (Eq. 4) and Randles-Sevcick equations: Ip = 0.4463nFSc(
?
I_----.
1.4(b) -0.4
0 log(v/
(9)
The values obtained are in good agreement with previous values calculated from the Fe(II)/Fe(O) exchange data as is shown in Table 1. The main source of error arises from the determination of the active surface of the working electrode. The values are also in the same order as those obtained by other authors such as Poignet and Barbier [ 151, Inman et al. [38] and Shuzhen et al. [20], who studied the Fe(I1) behaviour in different chloride melts.
I.L.?
1.3? -0.8
nF/RT)“*u’/‘D1/*
0.4
: 0.8
v s-‘I
Fig. 8. (a) Voltammetric oxidation of Fe&. [FeCI,l= 0.02550 mol kg-‘; electrode area 0.82+ 0.01 cm’. Sweep rates: (1) 0.3, (2) 0.4, (3) 0.5, (4) 0.6, (5) 0.7 and (6) 0.8 V s-‘. (b) Variation of the anodic potential peak with the logarithm of the sweep rate.
3.3.3. Reaction kinetics Linear sweep voltammetry can be used to determine the concentration and thermodynamic properties of a redox couple. Extracting mechanistic and kinetic details of a given electrochemical system is much more difficult. To
3.3.Fe(lll) / Fe(lI) exchange 3.3.1. Reversibility study Voltammograms corresponding to the B/B’ exchange were examined as a function of the scan rate (Fig. S(a)) and showed that the potential peak does not change with increasing sweep rate for values up to about 0.8 V s-l. On the other hand, the slope of the plot E vs. log[ l/(Zp - Z)] over the current range 0.31, to 0.71, approaches the theoretical value of 2.3 RT/ F, corresponding to a fast electrochemical process, whereas for higher sweep rates, when the peak potential is shifted positively (see Fig. 8(b)), the slope deviates from the theoretical value and the peak potential separation, AE,, increased with the scan rate and had a value larger than the theoretical value of 0.143 V expected for a one-electron reversible reaction at 450°C.
0.01 i
2
OI-L
0.005
-0.01-l 0.6
0.8
1
1.2
1.4
1.6
1.8
I 2
E/V Fig. 9. Linear sweep voltammogram of FeCI, oxidation - --, experimental results: -0-O-W simulated results corresponding to a reversible process. -, simulated results corresponding to a quasi-reversible process. Sweep rate: 0.5 V s- ’
146
Y. Custrillejo et al. / Journal ofElectroclnalyticcl1 Chemistry 397 (1995) 139-147
Table 2 Kinetic parameters of Fe(lII)/Fe(ll)
exchange
’
a
Technique
E, /, /V
log k” /cm s-
Simulation
I.378 & 0.002
- 1.96 + 0.07
0.38 + 0.03
E vs. log R
-
- 1.98kO.17
0.4
I & 0.07
accomplish this, we must first postulate an electrochemical mechanism. The results obtained led us to think that Fe(III)/Fe(II) exchange is a quasi-reversible process. Consequently, it was found that the information of interest could be easily extracted from the voltammograms by using a simulation computer program (M271 COOL), for a quasi-reversible mechanism in which the charge-transfer rate constant, k”, the transfer coefficient, LY, and the half-wave potential, E , ,2, were adjusted to give the best fit between the cxberimental and calculated results. We also tried to fit the system to a reversible process. However the best results were found for a quasi-reversible process. Representative examples of these simulations are shown in Fig. 9, and the average values obtained are in Table 2. In order to confirm these results, we have performed a logarithmic analysis of the convoluted voltammograms. Myland and Oldham [39] have derived linear plots of logarithmic functions of convoluted current as a function oxidation process. The equation of E for a quasi-reversible is: RT
D1/2
E=Eo+ (]_a)nF1n
k”
RT +
(1
_
+pR
The average values of k” and (Y obtained E vs. log R being:
(‘O) from the plot
I R=
-rnexp[(nF/RT)(E’-E)]
+m* -m
(ll)
were in very good agreement with the values obtained from the simulated voltammograms (see Table 21, which confirms the quasi-reversible mechanism of the Fe(III)/ Fe(I1) exchange [40].
4. Conclusions
By using voltamperometric, chronopotentiometric and chronoamperometric techniques, it was possible to determine accurately the kinetic parameters characterizing the mass and the charge transfers occurring in the electrochemical reduction and oxidation of Fe(I1) ions, The intrinsic rate constant k” and the transfer coefficient (Y of the Fe(II)/Fe(O) exchange can be extracted from the logarithmic analysis of convoluted curves by applying the equation corresponding to a soluble-insoluble quasi-reversible process. Moreover voltammograms and I-t current transients suggest that nucleation of metallic iron on a glassy
carbon electrode dominates the deposition process. Instantaneous three-dimensional nucleation and growth mechanism is observed. On the other hand, in the case of the Fe(III)/Fe(II) exchange it is possible to calculate the intrinsic rate constant k” and the transfer coefficient LY from voltammograms by comparison with simulated voltammograms calculated by using a simulation computer program, as well as by means of the logarithmic analysis of convoluted curves by applying the equation corresponding to a soluble-soluble quasi-reversible process, finding a very good agreement between both methods. The values of the k” and cy parameters showed that although both electrochemical systems are quasi-reversible, the Fe(III)/ Fe(U) exchange is closer to reversibility than the iron deposition process, which may explain why Eq. (4) gives too low values of diffusion coefficient of Fe(H) in contrast to the value obtained for the Fe(III)/Fe(II) couple.
