Charge Transfers Associated with Follow-Up Chemical Reactions
The Journal of Physical Chemistry, Vol. 82, No. 75, 1978 1723
Non-Volmerian Charge Transfers Associated with Follow-Up Chemical Reactions. A Convolution Potential Sweep Voltammetric Study of Benzaldehyde Reduction in Ethanol J. M. Saveant * and D. Tessier Laboratorie d'Electrochirniede I'Universi6 de Paris VIL 2, place Jussieu, 75 221 Paris Cedex 05,France (Recelved February 6, 1978) Publlcation costs asslsted by Laboratorie d' Nectrochirnle de I' Universl de Paris VII
The electrochemical kinetics of systems in which a charge transfer is associated with follow-up chemical reactions may involve both steps simultaneously depending upon their individual characteristics and the diffusion rate. Procedures are proposed to investigate such systems by convolution potential sweep voltammetry. They allow the determination of the rate characteristics of both charge transfer and chemical reaction provided the available sweep rate range is wide enough. It is not necessary as it is in cyclic voltammetry to a priori state the form of the charge transfer rate law which is then obtained as a result of data processing. The reduction of benzaldehyde in alkaline ethanol illustrates the practical applicability of the method. The dimerization rate constant is determined at two pH values and the results are compared with those of previous investigations. The transfer coefficient is found to vary with potential with a rate of the same order of magnitude as predicted by Marcus theory. The results obtained at the lower pH illustrate how the occurrence of a fast follow-up reaction may help to investigate the charge transfer kinetics.
In electrochemical reactions involving an electron transfer step associated with follow-up chemical reactions: (1) A+le-B B products (2) the simplest situations as far as kinetic control is concerned are the following: (i) The charge transfer reaction is intrinsically slow. Then the kinetic control of the whole electrochemical reaction is by the charge transfer step with no appreciable influence from the follow-up chemical reactions. (ii) The charge transfer reaction is fast so that the kinetic control implies the follow-up chemical reactions. These are the simplest conditions for analyzing the reaction mechanism as has been done extensively for complex organic reduction or oxidation reactions. However, even when the standard rate constant of the initial electron transfer is relatively large, increasingly fast associated chemical reactions will bring the system under the kinetic control of the charge transfer step. The backward charge transfer (B A) then does not have enough time to proceed before B has been chemically deactivated. A precise evaluation of these effects require the quantitative treatment of mixed kinetic control by the charge transfer step and the chemical reactions. This has been carried out in detail for various reaction schemes in term of linear sweep voltammetry.' Linear sweep voltammetry has however the disadvantage that the potential dependent rate law must be selected before the calculations are carried out. In practice, this limits the investigations to Volmer-type charge transfers and to a small number of values for the transfer coefficient a. It has been demonstrated recently2s3that convolution of the current with the function (pt)-lIzand data processing in terms of both current and convoluted current allow this limitation to be overcome. It is no longer necessary, under these conditions, to a priori state the charge transfer rate law which is instead obtained as a result of the treatment of data. Using these procedures, it has been possible to show that Volmerian kinetics are not followed in the reduction of nitro compounds in aprotic media, a Marcus type behavior being observed i n ~ t e a d . ~ , ~ On the other hand, convolution techniques have been applied extensively to mechanism analysis of organic
-
-
0022-3654/78/2082-1723$0 1.OO/O
reactions under conditions where the charge transfer can be considered as Nernstian and the kinetic control is by one of the follow-up chemical reaction^.^-^ One of the purposes of the present paper is to demonstrate the applicability of convolution procedures to the analysis of mixed charge-transfer-chemical reaction kinetics without imposing a particular form to the charge transfer rate law. It will be shown that, varying the sweep rate in the range 0.1-2300 V s-l, it is possible to obtain the characteristics of the charge transfer kinetics as well as those of the rate-determining chemical step. It has indeed been demonstrated previouslylO that meaningful data can be obtained up to high sweep rates provided the potentiostat and the current measurer have a sufficiently large band width and a fast analog-to-digital converter is used. The reduction of benzaldehyde in alkaline ethanol will be taken as an example to illustrate the practical applicability of the proposed procedures. The rate-determining chemical step is then a dimerization reaction. The same system has already been investigated by other techniques including linear sweep voltammetry11J2 and impedance measurement^.'^ From previous work1' it appears that the most probable mechanism for electrodimerization of benzaldehyde is the following: C6H6CH0+ l e
+ C6H6CHO-.
