Annual Reports C Dynamic Article Links · 126 Annu. Rep. Prog. Chem.,Sect. C:Phys. Chem., 2012,108,126Œ176 Thisjournal is' The Royal Society of Chemistry 2012 Citethis:Annu. Rep

126 Annu. Rep. Prog. Chem., Sect. C: Phys. Chem., 2012, 108, 126–176

This journal is © The Royal Society of Chemistry 2012

Cite this: Annu. Rep. Prog. Chem., Sect. C: Phys. Chem., 2012, 108, 126–176

Studies of ion transfer across liquid membranes

by electrochemical techniques

Angela Molina,*aCarmen Serna,

aJoaquın A. Ortuno

band

Encarnacion Torralbaa

DOI: 10.1039/c2pc90005j

The fundamentals and recent advances in ion transfer across the interfacebetween two immiscible electrolyte solutions (ITIES) are reviewed. Thedifferent strategies developed to overcome the limitations of the traditionalexperimental studies with ITIES and to broaden its scope of applicationsare discussed. Special attention is given to studies of ion transfer throughliquid membranes which contain two ITIES, one or both of which can bepolarized. Theoretical and experimental studies on the application of differentgalvanostatic and potentiostatic electrochemical techniques to the study ofsuch systems are described, emphasizing their unique characteristics. Thearticle also includes sections devoted to facilitated ion transfer, liquid/liquidmicro-interfaces and the use of weakly supported media.

Highlights

Recent theoretical and experimental studies on the implementation of different

electrochemical techniques for ion transfer processes across liquid membranes with

different configurations have allowed in-depth characterization of these processes.

These studies have paved the way for new practical applications.

1. Introduction

Ion transfer across the interface between two immiscible electrolyte solutions

(ITIES) is an important topic in many fields, such as liquid/liquid electrochemistry,

liquid/liquid extraction and membrane transport. It has applications in electro-

analysis, ion separation, sensor development, drug studies and more. It also serves as

a simple model for ion transport in biomembranes. The application of different

electrochemical techniques to the study of ion transfer at ITIES is a straightforward

aDepartamento de Quımica Fısica, Facultad de Quımica, Universidad de Murcia,30100 Murcia, Spain. E-mail: [email protected]; Fax: +34 968 364148Tel: +34 968 367524

bDepartamento de Quımica Analıtica, Facultad de Quımica, Universidad de Murcia,30100 Murcia, Spain

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Annu. Rep. Prog. Chem., Sect. C: Phys. Chem., 2012, 108, 126–176 127


way of obtaining the values of the standard Gibbs energy corresponding to the direct

transfer of many ions from water to different solvents, on the basis of an extra-

thermodynamic assumption.1 This parameter is directly related with Pi (partition

coefficient of the ion), which permits the quantification of the ion lipophilicity, a

crucial drug property for its transport in biological systems and for the design of new

drugs. All these reasons account for the great interest of theoretical and experimental

researchers from different disciplines in studies of ion transfer at ITIES.

Several strategies have been developed that, either alone or combined, overcome

the limitations of the traditional experimental studies with ITIES and broaden its

scope of applications. One of these limitations is the volatility of the organic phase.

This has been solved by replacing conventional solvents used in ITIES studies, such

as nitrobenzene and 1,2-dicloroethane, by 2-nitrophenyl octyl ether (NPOE). This

solvent has a low vapour pressure, relatively low mutual solubility with water and a

medium permittivity, all of which makes it an excellent solvent for ITIES studies.

Since NPOE is widely used as plasticizer in the construction on ion-selective

electrode membranes, the data values obtained on ion transfer at the NPOE|water

interface are particularly relevant for ion-sensor development. The standard Gibbs

energy values for the transfer of many ions or the corresponding Pi values have been

experimentally determined or theoretically predicted.2,3

Another type of organic phase that is recently being used is constituted by some

members of ionic liquids.4,5 These solvents combine low vapour pressure with high

electrical conductivity. Some advantages and disadvantages of these solvents are

mentioned below.