Acknowledgements
The authors are grateful to D.G.I.C.Y.T. CE93-0017 and the Junta de Castilla y Le6n, C. de Cultura y Turismo (Spain) f or f’ma n cla . I support of this research.
Appendix
Convolution procedure. exchange
Soluble-insoluble
quasi-reeuersible
Consideration will be given to the n-electron reduction yielding an insoluble product, Ox(soln) + ne- + R(S), occurring at an electrode. In the case of semi-infinite linear diffusion, Fick’s law solutions are expressed versus the current semi-integral: c,(O,t)
= c + m( z)/~FSD”~
(A’)
in which c,(O,t) is the concentration of oxidized species on the surface of the electrode at time t; c is the bulk concentration of oxidized species; m(t) is the convoluted current and m(t) -+ m * when c,(O, t) + 0. On the other hand, for a reduction quasi-reversible process yielding an insoluble product, the Buttler-Volmer equation is: I(t)
= -nFS[
k,.c,(O,t)
+ k,]
where k, and k,. are the potential-dependent rate constants equal to:
(AT) heterogeneous
k, = k’exp’
k,. = k”exp’
(A41
Y. Castrillejo
et al. /Journal
of”Electroanalytica1
where cr is the transfer coefficient, k” the charge-transfer rate constant and E” the standard potential of the redox couple. The expression where the convoluted current and the concentration of the oxidized species at the electrode surface are related can be deduced from Eq. (Al): cO(o,t)
= ( M( t) - m * ) /nFSD’/2
(-45)
S being the electrode surface and n the number of electrons transferred. Eqs. (A2)-(A5) may be combined into: I(t)
= -nFS{[m(t)
-m*]/nFSD’/2}k,+k,
(‘46)
which may be recast as:
(ni’ - nr)D-‘/* x In
+ nFSexp[(nF/RT)(EI
E”)] (A71
References [II F. Sean, G. Picard, B. Tremillon and Y. Bertaud, French patent 2 s14 028, 1981.
[21 D. Ferry, G. Picard and B. Tremillon,
Trans. Inst. Min. Metall., Sect. C (1988) 97, C2l. [31 G. Picard, F. Sean and B. Tremillon, in M. Blander, D.S. Newman, M.L. Sahoungi, G. Mamantov and K. Johnson (Ed.), Molten Salts, The Electrochemical Society Softbound Proceedings Series, Vol. X4(2), 1984, p. 694. ]41 B. Tremillon and G. Picard, Xiyou Jinshu (Rare Metals), 4 (1985) 19. [Sl B. Tremillon and G. Picard, in G. Mamantov and R. Marassi (Eds.), Molten Salt Chemistry-An Introduction and Selected Applications, NATO ASI Series, Ser. C., Vol. 202, D. Reidel Publishing Company, 1987, pp. 305, 327. [61 M. Garcia, Y. Castrillejo, P. Pasquier and G. Picard, Molten Salt Forum, 1 (2) (1993/94) 47. [71 G. Ptcard, Molten Salt Forum, I (2) (1993/94) 25. [81 G. Picard, V. Villard, D. Ferry, J.M. Hitter and Y. Bettaud, in CL. Hussey, S.N. Flengas, J.S. Wilkes and Y. Ito (Eds.), Molten Salts, The Electrochemical Society Softbound Proceedings Series, Vol. 90 (17) p. 550. [91 G. Picard, V. Villard, Y. Bertaud, J.M. Hitter and M. Leroy, French patent, 2 6.55 055, 1989. [lOI D. Ferry. Y. Castrillejo and G. Picard, Electrochim. Acta, 33 (1988) 1661.
Chemistry
397 (1995)
139-147
147
[I I] D. Ferry, Y. Castrillejo and G. Picard, Electrochim. Acta, 34 (1989) 313. [l2] D. Ferry, G. Picard and Y. Castrillejo, J. Appl. Electrochem., 23 (1993) 73s. [13] H.A. Laitinen and J.W. Pankey, J. Am. Chem. Sot., 81 (1959) 1053. [l4] D. lnman, J.C. Legey and R. Spencer, J. Appl. Electrochem., 8 (1978) 269. [IS] J.C. Poignet and M.J. Barbier, Electrochim. Acta, 17 (1972) 1227. [I61 G. Picard, F. Stan and B. Tremillon, J. Electrochem. Sot., 129 (1982) 1450. [I71 F. Stan, G. Picard and B. Tremillon, J. Electroanal. Chem., I38 (1982) 31.5. [I81 N.I. Komilov, V.E. Solomatin and N.G. Ilyuchenko, Sov. Electrochem., S (1969) 885. [I91 H.C. Gaur and H.L. Jindal, J. Electroanal. Chem., 23 (1969) 289. [20] D. Shuzen, P. Dudley and D. Inman, J. Electroanal. Chem., 142 (1982) 21s. [21] L.G. Boxall, H.L. Jones and R.A. Osteryoung, J. Electrochem. Sot., 121 (1974) 212. [22] Yu.K. Delimarskii. E.M. Skobets and L.S. Berenblyum, Zh. Fiz. Khim., 22 (1948) 1108. [23] N.G. Chovnyk and M.V. Myshalov, Sov. Electrochem., 6 (1970) 1583. [24] A.J. Bard and L.R. Faulkner, Electrochemical Methods Fundamentals and Applications, John Wiley and Sons, New York, 1980. [2S] D.D. Mcdonald, Transient Techniques in Electrochemistry, Plenum, New York, 1977. [26] G. Mamantov, D.L. Manning and J.M. Dale, J. Electroanal. Chem., 9 (1965) 253. [27] J.A. Harrison and H.R. Thirsk, in A.J. Bard (Ed.), Electroanalytical Chemistry, Vol. 5, Dekker, New York, 1971, p. 67. [28] G. Gunawardena, G. Hills, I. Montenegro and B. Scharifker, J. Electroanal. Chem., I38 (1982) 22.5, 241 and 2.5.5. [29] G.M. Haarberg, W. Rolland, A. Sterten and J. Thonstad, J. Appl. Electrochem., 23 (1993) 217. [30] D.C. Topor and J.R. Selman, J. Electrochem. Sot.. 140 (I 993) 252. 1311 Z. Galus, Fundamental of Electrochemical Analysis, John Wiley and Sons, New York, 1976. ]32] D.G. Peters and J.J. Lingane, J. Electroanal. Chem., 2 (1961) 1. [33] K.B. Oldham, J. Electroanal. Chem., 41 (1973) 3.51. ]34] D.H. Evans and J.E. Price, J. Electroanal. Chem., 5 (1963) 77. ]35] J.C. Imbeaux and J.M. Saveant, J. Electroanal. Chem., 44 (1973) 169. ]36] J.M. Saveant and D. Tessier, J. Electroanal. Chem., 61 (1975) 251 and 65 (1975) 57. [37] K.B. Oldham, Anal. Chem., 44 (1972) 196. 1381 D. Inman, J.C. Legey and S. Spencer, J. Appl. Electrochem, 8 (1978) 269. [39] J.C. Myland and K.B. Oldham, Anal. Chem., 66 (1994) 1866. [40] H. Matsuda and Y. Ayabe, 2. Electrochem., 59 (1955) 494.
