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Kinetic study on the dimerization reaction of 9-methoxyanthracene cation radical by means of fast scan cyclic voltammetry
191
J. Electroanal. Chem., 270 (1989) 191-204 Elsevier Sequoia S.A., Lausanne - Prmted
m The Netherlands
Kinetic study on the dimerization reaction of 9-methoxyanthracene cation radical by means of fast scan cyclic voltammetry Koichi Nozaki, Munetaka Oyama, Hiroyuki Hatano and Satoshi Okazaki * Department (Received
of Chemrstr?: Faculty of Scrence, Kwto 14 December
1988; m rewed
Untcwrsr~v. I(voto 606 (Japan)
form 2 May 1989)
ABSTRACT The instrumentation of a fast scan cychc voltammetric (FSCV) system with a maximum scan rate of 300 kV/s and tts apphcation to the kmetic studies of very short-hved electrogenerated intermedtates are presented. The time resolution of the system was Inspected by cychc voltammetry and chronoamperometry, and was found to be better than 1 ps at an ultramicrodisk electrode (UMDE) of micrometre stze. The mechanism and kmetics of the very rapid anodtc dtmerizrtion of 9-methoxyanthracene (9MeOA) are discussed in further detail for the first ttme by means of FSCV. The reductive wave of 9MeOA canon radical was detected successfully. although the reversible cychc voltammogram could not be observed even at a scan rate as high as 300 kV/s. It was concluded. from the dependences of the anodic peak potentials on both the scan rate and the substrate concentration. that the dimerization proceeded via coupling of 9MeOA cation radical wtth the substrate. The dtmerization rate constant was estimated to be (3.5 50.5)~ 10’ Mm’ ss’ from the results of digital simulation analysis of the observed fast scan cyclic voltammograms.
INTRODUCTION
Cyclic voltammetry (CV) has been utilized widely to obtain thermodynamic information as well as to study the reaction mechanism of electrogenerated intermediates. By employing a faster potential sweep rate. the information obtainable increases in principle. However, considerable distortions of the observed voltammograms are usually caused by the ohmic potential drop and by the band-pass limitation of the cell response at a sweep rate above several hundreds of volts per second with a conventional electrode. Since Howell and Wightman [l] demonstrated the feasibility of a fast scan rate above 10 kV/s by using an ultramicrodisk electrode
l
To whom correspondence
0022-0728/X9/$03.50
should
be addressed
Q 1989 Elsevter Sequoia
S.A.
192
(UMDE) of diameter 10 pm, fast scan cyclic voltammetry (FSCV) has received active attention [l-7]. This great progress is attributed to the extremely short response time and the decrease of the ohmic drop at the UMDE. Very recently, a scan rate above 1 MV/s could be reached without fatal distortion of the voltammograms using a UMDE of diameter 5.5 pm [2] and attempts are still being made to extend the upper limit of the scan rate. The use of FSCV allows the investigation of rapid heterogeneous electron-transfer kinetics. Several groups have determined successfully rate constants greater than 1 cm/s by inspecting cyclic voltammograms at above 10 kV/s [l-4]. FSCV is also expected to be an advantageous technique for observing directly electrogenerated intermediates of half-lives of sub-microseconds. So far, only a few applications of FSCV to kinetic studies have been reported. Amatore et al. [5] detected the electrogenerated 2,6-diphenyl pyrylium radical at a scan rate of sub-megavolts per second and evaluated a dimerization rate constant as large as 2.5 X lo9 M-’ s-‘, which was near to the diffusion-controlled limit. In this study, we first examined the instrumentation of the FSCV system. Inspection by cyclic voltammetry and chronoamperometry confirmed that the time resolution of the system was less than 1 ps at a UMDE of micrometre size. Then the anodic dimerization kinetics of 9MeOA were investigated using this FSCV system. The 9MeOA cation radical has been shown to dimerize to yield compound 1,
OMe quantitatively [8]. However, the rate of the dimerization reaction was so rapid that no reduction wave was observed with conventional cyclic voltammetry [9]. Thus, the mechanism and the reaction rate have not been reported. Although a totally reversible cyclic voltammogram could not be observed even at the highest scan rate used (300 kV/s) in this study, the reduction wave of 9MeOA cation radical was detected and analysed successfully. The mechanism and reaction rate are discussed. EXPERIMENTAL
System configuration
of FSCV
Figure 1 shows the configuration of the FSCV system developed. A fast response potentiostat and an I/V converter were designed to be as compact as possible to fit into a small head box of dimensions 14 X 8 x 2 cm. The head box was put very close to the electrolytic cell and they were electrically shielded together to minimize external noise. Operational amplifiers of OP16 (PMI, bandwidth 8 MHz) were employed in the potentiostat and I/V converter. The resistance and capacitance
193
Fig. 1 Schematic diagram of the FSCV system. (A) Digital function generator: (B) potentiostat controller; (C) head box contaimng three-electrode potentkostat and I/V converter; (D) wide-band width amplifier; (E) A/D converter (50 ns, 10 bit): (F) micro-computer.
used at the I/V converter were 10 kQ and 3 pF, respectively. When the scan rate was higher than 10 kV/s, a capacitance of 0.1 PF was connected between the counter and reference electrodes to suppress the ringing of the current signal occurring usually just after a voltage reversing point. A triangular wave function (max. 150 kHz) was generated by a digital wide function synthesizer (Model 1930, NF Electronic Instruments Co. Ltd., Japan). Transient signals from the Z/V converter were amplified 10-1000 times through a wide-bandwidth differential amplifier (DC-10 MHz, Model 5305, NF) and then recorded by a digitizer (Model S121, Outnics Co Ltd., Japan) which had a minimum acquisition time of 50 ns with a lo-bit resolution. The time constant of the 1/V converter was 0.2 PCSand scan rates ranging from 0.1 to 300000 V/s were available on the system. Data acquisition and analysis of the voltammograms were performed on a micro-computer (Model PC9801 VM2, NEC, Japan). For cyclic voltammograms with a poor S/N ratio, 5 or 20 scans were accumulated on the micro-computer. Data acquisition, analysis of the cyclic voltammograms and the simulation program were written in MS-FORTRAN 77. The fast response potentiostat (Model HEC972) was developed in cooperation with Fuso Co. Ltd. (Kawasaki, Tokyo). Conventional cyclic voltammetry at lower scan rates of 0.1-30 V/s were carried out on a Model 174 PAR Polarographic Analyser. A platinum electrode of diameter 1.25 mm was used as the working electrode. The solution resistance was compensated with an IR compensation circuit provided by a Model 174/50 Accessory. The response of the analyser was 110 ps at the range of 1 mA full-scale. The temperature of the measuring solutions was regulated to 25 -t 0.1” C. Solution resistances were measured with an impedance bridge (Model 12K, Derica, Japan) with a conventional conductivity cell. Ultramicrodisk
electrode (UMDE)
UMDEs were prepared as follows: a short length (7 mm) of platinum micro-wire of 100, 30, 10 or 5 pm diameter (The Japan Lamp Industries Co., Ltd.) was connected to a copper lead wire (diameter 30 pm) and then copper was elec-
194
trodeposited on the junction to ensure electrical contact. The silver coating of Wollaston wire (Pt, diameter 5 pm) or electrodeposited copper on the top end (2-3 mm) of the micro-wire was removed with dilute nitric acid solution. After washing and drying, the micro-wire and the lead wire were positioned in a soft glass capillary (id 0.3 mm. od 1 mm). The assembly was then sealed by inserting it very slowly (1 cm/h) into a laboratory-made electric furnace maintained at 670 + 10” C while applying a vacuum. The resulting assembly was sealed again into a soft glass tube (id 2 mm, od 4 mm). The electrode surface was ground successively with 600, 1000 and 3000 mesh emery papers and polished to a mirror finish with 0.3 and 0.05 pm alumina on a suede cloth. The diameter of the Wollaston micro-wire of 5 pm was found to be 5.5 pm by scanning electron micrograph measurement. A platinum wire of 0.5 mm diameter was used as the counter-electrode; its position was not important because the cell resistance of a UMDE cell system is dominated by the resistance near the electrode surface [lo]. The double-junction assembly consisting of a Pt/(I, + II) reference electrode recommended by Coetzee and Gardner [ll] was employed. A disk-shaped porous glass tip (40 nm pore size) was used at the junction. In terms of the extremely large exchange current of the reference electrode (ca. 3000 times greater than that of a Ag+/Ag electrode [ll]) and the low potential drift of less than 1 mV per week, this reference electrode was superior to the conventional silver electrode. The formal potential of the ferrocenium/ferrocene system in nitroethane solution was 0.173 V with this reference electrode. Chemical reugents Acetonitrile (AN, GR grade, Wakenyaku Co. Ltd.) was redistilled twice over P,O,. Nitroethane (NE), purchased from Nacalai Tesque, was dried over P,O, with stirring for 1 day and then distilled twice under reduced pressure. Tetraethylammonium hexafluorophosphate (TEAPF,) was synthesized from tetraethylammonium bromide and potassium hexafluorophosphate. It was recrystallized from acetonitrile + ethanol mixed solvent four times and finally from ethanol. It was dried in a vacuum oven at 60 o C prior to use. 9MeOA was synthesized by standard procedures [12]. It was purified by a silica-gel column with hexane benzene mixed solvent as the eluant. Ferrocene (Fc, Aldrich Co. Ltd.) was used without further purification. RESULTS
Fast stun cyclic voltummetry Figure 2 shows the cyclic voltammogram of 5 mM Fc in AN solution with the UMDE of 5.5 pm and at a scan rate of 100 kV/s. Although the fairly large charging
195
-l.O/ 0.0 E IV
0.5 t vs. &.I-)
Fig. 2. Cychc voltammogram of 5 mM Fc in AN containing with a Pt UMDE of diameter 5.5 pm.