A second limitation of conventional experimental studies with ITIES is the

mechanical instability of the liquid/liquid (L/L) interface. This has been solved in

different ways. One simple way is to increase the viscosity of the organic phase,

usually NPOE, with a polymer like PVC dissolved in it, which also produces an

increase in the electrical resistance. Plasticized (or solvent) polymeric membranes

similar to those used in ion-selective electrodes, which are durable and easy to

handle, are a practical example of this option,6–11 and could be easily commercialized. It

is noteworthy that the presence of PVC has no significant effect on thermodynamics of

the ion transfer. This option has favoured working with ITIES under flow-conditions.12

A second type of solution to mechanical instability of the interface consists of

supporting the organic solution within an array of micro- or even nano-holes13–16 made

on a rigid surface. Although this is more sophisticated, it benefits from the inherent

advantages of micro- and nano-electrodes, so making it competitive. Some interesting

aspects of micro-ITIES including fundamentals and development are commented in the

present report.

A third limitation of the study of ion transfer at ITIES is the reduced width of the

potential window. The simplest way to expand it is through a proper selection of the

electrolytes dissolved in both phases. Combined with an organic phase constituted

by mixed solvents, this has recently led to a potential window of up to 1.3 V.17 The

use of very hydrophobic ionic liquids as the organic phase has also led to a wide

potential window,18 although these solvents have the inconvenience of a slow

dynamic relaxation.19 A second way to expand the window is to use two polarized

interfaces.20–25 In classical ITIES studies, a reference and a counter electrode were

used in each constituent phase of the ITIES. However, in the case of plasticized

polymeric membranes and supported liquid membranes it is more convenient to

include the electrodes corresponding to the organic phase in another aqueous phase

in contact with the other side of the membrane. In most cases, the inner interface

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formed at this side is made non-polarizable by the use of a high concentration of a

common ion present in both contacting phases. In this way, the potential of the

working (external) interface can be easily controlled by the proper selection of the

potential applied between the reference electrodes present in the aqueous phases.

However, some researchers have studied the case in which the inner interface is also

polarizable. This type of system is much more complicated from a theoretical point

of view, since the applied potential between both references electrodes is divided

between both interfaces in a complex way. This theoretical problem has been solved

by some authors.21,22,24–29 It has been demonstrated that this type of system has

several advantages, including an expansion of the potential window, although, on

the other hand, the voltammetric peaks are broader than those obtained with a single

polarized interface. A striking advantage of the two-polarized interfaces system is

that the potential of the inner interface switches between two distinct values

depending on whether the ion transferred across the working interface is a cation

or an anion.27,30 As will be shown below, this effect has practical advantages.

Finally, since the addition of a supporting electrolyte reduces the size of the

polarizable potential window, making the ion transfer of extremely hydrophilic or

hydrophobic species unobservable, a third way of extending the potential window is

to use little or no supporting electrolyte.31–33 Through some of the approaches

described it has been possible to study the simple ion transfer of extremely

hydrophilic ions, such as proton, magnesium, calcium, hydroxyl and phosphate34

and uranyl and extremely hydrophobic ones, like tetraphenylborate33 and tetrahexyl-

ammonium.35

Earlier ITIES studies were limited to the transfer of some model ions, such as

tetraalkylammonium ions. Nowadays, the transfer of ions that are important in

many fields has been performed. The transfer can be facilitated by an appropriate

ionophore, usually dissolved in the membrane phase. The transfer, either simple or

facilitated, of important ions such as drugs,35–42 adenosine phosphates,43 the

polyions heparin44 and protamine,45 oligopetides,46 dopamine,47–49 noradrenaline,49

polycarboxylates,50 perfluoroalkyl oxoanions,51 protein digests,52 food additives,53

uranyl33,54 and hydrogen chromate55 has been studied.

