Contact Galvani potential differences at liquid j liquid interfacesPart I: Experimental studies on single salt distribution at liquid j liquid

interfaces using a streaming technique

Henrik Jensen, Valerie Devaud, Jacques Josserand, Hubert H. Girault �Laboratoire d’Electrochimie Physique et Analytique, Institut de Chimie Moleculaire et Biomoleculaire, Ecole Polytechnique Federale de Lausanne,

CH-1015 Lausanne, Switzerland

Received 6 June 2002; received in revised form 28 August 2002; accepted 30 September 2002

Abstract

The distribution potential established when two liquids are placed in contact has been measured using a streaming technique. In

particular the contributions from the diffusion potentials have been quantified. On the basis of the experimental results, the concept

of distribution potentials upon the partition of a salt between two phases is revisited. We also compare Galvani potential differences

for solutions in equilibrium and for situations where two liquids are placed in contact, as encountered in micro-TAS systems and

micro-reactors. Finally, it is shown that in potentiometry we can define, as in traditional amperometry, a half-wave potential that

takes into account the mass transfer of the salt to the interface.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Liquid j liquid interfaces; Diffusion; Potential; Ion flux; Conductivity

1. Introduction

When two electrolyte solutions are placed in contact,

the distribution of the ions between the two phases

induces a polarisation of the interface that results in a

Galvani potential difference being established between

the two phases. This polarisation of the interface can be

calculated at equilibrium, provided that the initial

concentrations of the ions in the two phases prior to

contact and the standard Gibbs energies of transfer of

the different ionic species are known [1,2].

The equilibrium polarisation of the interface resulting

from the distribution of a single salt has been known for

a long time [3] and several theoretical accounts have

appeared since the end of the 19th century [4,5]. By the

early 70s, the interest in interfaces between immiscible

electrolyte solutions had a revival following the pioneer-

ing work of Gavach and Davion [6]. In one of the more

recent contributions Hung has presented a general

methodology to calculate the Galvani potential differ-

ence when more than two ions are present [2,7].

Unfortunately no general analytical solution exists and

numerical methods are therefore required.

In practice, the potential across the interface between

two liquids (miscible as well as immiscible) is often far

from equilibrium. In fact, during the establishment of

equilibrium the diffusion of ions from one phase to the

other will establish a diffusion potential depending on

the ionic mobility differences. Although the concepts of

distribution and diffusion potentials are well known

only a few contributions have attempted to give a

uniform description of the phenomena [8].

In the present paper the subject is addressed from an

experimental point of view by using a streaming

electrode to ensure that equilibrium is not established

within the timescale of the potential measurements. A

uniform theoretical treatment based on theoretical work

by Hung [2,9] and Kakiuchi and Senda [8,10] is used to

interpret the results. The theoretical development is

extended to include a description of potentiometry and

amperometry in the equilibrium case as well as in the

non-equilibrium case.

� Corresponding author. Tel.: �/41-21-693-3145; fax: �/41-21-693-

3667

E-mail address: hubert.girault@epfl.ch (H.H. Girault).

Journal of Electroanalytical Chemistry 537 (2002) 77�/84

www.elsevier.com/locate/jelechem

0022-0728/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.

PII: S 0 0 2 2 - 0 7 2 8 ( 0 2 ) 0 1 2 5 0 - 0

One of the key motivations for this work is to be able

to predict the potential differences established when two

laminar flows are brought in contact in m-TAS and

micro-reactors. This has for instance implications for

the optimisation of synthesis [11] and ion extraction

[12,13] in microdevices.

2. Experimental

The streaming electrode concept has been widely used

to measure the potential of zero charge on mercury [14�/

16], but also that of liquid j liquid interfaces [17]. We

adapt here this methodology to measure either diffusion

potentials or contact potentials when using two immis-

cible electrolyte solutions. In fact, this experimental

methodology dates even further back, since systems

based on moving boundaries (albeit using a somewhat

different set-up) have previously been used to measure

liquid junction potentials [18�/22].

As shown in Fig. 1, the principle of the technique is to

flow one solution (solution 1) through a fine capillary

tip into another solution (solution 2). If the two

solutions are of the same solvent, solution 1 streams

into solution 2 whereas if the two solutions are

immiscible, a spray of solution 1 in solution 2 can be

observed. A syringe pump (Cole Palmer, 74900 series,

USA.) is used to control the flow rate of solution 1

through the capillary. The potential of Cell I is

measured using a high input impedance pH-meter/volt-

meter (Tacussel, LPH 530T, Ion-meter, Fr).