Journal of Electroanalytical
Chemistry
397 (1995) 139- 147
Electrochemical study of the properties of iron ions in ZnCl, + 2NaCl melt at 450°C ‘, A.M. Martinez a, M. Vega a, E. Barrado ‘, G. Picard b
Y. Castrillejo ’ Deptrrtanzmto h Labomtoire
de Quinzica Analiticu, d’Electrochinzie
Facultud
Analytiyue
de Ciencias, et Appliqube.
Uniwrsidcrd
de Valladolid.
Ecole Nationale
Superieure
Pmdo de In Mqdolencl de Chinlie de Paris,
S/II.
47005
Volltrdohd,
I I rue Pierre et Mrwir
Spun
Curie.
75231 Paris Cedex 05, Frunce
Received 8 December
1994; in revised form 10 May 199.5
Abstract The electrochemical properties of Fe(II) in the ZnCI, + 2NaCI melt at 450°C have been studied using a glassy carbon electrode. Iron oxidation states II and III have been shown to exist in the mixture and the stability of metallic iron has been confirmed. The kinetics of the electrodeposition and electrocrystallization of iron were studied finding that the process is quasi-reversible. In the same way, the Fe(III)/Fe(lI) exchange was found to be quasi-reversible. The values of the kinetic parameters, k” and cy for both reactions were obtained. Mass transport towards the electrode is a simple diffusion process. The diffusion coefficient was found (I .3 _t 0.4) x IO-’ cm’ s-1. Potential step measurements indicate instantaneous nucleation and growth of iron (I against r ‘I’> followed by diffusion control (Cottrell equation). Keywords~
Molten salts; Fe(H); Glossy carbon electrode
1. Introduction
Among the main applications of molten salts, one of the most promising is their use as reaction media for extractive metallurgy purposes. Fused salts can be employed at working temperatures ranging from the high temperatures corresponding to pyrometallurgy to the low temperatures used in the classical hydrometallurgy. Thus molten salt metallurgy combines the main advantages of pyrometallurgy, i.e. high kinetics of chemical reactions and the possibility of manufacturing reactive metals and materials, and that of hydrometallurgy, which is applying solution chemistry to increase the selectivity of a given process [l-7]. Molten salts are known as suitable media for metal electrowinning and electrorefining [8,9], the metallurgical properties of the deposit strongly being dependent on the operating conditions. In order to reach a better understanding and control of the deposition processes, accurate knowledge of the electrochemical deposition mechanism is essential. In this way, electrocrystallization studies are very important. Nucleation and growth in metal deposition depend to a great extent on the substrate onto which the electrochemical reduction is performed, because of not only its chemical nature, but also its structural state. The nucleation process is closely related to the active sites 0022-0728/95/$09.50
0
SSDI 0022.0728(95)04151-6
1995 Elsevier
Science S.A. All rights reserved
existing on the substrate. Thus, with the same bath and the same experimental conditions, different deposits can be obtained by using various substrates. This study is part of a systematic research [lo-121 concerning: (i) the possibility of using mixtures of ZnC1, with alkali chlorides for the electrolytic production of zinc; (ii) the effect of impurities present in the cell feed; (iii) the possibility of using these mixtures for the treatment and recuperation of metals, such as iron, contained in ores and industrial wastes of zinc. There have been many electrochemical studies of iron ions in molten salts. More of them have been carried out in molten alkali and alkaline-earth chlorides than in any other halide system. In this way the eutectic LiCl + KCI [13-I 71, the equimolar mixture of KC1 + NaCl [ 181, MgCl 2 + KC1 and MgCl, + NaCl + KCI mixtures [ 19,201, and the AlCI, + NaCl [21-231 (in which the Fe(II), Fe(II1) and Fe(O) oxidation states are known to be stable) have been investigated. In an early study using AlCl, + NaCl melts at 3OO”C, Delimarskii et al. [22] obtained two electrochemical reduction waves for Fe(II1) ions, presumably related to Fe(I1) and Fe metal, respectively, whereas Laitinen and Pankey [13], working with LiCl + KC1 and platinum electrode at 4OO”C, did not observe an electrochemical reduction wave for the step Fe(II1) + e-e Fe(II), which was
140
Y. Cmtrillejo
et al. /Joumni
of Electronnd~ticcd Chemistry 397 (1995) 139-147
explained in terms of the chemical reduction of Fe(I1) ions by platinum. Most authors have investigated the kinetics of the Fe(H) electrochemical reduction in molten chlorides, finding that the process was controlled by the mass transfer rate of F&I) ions to the electrode surface and that the electronic exchange was reversible. The present study is related to the electrochemical properties of iron in ZnCl, + 2NaCl melt. The stability of the different oxidation states was first investigated. The properties of the Fe(III)/Fe(II) and Fe(II)/Fe(O) exchanges were studied and the kinetic parameters for both systems were calculated, using different electrochemical techniques with glassy carbon as working electrode. In addition, electrocrystallization of iron on glassy carbon was examined.