The need for a four-electrode potentiostat for ITIES studies has been overcome by

three-phase systems, in which the presence of a redox couple at high concentrations

in the organic phase permits the use of a single electrode as reference and counter

electrode.56,57

With regard to the electroanalytical techniques used in ITIES, although cyclic

voltammetry continues to be used, pulse voltammetric techniques have dealt better

with systems showing high impedance and capacitance effects, such as polymeric

membranes, which are an excellent option for ion sensor development. Electro-

chemical techniques have permitted the elucidation of the reaction mechanism of

various facilitated ion transfer reactions58–60

Our research group has focused on theoretical and experimental advances in ion

transfer across membrane systems containing two ITIES, including the case in which

both are polarized. The theoretical treatments developed have led to very simple

analytical and explicit expressions for the application of different electrochemical

techniques–voltammetric and chronopotentiometric–to these membrane systems.

The expressions achieved have been successfully checked with experimental results

obtained using solvent polymeric membrane ion-sensors. Due to the relevance of

these results, their potential applications, and the experience of the authors on these

systems, they receive particular attention in this report.

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1.1. Fundamentals

An ITIES is the interface formed between two liquid solvents of a very low mutual

miscibility, usually less than 1% in weight, and each containing an electrolyte.

One of these solvents is usually water, and the other is a polar organic solvent of a

moderate or relatively high dielectric constant. The electrolytes should be able to

dissociate into ions to ensure conductivity across phases.1

Various charge transfer reactions can take place in the L/L interface.61 This report

focuses mainly on the application of classic and novel electrochemical methodologies

for studying the simple ion transfer (IT) and facilitated ion transfer (FIT) reactions.

There are several books61–67 and review articles1,68–72 in the literature dealing

with the fundamental concepts of simple or assisted ion transfer across ITIES

in which the structural, thermodynamic and kinetic aspects are treated. The aim of

this section is merely to highlight some of the thermodynamic aspects necessary

for studying the reversible ion transfer through L/L interfaces by electrochemical

methods.

Thermodynamic aspects. Let us consider the transfer of an ion Xz between the

aqueous phase (W) and the organic phase (M),

Xz (W) $ Xz (M) (1)

The distribution of the ion Xz between both phases in contact leads to the

development of a potential drop across the interface,

DWMf = f(W) �f(M) (2)

where f(p)is the inner potential of the phase p (p = W or M). This equilibriumpotential difference, when Xz is the only ion that can be transferred, obeys the Nernstequation,

DWMf ¼ DW

Mf0Xz þ

RT

zFln

aMXz

aWXz

� �¼ DW

Mf00Xz þ

RT

ziFln

cMXz

cWXz

� �ð3Þ

with DwMf00

Xz being the formal ion transfer potential given by,

DWMf00

Xz ¼ DWMf0

Xz þRT

zFln

gMXz

gWXz

� �ð4Þ

where R, T, and F have their usual meaning and apXz , gpXz and c

pXz are the activity,

the activity coefficient and the concentration, respectively, of the ion Xz in the phasep (p = W or M). Dw

Mf0Xz is the standard ion transfer potential, which is related with

the standard Gibbs energy of the transfer of Xz from phase M to phase W,

DWMf0

Xz ¼DMWG0

Xz

zFð5Þ

The standard Gibbs energy of the ion transfer is a direct measure of lipophilicity,

and is related with the standard partition coefficient of the ion in the biphasic system

through the following equation,

PXz ¼ exp �DOWG0

Xz

RT

� �ð6Þ

When an appropriate potential (or current) is applied, a net ion transport from

one phase to another occurs (the current flows) and a new equilibrium is established

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in which the ratio of the ion concentrations at two sides of the W/M interface is

correlated with the potential applied (or measured) by eqn (3).

Polarization measurements. The electrochemical study of ion transfer processes

across L/L interfaces is based on the polarization of ITIES using an external electric

current or voltage source. The conditions under which an ITIES can behave as an

ideally polarizable interface are defined by Koryta et al.73 and the classification of

ITIES as being polarizable or non-polarizable is clearly explained by Samec.1

A variety of different electrodes and cell configurations used for polarization

measurements at ITIES were described by Samec et al.,71 both for systems that

contain a single polarizable ITIES and for membrane systems such as supported,

gelified and polymeric membranes and, also, bilayer lipid membranes, in which the

organic phase is comprised between two aqueous solutions. In these systems there

are two ITIES with approximately the same interfacial area and in which both

membrane interfaces can be polarizable. These systems show a somewhat different

electrochemical behaviour from the systems with a single polarizable interface.