+ H"
CGHSCHOH
CGHSCHO-.
C,H,CHOH t C,H,CHO-.
-+
C,H,-CH-CH-C,H, I
OH PC,H,CHO-.
+
C,H,-CH-CH-C,H, I
0-
/
b-
(5)
(6)
0-
followed by fast and irreversible protonation of the monoand dipinacolate. However the possible variation of the transfer coefficient with electrode potential was not considered, the charge transfer kinetics assumed to be of the Volmer type. It was another purpose of the work reported here to investigate this potential dependence in the case of a relatively fast charge transfer (as will be seen below the apparent standard rate constant h:P is on the order of 0.1 cm s-' for benzaldehyde). Another point of 0 1978 American Chemical Society
1724
The Journal of Physical Chemistry, Vol. 82, No. 75, 1978
provides the expression of the h(E)function. Eo is given by eq 3 if the system can be experimentally studied in zone DO. If not, a combined use of cyclic voltammetry and convolution data allows the determination of Eo in the QR zone.3 For a Marcus-type behavior (see ref 4 and references therein) ME) = hsaP exp[-(aF/RT)(E - EO)]
! I
log A
with hSaP = ks exp[(aF/RT)+,] when A is an uncharged species (hs and hsaP are the true and apparent standard rate constants of electron transfer). a varies linearly with potential according to
IR
-4
4
0
log A
Figure 1. Kinetic zone diagram for an irreversibledimerization following the charge transfer process. The two oblique segments (1) and (2) show the shift of the system when varying the sweep rate from 0.07 to 2330 V S' for pH 17 and 15.5, respectively.
interest in this connection is the influence of the follow-up chemical reaction which may shift the reduction into a potential range positive of the standard potential which would not be accessible otherwise.
Theory The following analysis is carried out on the example of a reductive electron transfer followed by an irreversible dimerization. Reaction 2 is then 2B
kd
products
with hd being the second-order apparent rate constant. Transposition to oxidative processes and to other reaction schemes (EC, ECE, DISP, ...) on the basis of previous analysis1 involves no major difficulty. Figure 1 shows the various kinetic zones featuring the variations of the kinetic control with the following two dimensionless parameters: h = h,ap/(DFU/RT)1/2
J. M. Saveant and D. Tessier
= (RT/F)(hdCo/U)
(when D is the diffusion coefficient of A, Co the initial concentration, u the sweep rate) characterizing charge transfer and chemical reaction, respectively. This zone diagram was established on the basis of a Volmer type charge transfer with a = 0.5.' Although the precise location of the zones does depend upon these assumptions their very existence and their succession do not. The convolution characteristics of each of them are as follows: (i) Zone DO represents pure diffusion control with negligible influence of the chemical reaction, the charge transfer remaining Nernstian. Under such conditions
E = Eo + (RT/F) In [(Il - I)/1J2
(3)
where I is the convoluted current. I1is its limiting value corresponding to E = --m and Eo the A/B standard potential assuming the diffusion coefficients of A and B to be the same. (ii) Zone QR indicates no kinetic influence of the chemical reaction; kinetic control involves both the forward and the backward electron transfer reactions. If the charge transfer rate law is expressed as
i / F S = h(E)[(CA)o- (CB)o exp(F/RT)(E
- EO)]
(4)
213
with an unspecified potential dependent rate constant h(E) ( ( C A )and ~ (CB)oare the reactant concentrations at the electrode surface, i is the current, and S the electrode surface), the logarithmic analysis In [(Il - 1[1+ exp(F/RT)(E - E o ) ] ] / i = ] -In [h(E)/D'/*] (5) 233
a ( E ) = oi(Eo+ &)
+ (F/4X,-,)(E
- Eo - cjr)
The transfer coefficient can be defined alternatively by aaP= -(RT/F)a[ln k ( E ) ] / a E the relationships between the two a's being
(See ref 2, 3, and 4 and references therein,) IZS = 2 exp(-Xo/4RT) +r is the potential difference between the reaction site and the solution, 2 is the electrochemical collision factor (2 = ( R T / ~ T M ) ~M' ~the , molar mass, in terms of perfect gas approximation), Xo is the reorganization energy of the charge transfer process. (iii) The IR zone features a completely irreversible charge transfer control with no influence of the chemical reaction. The corresponding log analysis is a simplified form of eq 5:
In [(Zl- a / i ]= - In [h(E)/D1i2]
213
(6)
