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ELSEVIER Jouriuil of Bleclrounulyliuil Chemistry 440(I'Jy?) KB- l(W

The application of the concept of reaction layer to the study of electrode processes coupled with the second-order chemical reactions at

microelectrodes under steady-state conditions

Qian-kun Zhuang *, Dan-dan Sun nciiiirliiiailnfClicmisiry. PMiia Uiiirmily, Ikijina lOOHTI. People's Hcintbtic of Clilmi

Received 28 November 19%; reeeivcti In reviwd li.rni ? I'ebriiary I'Jy?

Abstract

Under steady-stale conditions, the current equations of the second-order EC, ECE and DISPl reactions at microdisk, microspherical and microring electrodes arc derived with the aid of the concept of the reaction layer. The conditions under which these equations would be valid are also discussed. Using these equations, methods to determine the kinetic parameters tor the .second-order EC, ECE and DISPl reactions are presented. The reduction ol" 2,6-diphenyl-pyrylium cation and oxidation of triphenylamine were investigated as examples of the second-order EC and ECE reactions. © 1997 El.scvier Science S.A.

Keywiinis: MIcroelcclrode; Second-order reactions; Concept ol' reaction layer; Kinetic parameters; Miiltislcp electrode processes

1. Introduction

The development of electrodes of micrometer dimension has expanded the .scope of electrochemical studies [1-4]. The unique features of microelectrodes assure that they will continue to be important in electrochemical studies. One striking characteristic of microelectrodes is that they have a high mass transport rate on the surface of the electrode. This makes it possible to study the electrode reactions coupled with homogeneous processes under steady state conditions [5-10]. In recent years, there has been an increasing interest in the second-order 'mediated' or 'indirect' electrode reactions at microelectrodes [9-12]. However, only the analysis of the second-order EC reactions has been made. So far the results of other multistep ck-node processes such as the second-order EC, ECE and DISPl reactions are not yet reported. In this paper based on the concept of reaction layer [8,9,13], some simple current expressions for the second-order EC, ECE and DISPl reactions are obtained at microdisk, microspherical and microring electrodes under steady-state conditions. This avoids solving the diffusion equations using complicated mathematical techniques. Obviously it expresses the electrode processes more concisely. The kinetic parameters for these systems can be obtained easily from these equations. As examples of the second-order reactions, the reduction of 2,6-diphenyl-pyrylium cation and oxidation of triphenylamine (TPA) were investigated in acetonitrile. The rate constants for these reactions were obtained from the gradients of simple straight line plots and were in agreement with values obtained more conventionally.

Corresponding author. E-rnaihycxz chenims.chcm.pku.edu.cn.

0022-0728/97/SI7.()0 © 1997 Elsevier Science S.A. All rights reserved. Pll 80022-0728(97)00108-3

KM i>.-L /.liiiimi;. P.-d. Swi/.lorn mil nfHIirliviimilylinilClici

2 . 'I'licMH-y

2. /. 'I'lic .si'coiid-nnli'r i'.C iiict'lKiiii.siii

A lypiciil sucoiul-ordcr liC ivaclion ciiii be expressetl as follows:

A-l-/;e rMJ

2M --' C

•l-liill'i'r/i lo.i I III)

in whicii the L'lcclron exchiinge step is levcrsihlc; k is (he chemical rale constaiil. f,( cleiioles Ihe hulk conceiilralion of species A. We assume ihat a reaclion layer exists at the siui'ace of the inicroeleclrocle within vviiich all molecules of H are candidates I'or reaclion, and that the concentration at the electrode surface is the same everywhere. Thus according to the concept of the reaction layer proposed hy Brdicka and Wiesner fl3], the steady-slate current of the second-order I C reactions can he expressed as

/ = /;/'/lA-|,(c,;-(''O (3)

/ =/(/••/l/ Tir'il- (4)

where A is the area of the microclectrode, (•,'( and r',', are the concentrations of species A and B at the surface of liie electrode, /j, is a so-called reaction layer thickness [K.I 3,14] and equals | Dfi/k(\\. A,, is the steady state mass transport rate constant [')], and under steady state conditions there are the following expressions [6,9,13]:

41) microdisk electrode

/) — hemispherical and spherical electrode

microring electrode l)iT/{l>~a)\n 7,2 a

ih -^exp

in which ;•„, and i\ are the radii of microdisk and microspherical electrodes, and a and h are the inner and outer radii of a microring electrode. Assuming equal diffusion coefficients for species A and B (D,\ = /.5„), the Nernst equation can be solved for the ratio of surface concentrations for a reversible system.