0.6 M TEAP at a scan rate of 100 kV/s
and
current was overlapping at the high scan rate, reversible faradaic waves were obtained without any significant distortion. The apparent double-layer capacitance evaluated from the background current was as small as 2.7 pF at 0 V (vs. I;, I-). When the distance between the working and reference electrodes is ten or more times larger than the electrode radius as in a usual UMDE cell system, the uncompensated solution resistance (R .,) is readily predicted utilizing the theoretical equation [lo]
(1)
R,, = p/Jr
where p is the specific resistance of the solution and Y is the radius of the UMDE. In the present cell system. R,, was estimated to be 35.5 k0 from p = 39 D cm. Taking the product of the double-layer capacitance and the value of R,,. the cell time constant was calculated to be as short as 100 ns. The overall response time of the signals was, however, limited by the response time at the Z/V converter, which was 200 ns. It should be noted that even at the extremely high scan rate, the extent of the ohmic potential drop at the oxidation peak was only 15 mV, which was calculated from the peak current (0.42 PA) and R”,. Fast response chronoamperometr):
The dotted curves for the to 0.5 V. The solid lines in equation [13] i(t)
lines in Figs. 3a and 3b show the observed current vs. time (i-t) AN solution of Fc immediately after the potential was stepped from 0 diameters of the UMDEs used were 30 and 10 pm, respectively. The Figs. 3a and 3b represent the calculated curves from the Cottrell
= ~zFAD”~c/‘~
(2)
where n, F and A denote the number of electrons involved in the electrode process, the Faraday constant and the geometrical surface area of the working electrode, respectively. D and c are the diffusion coefficient and concentration of Fc (D = 2.2
196
J “y ’ ‘“” ., _ “___ ,_ ,I ”
”
J
4
6
6
.;-
0
20
40
60
60
” 0
tip
” 2 t/p
Fig. 3. Transient I-I curves measured for the same solution as in Ftg. 2. (a) ExperImental (dotted line) and calculated (solid line) curves at a Pt UMDE of diameter 30 pm. (b) The same as (a) except for a 10 pm UMDE. (c) The observed curves for the sample (curve S) and the blank (curve B) at a 10 pm UMDE. (d) The faradax component in curve S obtained by subtracting curve B from curve S
X lop5 cm2 s-’ [14,15] c = 5 mM). Equation (2) is the special case for the diffusion-limited region of the transient response at a planar electrode in chronoamperometry. Good agreement between the observed and the calculated curves was obtained, indicating that in such an extremely short period of time, less than 100 ps, the planar diffusion was dominant even at a UMDE of micrometre size. Figure 3c shows the current response curves up to 10 ~LS at the UMDE of 10 pm. The calculated cell time constant for the UMDE was 200 ns. Curves S and B are for the sample solution and the blank, respectively. Immediately after stepping the electrode potential, the faradaic current was concealed in the large charging current. Then the pure faradaic current was extracted by subtracting curve B from curve S. The resulting curve is shown in Fig. 3d. It is worth noting that the diffusional current could already be observed within 1 ps after the potential step. Fast scan cybc
voltammograms
of 9MeOA
in NE
Hammerich and Parker reported that the dimer 1 is produced quantitatively from anodic oxidation of 9MeOA in AN (yield 95%) [S]. Up to now, AN solvent has been used extensively not only for the investigation of anodic and cathodic electrode reactions but also for electro-organic synthesis. However, most reactive cation species are known to react with this solvent, namely, to undergo acetamidation [16-191. Recent studies on anodic reactions or the structural determination of electro-oxidized intermediates have been performed in a less basic solvent, such as nitromethane or dichloromethane [20-221. In voltammetric studies with a higher scan rate, a lower solution resistance is required to avoid distortion of the voltam-
197
I
I
I
I
0.0
0.5
1.0
1.5
E/V
(vs.
&.I-)
Fig. 4. Cyclic voltammogram Pt UMDE of 100 pm.
of 5 mM 9MeOA
m NE containmg
0.5 M TEAPF,
at 100 V/s,
and with a
mograms by the ohmic potential drop. Nitro compounds whose dielectric constants are similar to that of AN were suitable for this purpose as solvents. In addition, because of the higher viscosity of these solvents than that of AN, the reaction rates are expected to be slower in the former solvent. Actually, the dimerization reaction of 9MeOA cation radical was observed to be slower in NE (n = 6.38 X 10P4 m’ SC’) than in AN (n = 3.41 X 1O-4 m2 SC’) [23]. For these reasons, the present studies were carried out in NE. Figure 4 shows the cyclic voltammogram of 9MeOA at a slower scan rate (100 V/s). The reductive wave of 9MeOA cation radical could not be seen on the reverse voltage scan while a new peak .was observed at 0.2 V, which was attributed to the reduction of the proton released in the dimerization process: 2 (9MeOA’+)
+ 1+ 2 H+
(3)
From the results, it was confirmed that the dimerization process of 9MeOA cation radical also took place in NE. When the concentration of the substrate was as high as 5 mM, only irreversible cyclic voltammograms were obtained even at the highest scan rate used (300 kV/s). This suggested that 9MeOA cation radicals in a high concentration level were dimerizing in a time as short as 1 ps. On the contrary, in a dilute concentration of the substrate (1 mM), a very small reductive current could be seen on the reverse voltage scan, as shown in Figs. 5a, 5b and 5c, although this is somewhat ambiguous due to the large residual current. Thus, the faradaic components were extracted by the background subtraction technique [16]. This method was accomplished by subtracting digitally the residual currents recorded for the blank solution from the observed curves for the sample. The solid lines in Fig. 6 show the resulting cyclic voltammograms (Figs. 6a-6c) together with that for 5 mM (Fig. 6d). The small peaks seen on the reverse scan can be assigned to the reduction of the cation radical from evidence that they become larger, the faster the scan rate used (Figs. 6a-6c) and diminish at high substrate concentration such as 5 mM (Fig. 6d).