(iv) Zone K P corresponds to a Nernstian charge transfer and a stationary state for B established through mutual balance of diffusion and chemical reaction (pure kinetic conditions). The follow-up dimerization then has its maximal influence on the overall kinetics. The corresponding log analysis is, under these conditions
+ ( R T / F ) In [(I1- n/i2l3]
2v6
(7)
Ek = Eo + (RT/3F)In (2kdC0/311)
(8)
E = Ek with
(v) In zone KI the pure kinetic conditions are still fulfilled. It follows that (CB)o/CO= (3/2hdC0)1/3i213/11213 Replacing (CB)oby this expression and (CA)oby (CA)o = Co(Il- 1)/11 in eq 4 provides the KI log analysis: In ( [Il- I - i2I3 exp(F/RT)(E - EK)]/i] = - In [ h ( E ) / W 2 ](9) with the same definition of Ek as in eq 8. h(E) can therefore be again obtained provided E k is known, i.e., that zone K P is accessible to the system. (vi) Zone KO features a Nernstian charge transfer with a moderately fast dimerization, the pure kinetic conditions being thus not fulfilled. No simple log analysis is available in this case. If convolution were to be used in such conditions this would imply a simultaneous finite difference approach of the problem as already d e ~ c r i b e d . ~ This is not considered in the present work since the experimental system described below has practically no
Charge Transfers Associated with Follow-Up Chemical Reactions -0,CV)
The Journal of Physical Chemistry, Vol. 82, No. 15, 1978 1725
d$h -
1
Ln
/
?J
/
.-6 01. sweep rate
.
:4 /
007
-1 5 5 ‘
1
-1 65
ECV) vs SCE
Figure 3. KP analysis as applied to the reduction of at pH 17 for v = 0.68, 0.22,and 0.07V s-‘.
I
~i ,
-0,5
-1 0
E ( V ) vs SCE
1
lo3 M benzaldehyde
LOG,o kCE)
Figure 2. Potential difference between the outer Helmoltz plane and the solution and its variations with potential for EtOH 4- 0.4% H20 1 M B u ~ N I 0.012 M Bu~NOH.
+
0.68
0.22
+
representative point in this region. (vii) The same remarks hold for zone KG which corresponds to the general case where again no simple log analysis approach can be followed. It is noted that for a given electrochemical system and a given starting concentration the main operational parameter is the sweep rate the variations of which shift the representative point in the zone diagram as shown in Figure 1.
Experimental Section The experiments were carried out at 22 O C in buffered ethanol (Prolabo RP) with 1 M tetrabutylammonium iodide (Fluka) as supporting electrolyte. The first buffer M solution of tetrabutyl(pH 1714) was a 1.2 X ammonium hydroxide in ethanol obtained from a commercial 40% aqueous solution (Prolabo). The resulting water content was 0.4%. The second buffer (pH 15.514) contained 0.73 X M Bu4NOH and 2 X M phenol. The water content was 0.55%. In each case, the Bu4NOH aqueous solution was passed three times on a cation exchange column (Amberlite IR120) in order to reduce the content in sodium ions which give rise to a wave interfering partially with that of benzaldehyde (Prolabo). Benzaldehyde was used after distillation in concentration of and 1.8 X M, respectively. The cell, electrodes, instrumentation, and procedures for cyclic voltammetry, digitalization, and convolution corrections (sphericity, ohmic drop, and double layer charging) were the same as already described (see ref 10 and references therein). The residual resistance after positive feedback compensation was typically 25 D and the sphericity correction factor D1/2/ro,0.10 s-ll2, The reference electrode was an aqueous saturated calomel electrode. The sweep rate was varied from 0.07 to 2330 V s-l by one half-decade each time. The diffusion coefficient was taken as equal to 6.3 X lo4 cm2 s-l.13 In order to compare the ME) data to the Marcus theory two extreme cases were considered as regards the value of the potential difference & between the reaction site and the s ~ l u t i o n .In~ the first = 0; In the second, c#+ = &, Le., the potential one difference between the outer Helmoltz plane and the solution according to Gouy-Chapman-Stern theory. c $ ~ was determined from differential capacity measurements, from the determination of the point of zero charge by electrocapillarity measurements, and from conductimetric measurements giving the dissociation of the supporting electrolyte. Impedance measurements were carried out at 1 kHz using a lock-in amplifier (PAR 129A). The results
.O 1
0
. A r
B
. c O D
1
-1 6
-1.7
ECVJ vs SCE
Figure 4. Char e transfer potential dependent rate constant for the reduction of 10- M benzaldehyde at pH 17 (QR log analysis) for v = 2330 (A), 700 (B),227 (C), and 69 (D) V s-’.