2. Experimental 2.1. Prepurutiorl
and purification
of the melt
The ZnCl, + 2NaCl melt (analytical grade Merck products) was contained in a 100 cm3 Pyrex crucible placed in a Pyrex cell. The temperature was maintained constant within +2”C by means of a Taner furnace and a West 3200 programmable device. The mixture was fused under vacuum, purified by bubbling hydrogen chloride and then kept under a dry argon atmosphere, a procedure used previously [I I].
concentrations the solutions became dark red-brown. After long experiments (aproximately 4-5 days) some volatilised material was found on the cooler parts of the cell.
3. Results
and discussion
3.1. Stable oxidation
states
After the purification of the ZnCl, + 2NaCl melt and using a glassy carbon electrode, the electrochemical window of the melt was 1.885 V, extending from 1.885 V (chlorine evolution) to 0 V (zinc deposition) with respect to the Zn(II)/Zn reference electrode (Fig. l(a)). Fig. l(b) shows a typical linear sweep voltammogram for the reduction of a Fe(I1) solution. In the potential range 0.6 to 0 V (zone 1). a cathodic peak, A, and one sharp anodic stripping peak, A’, are evident. The shape of the voltammogram, the break corresponding to the beginning of the Fe(I1) reduction (characteristic of the formation and the reoxidation of a constant activity product). and the peak potential values are typical of those expected for the
-__I
i
O.l-
0.05. s
2.2. Electrochemical
apparatus
The emf measurements were carried out with a high impedance voltmeter (Crison 2002). Cyclic voltammetry and pulse techniques were performed with a PAR (Princeton Applied Research) Model 273A potentiostat/ galvanostat controlled with the M270 software package. The simulated voltammograms were recorded with M271 COOL kinetic analysis software. A glassy carbon rod (3 mm diameter) was used as working electrode, while a graphite rod served as the counter electrode. The reference electrode consisted of a Pyrex glass tube filled with liquid zinc and covered with molten ZnCl 2 + 2NaCl. A tungsten wire was inmersed into the liquid zinc to ensure electrical connection with the reference electrode (Zn(II>/Zn(liq) redox couple).
0
1
-0.2
0
I
0.2
*
0.4
1
0.6
-
0.8
8
3
1
I
8
1
1.2
1.4
1.6
1.8
0.8 1 E/V
1.2
1.4
1.6
1.B
Elv
s c(
2.3. General features 20n.1-
The Fe(I1) ions were prepared in situ by anodic dissolution of the metal (Aldrich Chem. Co. iron wire, 1 mm diameter) at constant current. The amount of iron ions generated can be calculated by means of Faraday’s law (0.01866, 0.02801, 0.03850 and 0.02550 mol kg-‘). The presence of Fe(I1) in the purified melts produced, at low concentration, pale yellow solutions, whilst at higher
0.02 -0.2
0
0.2
0.4 0.6
(b)
Fig. 1. (a) Linear sweep voltammogram obtained at a glassy carbon electrode in a pure ZnCI, + 2NaCI melt (sweep rate 0.2 V s- ’; electrode area 0.45 5 0.01 cm*). (b) Typical linear sweep voltammogram for the reduction of iron chloride (0.01866 mol kg-’ ) on a glassy carbon electrode (sweep rate 0.2 V s- ’).
Y. Castrillejo
et al. /Journal
~~~Electmanulytical
(b)
Fe
Chemistry
397 (1995)
139-147
141
iron wire in different solutions containing Fe2’ in concentrations between 10e2 and 10-l mol kg-‘. A plot of the cell emf versus the logarithm of the Fe(I1) concentration was linear with a slope of 0.070 V (decade)-‘, which is in agreement with the theoretical value for a two-electron process at 450°C (0.072 V (decade)-‘). We found that E&,~,I~,Fe~is 0.341 f 0.001 V (molality scale). The experimental problems related to the low solubility and the hygroscopic characteristics of FeCl, prevented direct measurement of the standard potential of the Fe(III)/ Fe(B) re d ox system. Nevertheless, it was possible to estimate it from voltammetric measurements by applyE,,, = (Ei + Ei)/2 (where Ei and ing the relationship: EE are the anodic and the cathodic peak potentials respectively), assuming that the Fe(II1) and Fe(I1) diffusion coefficients are so similar that the standard potential of the Fe(III)/Fe(II) system can be taken equal to the half-wave potential of the Fe(I1) oxidation, E,,,. The average value obtained was E&l,,~,Fe~,,~ = 1.403 i 0.002 V. 3.2. Fe(H) / Fe(O) exchange
L
2
As shown in Fig. l(b), the cathodic peak corresponding to the electroreduction of Fe(B) ions presents a steep rise and slow decay, and the anodic peak has the expected characteristics of a stripping peak, decay steeper than rise. The ratios of the forward-to-reverse current peaks (,,“/I%> are typical of a process leading to an insoluble product. A more significant and less arbitrary parameter is the ratio Qa/Qc3 anodic charge/ total cathodic charge, including that after sweep reversal. This remains approximately constant and equal to unity with increasing sweep rate, which indicates that all deposited material on the electrode is electrochemically removed during the positive sweep and also that there are no chemical reactions coupled to the primary electrochemical process.