The reference electrodes are silver/silver halide elec-

trodes prepared daily and crosschecked between each

experiment.

3. Results and discussion

3.1. Experimental methodology and validation

In order to validate the streaming technique, we have

measured the diffusion potentials corresponding to

hydrochloric acid, lithium chloride, sodium chloride,

potassium chloride, tetramethylammonium chloride(TMACl), tetrapropylammonium chloride (TPrACl)

and tetrabutylammonium chloride (TBACl). The result-

ing electrochemical cell was (Fig. 1):

Ag ½ AgCl ½ MCl(1) (x mM)½½MCl(2) (10 mM)

½ AgCl ½ Ag Cell I

Fig. 2 shows the results obtained for TPrACl and Table

1 reports the data for the other salts studied.

The cell potential difference of cell I is simply a

diffusion potential due to the different ionic mobilities

of M� and Cl�. The slope of the variation of themeasured potential can be compared with the equation

describing diffusion potentials [23].

Dfdiff �RT

F(tC� �tA� ) ln

�c1

c2

�

�RT

F(2tC� �1) ln

�c1

c2

�(1)

If we assume that the Ag/AgCl electrodes give a

theoretical response of 60 mV per decade of chloride

concentration, the potential difference of Cell I should

be

Ecell I�RT

F(tC� �tA� �1) ln

�c1

c2

�

�RT

F(2tC� ) ln

�c1

c2

�(2)

A first observation when using a streaming technique

is that the diffusion potentials are established quasi-

instantaneously. The values of the variation of the

diffusion potential measured upon changes of concen-

tration corroborates quite well those predicted by Eq.

(2). We can therefore conclude that the streaming

Fig. 1. Streaming electrolyte cell. Fig. 2. Diffusion potentials for TPrACl measured using Cell I.

H. Jensen et al. / Journal of Electroanalytical Chemistry 537 (2002) 77�/8478

method provides a reasonable approach to measure

contact potentials, which in the case of streaming water

in water are simple diffusion potentials.

To calculate the variations given in Table 2, we

carried out a linear regression for the concentrations

of solution 1 greater or equal to that of solution 2. As it

happens, the diffusion potential values measured when

the concentration of solution 1 was lower than that of

solution 2 were often found to be lower than the

theoretical values. This finding may be due to the

geometrical potential distribution using the streaming

method, and will be discussed in part II of this series, by

using a finite element simulation of the potential map.

3.2. Contact and equilibrium partition of a single salt,

A�C�, between two immiscible phases

3.2.1. Equilibrium distribution potential and interface

polarisability

The Galvani potential difference, Dwof; between two

phases (o and w) in equilibrium can be expressed

according to the Nernst equations for the ionic distribu-

tions of the respective ions. The Nernst equation for the

cation C� reads

Dwof�Dw

ofoC� �

RT

Fln

�ao

C�

awC�

�(3)

and that for the anion

Dwof�Dw

ofoA��

RT

Fln

�ao

A�

awA�

�(4)

where Dwof

o is the standard transfer potential which is

related to the Gibbs energy of transfer by

Dwof

oi �DGo;w0o

tr;i =ziF (5)

Following the derivation by Hung [2], but taking into

account a volume phase ratio, f�/Vo/Vw, different from

unity we arrive at the following equation:

ctotC�

1 � f expF (Dwo f�Dw

o fo?C� )=RT

�ctot

A�

1 � f exp�F (Dwo f�Dw

o fo?A� )=RT

�0 (6)

where ctot is defined by ctoti �cw

i �fcoi and where Dw

ofo?

is the formal transfer potential taking into account theactivity coefficients [1].

