On the source of oscillatory instabilities in the electroreduction of thiocyanate complexes of nickel(II) at mercury electrodes

www.elsevier.nl/locate/jelechem Journal of Electroanalytical Chemistry 478 (1999) 118 – 127

On the source of oscillatory instabilities in the electroreduction of thiocyanate complexes of nickel(II) at mercury electrodes Rafal* Jurczakowski, Marek Orlik * Laboratory of Electroanalytical Chemistry, Department of Chemistry, Uni6ersity of Warsaw, ul. Pasteura 1, PL-02093 Warsaw, Poland Received 6 July 1999; received in revised form 11 October 1999; accepted 12 October 1999

Abstract The mechanistic aspects of the electroreduction of thiocyanate complexes of nickel(II) at mercury electrodes, responsible for the formation of the negative polarization resistance and oscillatory instabilities, were studied. Of two possible sources of negative resistance–adsorption of an inhibitory layer of NiS and the desorption of catalytic SCN− from mercury surface at negative potentials, the latter was found to predominate under the conditions studied. Nickel(II) sulphide was suggested as one of the causes for the limited lifetime of oscillations only, and not as a source of actually observed instabilities. An inner-sphere bridge mechanism of the electroreduction of thiocyanate complexes of nickel(II) was proposed, as this pathway is considerably faster than the irreversible outer-sphere reduction, occurring at more negative potentials. The proposed mechanism was confirmed quantitatively by its digital simulation and compared with that suggested earlier for In(III)SCN− complexes. An example of current oscillations is presented. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Thiocyanate complexes of nickel(II); Electrochemical oscillations; Electrocatalysis; Chronocoulometry; Adsorption simulation

1. Introduction In recent years studies of various kinds of chemical instabilities (particularly oscillations [1 – 6]) has become a subject of increasing interest, due to their significance for better understanding of the self-organization of matter, which can occur for non-linear irreversible processes. For various kinds of physical and chemical oscillators important universalities were observed [1– 12]. Among the chemical oscillators, an important class comprises electrochemical systems [13 – 16]. One of the typical sources of oscillations in such systems is the interaction of the negative polarization resistance and the ohmic drop, coupled with the transport (e.g. diffusion) of the reactant between the bulk solution and the electrode surface. An example of such an electrochemical oscillator which, however, was not investigated thoroughly enough till now, involves the thiocyanate complexes of nickel(II). Tamamushi and Matsuda [17] and recently Koper and Sluyters [18] were probably the only ones * Corresponding author. Fax: +48-22-822-5996. E-mail address: [email protected] (M. Orlik)

who reported that the region of negative resistance observed on dc polarograms of Ni(II) for lower ionic strength (1 to 2 mol dm − 3 NaSCN) can cause current oscillations in a two-electrode system (DME [17] or HMDE [18] — mercury pool), if the appropriate serial ohmic resistance (and also inductance [17]) is present in the circuit. In Ref. [18] transient and rather irregular oscillations were reported. On the basis of some similarities in the electrochemical behavior of In(III)SCN− [18–27] and Ni(II)SCN− complexes, Tamamushi and Matsuda suggested [17] that for both these systems a similar mechanism for the formation of a negative polarization resistance, caused by desorption of SCN− ions from the negatively charged mercury surface, operates. Furthermore [18], the accumulation of nickel amalgam was suggested as a cause for the transient character of the oscillatory regime for the Ni(II)SCN− system. One should add that similarities between the mechanism of In(III)SCN− and Ni(II)SCN− electroreduction, concerning the role of adsorbed SCN− ions, were suggested also by de Levie [28]. On the other hand, the non-oscillatory electroreduction mechanism of Ni(II)SCN− complexes was in past years quite intensively studied, by Krogulec et al. [29–

0022-0728/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 2 2 - 0 7 2 8 ( 9 9 ) 0 0 4 2 3 - 4

