Study of the bielectronic electro-oxidation of N,N,N',N'-tetramethyl naphthidine (TMN) in non-aqueous medium

41

J. Electroanal. Chem, 295 (1990) 41-58

Blsevier !kquoia S.A., Lausanne

Study of the bielectronic el~~oxi~tion of N,N,N ‘,iV’-tetramethyl naph~~e (TMN) in non-aqueous medium Determination of the individual kinetic parameters by a Laplace space analysis Maria A. Z&r and He&or Fem&ndez * Universidad National Cbrdoba (Argentina)

de Rio Cuarto, Departamento

de Qtdmica y fisica,

Esiafeta No. 9, 5800 Rio Cuarto,

(Received 6 March 1990; in revised form 18 June 1990)

ABSTRACT

The mechanism of the heterogeneous electron transfer between N, N, N ‘, N ‘-tetrarnethyl naphthidine (TMN) and its dication (T&IN*+ ) has been studied at platinum electrodes in sodium perchlorate+ acetonitrile solutions. Individual heterogeneous rate constants, transfer coefficients, diffusion coefficients and overall formal potentials were evaluated at different temperatures. The density of TMN was also determined at 298 K. The entropy of solvation of the dication and approximate activation parameters for the electron-transfer reactions were also obtained. In this study it has been confirmed that the two-electron oxidation of TMN conforms to an EE-type me&anism, with the second efectron transfer being the rat~dete~~g step, according to the results of the analysis in the Laplace space of single current-time chronoamperometric transients.

INTRODUCTION

One of the products obtained during the anodic oxidation of 1-naphthylamine on platinum electrodes in acetonitrile (ACN) is the l,l’-napht~~e dimer [l]. The electrochemical behaviour of this dimer is unusual compared with the electrochemical behaviour of homologous compounds such as benzidines under the same conditions [2,3]. While l,l’-naphthidine is oxidized through a bielectronic chargetransfer process (the two successive one-electron transfers are observed as a single

* To whom correspondence should be addressed. ~22~728/~/$03.50

0 1990 - Ekevier Sequoia S.A.

42

process [4], the benzidines show two systems of consecutive mono-electronic peaks as obtained by cyclic voltammetry [2]. It is known that the oxidation of l,l’-naphthidines to the corresponding dications is a complex electrode reaction because of the homogeneous chemical reactions following the charge transfer [1,4]. Similar reactions were proposed for the anodic oxidation of non-substituted benzidmes [2,3]. However, this behaviour is not expected for iV, N, N ‘, ~‘-tetr~ethyl l,l’-naph~~e (TMN). Previous studies have shown that TMN is readily oxidized to the corresponding dication, TMN2+, on platinum in acetonitrile (ACN), through a single bielectronic (n = 2) transfer process [5] according to TMN$TMN2++ kb

2 e-

where k, and k, are the potenti~-d~endent overall heterogeneous rate constants for the forward and backward reactions, respectively. From cyclic voltammetry and controlled-potential coulometric studies, it has been proposed that the TMN oxidation satisfies a mechanism of the EE type [5], as shown in the equations TMN2TMN*++ k bl

T&,fN”

2 ka2TMN2++

1 e-

(2)

1 e-

where k,, k,, and km k, are the forward and backward heterogeneous rate constants for each individual electron-transfer process, respectively. However, even from cyclic voltammetry, where only a single anodic peak corresponding to n = 2 is obtained, it is not possible to distinguish the mechanism mentioned above and one of EC type, where the chemical step would be the disproportionation of the mon~~tion radical generated according to eqn. (2) to the corresponding dication: 2 TMN-++

TMN + TMN2+

(4)

On the other hand, as stated elsewhere, the observation of a single reversible wave does not provide unequivocal evidence for a direct two-electron transfer. This can be deduced only from kinetic studies [6]. In addition, TMN fails to yield an ESR signal, suggesting that the TMN ‘+ intestate exists at imper~ptibly low ~on~ntratio~ [7]. Although mechanistic studies have been published for the o~dation/r~uction of organic compounds [2,3], values of the kinetic parameters for the individual two-step charge transfers are scarce [8-111. Recently, a mathematical model for the calculation of the individual charge-transfer rates, as well as the stepwise transfer coefficients, in an EE-type mechanism by analysis in Laplace space has been published

WI*

43

In this work, the kinetics of the bielectronic charge transfer of TMN on platinum electrodes in ACN were studied at different temperatures and supporting electrolyte concentrations by the single potential pulse technique. The overall heterogeneous rate constants were determined in solutions containing, initially, either both components of the redox couple or the reduced one only. In this way, it is demonstrated that TMN is electrochemically oxidized following an EE-type mechanism, the second electron-transfer step being the one dete~g the reaction rate. The individual forward heterogeneous rate constants (k, and ka) and the corresponding transfer coefficients ((1- a)i and (1 - CX)~)of the processes indicated by eqns. (2) and (3) were determined by the analysis of the current-time, transients in Laplace space according to the model previously presented by Dauyotis et al. [ll]. EXPERIMENTAL