I
I 0.5
I
10 E/V
Fig. 5. Cyclic voltammograms of 1 mM 9MeOA and (c) 100 kV/s, respectively.
I 10 E/V
with a 10 /lrn UMDE
Fig. 6. Cyclic voltammograms obtamed by background subtractlon (0). (a) [9MeOA] =l mM, D =lO kV/s: (b) [9MeOA] = 1 mM. u = 100 kV/s; (d) [9MeOA] = 5 mM. P = 100 kV/s.
Mechanism
I 05
(VS l;,l-)
of the anodic dimerization
at various
I
(vs,l;>C
scan rates: (a) 10, (b) 30
(sohd lines) and dlgital simulations o = 30 kV/s: (c) [9MeOA] =I mM,
reaction of 9MeOA
Nadjo and Saveant [24] have established the diagnostic criteria for distinguishing the 25 possible mechanisms of cathodic electrodimerization on the basis of the dependences of the peak potentials in linear-sweep voltammetry on both the potential scan rate (cl) and the substrate concentration (c). These mechanisms involve successive chemical processes such as radical-radical coupling (RRC). radical-substrate coupling (RSC) and ion-substrate coupling (ISC), as well as disproportionation and a protonation step as the rate-determining step (rds), etc. Voltammetric studies utilizing these diagnostic criteria have been applied to a number of cathodic dimerizations [25-281. It has been indicated that the criteria are applicable also to the mechanisms of anodic dimerization involving deprotonation reactions only by replacing a protonation step by a deprotonation process [29]. Thus, mechanistic studies of the present anodic dimerization involving deprotonation (eqn. 3) were carried out on the basis of the relationships between the anodic
199
Fig. 7. Plots of E,
VS. log ~1 for 0.1 mM (0) and 1 mM (0)
YMeOA
peak potentials (E,) and the logarithm of the potential scan rate (log u) or that of the substrate concentration (log c). Figure 7 shows the plots of E, vs. log u for 0.1 and 1 mM 9MeOA in NE. The E, data were measured by conventional cyclic voltammetry at scan rates below 30 V/s, where the electron transfer step is expected to behave reversibly. The slopes of the plots for 0.1 and 1 mM 9MeOA were estimated to be 28.7 and 29.5 mV per decade, respectively, and from the intercepts of these two plots, the value of d E,/d log c was evaluated to be 28.9 mV per decade. Although the rates of the peak potential shift on the scan rate and the substrate concentration, namely, dE,/d log u and dE,/d log c, vary depending on the reaction mechanism, their possible values in the diagnostic criteria established for the electrodimerization were limited in number as follows: 14.8. 19.7 and 29.6 mV per decade for the former, and - 14.8, 0, 14.8, 19.7, 29.6 and 39.6 mV per decade for the latter (at 25°C) [24]. The estimated values of 28.7 and 29.5 for dE,/d log 11were close to 29.6 mV in these possible values, and moreover 28.9 mV for dE,/d log c was also close to 29.6 mV. Application of these results to the diagnostic criteria and then replacement of a protonation step by a deprotonation one leads to the following four possible mechanisms for the present dimerization process. It is of interest to note that these schemes contain neither the coupling process between two cation radical molecules (RRC) nor that between the substrate and dication (ISC) at the initial stage.
SCHEME
I
RH ‘+ + RH 2 (RH) ;+ (RH);+ (RH):+
+ (RH);’ @1+2H+
rds by RH’+ or at electrode
(1-l) (I-2) (I-3)
SCHEME
II
RH -+ i- RH 2 (RH);+ s R-RH’+ Hi * R-RH + el+H+
VW ;” R-RH’ R-RH’ SCHEME
rds
(II-l)
by RH ‘+ or at electrode
(11-2) (11-3) (11-4)
III
RH’+ + RH:(RH);’ (RI-f;+
2 R-RH’+
R-RH’ R-RN+
G R-RH+ el+H+
SCHEME
RH’+
(III-l) II+
rds
(111-2)
by RH’+ or at electrode
(111-3) (1114)
IV
R’4 RH
zR.+ H+ k, -+ R-RH *
R-RH‘ R-RH+
a R-RH+ ?l+H+
(IV-l) rds
(IV-2)
by RH ‘+ or at electrode
(IV-3) (IV-4)
where RH denotes 9MeOA. As to the equilibrium (IV-l) in Scheme IV, it is hard to take into consideration that the tenth proton of 9MeOA cation radical is released spontaneously. In addition, the resulting anthyl radical will abstract the proton of the solvent before recombination with the released proton. For these reasons, Scheme IV cannot be applied to this dimerization mechanism. Schemes I, II and III involve interaction of the cation radical with its substrate, namely, a RSC reaction as the initial step. The RSC is the rate-deter~ning step in Schemes I and II. The resulting dimer cation is oxidized by the disproportionation reaction or at the electrode in Scheme I, and deprotonation from the dimer cation occurs before the reoxidation step in Scheme II. In Scheme III, the RSC is in equilib~um foilowed by the rate-dete~ning deprotonation. In order to discriminate between these mechanisms, measurements were carried out in different concentrations of a proton acceptor. However, the anodic peak potentials were not affected by the addition of a base such as 2,6-lutidine, 4-cyanopyridine or methanol. These facts clearly exclude the mechanism of Scheme III, in which the reaction rate is expected to increase in the presence of a proton acceptor and hence a negative shift of the peak potentials should be observed; on the other hand, the reaction rate is not affected in Schemes I and II. The remaining mechanisms of Schemes I and II cannot be discri~nated between since the different steps are preceded by RSC which is the rate-determining step. Therefore, it
201
can be concluded that the anodic dimerization of 9MeOA proceeds via Scheme II. The rate law for these mechanisms is represented by the equation -d[RH’+]/dt Determination
= 2k, [RH’+][RH] qf the dimerization
I or
(4) rate constant
The rate constant was evaluated by means of a conventional digital simulation [4] method taking into consideration both a heterogeneous electron-transfer rate and a homogeneous reaction rate represented by eqn. (4). The effect of uncompensated solution resistance was introduced by iterative calculation of the current and the potential of the working electrode, namely, the (k + 1)-th electrode potential ( Eh+l(t)) was calculated from the k-th current, ih( t), and the residual current (i,,(t)) observed for the blank solution: E’+‘(t)
= E(0) + vt - Ru,[ih(t)
+ ib(t)]
(5)
where E(0) is the initial potential and v is the scan rate which is positive before the potential reversing point during the triangular potential sweep and negative after it. In the digital simulation analysis, several parameters were fixed as follows: (Y= 0.5, r = 5.0 pm and R,, = 28 k& (Yis the transfer coefficient. The kinetic and thermodynamic data obtained by the curve-fitting method were k O = 3.0 + 0.5 cm s- ‘, D(9MeOA) = (1.45 * 0.1) x lop5 cm’ s-l, E”=935_t5 mV (vs. I;, I-) and 2k, = (3.5 + 0.5) x 10’ M-’ s-l, where k” denotes the standard rate constant of electron transfer and E o is the standard redox potential. The best fitting data were plotted on the measured curves in Fig. 6. The calculated curves were in good agreement with the observed ones except for a slight deviation seen in the vicinity of the potential reversing point at 100 kV/s (Figs. 6c and 6d). The reason for the deviation will be discussed later. Fairly large rate constants such as 3 cm s-’ were obtained for the electron-transfer process of 9MeOA. While it is one of the largest rates evaluated by FSCV, a reversible process can well be expected for the one-electron oxidation of an anthracene compound, especially one possessing a strong electron-donating group like a methoxy group. The assumption that the transfer coefficient is 0.5 is also considered reasonable for the reversible electrode process. DISCUSSION