R
e CC”)
Fig. 2. (a) SEM micrograph of an iron deposit. (b) ED analysis deposit shown in (a). (c) X-ray diffraction of the deposit formed.
for the
deposition and reoxidation of an insoluble product. This was confirmed by deposition of the metal under potentiostatic conditions (150 mV). The deposit obtained consisted of pure metallic iron (determined by energy dispersive X-ray analysis with the scanning microscope and by X-ray diffraction) (Fig. 2(a-c)). We will therefore assume that the reaction along cathodic peak A is Fe(H) + 2e- ti Fe(O). Moreover, Fig. l(b) shows an anodic wave B’ associated with the cathodic wave B in the potential range 1.0 to 1.8 V (zone 2). The shape of the B/B’ system was characteristic of a soluble-soluble exchange related to the Fe(III)/ Fe(I1) couple. The standard potential of the Fe(II)/Fe system was determined by measuring the equilibrium potential of an
3.2. I. Reuersibilit_v study Voltammograms yield more information about the iron deposition process. The study of the voltammetric curves recorded at different potential sweep rates (Fig. 3(a)) clearly shows that the cathodic as well as the anodic peak potentials shifted with increasing sweep rate, suggesting that the deposition is not a reversible process. In Fig. 3(b) Ei is plotted vs. log 0, giving AE,/Alogu = 84 mV. For a two-electron irreversible reaction with a transfer coefficient, cr, equal to 0.40, the variation 2,3RT/2anF is equal to 90 mV at 450°C. This criterion proves that the Fe(II)/ Fe(O) exchange is quasi-reversible [24,25] with a first approximation of the transfer coefficient equal to 0.43. The number of electrons transferred during the reduction process can be calculated from the half-peak width. For a reversible deposition of an insoluble product [26], the half-peak width is: E, - Ep/Z = -0.77RT/nF
(‘1
142
Y. Crtstrillejo
et cd. /Journal
of Electronnnlytical
where E, is the peak potential, E,,,z the half-peak potential and II the number of electrons transferred in the rate-determining step. R, T and F have the usual meanings. The average value of n calculated for the voltammograms recorded under conditions where any nucleation phenomenon does not occur by means of the above equation is unsatisfactory, which can be explained by the quasi-reversibility of the iron deposition. A further study of the electrochemical behaviour of iron ion reduction was made using chronopotentiometry. The plots of the electrode potentials vs. log [l - (Z/T>‘/‘] were linear, but the slope of the linear part of the curve (0.089 V (decade)-‘) is slightly different from the theoretical value for a two-electron reversible exchange process (0.072 V (decade)-‘> at 450°C. Taken together, these results show that the Fe(II)/ Fe(O) exchange dots not have a typical reversible behaviour and suggest that it is a quasi-reversible process. 3.2.2. Electrochemical nucleation The voltammogram presented in Fig. 4 suggests the presence of the nucleation process. A cross-over (hysteresis) of the cathodic peak after potential reversal may be
0 - 0.002 - 0.004 : H
-0.006 - O.OO& I-0.01
(a) Xi
o.i5
011
0:2
0
E/V
-I .4
-1.2
-I
-0.8 log
-0.6
-0.4
-0.2
0
cv/vs-‘)
Fig. 3 (a) Voltammetric reduction of iron chloride. FeCl? concentration 0 01 X66 mol kg ' ; electrode area 0.45 + 0.01 cm*; sweep rates: (1) 0.05 (2) 0.075 (7) 0. I V s ’ (b) Variation of the cathodic potential peak with the logarithm of the sweep rate.
