Simultaneous ion transfer across the microhole ITIES: an example of ternary electrodiffusion

Journal of Electroanalytical Chemistry 460 (1999) 149–159

Simultaneous ion transfer across the microhole ITIES: an example ofternary electrodiffusion

Bernadette Quinn, Riikka Lahtinen, Lasse Murtomaki *

Helsinki Uni6ersity of Technology, Laboratory of Physical Chemistry and Electrochemistry, P.O. Box 6100, FIN-02015 TKK, Finland

Received 14 April 1998; received in revised form 14 September 1998

Abstract

Ternary electrodiffusion at the immiscible liquid � liquid interface (ITIES) is considered in the case where a univalent cation istransferring from the water to the organic phase through a microhole, and simultaneously a univalent anion is transferring in theopposite direction. The process is assumed to take place at steady-state. If the separation between the formal transfer potentialsof these ions is large enough, a limiting current corresponding to the electrodiffusion of the ion with the lower formal transferpotential is observed. Thereafter, the current begins to rise again as a linear function of the cell potential because the Galvanipotential across the interface has reached its limiting value and the potential is expended in the form of ohmic loss in the diffusionboundary layers. The Galvani potential across the interface cannot overcome the average value of the formal transfer potentialsdue to the electroneutrality condition. The present case is analogous to a redox reaction at the ultramicroelectrode with signreversal (K.B. Oldham, J. Electroanal. Chem. 337 (1992) 91) but no suitable experimental system has yet been found with whichto test this prediction. Experiments without supporting electrolytes seem to have only little value in quantitative analysis of iontransfer. © 1999 Elsevier Science S.A. All rights reserved.

Keywords: ITIES; Ternary diffusion; Migration; Microhole; IR drop

1. Introduction

With the advent of microelectrodes, it is possible tocarry out measurements in the absence of the baseelectrolyte and in highly resistive solvents. Such mea-surements are not feasible at a conventionally sizedelectrode due to the resulting huge IR drop. There is anabundance of literature, both theoretical and experi-mental, on microelectrode voltammetry where thecharge of the ions, the permittivity of the solvent, theeffect of ion-pairing, etc. have been studied [1–11]. Theconcept of going micro at the interface between twoimmiscible electrolyte solutions (ITIES) was introducedfirst by Girault in 1986 whereby a micro liquid � liquidinterface was supported at the tip of a micropipette

[12]. Since then, micro interfaces have been obtained bya variety of means and examples of the more successfulinclude laser drilled microholes in a polyester film [13]and silicon etched square holes [14]. In most cases, anexcess of the base electrolyte has been present with theaim of the accurate determination of charge-transferkinetics [13–15]. However, Osborne et al. [16] alsovaried the concentration of the base electrolyte andillustrated that the theory for steady-state voltammetryat hemispherical electrodes under conditions of littlesupporting electrolyte [2] can be applied to studies atmicro ITIES. The authors postulated that such microinterfaces could be applied to study the effects ofion-pairing on charge-transfer.

Liquid � liquid interfaces are experimentally more de-manding than studies at conventional microelectrodes,in that there is a restricted number of solvents that canbe employed successfully and there are severe limita-

* Corresponding author. Tel.: +358-9-4512578; fax: +358-9-4512580; e-mail: [email protected].

0022-0728/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved.PII: S 0 0 2 2 -0728 (98 )00369 -6

B. Quinn et al. / Journal of Electroanalytical Chemistry 460 (1999) 149–159150

tions as to the choice of organic base electrolytes [17].The solvents used should be mutually immiscible andthe base electrolytes should not partition between thephases. While several cations of the organic base elec-trolyte have been used, to date only three anions havebeen studied in depth [17]. This is a fundamental prob-lem of ITIES as the size of the available potentialwindow is limited by the transfer of the base electrolyteions in either phase. The potential at which ions trans-fer is determined by their Gibbs energy of transfer(DG t

0) and ideally ions with large absolute values ofDG t

0 should be chosen thus increasing the size of thewindow. The use of tetraphenylborate (TPB−) or 3,3%-commo -bis(undecahydro-1,2-dicarba-3-cobalta-closo-dodecaborate) anions which have relatively low DG t

0

values means that these ions will transfer before K+,Li+ and Na+ [18–20]. The tetrakis(4-chlorophenyl)-borate anion (TPBCl−) has yet to be reported totransfer and its use has extended the number of ionswhich can be studied [21,22].