To evaluate the equilibrium Galvani potential differ-

ence by a graphical approach, we can draw the bulk

aqueous charge qw defined by Eq. (7) as a function of

the Galvani potential difference Df ,

qw�cwC� �cw

A� (7)

and then determine the Galvani potential value where

the bulk aqueous charge is equal to zero. This condition

Table 1

Diffusion potentials in mV measured using cell I at different flow rates

c /mM Flow rate/ml h�1

2.5 5 10

Potential for Cell I with HCl in 10 mM HCl

0.1 169.4 169.2 168.1

1 99.4 99.7 99.9

10 1.8 1.6 1.5

100 �91.2 �91.2 �90.7

Potential for Cell I with LiCl in 10 mM LiCl

0.1 62.9 64.9 56.6

1 40.0 39.5 38.5

10 1.3 1.2 1.1

100 �33.9 �34.2 �34.4

Potential for Cell I with NaCl in 10 mM NaCl

0.1 65.4 64.7 62.3

1 42.7 42.1 41.5

10 1.1 1.0 0.9

100 �44.1 �44.2 �44.3

Potential for Cell I with KCl in 10 mM KCl

0.1 46.5 48.2 49.0

1 54.8 50.4 48.8

10 �0.8 �0.8 �0.6

100 �53.5 �53.6 �53.4

Potential for Cell I with TMACl in 10 mM TMACl

0.1 94.9 96.2 92.3

1 43.4 43.0 42.9

10 0.7 0.4 0.2

100 �38.2 �38.4 �38.4

Potential for Cell I with TBACl in TBACl

0.1 44.4 46.5 42.8

1 22.8 22.7 22.1

10 0.7 0.4 0.1

100 �20.3 �20.4 �20.4

Table 2

Comparison of the variation of the experimental diffusion potential values as a function of concentration of solution 1 (in mV/decade) and the

theoretical values provided by Eq. (2). The values given are average values

Salt

HCl LiCl NaCl KCl TMACl TPrACl TBACl

Experimental values 95 37 43 52 42 26 21

Theoretical values 98 40 47 58 44 28 24

/tM�/ 0.821 0.336 0.396 0.490 0.370 0.235 0.203

The transport numbers are obtained from literature values of limiting equivalent conductivities of ions in water at 25 8C [33].

H. Jensen et al. / Journal of Electroanalytical Chemistry 537 (2002) 77�/84 79

represents the electroneutrality condition of the aqueous

phase and equivalently that of the oil phase.

In the case of a 1:1 electrolyte, the total concentration

of the cation and the anion are equal. Fig. 3 illustrates

the qw as a function of Df for different formal transfer

potential values. At very negative potential values, qw

corresponds to a hypothetical system where all the

cations are in water and all the anions are in the non-

aqueous phase. Inversely, at very positive potentials, qw

corresponds to the hypothetical case where all the

anions are in water and all the cations in the organic

phase. When the formal potentials of the cation and the

anion are separated by more than 180 mV, the formal

potential values represents the two inflexion points on

both sides of the graph. In any case, the equilibrium

Galvani potential difference is obtained as the central

inflexion point.

Fig. 3 shows that when the standard transfer poten-

tials are separated by more than 240 mV, the interface

becomes polarisable around the equilibrium value as it

becomes possible to vary the Galvani potential differ-

ences without altering significantly the chemical compo-

sition of the phases and therefore the electroneutrality of

the adjacent phases. Inversely, if the standard transfer

potentials are separated by less than 240 mV, the

interface is non-polarisable as the condition of electro-

neutrality fixes the equilibrium Galvani potential differ-

ence. By definition, a non-polarisable interface is one

where a small variation of the potential difference would

result in a significant charge transfer and thereby break

the electroneutrality rule.

It is also interesting to make a comparison of the

steady state amperometric response as a function of

potential for a system comprising a single salt distrib-

uted between two adjacent phases. When a species i

transfers from water to the organic phase under steady

state conditions (for example using a micro-interface or

a hydrodynamic method such as polarography) [24�/27],

we can define a diffusion limited current

Idw�ziFA Dwi cbw

i =dw (8)

Similarly, for a species transferring from the organic to

the aqueous phase, we have

Ido��ziFA Doi cbo

i =do (9)

The current, I , is defined as the transfer of a positive

charge from water to oil or of a negative charge from oil

to water. In a steady state mode, the surface concentra-

tions are related to the bulk concentrations by

cswi �cbw

i �dwI

ziFADwi

�dw

ziFADwi

(Idw�I) (10)

and

csoi �cbo

i �doI

ziFADoi

�do

ziFADoi

(I�Ido) (11)

By substituting these surface concentrations into the

Nernst equation for the species i, we can write

Dwof�Dw

ofo?i �

RT

ziFln

�Dw

i do

Doi dw

��

RT

ziFln

�I � Ido

Idw � I

�(12)

and also define the half-wave potential by

Dwof1=2�Dw

ofo?i �

RT

ziFln

�Dw

i do

Doi dw

�(13)

If we express the current as a function of potential, we

have:

I �Idw

1 � exp�ziF (Dwo f�Dw

o f1=2)=RT

�Ido

1 � expziF (Dwo f�Dw

o f1=2)=RT(14)

To establish a comparison between the amperometriccase and the equilibrium partition case, we can write Eq.