Chemistry
397
(I 9951
139-
147
o.w0.030.02-
s
O.Ol0--
P -o.Ol-0.02-0.03~
0
* 1 I 0.05 0.1 0.15 0.2 0.25 03
0.35
1
0.4
1
0.45
0.5
EN Fig. 4. Linear sweep voltammogram obtained at a glassy carbon electrode (0.45 kO.01 cm*) in ZnCI, +2NaCI at 450°C. Sweep rate 0.7 V s- ‘. FeCl 2 concentration 0.0 I866 mol kg- ’
observed. This phenomenon indicates a phase formation and growth. The current-time transients obtained were particularly sensitive to nucleation and growth phenomena. In this potentiostatic step or pulse method, the potential of the working electrode is stepped from a potential slightly positive of the metal deposition potential to a potential in the range where the deposition occurs (this potential step is named overpotential, though it is not a departure from a well-defined potential in the thermodynamic sense>. If the metal is deposited on a foreign substrate, the initial response of the current yields information about the nucleation behaviour of the metal on the substrate in question. Usually, the transient is compared with expressions from nucleation theory [27-301, which are valid for basic types of nucleation and growth. Fig. 5(a) shows typical I - t transients for the deposition of iron on a foreign surface (glassy carbon). As the applied potentials were between 180 mV and 100 mV, a significant change in the usual habit of l-t transients took place. After the initial double layer charging, the current dropped to a minimum and then rose with time. At even more negative potentials the current still passed through a minimum, and then a maximum, before finally decaying in the usual way with time. The appearance of the I-t transients indicated that nucleation and growth phenomena play a part in the overall deposition process. After every run the deposited iron was removed from the surface by polarizing the working electrode anodically. The most interesting part of the cathodic I-t transients is the rising portion of the curve which corresponds to the current before overlapping of the first monolayer of the growing nuclei and therefore it can be used to determine the kinetics of nuclei growth. The time corresponding to the maximum current, t,,,, is
Y. Castrillejo
et al. /Journal
of Electroancclytical
related to the time at which full coalescence of the crystallites occursThere are two types of nucleation [28] described by: (= nFS~(2D)‘/2c3/2M1/2No for instantaneous at the beginning I = (4/3)nF%(
p-‘/2t’/2
1/2ANot”/2
I
1 E
I
4
6
-0.004
T l-l
\
-0.006
\
165
mV
160 mV
-0.007 -0.008 155 mV -0.009*
0.2
0.4
0.6
0.8
coefficients
(b)
I
1.2
obtained by different techniques
Technique
IO’ D/cm’ 5-l from Fe(II)/Fe system values
IO’ D/cm2 s-’ from Fe(III)/Fe(II) system values
Voltammetry Semi-integral Chronopotentiometry Chronoamperometry
_
I.3 * 0.I I .4 + 0.2 I.2 & 0.2
I .2 * 0.4 I.3 i_0.3 I .6 & 0.4
_
mechanisms [28,29]. The products of current and time at the current maxima were evaluated. The product (I,, t,,,) was found to decrease rapidly with increasing overpotential, while the product (Ii . t,,,) showed a stable value. This indicates growth of three-dimensional centers randomly nucleated. 3.2.3. The diffusion coefficient of Fe(ll) The diffusion coefficients, DFeC,,), given in Table 1, were calculated from different electrochemical techniques by applying the appropriate equations. It has to be indicated that although a glassy carbon rod was used as working electrode, all the formulas used are relevant to the plane semi-infinite diffusion because under the experimental conditions, the corrections related to cylindrical geometry can be neglected [3 l-341. We can obtain the diffusion coefficient of Fe(B) from the boundary semi-integral values by means of the relationship: m’ = t~FscD’/~, where m* is the limiting value of the convoluted current, c the bulk concentration of the electroactive species, D its diffusion coefficient and S the electrode surface area. Chronopotentiometrical studies of the reduction of Fe(B) obeyed Sand’s law: [ri/2
(a)
-0.003
-0.005
Table I Iron (II) diffusion
143
139-147
(3)
for progressive nucleation in which the nuclei are continuously formed during the crystal growth. In the equations, M represents the mol mass, N, the number of nucleation sites at t = 0, p the density and A the nucleation rate constant. The analysis of the rising part of the cathodic l-t transients obtained (Fig. 5(a)), obeyed an I against t’/’ linear relationship according to Eq. (2) (Fig. 5(b)). Therefore, the initial stages at the surface of the substrate of electrochemical deposition of iron on the glassy carbon electrode can be explained in terms of a model involving instantaneous nucleation. Several diagnostic criteria have been developed for testing current transients with respect to the nucleation
- 0.002
397 (1995)
(2)
nucleation in which the nuclei are formed of the pulse; and D)3’2c”‘2M”~-
Chemistry
I:4I
tl/2,Sl/2
Fig. 5. (a) Potentiostatic current transients for electrochemical deposition of iron on a glassy carbon electrode in ZnCl, + 2NaCI at 450°C. [FeCI? 1 = 0.01866 mol kg-‘; electrode area 0.45 cm’. The applied potentials are: (1) 170, (2) 165, (3) 160, (4) 155, (5) 145 and (6) 130 mV. (b) Cathodic current against square root of time for the rising part of the potentiostatic current transient. The applied potentials are indicated on the curves.
= I FScD’/*n’/2 211
(4)
which confirms that the electrochemical reaction is diffusion controlled. The dependence of I on I/T’/~ (see Fig. 6(a)) was found to be a straight line whose slope was used to determine the diffusion coefficient. It is also possible to calculate the diffusion coefficient from I-t transients. Chronoamperograms obtained exhibited a linear I against t-II2 relationship indicating that diffusion control took over shortly after the initial nucleation. The long time behaviour of the current transients approached the limiting behaviour for the diffusion control, i.e. the Cottrell equation: I = nFSDt12c( rt)
-“2
(5)
Thus, we calculated the diffusion coefficient value from the slope of the straight line obtained by plotting I vs. I/t’/’ (Fig. 6(b)). In the case of a quasi-reversible process, most of the authors consider that the Berzins-Delahay equation: I,, = 0.61 nFSc( nF/KT)“2u’/2D’/”
(6)
Y. Ca.strillejo
144
et al. /Journal
of Electroanalyt~cal
Clzemstry
397 (1995)
139-147
O-
for a reversible diffusion-controlled process can be used. We have calculated the value of the diffusion coefficient from the slope of the plot I, vs. u’/* (Fig. 6(c)), obtaining a value lower than the values obtained by other electrochemical techniques (0.9 X 10m5 cm2 s-‘1, which indi-
-0.002- 0.004-0.006-0.008a -O.Ol\ E - -0.012H -0.014-0.016-
0
-0.018-
(a
-0.02-
-5
-0.0221 0
0.05
0.1
0.15
0.2
0.25
C 3
-10
E/V
-z 6
is
Fig. 7. Linear sweep voltammogram of FeCI, reduction and its convoluted curve. Sweep rate 0.4 V SK’. [FeCI,] = 0.01866 mol kg-’ ; electrode area 0.45 f 0.01 cm’,
-IS
-20
-25
+
0
cates that in our conditions this equation.
