ELSEVIER Journal of Eledroanalytical Chemistry 388 (1YYS) IS l- IS9

The kinetics of electron transfer in Fe( CN) lA3- redox system on platinum standard-size and ultramicroelectrodes

Krzysztof Winkler Imtitute (;f Chemistq, Unil,ersi& of Wamaw, Bidystok Branch, Pil.wdskityy~ 11 / 4, 15443 Bidystok, Polrrnd

Received 12 August 1994; in revised form 22 November 19Y4

Abstract

The heterogeneous electron transfer rate constant for Fe(CN),~~ redox system was measurcd with platinum standard-sizc and ultramicroelectrodes in NaCl solutions using fast cyclic voltammetry, stcady-state voltammetry and FFT-square wavc voltammetry. A k, of about 0.1 cm s- was obtained with a Pt (0.2 mm radius) electrode. At a standard-size electrode, thc electron transfer is also strongly inhibited by the reactant decomposition products. A significant increase in thc standard rate constant up to 0.2 cm s - was observed with ultramicroelectrodes. Additionally, the effect of partiai blocking of electrode surfacc by thc ferro- and ferricyanide ion decomposition products is significantly reduced at platinum ultramicroelectrodes.

Keywords: Platinum electrodes; Ultramicroelectrodes; Fe(CN),- redox system: Electron transfer kinctics

1. Introduction

The Fe( CN), -j ~ redox system belongs to the most extensively studied redox couples in electrochemistry. [t has been used as a model system for characterization of electrochemical techniques [ 1-61, for electrode ki- netics study [7,81, for examination of solid electrode surfaces [9-191 and for diffusion coefficient determina- tion [20]. For a long time, the charge transfer was treated as a simple outer-sphere electron transfer be- tween two species present in the solution. However, detailed electrochemical study and spectroelectro- chemical investigations have shown that this process is considerably more complex.

The effect of the supporting electrolyte cation on the electron transfer kinetics in the Fe(CN),4-3- re- dox system was described in numerous papers [21-261. The effect was postulated to be associated with ion-pair formation. Landsberg and co-workers [25,26] suggested a dimeric structure of the activated complex containing the oxidized and reduced redox system forms linked by the supporting electrolyte cation. According to Peter et al. [23], the activated complex is formed by interaction of the cation with the reactant already paired with at least one cation. The effect of the supporting elec- trolyte concentration on the electron-exchange rate constant was also found in the Fe(CN),4p3- system

3022-072X/Y5/$09.50 0 1995 Elsevier Science S.A. Al1 rights reserved SSDI 0022-0728~94~03847-3

[27,28], supporting the concept of ion-pair formation in the active complex.

The effect of the supporting electrolyte anion on the charge transfer kinetics was also observed [ 16,19,29,30]. Galus and co-workers 129,301 and Huang and Mc- Creery [16] observed the increase in the standard ratc constant for solutions containing CN- ions. According to these authors, the CN- ion excess prevents Prus- sian-blue-like film formation on the electrode surface.

The adsorption process coupled with the charge transfer in the Fe(CN),4-3 _ system was investigated in numerous spectroelectrochemistry [31-371 and ra- diometry 1381 studies. There is no agreement between the authors about the composition and the structure of compounds adsorbed on the electrode surface. Some of them suggested ferro- and fcrricyanide ion adsorp- tion on the Pt surface [33,34,38]. The decomposition of iron cyanide complexes with formation of species ad- sorbed on the electrode surface (e.g. CN-- and Fe(CN),) was also postulated [3 1,32.36].

Therefore, many problems related to the charge transfer mechanism in the Fe(CN),-- system stil1 require investigating. Even such a fundamental prob- lem as that of the charge transfer kinetics has not been definitely solved. Standard rate constant values from 0.02 [5,29] to 0.5 cm s- [16] have been reported in thc literature. The range of experimental k, values is

152 K. Winkler/Journal of Electroanalytical Chemistry 388 (1995) 151-159

extremely large. This probably results from different electrode surface pre-treatment methods and solution compositions. Finally, most standard rate constant val- ues were obtained with standard-size electrodes. Ultra- microelectrodes, recently used widely in the study of electrode kinetics, are very useful in studies of fast electrode reaction kinetics. However, only a few papers [5,6,15,16] were devoted to the study of electron ex- change kinetics on ultramicroelectrodes in the Fe(CN),4-- system. Even then, the k, values ob- tained by various authors with ultramicroelectrodes differ significantly. McCreery and co-workers [15,161 obtained a k, of about 0.5 cm s- using fast cyclic voltammetry and Pt- and glassy-carbon laser-activated ultramicroelectrodes. Much lower standard rate con- stant values equal to 0.02 [5] and 0.05 cm s- 161 were obtained in steady-state voltammetry experiments with Pt and glassy-carbon ultramicroelectrodes.