R. Jurczakowski, M. Orlik / Journal of Electroanalytical Chemistry 478 (1999) 118–127

32] among others, who proved that the Ni(II)SCN− system undergoes electroreduction according to a more complicated mechanism than that of In(III)SCN− complexes, involving two parallel reaction pathways. One reaction route involved direct reduction of Ni(II)SCN− complexes to the nickel(0) amalgam with the liberation of coordinated SCN− ions. The second one, occurring at similar potentials, proceeded through the reduction of SCN−, catalyzed by Ni(II) ion, which led to the formation of a surface active nickel(II) sulfide NiS and to the release of CN− ions which could further form Ni(CN)24 − ions in the solution. For our present considerations it is particularly noteworthy that in the typical experimental conditions used by Krogulec et al. (cf. fig. 2 in Ref. [30]), i.e. for high ionic strength = 4.8 mol dm − 3, scarcely any region of remarkable negative polarization resistance was observed on the dc chronocoulometric curves. Instead, it was incidentally reported for 1 mol dm − 3 NaSCN and was then ascribed not to the desorption of catalytic SCN− ions, but to the formation of a self-inhibitory layer of NiS on the mercury surface (cf. fig. 1 in Ref. [30]). As in this way a controversy had appeared as to which species (adsorbed SCN− or NiS) was responsible for the formation of a negative polarization resistance and thus for the oscillations, we extended our mechanistic studies of the Ni(II)SCN− system. The results of such experimental and theoretical considerations, supported with a digital simulation of the crucial points of the proposed mechanism, are described in this paper.

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2. Experimental

2.1. Reagents Crystalline nickel(II) perchlorate, Ni(ClO4)2·6H2O, was obtained by the neutralization of the p.a. basic nickel(II) carbonate (POCh) with the appropriate amount of p.a. perchloric acid (APOLDA), followed by recrystallization from triply distilled water. The concentrations of aqueous solutions of Ni(ClO4)2·6H2O were determined by complexometric titration with EDTA [33]. Pure crystalline indium(III) nitrate (POCh, Poland) was used without further purification. Commercially available pure (Reachim) and p.a. sodium thiocyanate (Fluka), NaSCN and p.a. NaClO4·H2O (APOLDA and FERAK-Berlin) were purified by recrystallization from triply distilled water. The concentrations of stock NaSCN and NaClO4 solutions were determined by measurements of their density and comparison with literature data [34]. Thiocyanate complexes of nickel(II) and indium(III) were prepared ex tempore in the electrolytic cell by mixing of appropriate amounts of solutions of nickel(II) perchlorate or indium(III) nitrate with sodium thiocyanate. All solutions were prepared with triply distilled water, purified in a final step using Millipore filters. Commercially available p.a. mercury (POCh), purified from traces of mercury oxide by filtration, was used. Commercially available pure 1-octanol (Reachim) and hexamethylphosphoramide (Fluka) were used without additional purification. The saturated solutions of 1-octanol in the presence of supporting electrolyte were obtained by prolonged shaking of an excess of this alcohol with 1 mol dm − 3 NaSCN at ambient temperature. Prior to measurements the sample solutions were deaerated using pure argon (Multax, Poland) which had been purified from traces of oxygen by passage through a wash-bottle filled with an acidified solution of vanadium(II) in contact with zinc amalgam. Two additional traps, one filled with the solution of NaOH (pure, POCh), and the next one with triply distilled water were used, in order to avoid the contact of the solution being studied with the vapours of acid and traces of hydroxides.

2.2. Apparatus

Fig. 1. Dc chronocoulometric wave of the solution 1 × 10 − 3 mol dm − 3 Ni(ClO4)2 + 1 mol dm − 3 NaSCN. Current integration time t1 =3 s, T = 298 K, potential scale with respect to Ag AgSCN electrode.

2.2.1. Electrodes For chronoamperometric experiments a static mercury electrode (SMDE), manufactured by Laboratorni Prˇistroje (Czechoslovakia) was used as a working electrode of surface area A1 = 0.0296 cm2 or A2 = 0.0216 cm2. In dc and ac polarographic (chronocoulometric) measurements a dropping mercury electrode

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Fig. 2. Kinetic analysis of the normal pulse chronocoulometric curves, at potentials: E1 = −0.73 V, E2 = − 1.08 V and E3 = −1.33 V. Electrode surface area A =1.49× 10 − 2 cm2, T= 298 K, potential scale with respect to Ag AgSCN electrode. The Q–E curves were obtained by substraction of the charge recorded for pure 0.5 mol dm − 3 NaSCN solution from that recorded for the sample containing also 5×10 − 4 mol dm − 3 Ni(ClO4)2.

of a mechanically controlled lifetime t1 =1 to 5 s was applied. The flow of mercury was m =0.773 mg s − 1 at h = 33.5 cm. For chronocoulometric measurements the potential of the working mercury electrode was controlled in a three-electrode setup with respect to the Ag AgSCN 0.1 mol dm − 3 NaSCN reference electrode, separated by a glass frit from the solution being studied. As a counter electrode a platinum foil (surface area of 1.5 cm2) was used. For chronoamperometric measurements of the oscillatory phenomena, in order to minimize the resistance of the electrode system itself, the mercury pool was used as both a low-ohmic anode and a reference electrode. The potentials of both reference electrodes were occasionally monitored with respect to a calomel electrode (Radelkis) filled with saturated aqueous NaCl solution (SSCE). The potential of the mercury pool in contact with 1 mol dm − 3 NaSCN was found to be 63 mV more negative than that of the Ag AgSCN 0.1 mol dm − 3 NaSCN reference electrode. The potential of the latter electrode was found to be 88 mV more negative than that of the SSCE (both potential differences include liquid junction potentials).

