Journal of

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Journal of Electroanalytical Chemistry 602 (2007) 70–76

ElectroanalyticalChemistry

Measurement of rapid electron transfer across a liquid/liquidinterface from 7,7,8,8-tetracyanoquinodimethane radical anion

in 1,2-dichloroethane to aqueous tris(2,2-bipyridyl)-ruthenium (III)

Fei Li, Anna L. Whitworth, Patrick R. Unwin *

Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom

Received 7 August 2006; received in revised form 26 November 2006; accepted 4 December 2006Available online 25 January 2007

Abstract

Rate constants for the reduction of tris(2,2-bipyridyl)-dichlororuthenium (III) ðRuðbipyÞ3þ3 Þ in water by 7,7,8,8-tetracyanoquinodime-thane radical anion (TCNQ��) in 1,2-dichloroethane (DCE) have been measured as a function of the Galvani potential across an ideallynon-polarizable interface using scanning electrochemical microscopy (SECM). The Galvani potential was varied by changing the con-centration of tetrabutylammonium chloride in the aqueous phase, with a fixed concentration of the organic electrolyte, tetrabutylammo-nium tetrakis(penta-fluoro)phenylborate, employed in the DCE phase. By selecting appropriate concentration ratios of the reactants inthe two phases, fast electron transfer (ET) rate constants were measured which were found to increase with increasing driving force. Theexperimentally obtained ET rate constants have been compared to the corresponding theoretical values calculated from the sharp bound-ary and thick layer models of Marcus. The results are consistent with the sharp boundary model, providing further evidence for the appli-cability of this model for the description of simple ET processes across liquid/liquid interfaces.� 2007 Elsevier B.V. All rights reserved.

Keywords: SECM; Interface between two immiscible electrolyte solutions; Galvani potential; Electron transfer; Marcus theory

1. Introduction

The study of electron transfer (ET) processes across theinterface between two immiscible electrolyte solutions(ITIES) is an area of considerable research activity, forboth fundamental reasons and possible applications [1,2].As a consequence, many new electrochemical techniqueshave been developed to measure the kinetics of ET pro-cesses which were previously difficult to study [3–19].

A fundamental question addressed in these studies con-cerns the dependence of ET rate constants on the Galvanipotential across the ITIES. Scanning electrochemicalmicroscopy (SECM) [20] has proven a powerful tool foraddressing this question and the advantages of SECM overalternative methods have been pointed out [4–6]. Since the

0022-0728/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.jelechem.2006.12.002

* Corresponding author. Tel.: +44 2476 523264; fax: +44 2476 524112.E-mail address: p.r.unwin@warwick.ac.uk (P.R. Unwin).

initial studies of Soloman and Bard [21], SECM has pro-vided significant information on the effect of driving forceon ET kinetics across the ITIES [4–6,22–34]. Most of theprevious reports have described potential-dependent ETrate constants at the ITIES [4–6,26–31], although someET systems appear to be characterized by potential-inde-pendent ET rate constants [32,33]. Significantly, there is agrowing body of evidence that the kinetics of the most sim-ple ET reactions at the ITIES follow Butler–Volmer (B–V)theory at low overpotentials [3–5], with an inverted regionat high driving force as predicted by Marcus theory [3–5,9,31,35–41].

Photoinduced ET, recognized as a model system for nat-ural photosynthesis and heterogeneous photocatalysis[1,42,43], is an interesting approach for investigating therates of ET reactions across the ITIES. In this context,the reaction between the photoexcited sensitizer tris(2,2-bipyridyl)-ruthenium (II) ðRuðbipyÞ2þ3 Þ, dissolved in an

F. Li et al. / Journal of Electroanalytical Chemistry 602 (2007) 70–76 71

aqueous phase, with the quenching species 7,7,8,8-tetra-cyanoquinodimethane (TCNQ), located in an immiscibleorganic phase, has been studied with electrochemical andspectroelectrochemical techniques [44,45]. A key aspect ofphotoelectrochemical technologies based on this type ofprocess is to enhance the efficiency of product separationby diminishing the probability of back electron transferprocesses. Consequently, knowledge of the kinetics of backelectron transfer reactions is important [41,46–48], but therate of such processes is usually treated as a fitting param-eter within a more complex photoelectrochemical scheme.Furthermore, to the best of our knowledge, the reactionbetween RuðbipyÞ3þ3 and TCNQ�� has not been studiedpreviously.

