Electroanalytical Chemistry and Interfacial Electrochemistry, 47 (1973) 215-221 215 © Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

C O N V O L U T I O N P O T E N T I A L SWEEP VOLTAMMETRY

II. MULTISTEP NERNSTIAN WAVES

F. AMMAR and J. M. SAVI~ANT

Laboratoire d'Electrochimie de I'Universitd de Paris VII, 2 place Jussieu, 75221 Paris Cedex 05 (France)

(Received ist February 1973)

The first paper of this series 1 has described the main features of convolution potential sweep voltammetry (CPSV). In particular, the problem of two successive equal Nernstian waves was analyzed in the simple case of a large separation between the standard potentials leading to two independent waves. The purpose of the present paper is to discuss this problem in a more general way including the case of closely spaced or even fused waves. Emphasis will be laid on the application to measuring the standard potential separation AE °. This will be illustrated by the analysis of some typical experimental curves obtained in the reduction of di-nitro compounds in aprotic medium.

The same problem has already been studied with linear sweep voltammetry (LSV) 2-5. Accurate determination of the standard potential separation in the case of independent waves requires the reconstruction of the second wave from the ideal extension of the first wave. For fused waves the standard potential separation can be derived f ro~ the measurement of the peak width by use of a working curve 5. It will be shown that the procedures of measuring AE ° in CPSV are much simpler.

FORMAL KINETICS

A + ne B (E °) B + ne ~=~ C (E °)

Both charge-transfers are assumed to be Nernstian. The diffusion coefficients are considered gs equal. Defining the convoluted current as:

1 i ' i(o) I =v~ o(t--:°) ~d°

and the dimensionless convoluted current as:

I ~ = - - - - do

where z = t/O (0" arbitrary period of time), ~ = iO~/nFSC ° D~ it has been shown 1 that for linear and semi-infinite diffusion I~P can be expressed as

I ~ = 2 + exp [(nF/RT) (E- E~)] 1 + exp [(nF/RT) (E- E~)] + exp {(2nF/RT) [E-½(E~ + E~)]}

Let AE ° be the standard potential separation: A E o = E o _ E o

and E ° the mean standard potential:

1 0 E ° = (el + E °)

Then :

17 j = _ _ 2 + exp [(nF/RT)½AE °] exp [(nF/RT)(E - E°)] 1 + exp [(nF/RT)½AE °] exp [(nF/RT)(E - E°)] + exp [(2nF/R 7)(E - E°)]

When E--*-oo, I~--.2, i.e., 1---.11 =2 nFSC° D ½. The logarithmic analysis of the whole polarization pattern is thus expressed as :

ln(I 1 - I)/I = l n ( 2 - l ~ ) / I ~

i.e.

In (11 - I ) / I

l n l l - I [nF 1 ½exp[(nF/RT)½AE°]+exp[(nF/RT)(E-E°)] I - ~ - ~ ( E - E ° +In l+½exp[(nF/RT.)½AEO]exp[(nF/RT)(E_EO)] (1)

This function of the electrode potential is symmetrical around the point [(nF/RT] E °, 0]. It exhibits two asymptotes:

E >> E ° In (11 - I)/I = [(nF/R T ) ( E - E °)] + In 2

E < E ° ln(I1 - I)/I = [(nF/RT)(F.- E°)]-In 2

An inflexion is observed for E = E ° and there the slope is:

4 nF S = 2+exp[(nF/RT)½AEO] RT (2)

The form of the logarithmic plot is represented in Fig. 1 for typical values of AE °:

,dE* ~,.7(RT/nF) 4.2(RT/nF) (RT/nF)ln4 0 -co mV at 25 C) (223.4) (1079) (35.6) (0) (-co)

n__F

5

4 nF 3 -#-f~

2 ~ nF ggN o l

_, i n F o

-2 -'R'T "El

-3 -4

-5

k k nFE~ ~ ~ nF .

5

216 F. AMMAR, J. M. SAVI~ANT

n F .

(nF/RTM E* i I

Fig. 1. Formal logarithmic analysis of a two-wave system for various values of the standard potential separation AE °.

CPSV--MULTISTEP WAVES 217

For large values of AE °, the slope at the point of inflection becomes small and the two asymptotes are widely separated. This corresponds to two independent waves, each of which can be logarithmically analyzed separately.

If, on the contrary, A E ° ~ - ~ , i.e., the second charge transfer is much easier than the first one, the entire logarithmic plot becomes a straight line the slope of which is 2nF/RT.