ACN (Sintorg~ HPLC) and NaGlO, (Fhrka p.a.) were purified as described previously [ 121. TMN was synthesized from naphthidine [S]. For those experiments in which both components of the redox couple (TMN and TMN2+) were present in solution, the required concentration ratios (x M TMN/y M TMN’+) were fixed by anodic oxidation of TMN through constant current coulometry and determined exactly by UV absorption spectroscopy. The spectral characteristics of TMN taken from the literature are .&zE = 330 nm, log (e/l mol-’ cm-‘) = 4.2 and for TMN2+ A%E nm (log (e/l mol-’ cm-‘)) = 503 (4.5), 380 (4.2), 330 (sh) [5]. The molar concentration ratios ranged from 1.96 to 4.75. The equilibrium potentials for solutions of different concentration ratios were very stable and conformed satisfactorily with the Nernst equation (correlation coefficients r a 0.9998) for a redox couple such as that described in eqn. (1). They were measured by an electrometer probe connected to the voltage follower of the potentiostat. The formal potentiaI, Et, determined in 1 M NaClO, solutions at 273 K was Era = 0.380 of:0.002 V, and in 0.1 M NaClO, solutions, in which most of the experiments were performed, Ef” = 0.451 f 0.002 V at the same temperature. The formal redox potentials of the overall two-electron processes were also calculated from the cyclic voltammograms and reproduced, satisfactorily, the values indicated above. The Efo ‘s for different temperatures were determined from cyclic voltammetry. For comparison, the only potential datum found in the literature for this system curves in is El,2 = 0.384 V, which was obtained from stationary current-potential 0.4 M NaClO, + ACN at 273 K IS]. As indicated, Ep of the TMN/TMN2+ couple shifts to more negative values when the electrolyte concentration is increased to 1 M. This phenomenon is attributed mainly to ion pairing of the dication with CIO; , by analogy with the same behaviour observed in other systems [13-163. This result is not surprising for high ClO; concentrations, but it is presumed that, at about 0.1 M, the ion pairing should be less significant because dications are stabilized because of the higher solvation properties of ACN [5,17]. Kinetic determinations were performed at 0.1 M as well as at 1 M NaClO, to determine whether or not the

mechanism of electro-oxidation of TMN changes with the supporting electrolyte concentration. From solutions containing both species, kinetic data were extracted by analysing the current-time (i-t) transients obtained from single potential pulses to the working electrode. The initial potentials were the corresponding equilibrium potentials and the i-t transients were recorded up to 100 ms. The over-potentials, q {or final static), were increased in steps of 0.010 V up to vrnm = 0.040 V for each T~~~2+ concentration ratio. The charge-transfer currents, i(O), for given over-potentials were determined through numerical analyses of the i-t transients by the method of Niki et al. [l&19]. This method considers as optimum the kinetic parameters (i(0) and H), see below) which minimize the variance in the fitting of the experimental i-t values and those calculated from eqn. (5) corresponding to a system with fast kinetics (eqn. 1). For those experiments performed in solutions initially containing only the reduced species, TMN, its concentration was varied in the range (0.24 to 1.5) x 10v3 M. More concentrated solutions could not be used because TMN is sparingly soIuble in ACN. The dectrochemical experimental technique was the same as that described above except for the initial potential, which was fixed at an arbitrary value where no faradaic current flows. The i-r transients were recorded between 0.5 and 500 ms. The analysis of these transients was performed in Laplace space as described previously [20]. The diffusion coefficients of TMN used either for comparison or calculation (eqns. 10 and 11, see below) were determined from the slope of charge vs. square root of time plots ~c~on~ulornet~) for potential steps where the charge-transfer rate is controlled only by semi-infinite linear diffusion to the electrode surface [13,21]. We have found by double potential step chonocoulometry that TMN does not adsorb significantly on Pt from ACN solutions, at least within the potential range studied. Plots of Q(t < 7) vs. t1j2 and Q( r < t < 27) vs. @/2 + (1 - #/2 - t”2] gave equal (and opposite) slopes within experimental error [slopes = (2.23 +_0.18) X lo-’ C s-*/’ and intercepts corresponding to TMN-free support~g electrofyte solutions f2OJ.These data correspond to a solution of c;~ = 0.27 mM, 1 M NaClO, and 3Zf= 0.460 V. These results show that reactant (and/or product) adsorption is negligible ]13,21). From the slope of the Q( t < 7) vs. t’j2 plot indicated above, a value of D = (0.73 f 0.06) X 10v5 cm* s-* was calculated for TMN in 1 M NaCIO, solution at 273 K. The cell, electrodes, electrochemical instrumentation and data processing have been described elsewhere ]3,19,20]. The potentials are referred to a SCE and are corrected for ohmic drop. All solutions were d~xygenat~ by bubb~ng dry nitrogen for at least 30 min prior to the experiments. An atmosphere of this gas was maintained over the solutions during the experiments. The working temperatures were in the range (273 to 303) f 0.1 K. The UV-visible absorption spectra were recorded on a Cary 17 spectrophotometer. Programs for calculating i(0) and H by the variance minimum and the rate constants by Laplace space analysis are available upon request from the authors.