It has been noticed that the anion in the organicphase plays a role in the transfer process of a cation inthe aqueous phase [18,23–25]. Interfacial and bulkion-pairing in the low permittivity organic phase (e.g.1,2-dichloroethane or o-nitrophenyl octylether) betweenthe transferring ion and the counter-ions hinder theinterpretation of data [18,19,26,27]. There is some con-fusion as to how to describe this phenomenon as someauthors refer to a form of facilitated ion transfer [18–20], others call it an EC mechanism [28] while manysimply refer to it as ion-pairing [21,27,29–31]. The useof micro interfaces has been suggested as a means ofcircumventing this problem as it is possible to observeion transfer in the complete absence of the base elec-trolyte. Also, it should enable the study of ions whichare normally used as the supporting electrolyte (TPB−

and TPBCl−). Osborne et al. concluded that in thecomplete absence of base electrolyte in the aqueousphase, there should be no restrictions from the potentialwindow and that all analyte ions could be studied—thepurpose of the present paper was to consider fully theimplications of this statement [16].

However, the transfer potentials of the base elec-trolyte ions may overlap with the transfer potential ofthe ion under study within the potential region usedand simultaneous ion transfer can occur. Also, as illus-trated by Oldham [1,6], the increased role of migrationto the transport problem must be considered. Thesolution to the diffusion–migration problem in theabsence of the supporting electrolyte was shown todepend in a surprisingly complicated way on the chargenumber of the reactant, product and counter ion. Asthe limiting current region is approached, the systemchanges from binary to ternary because the concentra-tion of the product becomes comparable to that of thereactant in the diffuse layer. This paper investigates ion

transfer across the ITIES in the absence of the support-ing electrolyte in the case where simultaneous transfercan occur and the theory outlined below was developedto explain the experimental findings. Due to the pres-ence of two phases, the degree of freedom is three [32]and the underlying theory becomes more complicatedthan in Oldham’s approach [1] which needs to bemodified to the present case.

2. Theory

Consider the scheme given in Fig. 1: an aqueousphase containing a 1:1 electrolyte MCl is placed incontact with an organic phase containing a 1:1 elec-trolyte CA, via a microhole of the radius r0. Thediaphragm where the microhole resides is assumed tobe infinitely thin. The bulk concentrations of the elec-trolytes are cb

w and cbo in the aqueous and organic

phase, respectively. From here on, the subscript 1 de-notes M+, 2 Cl−, 3 C+ and 4 A−. For the sake ofsimplicity, only reversible ion transfer is considered,and therefore, the Nernst equation is valid for both thetransferring ions:

ÍÃ

Ã

Á

Ä

u1=c1

o,s

c1w,s=exp

� FRT

(Dowf−Do

wf10%)n

u4=c4

w,s

c2o,s =exp

� FRT

(Dowf−Do

wf40%)n (1)

Dowf is the Galvani potential difference across the inter-

face defined as Dowf=fw−fo; Do

wf10 and Do

wf40% are

the formal transfer potentials of M+ and A−. Thesuperscript s denotes the interfacial concentration.When a sufficiently positive external potential differ-ence is applied across the interface, M+ is transferredfrom the aqueous to the organic phase and A− in theopposite direction. The electroneutrality conditions are!c1

w=c2w+c4

w;c1

o+c3o=c4

o;c3

w=0c2

o=0(2)

Spherical electrodiffusion prevails in both phases andthe flux density of an ion k, jk, at steady-state is givenby the Nernst–Planck equation as

Fig. 1. A schematic view of the microhole system.

B. Quinn et al. / Journal of Electroanalytical Chemistry 460 (1999) 149–159 151

− jk=Dk

�dck

dr+zkck

d8

dr�

(3)

where Dk, ck and zk are the diffusion coefficient, con-centration and the charge number of the ion k, and8=Ff/RT. Introducing new variables

x=r0

r; Jk=2pr2jk (4)

Eq. (3) is transformed to

Jk

2pr0

=Dk�dck

dx+zkck

d8

dx�

(5)

Notice that the flux density is a function of the radialdistance r from the microhole while the flux, Jk, isconstant throughout the whole system. The electriccurrent is

I=F(J1−J4) (6)

During transfer, a ternary system prevails in the vicinityof the microhole, and in the following paragraphs, thesolution of this transport problem is outlined.

Actually, the transport problem should be solved inthe circular cylinder coordinate system, taking intoaccount the finite thickness of the diaphragm. Thiswould probably not change the results of the treatmentbelow, but only make the theory rather difficult tofollow due to the modified Bessel’s functions then in-volved; the question of the microhole geometry hasbeen discussed in Ref. [33].