In this paper, the electron exchange kinetics is com- pared for the Fe(CN),4-3- system with standard-size Pt electrodes and ultramicroelectrodes. The results of blocking of the electrode process by the decomposition products of the reactant are also presented. Three techniques - fast cyclic voltammetry, steady-state voltammetry and FFT-square wave voltammetry - were used to obtain reliable data.

2. Experimental details

Al1 substances were analytical grade and were used without further purification. Water purified with a Milli-Q apparatus (Millipore) was used to prepare al1 solutions. The solutions were always prepared just be- fore each experiment.

The voltammetric experiments and FFT-square wave voltammetry experiments were performed using the apparatus built in Prof. Baranskis laboratory (De- partment of Chemistry, University of Saskatchewan, Saskatoon, Canada). The system consisted of a poten- tiostat interfaced with a PCL-818 data acquisition card (B&C Microsystems Inc. and Advantech Co. Ltd.). The operation diagram of the potentiostat and data acquisition card has recently been described by Baran- ski and Szulborska [39]. The FFT-square wave voltam- metry experimental data were processed in the way given by Baranski and Szulborska [39].

In al1 experiments, a Pt wire (surface area about 0.1 cm21 was used as the counter-electrode. A saturated NaCl calomel electrode (SSCE), separated from the electrolytic cel1 by a glass frit, served as the reference electrode. Al1 potentials given in this paper are ex- pressed with respect to this electrode potential. The platinum disk electrodes (radius 0.2 mm, 12.5 ,um and 5 Pm) which served as working electrodes were manu- factured by sealing a metal wire (Goodfellow Metals

Ltd., UK) into a soft-glass capillary using a Bunsen flame. The capillary was then cut perpendicular to its length. Electric contacts were made using silver-epoxy (Johnson Matthey Ltd., UK). Before each experiment, the electrode surface was polished for 1 min using an extra-fine carborundum paper and then for 10 min with 0.3 Pm alumina. Then the electrode was treated with concentrated H,SO,. The treatment was followed by electrochemical cleaning in 1 M H,SO, solution by anodic-cathodic polarization for 1 h. The roughness factor calculated from the hydrogen adsorption charge was equal to 2.8, 2.2 and 2.9 for Pt(0.15 mm), Pt(12.5 Pm) and Pt(5 Pm) electrodes, respectively.

3. Results and discussion

3.1. Cyclic voltammetry with large-size Pt disk electrode

The experiments were carried out with solutions containing Fe(CN),4- or Fe(CN),3- ions. NaCl was used as the supporting electrolyte. The sweep rate was varied in the 0.02 to 180 V s- range. In al1 experi- ments, the electrode was kept at 200 mV potential (the rest potential) before the voltammetric curve record- ing. The evolution of hydrogen takes place at this potential and the electrode surface is cleaned. The following experiments were carried out with a platinum disk electrode of 0.2 mm radius to determine the optimum conditions for studying the charge transfer kinetics in the Fe(CNl,4-3- system:

(i) the dependence of the cathodic and anodic peak potential separation (AE,) on the sweep rate was studied,

(ii) the influence of the initial potential on AE, was examined,

(iii) variation of the anodic and cathodic peak poten- tial differente was analysed in subsequent voltam- metric cycles,

(iv) the dependence of AE, on the reactant concen- tration was studied,

(vl the influence of the rest potential on the electrode reaction kinetics was examined.

In Fig. 1 the dependences of the Yf parameter on v- 1 are presented for different initial potentials and different forms of redox system (Fe(CN),4- or Fe(CN>,3-) present in solution. According to the Nicholson equation [40], the dependence of Y on u-l/ should be linear, with the slape proportional to the standard rate constant. However, the results ob- tained for solutions containing Fe(CN),4- showed de- viations from linearity at low sweep rates (Fig. l(a), solid line). The slope of the T-v-/~ dependence was also found to depend on the initial potential even at high sweep rates.