45 THEORY

Solutions of x M TMN/y M TMN2+ The mathematical relationships to calculate the kinetic parameters for potential steps imposed in a system such as that given in eqn. (1) are, on the whole, well known ]21]. So, only forms specific to the conditions and assumptions adopted will be included. The overall formal rate constant of the process, kp, may be determined by i(O) and/or If, both experimental kinetic parameters being related by (211 i/i(O) = exp(H2t)

erfc( Htfj2)

(5)

i(0) is the current at t = 0 and H = k@‘R/” + kb/D&j2, where DR and Do are the diffusion coefficients of the reduced and oxidized species, respectively. From the dependence of i(0) and the electrode potential, E, depicted by ln{i(O)/(c~

exp[nf(E-EF)]

= ln(nFAkp)

-ci;l)}

= Y

- anf (E - Ep)

(6)

k,? and CY,the overall cathodic transfer coefficient, can be determined. Ep is the overall formal potential, c; and co* are the bulk concentrations of the reduced and oxidized species, respectively, and f = F/RT. The other terms have their usual meaning. Equation (6) allows kp and (Y to be obtained from the values of i(0) determined for different concentration ratios and potential steps. The kinetic parameters can also be derived from the values of H by k, = H/[D,

v2 + ( c;/c;

) D; 1’2 exp(-nfdj

(7)

from which k, can be calculated as a function of the overpotential, q, for each concentration ratio. From logarithmic plots of k, vs. (E - EP) it is then possible to obtain kp and the overall anodic transfer coefficient, (1 - cr), from [21] In k,=ln

kp +(l--cu)nf(E-ET)

(8)

solutions of x M TMN. Laphe space anaiysis For the reaction scheme represented by eqn. (1) (i.e. an EE-type mechanism) the kinetic equation in Laplace space assuming that the oxidized species of the redox couple is absent at t = 0 is [22] l/+)~“~

= (H/nFAc;k,)

+ (s”2/nFAc;k,)

(9)

where i(s) is the current in the Laplace space, s is the Laplace parameter, and H = (k, + kb)/D1/’ if D, = Do. Plots of l/i‘(s)&2 vs. C2 are Linear and k, and H/k, cm be calculated from their slopes and intercepts, respectively, for a given nFAcg factor. For an EE-type mechanism (see below) according to eqns. (2) and (3) the individual heterogeneous rate constants k,, and k, and anodic transfer coefficients (1 - a)r and (1 - EY)~can be determined by a recently proposed method [ll]. This method is based on the analysis of the i-t transients in Laplace space assuming that

only the reduced species is present in solution at t = 0 and that the mass transport is controlled by linear semi-infinite diffusion to a plane. The individual rate constants can be evaluated assuming the following approximations: (a) k, ~-k,, i.e. the second charge-transfer step is the one which determines the reaction rate (see below), and (b) the potential pulse amplitudes are adjusted to values positive enough to ensure that the first transfer is far from the equilibrium (kn + co). Then the following approximate equation of the current in Laplace space is obtained 111J: F-v=={l/[I(S)sl’*

- FAc;TL)“/2]> = (H,/R4c&2)

+ (~1’2/~~C~~~~~

00)

where Hr = (k, + kbz)/D’/2 and krz and kb2 have been defined previously. According to eqn. (lo), plots of the left-hand term against s112 should be linear, kn and H,/kn being determined from the slope and intercept, respectively. If the potential pulse is made positive enough, it is easy to observe that HI/k, + D-‘L2. From the k, values determined at different potential steps, it is possible to calculate k,, values if the applied potential step is made positive enough, such that k,, --, 0. A new approbate equation is obtained fllJ: P = (1 + k,J[

(sl$”

= (l,‘E4c~D”*)

+ kf2]]/~(~)~1/2

+ ( s1”2/FAc;k,, >

(11)

Plots of P vs. s*/~ are linear, the k, values being determined from their slopes. An interesting internal check of the validity of eqns. (10) and (11) consists in comparing the values of the diffusion coefficients of the electroactive species used to calculate the left-hand side of both equations ( W and P) with those evaluated from the intercepts of W and P vs. s”‘~ plots, respectively fll]. When analysing experimental data via eqns. (10) and (ll), it is necessary to choose the correct range for the Laplace parameter 8. Proper selection of s implies that the range of this parameter should be numerically greater for the calculation of kfl than for the calculation of k,. These criteria have already been discussed in previous reports [11,23]. For the present study, the ranges used for the parameter s were from 10 to 20 s-l for k, and from 60 to 100 s-l for k,,. RESULTS AND DISCUSSION

Experimental current values obtained for different TMN/TMN*+ concentration ratios and different overpotentials (q) are listed in Table 1 for 1 M NaClO, -t ACN solutions. In addition, the kinetic parameters i(0) and Ii obtained from the best fit of the i-t transients with the corresponding values of variance (a2) are also given. The theoretical currents in columns 3 and 8 of Table 1 were determined from eqn. (5) using i(0) and H, which minim&s the variance during the fitting procedure of experimental and theoretical i-t transients [l&19]. As can be observed, there is

41 TASLE

1

Experimental and theoretical current-time transients and overaU kinetic parameters for 1 M NaCIO, solutions of different TMN/TMN’+ concentration ratios at 273 K c&.q/cj+&Jz+

= 4.14 a

C&q/C&q2+ 2

t/ ms

i,, / PA

iti’/ CA

W s-1/2

;/LL)~

i(O)/ pA

10 20 30 40 50 60 70 80 90

335 262 228 200 181 169 158 148 140

334 263 225 200 183 169 158 149 141

9.30 9.40 9.50 9.60 9.70 9.80 9.90 10.00 10.10 10.20 10.30

43.9 53.0 44.6 38.9 35.8 35.4 37.6 42.4 49.7 59.7 72.2

744 750 755 760 766 172 777 783 789 794 800

= 2.54 b

:L’

i,h “/ pA

H/ s-1/2

u’/ (PA)~

i(O)/ PA

242 191 164 146 132 124 115 108 103

241 191 164 146 133 123 115 108 103

9.00 9.10 9.20 9.30 9.40 9.50 9.60 9.70 9.80 9.90 10.00

29.2 23.0 18.4 15.2 13.4 13.1 14.2 16.7 20.7 26.0 32.8

527 531 535 539 543 541 551 555 559 563 567

’ E_ = 0.362 V, t) = 0.060 V. b Eq = 0.371 V, r) = 0.050 V. c I~: theoretical current calculated from eqn. (S), with i(0) = 770 pA and H = 9.77 s-‘/*, as obtained from the best fit ( minimum variance, 02) between experimental and theoretical i-i transients. d Same as c, with i(O) = 545 PA and H = 9.45 s-l”‘.