;/'•;; e x p i — ( £ - r )

where l-^ is the formal potential. Combining Eqs. (3)-(5), we can obtain the l-li e(|uati(>n for the second-order HC reactions as follows:

= exp — ( / : - / v ' )

where /,, is the limiting steady-slate current, which equals /;/'/\A|,c,.;. Rearranging Eq. (6) we have

t: =

F'rom Fiq.

For i

/ • i =

disk

i: =

/'•. =

RT Dki r + - — i n - ^

(7) the half-wave

RT = r -—: ln2 +

microclectrode:

- -f RT 1 - / / / , - - In —

potential. E.

RT

RT TT-rikc: l-r + In ^

3«F \bD

RT A - - - — I n 2 +

3/;/-

RT

Jiir

Dkcl

RT + — I n

111-

kTT-C,

!n 16/;

s given by

1 - ///.I

2RT - + In

3/(/-

(3)

(7)

(«)

(y)

(10)

(J.-k. •/.Iimuty,. I). (I. Sim/.l(iiinuilofi:i(rlr(iiiiiiilyliiiil('lii'misliy-l-lll(IW7l lO.tIO')

iinci lor ii spherical micnieleclnKle:

RT r:kc: Ii /,; := /." + -—- 111 h ~ In 577 ( I I )

RT

rikv

"-7 I i i2-h

-- -h

A'V

RT

1 ; l n -

In T7T

^r,; 2RT /,; = /,- - — - In 2 -h r - - I n -— -I- ~ - In /; (12)

3/i/' 3H/ ' f) 3 III' In ['CIS. (<;) and (II) and Hqs. (10) and (12). die plols of (/i' - IC') vs, ln{[ 1 - ( / / /„)] /( / / ( , ) - / '} and (/• >-ir) vs. In /• were linear. Tims, the kinetic parameters can be obtained in two ways. The slope and the intercept ol' the curve of (A'- I-") vs. In{[i - (///, |)l/(///,,)-' ' '} allowed lis to evaluate the number of electrons /; and the rate constant A', and the other method is from the curve of (/: i-/i") vs. In r.

2.2. The secoiul-onlcr ECE iiwcliani.iiii

A simple model of the second-order liCE reactions is depicted as follows:

A-f-z/iC ^F3 (13)

2B->C (14)

C + /).c ^ ' D (13)

in which the electron exchange steps arc reversible and the second step (Ecj, (14)) is the rate determining step. The second-order ECE mechanism is analogous to the I'irst-order case. According to the concept of the steady-state dilTusion-rc-aclion layer [9,16], the limiting steady-state current for the second-order ECE reactions is

y,, = H,/''/^A-„,\r; 4-/' = /,, 4-/ ' (16)

and

I'^ii^rAk^fxcf (17)

/' = «,/-/\;-„„c;, (18) where k^,,^ and A,,,, are the steady state mass transport rate constants [9] of species A and D, /x is equal to fDf^/k,c\\ and /j = //, F/4A|,,\f,(. Under limiting steady-state current conditions, the two electron transfer reactions (Eqs. (13) and (15)) for the second-order ECE reactions arc very fast. This means that every molecule of C formed immediately takes part in the second electron transfer reaction, i.e. rj ~ 0 and c'^. ~ 0. Then we have

D„r;;-f2D„r;', = D^c,- (19)

From Eqs. (16)-(19) we have the following equation:

2«, l - f - - i ( l - / , / / , )

(20)

Assuming equal diffusion coefficients for species A and B. and //T = 2/ / | , then for a microdisk electrode we have

( 2 - / , / / . , ) / I6D V^' ^ ^ ,

From Eq. (21), the plot of [2 - (/|.//u)]/[(A,/^) - I]"'''' vs. /•;,-'" is linear. The rate constant A:, can be obtained from the slope of the straight line.

