q. E<e&-r&z&. @hem_, 65 (19’75) 57-66 Q Usevier Seauoia S.A., lkusarme - Prinled in ‘I’he Netherlands

CC9~‘NVOLUTION POTEIW3A.L SWEEP VOLTAiiMETRY

V. DETERMINATION OF CHARGE TRAJXSFER KINETICS DEVIATING FROM THE BUTLER-VOLlWER BEHAVXOUR*

J.M_ SAVl%NT and D. TESSIER

Laboratoire d%lecfrochimie de I’LhiuersiCt? de Paris VII, 2, Place Jussieu, 75221 Paris Cedex 05 (France) (Received 19th May 197 5)

ABSTRACT

Convolution potential sweep voltammetry is applied to the analysis of charge transfer kinetics. The possibility of using the method without assuming a priori the validity of a given kinetic law, e.g. the Butler-Volmer law as usually done, is illustrated on the example of the reduction of terf-nitrobutane in acetonitrife and dimethylformamide. It is found that the post-facturn experimental kinetics indeed deviate significantly from the Butler- Volmer behavior, involving a dependence of the transfer coefficient a upon the e!ectrode potential. It is shown that the experimental variations of CY match the orders of magnitude predicted by the Marcus theory. A procedure is proposed and applied for determining the reversibie half-wave potential for redox couples in which one species is not quite stable chemically by combining the cyclic voltammetry and CPSV data.

INTRODUCTION

Convolution potential sweep voltammetry (CPSV) has recently been success- fully applied to the mechanism analysis of several electrochemical processes involving homogeneous reactions cou@d with an initial nern&ian charge transfer [l--3] _ As concerns the charge transfer kinetics itself, some determina- tions of the rate parameter and transfer coefficient knave also been performed lately f4-7]_ It was shown in the very first.presentation of the method [8] (see p. 176 jn ref, 8) that treating the data by CPSV does not require the a priori knowledge of the electron transfer kinetic law thus eliminating a serious drawback of cotiventional linear sweep vbltammetry (LSV). However, this pos- sidility has not yet been utilized, the forward and backward rates being ex- pressed as functions of the electrode potential under the Butler-Volmer form in treat& the experimenta!.da_&. -- It is _the p&pose _of the present paper-to illustrate experimentally this possi- biW,$ and th&&forti to shoti that CPSV C&I be used to display deTeations from _. .- * ti honoti of Academician A.N. Fru.n&ic’s 80th birthday_

58

the Butler-Volmerr behavior_ The example we chose is the reduction of tert- nitrobutane into iti radical anion in acetonitrile (ACN) and dimethyiforma- tide (DMF). The rate constant and the transfer coefficient for this system have already-been determined in the latter solvent by the impedance method aroune the standard potential [IO]_

If A designates the substrate and B its radical anion, the rate law can be written under a general form as:

i= FSk(E) f(~~)~ - (c,)~ exp(F/RT) (E -E”)]

where i is the current, E the electrode notential, E* the standard potential of - the A/B couple, S the electrode surface area, (cA jO and (c~)~ the surface con- centrations of A and B, k(E) the potential dependent forward rate. The kinetics of the electron transfer is readily derived by the following equation [9].

In k(E) = fn D’A/” - In {I, -I [l t- exp(F/RT) (E

from the LSV current i, the convoluted current

When the rate parameter is small and/or the sweep rate is large the above equation featuring ccquasi-reversible” behaviour simplifies into :

ln k(Ej -= In 02,” -En [(II -1)/i] (2)

which characterizes the completely irreversible behavior- In the opposite con- &tions a diffusion control nemstian 1-E curve is obtained:

E=E,,;+ (ET/F) fn [(1;---Q/l] (3) It _is seen in eqn. (1) that the wetic analysis of the system requires knowl-

edge 0~23,~. E I lz can be obtained, e:g_ from the 1-E curve through-eqn. (3) at sweep r&es sufficiently low compared to the rate parameter for. pure diffu- sion control to- be _reached. Htiwever, thjs -may not be so straightforward a -m&hod if the rate- ptiam&er is relatively- small and if the-anion radical is not -quite &&~%a&sf~&I& Zs it is she- case with tert-nitrobutane. Potentiorntitzic tecl$&u+ tiFot.be used eFther s&ce~mix$Gres of &he-&b&rate and its radical +$&I are:not sufficitintly stabl& A me+,hod f&deritig he &ue of El ,2 from &e LSV-_i=%!Sv data-under quasi-reve&Zole condi&nswould therefore be us~f’d in stich a &ua.tion. This method which u&es the data of cyclic voftarn- m$f$ (C!V:)-will &des&bed fi@: . . z

..- .- -.