satisfactory agreement between the theoretical (eqn. 5) and experimental i-t transients. The Y vs. (E - Ep) plot (eqn. 6) for different TMN/TMN2” concentration ratios and potential steps is shown in Fig. 1. The values of kp = (0.97 f 0.06) x lo-’ cm s-i and a[ = 0.72 f 0.03 were determined from the intercept and slope, respectively, of that plot. On the other hand, with values of k, obtained through eqn. (7) (from H values), linear In k, vs. (E - Efo ) plots (eqn. 8) were obtained. The values -4.65, 22.33 and 0.979 were obtained for the intercept, slope and correlation coefficient, respectively, from the least-squares procedure. Then kp = (0.96 f 0.07) x lop2 cm s-l and (1 - CX)= 0.26 It 0.02 were obtained from those values. It can be observed that the values of kp obtained by the two methods agree. An alternative expression for H as a function of kp and the electrode potential is 1221 H=k~{exp[(l-ol)nf(E-EP)]/D~2+exp[-cynf(E-EP)]/~~‘2}

(12)

which predicts an exponential variation of H vs. (E - Efo) on both sides of a minimum defined by the condition aH/a( E - EP) = 0. An experimental H vs. (E - E;” ) plot is shown in Fig. 2, where the dotted line is the theoretical one constructed from eqn. (12) with the following parameters: cr = 0.72; (1 - o) = 0.26; kp = 0.97 x 10m2 cm s-i and assuming that Da = Do = 0.65 x 10S5 cm2 s-i. This value of the diffusion coefficient produced the best fit between the theoretical and experimental H vs. (E - Efo) curves and may be compared with D,,, = (0.73 f

3

Fig. 1. Plot of Y vs. (E - EP), according to eqn. (6), for different TMN/TMN2+ concentration ratios and potential steps in 1 M NaClO., + acetonitrile solutions. T = 273 K. c&/mM, c&,z+/mM = (0) 1.123, 0.237; (v) 1.092, 0.267; (0) 0.975, 0.384; (v) 0.901, 0.459. Parameters of the linear regression: intercept = 5.45; siope = -61.00 V-l; correlation coefficient r = 0.992.

0.06) x 10e5 cm2 s-l obtained by chronocoulometry of 1 M NaCIO, + ACN solutions (see Fkperimental section). The asymmetry of the curve is attributed to the difference in the values of the anodic and cathodic transfer coefficients, although a

-ix-6 I

0

0.010

0.020

0.030

0.0&o

(E-E;)/v

Fig. 2. Plot of H vs. (E - Er”), according to eqn. (12), for different ThSN/TMN2’ concentration ratios = (0) 1.123, 0.237; (r) 1.092, 0.267; in 1 M NaCIO, +acetonitrile solutions. c&&nM, c &z+/mM (0) 0.975, 0.384; (a) 0.901, 0.459. (- - -) Theoretical curve calculated from eqn. (12) with the parameters (Y= 0.72, (1 - (I) = 0.26, kp = 0.97 x 10m2 cm s-’ and D = 0.65 x IO-” cd s-l (see text). T= 273 K. 8: = 0.380 V. (E - Ep)min = 0.012 V (from eqn. 13, with Da = Do).

49

rather high deviation (20% m~mum) is observed in the cathodic branch between the theoretical and experimental H values, perhaps because of poorer precision in the determination of the kinetic parameters for potentials less positive than the formal potential by the technique used. However, at potentials around and even more positive than Ep, good agreement is found between the experimental and theoretical variation of H vs. (E - EP ). The minimm vahe of Hf appears in the range between 0.008 and 0.016 V approximately. From the minimum condition in eqn. (12) it is possible to obtain (E - E&i,

= tI/n#)

1”[ [w’(I

- a)] &/‘~o)“*]

(33)

Using eqn. (13) with (Y= 0.72, (1 - o) = 0.26 and assuming that D, = Do, (E - Ep )min = 0.012 V, which is within the potential range mentioned above. If we consider an arbitrary difference of about 30% between the diffusion coefficients of R and 0, a difference of only 2 mV, i.e. (E - Efo )min = 0.014 V, is found for the given parameters. This difference is within experimental error, so the previous assumption of equal diffusion coefficients of the reduced and oxidized species does not introduce appreciable error in the calculation. The rate constant k, can be determined from the definition of H (see above) with the calculated values of II and k,, assuming that D, = Do. The experimental slopes arising from the dependence of k, and k, on the potential were a(ln k,)/ilE = (22 f 2) V-’ and a(hr k~)/~E = (62 j, 4) V-‘. From these results and using the Bockris and Reddy formalism 1241, the mechanism of the electrochemical oxidation of TMN in 1 M NaClO, + ACN solution was determiued. According to this formalism, the anodic transfer coefficient for a multiple step reaction, & is given by Z=(n-~)/v-r/3