A feature of photoinduced ET studies of the type men-tioned is that the driving force for back ET is usually large,which places demands on the techniques used to elucidatethe kinetics. We have shown that by using a small concen-tration ratio of the reactants in the two liquid phases, it ispossible to use SECM to measure rapid dark ET reactionsacross the ITIES that are inaccessible to other techniques[9]. This approach has also been used by others to measurelarge ET rate constants [31].

In this paper, we investigate the rate of oxidation ofTCNQ�� in 1,2-dichloroethane (DCE) by aqueousRuðbipyÞ3þ3 . We establish that ET is fast and the ratedepends on the Galvani potential across the ITIES. Therate constants measured have been compared with the the-oretical values arising from the sharp boundary and thicklayer models of Marcus [35–39]. The studies of ET at highdriving force presented in this paper provide evidence thatthe sharp boundary model, which has been shown to applyat relatively low driving forces [49,50], also applies to darkET reactions at high driving force.

2. Experimental

2.1. Chemicals

Ru(bipy)3Cl2 (99.95%, Aldrich), TCNQ (P98%, Fluka),tetrabutylammonium chloride (TBACl, P97%, Fluka),lithium tetrakis(penta-fluoro)phenylborate ethyl etherate(LiTPBF, Fluka), sodium chloride (A.R., Fisher) andDCE (HPLC grade, Sigma–Aldrich) were used as received.The organic salt, tetrabutylammonium tetrakis(penta-flu-oro)phenylborate (TBA+TPBF�), was prepared bymetathesis of TBACl and LiTPBF in a 2:1 mixture ofmethanol and water. The product was filtered and desic-cated overnight. Aqueous and organic solutions were pre-pared, respectively, from Milli-Q reagent water (MilliporeCorp.) and water-saturated DCE.

Fig. 1. Schematic of the SECM setup for the measurement of ET rateconstants at the aqueous/DCE interface.

2.2. Apparatus and procedures

The SECM setup and experimental method used tomeasure the ET rate constants were similar to those

reported previously [49]: a layer of DCE covered aninverted glassy carbon electrode (GCE) (3 mm diameter)by depositing a 35 lL drop of DCE solution containing2 mM TCNQ and 0.05 M TBATPBF on the surface. Aschematic of the SECM arrangement is shown in Fig. 1.The cell was filled with aqueous electrolyte containing 1–4 mM RuðbipyÞ2þ3 , 0.1 M NaCl and 0.01–0.1 M TBACl.

Prior to SECM experiments, a three-electrode systemwas employed to generate TCNQ�� by electrolyzing TCNQin the DCE phase on the GCE working electrode with asaturated calomel electrode (SCE) and a Pt mesh as the ref-erence and counter electrodes, respectively. The electrolysisprocedure is described as follows: TCNQ in the DCE drop-let on the GCE was exhaustively reduced to TCNQ�� in theabsence of O2 by biasing the potential of the GCE at 0 Vvs. SCE in the aqueous phase with a Pt mesh counter elec-trode, such that the reduction of TCNQ to TCNQ�� wasdiffusion-controlled. The electrolysis process was deemedto be complete when the recorded charge approached alimiting value (as shown in Fig. 2), consistent with thequantity of TCNQ in the droplet. The extent of electrolysisand concentration of TCNQ�� in the DCE phase was alsoconfirmed by dipping an ultramicroelectrode (UME) intothe organic layer and measuring the concentration ofTCNQ�� from the steady-state diffusion-limited current.