59

EXPERIMENTAL

The experiments were performed in ACN and DMF containing Q-1 mol 1-I tetrabutylammonium iodide. The water contents of the soIutions was 0.3% for the first solvent and 0.14% for the second as determined by the Karl-Fischer method: The tert-nitrobutane was a Fluka product and was used as received. The temperature was 22°C.

The cell, electrodes, LSV apparatus, digitalization, convolution and correc- tion (ohmic drop and sphericity) procedures were the same as previously described [ 1,11]1. The reference electrode in DMF was an Ag/AgI electrode the potential of which is about 400 rqV negative to the SCE. The potential of the Ag/AgCIOB- 0.01 M electrode used in ACN is -290 mV positive to the SCE- The residual resistance remaining between the working and the reference electrodes after positive feedback compensation was 12 a in ACN and 25 ZZ in DMF. The sphericity correction factor Di”/re was 0.10 sm112 in ACN and DMk _ The sweep rate was varied between about 0.6 and 180 V s-l in ACN and between 0.18 and 180 V s-l in DMF every half-decade. In these ranges the chemical instability of the anion radical is not such as to have a noticeable effect on the overall kinetics. The concentration of the substrate was 2 mmol 1-l in ACN and 1.5 mmol 1-l in DMF.

DETERMINATION OF ,?2& UNDER QUASI-REVERSIBLE CONDITIONS

Let us consider the CV i-E curve under quasi-reversible conditions and the corresponding I-. convoluted pattern. An example of this is given in Fig. 1

i 11

F&. I_ CV and CPSV of tert-titrobutane in DM3? f 0.1 g Bu4NI concr 1.5 mmol 1-l. Swee,D rate: 17.9 V s --I_ E is refqed to the Aa/A@I el+rode_

$0 .- __ -- -which khok these cw+es for ter,t-nitrobutane in DMF at a sweep rate of x7:9 v s-l.

The backward CV trace .inte&ects the potential axis at a po&tial Ej= 0. At this potential let the convoluted current be 1i= a;- The application of eqn. (1) to this &rticuiar potential shows tlnat the numer&or of the- second right-hand term must be zero since k(E+c) has a finite value:

Pr--i {l + eup(F/IZT) (E -EE,lz)] = 0

and therefore:

E r/i =Ee -(RT/F) 111 [(Ix --i=o)/‘li=c]

The deter_mizlation crf E, /Z *bus simply require& the measurement of the potential corresponding to the i&+-section of the backward CV c&ve with the horizonti,- r’ = 0, axis and the v&ue of the convolute’d current at this very potential. It is seen that the accuracy of such a determination c@creases as the system tends to become more and more irreversible (lowering the rate param- eter and/or raising -the sweep rate) since the slope of the CV backward curve- around *he intersection becomes accordingly smaller and‘smaller.

RINFCI’IC ANALYSIS BY CPSY

Tne LSV i--E curves were recorded for v = O-59; 1.81; 5.84; 18.2; 59; 183 -V s-l. After correction for ohmic drop and sphericity they were con- voluted with (nt)-l I2 as shown in Fig; 1. The half wave potential was deter- mined according to the above procedure using the lowest sweep rate since for the other ones the system -becomes too irreversible. The value found in this way was:

E l/2 = -1,950 v .-

The forward 1-E turve for each Sweep rate was then logarithmically ana- lyzed according to eqn. (1) and also to eqn (2). It wasfo~nd that the~differ- ence _m the results of these two analyses is negligible. From this point of view the-system thus behaves as-an-irreversible one, The resulting plbts’- ln[k(E)/ D’,‘“l vs.23 obtained for each--sweep rate are-shown in_Fig. 2_ It-is seen that %I+? CW&XU curve is- slightly but definitely._bent toward the- bottom of the -diagrk-.: _-

Dim+iyIform~mkSe I -- . . .

-$,he same- operations as abqve were p_erform&d in; a slightly larger sweep rate : .-. ranger..5-k O_iS; 0.6cT; 1._805.5_83;.-17__9;158;3; -l_SO--V-s:‘_ Eere the-Eli& Can be_ i .dete&n&;ed~ f&the 6lowe&sweep rates. -The-media- of these meaSurem@nt%_

61

4-

2

t

O-

A-

A J

d

x2 2’

9 Syeep rate/%-’

o 183 A 59 A 18.2

& x S-64 St3 II 1.87

z& 0 0.59

a? 0

I I -2.0 -2.2 - 2.4

E/V

Fig_ 2. Terf-nitrobutane in ACN + 0.1 _M Bu4NI. Charge transfer rate k(E) as a function of the electrode potential for different sweep rates. E is referred to the Ag/AgC104 O-01 A4 electrode_

Fig. 3, Terf-ritrobutan-e in D&W f 0.1 .M. BuaNI_ Charge. transfer rate k(E) as a function of the electrode potenkiai fdr different swe.++p:rates, E is referred to the Ag/AgI eltictrode_.