04)

and the corresponding equation for the cathodic transfer coefficient, z=

(y’/Y) + rp

a’, is 05)

where n is the total number of electrons exchanged in the overall reaction; 7 is the number of steps that precede the rate-determining step (rds); r is the number of electrons that participate in one occurrence of the rds; B is the symmetry factor; and v is the number of occurrences of the rds during one occurrence of the overall reaction. From the experimental slopes of In k, and In k, vs. E plots, respectively, and considering that F/RT = 42.46 V-’ at 273 K, we obtain &= 22/42.46

= 0.52 = 0.5

(16)

ty’= 62/42.46

= I.46 = I.5

(17)

(;rc+ 2) = 1.98 = 2.0

03)

and (from eqns. 13 and 14): (&+ Z) = n/v = 2.0

09)

50

Since it is known that the number of electrons exchanged in the overall process is 2, it can be concluded that P = 1, i.e. the rds occurs once during one occurrence of the overall reaction. According to this scheme, the rds cannot be a homogeneous chemical step, since then r = 0 and z= 1.5, yielding T= 1.5, which has no meaning. As the oxidation proceeds via two electron steps, r can be equal to 1 or 2, corresponding either to a consecutive two mono-electronic transfer or a simultaneous bielectronic transfer. Since there are good experimental and theoretical grounds for assuming that the o~dation proceeds via two consecutive fast electron transfers, this requires that r = 1 and (y’= ($1)

+0.5 = 1.5

(20)

from which it can be concluded that y= 1, i.e. the second electron transfer is the rate-determining step. Alternatively, if we choose 1”= 2 then r;= ($1)

+ 1= 1.5

(21)

from which y= 0.5, a value that does not make sense electrochemically. On the other hand, the slope of a linear In(k,/k,) vs. E plot is -(83 f 5) V-‘. According to the findings of Dauyotis et al. for a similar model (111, such a slope value indicates that EP x ET, Ep and ET being the standard potentials of the first and second charge-transfer steps, respectively. This phenomenon indicates that the second electron transfer is the~od~~c~y more favourable than the first (see below). This result is similar to that found for the oxidation of o-dianisidine in aqueous sulphuric acid [ll]. As far as TMN is concerned, the above conclusions, reached from mechanistic studies, confirm the proposition of Miras et al. who also proposed an EE mechanism for the oxidation of TMN from considerations of cyclic volt~o~~ shapes IS]. x M TMN solutions. Laplace space analysis

The i-t transients obtained from 0.1 M NaClO, + ACN solutions initially containing only TMN were analysed in Laplace space to establish whether the previously determined (EE-type) mechanism for the TMN electro-oxidation depends on the supporting electrolyte concentration and, if not, to determine the individual heterogeneous rate constants through the model proposed by Dauyotis et al. [ll]. For the determination of k, via eqn. (9), potential steps of small amplitude were applied to the working electrode from an initial potential corresponding to zero current up to a final potential at the foot of the i-E voltammetric wave, in an attempt to minimize any con~ntration perturbations. The above condition is also necessary from the following consideration. If Z is defined as H/k,, then Z = (k, + k,),‘D”*k,

= (l/O”‘“)

+ ( k,/kf)(l/D”*)

(22)

51

and ln( k&t)

= hr( Z - D1’/2) + ln( Dli2)

(23)

If the applied potential step is made very positive (k, z- kb), then Z + D-l/’ and eqn. (23) becomes undefined. Values of Z can be obtained from the intercepts of plots of l,/~(~)&“~ vs. .r1j2 (eqn. 9), and In(k,/k,) may thus be determined for a given diffusion coefficient. A l,‘&)~“~ vs. s”~ plot is shown in Fig. 3a for E, = 0.500 V. When the logarithmic values of kf determined from the slope of these plots for different potential steps are plotted as a function of the electrode potential, a slope of (19 f 2) mV is obtained. In addition, plots of ln(k,/k,) (eqn. 23) as a function of the electrode potential give slopes of (80 f 5) mV. These values agree with those calculated previously from x M TMN/y M TMN*+ solutions, and the formalism of Bockris and Reddy 1241applied to them gives, naturally, the same results, i.e. an EE-type mechanism, with the second electron transfer being the rate-dete~g step and El0 > EC, as arrived at previously for the el~~~he~c~ oxidation of ThfN in 1 M NaClO, -t ACN solutions. These results show that the supporting

14 @ii 2 2 13 -

11-

7

3 I

5

9

7 I

17.1 -

r z 17.0 “: f: 16.9 16.8 , 7

t 8

9

Ja/s-1’2

Fig. 3. Laplace analysis of TMN oxidation for E, = 0.500 V. (a) Plot of eqn. (9) to obtain k,. Regression parameters: intercept =10259 &” C-‘; slope = 458 s C-l; r = 0.99996. (b) Plot of eqn. (11) to obtain kn. kn = 0.061 cm s-l. Regression parameters: intercept = 15 771 s’/* C-‘; slope = 141 s C-l; r = 0.99991.