2.2.2. Instrumentation Chronoamperometric experiments were performed with the use of an EG&G PARC potentiostat (model 273) working either in a three- or in a two-electrode mode. The data were collected and stored with the help of commercial software M270 (EG&G PARC). Chronocoulometric dc and normal pulse experiments were performed with the use of a home-made instrument constructed according to the model developed in

Gierst’s laboratory [35]. The total drop time was divided into t1 = 1 to 5 s and t2 = 16 to 100 ms (pulse duration time). The elimination of double layer charging was undertaken, either by using a 1 ms delay in recording the charge after pulse application, or by subtraction of the charge recorded for a blank probe (supporting electrolyte) from the total charge recorded for the sample containing also Ni(II) species. Charge–potential curves were recorded with an X-Y EG&G/PAR recorder, model RE 0089 or a Hewlett– Packard 7090A measurement plotting system. Ac polarographic measurements (amplitude 2 mV, frequency 60 Hz, scan rate 0.2 V s − 1) were carried out using an OH-105 polarograph (Radelkis). The serial ohmic resistance (0.1 to 500 kV) was supported by the decade resistor RU-71 (Urania, Poland), with a maximum resolution of 0.1 V. All measurements were carried out within the temperature range from 260 to 340 K, precisely controlled (9 0.02 K) using the U4 or MK70 ultrathermostat (VEB MLW Pru¨fgera¨te-Werk Medingen-Dresden).

3. Results

3.1. Dc and normal pulse chronocoulometric studies of the Ni(II) SCN− electroreduction Fig. 1 shows a typical dc cathodic chronocoulometric polarogram of the 1.0× 10 − 3 mol dm − 3 Ni(ClO4)2 solution in 1.0 mol dm − 3 NaSCN, at 298 K. At the limiting cathodic charges a minimum forms at potentials more negative than −1.05 V (with respect to Ag AgSCN). For these experimental conditions the charge in the minimum drops to 75% of the maximum charge at the plateau. The minimum is more pronounced for short sampling times. This tendency is particularly remarkable if one compares dc waves with normal pulse ones. It is also observed for sampling times decreasing from 100 ms down to 16 ms. For example, for 5× 10 − 4 mol dm − 3 Ni(ClO4)2 in 0.5 mol dm − 3 NaSCN, the ratio of the charge in the minimum to the diffusion-limited charge of the normal pulse curves: r= Qmin/Qplateau takes the following values: 0.42, 0.37, 0.30 for t2 =100, 49 and 16, respectively. Fig. 2 shows the kinetic analysis of the limiting charges of normal pulse waves for three different potentials. For the plateau, preceding the formation of the 1/2 minimum (E= E1) a slight positive slope of the Qt − 2 − 1/2 versus t 2 relationship indicates a slight adsorption contribution to a limiting, presumably mainly diffusioncontrolled charge. At two other potentials (E2, E3), occurring in the region of the formation of negative polarization resistance, a slight negative slope suggests some kinetic control of the process.

R. Jurczakowski, M. Orlik / Journal of Electroanalytical Chemistry 478 (1999) 118–127

For a given solution composition and sampling time, the decrease in temperature makes the minimum more pronounced; for example, for 1 mol dm − 3 NaSCN and sampling time t2 = 100 ms the ratio r=Qmin/Qplateau is equal to 0.19 at 288 K and 0.11 at 278 K. For 5 mol dm − 3 NaSCN the following ratios were found: r = 0.88 (at 303 K); r =0.66 (at 283 K) and r= 0.34 (at 263 K). For constant concentration of Ni(II) and increasing concentration of either NaSCN (source of complexing ligands) or NaClO4 (the indifferent supporting electrolyte), the minimum in faradaic charge becomes less pronounced and eventually a plateau develops which reaches the diffusion-controlled value. Thereby, it is particularly noteworthy, and was not reported before, that the shape of this minimum correlates well with the sum of the total concentrations of NaSCN and NaClO4 (or ionic strength), practically regardless of the individual concentration ratio of these salts; e.g. the charge ratio r =0.39 for (1 mol dm − 3 NaSCN +1 mol dm − 3 NaClO4) and r = 0.40 for 2 mol dm − 3 NaSCN (cf. Fig. 3). Of course, [NaSCN] cannot be diminished below the value, at which the formation of thiocyanate complexes of nickel(II) practically does not occur. The waves shown in Fig. 3 have slightly different heights, pre-