.-

-62

.was found as: . .

E Ii2 = -_r.i30 v-

The logarithtiic analyses according to eqn. (1) and eqn. (2) differ appre- ciably for the .4 lo&& sweep-rates showing that the ch&ge transfer is faster than in ACN : The plots -In’ fk (E) /Dii"] vs. E obtained-for eacfi sweep rate using. eqn. (1) are shown in Fig. 3. A slight but definite curvature is se& as -_ the prece&ng case,

It-was checked in both cases that the value of the limiting~convoluted current 1, is independent of the sweep rate tithin a few percent, showing that the ECE-type process which results from the chemic@i instabiZity.of the anion- radical 1127 doesnot interferesignificantlyinthe sweep rate range explored. Also, if adsorption of the reac&&nts were to play a significant role in the elec- trode-process the i--E curves would vary with the sweep rate faster than u1’2 leading to a dependence of ZI upon ZJ which is not actually observed.

DISCUSSION

Two main facts emerge from the preceding results: (i) the charge transfer is faster in DMF than in ACN; (ii) the Butler-Volmer kinetics are not exactly followed; Le. the-transfer coefficient cy- is not independent of the potential over the 350-400 mV range where the experimental kinetics were examined.

The first phenomenon can be interpreted as resulting from a larger solva-

_FSg. -4. Terf-nitrobutane in ACN + O,ieikf Bu4M. l<RT/F)dfnk(E)/dEasafunctionof _f&eelectrode p&ential.E is refeTed.to th" Ag/A&04 6.01 MeIectrode. --

-.

63

Fig. 5. Terr-nitrobutane in BMF f 0.1 Bir Eu~NI. -CRT/F) d In k(E)/dE as a function of the electrode potential. E is referred to the Ag/AgI electrode_

tion of the anion radical in ACN than in DMF, Indeed, ACN has a larger anion solvating power than DMF, or alternatively, if the residual water is considered as playing a 1major role in the solvation of the anion radicals, water is less anion solvating in DMF than in ACN being more tightly bound to the solvent mole- cules in the first case than in the second one.

The variations of the slope of the In k(E) vs.E plots are given in Figs. 4 and 5 for ACN and DMF respectively. The observed variation cannot be interpreted as resulting from the dependence of the Helm’holtz plane potential & from the electrode potentidi through the Frumkin correction of the double layer effect_ It can be seen indeed in Fig. 6, which shows the Q2 (E) plot according to previous measurements by Dietz and Peover in DMF + 0.1 M BuqNI [12] that & varies linearly with E in the region of interest. A similar dependence is very likely to hold for ACN too.

The Marcus theory of outer-sphere electrochemical electron transfer [13,14] predicts a dependence of the transfer coefficient (;Y upon the electrode potential:

(Y = 0.5 + (W4h) fE - E0 - 921

and leads to the following expression of the rate:

k(E) = Zel exp(-h/4RT) exp[--(arF/RTj (E FE’ - qi2)]

for the reduction of an initially uncharged species (E’ is the standard potential, Z,, the electrochemical collision %&or, X the sdlvent reorganization fa@tor and #2 the.pof;ential difference betiveen the reaction site and the solution)_

1 I

-1.75 -2.0 -225

E/V

Fig. 6. Variaiicz~ of the Helmholtz plane potential ~$2 with the electrode potential in DMP + 0.1 M Bu4N’I (from ref. 12). E is referred to the SCE electrode.

The rate iaw can a&o be expressed as:

k(Ej = k,, exp[--(atF/RT) (E-X0)]

where the apparent rate constant k,, is defined by:

We shall now examine if the cy variation Zispl_ayed by the above results matches the orders of magnitude predicted by the theory. As a consequence of the preceding equations CY can be derived Tom the experimen’t, dak ac- cording to:

or = -(RT,&?Fj d ln k(E)/dE t-0.25

It &seen in Figs, 4 and 5 that dcu/dB is appro&mately csnstant and equal to 0.14 V--l in-kN-and ~;23~v-‘-in DMF,

The appare& rai?e :zonstStIlt ka, is obkjmzd from the c&es in Figs. 2 and- 3, u&r-& the-& V&I&S deduced~from Figs. 4_ed 5. It is Mumed th-at the St&d&d potenti+ is practkl.l~ equal-to -*he E 1 ,* previously determined. The-diffusioti-

_ -.

65

coefficient in DL&@’ is 1.3 X lOA cm2 ‘s-l [lo]. From this value the diffusion coefficient in ACN can be estimated as 3-O X lo-’ cm2 s-l (the ratio of the viscosity coefficients is 2_3)_

The values thus obtained for kap along the In k(E)-E curves range between 4.2 an?d 4.8 X 10m3 cm s-l in DMF and 6.2 ar,d 8-7 X f0-4 cm s-l in ACN.