Another recent arrangement for ion transfer studies is that proposed by Scholz

et al. using three-phase electrodes in which the ion transfer across the L/L interface is

coupled to an electron transfer through a liquid/solid electrode interface.56,57

In 2006, from the author’s laboratory, a new device based on a modification of a

commercial ion-selective electrode body was proposed to study the ion transfer across the

water-solvent polymeric membrane interface.11 Since then, this device has been used with

different electrochemical techniques to investigate several ion transfer processes, which are

summarised later on this report. The design of this device is shown in Fig. 1.

Measurements with this sensor involve a membrane system in which a planar

organic phase (the membrane, M) containing a hydrophobic supporting electrolyte

separates two aqueous solutions containing a hydrophilic supporting electrolyte: the

inner aqueous solution (phase W0) and the outer one (phase W), which is the sample

solution that also contains the semi-hydrophobic ion, Xz, whose transfer is going to

be studied (see Fig. 2).

The polarization phenomena taking place in this system as a consequence of the

application of an electrochemical perturbation (either a given potential or a current) can be

described in terms of the individual electrochemical processes occurring at the two ITIES.

Depending on the supporting electrolytes chosen for the different phases, the polarization

phenomena can be effective at only one (the outer interface) or at the two L/L interfaces

involved, giving rise to systems of a single polarized interface and of two polarized

interfaces. So, when the electrolytes of membrane and inner aqueous solution have

a common ion in sufficiently high concentrations, the inner interface behaves as non-

polarizable and the constant potential drop across this interface is set by the concentration

of this ion. Otherwise, both L/L interfaces in the membrane system are polarized.

In any case, coupled to the transfer of the target ion through the outer interface,

another ion is transferred through the inner one in order to maintain electroneutrality.

The coupled transfer can be either that corresponding to the ion of the membrane

electrolyte with the same charge sign as Xz to the inner solution (W0) or that of the ion

of the inner electrolyte solution with opposite charge to Xz to the organic phase (M).

The easiest ion to transfer will be the one that is transferred, and this is given by the

values of their standard ion transfer potential. In Fig. 2 and in the following it is

supposed that the coupled ion transfer in the inner interface is that of ion of the

membrane electrolyte, Rz0, but the treatment is similar in the other case.

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Assuming that all the phases, W, W0 and M, contain sufficient concentrations of

electrolytes such that the different ohmic drops can be neglected, the applied or

measured potential, E, can be written as the difference of the two interfacial potential

differences,

E = Eout �Einn (7)

due to the transfer of Xz through the outer interface (Eout = DwMfXz) coupled with

the transfer of the membrane electrolyte ion, Rz0, through the inner interface(Einn ¼ Dw0

MfRz0 ). This last potential difference, Einn, will be constant for systemswith the inner interface non-polarizable, i.e. for systems with only one polarizableL/L interface, and variable with the current flowing for systems with the twoL/L interfaces polarized. In both cases, the standard ion transfer potential of theion studied, DW

Mf0Xz, can be determined from the difference between the half-wave

potentials obtained with the appropriate electrochemical technique for the target ionand for a reference ion with the same charge number, Yz, whose standard ion

Fig. 1 Amperometric ISE body design. Reproduced from [J. A. Ortuno, C. Serna, A. Molina

and A. Gil, Anal. Chem., 2006, 78, 8129] with permission of [American Chemical Society].

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transfer potential, DwMf0

Yz, is known. By using the same experimental conditions forboth ions, this difference holds for

E1=2Xz � E

1=2Yz ¼ DW

Mf0XZ � DW

Mf0YZ þ

RT

zFlngMXzgWYz

gWXzgMYz

þ RT

2zFlnDW

XzDMYz

DMXzDW

Yz

ð8Þ

for systems with a single L/L polarized interface, and

E1=2M;Xz � E

1=2M;Yz ¼ DW

Mf0XZ � DW

Mf0YZ þ

RT

zFln

gMXz

gWXz

gWYz

gMYz

� �þ RT

zFln

DMYz

DMXz

� �1=2DW

Xz

DWYz

" #

ð9Þ

for systems with the two L/L polarized interfaces (see Notation).