52

electrolyte concentration does not affect the mechanism. The overall heterogeneous rate constant, k,!‘, and transfer coefficient, (1 - n), determined from the ln kr vs. E plot at 273 K were kp = (1.0 it: 0.1) x lo-’ cm s-* and (1 - ‘Y)= 0.39 f 0.04. The value of kp agrees satisfactorily with that obtained by the minimum variance method (kp = 0.97 x 10e2 cm s-t), but the transfer coefficient is slightly higher than the value calculated previously, i.e. (1 - a) = 0.26 (see above). It is worthw~e mentio~g that the use of eqn. (9) represents an advantage in the sense that it also permits a check on the validity of the method, since H/k, --f l/D “’ for sufficiently positive potential steps. Thus, it is possible to calculate diffusion coefficients from the intercepts of plots of eqn. 9 (Fig. 3a) and compare them with those determined by an independent method. An average D value of (1.12 f. 0.03) X lo-’ cm’ s-r is obtained for TMN with a 95% confidence level, according to the Student t-test, from the intercepts (eqn. 9, see above) for six potential steps where the condition k, 4 0 is satisfied. This value can be compared with D = (1.09 f 0.05) X lo-’ cm* s-l determined from c~on~oulomet~ experiments. The a~~rnent found between them is excellent. The determination of the individual rate constants was accomplished by the analysis of the i-f transients in Laplace space for potential steps positive enough to ensure the validity of eqns. (10) and (11). Table 2 lists values of W (eqn. 10) determined as a function of s at different potential steps. At the foot of this table the values of the intercept, slope and correlation coefficient obtained by the least-square procedure are reported, from which the values of D and k, were determined. A plot of P vs. s112 (eqn. 11) f or a final potential of I$ = 0.500 V is shown in Fig. 3b. From the slopes of similar plots and the values of k, calculated TABLE 2 Values of W as a function of .s (eqn. 10) at different potential steps for the anodic oxidation of TMN in 0.1 M NaQO, +ACN solutions at 273 K (FAc&_, = 0.0185 C cm-‘; D =1.09X lo-’ cm* s-l)

s--1

g/2

w “/c-1

y2

w “/c-1

$/2

11 12 13 14 15 16 17 18 19 20

19699 19818 19938 20057 20175 20290 20403 20514 20523 20 730

18952 19042 19134 19226 19318 19408 19497 19584 19670 1975s

18 773 18851 18932 19011 19091 19169 19245 19 320 19394 19466

s/

w 1 c-1

a Calculated for Ef = 0.500V. The W vs.sI'*plots gave the following regression parameters: intercept = 16712 s”* C-‘; slope = 8% s C-r and r d = 0.997. b E, = 0.510 V; intercept = 16620 s’/~C-‘; slope = 699 s C-t; r * - 0.9996. ’ Et = 0.520 V; intercept -16760 s”* C-l; slope = 603 s C-‘; r d =r 0.997. * r: correlation coefficient.

53 TABLE 3 Experimental i-r transient and kinetic and diffusion parameters for the anodic oxidation of TMN on Pt electrodes at 273 K (chMN = 1.50 X 10e3 M; clfi,,,, = 0.1 M)

t a/ms

i/PA

Er/V

10s D b/cm2 s - ’

&,/cm

0.5 1.0 5.0 10.0 15.0

1990 lSS0 823 610 so1 43s 363 288 206 151 12s 113 101

0.470 0.480 0.490 0.500 0.510 0.520 0.530

0.68 1.08 1.11 1.07 1.09 1.07 1.16

0.0093 0.023 0.042 0.061 0.078 0.091 0.097

20.0 30.0 SO.0 100.0 200.0 300.0 400.0 500.0

s-l

a E, = 0.150 V; E,= 0.480 V. b D obtained from the intercepts of W vs. s “* plots (eqn. 10). B = (1.10*0.036)~ 95% confidence level, excluding the first value of the c&mm. ’ r: correlation coefficient.

r= 0.9992 0.9998 0.9999 0.9997 0.9996 0.9997 0.9996

10e5 em2 s-’ with a

previously using eqn. (lo), the values of k,, were determined for different electrode potentials. The diffusion coefficient of TMN can also be determined from the intercepts of the W vs. s ‘I2 plots, provided that k,, -+ 0 and k&H, + D1/2 when the potential steps are made positive enough. In Table 3, an experimental i-t transient is shown together with the values of k, and I) determined from the slope and intercept, respectively, of eqn. (10) for different potential steps. An average D value of (1.10 f 0.036) X 10m5 cm2 s-r is obtained for TMN with a 95% confidence level, which again agrees satisfactorily with the value obtained from chronocoulometry (D = (1.09 f 0.05) X 10m5 cm’ s-l ) and with that obtained from eqn. (9) (D = (1.12 f 0.08) x 10m5 cm* s-l) as explained above. Furthermore, from the intercepts of P vs. s ‘I2 plots (eqn. 11, Fig. 3b) a diffusion coefficient for TMN of D = (1.20 * 0.012) X 10V5 cm2 s-l was calculated with a 95% confidence level. The deviations of the diffusion coefficients obtained for TMN from the different extrapolations and even from ~~on~ulomet~, from an average value resulting from all the D values considered, can be fully explained by measurement errors according to the x2 test 1251. The values of the diffusion coefficients determined in this work by chronocoulometry and also by Laplace space analysis have been found to be higher than that determined previously by cyclic voltammetry, i.e. D,,, = 0.51 X low5 cm* s- * [ 5] . The difference may be due to the different techniques used. Chronocoulometry is perhaps the most reliable method for the determination of the parameters under study, as suggested previously [13,21,26]. The linear dependence between both In k,, and In kf, on the potential is shown in Fig. 4. From the slopes of these plots the transfer coefficients (1 - (~)r and

54

3 3

4

0.450

0.500

E/V

Fig. 4. Anodic individual charge-transfer rate mnstants as a function of the electrode potential for the anodic oxidation of TMN on Pt in 0.1 M NaClO, + acetonitrile at 273 K. C&~/M (0) 1.20 X 10w3; (0) 1.41 x10-3; (0) 1.50x10-3.