Aromatic cation radicals possess an unpaired electron and a positive charge. This accounts for the complex mechanism shown in the anodic reaction of aromatic compounds. For the anodic dimerization of aromatic compounds, two different mechanisms, RRC and RSC, are proposed [30]. If an aromatic cation radical behaves just like a molecular radical, the dimerization will be dominated by the RRC mechanism. The well-investigated anodic dimerization of triphenylamine and its derivative cation radicals 1311 follows the RRC mechanism. A good correlation
202
between the dimerization rates and the spin densities at the reaction site has been reported [32]. On the other hand, 4-methoxybiphenyl [33,34], tetrahydrocarbazole [29], N, N-dimethyl-m-toluidine [35] and 4,4’-dimethoxystilbene [36] cation radicals have been shown to dimerize through the RSC mechanism. In those systems including 9MeOA, relatively high electron densities are expected at the reaction site of substrates owing to an electron-donating group such as a methoxy or a N, N-dimethylamino group. Their cation radicals, showing electrophilicity due to a positive charge, will couple readily with substrates. However, a large reaction rate above about 10’ M-’ s- ’ may not be predicted from the simple electrophi~ic reaction of 9MeOA cation radical with its substrate. The above explanation is, therefore, only one of the aspects of the RSC process. The detailed mechanism of the RSC process is still unclear. The mechanistic elucidation of the rapid electro-dimerization can be carried out by using Nadjo and Saveant’s criteria and with conventional cyclic voltammetry. However, the rate constant cannot be determined with this method alone, since in the solution of the corresponding diffusional problem the reaction rate is lumped together with the standard potential (E” ) of the RH’+/RH couple, which can hardly be obtained with conventional cyclic voltammetry. On the other hand, FSCV combined with a UMDE permits the detection of the reduction current of the interme~ate cation radical and hence an estimation of E *, even if the dimerization rate is close to the diffusion-listed one. Thus, the rate constants can be calculated from these criteria and the estimated E”, or can be determined precisely with background subtraction and the digital simulation analysis as demonstrated in this paper. Although FSCV combined with background subtraction and the digital simulation analysis is expected to be employed extensively for elucidating the mechanisms and kinetics of very short-lived electrogenerated intermediates, there are some problems to be overcome as follows: One is the distortion of the cyclic voltammograms produced by the background subtraction. Although the residual current of the sample solution was approximated by the measured one in the blank solution, the two residual currents are not exactly the same when the ohmic potential drop cannot be ignored. In particular, at the potential reversing point, where the direction and magnitude of the ohmic drop are greatly changed, the above approximation does not hold. Consequently, an artefact will appear near the reversing point. The deviations from the simulated curves in Figs. 6c and 6d are probably attributable to the artefact because the ohmic drop was not small at a scan rate of 100 kV/s. Another problem was the change of the surface characteristics of the working electrode in measuring the cyclic voltammograms. Because it is difficult to maintain the surface condition of the working electrode exactly constant in batchwise measurement, the residual currents observed in the sample and blank solutions are not quite the same, and hence the cyclic voltammograms obtained by background subtraction contains some distortions. In this work. the reprod~cibilities in measur-
203
ing the residual currents were within 1% owing to very careful handling of the surface conditions of the working electrode. FSCV combined with the FIA system described by Howell et al. [6] will be desirable for more accurate analysis. To avoid these problems. Andrieux et al. [2,3] performed curve-fitting without background subtraction assuming that the double-layer capacitance was independent of the potential. On our system, however, the residual currents did depend on the potential. Besides, the faradaic currents were remarkably small in comparison with the residual one, so that accurate curve-fitting was hardly applicable without background subtraction. CONCLUSION
The anodic dimerization of 9MeOA was investigated using the FSCV system. The dependences of E, on log u and log c indicated that the dimerization mechanism involved a cation radical-substrate coupling process in the initial step and that the rate law was rate = k0,,[9MeOA+][9MeOA]. Even though the reaction rate was very rapid, 9MeOA cation radical was easily detected at a fast scan rate above 10 kV/s and with a low substrate concentration below I mM. From the results of digital simulation analysis for the background-subtracted cyclic voltammograms, the rate constants was estimated to be (3.5 k 0.5) X 10’ M-’ ss’. ACKNOWLEDGEMENTS
The authors express their gratitude to Dr. Katsuo Takahashi (Riken Institute of Physical and Chemical Research, Wako) and Mr. Masakatsu Karatsu (Fuso Co., Ltd, Kawasaki) for their continuing interest and for providing facilities for the rapid response potentiostat during this work. This work was supported in part by a Grant-in-Aid for Scientific Research, No. 61540421, from the Ministry of Education and Culture. Japan. REFERENCES 1 J.O. Howell and R.M. Wlghtman, Anal. Chem., 56 (1984) 524. 2 C.P. Andneux, D. Garreau, P. Haplot and J.M. Saveant. J. Electroanal. Chem., 248 (1988) 447. 3 C.P. Andneux. D. Garreau, P. Hapiot, J. Pinson and J.M. SavCant. J. Electroanal. Chem., 243 (1988) 321. 4 D.O. Wipf. E.W. Kristensen, M.R. Deakm and R.M. Wlghtman, Anal. Chem., 60 (1988) 306. 5 C.A. Amatore, A. Jutand and F. Pfliiger, J. Electroanal. Chem.. 218 (1987) 361. 6 J.O. Howell, W.G. Kuhr, R.E. Ensman and R.M. Wightman. J. Electroanal. Chem., 209 (1986) 77. 7 J.O. Howell and R.M. Wightman, J. Phys. Chem., 88 (1984) 3915. 8 0. Hammerich and V.D. Parker, Acta Chem. Stand.. Ser. B. 36 (1982) 519. 9 J.M. Masnovi, E.A. Seddon and J.K. Kochi, Can. J. Chem.. 62 (1984) 2552. 10 J. Newman. J. Electrochem. Sot.. 113 (1966) 501. 11 J.F. Coetzee and C.W. Gardner, Jr.. Anal. Chem., 54 (1982) 2530. 12 J.S. Meek, P A. Monroe and C.J. Bouboulis, J. Org. Chem., 28 (1963) 2572. 13 F.G. Cottrell. Z. Phys. Chem., 42 (1902) 385.