2.1. Aqueous phase

It is convenient to drop the superscript w temporar-ily. First Eq. (5) is written for M+, Cl− and A−.Adding them together gives (J2=0)

J1/D1+J4D4

2pr0

=2dc1

dx=constant (7)

The concentration profile in the new coordinates, c1(x),thus is linear. Using the boundary conditions c1(1)=c1

s

and c1(0)=cbw, it is found that

c1=cwb + (c1

s −cwb )x (8)

Therefore, Eqs. (7) and (8) give,

dc1

dx=c1

s −cwb [J1+j4 J4=4pr0D1(c1

s −cwb ) (9)

where j4=D1/D4. Adding J1/D1−J2/D2−J4/D4 gives

J1/D1−J4/D4

2pr0

=2c1

d8

dx(10)

Using Eq. (9) it is found that

c1

d8

dx=

J1−j4 J4

4pr0D1

=J1−j4 J4

J1+j4 J4

(c1s −cw

b )=g(c1s −cw

b )

(11)

which defines the dimensionless parameter g. It willplay a key role in what follows; it takes values from91 to 9�, the plus sign corresponding to the casewhere M+(‘1’) is transferred first. When inserting Eqs.(9) and (11) back into Eq. (5) an important relationshipis obtained:

J1

2pr0D1

= (1+g)(c1s −cw

b ) (12)

Applying the expression for the electric current, Eq. (6),it also follows that

J4

2pr0D4

= (1−g)(c1s −cw

b ) (13)

Eqs. (12) and (13) will be used to calculate the currentafter the determination of g.

Eq. (13) can be written also in the form of Eq. (5),making use of Eqs. (8) and (11):

J4

2pr0D4

=dc4

dx−

gc4

x+a; a=

cwb

c1s −cw

b (14)

The solution of this differential equation is

c4= (x+a)g�K+J4

2pr0D4

(x+a)1−g

1−gn

= (x+a)g[K+ (c1s −cw

b )(x+a)1−g] (15)

where Eq. (13) has been utilized. The constant K can beeliminated by the boundary condition c4(0)=0, and theboundary condition c4(1)=c4

s leads finally to the fol-lowing form:

c4

c4s =

x+a1+a

1−�x+a

a�g−a

1−�1+a

a�g−1 (16)

After some practice of algebra, the gradient of c4 at theinterface is obtained as�dc4

dx�

x=1

=c4

s

c1s (c1

s −cwb )

1−g(c1s/cw

b )g−1

1− (c1s/cw

b )g−1 (17)

because

11+a

=c1

s −cwb

c1s ;

1+aa

=c1

s

cwb (18)

Since the fluxes are constant throughout the wholesystem, they can be evaluated most conveniently at theinterface. Noticing that d8/dx=g/1+a at the inter-face and using Eqs. (13) and (17), it is finally found that

(1−g)(c1s −cw

b )=c4

s

c1s (c1

s −cwb )�1−g(c1

s/cwb )g−1

1− (c1s/cw

b )g−1 −gn(19)

from which a crucial relationship is obtained:

c4s

c1s =1−

�c1s

cwb

�g−1

Ug=ln (1−c4

s/c1s)

ln (c1s/cw

b )+1 (20)


The fluxes J1 and J4 are given now by (bringing thesuperscript w back)

J1w

2pr0D1wcb

w=�c1

w,s

cwb −1

��ln(1−c4w,s/c1

w,s)ln(c1

w,s/cwb )

+2n

(21)

J4w

2pr0D4wcb

w= −�c1

w,s

cwb −1

� ln (1−c4w,s/c1

w,s)ln (c1

w,s/cwb )

(22)

The potential drop in the diffusion boundary layer canbe calculated by writing Eq. (5) for the species ‘2’, i.e.chloride, and recalling that J2=0. Thus,

d8w=d ln c2w[8w,b−8w,s= ln

� cwb

c1w,s−c4

w,s

�(23)

Two unknown variables, c1w,s and c4

w,s, remain to besolved. This can be achieved by solving the transportproblem in the organic phase in a similar manner to thetreatment above, taking into account the condition ofthe continuity of the fluxes at the interface, along withthe relationships in Eq. (1).