K. Winkler /Journal of Electroanaiytical Chemistp 388 (199.5) 151-159 153

Multicyclic voltammetric curves were also recorded and analysed. The slope of the q-r:-/2 relationship obtained from the second and subsequent voltammet- rit cycle analyses was found to be independent of the initial potential (0 or 700 mV>. In addition, the differ- ences of cathodic and anodic peak potentials in the second and subsequent cycles were much lower than in the first cycle for Bn initial potential equal to 700 mV. As with the results presented earlier [29,30], a decrease of the standard rate constant with increasing Fe(CN),- concentration was observed. The standard rate con- stants obtained for different reactant concentrations and initial potentials are collected in Table 1.

Similar experiments were carried out in solutions containing Fe(CN),-. The dependences of p on I~--/~ are presented in Fig. I(b) for two different initial potentials. The initial potential had no effect in this case.

The experimental results presented above clearly show that the charge transfer process in the Fe(CN),3 -- - system cannot be classified as a simple

1.6 - . .

YJ .

0 02 0.4 06 0.8 1 1.2 14

(a)

1- .

Y

0.8 --

06-: 1/____1)

kS = 0.11 * 0.05 cmk L

0.4 -

,-l/2,-1/2 SI/2

l

0 0 05 01 0.15 0.2 0.25 03 0.35

(b)

Fig. 1. Dependence of Nicholson function q on the square root of rhe sweep rate recipity (L -lj2) calculated on the base of voltammet- rit curves. recorded in solution containing (a) 4.75 mM Fe(CN),- and 1.8 M NaCl, and (b) 8.5 mM Fe(CN),- and 1.8 M NaCI, for an mitial potential E, of 0 mV (m) and 700 mV (0) (Pt(0.2 mm)).

Table I The dependence of standard rate constant on the Fe((yN),,J con- centration for initial potential equal to 0 and 700 mV. (Pt(O.2 mm). 1.X M NaCI)

Initial potential [Fe(CN): 1 Swcep rate x, CmV) (mM) CV\ ) (cm b )

0 1 .o 2.5 5.0

10.0 20.0

700 1 .o 2.5 -1.75 8.7

lh.0

IO~IXO O.IO 0.095 0.091 0.08X ~l.085

IOL 130 OOk! 0.04x 0.041 0.032 0.023

outer-sphere electron exchange, but is probably com- plicated by a process resulting in electrode surface modification. Three processes can be taken into ac- count to explain the electrode surface modification:

(i)

(ii)

(iii)

oxide layer formation on the platinum surface during the anodic polarization, adsorption of ferro- and ferricyanidc ions on the electrode surface, decomposition of active complex with formation of products adsorbed on the electrode surface.

The fact that the standard rate constant is inde- pendent of the initial potential for solutions containing Fe(CN),- cnables US to eliminate case (i) as thc cause of the electrode process inhibition. Cases (ii) and

154 K. Winkler/Journal of Electroanalytical Chemstry 388 (1995) 151-159

25 11.~ A \ \ 1

-15

t

\

-20 I

Fig. 2. Cyclic voltammetric curves of Pt electrode (roughness factor was about 6) in 1 M H,SO, electrolyte: ( -) pure Pt elec- trode surface; (- - - - - -) after Cl- adsorption at 200 mV in 1.8 M NaCI; (- - -) after Fe(CN),4- adsorption at 200 mV in 5 mM Fe(CN),4- +1.8MNaCI(t,,,=60s,c=lVs-1.

360 - Et /mV

350 _* Et / mV

340 .-

330 --

cl

320 -- 0 0 0

310-- . , . .

300 1

z 250 -

. . ?? . . . . .

??o 0: u

z 250 T

240 --

0 ??

230 -- 0 0 0

220 -- Ei =

210 --

200 --

OmV 220

t

Ei = 700 mV n

00 . .