Fig. 3. Normal pulse chronocoulometric waves of solutions of 1 × 10 − 3 mol dm − 3 Ni(ClO4)2 with constant ionic strength: (1) [NaSCN]=2 mol dm − 3, (2) [NaSCN] =[NaClO4] = 1 mol dm − 3. For comparison curve (3) for [NaSCN] = 1 mol dm − 3; [NaClO4]= 0, was also included. Current sampling time t2 = 100 ms. Table 1 Diffusion coefficients of nickel(II) ions in the presence of excess complexing SCN− ions of various concentrations Composition of the supporting electrolyte /mol dm−3

106 DNi2+ /cm2 s−1

0.5 1.0 1.0 2.0 5.0

6.38 6.45 5.35 5.12 3.41

NaSCN NaSCN NaSCN+1.0 NaClO4 NaSCN NaSCN

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sumably due to differences in solution viscosities and thus in diffusion coefficients. The values of the latter, determined for different ionic strengths controlled by NaSCN and NaClO4, are collected in Table 1. For constant NaSCN concentration equal to 1 mol dm − 3 and increasing concentrations of nickel(II) (within the range 5× 10 − 5 to 7× 10 − 4 mol dm − 3) one can observe that the relative depth of the minimum in faradaic charge increases only slightly. It is noteworthy that this conclusion becomes clear if faradaic Q–E responses are obtained by subtraction of the charges recorded for pure 1 mol dm − 3 NaSCN solution from the charges measured for the same electrolyte with added Ni(ClO4)2. If this procedure is not applied, a relatively large background contribution, originating not only from double-layer charging, but also from side faradaic processes of electroactive contaminants, may lead to the erroneous conclusion that the minimum develops much more significantly, when Ni(II) concentration increases, thus indicating apparently a self-inhibition process. Finally, addition of a small amount of surface active substance (1-octanol) decreases the faradaic current of the Ni(II)SCN− reduction significantly within the potential range of the adsorption of organic surfactant on the mercury surface (Fig. 4). Thus, the shape of the dc polarographic curve (2) in Fig. 4A, compared with the ac curve (1) in Fig. 4B indicates that in the presence of 1-octanol there are even two regions of negative resistance, both of which may be a source of oscillations, as we checked in additional experiments. The first region of negative resistance occurs from − 0.75 to −0.85 V where the adsorption of 1-octanol decreases with negative potential and thus this negative resistance cannot be associated with the increasing presence of organic inhibitor on the mercury surface. The course of current in the second region, starting at about −1.1 V, where desorption of 1-octanol is almost complete (cf. Fig. 4B) overlaps with the region of negative resistance that is observed in the absence of 1-octanol in the sample. Similar effects were observed for samples of Ni(ClO4)2 and NaSCN, enriched with small amounts of HMPT, instead of 1-octanol. Finally, comparative experiments of the electrochemical behavior of In(III)SCN− and Ni(II)SCN− were performed. Here, one should remember that the formation of an inhibitory layer of adsorbed indium(III) sulfide is much less probable than that of NiS. The influence of temperature, already reported by de Levie and Husovsky [19] seems to be at least qualitatively similar to that reported by us for the Ni(II)SCN− system. Furthermore, we observed that with decreasing sampling time, the minimum on the normal pulse charge– potential curves of In(III)SCN− appears to be remarkably more pronounced and it develops within a wider potential range, than for the Ni(II)SCN− system.

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one of the simple oscillatory regimes, reported by us for chronoamperometric conditions in a two-electrode system, with appropriate serial ohmic resistance added to the circuit. Before these oscillations decay, they exhibit quite a regular shape, different from the rather irregular one, reported earlier incidentally by Koper and Sluyters [18]. In our experiment, a certain irregularity appears only at the end of the lifetime of these oscillations, when their course exhibits first period doubling and then coexistence of low- and high-amplitude signals, suggesting the so-called homoclinic characteristics of this dynamical behavior (cf. e.g. [6,12]). It is noteworthy that the amplitude of the effective interfacial potential drop always remains largely within the potential range of the formation of the negative polarization resistance (cf. Fig. 1). The lifetime of the oscillations can be considerably prolonged (up to about 8 min) by decreasing the temperature from a typical ambient one to 263 to 273 K. On the other hand, for constant temperature and concentration of nickel(II), the lifetime of oscillations gets shorter if the concentration of NaSCN increases. More complicated oscillatory regimes were also observed, which will be a subject of a further, separate study.