2.2. Organic phase

The calculations are not repeated here because theyare very similar, only the roles of M+ and A− areinterchanged. The final expressions for the fluxes andthe potential drop in the diffusion boundary layer are:

J1o

2pr0D1oco

b= −�c4

o,s

cob −1

� ln (1−c1o,s/c4

o,s)ln (c4

o,s/cob)

(24)

J4o

2pr0D4oco

b=�c4

o,s

cob −1

� �ln (1−c1o,s/c4

o,s)ln (c4

o,s/cob)

+2n

(25)

d8o= −d ln c30[8o,s−8o,b= ln

� cob

c4o,s−c1

o,s

�(26)

2.3. Conditions of continuity

Because r has been taken as a positive distance fromthe interface in both phases, although it is pointing inopposite directions, the signs of the fluxes have to beconverted for the condition of flux continuity:!−J1

w=J1o=J1

−J4w=J4

o=J4

(27)

Comparison of Eq. (21) with Eq. (24) and Eq. (22) withEq. (25) gives after some rearrangement! A+2=CB

A=DC(B+2)(28)

where

A=ln (1−c4

w,s/c1w,s)

ln (c1w,s/cw

b )(29)

B=ln (1−c1

o,s/c4o,s)

ln (c4o,s/co

b)(30)

C=D1

o(c4o,s−co

b)D1

w(c1w,s−cw

b )(31)

D=D1

wD4o

D1oD4

w:1 (32)

Assuming D=1, we obtain from Eq. (28), that C=−1 and consequently the desired relationship betweenc1

w,s and c4w,s:

c4o,s=c4

w,su4−1=co

b−D1

w

D1o (c1

w,s−cwb ) (33)

Inserting Eq. (33) into Eq. (28) leads to a transcenden-tal equation of c1

w,s which needs to be solvednumerically:�

−u4

y(C r

−1−j1(y1−1))n

ln (y1)+2

=− ln

�1−

u1y1

C r−1−j1(y1−1)

nln [1−Crj1(y1−1)]

(34)

In Eq. (34) the following dimensionless quantities havebeen used:

y1=c1

w,s

cwb ; Cr=

cwb

cob; j1=

D1w

D1o (35)

Finding y1 from Eq. (34) for the given values of u1 andu4 gives c1

w,s. c4w,s can then be calculated from Eq. (33)

and the fluxes from Eqs. (21) and (22). Subtractingthem from each other finally gives the current I.

The present transport problem has a very interestingfeature under limiting conditions. Let us assume arbi-trarily that the formal transfer potential of M+ is lesspositive than that of A−. When the interface is polar-ised, M+ begins to transfer before A−. Apparently, thecurrent limit is reached when c2

w,s=c1w,s−c4

w,s=0, i.e.when c1

w,s=c4w,s. At this potential, c3

o,s=c4o,s−c1

o,s=c1

w,s(u4−1−u1) which must also be positive or zero.

Therefore, u1u451 which means that

Dowf51

2(Dowf1

0%+Dowf4

0%) (36)

This result is rather surprising. Eq. (36) means thatelectroneutrality dictates the upper limit which the Gal-vani potential difference can reach. Increasing the ap-plied cell potential further does not increase theGalvani potential but the potential drop is expended inthe form of ohmic loss. As shown in the Appendix A,the current increases as a linear function of the appliedcell potential. In this communication, this has actuallybeen observed for the first time. It has to be emphasisedthat Eq. (36) results from electroneutrality consider-ations only, and does not assume any particular trans-port process, but only that the partition equilibria, Eq.(1), apply.


Fig. 2. The effect of the separation between the formal transferpotentials on the current–voltage curve: Do

wf10%−Do

wf40%= −100 mV

(—), −200 mV (– · – · –), −300 mV (– · · – · · –), −400 mV(– – –) and −500 mV (- - -). Cr=1 and j4=5.

Fig. 3. The effect of the concentration ratio, Cr, on the current–voltagecurve: Cr=100 (—), 10 (– · – · –), 1 (– · · – · · –), 0.1 (– – –) and 0.01(- - -). Do

wf10%−Do

wf40%= −300 mV and j4=5.

formal transfer potentials, as could be anticipated. InFig. 3, the concentration ratio is varied between 0.01and 100, keeping the difference between the formaltransfer potentials constant, −300 mV; j4=5. Varyingj4 does not introduce any significant differences be-tween the curves. The lower j4 is, the steeper is theslope of the second current wave as it is mainly due toA− transfer, and the decrease of j4 means the increaseof D4

w.

3. Experimental

Tetrabutylammonium tetraphenylborate (TBATPB)and tetrabutylammonium tetrakis(4-chlorophenyl)borate (TBATPBCl) were prepared as previously de-scribed [21]. 1,2-dichloroethane (Rathburn Chemicals)was used as received and aqueous solutions were pre-pared using MQ® water. All other reagents used wereof analar grade. The experimental arrangement for themicrohole assembly is as described elsewhere [16]. Mi-croholes used in this study were a kind gift fromProfessor H.H. Girault, EPFL Switzerland. Thepolyester films containing a single microhole were gluedto a glass cylinder using a solvent resistive glue (730RTV Dow-Corning, UK). The diameter used was 10mm. The cells used were as shown in Scheme 1, whereX=Li, Na, K, H, Cs, Rb or tetraethylammonium(TEA); DCE denotes dichloroethane. The concentra-tion of the aqueous phase chloride (y) was varied in therange from 0.001 to 1 M while that of the organic base(x) was varied from 10 mM to 50 mM. Slow sweepcyclic voltammetry was used to investigate the transfer.The scan rate used was 25 mV s−1 and the resultingI–E plots were taken to be at steady-state.