2.3. The seeoiid-order DISPI reactions

The second-order DISP! mechanism

A 4 - / i c - ^ B (22)

2B ^ C (23)

2B-f C-> 2A-t-D (24)

I(K) (J.-k. /.hiuiiii;. I).-(I. Sim/.liiiimihif h:iirliv(tiiiil\liriil Cliciiiisny -l-ll) <IW7I l(U- lll'l

is cxiic'lly aiiiilogous lo ihe lirsl-orclcr case. Ilcic Ihc election exchange step is reversible, /c, and A-, are the chemical rate constants for the two irreversihie chemical reactions and As » A,; the second ste,.- (Bq. (23)) is rate determining. According to the concept of the steady state dilTusion-reaction layer, under steady-state conditions the limiting steady-slate cnrrent for the second-order DISPI reactions is

/i, = /)/''/\A|„^c; -I-/, = /,,-h/,. (25)

and

/^--=iiFAk2iJic\\-cl'. (26)

/,-2;;/''/\A|,|,(;, (27)

where

/l.= ^'/V(2Av•l;) (28)

A,cf = A.ri;-c;: (2y)

From Eqs. (25)-(3()) we have

( 2 - / , , / ( , ) / 2A7 (31]

Assuming equal dilTusion coclTicients for species A and B, then for a microdisk electrode we have

( 2 - / , / / . , ) _ / 32/)

(A./Ai-')' '•' I ^ ' ^ V A

A plot or[2 - (/|,//j)]/[(/|.//.|) - i]-^' vs. /•„;=/•' would be linear with a slope of (32D/77-A,r,;)'/ '. This can be u.scd to calculate the rate constant.

(32)

3. Expcrimcntul

The steady state voltammograms were carried out by using a three-electrode system with a platinum disk microclectrode, satuivjicd calomel electrode (SCE) (Ottcd with a Luggin capillary in acetonitrile), and Pt wire as the working, reference, and auxiliary electrodes respectively. Pt microdisk electrodes were prepared by sealing Pt wire of a series of radii into the tip of a pre-drawn glass capillary with a llamc. The lip of the microclectrode was polished Hat with successive grades of alumina polishing powder down to 0.3 fim. The radius of the electrode was measured by averaging a number of diameters read through a microscope. Only electrodes with less than \Vr deviations from readings of the diameter were employed in the experiment.

Experimentally, steady-state voltammograms may be recorded in a poinl-by-point fashion by performing a series of chronoamperomctric experiments, each at a slightly different potential. More conveniently, they result from applying a potential ramp to the microclectrode. provided that the sweep rate is slow enough that the voltammogram retraces itself when the direction of the ramp is reversed. It is a valuable characteristic of steady-state voltammctry that the resulting current-voltage curves are totally independent of the details of the method used to obtain them [3]. In this work we used the second method to record the steady-state voltammograms at the smaller radius microdisk electrodes (/•„, = 5.8, 10.2 and 15.6 ixm), and used the first method to record them at the larger radius microdisk electrodes (/•„, = 26.1, 31.4 and 5l.3(jLm). The experimental .set-up consisted of a Model 174A polarographic analyzer (EG&G, Princeton Applied Research, USA), a Mctrohm EG: Polarccord E506, VA-Scanner E612 (Switzerland), a type 3036 X-Y recorder (Yokogawa Hokushia Electric Tokyo, Japan), and a home-made H-typc cell thermostatcd at (25 + 1)°C. The cell was equipped with the working electrode, a Luggin capillary connected to the SCE. an auxiliary electrode of a platinum wire and a tube for passing nitrogen gas. The 2,6-diphenyl-pyrylium perchlorate salt was prepared according to reported procedures [17]. TPA (Aldrich) was recrystal-lized from absolute cthanol and dried under vacuum at 70°C. Acetonitrile was HPLC grade (Fkika) and was carefully dried over alumina. Tetracthylammonium perchlorate (TEAP) (Fluka) was recrystallized from methylene chloride and then dried at 100°C for I day. All other chemicals were of analytical grade. High purity nitrogen was used for de-aeration and was bubbled through the .solution for I5min.