An interesting particular case is obtained when:

AE ° = (RT/nF) In 4

which constitutes a singular point in the evolution of the logarithmic plot with AE °. Equation (1) then reduces to:

In(/1 - I)/I -- ( nF / R T)( E - E °)

i.e. a straight line with a slope nF/RT. In LSV, this corresponds to a wave which is exactly double the ne, E ° wave and not 2 ~ times this wave as it is the case when A E ° ~ - ~ . Note that this situation arises for AE°=(RT/nF)ln4 and not for AE ° =0. This amounts to taking into account the symmetry factors 6 for the first and the second charge transfers.

From the above analysis it follows that a simple method for determining the standard potential separation is to measure the slope of the logarithmic plot at the point of inflexion.

The estimation of the error on AE ° may be performed as follows: The slope actually measured in experimental practice is

s = (2.3R T/4nF){2 + exp [(nF/R T)½AE°] }

which may be expressed in mV per decade of E. If the waves are largely separated s becomes very large and the error on

its determination increases exceedingly. A better procedure is then to simply measure the potential separation between the two asymptotes representing the logarithmic plot of each individual wave (see first diagram in Fig. 1).

If, conversely, AE ° is small or even negative the whole logarithmic plot is almost entirely linear (see the three last diagrams in Fig. 1). The slope s is then in the region of 2.3 RT/nF-2.3 RT/2 nF. The accuracy of the slope determination is then best. It can be estimated to be about _ 1 mV. The resulting error on AE ° depends on the magnitude of AE °. It increases rapidly when A E ° ~ - oo and becomes infinite when: s=(2.3RT/2nF+O.O01) V per decade. If, at 25°C and for n = 1, the measured value of s is, e.9., 30.6 mV it follows that the only conclusion to be drawn is that: AE°~< - 1 0 2 mV.

Between these two limiting situations the error on AE ° can be estimated as being the worse of the two values deriving (i) from the measurement of the potential separation of the two asymptotes, i.e. + 2 mV in the present case, (ii) from the slope determination, i.e.:

I A(AE°)[ = 3.5 exp [ - (nF/RT}½AE °] IAs[

within I Asl = 1 mV in the present case. The resulting variation of IA(AE°)I as a function of (nF/RT)AE ° is shown

in Fig. 2.

218 F. AMMAR, J. M. SAVI~ANT

Ia(AE°)t/mV~

0 -1 (nF/RT~E*

Fig. 2. Errors on the determination of the standard potential separation.

The preceding results are valid in the case of linear diffusion. The correction for the effect of sphericity described previously 1 is applicable without modification. This is also true for the correction of the ohmic drop effect.

The above treatment shows that once the current has been convoluted with the function t- ~, the remainder of the analysis follows the same lines as in classical polarography. This can be generalized to more complex problems involving suc- cessive waves corresponding to more than one electro-active species and to Nernstian or non-Nernstian charge-transfers. The available corresponding analysis in polaro- graphy could then be used (see ref. 7 and refs. therein).

EXPERIMENTAL

Four experimental examples involving the reduction of a series of dinitro- compounds are now given for the purpose of illustrating the above analysis and the procedures of AE ° determination: p-dinitrobe'nzene in acetonitrile (ACN) at -30°C; 4,4'-dinitrodiphenyl in dimethylformamide (DMF) at 40°C; 4,4'-dinitrostil- bene in DMF at 20°C; tetrakis(p-nitrophenyl)ethylene in DMF at 25°C. The case of two well separated waves has already been studied I for the example of m-dinitro- benzene in DMF at 25°C. From this last study and from others involving two-wave systems 8 it follows that, at the slow sweep rates used here, the charge-transfers can be considered as Nernstian.

Chemicals p-Dinitrobenzene and dinitrodiphenyl were reagent grade products obtained

from Eastman Kodak. Tetrakis(p-nitrophenyl)ethylene was prepared according to Gorvin 9 and 4,4'-dinitrostilbene according to Dilling et al. 1°. DMF and tetra- ethylammonium perchlorate were obtained from Carlo Erba and used without further purification. The ACN was purified by distillation over sodium hydride.

Apparatus and procedures The cell, electrodes, LSV apparatus, digitalization and convolution procedures

were the same as already described 1.

CPSV--MULTISTEP WAVES 219

RESULTS

The results are shown in Figs. 3-6 which represent for each of the considered reductions, the current-potential curve, the convoluted current corrected for sphericity and ohmic drop effects and its logarithmic analysis. In every case, the depolarizer concentration was 1 mmol 1-1 and the concentration of supporting electrolyte 0.1 mol 1-1.