In DMF Peover and Powell found a value of 9 X lo-’ cm s-l. It is difficult to say if this represents an actual discrepancy with our own result. Indeed the residual water, the amount of which is not precisely controlled, may well play an important role in solvating the anion radic&l since its charge is concentrated in a fairly small volume, and may therefore influence significantly the magni- tude of the charge transfer rates.

It is seen that the strongest dependence of a with the potential corresponds to the largest rate constant as can be expected qualitatively from the Marcus theory_ Z,, is given by:

Zel = (RT,&rM) x/2 (M: molar mass)

i.e. in the present case Zel = 6 X lo3 cm s-l_ In DMF, assuming that the reaction site is located in the Helmholtz plane

and that the Helmholtz plane potential is correctly expressed by the Gouy- Chapman theory, @a is given by the diagram shown in Fig. 6. For E = E* (- -1.630 V vs. SCE): @I~ = -1330 mV_ From this and the mean value of k,, the solvent reorganisation factor can be estimated as:

x/F = 1.17 V, which would imply a variation of or with the potential of: da/dE = 0.21 V--l If the & potential were neglected considering that the reaction site is

farther from the electrode than the Helmholtz plane, the corresponding values of WS’ and dcr/dE would be:

x/F = 1.43 V, de/U = 0.18 V--l. In any case it is seen that the values thus found agree fairly well with the a:

variation directly determined from the In k(E)-E c*urves_ In ACN, assuming the same +2 value as above: A/F = 1.36 V and da/dE = 0.18 V-l. For& -0 NF = l-.62 V and da/&Z = 0.15 V-l

There is again a fair agreement with the a variation directly measured from the ln k(E)-+_

q7he experimental studies of the dependence of QI upon the electrode poten- tial are very few [15-183, the most s?gnificant example dealing with the Fe(IfI)/Fe(II) couple on platinum [ 17,18]_ The present results indicate a significant deviation f&m the Butler-Volmer behavior, clearly larger than the experimental errors. The extent of the deviation is of the same order of magnitude as predicted by the Marcus theory although the present study cannot be-eensidered as an accurate verification of the theory due to the small variation of CK as cdmpared to the magnitude of the experimental errors_

. .-. 66 -. .-

AtiKwWLtiGMENTg

The n&k‘mas supported in pa&by the C_N_R.S_ @q&x de Rkherche ibsLcoci& No. 309: E&ctrcchimie Orgzmiqtie).Prof_ M.Hul.in,Uti~versit~ de_ Pa& VI, is tktanked for the permissibn to use the 1130 fBM computer of the "Gr&pe~de Physique des Solides de 1'Ecole Normale Sup&e-ure,Paris".

REFERENCES

J-M_ Savkmt and D. Tessier, J_ Eiectroanal. Chem., 61 (1975) 251. L_ Nadjo, J_M_ Savean& and D. Tessier, J. Electroanal. Chem_, 64 (1975) 143. C.P. Andrieux,- J.M. Saveant and D. Tessier, J_ Electroanal. Chem., 63 (1975) 429. M. Goto and K_B. Oldham, And. Chem., 45 (1973) 2043. J-IX_ Carney and H_C_.Miller, Anal_ Chem.. 45 (X973) 2175. H.W. 17a.ndenEorn and D-H. Evans, Anal. Chem., 46 (1974) 643. R_S_ Rodgers, Anal. Chem., 47 (1975) 281. C.P; Akdrieux, L. Nadjo and J.M_ Saveant, 3. Electroanal. Chem., 26 (1970) 147. J.C:Imbeaux and J.M. Saveant, J. EIectroanal. Chem., 44 (1973) 269. M_E:Peover and $.S. Powell, J. Electroanal. Chem., .20 (1969) 427. L_ NadjO, J.M. Saveant and D. Tessie,, r J. Electroanak Chem,, 52 (1974) 403. R. Dietz and IKE. Feover, Discuss. Faraday Sot., 45 (1968) 154: R.A_ M?rcus, J_ Chem. Phys., 24 (1956) 966. R.A. Marcus, J_-Chem. Phys., 43 (1965) 679. R. .I$rsozu and E_ Passeron, 3. Electroanal. Chem., 12 (1966) 524. F-C._ Anson, N. Rathjen and R.D. Frisbee, 3. Electrochem. Sot., I.17 (1970) 477. D.H. Angel1 and T. Dickinson, 5. Electroanal. Chem.,.35 (1972) 55. E. Momot-&nd G. Bronoel, C-R. _4cad_ Sci. Paris, Ser_ C, 278 (1974) 31!3_