In the above equations, the two last terms on the right hand side are practically

zero,10 in such a way that:

E1=2Xz � E

1=2Yz ¼ DW

Mf0Xz � DW

Mf0Yz

E1=2M;Xz � E

1=2M;Yz ¼ DW

Mf0Xz � DW

Mf0Yz

)ð10Þ

Moreover, regardless of whether the membrane system is of one or two L/L

polarized interfaces, the current flowing through the system will be controlled by

diffusion and is given by

I ¼ �zFADWXz

@cWXz

@x

� �x¼0

ð11Þ

where A is the interfacial area and ð@cWXz=@xÞx¼0 is the concentration gradient at the

W/M interface, whose analytical expression can be obtained in some cases by solving

Fick’s laws of linear diffusion with the appropriate initial and boundary conditions

Fig. 2 Schematic representation of the electrochemical cell (A), and the ion transfer at the

liquid/liquid interfaces (B) for systems with (a) one single polarizable interface; (b) two

polarizable interfaces.1. Sensor; 2. External reference electrode; 3. External counter electrode;

4. Sample solution (outer aqueous phase); 5. Inner aqueous solution; 6. Membrane.

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2. Voltammetry and chronoamperometry

The voltammetry of ion transfer through bilayer and different types of liquid

membranes has been studied theoretically and experimentally by several

authors.9,10,14,20–23,26 It has been applied mainly in the determination of standard

transfer potentials of inorganic and organic ions, which is very useful, for instance,

in the study of the pharmacological activity of ionisable drugs. Within the broad

scope of voltammetric techniques, mainly numerical methods have been applied to

study the I/E response of ion transfer processes, with Cyclic Voltammetry (CV)

being the most widely employed technique. Electrochemical techniques based on the

application of multipotential steps like Differential Pulse Voltammetry (DPV),

Staircase Voltammetry (SCV) and Square Wave Voltammetry (SWV) have scarcely

been tackled. Nevertheless these techniques have proved to be more suitable than

CV for quantitative analysis.

This section gives the theoretical solutions for the I/E responses corresponding to

the application of some of the most powerful voltammetric techniques to ion transfer

processes taking place at membrane systems comprising two L/L interfaces and

analyzed them in depth. Some interesting and representative applications are also

shown. Systems of only one and or two polarized interfaces have been distinguished.

The main differences in the behaviour of the responses of both kinds of membrane

systems are referred to, and the advantages and disadvantages of the use of one or

another have been discussed.

2.1. One polarized interface systems

Many of the systems used for electrochemical studies of ion transfer processes taking

place at the L/L interfaces are systems of a single polarized interface. In these kinds

of systems the polarization phenomena is only effective at the sample solution/

membrane interface, since the potential drop through the other interface is kept

constant whatever the nature of this interface (i.e. either liquid/liquid or solid/

liquid23,57,69). In the specific case of a membrane system that separates to aqueous

solutions, the non polarizable interface is achieved by adding a sufficiently high

concentration of a common ion in the membrane and inner aqueous solution, by

choosing two salts of this common ion with lipophilic and hydrophilic counterions,

respectively.11

2.1.1. Multipulse Voltammetry

2.1.1. (a) Normal Pulse Voltammetry (NPV), Differential Double Pulse Voltam-metry (DDPV) and Differential Multi Pulse Voltammetry (DMPV). In NPV

technique, the potential-time wave-form consists of a series of potential steps of

amplitude E and duration t. After each step, the equilibrium is re-established,

returning to a base potential in which there is no current flux through the system.

The potential amplitude is varied between consecutive potential steps. When NPV is

applied to characterize the uptake of a target ion Xz from an aqueous sample

solution to a liquid membrane in a membrane system of a single polarized interface,

the current response obtained can be described by74

I

Id¼ gJ

1þ gJð12Þ

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where

IdðtÞ ¼ zFAc�Xz

ffiffiffiffiffiffiffiffiffiDW

Xz

pt

rð13Þ

J ¼ eZ; Z ¼ zF

RTðE � DW

Mf00XzÞ ð14Þ

g ¼ DMXz

DWXz

� �1=2

ð15Þ

and other symbols are given in the Notation.