2.4. Simulations

The theoretical steady-state I–E curves were simu-lated assuming that Do

wf10%BDo

wf40%, thus M+ is trans-

ferred before A−. This does not restrict the analysis byany means because of the symmetry of the case hereconsidered. A more general approach with arbitrarycharge numbers, as in Oldham’s treatment [1], would beunnecessarily difficult to follow. A simulation pro-gramme was written in Microsoft Fortran® 5.1 and runin a Pentium processor PC. In all the simulations j1 hasbeen given a value of 0.7.

In Fig. 2, a simulation showing the effect of thedifference between the formal transfer potentials isshown. The concentration ratio Cr is 1 and j4=5which corresponds roughly to the experimental systemused. In the y axis, Id means the diffusion limitedcurrent

Id=2pFD1wcb

wr0 (37)

In practice, the limiting current is Id=4FD1wcb

wr0 (seeSection 4) but it does not matter here because the effectof the microhole geometry is cancelled in the nor-malised current. As can be seen, the normalised limitingcurrent takes the value of 2 because of the migrationcomponent. The notation of the potential axis is E−E1°to emphasize the difference between the Galvani poten-tial and the cell potential, the latter of which includesalso the potential drops in the diffusion boundarylayers as given by Eqs. (23) and (26):

E=Dowf+ (fw,b−fw,s)+ (fo,s−fo,b) (38)

The second current wave is shifted towards more posi-tive potentials with an increasing difference between the


Scheme 1.

The potential was that of the water phase with respectto the organic phase and a positive current was definedto correspond with the transfer of an anion from theorganic to the aqueous phase or a cation in the oppo-site direction. The contribution of the reference junc-tion, TBACl(w%), was subtracted from the total cellpotential as usual [34].

4. Results and discussion

Microhole supported ITIES have been found previ-ously to behave analogously to an inlaid microdiscelectrode of similar dimensions [16] and the diffusionlimited current for the transferring species in the pres-ence of an excess base electrolyte is Id=4FDcr0. Asalready stated, in the absence of the base electrolyte,this equation needs to be modified to account for themigration contribution from charged species to themeasured current and the limiting current is enhancedor, in some special cases [6], diminished. Previously,Osborne et al. [16] studied the transfer of tetramethyl-ammonium cation (TMA+) from the aqueous phase,where it was a trace ion, to the organic phase, theelectrolyte concentration of which was lower than thatof the transferring ion. In that case, TMA+ is trans-ferred in the aqueous phase, solely by diffusion,whereas in the organic phase, by diffusion and migra-tion. Therefore, the limiting current was unaffected bythe decreased concentration of the organic phase elec-trolyte but the half wave potential shifted as it wasdecreased from excess to trace.

When base electrolytes are completely absent in bothphases, diffusion–migration prevails for the transfer-ring ions. As a consequence, the limiting current will beincreased by a factor of two in the absence of the baseelectrolyte, as can be seen easily by setting A=0 inEqs. (21) and (22), with A being defined in Eq. (29).This enhancement can be seen only if the ion can alsobe transferred as a trace ion, e.g., TPB− and TEA+.For these ions, measurements were carried out both inthe presence of excess base electrolyte and in its com-plete absence. The ratio of the limiting currents in thesetwo experiments, scaled by the concentrations, wasapproximately 2, see Fig. 4. This was also observed forTEA+, although not shown here. It was not possible toobserve the transfer of the other cations (Na+, Li+,H+, K+) as trace ions, because base electrolyte ions

with more positive transfer potentials are not available.Similarly, for TPBCl− which is normally used as a baseelectrolyte anion, the trace case could not beinvestigated.