( b)
-10
0
0.2
0.4
0.6 p,;m
0.0
1
1.2
it is not fully correct to apply
3.2.4. Determination of the charge-transfer kinetic parameters An alternative approach to the interpretation of the mechanism and the estimation of kinetic parameters that has proved to be very successful is the convolution [35,36] or semi-integration transform [37]. Fig. 7 shows a linear sweep voltammogram and its convoluted curve. The convolution transformation is readily performed on a small computer using numerical techniques. For non-reversible processes, it is possible to derive linear plots of logarithmic functions of convoluted current as a function of E to enable kinetic parameters to be determined. In the case of a quasi-reversible exchange with formation of an insoluble product, the expression obtained was (see Appendix): E=E”+
RT -Ink” anF
RT + -1nR anF
(7)
where: k” and a are the charge-transfer rate constant and the transfer coefficient, respectively, and E” is the standard potential of the Fe(II)/Fe(O) system. The electrode potential varies linearly with the logarithm of the function R, being: (m* -rn)D0
0.2
0.4
I r.~(Vi’~z
O-‘
l
Fig. 6. (a) Chronopotentiometric data for the reduction of 0.01866 mol kg- ’ FeCI,, S = 0.64+ 0.01 cm’. Verification of Sand’s law. (b) Current versus the inverse square root of time from chronoamperometry. [FeCI,] = 0.01866 mol kg-’ ; electrode area 0.45 50.01 cm’; &, = 90 mV. Verification of Cottrell’s law. (c) Variation of the cathodic current peak with the square root of the sweep rate. [FeCl,]= 0.01866 mol kg-‘; electrode area 0.45 & 0.01 cm2.
R=
‘I2 + nFSexp[ ( nF/RT)
( E - E”)]
I
(8) where m is the convoluted current. The slope of the linear part of the curve yields the transfer coefficient, CY, and from the intercept we can calculate the charge-transfer rate constant. The average values so obtained were: (Y= 0.45 & 0.10 and log(k”/cm s-l) = -4.44 k 0.50.
Y. Castrillejo et al./Journal
of Electroanalytical Chemistry 397 (1995) 139-147
145
All these characteristics indicate that under these conditions the electron transfer rate is significantly lower than that of mass transport [24]. Another reversibility test was performed by comparing the convoluted voltammograms. The convoluted curves were practically identical and independent of the sweep rate. However, the direct and reverse scans do not remain unchanged. The electrode potential varies linearly with log[ m/( m * - m)] and the slope of the linear part of this curve (0.211 V (decade)-‘) is different from that expected for a reversible exchange process (0.143 V (decade)-’ ). All these criteria indicate that the electrochemical Fe(III)/ Fe(I1) process is not fully reversible.
1.2
1.4
1.6
1.8
2
3.3.2. Diffusion coefficient of Fe(H) The diffusion coefficients summarized in Table 1 were calculated from the boundary semi-integral values (m * = nFSCD”*), and by applying the Sand (Eq. 4) and Randles-Sevcick equations: Ip = 0.4463nFSc(
?
I_----.
1.4(b) -0.4
0 log(v/
(9)
The values obtained are in good agreement with previous values calculated from the Fe(II)/Fe(O) exchange data as is shown in Table 1. The main source of error arises from the determination of the active surface of the working electrode. The values are also in the same order as those obtained by other authors such as Poignet and Barbier [ 151, Inman et al. [38] and Shuzhen et al. [20], who studied the Fe(I1) behaviour in different chloride melts.
I.L.?
1.3? -0.8
nF/RT)“*u’/‘D1/*
0.4
: 0.8
v s-‘I
Fig. 8. (a) Voltammetric oxidation of Fe&. [FeCI,l= 0.02550 mol kg-‘; electrode area 0.82+ 0.01 cm’. Sweep rates: (1) 0.3, (2) 0.4, (3) 0.5, (4) 0.6, (5) 0.7 and (6) 0.8 V s-‘. (b) Variation of the anodic potential peak with the logarithm of the sweep rate.
3.3.3. Reaction kinetics Linear sweep voltammetry can be used to determine the concentration and thermodynamic properties of a redox couple. Extracting mechanistic and kinetic details of a given electrochemical system is much more difficult. To
3.3.Fe(lll) / Fe(lI) exchange 3.3.1. Reversibility study Voltammograms corresponding to the B/B’ exchange were examined as a function of the scan rate (Fig. S(a)) and showed that the potential peak does not change with increasing sweep rate for values up to about 0.8 V s-l. On the other hand, the slope of the plot E vs. log[ l/(Zp - Z)] over the current range 0.31, to 0.71, approaches the theoretical value of 2.3 RT/ F, corresponding to a fast electrochemical process, whereas for higher sweep rates, when the peak potential is shifted positively (see Fig. 8(b)), the slope deviates from the theoretical value and the peak potential separation, AE,, increased with the scan rate and had a value larger than the theoretical value of 0.143 V expected for a one-electron reversible reaction at 450°C.