204 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
M.I. Montenegro and D. Pletcher. J. Electroanal. Chem.. 200 (1986) 371. T. Kuwana, D.E. Bublitz and G. Hoh, J. Am. Chem. Sot.. 82 (1960) 5811. 0. Hammerich and V.D. Parker, J. Chem. Sot., Chem. Commun.. (1974) 245. Y. Matsuda, K. Kimura, C. Iwakura and H. Tamura, Bull. Chem. Sot. Jpn.. 46 (1973) 430. I.N. Rozhkov and I.Y. Alyev, Tetrahedron, 31 (1975) 977. L. Eberson and K. Nyberg, Tetrahedron Lett., 22 (1966) 2389. K. Nyberg, Acta Chem. Stand., 25 (1971) 2499. 3770. U. Svanholm and V.D. Parker, J. Am. Chem. Sot., 98 (1976) 2942. J. Phelps. K.S.V. Santhanam and A.J. Bard, J. Am. Chem Sot., 89 (1967) 1752. J.A. Riddick, W.B. Bunger and T.K. Sakano. Orgamc Solvents. Physical Properties and Methods of Purification, 4th ed.. John Wiley, New York, 1986. L. NadJo and J.M. Saveant, J. Electroanal. Chem., 44 (1973) 327. L. Nadjo and J.M. Saveant, J. Electroanal. Chem.. 33 (1971) 419. L.A. Powell and R.M. Wightman. J. Electroanal. Chem., 117 (1981) 321. E. Lamy, L. Nadjo and J.M. Savtant, J. Electroanal. Chem , 42 (1973) 189. J.F. Rusling, J. Electroanal. Chem., 125 (1981) 447. C.L. Kulkarni, B.J. Scheer and J.F. Rusling, J. Electroanal. Chem., 140 (1982) 57. 0. Hammertch and V.D. Parker, Adv. Phys. Org. Chem., 20 (1984) 55. R.F. Nelson and R.H. Philp, Jr., J. Phys. Chem., 83 (1979) 713. S.C. Creason, J. Wheeler and R.F. Nelson, J. Org. Chem., 37 (1972) 4440. B. Aalstad, A. Roman and V.D. Parker, Acta Chem. Stand.. Ser. B, 35 (1981) 649. V.D. Parker, Acta Chem. Stand., Ser. B, 37 (1983) 393. K. Yasukouchi, I. Tamguchi, H. Yamaguchi and T. Tanoue, Bull. Chem. Sot. Jpn., 52 (1979) 1573. B. Aalstad, A. Ronlan and V.D. Parker, Acta Chem. Stand., Ser. B, 35 (1981) 247.
J. Electroanal. Chem., 270 (1989) 191-204 Elsevier Sequoia S.A., Lausanne - Prmted
m The Netherlands
Kinetic study on the dimerization reaction of 9-methoxyanthracene cation radical by means of fast scan cyclic voltammetry Koichi Nozaki, Munetaka Oyama, Hiroyuki Hatano and Satoshi Okazaki * Department (Received
of Chemrstr?: Faculty of Scrence, Kwto 14 December
1988; m rewed
Untcwrsr~v. I(voto 606 (Japan)
form 2 May 1989)
ABSTRACT The instrumentation of a fast scan cychc voltammetric (FSCV) system with a maximum scan rate of 300 kV/s and tts apphcation to the kmetic studies of very short-hved electrogenerated intermedtates are presented. The time resolution of the system was Inspected by cychc voltammetry and chronoamperometry, and was found to be better than 1 ps at an ultramicrodisk electrode (UMDE) of micrometre stze. The mechanism and kmetics of the very rapid anodtc dtmerizrtion of 9-methoxyanthracene (9MeOA) are discussed in further detail for the first ttme by means of FSCV. The reductive wave of 9MeOA canon radical was detected successfully. although the reversible cychc voltammogram could not be observed even at a scan rate as high as 300 kV/s. It was concluded. from the dependences of the anodic peak potentials on both the scan rate and the substrate concentration. that the dimerization proceeded via coupling of 9MeOA cation radical wtth the substrate. The dtmerization rate constant was estimated to be (3.5 50.5)~ 10’ Mm’ ss’ from the results of digital simulation analysis of the observed fast scan cyclic voltammograms.
INTRODUCTION
Cyclic voltammetry (CV) has been utilized widely to obtain thermodynamic information as well as to study the reaction mechanism of electrogenerated intermediates. By employing a faster potential sweep rate. the information obtainable increases in principle. However, considerable distortions of the observed voltammograms are usually caused by the ohmic potential drop and by the band-pass limitation of the cell response at a sweep rate above several hundreds of volts per second with a conventional electrode. Since Howell and Wightman [l] demonstrated the feasibility of a fast scan rate above 10 kV/s by using an ultramicrodisk electrode
l
To whom correspondence
0022-0728/X9/$03.50
should
be addressed
Q 1989 Elsevter Sequoia
S.A.
192
(UMDE) of diameter 10 pm, fast scan cyclic voltammetry (FSCV) has received active attention [l-7]. This great progress is attributed to the extremely short response time and the decrease of the ohmic drop at the UMDE. Very recently, a scan rate above 1 MV/s could be reached without fatal distortion of the voltammograms using a UMDE of diameter 5.5 pm [2] and attempts are still being made to extend the upper limit of the scan rate. The use of FSCV allows the investigation of rapid heterogeneous electron-transfer kinetics. Several groups have determined successfully rate constants greater than 1 cm/s by inspecting cyclic voltammograms at above 10 kV/s [l-4]. FSCV is also expected to be an advantageous technique for observing directly electrogenerated intermediates of half-lives of sub-microseconds. So far, only a few applications of FSCV to kinetic studies have been reported. Amatore et al. [5] detected the electrogenerated 2,6-diphenyl pyrylium radical at a scan rate of sub-megavolts per second and evaluated a dimerization rate constant as large as 2.5 X lo9 M-’ s-‘, which was near to the diffusion-controlled limit. In this study, we first examined the instrumentation of the FSCV system. Inspection by cyclic voltammetry and chronoamperometry confirmed that the time resolution of the system was less than 1 ps at a UMDE of micrometre size. Then the anodic dimerization kinetics of 9MeOA were investigated using this FSCV system. The 9MeOA cation radical has been shown to dimerize to yield compound 1,
OMe quantitatively [8]. However, the rate of the dimerization reaction was so rapid that no reduction wave was observed with conventional cyclic voltammetry [9]. Thus, the mechanism and the reaction rate have not been reported. Although a totally reversible cyclic voltammogram could not be observed even at the highest scan rate used (300 kV/s) in this study, the reduction wave of 9MeOA cation radical was detected and analysed successfully. The mechanism and reaction rate are discussed. EXPERIMENTAL
System configuration
of FSCV
Figure 1 shows the configuration of the FSCV system developed. A fast response potentiostat and an I/V converter were designed to be as compact as possible to fit into a small head box of dimensions 14 X 8 x 2 cm. The head box was put very close to the electrolytic cell and they were electrically shielded together to minimize external noise. Operational amplifiers of OP16 (PMI, bandwidth 8 MHz) were employed in the potentiostat and I/V converter. The resistance and capacitance
193
Fig. 1 Schematic diagram of the FSCV system. (A) Digital function generator: (B) potentiostat controller; (C) head box contaimng three-electrode potentkostat and I/V converter; (D) wide-band width amplifier; (E) A/D converter (50 ns, 10 bit): (F) micro-computer.