4. Discussion

4.1. Origin of the negati6e polarization resistance in the Ni(II) SCN− electroreduction Fig. 4. (A) Effect of addition of organic surfactant on the shape of the dc polarogram of the Ni(II)SCN− system; curves: (1) for 1× 10 − 3 mol dm − 3 Ni(ClO4)2 in 1 mol dm − 3 NaSCN, (2) as (1), saturated with 1-octanol; (B) ac polarogram of 1 mol dm − 3 NaSCN saturated with 1-octanol (curve 1), compared with the ac response for pure 1 mol dm − 3 NaSCN (curve 2). Measurements done at DME with drop lifetime t1 =5 s. T= 298 K.

Experiments with varying concentrations of NaSCN and NaClO4 showed that, unlike the Ni(II)SCN− system, for In(III)SCN− the influence of ionic strength on the shape of the charge – potential curves is much less pronounced (a remarkable minimum in faradaic charge persists even in 5 mol dm − 3 NaSCN, cf. also [21]). It may be concluded that there are some remarkable qualitative, but not strictly quantitative similarities between the chronocoulometric characteristics of nickel(II) and indium(III) in the presence of thiocyanates.

3.2. Exemplary current oscillations for the Ni(II) SCN− system Fig. 5 shows the induction and temporary course of

In view of our results it becomes clear that the side production of NiS cannot explain the formation of a region of a negative resistance on chronocoulometric curves, for the following reasons: 1. The minimum is more pronounced for a short sampling time; for NiS as a side product which accumulates on the surface with time of electrolysis, the opposite dependence should be expected. 2. The minimum is more pronounced at lower temperatures, when the formation of NiS is less advanced. 3. The minimum becomes less pronounced for higher SCN− concentration and remains roughly constant for varying concentrations of Ni2 + ions, while the formation of NiS should be more pronounced for higher concentrations of both Ni(II) and SCN−. 4. The effect of adsorption of organic surfactants, worth a more detailed description, also proves that NiS is not responsible for the formation of the negative polarization resistance. Small amounts of 1-octanol most probably do not modify the bulk thermodynamic equilibria of Ni(II)SCN− complexes, but cause a significant change of the composition of the surface layer (see for instance Refs.

R. Jurczakowski, M. Orlik / Journal of Electroanalytical Chemistry 478 (1999) 118–127

[36,37]). The observed inhibitory effect of 1-octanol is possible to understand, in terms of a mechanism, such that the faradaic current decreases because the molecules of organic surfactant partly remove not the inorganic inhibitor but rather an inorganic catalyst from the mercury surface. Thereby, the first region of negative resistance (cf. Fig. 4A) which develops in spite of decreasing adsorption of 1-octanol, is caused by progressive desorption (with increasing negative potential) of these residual catalyst species (like SCN− ions), which were not completely removed from the mercury surface by a competitive organic surfactant. When, at more negative potentials, this organic surfactant becomes completely removed to the solution, the surface layer can again be penetrated by a catalyst (like SCN−), the concentration of which rises to the same value which is observed for solutions free of 1-octanol. Accordingly, the rate of the electrode process also increases to a value observed for octanol-free solutions, until the growing negative surface charge of the metallic electrode repels the catalyst again and the rate of the Ni(II) electroreduction decreases (this forms a second region of negative resistance). Of course, a full explanation for the formation of a minimum, needs the understanding not only of a cause for a decrease in the current (or charge) with increasing negative potential, but also a reason why this decrease is followed by an increase of current. Therefore we suggest that Ni(II)SCN− complexes can be reduced according to two reaction pathways: an inner-sphere

123

bridge and outer sphere, with the latter setting in at considerably more negative potentials than the former.