0 LOG (v / v s-1 LOG (v / V s-l

1904 i 190-1 i -2 -1 0 1 2 3 -2 -1 0 1 2 3

Fig. 3. Dependence of anodic and cathodic peak potentials (EnA solution containing 5 mM Fe(CN),3-

and EnC) on logu calculated on the basis of voltammetric curves recorded in and 1.8 M NaCI for (a) Ei = 0 mV and (b) 700 mV: (0) experimental values; ( ??) theoretical values. The

method of calculating the theoretical values of EpA and E, is described in text.

Ca)

rate constant increase in the second and subsequent cycles compared with the first one in case (ii) where the initial potential is 700 mV.

The mechanism of electrode surface blocking by the products of activated complex decomposition seems to be the most probable. The results presented do not allow US to present the formation mechanism and the structure of compounds adsorbed on the electrode surface. However, it can be assumed that decomposi- tion of the reactant is possible during the active com- plex formation because of the changes in symmetry and interaction forces between the centra1 ions and the ligands. The adsorption of the reactant on the elec- trode surface is probably important for active complex decomposition. The comparison of experimental re- sults presented in Fig. 1 indicates that the degree of electrode surface modification during the Fe(CN),4- oxidation process is higher than during the Fe(CN),3- electroreduction. This interpretation is supported by the study of the effect of sweep rate and initial poten- tial on the anodic and cathodic peak potentials for solutions containing Fe(CN),3- as presented in Fig. 3. The dependences of the experimental and theoretical peak potentials on logu are shown in Fig. 3 for initial potentials of 0 and 700 mV. The theoretical EpC and

360 Et /mV

350 Ef /mV

(bl

K. Winkler /Journal of Electroanalytical Chemistry 388 (199.5) 151-159 155

0.8 /

0.7

06

05

0.4

0.3

0.2

0.1

0 0 0 05 01 0 15 02 0.25 0.3 035

hg. 4. Dependence of 1v on I for Pt(12.5 Pm) f + ) and Ptt0.2 mm) (0). The standard deviation errors are indicated.

EpA values were calculated in the following marmer: the p vs. I ~ dependence was plotted for sweep rates from 10 to 180 V s- and the standard rate constant was calculated from the slope. The standard potential of the Fe(CN),-- system and the Nichol- son function were calculated from the resulting k, value for the whole sweep rate range studied.

The experimental and theoretical cathodic peak po- tential values proved to be almost the same for an initial potential of 700 mV (Fig. 3(b)). However, dis-

0.8

0.6

04

0.2

0

-0.2

-0 4

-0 6

~0 8

-1

crepancies were observed between the theoretical and experimental anodic peak potential values. This indi- cates that the electrode surface is modified very little during the electroreduction of Fe(CN):- ions. in the reverse (oxidative) scan, the electra-oxidation of Fe(CNjh4 takes place and the blocking of the elcc- trode surface is observed. The dependence of the de- gree of electrode surface modification on the swecp rate indicates that the surface modification process is probably a potential-independent consecutive chemical process. Marked differences are observed between the theoretical and experimental values for the cathodic and anodic peaks at an initial potential of 0 mV and low sweep rates. Under these conditions. the electrode modification takes place in the forward (oxidative) scan, and both oxidation and reduction processes occur at the modified electrode.

3.2. Voltammetry at platinum ultramicro-disk electrode

A Pt disk electrode of 12.5 Frn radius was used as the working electrode in fast cyclic voltammetry. The sweep rate was varied from 100 to 350 V s -. Thc simulations show that the non-linear diffusion effect with a disk electrode of 12.5 Pm radius can be omittcd for sweep rates higher than ISO V s . A substantial decrease in the differente between the cathodic and anodic peak potentials can bc obscrved with the ultra-

b)

Cd)

Fig. 5. (a),(b) Cyclic voltammetric curves recorded in solution containing 15 mM Fe(CN)h3 and 1.8 M NaCI at Pt (12.5 grn) electrode for (a) ?=28ovs- and (b) IS = 140 V s- (the dashed curves are the background currents). (c),(d) Comparison of experimental cyclic voltammograms after background current correction (solid curves) and simulated cyclic voltammograms for cy = O.S. T= 25 C. k, = 0.1X cm s- and D,,=D,,,=8x 10 h cm s-, andfor(c)u=280Vs-andtd)r~=140Vs~.