Q
. A
* B .0.2
o c O
-1,6
-1,7
D
E(V) vs SCE
Figure 5. Benzaldehyde reduction at pH 17. Variation of the transfer coefficient with electrode potential for v = 2330 (A), 700 (B), 227 (C), and 69 (D) V s-I.
were practically the same at both pH values. They are E d2&JdE2 as shown in Figure 2 together with d ~ $ ~ / dand a function of the electrode potential E.
Results p H 17. At low sweep rates (0.68, 0.22, and 0.07 V s-l), the system lies in zone KP. The corresponding log analysis (eq 7) gives rise to a straight line with a correct slope (59 f 1 mV) (Figure 3). The location of the straight line provides a value of Ek of -1.451 V. A t high sweep rates (2330, 700, 227, and 69 V s-l) the system is shifted into the QR zone. The standard potential can then be determined as Eo = -1.615 V. From the above value of Ekand from eq 8, it follows that k d = (3.3 f 1.5)105mol-l L s-l. On the other hand, the QR log analysis (eq 5) in the high sweep rate region provides the potential dependent rate constant k(E) (Figure 4). It is seen that the log k ( E ) plot is slightly but definitely bent indicating a variation of the transfer coefficient with potential. The variations of aap with potential are shown in Figure 5 with the least-squares line obtained assuming the validity of Marcus theory.
1726
The Journal of Physical Chemistry, Vol. 82,
No. 15,
J. M. Saveant and D. Tessier
1978
1
LOG,ek(E)
% .
P.
.-
I
TABLE I : Analysis of Charge Transfer K i n e t i c s in Terms of t h e Marcus Theory a t pH 17
0 @,(GCS)
0.17 1.5
o,85
1.07 0.84
0.42 0.44
0.24 0.30
0.52 0.43
TABLE 11: Analysis of Charge Transfer K i n e t i c s in Terms of t h e Marcus Theory a t pH 15.5
i" 1
A
-1 6
-1 7
0 0.12 @,(GCS) 1.2
ECV) vs SCE
Figure 6. Charge transfer potential dependent rate constant for the M benzaldehyde at pH 15.5 (KI log analysis) reduction of 1.8 X for v = 2200 (A), 689 (B), 222 (C), 69 (D), 22.4 (E), 6.80 (F), 2.27 (G), 0.69 (H), and 0.22 (I) V s-'.
I
I
17
V'
@r
I
E(V) v s S C E
Flgure 7. Benzaldehyde reduction at pH 15.5. Variation of the transfer coefficient with electrode potential for v = 2200 (A), 689 (B),222 (C), 69 (D), 22.4 (E), 6.80 (F), and 2.27 (G) V s-'.