4.2. The inner-sphere bridge and the outer-sphere routes of the electroreduction of nickel(II) SCN− complexes Krogulec et al. [30], on the basis of their studies of reaction orders with respect to SCN− ions, established the stoichiometry of the directly reactive species of Ni(II)SCN− complexes as NiSCN+ (cf. fig. 4 in Ref. [30]), independently of the concentration of NaSCN, ranging from 0.1 to 4.8 mol dm − 3. From this result and from the analysis of the mean coordination number of Ni(II)SCN− complexes it follows further that, within the concentration range of NaSCN studied by us, the following complex species predominate in the bulk: Ni(SCN)2 (for 0.5 mol dm − 3 NaSCN), Ni(SCN)− (for 1 to 2 mol dm − 3 NaSCN) and 3 2− Ni(SCN)4 (for 5 mol dm − 3 NaSCN). As the minimum in faradaic charge is observed for this entire concentration range of NaSCN, where either neutral or negatively charged complex species predominate, and since the minimum is even less pronounced for 5 mol dm − 3 NaSCN than for 0.5 mol dm − 3 NaSCN, it becomes quite clear that the region of negative resistance should be caused by the electrostatic desorption of the species which remains anionic for every concentration of NaSCN considered. This is of course the simple thiocyanate anion, SCN−, and not any Ni(II)complex compound. Such a conclusion, confirming one of the literature concepts described in Section 1,

Fig. 5. Example of experimentally observed oscillations for the electroreduction of 2 × 10 − 3 mol dm − 3 Ni(ClO4)2 in the presence of 1 mol dm − 3 NaSCN. Parameters of the chronoamperometric experiment: external voltage U = −1.1 V applied between the static mercury electrode and the mercury pool, through a serial resistance Rs = 220 kV. Electrode surface area A = 0.0296 cm2, T =298 K.

R. Jurczakowski, M. Orlik / Journal of Electroanalytical Chemistry 478 (1999) 118–127

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can now be extended to account for more details of the mechanism of Ni(II)SCN− electroreduction. We further suggest that it is this single SCN− ion in the coordination sphere of directly reducible Ni(SCN)+ species, which has to remain in the adsorption state on the electrode surface and therefore the structure of the activated complex should now be more appropriately written as Ni(NCSads)+. In other words, thiocyanate complexes of nickel(II) undergo the electroduction on mercury via the inner-sphere mechanism, with the SCN− ion acting as the bridge facilitating the electron transfer from the electrode on the nickel(II) ion. Although the bidentate SCN− ions can interact with Ni(II) either via the N or S atom [38,39], it seems that for the bridging ligand the formation of NiN and HgS bonds is most probable, due to remarkable chemical affinity between Hg and S. Also the interaction of Ni(II) with N atom is more probable. The participation of the adsorbed intermediate could be considered confirmed by the fact that the kinetic analysis of the limiting charge of the normal pulse waves exhibits a slight adsorption contribution (cf. Fig. 2) which corresponds to G = 1.8 ×10 − 11 mol cm − 2 (for a two-electron process). However, this effect can originate also from the reduction of a small amount of adsorbed side product, NiS and it is actually difficult to separate these contributions. Summarizing the above considerations, electroreduction of Ni(II)SCN− complexes via the inner-sphere bridge mechanism can be represented by the following reaction scheme: rds for u(SCN−)  1

− 2) − + SCN− Ni(SCN)(p p ads

[(SCN)p Ni(NCS)ads]

(R1)

[(SCN)p Ni(NCS)ads]“ pSCN− +[Ni(NCS)+ ads] + ads

[Ni(NCS)

]+2 e “Ni(Hg) + SCN −

− ads

(R2) (R3)

Concerning the two-electron step (Eq. (R3)) it is noteworthy to recall [30] that the transfer of a second electron was found to be the rate-determining step (as an = 1.5), i.e. the slowest charge-transfer process is the discharge of electroneutral NiSCN species. The electroreduction of Ni(II)SCN− complexes via the non-catalytic, outer-sphere mechanism is observed at considerably more negative potentials. Therefore the potential region of a negative polarization resistance is followed by the increase of faradaic current (charge). Theoretically, the second wave should eventually attain the diffusion-controlled plateau again, but before it happens, the current of nickel(II)SCN− reduction overlaps with that of a hydrogen evolution at far negative potentials. For comparison, the indium(III)SCN− system exhibits the minimum on the polarographic curves within a wider potential range, since the outer sphere discharge of metal ion is more

irreversible for indium(III) and occurs at more negative potentials than that for nickel(II). In view of the above idea of partially overlapping inner- and outer-spheres pathways of Ni(II)SCN− electroreduction one can conclude that the specific influence of the ionic strength on the shape of the minimum is caused by the acceleration of (mainly) the outer-sphere process, e.g. by the effect of the double layer on the electroreduction of anionic species. If this acceleration were the effect of increasing SCN− concentration only, one could suppose that higher complexes of Ni(II) undergo electroreduction at less negative potentials, but the analogous effect of an indifferent salt makes such an explanation doubtful.