To ensure that the generated TCNQ�� was stable, thewhole system was thoroughly deaerated throughout allexperiments. The stability of TCNQ�� was checked byrecording a voltammogram before and after the SECMmeasurements, with the UME dipped into the organicdrop. The change in the diffusion limited current forTCNQ�� oxidation to TCNQ was negligible (<2%), indi-cating that TCNQ�� is stable under these conditions. Afterthe electrolysis process, the GCE was disconnected. Itshould be noted that the SECM process itself barely con-verts any of the TCNQ�� compared to the total amount

0 1000 2000 3000 4000 5000 6000 7000 80000.000

-0.001

-0.002

-0.003

-0.004

-0.005

-0.006

-0.007

Ch

arg

e / C

Time / s

Fig. 2. Charge–current curve for the electrolysis of 2 mM TCNQ toTCNQ�� in a 35 lL drop of DCE solution (0.05 M TBATPBF supportingelectrolyte) on a graphite electrode. The potential applied to the graphiteelectrode was 0 V vs. SCE in the aqueous phase with 0.1 M NaCl and0.01 M TBACl.

72 F. Li et al. / Journal of Electroanalytical Chemistry 602 (2007) 70–76

in the bulk of the drop, as discussed in previous studies ofUME voltammetry in microlitre volumes [51]. Thus, thebulk solution in the drop, and that bathing the graphiteelectrode is predominantly TCNQ��.

For the SECM experiments a two-electrode arrange-ment was employed in the top aqueous phase, with eithera silver quasi-reference electrode (AgQRE) or SCE servingas the reference electrode in the aqueous phase. A 25 lmdiameter Pt disc UME with a RG value of 10 (ratio ofthe overall tip radius to that of the platinum disc) was func-tioned as the working electrode. The UME was fabricatedand polished as reported previously [52]. The UME in theaqueous phase was used to generate RuðbipyÞ3þ3 by the oxi-dation of RuðbipyÞ2þ3 at a diffusion-controlled rate. Thisprocess resulted in the feedback of RuðbipyÞ2þ3 to theUME tip in the aqueous phase by the following ET reac-tion with TCNQ�� in the DCE phase:

TCNQ��ðDCEÞ þRuðbipyÞ3þ3 ðaqÞ

! TCNQðDCEÞ þRuðbipyÞ2þ3 ðaqÞ ðat the ITIESÞ ð1Þ

so enhancing the tip current compared to the situationwhere there was no reaction at the ITIES.

A series of SECM approach curves were recorded byapproaching the UME towards the ITIES and recordingthe steady-state current for RuðbipyÞ2þ3 oxidation as a func-tion of d (the distance between the tip and the ITIES). Toensure that the tip to interface distance was known withhigh precision, the closest distance between the tip andthe ITIES was determined by running negative feedbackapproach curve measurements for RuðbipyÞ3þ3 oxidationwithout TCNQ in the DCE phase and analyzing the datawith negative feedback theory [53]. The tip could typi-cally be approached to a distance of 1–2 lm from theITIES.

3. Results and discussion

3.1. Driving force for interfacial ET from TCNQ�� to

RuðbipyÞ3þ3

The driving force (v) for the ET reaction at a non-polar-izable ITIES is determined by two terms: the Galvanipotential across the ITIES ðDw

o /Þ and the difference in theformal potentials of the organic electron donor and aqueouselectron acceptor species ðDE00 ¼ E00 ;w

RuðbipyÞ3þ=2þ � E00 ;o

TCNQ0=��Þ[5,6]:

v ¼ DE00 þ Dwo / ð2Þ

Provided that the potential determining ion is present inlarge excess, compared to the redox species, the Galvanipotential across the ITIES is governed by the distributionpotential imposed by the common ion, i. Under these con-ditions Dw

o / depends on the concentration ratio of the com-mon ion in the two liquid phases [2]:

Dwo / ¼ Dw

o /00 þ RTzF

lnco

i

cwi

� �ð3Þ

where cwi and co

i are the concentrations of the common ionin the aqueous and organic phases, respectively, Dw

o /00 isthe formal transfer potential of the common ion, whichhas a charge, z.