40

30

20

10

i/jJA [/JJA V q/2 I n I ~ -I

S -0.75 -0.85 -0.95 -1.05 -1.15

21

1.4

0.7

-0.65

Fig. 3. p-Dinitrobenzene, ACN, -30°C. v = 2 V s-1.

£/V

i/JJA I / u A V -I12 ~ in_._-r~ I

_

3C 8.16 "~ 1

i

2C 5.44 0

10 272 -1

0 - Q 7 - Q 8 - Q 9 - 1 0

Fig. 4. 4,4'-Dinitrodiphenyl, DME, 40°C. v = 3 V s-1. -1.1 E/V

220 F. AMMAR, J. M. SAVI~ANT

i/JJA _-r/jJA V -1/2 ~ in.~.I.

30 10.5 -

20 70

10 3.5 -I

0 -0.75 -0.85 -0.95 E/V

Fig. 5. 4,4'-Dinitrostilbene, DMF, 20°C. v=2.5 V s-1.

i/.uA Z/uA V 1/2

2.'7

1.8

2 Q £ -

in i~ I

- 0.65 -0.75 - Q85 Fig. 6. Tetrakis(p-nitrophenyl)ethylene, DMF, 25°C. v= 1.2 V s-1.

E/v

The AE ° values were then deduced from the values of the inflexion slopes according to eqn. (3). These results are shown in Table 1. Reproducibility tests showed that the error on the determination of the slope is about + 1 mV and ___ 2 mV on the asymptote separation. The resulting uncertainties, on the AE ° values are figured in the same table.

In the case of p-dinitrobenzene in A C N at - 30°C, AE ° can be determined through the slope procedure: ( A E ° = 138 mV) and also by the potential separation

CPSV--MULTISTEP WAVES

TABLE 1

DETERMINATION OF THE STANDARD POTENTIAL DIFFERENCE

221

Compound Temp/°C Solvent Slope, s/ AE°/mV m V (decade)- 1

p-Dinitrobenzene - 30 ACN 350.0 138 _ 2 4,4'-Dinitrodiphenyl 40 DMF 84.4 67 _+ 2 4,4'-Dinitrostilbene 20 DMF 46.4 9 _ 3 Tetrakis(p-nitrophenyl)ethylene 25 DMF 30.0 ~< - 120

between the two asymptotes : ( A E ° = 1 3 9 mV) leading to values that are in fair agreement.

In the case of te trakis(p-ni trobenzene)ethylene in D M F at 25°C, the slope is so close to 29.6 mV per decade that it is not practically possible to determine AE °. The only conclusion reachable is that : AE°~< - 1 2 0 mV.

ACKNOWLEDGEMENTS

W o r k was suppor ted in par t by the C.N.R.S. (Equipe de Recherche Associ6e no. 309: Electrochimie Organique) .

Prof. M. Hulin, Universit6 de Paris VI, is thanked for permission to use the 1130 IBM compute r of the Groupe de Physique des Solides, Ecole Norma le Su- p6rieure, Paris.

SUMMARY

The theory of convolu t ion potential sweep vo l tammetry is extended to the case of two consecutive equal Nernst ian waves. A procedure for determining the s tandard potential separat ion for closely spaced and fused waves is derived and discussed. The method is illustrated by the experimental results obtained in the reduct ion of some d in i t ro -compounds in d imethylformamide and acetonitrile.

REFERENCES

1 J. C. Imbeaux and J. M. Sav6ant, J. Electroanal. Chem., 44 (1973) 169. 2 Y. P. Gokhshtein and A. Y. Gokhshtein in I. S. Longmuir (Ed.), Advances in Polarography, Vol. 11,

Pergamon Press, New York, 1960, p. 465. 3 Y. P. Gokhshtein and A. Y. Gokhshtein, Dokl, Akad. Nauk. SSSR, 128 (1959) 985. 4 D. S. Polcyn and I. Shain, Anal. Chem., 38 (1966) 370. 5 R. L. Myers and I. Shain, Anal. Chem., 41 (1969) 980. 6 S. W. Benson, J. Amer. Chem. Soc., 80 (1958) 5151. 7 I. Ruzic, J. Electroanal. Chem., 36 (1972) 447. 8 F. Ammar and J. M. Sav6ant, submitted. 9 J. H. Gorvin, J. Chem. Soc., (1959) 678.

10 W. L. Dilling, R. A. Hickner and H. A. Farber, J. Org. Chem., 32 (1967) 3489.