156 K. Winkler/Journal of Electroanalytical Chembry 388 (1995) 151-159

microelectrode. The q vs. u-/ dependences are compared in Fig. 4 for the standard-size electrode and the ultramicroelectrode. At high rates, the standard deviation of AE, calculated for five experimental val- ues is lower in the case of the Pt(12.5 Pm) electrode than in the case of the Pt(0.2 mm) electrode. The standard rate constant obtained for the ultramicroelec- trode is almost two times higher than reported in this paper for the standard-size electrode. The k, value calculated for the results presented in Fig. 4 from the slope of the 1v-u - 1/2 dependence is equal to 0.18 cm s- for the Pt(12.5 Pm) disk electrode.

The charge transfer kinetics was also calculated by comparing the experimental and simulated Z-E curves (Fig. 5). Figs. 5(a) and 5(b) show the recorded cyclic voltammetric curves of solutions containing Fe(CN),4- and the background currents for two sweep rates. Figs. 5(c) and 5(d) show the I-E curves after background subtraction (solid lines) and the simulated Z-E plots for LY = 0.5, k, = 0.18 cm s- and Do, = DRed = 8 X 10p6 cm2 s-. The agreement of theory with experi- ment is quite good. The effect of reactant concentra- tion and of the initial potential on the charge transfer kinetics was also studied for the ultramicroelectrodes. The Fe(CN),4- concentration was found to have no substantial effect on AE,. The effect of initial poten- tial was observed to be similar to that of the standard- size Pt electrode case. However, the differences in k, values obtained for initial potentials equal to 0 and 700 mV are much lower for Pt(12.5 Pm> (k, = 0.185 cm s- for Ei = 0 mV, and k, = 0.15 cm s- for Ei = 700 mV> than for Pt(0.2 mm> (k, = 0.091 cm s- for Ei = 0 mV and k, = 0.041 cm s- for Ei = 700 mV and [Fe(CN>,4-] = 5 mM). It can be stressed that the re- sults of charge transfer kinetics study in the Fe(CN),4-- system are much less sensitive to experi- mental conditions when ultramicroelectrodes are used.

The charge transfer kinetics in the Fe(CN),4-- system was also studied by steady-state voltammetry. The normalized steady-state voltammetric curves of Fe(CNjG4- electra-oxidation at Pt(12.5 Pm> and Pt(5 Pm> electrodes are presented in Fig. 6(a). The logarith- mic analysis of the I-E curve obtained for the Pt(12.5 Pm> electrode is shown in Fig. 6(b). The slope of E-log[(Z, - Z)/Z] dependence equal to 57.5 mV per logarithm unit indicates that the charge transfer pro- cess is totally reversible. The decrease in the electrode radius to 5 Pm results in the shift of the oxidation curve to more positive potentials.

The kinetic parameters of the electrode process can be calculated by the method proposed by Oldham et al. [41] from the base of the differente of the standard potential and the half-wave potential of the quasi-re- versible Z-E curve recorded with a Pt electrode of 5 Pm radius (EO - E,,*) and from the differente be- tween the one-quarter wave potential and the three-

360

T E/mV

320

240

-1 -0.5 0 05 1 15

(b)

Fig. 6. (a) Normalized steady-state voltammograms recorded in solu- tion containing 5 mM Fe(CNjG4- and 1.8 M NaCI at Pt(12.5 pm) (solid curve) and Pt(5 pm) (dashed curve). (b) Logarithmic analysis of steady-state voltammetric curve recorded at Pt(12.5 pm) elec- trode.

quarters wave potential (E,,4 - E3,4). An LY parameter of 0.4 and a k, of 0.15 cm s-l were obtained for E - E 1,2 = 3.5 mV and E,,4- E3,4 = 63 mV. The steady-state voltammograms were also analysed by the method proposed by Galus et al. [42]. According to them the quasi-reversible steady-state votammogram can be described by the following equation:

1

44+_, aF = ln-

rksro - &E-E) (1)

where Z is the reversible (i.e. diffusion-controlled) current at potential E, Z is the measured current for the kinetically controlled process at potential E, and Z, is the limiting current. The (ZL - Z)/Z expression was easily calculated from the equation describing the reversible process:

Z' E=E;,,+ $ln--

z,-Z

For the process of Fe(CN),4- oxidation, the linear relation between ln[(Z, - Z)/Z - (Z, - Z>/Zr] and E

K. Winkler/.lournal of Elecrroar~alytical Chemistrv 3X8 il99Si lSl-ISY l.i7

1

0 20 -40 -60 -80 -100 -120 ~140

FIT. 7. Dependence of In[(I,, - I)// -(I,, - I)/I] on E - I:,,zr (I:q. (1)) for steady-state voltammograms recorded in solution con- taining 5 mM Fe(CN), and 1.8 M NaCI at Pt(S Km) electrode.