4.1. M+ –TPBCl− systems

Interest here is limited to the positive portion of thepotential window, i.e. as the aqueous side of the inter-face becomes increasingly positive. Here, it is assumedthat the aqueous cation transferring first as TPBCl− isvery hydrophobic. According to the theory, a limitingcurrent is observed only when the transfer potentials ofthe anion in the organic phase and the cation in theaqueous phase are sufficiently different. For Li+, K+,H+ and Na+, a wave was not obtained but the currentincreased almost linearly with potential, see Fig. 5. Theion with the lower Gibbs energy of transfer is predictedto transfer first. Comparing a series of ions as in Fig. 5,this should be in line with the order of increasingtransfer energies. As can be seen from the figure, theorder is Li+\Na+\H+\K+ and this is consistentwith some literature data, but not all [20–22], Ch. 1 in[17]. It has to be noted, however, that Fig. 5 actuallyreflects the order of the formal transfer potentials of thecations. This quantity includes the effect of ion-pairing[23]. Furthermore, for the case of H+, an EC mecha-

Fig. 4. Comparison of the trace ion transfer and the present theory:0.5 mM TBATPB in 10 mM TBATPBCl (—) and 1 mM TBATPB asthe base electrolyte (– · · – · · –). The aqueous phase is 1 mM LiCl.The first current is multiplied by two to make the comparison clearer.E refers to the cell potential corrected for the reference junction.


Fig. 5. Steady-state I–E curves for different cations in the aqueousphase: K+ (—), H+ (– – –), Na+ (– · – · –), Li+ (- - -), andTEA+ (– · · – · · –). Organic phase 1 mM TBATPBCl, aqueousphase 1 mM MCl. (E as in Fig. 4.)

Fig. 6. Steady-state I–E curves keeping the concentration ofTBATPB at 10 mM, and varying the aqueous phase concentration(LiCl): 1 mM (—), 10 mM (– – –) and 1 M (- - -). (E as in Fig. 4.)

4.2. M+ –TPB− systems

TPB− is predicted to transfer first as its transferpotential is less positive than most cations studied[17,20,21]. For M+ =Li+, Na+or H+ a wave wasobserved followed by a ramp increase in current withpotential, the slope of which was dependent on theconcentration of the aqueous cation, see Fig. 6, wherethe Li+ case is shown as an example. As the limitingcurrent followed the TBATPB concentration (see Fig.7), TPB− is the ion which transfers before thesecations, consistent with the earlier observations usingmicropipettes [23,24]. Comparing Fig. 6 with the simu-lations given in Fig. 3, it can be seen that the effect ofthe concentration ratio on the experimental I–E curves

nism, where the proton reacts with TPBCl− in theorganic phase, has been verified [25].

Comparing Fig. 5 with Fig. 2, it can be seen that theramp shape is obtained where the transfer potentialsare not well separated. It can be concluded that theformal transfer potential of TPBCl− is of the order of100 mV higher than those of the above listed cations.Obviously, its accurate determination is not feasiblefrom a voltammetric wave. Note also that in the simu-lations of Fig. 2, the potential axis is scaled by aconstant E1°% whereas in Fig. 5 each cation has its ownE1°%. The slopes of the ramps are varying because theydepend on both j4 and y1, the latter of which in turndepends on u1 (see Appendix A). Previously, Oldham[1] predicted this type of behaviour for a reaction wherea univalent cation is reduced to a univalent anion, yetthis case has not been observed experimentally at solidelectrodes.

The transfer potentials of TPBCl− and TEA+ are,however, separated by at least 500 mV, and as ex-pected, a wave corresponding to TEA+transfer wasobtained in Fig. 5. For further increases in cell poten-tial, surface phenomena could be noted as the voltam-mogram became noisy with current spikes indicatingpossible formation of TEATPBCl in the interfacialregion. The other two cations studied, the transferpotentials of which should have been separated suffi-ciently from that of TPBCl− were Rb+ and Cs+. Inthis case, prior to the expected limiting current region,there was an abrupt decrease in the current during theforward scan while on the reverse scan a sharp peaksimilar to that observed in the anodic stripping of asurface film [35] was observed. From this, it can beconcluded that Rb+ and Cs+ form an interfacial filmwith TPBCl−.

Fig. 7. Steady-state I–E curves scaled by the concentration ratio. Theaqueous phase concentration (LiCl) is kept constant, at 1 mM, andthe concentration of TBATPB is varied: 1 mM (—), 10 mM (– – –)and 50 mM (- - -). (E as in Fig. 4.)


Fig. 8. Steady-state I–E curves of the system 1 mM TBATPB in1,2-dichloroethane and 1 mM KCl in water: experimental curve(– · · – · · –) and after correction for the ohmic drop (—). (E as inFig. 4.)

Fig. 9. A plot of Dowf versus ln (Ilim /I−1) in the same case as in Fig.

8 after correction for the ohmic drop. The solid line has the slope of60 mV per decade.