Since the diffusion coefficients of the oxidized andreduced forms are similar for the two redox couples ofinterest, the formal potentials can be assumed to approxi-mate to the reversible half-wave potentials. The differencebetween the half-wave potentials measured with respectto a common reference electrode (in the aqueous phase),DE1/2, gives the absolute value of the driving force forthe interfacial ET reaction, v:

v ¼ DE00 þ Dwo /00 ¼ DE1=2 ð4Þ

In the present studies, Dwo / was controlled and varied by

changing the concentration of TBA+ in the aqueous andDCE phases. The absolute value of the driving force forthis system was obtained as the difference between thehalf-wave potentials of RuðbipyÞ2þ3 oxidation in the aque-ous phase and TCNQ reduction in DCE, measured with re-spect to the same SCE reference electrode in the aqueousphase, with different values of [TBA+]w/[TBA+]o.

Fig. 3 is the cyclic voltammogram of RuðbipyÞ2þ3 oxida-tion in the aqueous phase, for which the half-wave poten-tial is 1.043 V (vs. SCE). Fig. 4 displays a series of linearsweep voltammograms for the reduction of TCNQ toTCNQ�� vs. the same SCE positioned in a contacting aque-ous phase containing different [TBA+]w in the range from0.01 to 0.1 M with [TBA+]o fixed at 0.05 M. The depen-dence of the half-wave on [TBA+]w is illustrated in the insetto Fig. 4 with a slope of about 60 mV per decade, whichagrees well with the prediction that the formal potentialfor TCNQ reduction should shift by 59 mV to more posi-tive values per decade increase in [TBA+]w at 298 K, sinceDw

o / varies according to Eq. (3).

0.2 0.4 0.6 0.8 1.0 1.2 1.4-2

0

2

4

6

8

10

12

14

i / n

A

E / V vs SCE

Fig. 3. Cyclic voltammogram at a 25 lm diameter Pt UME in an aqueousphase for the oxidation of 5 mM RuðbipyÞ2þ3 , containing 0.1 M NaCl and0.01 M TBACl with SCE as the reference electrode (scan rate 20 mV s�1).

1.0 0.8 0.6 0.4 0.2 0.0 -0.2

0.0

-0.5

-1.0

-1.5

-2.0

-2.5

i / n

A

E / V vs SCE

-2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8

0.28

0.29

0.30

0.31

0.32

0.33

0.34

0.35

E1/

2,TC

NQ/ V

vs

SC

E

log[TBA]w

+(M)

Fig. 4. Linear sweep voltammograms for TCNQ reduction to TCNQ�� ata 25 lm diameter Pt UME in a DCE phase with an SCE placed in acontacting aqueous phase, at different concentrations of TBA+ in aqueousphase. The scan rate was 20 mV s�1. The DCE phase contained 0.5 mMTCNQ and 0.05 M TBATPBF and the aqueous solution contained 0.1 MNaCl and 0.01–0.1 M TBACl (from right to left). The inset figure is thedependence of half-wave potential of TCNQ reduction on [TBA+]w.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

k

3

21

No

rmal

ized

cu

rren

t

L= d / a

1000 100 50 30 20

Fig. 5. Experimental approach curves (solid curves) alongside theoreticalcurves for various normalized ET rate constants, k, for Kr = 2. The DCEdroplet on the graphite electrode contained 2 mM TCNQ�� and 0.05 MTBATPBF. The aqueous phase contained 1 mM RuðbipyÞ3Cl2, 0.1 MNaCl and TBACl at concentrations of (1) 0.01 M; (2) 0.05 M and (3)0.1 M. SECM approach curves were recorded at 0.5 lm s�1.