4.3. Digital simulation of the chronocoulometric cathodic wa6e of Ni(II) SCN− complexes In order to confirm more quantitatively the electrode mechanism, explaining the experimentally reported electrochemical behavior of the Ni(II)SCN− system, we elaborated its numerical model. For the purposes of this paper it was not necessary to simulate all the possible details of this quite complicated mechanism (like, e.g. the prior dissociation of excess SCN− ligands and side formation of NiS). Instead, we focused our attention on the electrocatalytic inner-bridge, and noncatalytic outer-sphere pathways of Ni(II)SCN− reduction (i.e. summarized steps (Eq. (R1)) and (Eq. (R2)) followed by (Eq. (R3))), for such a low surface concentration of adsorbed electroactive species that this adsorption is practically beyond experimental detection. This simplifies the model electrode process to the following reaction scheme. Electrocatalytic route involving adsorbed intermediate: box

Ox = Ox*

(R4) ks,2

Ox* + n e− = Red

(R5)

Non-catalytic route: ks,1

Ox+ n e− = Red

(R6)

where Ox is the bulk complex species (e.g. Ni(SCN)− 3 ), Ox*Ni(SCNads)+, Rednickel amalgam (or species soluble in solution, without loss of generality) and n=2. box is the adsorption constant of Ox which describes the surface equilibrium (Eq. (R4)) in terms of the appropriate isotherm that (because of numerical difficulties) was simplified here to the Langmuir model: boxcox(0, t)=Gox/(G ox − Gox)

(1)

− 10 The value of G mol ox was assumed to be 1.8×10 −2 cm , thus comparable to the maximum surface excess of SCN− ions [40,41]. For modeling of development of negative polarization resistance at appropriate negative

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Fig. 6. Results of digital simulation of normal pulse chronocoulometric response for the electroreduction of thiocyanate complexes of nickel(II), according to scheme (R4–R6). The first cathodic wave corresponds to the reduction through the weakly adsorbed intermediate (Ox*) only (inner-sphere bridge mechanism), and the more cathodic wave, partly overlapping with the first one, is due to the outer-sphere mechanism; curves (1–4) correspond to fixed constant Ks,2 = 4×10 − 4 and increasing standard rate constants of the process (R6): (1) ks,1 =0; (2) ks,1 =1 × 10 − 20, (3) ks,1 = 1 ×10 − 18, (4) ks,1 = 1×10 − 16 cm s − 1. Other parameters of the model: E 0f = −0.59 V, Dox =6.38 ×10 − 6 cm2 s − 1, Dred =6.5 ×10 − 6 cm2 s − 1 (equal to diffusion coefficient of nickel(0) in mercury [44], an = 1.5, bn= 0.5, ( ) experimental Q – E curve recorded for the same conditions: 5 ×10 − 4 mol dm − 3 Ni(II), 0.5 mol dm − 3 NaSCN, sampling time t2 =100 ms, electrode surface area A =1.49 ×10 − 2 cm2.

potentials, the adsorption constant was assumed to have the following potential-dependent form: 4 × 10 − 6/cm box= −2 G ox/mol cm {1+exp[−275(E/V+0.682)]} (2) The diffusion transport of Ox and Red was assumed to obey Ficks law for linear diffusion, since we simulated normal pulse curves with sampling times (t2) short enough to make the contributions from spherical diffusion negligible: #cox # cox =Dox #t #x 2

(3a)

#cred # cred =Dred #t #x 2

(3b)

DGox = Dt k%Dx k% Dx −fox(0, t) 1+ f + b −k%fcox(1, t)+k%bcred(1, t) 2Dox 2Dred k% Dx 1+ b 2Dred (5)









k%b = k%f exp





DGox DGred DG + $ − ox Dt Dt Dt

nF(E− E 0f ) RT

exp

− anF(E− E 0f ) RT

n

(6a) (6b)

where as is the surface activity [42,43] and a constant Ks,2 = ks,2b (an/n) red , as a product of two unknown quantities, had to be treated as a single parameter. The faradaic current is calculated according to the following relationship:



(4)

where fox(0, t) and fred(0, t) are the diffusion fluxes of Ox and Red, respectively, at the electrode surface. For the numerical procedure we used the finite-difference algorithm with the implementation of adsorption phenomena, based on Feldberg’s approach [42] generalized here for the n-electron process. At every time step Dt of the simulation of the faradaic response to the single normal pulse of the potential, the actual change of the surface excess of Ox (Gox) was calculated using the relationship:

n  n 

n − an n

k%f = as ks,1 + Ks,2b ox

2

fox(0, t)+fred(0, t)= −

 

in which Dx is the spatial step and the complex rate constants k%f and k%b are defined by:

2

Also, due to the negligible adsorption of Red species the boundary conditions were simplified:

n

If = nFA fox(0, t)+

DGox Dt



(7)

and then it is numerically integrated over sampling time t2, yielding a faradaic charge: q(t2) =

&

t2

0

If(t) dt$ Dt % If( j)

(8)

j

The q(t2) versus E relationship obtained forms a simulated normal pulse chronocoulometric curve. Other simulation parameters are listed in the caption to Fig. 6 which shows representative results of our

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numerical calculations compared with a corresponding experimental normal pulse chronocoulometric curve. The shapes of these curves prove that the mechanism of the formation of the full chronocoulometric Q– E response as the manifestation of two reaction routes — via adsorbed intermediate (of such a low, that experimentally hardly detectable, coverage u) and via outersphere charge transfer at more negative potentials, is quite probable. Some differences in the shapes of the experimental and simulated curves at far negative potentials originate mainly from the simplifying assumption that pairs of (an, bn) coefficients are the same for both (Eqs. (R5) and (R6)) reaction routes. For the lower an of the outer-sphere pathway (e.g. equal to 0.5) the apparent standard rate constant of this process (ks,1) would also attain higher, physically more reliable values (10 − 6 to 10 − 8 cm s − 1) than the very low and rather formal values actually used: 10 − 20 to 10 − 16 cm s − 1. Using an analogous approach one can also simulate the Q –E (or I – E) dependence for the indium(III) SCN− system with the difference that the wave of the outer-sphere reduction of indium(III) is much more diffuse (lower an) and is shifted to more negative potentials, with respect to the electrocatalytic wave, than in the case of nickel(II)SCN− complexes.

4.4. Conclusions: the source of oscillatory instability Our experiments confirm that oscillatory instabilities reported for the Ni(II)SCN− system, studied under potentiostatic conditions (i.e. for external U =constant) should be ascribed to the negative polarization resistance, formed at least mainly due to the desorption of electrocatalytic SCN− ions from the mercury electrode. Since the adsorption of SCN− is reversible, the electrode coverage by these ions can change periodically, according to the actual value of oscillating interfacial potential drop. Contrary to SCN−, NiS adsorbs irreversibly, and can be removed from the electrode surface only at significant negative potentials (E B −1.2 V vs. Ag AgSCN), quite distant from the foot of the polarographic wave (E= − 0.5 V) when NiS can already form and adsorb. For the conditions of our experiments it was thus not possible to form and destroy alternately a layer of NiS within the oscillation cycle. However, as an inhibitor, NiS is known [32] to slow down the rate of the charge-transfer step continuously, and therefore it has to modify the oscillating regime. From the comparison of the potential amplitude of oscillations and the potential region of existence of nickel(II) sulfide [32], it becomes clear that the oscillations are observed in the presence of a certain amount of adsorbed NiS. Thus, in our opinion, the accumulation of NiS on the mercury surface has a significant contribution to the transient character of oscillations.

This point of view is confirmed particularly by the possibility of prolonging the oscillations by the decrease both in temperature and NaSCN concentration, when the formation of NiS is less pronounced. As at lower temperatures the solubility of metallic nickel amalgam, also continuously being formed, should be lowered, we think that its accumulation cannot provide the main cause for the damping of oscillations as was suggested in Ref. [18]. Of course, the limiting lifetime of oscillations observed at stationary electrodes with linear or mixed linear-spherical diffusion can, to some extent and even more generally, originate also from the continuous expansion of the diffusion layer towards the bulk, which may eventually result in recovery of the stable behavior by the system. These problems were recently discussed and simulated by Orlik [45] and Rudolph et al. [46]. The relative contribution of all the factors discussed could probably be assessed by comparison of experimental oscillatory I– t behavior with that simulated with the use of partial differential equations [45]. The present work can now be extended for further experimental and theoretical studies of oscillatory instabilities in Ni(II)SCN− and other complex systems, for which the charge transfer is catalyzed by the adsorbed anionic ligand [28].

Acknowledgements Financial support through grant BW-1418/4/98 from the University of Warsaw (Poland) is gratefully acknowledged. The authors are also very grateful to Professor Z. Galus for helpful discussions.

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