The absence of a subsequent current increase cannotalso be due to the extremely large (2 V) separation ofthe transfer potentials. A more probable reason isextensive ion-pairing in the organic phase. The ion-pairing constant, Ka, between Rb+ and TPB− has beenestimated previously to be as high as 7.4×107 M−1

[36] and it is reasonable to assume that Ka for K+ andTPB− is of the same order of magnitude. In Fig. 10,the concentration profiles of all the four ions have beenpresented in the absence of ion-pairing and close to thelimiting conditions. As can be seen, the polarisation ofthe counter ions (Cl− in the aqueous and C+ in theorganic phase) is responsible for the potential drops inthe diffusion boundary layers. Assuming extensive ion-pairing, there are only trace amounts of free M+ in the

is in line with theoretical predictions. Note that in thesimulations M+ is transferred first and therefore, theconcentration ratio has to be inverted in Fig. 3. Theexperimental curves in Fig. 6 intersect and a probablereason for this is the inaccuracy in the estimation of thesingle ionic activities, when subtracting the referencejunction potential from the total cell potential.

An interesting behaviour was noted for K+ andRb+ transfer in that only one wave was observed andthere was no subsequent increase in current. Instead thelimiting current remained constant for increases in thecell potential of up to 2 V for all concentration ratios.The limiting current followed the TBATPB concentra-tion from 10 mM to 10 mM with some deviations athigher concentrations of TBATPB. From this, it couldbe assumed that only one ion, TPB−, is transferred. Inthis case, Oldham’s treatment [2] can be modified toapply at ITIES, and the potential drop in the diffusionboundary layers is given by

(fw,b−fw,s)+ (fo,s−fo,b)=RTF

ln�1+ (Crj)−1X

1−X�(39)

where X=I/Ilim, and the limiting current, Ilim=2×Id=8FD4

ocbor0. Eq. (39) shows that when X ap-

proaches 1, the potential drop goes to infinity. There-fore, an infinitely wide plateau region is observed in theexperimental curve. Applying Eq. (39) to the case ofK+ where a definite limiting current is observed, alinear slope of 57.5 mV per decade is obtained in theplot of Do

wf versus ln [(Ilim−I)/I ], thus indicating re-versible transfer, see Figs. 8 and 9. This is one explana-tion, which is however not very plausible as this wouldpredict that K+ and Rb+ do not transfer at all.Considering work published previously, this is clearlynot the case.

Fig. 10. Simulated concentration profiles at Dowf−Do

wf01%=48 mV;

Dowf1

0%−Dowf4

0%= −100 mV and Cr=1; M+ (—), Cl− (- - -), C+

(– · – · –) and A− (– – –). Aqueous phase resides at r/r0B−1 andthe organic phase at r/r0\1.


Fig. 11. Steady-state I–E curves keeping the concentration ofTBATPB at 1 mM, and varying the aqueous phase concentration(KCl): 1 mM (—), 10 mM (– · · – · · –), 0.1 M (– – –) and 1 M(- - -). (E as in Fig. 4.)

even at its limiting current, the organic phase remainspractically binary, the fluxes of TEA+ and TPB− arenot coupled and consequently, the ramp shaped currentdoes not develop. At higher values of Cr, the first wavewas still visible but the rest of the voltammogram wascompletely distorted by current spikes thus hiding thepossible current ramp.

In this communication, Tafel slopes or other diag-nostic criteria have not been presented, apart from theexemplary case of K+. This is due to the difficulty ofcorrecting the experimental potential scale for theohmic drop as the correction is extremely sensitive tothe exact determination of the limiting current. Also,the present theory gives the ohmic drop as a function ofthe surface concentrations which are not directly mea-surable, and not as a function of the current. It is ofquestionable merit deriving new diagnostic criteria forthe present, undoubtly special case. The aim of thepresent paper was, however, to assess the viability ofzero added base electrolyte in studies at ITIES and todetermine why the current increased linearly as a func-tion of the potential without reaching a limiting valueunder certain experimental conditions.

5. Conclusions

To summarise, the model outlined in the theoreticalsection predicts that in the absence of added baseelectrolyte a wave shaped voltammogram characteristicof diffusion limited transfer can be observed only if thetransfer potentials of the aqueous and organic ionstransferring simultaneously are sufficiently separated.The species with the lower transfer potential will limitthe current and subsequent increase in current after theplateau region is due to the transfer of the ion to theopposite phase. Agreement with these predictions isexcellent for the case where TPBCl− was used as theorganic anion for most aqueous cations studied. Theonly deviations were observed for Rb+ and Cs+ and inthis case, solid phase formation was obvious, as hasbeen noted previously [35]. For the case where TPB−

was used as the organic anion, the agreement wassatisfactory for Na+, Li+ and H+. However, K+,Rb+ and Cs+ are known to be strongly ion-pairedwith TPB− [18,27,29,31,34] and the current theory doesnot describe this phenomenon.