In the intermediate range of sweep rates the system crosses zone KG and a small portion of zone KI. This last portion is however too small for the KI log analysis to give meaningful results. p H 15.5. In almost all the sweep rate ranges the system lies in zone KI. Zone K P is only reached for the lowest sweep rate (0.07V s-l). From the K P log analysis at this sweep rate, Ek is -1.413 V. Assuming, as seems reasonable, that the standard potential is the same as in the other buffered medium, the resulting value of the dimerization rate constant is kd = (5.3 f 3)107 mol-l L s-l. The results of KI log analysis (eq 9) for the other sweep rates are shown in Figure 6. For the highest sweep rates (2200and 689 V s-l) the KI log analysis becomes practically the same as the IR log analysis (eq 6). The values of aaP resulting from the h(E) plot are represented in Figure 7 as a function of potential. Discussion The above results show that the application of convolution procedures to cyclic voltammetry data allow the charge transfer as well as the follow-up reaction to be kinetically characterized. As expected, the dimerization rate constant is found to increase with the acidity of the medium. There is a variation of about 2.2 in log hd when the pH decreases by 1.5 which is only slightly higher than what could be predicted on the basis of a dimerization process involving
o.94
1.10 0.87
e x p t Marcus t'@,) 0.47
0.48
0.23 0.29
0.54
0.43
a coupling between the anion radical and the protonated neutral radical.ll The values of hd thus found compare satisfactorily with the results of previous determinations. Nadjo and SavBantl' found 7 X lo5mol-l L s-l for a slightly more alkaline medium (pH 17.9)containing however more water (4%) which is likely to accelerate the direct coupling of two anion radicals through specific solvation. This effect has been previously evidenced in the case of acetophenone electr~dimerization~ and is very likely to occur in the present case too. The results of Hayes, Ruzic, and Smith13 (8 X lo6 mol-' L s-l) are also compatible with the present ones since they correspond to a much more aqueous medium than ours resulting in a larger solvation of the anion radicals and a possible decrease of OH- activity. The results concerning the charge transfer kinetics are analyzed in terms of Marcus theory in Tables I and I1 for pH 17 and 15.5,respectively. The experimental variations of a are compared to those predicted by Marcus theory along an already described procedure3i4(the collision factor 2 was taken as equal to 6070 cm 9-l). It is seen that the experimental and theoretical variations are of the same order of magnitude; quantitative agreement is however not very good as could be expected due to the rather large experimental uncertainty which results from the fact that the charge transfer is relatively fast. The results obtained at pH 15.5 illustrate how the occurrence of a fast follow-up reaction may help in investigating charge transfer kinetics. The available potential range is indeed more than 200 mV under these conditions whereas it was only 100 mV at pH 17 where the chemical reaction is slower and consequently a very restricted range of mixed kinetic control is observable. The values of ks found at each pH are of the same order of magnitude as that determined previously13 in a 3:l H20-EtOH mixture. On the basis of the above results for the rates of charge transfer and dimerization, two segments have been drawn on the kinetic zone diagram (Figure 1) which show how the representative point of the system shifts when changing the sweep rate from 0.07 to 2330 V s-l for the two pH values. Acknowledgment, The work was supported in part by the CNRS (Equipe de Recherche AssociBe 309 Electrochimie MolBculaire). Dr. D. Garreau is gratefully thanked for his help in impedance determinations. References and Notes (1) L. Nadjo and J. M. Saveant, J. Nectroanal. Chem., 48, 113 (1973). (2) J. C. Imbeaux and J. M. Sadant, J . flectroanal. Chern., 44, 169 (1973). (3) J. M. Saveant and D. Tessier, J. Electroanal. Chem., 65, 57 (1975). (4) J. M. Saveant and D. Tessier, J . Phys. Chem., 81, 2192 (1977). (5) J. M. Saveant and D. Tessier, J. flectroanal. Chem., 61, 251 (1975). (6) L. Nadjo, J. M. Saveant, and D. Tessier, J . Nectroanal. Chem., 64, 143 (1975).
Image Force Influences on Double Layers (7) C. P. Andrieux, J. M. SavBant, and D. Tessier, J. Electroanal. Chem., 63,429 (1975). (8) L. Nadjo and J. M. SavBant, J. Electroanal. Chem., in press. (9) C. Amatore, L. Nadjo, and J. M. Savbant, J. Electroanal. Chem., In press. (10) J. M. Savbant and D. Tessier, J. Electroanal. Chem., 77, 225 (1977).
The Journal of Physical Chemistry, Vol. 82, No. 15, 1978 1727 (11) L. Nadjo and J. M. SavBant, J. Nectroanal. Chem., 33, 419 (1971). (12) F. Ammar, L. Nadjo, and J. M. Savbant, J . Electroanal. Chem., 47, 146 (1973). (13) J. W. Hayes, I. Ruzlc, and D. E. Smith, J . Electroanal. Chem., 51, 269 (1974). (14) E. Laviron and E. Lucy, Bull. SOC. Chim. Fr., 2140 (1966).
Image Forces Influencing the Capacitance and Interaction of Double Layers Stephen L. Brenner,” V. Adrian Parsegian, and David Gingell Physical Science Laboratory, Division of Computer Research and Technology, National Institutes of Health, Bethesda, Maryland 200 14 (Received December 14, 1977; Revised Manuscript Received May 2, 1978) Publication costs assisted by the National Institutes of Health
We assess modifications of the capacitance and interaction of planar double layers due to image forces. These forces come from the polarization induced at the salt solution/electrode interface by the ions in the aqueous phase. For both metallic and low dielectric electrodes, image forces have a small (