Q.-k. y.lnumj', D.-d. Smi/Jimiviil of r:l(rliviiiuilylir(il Cli(wi\lry -NO IIW7I IO.^~ll)>J 107

4. RustiKs and discussions

The steacly-slalc current ec|iiati()ns and liie methods of determining l<inetic parameters at microdisl<. microsphcrical and microring electrodes have heen presented. Obviously, liiesc expressions descrilie the electrode processes more concisely. For a spherical microclectrode, it is well known that the concentrations ofclectroaetive species arc equal at all points on the siui'acc. This allows the electrode processes to be studied on the basis of uniform surface concentration. But on the surface of a microdisk electrode the concentrations are uniform only in reversible and limiting ca.ses [18,19], and for the ciuasi-revcrsible and irreversible cases this assumption is sufficiently accurate only when / / / j , < 0.23. Unlike the microdisk electrode, the error at the microring electrode can be reduced as the ring becomes thinner. Therefore, the results presented in this paper are most accurate for the reversible and limiting cases at microdisk, microsphcrical and microring electrodes.

Merc it must also be pointed out that the results treated with the concept of the reaction layer are valid only under the conditions in which /i is less than 3/3 [20] (('5 is the thickness of the diffusion layer). In the case of a steady state at a microdisk electrode, 8 is equal to Trr„y4, i.e. when jU, < 7r;-|„/l2 the results of the second-order EC reactions are valid. For the second-order EC reactions, ix= \iD/kc\\ and rjj = {I-/kDirF~A~y''^. Then we have following condition:

k> \2^nFD~/{TT-r„j) (33)

Usually, it is useful to quantify the slope of a voltammetric curve between the one-quarter-wave current and the three-quarter-wave current. Assuming that D = 5X 10" ' ' cnrs" ' , /•„, = 15|jLm, c' =2X 10"- m o l l ' and / = / j /4, then k> 1.9 X 10 m o r ' l s~ ' . This implies that for the second-order EC reactions the concept of reaction layer can be applied at the microdisk electrode when the rale constant is not less than 2 X lO'' moP' I s" ' .

Because the rates of disappearance of species B both by diffusion and by reaction have been considered in the concept of the steady-state diffusion-reaction layer, for microelectrodes the method would be suitable for those cases in which the dimension of the reaction layer is not larger than that of the diffusion layer (/x < 5) [9]. Under these conditions we have the following expression for the second-order ECE reactions:

/t, >4'/;/'"'D-/'n- '-...(A.-Zci) (34)

Combining Eqs. (21) and (34) we have

A-1 > 32 D / ( 77-/-,;(•;) (35)

A.ssuming that D = 5 X lO'^'cm" s"', /•,„ = l5|jLm and r, = 3 X 10"'mol T ' , then A, > 2.4 X lO' moP' Is" ' , This means that the results of the second-order ECE reactions presented in this paper would be accurate when A, > 2.4 X lO' mol"' I s " ' under the above conditions. If A, > l2/V(7r"/-,^,c,^), the results will be less accurate. In the .same way, similar conditions for tlr .second-order DISPI reactions have also been obtained, i.e. the results of the second-order DISPI reactions presented in this paper would be accurate when A, < 32D/iir-rli\).

( / • - ^ ' • • j / m V

Fig. I. The plot of ili-Ii^) vs. In{[l-( / / / j ) ] / ( / / / j ) -^ ' ) of 2,04x 1 0 ' ' m o l l ' ' 2.6-cliphenyl-pyryliuin salt in acelonitrile solution containing 0.1 inoir ' TI-AP with radius (a) 10.2jxin and (b) lfi.6|im.