F. Li et al. / Journal of Electroanalytical Chemistry 602 (2007) 70–76 73

3.2. Kinetics of ET from TCNQ�� to RuðbipyÞ3þ3

Based on our previous work [9], the concentration ratioof reactants in the two phases Kr ðKr ¼ C�Red2=C�Red1;C�Red1 and C�Red2 denote the initial concentrations of Red1

and Red2 in the two phases, respectively) determines theupper limit of accessible rate constants that can be mea-sured by SECM. Studying systems under conditions whereKr is small opens up the possibility of measuring large rateconstants as approach curves in the fast kinetic limit aremore readily distinguished from one another [9]. In thiswork, we further illustrate how the use of small values ofKr is optimal for fast kinetics studies.

Typical current–distance approach curves for a tip in theaqueous phase approaching the ITIES while electrogener-

ating RuðbipyÞ3þ3 from RuðbipyÞ2þ3 when Kr = 2 are shownin Fig. 5. The Galvani potential across the ITIES was var-ied by changing [TBA+]w (0.01–0.1 M) in the aqueousphase with a fixed [TBA+]o (0.05 M). Each of the approachcurves was fitted to theoretical curves to determine theoptimal dimensionless rate constant, k ¼ k12aCTCNQ��=D,where k12 is the bimolecular ET rate constant, a is the elec-trode radius, D is the diffusion coefficient of TCNQ�� inDCE and CTCNQ�� is the bulk concentration of TCNQ��

in DCE. For this purpose, the numerical model outlinedpreviously [49] was employed using a program written inFORTRAN run on the University of Warwick centralUNIX system. It can be seen that even at relatively smallKr, the approach curves at different Galvani potentialsare closely similar – all increase sharply with decreasingtip–interface distance and are difficult to distinguish froma purely diffusion-controlled process, which manifests inthe limit of high values of Kr. Under these conditions, theET rate is too fast to be measured by SECM.

Typical experimental results obtained at lower Kr valuesare shown in Fig. 6a and b. In Fig. 6a, for Kr = 1, approachcurves at different driving forces are more readily distin-guished from each other than those in Fig. 5. WhenKr = 0.5 (Fig. 6b), the experimental approach curves arefar away from the theoretical curves of the diffusion-con-trolled region (top curves in the figure) and the differencebetween them is more obvious. In this case, the curves havecharacteristic peaks with magnitudes that are diagnostic ofthe rate constants. The corresponding bimolecular rate con-stants (k12) obtained were 80 ± 5 cm s�1 M�1 ([TBA+]w =0.01 M), 72 ± 5 cm s�1 M�1 ([TBA+]w = 0.025 M),66 ± 5 cm s�1 M�1 ([TBA+]w = 0.05 M), 58 ± 4 cm s�1 M�1

([TBA+]w = 0.075 M) and 52 ± 4 cm s�1 M�1 ([TBA+]w =0.1 M). Thus, the ET rate constants are large and depend

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.1

1.2

1.3

1.4

1.5

1.6

1.7

k

54321

1000 100 50 25 20 1816.5 14.5 13

No

rmal

ized

cu

rren

t

L = d / a

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

k

32

1

No

rmal

ized

cu

rren

t

L = d / a

28 16 14

Fig. 6. Experimental approach curves (solid curves) alongside theoreticalcurves for various ET rate constants for the reaction between TCNQ��

and RuðbipyÞ3þ3 . The DCE droplet on the graphite electrode contained2 mM TCNQ�� and 0.05 M TBATPBF. The aqueous phase contained0.1 M NaCl, different concentrations of TBACl and (a) 2 mMRuðbipyÞ3Cl2 ðKr ¼ 1Þ and (b) 4 mM RuðbipyÞ3Cl2 ðKr ¼ 0:5Þ. The con-centrations of TBACl in (a) were: (1) 0.01 M (k = 28), (2) 0.05 M (k = 16)and (3) 0.1 M (k = 14); (b) the concentrations of TBACl were (1) 0.01 M(k = 20), (2) 0.025 M (k = 18), 0.05 M (k = 16.5), (4) 0.075 M (k = 14.5)and 0.1 M (k = 13). SECM approach curves were recorded at 0.5 lm s�1.