used at the I/V converter were 10 kQ and 3 pF, respectively. When the scan rate was higher than 10 kV/s, a capacitance of 0.1 PF was connected between the counter and reference electrodes to suppress the ringing of the current signal occurring usually just after a voltage reversing point. A triangular wave function (max. 150 kHz) was generated by a digital wide function synthesizer (Model 1930, NF Electronic Instruments Co. Ltd., Japan). Transient signals from the Z/V converter were amplified 10-1000 times through a wide-bandwidth differential amplifier (DC-10 MHz, Model 5305, NF) and then recorded by a digitizer (Model S121, Outnics Co Ltd., Japan) which had a minimum acquisition time of 50 ns with a lo-bit resolution. The time constant of the 1/V converter was 0.2 PCSand scan rates ranging from 0.1 to 300000 V/s were available on the system. Data acquisition and analysis of the voltammograms were performed on a micro-computer (Model PC9801 VM2, NEC, Japan). For cyclic voltammograms with a poor S/N ratio, 5 or 20 scans were accumulated on the micro-computer. Data acquisition, analysis of the cyclic voltammograms and the simulation program were written in MS-FORTRAN 77. The fast response potentiostat (Model HEC972) was developed in cooperation with Fuso Co. Ltd. (Kawasaki, Tokyo). Conventional cyclic voltammetry at lower scan rates of 0.1-30 V/s were carried out on a Model 174 PAR Polarographic Analyser. A platinum electrode of diameter 1.25 mm was used as the working electrode. The solution resistance was compensated with an IR compensation circuit provided by a Model 174/50 Accessory. The response of the analyser was 110 ps at the range of 1 mA full-scale. The temperature of the measuring solutions was regulated to 25 -t 0.1” C. Solution resistances were measured with an impedance bridge (Model 12K, Derica, Japan) with a conventional conductivity cell. Ultramicrodisk
electrode (UMDE)
UMDEs were prepared as follows: a short length (7 mm) of platinum micro-wire of 100, 30, 10 or 5 pm diameter (The Japan Lamp Industries Co., Ltd.) was connected to a copper lead wire (diameter 30 pm) and then copper was elec-
194
trodeposited on the junction to ensure electrical contact. The silver coating of Wollaston wire (Pt, diameter 5 pm) or electrodeposited copper on the top end (2-3 mm) of the micro-wire was removed with dilute nitric acid solution. After washing and drying, the micro-wire and the lead wire were positioned in a soft glass capillary (id 0.3 mm. od 1 mm). The assembly was then sealed by inserting it very slowly (1 cm/h) into a laboratory-made electric furnace maintained at 670 + 10” C while applying a vacuum. The resulting assembly was sealed again into a soft glass tube (id 2 mm, od 4 mm). The electrode surface was ground successively with 600, 1000 and 3000 mesh emery papers and polished to a mirror finish with 0.3 and 0.05 pm alumina on a suede cloth. The diameter of the Wollaston micro-wire of 5 pm was found to be 5.5 pm by scanning electron micrograph measurement. A platinum wire of 0.5 mm diameter was used as the counter-electrode; its position was not important because the cell resistance of a UMDE cell system is dominated by the resistance near the electrode surface [lo]. The double-junction assembly consisting of a Pt/(I, + II) reference electrode recommended by Coetzee and Gardner [ll] was employed. A disk-shaped porous glass tip (40 nm pore size) was used at the junction. In terms of the extremely large exchange current of the reference electrode (ca. 3000 times greater than that of a Ag+/Ag electrode [ll]) and the low potential drift of less than 1 mV per week, this reference electrode was superior to the conventional silver electrode. The formal potential of the ferrocenium/ferrocene system in nitroethane solution was 0.173 V with this reference electrode. Chemical reugents Acetonitrile (AN, GR grade, Wakenyaku Co. Ltd.) was redistilled twice over P,O,. Nitroethane (NE), purchased from Nacalai Tesque, was dried over P,O, with stirring for 1 day and then distilled twice under reduced pressure. Tetraethylammonium hexafluorophosphate (TEAPF,) was synthesized from tetraethylammonium bromide and potassium hexafluorophosphate. It was recrystallized from acetonitrile + ethanol mixed solvent four times and finally from ethanol. It was dried in a vacuum oven at 60 o C prior to use. 9MeOA was synthesized by standard procedures [12]. It was purified by a silica-gel column with hexane benzene mixed solvent as the eluant. Ferrocene (Fc, Aldrich Co. Ltd.) was used without further purification. RESULTS
Fast stun cyclic voltummetry Figure 2 shows the cyclic voltammogram of 5 mM Fc in AN solution with the UMDE of 5.5 pm and at a scan rate of 100 kV/s. Although the fairly large charging
195
-l.O/ 0.0 E IV
0.5 t vs. &.I-)
Fig. 2. Cychc voltammogram of 5 mM Fc in AN containing with a Pt UMDE of diameter 5.5 pm.
0.6 M TEAP at a scan rate of 100 kV/s
and
current was overlapping at the high scan rate, reversible faradaic waves were obtained without any significant distortion. The apparent double-layer capacitance evaluated from the background current was as small as 2.7 pF at 0 V (vs. I;, I-). When the distance between the working and reference electrodes is ten or more times larger than the electrode radius as in a usual UMDE cell system, the uncompensated solution resistance (R .,) is readily predicted utilizing the theoretical equation [lo]
(1)
R,, = p/Jr
where p is the specific resistance of the solution and Y is the radius of the UMDE. In the present cell system. R,, was estimated to be 35.5 k0 from p = 39 D cm. Taking the product of the double-layer capacitance and the value of R,,. the cell time constant was calculated to be as short as 100 ns. The overall response time of the signals was, however, limited by the response time at the Z/V converter, which was 200 ns. It should be noted that even at the extremely high scan rate, the extent of the ohmic potential drop at the oxidation peak was only 15 mV, which was calculated from the peak current (0.42 PA) and R”,. Fast response chronoamperometr):
The dotted curves for the to 0.5 V. The solid lines in equation [13] i(t)
lines in Figs. 3a and 3b show the observed current vs. time (i-t) AN solution of Fc immediately after the potential was stepped from 0 diameters of the UMDEs used were 30 and 10 pm, respectively. The Figs. 3a and 3b represent the calculated curves from the Cottrell
= ~zFAD”~c/‘~
(2)
where n, F and A denote the number of electrons involved in the electrode process, the Faraday constant and the geometrical surface area of the working electrode, respectively. D and c are the diffusion coefficient and concentration of Fc (D = 2.2
196
J “y ’ ‘“” ., _ “___ ,_ ,I ”
”
J
4
6
6
.;-
0
20
40
60
60
” 0
tip
” 2 t/p
Fig. 3. Transient I-I curves measured for the same solution as in Ftg. 2. (a) ExperImental (dotted line) and calculated (solid line) curves at a Pt UMDE of diameter 30 pm. (b) The same as (a) except for a 10 pm UMDE. (c) The observed curves for the sample (curve S) and the blank (curve B) at a 10 pm UMDE. (d) The faradax component in curve S obtained by subtracting curve B from curve S
X lop5 cm2 s-’ [14,15] c = 5 mM). Equation (2) is the special case for the diffusion-limited region of the transient response at a planar electrode in chronoamperometry. Good agreement between the observed and the calculated curves was obtained, indicating that in such an extremely short period of time, less than 100 ps, the planar diffusion was dominant even at a UMDE of micrometre size. Figure 3c shows the current response curves up to 10 ~LS at the UMDE of 10 pm. The calculated cell time constant for the UMDE was 200 ns. Curves S and B are for the sample solution and the blank, respectively. Immediately after stepping the electrode potential, the faradaic current was concealed in the large charging current. Then the pure faradaic current was extracted by subtracting curve B from curve S. The resulting curve is shown in Fig. 3d. It is worth noting that the diffusional current could already be observed within 1 ps after the potential step. Fast scan cybc
voltammograms
of 9MeOA
in NE
Hammerich and Parker reported that the dimer 1 is produced quantitatively from anodic oxidation of 9MeOA in AN (yield 95%) [S]. Up to now, AN solvent has been used extensively not only for the investigation of anodic and cathodic electrode reactions but also for electro-organic synthesis. However, most reactive cation species are known to react with this solvent, namely, to undergo acetamidation [16-191. Recent studies on anodic reactions or the structural determination of electro-oxidized intermediates have been performed in a less basic solvent, such as nitromethane or dichloromethane [20-221. In voltammetric studies with a higher scan rate, a lower solution resistance is required to avoid distortion of the voltam-
197
I
I
I
I
0.0
0.5
1.0
1.5
E/V
(vs.