(1 - (Y)* were determined. The values found were (1 - a)r = 0.52 f 0.03 and (1 - a)Z = 0.58 f 0.03 at 273 K. The disregard of the individual formal potentials corresponding to each electron-transfer step, El and E,O, does not allow the corresponding formal heterogeneous rate constants, ki and I$, to be determined. The application of current electron-transfer theories [27,28] to the expe~en~ data is not possible because they establish a functional dependence between the standard (or formal) rate constants and different experimental parameters (temperature, solvent parameters, etc.). The linear correlations obtained between the heterogeneous rate constants determined at the overall formal potentials, k,( E = Et“ ) and k&E = EP), respectively, and the temperature, were, nevertheless, examined in order to obtain a semi-quantitative picture of the electron-transfer process. Up to now, the activation parameters for heterogeneous electron-transfer reactions have been evaluated at only one temperature (and hence the theories of such reactions have also been tested at only one temperature) despite the fact that dete~nations of activation parameters from heterogeneous rate constant vs. temperature variations represent important advantages [29]. To our knowledge, the temperature dependence of the electron-transfer rate in heterogeneous cases has been studied only for p-phenylenediamines in non-aqueous media [13,30], although similar studies have been reported for aqueous inorganic systems [31]. Thus, it was considered of interest to determine the effects of temperature variation on the kinetics of the electron transfer of TMN at Pt electrodes. Arrhenius-type plots (In kfo2) = In Aoz, - E,,&RT) [32] were obtained with correlation parameters as follows: from in k,,(E = Et0 ) vs. T-‘: In A, = 0.392 f

55

0.004, E,,/R = (66’7 f 20) K, correlation coefficient = 0.999; from In k&E = EP) vs. T-‘: In A, = 1.7 f 0.5, Ed/R = (1.6 f 0.13) x lo3 K, correlation coefficient = 0.987, where A, and A, are frequency factors and E,, and Ea2 are the energies of

activation for the first and second electron-transfer steps, respectively. These quantities can be related to the Marcus expression for the standard rate constant [27] kp = KZ,,,, exp( - AG,*/RT)

(24)

to calculate the Gibbs energy of activation, AG,*. In eqn. (24) Zhet = (kT/2nm)‘~Z (k is Boltzmann’s constant and m is the reduced mass of the reactant species) and K is the electronic transmission coefficient (assumed to be 2 1). AGe* can be calculated from experimental data through the enthalpy and entropy terms via AG,* = AH,* - TAS,* = -R(8ln k&IT-‘) - TR ln[A/(ekT/2am)‘/2] [32]. Thus, the values obtained were AG,T(298) = (21.5 f 1) kJ mol-’ and AG$(298) = (32.6 * 2) kJ mol-’ for the first and second electron-transfer steps, respectively. They can be compared with values available in the literature which were determined in systems comprising two consecutive electron-transfer steps (EC > ET ) [S] as well as monoelectronic transfer [13,30]. From the consecutive double-step electroreduction of 13 organic compounds in dimethyl formamide, values of AG,1;(298) and AG,1(298) ranging from 28.2 and 39.0 kJ mol-” for l&benzoquinone to 21.1 and 25.7 kJ mol-l, respectively, for a larger molecule such as l,lO-naphthacenequinone have been reported f8]. For mono-electronic redox systems, values ranging from 25.3 kJ mol-’ for N,N,N’,N ‘-tetramethyl ~-phenylene~~e (TMPD) in ACN 1131up to 30.7 kJ mol-’ for p-phenylenedi~e in ACN 1301 were found. F~the~ore, it should be mentioned that, for TMN, the observed Gibbs energy of activation of the . . second oxidation step, AGe2, * is much higher than that of the first oxidation step, AGZ, their ratio, AGz/AG$, being = 1.5, in rather good agreement with those found (ratio = 1.3) for several consecutive electron-transfer step processes [8]. Thus, the values of AG,T and AG$ determined in this work are certainly comparable to those of other organic aromatic systems. In addition, the experimental AG=; value can be used to calculate the molecular radius of TMN, urMN, through the Marcus equation, which is valid in a dielectric continuum, AG* = 0.0945/a (ev) [27,32] and to compare it with that calculated from the simplest method which uses the molar mass M (M,,, = 340.47 g mol-‘) and the density, S, of TMN to obtain rsphere= (3M/4N,6)“3, where NA is Avogadro’s constant. As the density of TMN was unknown, it was determined by the conventional Weld pycnometer method for solid substances [33a] with water density data taken from the literature [33b]. The value found was a,,, = (1.21 + 0.02) g cme3. Thus, army = 0.424 nm was calculated from the Marcus equation using AG,$ = 0.223 eV (21.5 kJ mol-‘) and rsphere= 0.481 nm was calculated from the spherical model. Despite the simplicity of the models, good agreement is found (within 15%) between the calculated radii. It may be concluded that the above results suggest that the use of individual heterogeneous rate constants estimated at the overall formal potential, even if rather inappropriate for a strictly quantitative study of the transfer process, appears to be satisfactory for a semi-quantitative characterization of the transfer process.