74 F. Li et al. / Journal of Electroanalytical Chemistry 602 (2007) 70–76

on the Galvani potential across the ITIES. The trendappears to be that the ET rate constant increases withincreasing driving force, by decreasing [TBA+]w. Althoughthis type of trend has been seen for other systems [3–5,26,33], this has tended to be at much lower driving forces.Moreover, the dependence seen here is not as strong as atlower driving force, qualitatively consistent with Marcustheory [40].

3.3. Assessment of data in terms of Marcus theory

The applicability of Marcus theory [35–39], to ET reac-tions at the ITIES has recently considered in several papers[5,25–33,40]. Thus, the ET rate constants of RuðbipyÞ3þ3 /TCNQ�� system at different driving forces obtained above

have been compared with theoretical values, calculatedbased on the two main models of Marcus.

The Gibbs activation energy for the ET reaction (DG 6¼)is defined by [35]:

DG 6¼ ¼ wr þ k4

1þ DG00 þ wp � wr

k

!2

ð5Þ

where k is the reorganization energy, wr and wp are, respec-tively, the work terms for bringing the reactants togetherand for separating the products, DG00 is the formal Gibbsenergy for the electron transfer process which can be ex-pressed by

DG00 ¼ �F ðDE00 þ Dwo /Þ ¼ �F DE1=2 ð6Þ

The values of wr and wp can be calculated [35,54]:

wr ¼ N Ae2

4pe0

� ðzr1Þ

2

4d1DS1

� ðzr2Þ

2

4d2DS2

!DS

2 � DS1

DS2 þ DS

1

� �þ 2

Rd

zr1zr

2

DS1 þ DS

2

" #

ð7Þ

and

wp ¼ N Ae2

4pe0

� ðzp1Þ

2

4d1DS1

� ðzp2Þ

2

4d2DS2

!DS

2 � DS1

DS2 þ DS

1

� �þ 2

Rd

zp1zp

2

DS1 þ DS

2

" #

ð8Þ

where e is the elementary charge, e0 is the vacuum permit-tivity, DS

1 and DS2 are the static dielectric constants of the

two phases (which have values of 10 for DCE and 78.4for water), zr

i and zpi are the charge numbers of the reactant

and product in solvent i (in this case, ignoring ion pairing,zr

1 ¼ þ3; zr2 ¼ �1; zp

1 ¼ þ2; zp2 ¼ 0). The parameters d1

and d2 are the perpendicular distances from the centres ofthe two reactants to the interface boundary and we approx-imate these distances by the radii of the two reactants, a1

and a2, for simplicity (for this system, a1 = 6.8 A forRuðbipyÞ2þ3 [55] and a2 = 4.0 A for TCNQ [56]), Rd is thecentre-to-centre separation between the two reactants givenas Rd � d1 + d2 � a1 + a2 = 10.8 A, in this case.

The reorganization energy, k, is the sum of the contribu-tions of the outer and inner sphere reorganization energies,k0 and ki, respectively [35–39]:

k ¼ k0 þ ki ð9Þ

ki for biomolecular ET can be approximately defined as themean value of ki of the two redox couples:

ki ¼ ðki;1 þ ki;2Þ=2 ð10Þ

while k0 is given by [36].

Table 1Experimental ET rate constants k12 and theoretical values calculatedbased on the sharp boundary model ðk012Þ and thick layer model ðk0012Þ atdifferent driving forces (v) for ET from TCNQ�� in DCE to aqueousRuðbipyÞ3þ3v (V) k12(exp) (cm s�1 M�1) k012 ðcm s�1 M�1Þ k0012 ðcm s�1 M�1Þ0.76 80 ± 5 142 3.6 · 104