QAr/Jw(ini;Jl-(I.Sim/JimnMlori:irrnmwilyli<viauwims'M0(IW7l l(U-l(N

Table 1

KiiiLMic panimclcrs for the reduction of 2.6-tliplienyl-pyiyliiim ciilion

Rii(l ius/|xm Slope/mV Intcrccpt/V

10.2 26.1 0.110

15.6 25.y O.II.S

" 1.02

1.01

H/ 'O/cm- .s - '

8.yi

IO- "A /m( . l ' I s '

2.0.S

As a Icsl of the .second-order EC system, the dimerization mechanism of radicals generated by reduction from tiieir parent cation was investigated as in the following reaction:

Q.H.,'

Q,H.,

QH,

This mechanism was first proposed to interpret pyrylium cation reduction by zinc in acetonitrile [21] and was established further by electrochemistry [22-24].

The steady-state voltammograms for "eduction of 2,6-diphenyl-pyrylium cation in acetonitrile at microdisk electrodes with radii of 10.2 and 15.6 p,m were recorded in our experiment. From the steady-state limiting currents, the values of the diffusion coefficient D can be obtained. The formal potential of the pyrylium reduction wave was -0.435 V vs. SCE measured by using fast cyclic voltammetry [24]. For the EC mechanism if the plot of (E - £") vs. In[(/j - / ) / / ] falls on a straight line, the electrode reaction process must be the first-order EC mechanism [8]. If the plot of {E-E^) vs. ln([l - (///d)]/(///j)''^^} is linear, the electrode process would be the second-order EC mechanism. In this work, for the steady-.state voltammograms of 2,6-diphenyl-pyrylium cation, the plots of ( £ - £ " ) vs. In([l - ( / / / j ) ] / ( / / / , , ) - / ' ' } were linear, and the plots of ( £ - £") vs. In[(/j - / ) / / ] did not fall on a straight line. The former are shown in Fig. I. From the slopes and intercepts of these plots, the homogeneous rate constant k and the electron number n of the electrode reaction can be obtained. All the values are given in Table I. The rate constant determined in this work is in good agreement with

Fig. 2. The plot of ( 2 - /,. / / , | ) / ( / L / / , , -\)-'^ '^ of 3.15 X 10 ' mol 1 ' TPA in acetonitrile .solution containing 0.1 mol 1 ' TEAP.

U.-k. /.Iiiiiiiit;. n.-il. Sim/.IdiiiiKil (ij i:i('riiniiiiiil\lii(il Cliniii.'iliy -l-lll II'W) UIJIO'J l(W

those obtained by lliish photolysis experiments [25] il<= 1.2 X !()'' mol ' Is" ' ) and by nanosecond time-iesolvcd cyclic

voltainmeli-y [24] (A = 2.5X !()' 'mol ' Is ' ) . Mere the second-order EC mechanism for the reduction of 2.v'i-diphcnyi-

pyrylium cation is established again.

As an example of the second-order ECE reactions, the oxidation o fTPA was studied. The reaction mechanism has been

.'.hown by Sco et al. [26] to be an ECE-type reaction.

T P A ^ T P A ' + e

2 T P A " ->TPB 1-21-1'

T P B ^ T P B ' - H e

T P B ' ^ ^ T P B - ' - l - e

where the dimeri/ation of 2TPA' to form tetraphenylben/.idine (TPB) is the rate determining step. The steady state

voitammograms oFTPA in acctonitrilc were obtained at disk microelectrodes with the radii of .5.8, 10.2, 1.5.6, 26.1. 31.4 and

5l..3)xm. The plot of [ 2 - ( / , / / , , ) ] / [ ( / , / / , , ) - 1 ] - / ' v.s. / • , ; , - / ' given by Eq. (21) is shown in Fig. 2. The plot is linear with

a slope of 1.51 X 10 - c m - / ' . From the slope the value of the rate constant lor oxidation of TPA was obtained; this equals

2.44 X 10' mol ' I s " ' . The diffusion coefficient of TPA is \.6? X 10 ' 'cm- s " ' [27]. It can be seen that there is good

agreement with those parameters obtained by various workers [27-29] (k = (l-. '^) X lO ' moF ' Is ' ) .

AckncuvledRcmcnts

This project was supported by the National Natural Science Foundation of China.

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