(6) as

ctotC�

1 � expF (Dwo f�Dw

o f1=2;C� )=RT�

ctotA�

1 � exp�F (Dwo f�Dw

o f1=2;A� )=RT

�0 (15)

with

Dwof1=2�Dw

ofo?�

RT

ziFln f (16)

We can therefore conclude that for both a potentio-

metric approach and an amperometric approach, it is

possible to define a half-wave potential that corresponds

to an apparent standard transfer potential.

The concept of half-wave potential in potentiometryis interesting when dealing with the polarisability of an

interface upon distribution of a single salt. For example,

consider a salt such that the difference of the standard

transfer potentials of the two ions is 120 mV. As seen

Fig. 3. qw as a function of the Df for a system comprising a cation

having a formal transfer potential value DfoC���0:12 V and an anion

A� with the respective formal transfer potential values DfoA��

0:06; 0:12; 0:18; 0:24 V: The phase ratio was assumed to be one.

H. Jensen et al. / Journal of Electroanalytical Chemistry 537 (2002) 77�/8480

above, when the phase ratio is unity the interface is non-

polarisable as the potential is unequivocally fixed.

However, when the phase ratio is 1000 the half-wave

potential shift according to Eq. (16) as shown in Fig. 4and the interface becomes more polarisable. In terms of

absolute value, the distribution potential does not

depend on the phase ratio and the equilibrium distribu-

tion potential for this simple case of the distribution of a

single salt can be calculated using Eqs. (3) and (4) which

simply yields

Dwofdis�

Dwof

o?C� � Dw

ofo?A�

2

�Dw

ofoC� � Dw

ofoA�

2�

RT

2Fln

�go

C�gwA�

gwC�go

A�

�(17)

The salt concentration ratio, also called the salt

partition coefficient, is given by:

KP�co

C�A�

cwC�A�

�exp�F (Dwo f

o?C��Dw

o fo?A� )=2RT (18)

In conclusion, Fig. 4 shows that the distribution

potential is independent of the phase ratio, whereas

the polarisability is strongly dependent on it.

3.2.2. Contact distribution potential

The streaming technique validated above for stream-

ing water in water may be used for immiscible electrolyte

solutions as well. Obviously, in this case the choice of

salt is more restricted. We have measured the potential

of the following cell:

Ag ½ AgBr ½ TBABr(1) (streaming) (x mM)½½TBABr(2)

(0:46 mM in DCE)½½14:53 mM TBABr(3)½AgBr ½ Ag

Cell II

At the right end of the cell, the Galvani potential

difference between the organic and the aqueous side is

governed by an equilibrium distribution potential (Eq.

(17)) whereas that on the left side is a contact potential

difference (i.e. a non-equilibrium situation). To reach an

equilibrium partition on the right side, 100 ml of 10 mM

TBABr dissolved in 1,2-dichloroethane was equilibratedwith 50 ml of 10 mM TBABr dissolved in water. The

partition coefficient of this salt can be calculated from

Eq. (18) and found to be equal to 0.032 (/DGotr; TBA� �

�22; DGotr; Br� �39 kJ mol�1); which gives the concen-

trations listed in the diagram of cell II assuming a

complete equilibrium.

When two electrolyte solutions are placed in contact,

for example by flowing one phase into another (as in thiswork) or by contact of two laminar flows (as in a micro-

TAS device), the surface concentrations adjust quasi-

instantaneously according to a surface equilibrium. To

make an analogy with chronoamperometry, we state

that, considering that the ion transfer reaction is fast

compared with mass transfer of the ions in the adjacent

phases, we have a ‘reversible system’ where the inter-

facial Galvani potential difference is always given by theNernst equation for the interfacial concentrations.

To calculate the Galvani potential difference which

results from this surface equilibrium, the equation

corresponding to the conservation of the mass has to

be replaced by a condition of zero current. The latter

can also be written as an equality of the flux of the two

species across the interface.