0.74 72 ± 5 130 3.5 · 104

0.72 66 ± 5 118 3.2 · 104

0.71 58 ± 4 113 3.1 · 104

0.70 52 ± 4 108 2.9 · 104

F. Li et al. / Journal of Electroanalytical Chemistry 602 (2007) 70–76 75

k0 ¼N AðDeÞ2

8pa1e0

1

Dop1

� 1

DS1

� �þ NAðDeÞ2

8pa2e0

1

Dop2

� 1

DS2

� �

� N AðDeÞ2

16pd1e0

Dop2 � Dop

1

Dop1 ðD

op2 þ Dop

1 Þ� DS

2 � DS1

DS1ðDS

2 þ DS1Þ

� �

� N AðDeÞ2

16pd2e0

Dop1 � Dop

2

Dop2 ðD

op2 þ Dop

1 Þ� DS

1 � DS2

DS2ðDS

2 þ DS1Þ

� �

� N AðDeÞ2

2pRde0

1

Dop1 þ Dop

2

� 1

DS1 þ DS

2

� �ð11Þ

where De is the charge transferred, Dop1 and Dop

2 are theoptical dielectric constants of the two phases (with valuesof 2.09 for DCE and 1.78 for water). Here, ki is9.9 kJ mol�1 for the TCNQ0/�� couple [56] and 55 kJ mol�1

for the RuðbipyÞ3þ=2þ3 couple [55].

Marcus has considered two forms of the ITIES: as asharp boundary or as a region several molecular layersdeep [35–39,55]. In the sharp boundary model, the bimolec-ular electron transfer rate constant for ET is given by anArrhenius-type general kinetic equation [39]:

k012 ¼ 2pNAða1 þ a2ÞðDRÞ3km expð�DG6¼=RT Þ ð12Þ

where DR defines the dependence of electron transfer rateon separation distance R between the reactants, with a typ-ical value of 1 A [55], the parameter k is the Landau–Zenertransmission coefficient and m is a typical frequency ofmolecular motion; usually km � 1012 s�1 [35–39,54,57]. Inthe thick layer model, the rate constant is given by

k0012 ¼ 4pNAða1 þ a2Þ2DRkvL expð�DG 6¼=RT Þ ð13Þ

where L is the thickness of the interface, normally �8–10 A[3]. For the RuðbipyÞ3þ3 =TCNQ�� system, based on theabove-mentioned parameters, we calculate wr =6.506 kJ mol�1, wp = 2.003 kJ mol�1, ki = 32.5 kJ mol�1

and k0 = 59.7 kJ mol�1. Thus, the overall reorganizationenergy is k = 92.2 kJ mol�1. Then, using Eqs. (12) and(13), we calculate k012 and k0012 and compare the values tok12 (as a function of v), as summarized in Table 1. Fromthe table, it can be seen that the experimental rate constantsare reasonably close to the theoretical values obtained fromthe sharp boundary model. The agreement is particularlysatisfactory, given the approximations used in the calcula-tions. In contrast, the thick layer model provides pooragreement with experiments. Thus, these studies provide

further evidence for the applicability of the sharp boundarymodel.

4. Conclusions

SECM has been used to investigate the effect of Galvanipotential on the ET rate constants of the reaction betweenTCNQ�� and RuðbipyÞ3þ3 at the ITIES. By using a smallconcentration ratio of reactants in the two phases, it hasbeen possible to measure rapid ET rate constants at rela-tively high driving force. Experimental results indicate thatthe ET rate constants increase with increasing drivingforce, by decreasing [TBA+]w at constant [TBA+]o. TheET rate constants measured have been compared withthose calculated from the sharp boundary and thick layermodels of Marcus and results indicate that the sharpboundary model is more appropriate to describe ET acrossthe ITIES.

Acknowledgements

F.L. gratefully acknowledges a scholarship from theDorothy Hodgkin Postgraduate Awards Scheme andA.L.W. thanks the Royal Society for a Royal Society BPDorothy Hodgkin Research Fellowship. We are also veryappreciative of helpful discussions with Prof. David Fer-min (University of Bern, Switzerland).

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