Differential pulse voltammetry (DPV) is one of the most suitable electrochemical

techniques for quantitative analysis and determination of the characteristic para-

meters of a system. It shows very well defined peaks, from whose coordinates the

thermodynamic ðDWMf00

XzÞ and dynamic ðDWXz or DW

Xz=DMXzÞ parameters can be deter-

mined with much greater accuracy than with NPV or CV. This is because the limit

current plateau in NPV is difficult to reach within the potential window and because

the CV curves present great distortion due to the effect of the ohmic drop and the

charging current. In DPV the dependence of the location and the height of the

current peaks with the potential amplitude, DE, permits this variable to be tuned to

centre the peak within the potential window and improve sensitivity. These

characteristics make DPV more advantageous than the derivative NPV, which has

sometimes been used as an approximation of DPV.75

Currently, two types of waveforms are usually considered when studying or

employing DPV technique: successive double potential pulses recovering the initial

equilibrium condition after each one (double pulse mode, Scheme 1a), and a train of

pulses superimposed on a staircase waveform (multipulse mode, Scheme 1b). In line

with the nomenclature proposed in an early paper,76 these two variants of DPV

technique are Differential Double Pulse Voltammetry (DDPV) and Differential

Multi Pulse Voltammetry (DMPV).

In DDPV, on a base potential, E0, two consecutive potential steps, E1 and E2, are

applied during times t1 and t2, respectively, with t2 { t1. The magnitude of E1 is

changed between consecutive double pulses, while the pulse amplitude, DE= E2 – E1,

is kept constant. The resulting currents, I1 and I2, are sampled at the end of both

potential steps and the difference, IDPV = I2 – I1, is plotted versus E1. The delay time

between each pair of pulses, td, allows the uptaken ion Xz that has entered the

membrane during the application of the pulses to egress, leaving the membrane ready

for the application of a new double pulse. On the other hand, DMPV can be

considered as a variant of DDPV in which the initial conditions are not totally

recovered during the experiment.

Recently, the use of a potential axis which takes the average of the two stepped

potentials (Eindex = (E1 + E2)/2) instead of the usual E1 value has been proposed.77

This choice is of great interest, since the IDDPV – Eindex plots are centred on the half-wave

potential, as in the case of SWV.

From the transposition of the theory for DDPV to the study of the ion transfer

across L/L interfaces, the theoretical equations obtained with the semi-infinite linear

diffusion model can be used to quantify the current response of the ion transfer in

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this technique.78,79 Thus, the equation for the current in DDPV for reversible ion

transfer can be written as11

IDDPV ¼ I2ðE2Þ � I1ðE1Þ ¼ zFADW

Xz

pt2

� �1=2

c�Xz

1

1þ gJ1� 1

1þ gJ2

� �ð16Þ

where

Jj ¼ eZj ; j ¼ 1; 2

Zj ¼ zFRTðEj � DW

Mf00XzÞ

)ð17Þ

The peak parameters, Epeak and IpeakDPV, of the differential double pulse voltammo-

gram are:80

Epeakindex = E1/2 (18)

IpeakDDPV ¼ zFADW

Xz

pt2

� �1=2

c�Xz tan hzFDE4RT

� �ð19Þ

with E1/2 being the half-wave potential of the one polarized interface system

E1=2 ¼ DWMf00

Xz þ RTzF

ln 1g

� �ð20Þ

Scheme 1 Potential time waveform of DDPV and DMPV techniques. Reproduced from[J. A. Ortuno, C. Serna, A. Molina and A. Gil, Anal. Chem., 2006, 78, 8129] with permission of[American Chemical Society].