JwC� ��Jo

C� (19)

JwA� ��Jo

A� (20)

I �JwC� �Jw

A� �JoC� �Jo

A� �0 (21)

In the absence of a current contribution from convec-

tion, the flux in the diffusion layers adjacent to the

interface comprises diffusion and migration terms,

which can be written as:

Ji��ciui grad mi��Di grad ci�ziFciui grad f (22)

where ui is the electrochemical mobility of the species i.

The zero current condition in the electrolyte means that

in the diffusion layer both the anion and cation move at

the same speed as a diffusion potential difference is

established to slow the ion with the highest electro-chemical mobility and speed up the ion with the lowest

electrochemical mobility. Indeed, from the zero current

condition which reads

I �F (�DwC� grad cw

C� �FcwC� uw

C� grad f)

�F (�DwA� grad cw

A� �FcwA� uw

A� grad f)

�0 (23)

it is easy to show by rearranging Eqs. (21) and (22) that

the system behaves as if the salt was diffusing with a

mean diffusion coefficient defined by [28]

JC� �JA� ���DC�A��grad cC�A� (24)

with

Fig. 4. qw as a function of the Df for a system comprising a cation

having a formal transfer potential value DfoC���0:06 V and an anion

A� with the respective formal transfer potential value DfoA��0:06 V

when the apparent phase ratio is equal to 1, 10, 100, 1000.

H. Jensen et al. / Journal of Electroanalytical Chemistry 537 (2002) 77�/84 81

�DC�A���DC� uA� � DA� uC�

uC� � uA�

�2RTuC� uA�

uC� � uA�

(25)

For systems where a diffusion layer of thickness d is

established on either side of the interface (e.g. micro-liquid j liquid interfaces or interfaces with hydrody-

namic control) [24�/27], Eqs. (20), (21) and (24) yields

�DwC�A��

dw(cw

C�A� �cwsC�A�)

���Do

C�A��

do(co

C�A� �cosC�A�) (26)

where csi is the surface concentration just outside the

diffuse layer also called the Gouy�/Chapman layer. To

establish a correlation between the case of equilibrium

partition and the case of contact partition, we can write

the conservation of mass as [10]

cwsi �fd cos

i �ctoti (27)

by defining a dynamic phase ratio, fd which depends on

the thickness of the diffusion layers and the mean

diffusion coefficient of the salt

fd�dw�Do

C�A��

�DwC�A��do

(28)

and with the apparent total concentration defined fromthe bulk concentrations by

ctoti �cw

i �fdcoi (29)

In the contact mode, we can also write

Dwof1=2�Dw

ofo?�

RT

ziFln fd

�Dwof

o?�RT

ziFlndw�Do

C�A��

�DwC�A��do

(30)

To calculate the distribution potential in the contact

mode, it is necessary to solve Eq. (15) by substituting the

volume phase ratio by the dynamic phase ratio. Eq. (30)

highlights as above that the absolute distribution

potential will be independent of the mass transfer

conditions (i.e. the dynamic phase ratio) and that the

polarisability of the interface will vary as shown in Fig.4.

The diffusion potential for a 1:1 salt in the diffusion

layer between the bulk solution (b) and the interface just

outside the diffuse layer (s) can be written

Dbsfd��

RT

F

�uC� � uA�

uC� � uA�

�ln

�cb

C�A�

csC�A�

�

��RT

F(tC� �tA�)ln

�cb

C�A�

csC�A�

�(31)

In this equation tC�/and tA� represents the transport

numbers of C� and A�, respectively. As previously

noted [8], the overall Galvani potential difference

between the two bulk phases can be expressed as

Dwof�Dwb

obf�Dosobfd�Dws

osf�Dwbwsfd (32)

The three terms in this equation are illustrated in Fig. 5.If we assume that the relative transport numbers are

equal in the two phases, then we have

Dwof��

RT

F(tC� �tA�)ln

�cos

C�A�cwbC�A�

cobC�A�cws

C�A�

��Dws

osf (33)

From an experimental viewpoint, only the bulk con-

centrations are known a priori; it is therefore advanta-

geous to re-write Eq. (23):

Dwof�(tC� �tA� )

�(Dw

ofo?C� � Dw

ofo?A�)

2�

RT

Fln

�cwb

C�A�

cobC�A�

��

�(Dw

ofo?C� � Dw

ofo?A�)

2(34)

Eq. (34) follows from Eqs. (17) and (18) applied to the

surface plane s, where a classical equilibrium partition

exists.