-- Ei,2 r is presented in Fig. 7. From the slope of this relation, (Y equal to 0.47 was calculated. The k, value calculated for E = E is equal to 0.135 cm s-. There- fore, a good agreement of the k, values obtained by both methods is observed. However, the accuracy of standard rate constant determination is relatively low because of the smal1 deviation from reversibility of thc charge transfer process on the Pt(5 Pm> electrode.

It was also found that the slope and the half-wave potential of the steady-state voltammetric curves recorded with a Pt(5 Pm) electrode is almost inde- pendent of the sweep rate in the 0.01 to 0.5 V s- range, of the reactant concentration (from 0.5 to 10 mM) and of the direction of the studied process (Fe(CN), ~ oxidation or Fe(CN),~ reduction).

The standard rate constants obtained from the anal- ysis of the steady-state voltammograms are slightly lower than k, values obtained on the basis of the analysis of the fast cyclic voltammetric curves. This can be associated with the partial modification of the elec- lrode surface. However, the degree of modification of l.he ultramicroelectrode surface is much lower than the surface modification of standard-size electrodes at low sweep rates. This behaviour can be explained by spe- cific transport conditions at the ultramicroelectrodes. ln steady-state conditions, the specific diffusion of the substrate and of the electrode reaction product is very fast. Therefore, the fast transport of products of the activated complex decomposition from the surface into the bulk solution can be expected to make the ultrami- croelectrodes less sensitive to electrode surface modifi- cation during the charge transfer process in the Fe(CN), -j system.

The limiting steady-state currcnt values were used for determination of the diffusion coefficient of oxi- dized and reduced forms. Values of 7.8 X IO- and 8.2 X lO_ cm s- were obtained with the Pt(12.5 Pm) disk electrode for the Fe(CN),J- and Fe(CN),- ions, respectively. These values were used to calculate kinetic parameters in the present paper.

3.3. FFT-square walc r~~&anzmrtry rrt ultramicrodisk Pt electrode

The FFT--square wave voltammetry technique, re- cently developed by Baranski and Szulborska [39] was applied to the study of charge transfer kinetics in the Fe(CN),, - system. It was dcmonstrated [39] that this technique applied with ultramicroelectrodes allows the standard rate constant of fast charge-transfer pro- cesses to be determined accurately.

Admittance vs. potential plots were obtaincd for different fundamental frequenties in the potential rangc of thc electrode process. The odd harmonics were analysed using the procedure described by Baran-

400

300

200

100 -~

~_ -_- 4

0 100 200 300 400 500 600 700 800

(0)

2 -- i____- E/mV

I 0 100 200 300 400 500 600 700 800

(b)

Fig. 8. Real and imaginary admittance and Tafel plots for oxidation of 5 mM Fe(CN), - in 1.8 M NaCI at (a) Pt(0.2 mm) and (b) Pt(12.5 Pm). The square-wave frequency was (a) 1.39 kHz and 01) ll.16 kHL. the amplitude was 20 mV. and 16 square-wave cycles were applied at each potential step.

158 K. Winkler/Journal of Electroanalytical Chemistry 388 (1995) 1.51-159

Table 2 The kinetic parameters of electron transfer in Fe(CN),4-- system (CU and k,) and diffusion coefficients of Fe(CN),4m for different frequences (odd harmonics) of square wave (5 mM Fe(CN)h-, 1.8 M NaCI)

the Pt surface during the cyclic voltammetric curve recording.