56 TABLE 4 Format potentials, diffusion coefficients and Kinetic parameters for TMN oxidation at Pt electrodes at different temperatures in 0.1 M NaC104 +ACN solutions (c& = 1.41 X 10e3 M) T/ K

EP “/ V

1O’D “/ cm2 s-l

kn/ cm s-t

U-4,

k,/ cm s-l

(1-a)

273 283 293 303

0.451 0.463 0.475 0.486

1.09 1.17 1.43 1.63

0.13 * 0.01 0.14f 0.01 0.15 io.01 0.16 f 0.01

0.52 0.50 0.49 0.55

0.016 0.019 0.022 0.029

0.56 0.70 0.67 0.74

4 0.002 f 0.002 If:0.002 f 0.003

a dEP/dT= (1.17&0.16) mV K-l; AS* = (226k 31) J K-’ mol-r, calculated from nF(dEP/dT) with n = 2, where AS o = S&, - S&,2+; r ’ = 0.9998. b dln D/d(l/T) -1212 K-l; E d,tact.= 10 kJ mol - ’ ( Edif,ac,.: diffusional activation energy). ’ r: correlation coefficient.

2

AS” =i

On the other hand, as can be inferred from Table 4 for 0.1 M NaClO, + ACN solutions, a linear variation in the formal potential with temperature was observed. The value of dEP/dT measured is indicated with the corresponding error determined with the confidence level of 95%. This phenomenon indicates a negative solvation entropy for the TMN’+ cation according to AS’ = (S&N - S$‘m~+) = 2F(dEy/dT), where AS0 is the reaction entropy of the redox couple (the S’s are the partial molal entropies of TMN and TMN2+, respectively), and corresponds to greater solvation of the ionic product than of the neutral parent molecule [13,14]. Up to now, ele@ochemical reaction entropies have been obtained almost exclusively for singly charged aromatic ions [13,14,30,34-381, experimental entropies of solvation for organic dications being very rare. In a recent paper, the values of reaction entropies of a few dianions and dications in systems of two one-electron steps appeared to verify the simple Born equation [39]. The determination of AS” was attempted to gain more details on electron-transfer processes as well as on ionic solvation 114,391.The value of AS ’ determined in the present work, i.e. AS o = 226 f 31 J mol- ’ K- ’ (see Table 41, corresponds to a single two-electron step. In the simplest theoretical treatment of the reaction entropy found from the Born dielectric continuum model [14], AS” depends on the difference in charge numbers of the oxidized and reduced species, .z& - z&,, the ionic radius, r, the static dielectric permittivity of the solvent used, 6, and its temperature coefficient, de/dT, through AS,: = -[Ne2 (z& - z2R,d)/8m,rr2](df/dT), where N is Avogadro’s constant, e is the electronic charge and c0 is the permittivity of a vacuum. There is no TMN*+ radius value available in the literature to permit the evaluation of AS, by means of the above equation. The expe~ent~ AS” value together with c = 36.0 (determined at 298 K} and de,/dT= -0.160 K-r for ACN data taken from the literature [40] predicts an unrealistically small radius, i.e. r = 0.15 run, for TMN2+. This value is much smaller, as expected, than that estimated for the neutral parent compound, TMN, from the spherical model, rsPhc_= 0.481 run, as well as from the Marcus expression, aTMN= 0.424 nm (see above). This result implies disagreement between the experimental and the theoretically calculated entropies. Although it is

highly probable that the double positive charge of the cation is generally delocalized over a large volume [5], it is not correct to treat the TMN’+ ion as a sphere with a given radius and uniform distribution of the charge as required in the original Born approach. Nevertheless, although the results of Svaan and Parker 134-36391 mdicate that the geometry of an aromatic molecule, the charge distribution on an ion and the steric factors have an important effect on ASo, it has to be recognized that the effect of the solute properties on the entropy of reaction is far from being understood in detail 1371. As far as we know, no determination of AS” for a reaction which follows an EE-type mechanism reaction (with El0 > E,O) has been attempted until now, the reason perhaps being the scarcity of single two-electron step electrochemical reactions. However, we can compare the value of the reaction entropy of the TMN system (AS” = 226 J mol-’ K-l, Table 4) with some values found in the literature for two one-electron step systems. Comparable values have been found only for the entropies of formation of the dianion of l&bibenzoylbenzene in ACN (AS0 = 215 J mol-’ K’) and for the reduction of the dimethyl viologen dication to the neutral parent compound (AS O = - 221 J mall ’ K- ‘) in propylene carbonate, although most of the very few values found in the literature [39] are, in general, lower (in absolute values) and also correspond to solvents different from the one used in this work.

CONCLUSIONS

The results obtained from potential step experiments as well as from a mathematical model of the mechanism using Laplace space formalism show that the electr~he~~ oxidation of N, N, N’, ~‘-tetr~ethyl napht~~e occurs according to an EE-type mechanism at a planar platinum electrode in sodium perchlorate + acetonitrile solutions. It was found that the second electron transfer is the rate-determining step. The entropy of reaction of the dication was calculated from the shifts of formal potentials with temperature. From a semi-quantitative analysis of approximate experimental activation parameters, it was found that the Gibbs energy of activation of the second oxidation step was much higher than that of the first oxidation step. The transfer coefficients at 273 K were estimated to be (1 - ar)l = 0.52 f 0.03 for the first transfer, and (1 - a)z = 0.58 i- 0.03 for the second oxidation step. ACKNOWLEDGEMENTS

Financial support from the Consejo de Investigaciones Cientificas y Tecnolbgicas de la Provincia de Cbrdoba (CONICOR) and Secretarla de Ciencia y T&mica from the Universidad National de Rio Cuarto is gratefully acknowledged. The authors are grateful to Dra. M.C. Miras and Dr.L. Sereno for providing samples of the compound studied. We are indebted to Lilia Fem&ndez for language assistance.

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