The first term of this equation represents the diffusion

contribution to the total Galvani potential differencewhereas the second represents the interfacial potential

difference that is quasi-instantaneously established when

the two solutions are placed in contact.

The potential response of cell II, Ecell II, can be

calculated according to the cell diagram, Eqs. (34) and

(18). It is given by:

Ecell II�2tTBA�

RT

Fln

�c1;w

TBA�Br�

c2;o

TBA�Br�

�

�tTBA� (Dwof

o?TBA� �Dw

ofo?Br�)

�2tTBA�

RT

Fln

�c1;w

TBA�Br�

c2;o

TBA�Br�

Kp

�(35)

It may be noted that when Kp�/1 the standard term

vanishes and the expression corresponding to cell I is

recovered. When the concentration ratio c1/c2 is K�1p ;

the cell potential is, as expected, zero, since the initial

concentrations are already equal to the equilibrium

values. The data obtained from cell II are shown inFig. 6. The theoretical slope resulting from Eq. (35) is

23.6 mV/(dec. concentration of flowing electrolyte)

assuming that the limiting molar ionic conductivities

are 19.5 and 78.14 for TBA� and Br�, respectively.

This value is lower than the experimental value of 38.5

mV/(dec. concentration of flowing electrolyte) obtained

from the experimental data. The broken line in Fig. 6

corresponds to Eq. (35) and it appears that the agree-ment with Eq. (35) is rather good at high concentrations

of electrolyte in the streaming solution. Apparently, the

transport number of TBA� is higher in DCE (or

H. Jensen et al. / Journal of Electroanalytical Chemistry 537 (2002) 77�/8482

equivalently the transport number of Br� is lower). The

hydration of TBA� is expected to be rather modest

both in DCE and water [29], but Br� is known to be

hydrated in nitrobenzene [30,31]. In the less polar DCE

the hydration of Br� might even be more significant. Alarger effective radius of Br� in DCE caused by a strong

hydration would lead to a lower mobility and thereby a

lower transport number of Br� (i.e. a higher transport

number of TBA�). One way to clarify this point would

be to measure the diffusion potential of TBABr in DCE

streaming in a DCE solution of TBABr. This proved,

however, to be rather difficult due to the low conduc-

tivity of DCE and consequently no further experimentalstudies were carried out.

4. Conclusion

We have shown that when two liquids are placed in

contact, the Galvani potential difference is quasi-in-

stantaneously established according to Eq. (34). This

process can be called ‘potentiometry of a reversible

system’ by analogy with the expression ‘amperometry ofa reversible system’.

When the two solutions are from a common solvent

(e.g. water), the standard transfer potentials are equal to

zero and Eq. (34) reduces to the classical Henderson

equation for diffusion potentials. We shall present in

Part II of this series, the potential distribution associatedwith diffusion potentials in the case of micro-devices

with mixing of solutions as illustrated in ongoing work

[32].

In the more general case of immiscible electrolyte

solutions, the overall Galvani potential difference mea-

sured is composed of three contributions, namely the

diffusion potential in phase 1, the interfacial Galvani

potential difference and the diffusion potential in phase2. It is worth pointing out that in the case of the

distribution of a single salt between two phases, the

interfacial potential difference is the distribution poten-

tial, which is independent of the phase ratio whereas the

polarisability of the interface is dependent on the phase

ratio. If more than two ions are involved, the interfacial

Galvani potential difference is determined by the half-

wave potential as given by Eq. (13). The latter point willbe published later in Part III of this series which

describes the case of systems with a potential determin-

ing ion.

Acknowledgements

The authors wish to thank Professor T. Kakiuchi for

helpful discussions. Methrom (CH) and the Swiss

Commission for Technology and Innovation (CTI) areacknowledged for financial support.

References

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vol. 15, Marcel Dekker, New York, 1989, pp. 1�/141.

[2] L.Q. Hung, J. Electroanal. Chem. 115 (1980) 159.

[3] W. Nernst, Wied. Ann. 45 (1892) 360.

[4] R. Luther, Z. Phys. Chem. 19 (1896) 527.

[5] F.M. Karpfen, J.E.B. Randles, Trans. Faraday Soc. 49 (1953)

823.

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