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and other symbols are as given in the Notation. Interestingly, eqn (16)–(19) forDDPV are also applicable for characterizing the response provide for DMPV forreversible processes, as demonstrated in reference 76 since, as the process is fast andthe period between pulses (t1) is much longer than the length of the pulse (t2), inDMPV, the system is able to establish conditions equivalent to DDPV near theinterface during the first period, as if a previous pulse had not existed. Therefore,under these conditions the simple analytical expressions for the DDPV techniquetogether with the faster potential-time program of DMPV can be made use of.

Fig. 3 shows the DDPV voltammograms corresponding to the tetraethylammonium

transfer across a liquid membrane system of a single polarized interface obtained at

several positive and negative values of the pulse amplitude.

Fitting experimental data to the theoretical equations means the average value for

the half-wave potential of a given ion can be estimated and quite an accurate value

for its diffusion coefficient can be obtained11. The standard ion-transfer potential of

the ion ðDWMf0

XzÞ can also be obtained from the experimental-theoretical fitting by

the procedure described in Fundamentals (see eqn (10)), and from this, the corresponding

standard molar Gibbs energy, DOWG0

Xz , and the partition coefficient, PXz, can be easily

calculated.13 Thus, DDPV (orDMPVunder reversible conditions) exhibits great efficiency

in acquiring both dynamic and thermodynamic information of the system under study.

DDPV technique has been applied, for instance, to study the relationship between

the pharmacological potency of different catamphiphilic drugs with the standard ion

transfer potential, or the relation between this parameter and the detection limit of

an amperometric sensor based on the ion transfer across the water-solvent polymeric

membrane interface.42

2.1.1. (b) Multipulse chronoamperometry. In this technique, a sequence of successive

potentials steps,Ej, with the same duration,t, and opposite direction, is applied to the

system. Its use is of great interest in electrochemistry, especially for an accurate

Fig. 3 Background-substracted DPV recordings obtained for 1 � 10�4 M TEA+ and

backgrounds recording, respectively, at the following |DE| values: (K,—) 30 mV; (&, � � �)40 mV; (D, – –) 50 mV; (J,–��) 60 mV. Reproduced from [J. A. Ortuno, C. Serna, A. Molina

and A. Gil, Anal. Chem., 2006, 78, 8129] with permission of [American Chemical Society].

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determination of diffusion coefficients. When multipulse chronoamperometry is

applied to L/L membrane systems to calculate the diffusion coefficients of the target

ion in both organic and aqueous phases, two different situations are of special

interest regarding the applied potentials:74

- The values of both uptake and stripping potential correspond to diffusion controlled

conditions, i.e. E2j�1 � DWMf00

Xzþand E2j � DWMf00

Xzþ (or E2j�1 � DWMf00

Xz�and E2j�1 �DWMf00

Xz� if the transfer of an anion is considered).

- Only the uptake pulse value corresponds to diffusion controlled conditions,

i.e. E2j�1 � DWMf00

Xzþ and E2j�1 ! DWMf00

Xzþ (or E2j�1 � DWMf00

Xz� and E2j�1 !DWMf00

Xz� for the anion transfer).

In order to show the difference between the two situations, in Fig. 4 the

chronoamperograms corresponding to the application of a sequence of four successive

potentials steps (E1 = E3 and E2 = E4) to study the transfer of a monopositive cation X+

in a single polarized interface system are plotted, when both uptake and stripping potential

correspond to diffusion controlled conditions (Fig. 4a) and when only the uptake pulse

value corresponds to diffusion controlled conditions (Fig. 4b).

Somewhat contrary to expectations, it can be noted from Fig. 4a that when the

uptake and stripping potentials are respectively much greater and much smaller than

the formal ion transfer potential, the chronoamperograms corresponding to the

stripping steps do not depend on the diffusion coefficient in the organic phase, and

therefore, DMX+ cannot be estimated from any curve. In contrast, if the stripping

potential lies close to the formal potential (Fig. 4b), the two diffusion coefficients can

be calculated from these curves. So, for the dynamic characterization of the system

to be accomplished, stripping potentials near to the formal potential are required.