&.I-)
Fig. 4. Cyclic voltammogram Pt UMDE of 100 pm.
of 5 mM 9MeOA
m NE containmg
0.5 M TEAPF,
at 100 V/s,
and with a
mograms by the ohmic potential drop. Nitro compounds whose dielectric constants are similar to that of AN were suitable for this purpose as solvents. In addition, because of the higher viscosity of these solvents than that of AN, the reaction rates are expected to be slower in the former solvent. Actually, the dimerization reaction of 9MeOA cation radical was observed to be slower in NE (n = 6.38 X 10P4 m’ SC’) than in AN (n = 3.41 X 1O-4 m2 SC’) [23]. For these reasons, the present studies were carried out in NE. Figure 4 shows the cyclic voltammogram of 9MeOA at a slower scan rate (100 V/s). The reductive wave of 9MeOA cation radical could not be seen on the reverse voltage scan while a new peak .was observed at 0.2 V, which was attributed to the reduction of the proton released in the dimerization process: 2 (9MeOA’+)
+ 1+ 2 H+
(3)
From the results, it was confirmed that the dimerization process of 9MeOA cation radical also took place in NE. When the concentration of the substrate was as high as 5 mM, only irreversible cyclic voltammograms were obtained even at the highest scan rate used (300 kV/s). This suggested that 9MeOA cation radicals in a high concentration level were dimerizing in a time as short as 1 ps. On the contrary, in a dilute concentration of the substrate (1 mM), a very small reductive current could be seen on the reverse voltage scan, as shown in Figs. 5a, 5b and 5c, although this is somewhat ambiguous due to the large residual current. Thus, the faradaic components were extracted by the background subtraction technique [16]. This method was accomplished by subtracting digitally the residual currents recorded for the blank solution from the observed curves for the sample. The solid lines in Fig. 6 show the resulting cyclic voltammograms (Figs. 6a-6c) together with that for 5 mM (Fig. 6d). The small peaks seen on the reverse scan can be assigned to the reduction of the cation radical from evidence that they become larger, the faster the scan rate used (Figs. 6a-6c) and diminish at high substrate concentration such as 5 mM (Fig. 6d).
I
I 0.5
I
10 E/V
Fig. 5. Cyclic voltammograms of 1 mM 9MeOA and (c) 100 kV/s, respectively.
I 10 E/V
with a 10 /lrn UMDE
Fig. 6. Cyclic voltammograms obtamed by background subtractlon (0). (a) [9MeOA] =l mM, D =lO kV/s: (b) [9MeOA] = 1 mM. u = 100 kV/s; (d) [9MeOA] = 5 mM. P = 100 kV/s.
Mechanism
I 05
(VS l;,l-)
of the anodic dimerization
at various
I
(vs,l;>C
scan rates: (a) 10, (b) 30
(sohd lines) and dlgital simulations o = 30 kV/s: (c) [9MeOA] =I mM,
reaction of 9MeOA
Nadjo and Saveant [24] have established the diagnostic criteria for distinguishing the 25 possible mechanisms of cathodic electrodimerization on the basis of the dependences of the peak potentials in linear-sweep voltammetry on both the potential scan rate (cl) and the substrate concentration (c). These mechanisms involve successive chemical processes such as radical-radical coupling (RRC). radical-substrate coupling (RSC) and ion-substrate coupling (ISC), as well as disproportionation and a protonation step as the rate-determining step (rds), etc. Voltammetric studies utilizing these diagnostic criteria have been applied to a number of cathodic dimerizations [25-281. It has been indicated that the criteria are applicable also to the mechanisms of anodic dimerization involving deprotonation reactions only by replacing a protonation step by a deprotonation process [29]. Thus, mechanistic studies of the present anodic dimerization involving deprotonation (eqn. 3) were carried out on the basis of the relationships between the anodic
199
Fig. 7. Plots of E,
VS. log ~1 for 0.1 mM (0) and 1 mM (0)
YMeOA
peak potentials (E,) and the logarithm of the potential scan rate (log u) or that of the substrate concentration (log c). Figure 7 shows the plots of E, vs. log u for 0.1 and 1 mM 9MeOA in NE. The E, data were measured by conventional cyclic voltammetry at scan rates below 30 V/s, where the electron transfer step is expected to behave reversibly. The slopes of the plots for 0.1 and 1 mM 9MeOA were estimated to be 28.7 and 29.5 mV per decade, respectively, and from the intercepts of these two plots, the value of d E,/d log c was evaluated to be 28.9 mV per decade. Although the rates of the peak potential shift on the scan rate and the substrate concentration, namely, dE,/d log u and dE,/d log c, vary depending on the reaction mechanism, their possible values in the diagnostic criteria established for the electrodimerization were limited in number as follows: 14.8. 19.7 and 29.6 mV per decade for the former, and - 14.8, 0, 14.8, 19.7, 29.6 and 39.6 mV per decade for the latter (at 25°C) [24]. The estimated values of 28.7 and 29.5 for dE,/d log 11were close to 29.6 mV in these possible values, and moreover 28.9 mV for dE,/d log c was also close to 29.6 mV. Application of these results to the diagnostic criteria and then replacement of a protonation step by a deprotonation one leads to the following four possible mechanisms for the present dimerization process. It is of interest to note that these schemes contain neither the coupling process between two cation radical molecules (RRC) nor that between the substrate and dication (ISC) at the initial stage.
SCHEME
I
RH ‘+ + RH 2 (RH) ;+ (RH);+ (RH):+
+ (RH);’ @1+2H+
rds by RH’+ or at electrode
(1-l) (I-2) (I-3)
SCHEME
II
RH -+ i- RH 2 (RH);+ s R-RH’+ Hi * R-RH + el+H+
VW ;” R-RH’ R-RH’ SCHEME
rds
(II-l)
by RH ‘+ or at electrode
(11-2) (11-3) (11-4)
III
RH’+ + RH:(RH);’ (RI-f;+
2 R-RH’+
R-RH’ R-RN+
G R-RH+ el+H+
SCHEME
RH’+
(III-l) II+
rds
(111-2)
by RH’+ or at electrode
(111-3) (1114)
IV
R’4 RH
zR.+ H+ k, -+ R-RH *
R-RH‘ R-RH+
a R-RH+ ?l+H+
(IV-l) rds
(IV-2)
by RH ‘+ or at electrode
(IV-3) (IV-4)
where RH denotes 9MeOA. As to the equilibrium (IV-l) in Scheme IV, it is hard to take into consideration that the tenth proton of 9MeOA cation radical is released spontaneously. In addition, the resulting anthyl radical will abstract the proton of the solvent before recombination with the released proton. For these reasons, Scheme IV cannot be applied to this dimerization mechanism. Schemes I, II and III involve interaction of the cation radical with its substrate, namely, a RSC reaction as the initial step. The RSC is the rate-deter~ning step in Schemes I and II. The resulting dimer cation is oxidized by the disproportionation reaction or at the electrode in Scheme I, and deprotonation from the dimer cation occurs before the reoxidation step in Scheme II. In Scheme III, the RSC is in equilib~um foilowed by the rate-dete~ning deprotonation. In order to discriminate between these mechanisms, measurements were carried out in different concentrations of a proton acceptor. However, the anodic peak potentials were not affected by the addition of a base such as 2,6-lutidine, 4-cyanopyridine or methanol. These facts clearly exclude the mechanism of Scheme III, in which the reaction rate is expected to increase in the presence of a proton acceptor and hence a negative shift of the peak potentials should be observed; on the other hand, the reaction rate is not affected in Schemes I and II. The remaining mechanisms of Schemes I and II cannot be discri~nated between since the different steps are preceded by RSC which is the rate-determining step. Therefore, it
201
can be concluded that the anodic dimerization of 9MeOA proceeds via Scheme II. The rate law for these mechanisms is represented by the equation -d[RH’+]/dt Determination
= 2k, [RH’+][RH] qf the dimerization
I or
(4) rate constant
The rate constant was evaluated by means of a conventional digital simulation [4] method taking into consideration both a heterogeneous electron-transfer rate and a homogeneous reaction rate represented by eqn. (4). The effect of uncompensated solution resistance was introduced by iterative calculation of the current and the potential of the working electrode, namely, the (k + 1)-th electrode potential ( Eh+l(t)) was calculated from the k-th current, ih( t), and the residual current (i,,(t)) observed for the blank solution: E’+‘(t)