Electrode Frequency Diffusion ru (kHz) coefficient :C, sml)

(lO-h cm2 sst)

Pt (0.2 mm) 0.28 11 0.50 0.135 0.84 11 0.51 0.15 1.39 11 0.52 0.15 1.95 10 0.53 0.15 2.51 9.5 0.53 0.15

Pt (12.5 Pm) 2.23 4.2 0.54 0.18 6.70 4.3 0.53 0.17

11.16 6.2 0.58 0.18 15.62 8.6 0.57 0.20 20.09 0.60 0.25

ski and Szulborska [39]. Fig. 8 presents typical depend- ences of the in-phase and out-of-phase admittance on potential for Pt(12.5 Pm) and Pt(0.2 mm> electrodes. The analysis of these curves yields the Tafel relation- ships between the rate constant logarithm and the over-potential (Fig. 8).

The differences between k, obtained with stand- ard-size electrodes and with ultramicroelectrodes are higher for the solutions of higher Fe(CN),4- concen- trations. For [Fe(CN),4-] = 15 mM, the k, values ob- tained with Pt electrodes of 12.5 Pm and 0.2 mm radius are equal to 0.17 and 0.10 cm s-l, respectively. Substantial differences were observed in the diffusion coefficients calculated from the FFT-square wave voltammetry experimental data for ultramicro- and standard-size Pt electrodes. The diffusion coefficient values obtained for the ultramicroelectrode are much closer to those obtained from the steady-state voltam- metric curve analysis. A dependence of the diffusion coefficient on the frequency can be observed. However, it should be stressed that the frequency range was optimized for the maximum accuracy of activation re- sistance determination.

4. Conclusions

The results of admittance vs. potential plot analysis obtained for first five odd harmonics are presented in Table 2. The studied frequency range is much higher for the ultramicroelectrode because of significant re- duction of the solution resistance effect. The standard charge-transfer rate constants in the Fe(CN),4-3- sys- tem obtained in the experiments carried out with ultra- microelectrodes by fast cyclic voltammetry and by FFT-square wave voltammetry are almost the same. The smal1 differente of rate constants obtained by FFT-square wave voltammetry with Pt ultramicro- and standard size electrodes is rather puzzling. The admit- tante measurement method (32 points for every poten- tial square-wave cycle) requires relatively low sweep rates. The sweep rate was equal to 0.068 and 0.5 V SKI for fundamental frequency equal to 0.28 kHz (Pt(0.2 mm)> and 2.23 kHz (Pt(12.5 Pm>>. A strong inhibition effect should be expected at these sweep rates for standard-size platinum electrodes. However, the charge transfer kinetics in the FFT-square wave is measured in the anodic cycle and in the potential range close to the standard potential. Therefore, the degree of elec- trode surface modification is much lower than that of

The standard rate constants obtained for standard- size electrodes and ultramicroelectrodes are summa- rized in Table 3. Quite good agreement of the values obtained with ultramicroelectrodes can be observed. The charge-transfer standard rate constant in the Fe(CN),4-3- system in NaCI solution is equal to about 0.2 V s-l.

With the standard-size platinum electrodes, the electrode surface is blocked by reactant decomposition products. This effect complicates the study of charge transfer kinetics in the Fe(CN),4-3- system. It is particularly significant for the experiments with a large time window. Therefore, electroanalytical techniques requiring a long measurement time cannot be applied in kinetic parameter determination using standard-size electrodes in the systems studied. The effect of elec- tron transfer inhibition can be reduced significantly with ultramicroelectrodes. In this case, the transport of products of ferro- and ferricyanide ion decomposition into the bulk of solution is so fast that the electrode surface is modified only to a minima1 degree. There- fore, ultramicroelectrodes seem to be a very important tool for electron transfer study in the Fe(CN),4-3- system.

Table 3 The comparison of kinetic parameters obtained by different techniques at different electrodes

Qclic voltammetry Steady-state FFT-square-wave voltammetry voltammetry

Pt (0.2 mm) k, = 0.085 cm/s

Pt (12.5 wrn) k, = 0.1s cm/s

Pt (5 flm) k, = 0.14 cm/s (Y = 0.45

Pt (0.2 mm) k, = 0.15 cm/s (Y = 0.52

Pt (12.5 urn) k, = 0.19 cm/s

K Winkler/Joumal of Electroanalytical Chernistry 3RR (1995) 151-159 ISY

Acknowledgement

The author expresses his gratitude to Professor A.S. Baranski for providing the electronic system and com- puter program used in this work.

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