0.01 i
2
OI-L
0.005
-0.01-l 0.6
0.8
1
1.2
1.4
1.6
1.8
I 2
E/V Fig. 9. Linear sweep voltammogram of FeCI, oxidation - --, experimental results: -0-O-W simulated results corresponding to a reversible process. -, simulated results corresponding to a quasi-reversible process. Sweep rate: 0.5 V s- ’
146
Y. Custrillejo et al. / Journal ofElectroclnalyticcl1 Chemistry 397 (1995) 139-147
Table 2 Kinetic parameters of Fe(lII)/Fe(ll)
exchange
’
a
Technique
E, /, /V
log k” /cm s-
Simulation
I.378 & 0.002
- 1.96 + 0.07
0.38 + 0.03
E vs. log R
-
- 1.98kO.17
0.4
I & 0.07
accomplish this, we must first postulate an electrochemical mechanism. The results obtained led us to think that Fe(III)/Fe(II) exchange is a quasi-reversible process. Consequently, it was found that the information of interest could be easily extracted from the voltammograms by using a simulation computer program (M271 COOL), for a quasi-reversible mechanism in which the charge-transfer rate constant, k”, the transfer coefficient, LY, and the half-wave potential, E , ,2, were adjusted to give the best fit between the cxberimental and calculated results. We also tried to fit the system to a reversible process. However the best results were found for a quasi-reversible process. Representative examples of these simulations are shown in Fig. 9, and the average values obtained are in Table 2. In order to confirm these results, we have performed a logarithmic analysis of the convoluted voltammograms. Myland and Oldham [39] have derived linear plots of logarithmic functions of convoluted current as a function oxidation process. The equation of E for a quasi-reversible is: RT
D1/2
E=Eo+ (]_a)nF1n
k”
RT +
(1
_
+pR
The average values of k” and (Y obtained E vs. log R being:
(‘O) from the plot
I R=
-rnexp[(nF/RT)(E’-E)]
+m* -m
(ll)
were in very good agreement with the values obtained from the simulated voltammograms (see Table 21, which confirms the quasi-reversible mechanism of the Fe(III)/ Fe(I1) exchange [40].
4. Conclusions
By using voltamperometric, chronopotentiometric and chronoamperometric techniques, it was possible to determine accurately the kinetic parameters characterizing the mass and the charge transfers occurring in the electrochemical reduction and oxidation of Fe(I1) ions, The intrinsic rate constant k” and the transfer coefficient (Y of the Fe(II)/Fe(O) exchange can be extracted from the logarithmic analysis of convoluted curves by applying the equation corresponding to a soluble-insoluble quasi-reversible process. Moreover voltammograms and I-t current transients suggest that nucleation of metallic iron on a glassy
carbon electrode dominates the deposition process. Instantaneous three-dimensional nucleation and growth mechanism is observed. On the other hand, in the case of the Fe(III)/Fe(II) exchange it is possible to calculate the intrinsic rate constant k” and the transfer coefficient LY from voltammograms by comparison with simulated voltammograms calculated by using a simulation computer program, as well as by means of the logarithmic analysis of convoluted curves by applying the equation corresponding to a soluble-soluble quasi-reversible process, finding a very good agreement between both methods. The values of the k” and cy parameters showed that although both electrochemical systems are quasi-reversible, the Fe(III)/ Fe(U) exchange is closer to reversibility than the iron deposition process, which may explain why Eq. (4) gives too low values of diffusion coefficient of Fe(H) in contrast to the value obtained for the Fe(III)/Fe(II) couple.
Acknowledgements
The authors are grateful to D.G.I.C.Y.T. CE93-0017 and the Junta de Castilla y Le6n, C. de Cultura y Turismo (Spain) f or f’ma n cla . I support of this research.
Appendix
Convolution procedure. exchange
Soluble-insoluble
quasi-reeuersible
Consideration will be given to the n-electron reduction yielding an insoluble product, Ox(soln) + ne- + R(S), occurring at an electrode. In the case of semi-infinite linear diffusion, Fick’s law solutions are expressed versus the current semi-integral: c,(O,t)
= c + m( z)/~FSD”~
(A’)
in which c,(O,t) is the concentration of oxidized species on the surface of the electrode at time t; c is the bulk concentration of oxidized species; m(t) is the convoluted current and m(t) -+ m * when c,(O, t) + 0. On the other hand, for a reduction quasi-reversible process yielding an insoluble product, the Buttler-Volmer equation is: I(t)
= -nFS[
k,.c,(O,t)
+ k,]
where k, and k,. are the potential-dependent rate constants equal to:
(AT) heterogeneous
k, = k’exp’
k,. = k”exp’
(A41
Y. Castrillejo
et al. /Journal
of”Electroanalytica1
where cr is the transfer coefficient, k” the charge-transfer rate constant and E” the standard potential of the redox couple. The expression where the convoluted current and the concentration of the oxidized species at the electrode surface are related can be deduced from Eq. (Al): cO(o,t)
= ( M( t) - m * ) /nFSD’/2
(-45)
S being the electrode surface and n the number of electrons transferred. Eqs. (A2)-(A5) may be combined into: I(t)
= -nFS{[m(t)
-m*]/nFSD’/2}k,+k,
(‘46)
which may be recast as:
(ni’ - nr)D-‘/* x In
+ nFSexp[(nF/RT)(EI
E”)] (A71
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