= E(0) + vt - Ru,[ih(t)
+ ib(t)]
(5)
where E(0) is the initial potential and v is the scan rate which is positive before the potential reversing point during the triangular potential sweep and negative after it. In the digital simulation analysis, several parameters were fixed as follows: (Y= 0.5, r = 5.0 pm and R,, = 28 k& (Yis the transfer coefficient. The kinetic and thermodynamic data obtained by the curve-fitting method were k O = 3.0 + 0.5 cm s- ‘, D(9MeOA) = (1.45 * 0.1) x lop5 cm’ s-l, E”=935_t5 mV (vs. I;, I-) and 2k, = (3.5 + 0.5) x 10’ M-’ s-l, where k” denotes the standard rate constant of electron transfer and E o is the standard redox potential. The best fitting data were plotted on the measured curves in Fig. 6. The calculated curves were in good agreement with the observed ones except for a slight deviation seen in the vicinity of the potential reversing point at 100 kV/s (Figs. 6c and 6d). The reason for the deviation will be discussed later. Fairly large rate constants such as 3 cm s-’ were obtained for the electron-transfer process of 9MeOA. While it is one of the largest rates evaluated by FSCV, a reversible process can well be expected for the one-electron oxidation of an anthracene compound, especially one possessing a strong electron-donating group like a methoxy group. The assumption that the transfer coefficient is 0.5 is also considered reasonable for the reversible electrode process. DISCUSSION
Aromatic cation radicals possess an unpaired electron and a positive charge. This accounts for the complex mechanism shown in the anodic reaction of aromatic compounds. For the anodic dimerization of aromatic compounds, two different mechanisms, RRC and RSC, are proposed [30]. If an aromatic cation radical behaves just like a molecular radical, the dimerization will be dominated by the RRC mechanism. The well-investigated anodic dimerization of triphenylamine and its derivative cation radicals 1311 follows the RRC mechanism. A good correlation
202
between the dimerization rates and the spin densities at the reaction site has been reported [32]. On the other hand, 4-methoxybiphenyl [33,34], tetrahydrocarbazole [29], N, N-dimethyl-m-toluidine [35] and 4,4’-dimethoxystilbene [36] cation radicals have been shown to dimerize through the RSC mechanism. In those systems including 9MeOA, relatively high electron densities are expected at the reaction site of substrates owing to an electron-donating group such as a methoxy or a N, N-dimethylamino group. Their cation radicals, showing electrophilicity due to a positive charge, will couple readily with substrates. However, a large reaction rate above about 10’ M-’ s- ’ may not be predicted from the simple electrophi~ic reaction of 9MeOA cation radical with its substrate. The above explanation is, therefore, only one of the aspects of the RSC process. The detailed mechanism of the RSC process is still unclear. The mechanistic elucidation of the rapid electro-dimerization can be carried out by using Nadjo and Saveant’s criteria and with conventional cyclic voltammetry. However, the rate constant cannot be determined with this method alone, since in the solution of the corresponding diffusional problem the reaction rate is lumped together with the standard potential (E” ) of the RH’+/RH couple, which can hardly be obtained with conventional cyclic voltammetry. On the other hand, FSCV combined with a UMDE permits the detection of the reduction current of the interme~ate cation radical and hence an estimation of E *, even if the dimerization rate is close to the diffusion-listed one. Thus, the rate constants can be calculated from these criteria and the estimated E”, or can be determined precisely with background subtraction and the digital simulation analysis as demonstrated in this paper. Although FSCV combined with background subtraction and the digital simulation analysis is expected to be employed extensively for elucidating the mechanisms and kinetics of very short-lived electrogenerated intermediates, there are some problems to be overcome as follows: One is the distortion of the cyclic voltammograms produced by the background subtraction. Although the residual current of the sample solution was approximated by the measured one in the blank solution, the two residual currents are not exactly the same when the ohmic potential drop cannot be ignored. In particular, at the potential reversing point, where the direction and magnitude of the ohmic drop are greatly changed, the above approximation does not hold. Consequently, an artefact will appear near the reversing point. The deviations from the simulated curves in Figs. 6c and 6d are probably attributable to the artefact because the ohmic drop was not small at a scan rate of 100 kV/s. Another problem was the change of the surface characteristics of the working electrode in measuring the cyclic voltammograms. Because it is difficult to maintain the surface condition of the working electrode exactly constant in batchwise measurement, the residual currents observed in the sample and blank solutions are not quite the same, and hence the cyclic voltammograms obtained by background subtraction contains some distortions. In this work. the reprod~cibilities in measur-
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ing the residual currents were within 1% owing to very careful handling of the surface conditions of the working electrode. FSCV combined with the FIA system described by Howell et al. [6] will be desirable for more accurate analysis. To avoid these problems. Andrieux et al. [2,3] performed curve-fitting without background subtraction assuming that the double-layer capacitance was independent of the potential. On our system, however, the residual currents did depend on the potential. Besides, the faradaic currents were remarkably small in comparison with the residual one, so that accurate curve-fitting was hardly applicable without background subtraction. CONCLUSION
The anodic dimerization of 9MeOA was investigated using the FSCV system. The dependences of E, on log u and log c indicated that the dimerization mechanism involved a cation radical-substrate coupling process in the initial step and that the rate law was rate = k0,,[9MeOA+][9MeOA]. Even though the reaction rate was very rapid, 9MeOA cation radical was easily detected at a fast scan rate above 10 kV/s and with a low substrate concentration below I mM. From the results of digital simulation analysis for the background-subtracted cyclic voltammograms, the rate constants was estimated to be (3.5 k 0.5) X 10’ M-’ ss’. ACKNOWLEDGEMENTS
The authors express their gratitude to Dr. Katsuo Takahashi (Riken Institute of Physical and Chemical Research, Wako) and Mr. Masakatsu Karatsu (Fuso Co., Ltd, Kawasaki) for their continuing interest and for providing facilities for the rapid response potentiostat during this work. This work was supported in part by a Grant-in-Aid for Scientific Research, No. 61540421, from the Ministry of Education and Culture. Japan. REFERENCES 1 J.O. Howell and R.M. Wlghtman, Anal. Chem., 56 (1984) 524. 2 C.P. Andneux, D. Garreau, P. Haplot and J.M. Saveant. J. Electroanal. Chem., 248 (1988) 447. 3 C.P. Andneux. D. Garreau, P. Hapiot, J. Pinson and J.M. SavCant. J. Electroanal. Chem., 243 (1988) 321. 4 D.O. Wipf. E.W. Kristensen, M.R. Deakm and R.M. Wlghtman, Anal. Chem., 60 (1988) 306. 5 C.A. Amatore, A. Jutand and F. Pfliiger, J. Electroanal. Chem.. 218 (1987) 361. 6 J.O. Howell, W.G. Kuhr, R.E. Ensman and R.M. Wightman. J. Electroanal. Chem., 209 (1986) 77. 7 J.O. Howell and R.M. Wightman, J. Phys. Chem., 88 (1984) 3915. 8 0. Hammerich and V.D. Parker, Acta Chem. Stand.. Ser. B. 36 (1982) 519. 9 J.M. Masnovi, E.A. Seddon and J.K. Kochi, Can. J. Chem.. 62 (1984) 2552. 10 J. Newman. J. Electrochem. Sot.. 113 (1966) 501. 11 J.F. Coetzee and C.W. Gardner, Jr.. Anal. Chem., 54 (1982) 2530. 12 J.S. Meek, P A. Monroe and C.J. Bouboulis, J. Org. Chem., 28 (1963) 2572. 13 F.G. Cottrell. Z. Phys. Chem., 42 (1902) 385.
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