The model shows that due to the coupling of thefluxes via the electroneutrality condition, the Galvanipotential difference across the interface cannot exceedan upper limit, namely the average value of the transferpotentials of the transferring ions. Coupling has alsoanother important consequence, i.e. the position of thecurrent ramp due to transfer of an ion with a higherabsolute transfer potential depends on the transfer po-tential of the ion transferring first. Therefore, this

organic phase, hence the system remains binary. There-fore, the concentration profile of TPB− is practicallyidentical to the one of C+ (TBA+), and consequently,the potential drop in the organic phase approaches thatof Eq. (39). In this case the current is carried solely byTPB− and it cannot exceed Ilim defined above, resultingin an infinitely wide plateau. Quantitative mathematicalanalysis is not feasible and neither can Oldham’s recenttheory [3], which considers ion-pairing at ITIES assuch, be applied due to the different degrees offreedom.

If ion-pairing is considered as a form of facilitatedion transfer (FIT), the position of the current wavevaries with the concentration ratio Cr. For FIT, when[M+]� [A−], the half-wave potential is shifted 59 mVper log [M+] in the negative direction [37], and this wasactually observed for the case of K+ and TPB−, seeFig. 11. Yet it should be noted that only the first sweepwas at steady-state and on repetitive scanning, a broadcurrent peak was developed during the forward scan.When [M+]� [A−] a similar shift in the half-wavepotential should be obtained. In our case, however, theshift was in the opposite direction and the limitingcurrent did not follow [K+]. Therefore, this clearlyindicates a change of transfer mechanism when TPB−

is in excess. For Cs+, the current was distorted byphase formation, similar to the case where TPBCl−

was used as the organic anion. The ion-pairing constantof CsTPB is probably of the same order of magnitudeas that of KTPB or RbTPB but the solubility of CsTPBis very low [18], thus causing precipitation.

For TEA+, two waves were observed with low Cr

(0.01), the first corresponding to the transfer of TEA+

and the second to TPB−. Because the concentration ofTEA+ in the organic phase remains at the trace level


makes the determination of the transfer potential of thesecond transferring ion more difficult.

As can be seen, the advantage of zero added baseelectrolyte is questionable as little additional informationcan be obtained, while the transport problem is compli-cated by migration contributions. Therefore, when study-ing the detailed mechanism of ion transfer across theITIES, the use of supporting electrolyte at sufficientconcentration is more advantageous. In this case, thepolarisation of the supporting electrolyte becomes in-significant, and as a consequence, coupling between theionic fluxes is weakened. Also, ion-pairing can simply betaken into account through the formal transfer potential[18,19,23], because the counter-ion concentration can betaken as a constant. Ion-pairing thus only shifts theformal potential.

Acknowledgements

B.Q. and L.M. thank the Academy of Finland forresearch fellowships. R.L. acknowledges the Neste Foun-dation for financial support.

Appendix A. Why is the I–E curve a ramp close to thelimiting conditions?

The total cell potential (corrected for the referencejunction) is the sum of the Galvani potential differenceand the ohmic loss:

E=Dow8+ (8w,b−8w,s)+ (8o,s−8o,b) (A1)

where E is also scaled by F/RT. Using Eqs. (20), (23) and(35) gives in the aqueous phase

8w,b−8w,s= − ln (y1−y4)= −g ln (y1) (A2)

where y4=c4w,s/cw

b . In the organic phase we have

8o,s−8o,b= − ln [C r−1(y4/u4−y1u1)]

= − ln [u1C r−1(y1−y4)] (A3)

The latter equality holds because at the limiting condi-tions 1/u4=u1 and y1=y4 (see the discussion above Eq.(36)). Let us choose for the sake of convenience Cr=1.Eq. (A3) then gives, extracting ln (u1)

8o,s−8o,b= − (Dow8−Do

w810%)− ln (y1−y4) (A4)

From Eqs. (A1), (A2) and (A4) one obtains:

E−Dow81

0%= −2 ln (y1−y4)= −2g ln (y1) (A5)

The current is given through Eqs. (12) and (13), notingthe sign reversal in Eq. (27), as

IId

= − (1+g)(y1−1)+j4−1(1−g)(y1−1)

= (y1−1)[j4−1−1−g(j4

−1+1)] (A6)

where Id is defined by Eq. (37) and j4 below Eq. (9).Solving g from Eq. (A5) gives

IId

= (y1−1)�

j4−1−1− (j4

−1+1)E−Do

w810%

2 ln (y1)n

(A7)

which is the desired equation for the straight line. y1 canbe solved from Eq. (33) as

y1=C r

−1+j1

u1+j1

(Cr=1) (A8)

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