2.1.1. (c) Square Wave Voltammetry (SWV). Joining the main features of cyclic

voltammetry and differential pulse techniques makes SWV a very fast technique with a

strong resolving power and high sensitivity and, hence, it is one of the most widely

employed in voltammetric studies. It allows the accurate and easy determination of the

characteristic electrochemical parameters of the systems studied because of themorphology

of the responses and the fact that it is a subtractive technique and, therefore, the

nonfaradaic and background currents are minimized. The shape of the SWV recordings

permits the determination of the standard ion transfer potential from the potential peak

measurement, since Epeak = E1/2 for a reversible ion transfer.81

In SWV a square wave sequence of potential pulses of the same duration,t,superimposed on a staircase potential of width 2t is applied according to Scheme 2.

The potential sequence of SWV for a single scan, can be described by

Ep ¼ Ein � Intpþ 1

2

� �� 1

� �DEs þ ð�1Þpþ1Esw

� �ð21Þ

where the positive sign is used for cationic uptake studies and the negative one for

anionic uptaking. Symbol definitions are given in the Notation.

The net current for the transfer of a target ion Xz through the L/L interface is given by

Isw ¼ I2p�1 � I2p ¼ IdðtÞX2p�1j¼1

1

1þ gJj� 1

1þ gJj�1

� �1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2p� j þ 1p � 1ffiffiffiffiffiffiffiffiffiffiffiffiffi

2p� jp

� �"

þ 1

1þ gJ2p� 1

1þ gJ2p�1

�ð22Þ

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Where

IdðtÞ ¼ zFAc�Xz


Xz

pt

rð23Þ

and Ji is given by eqn (17) for i Z 1 and J0 = 0.81

From the above equations, an expression for the maximum current can be

deduced when very large values of Esw are applied (|Esw| Z 100 mV).81,82

Imaxsw (|Esw| Z 100 mV) = 1.21 Id(t) (24)

and for the half-peak width in these conditions it is fulfilled that W1/2 E 2Esw.

Fig. 5 shows the background corrected SWV recordings corresponding to the

transfer of different ionic liquid cations from water to a solvent polymeric membrane

Fig. 4 Current-time curves corresponding to four potential steps when transport takes place by

diffusion in both phases, for values of the diffusion coefficient of the organic phase,Do: (—) 10�6,

(� � �� ) 10�8 and (- - - - - -) 10�10 cm2/s; Dw= 10�5 cm2/s, t= 1s, E00= 0.00, V, E1 = E3 -N

and: (a) E2=E4 - �N,.(b) E2 = E4 = 0.05, V. Reproduced from [A. Molina, C. Serna,

J. A. Ortuno and E. Torralba, Int. J. Electrochem. Sci., 2008, 3, 1081] with permission of

[Electrochemical Science Group].

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together with that corresponding to TEA+ as reference ion. As can be seen, a really

good agreement between theoretical and experimental data is obtained in all cases.

The values obtained for the standard ion transfer potential of the different ionic

liquid cations by using SWV are presented in Table 1.

Several interesting conclusions about the effect on the ionic liquid cation lipophilicity of

the alkyl chain length and that of the substitution of the imidazolium by pyridinium can

be extracted from these data. One example is that an increase in the alkyl chain length

of the alkylmethyl imidazolium homologues series (BMIm+, HxMIm+, OctMIm+)

gives rise to an increase in the lipophilicity of this species. Another is that the same

Scheme 2 Potential-time waveform of SWV technique.

Fig. 5 Background-subtracted SWV recordings obtained for 5 � 10�4 M solutions of several

cations, X+: TEA+(K), BMIm+(n), BMMIm+(’), BzMIm+(,), BMPy+(J), HxMIm+(E)

and OctMIm+(&). Esw = 50 mV, Es=10 mV, t =0.3 s and AffiffiffiffiffiffiffiffiffiffiDw

Xþp

in cm3 s�1/2: (a) TEA+,

4.83 � 10�4, (b) BMIm+, 5.69 � 10�4, (c) BMMIm+, 5.62 � 10�4, (d) BzMIm+, 5.43 � 10�4,

(e) BMPy+, 4.30 x 10�4, (f) HxMIm+, 5.14� 10�4 and (g) OctMIm+, 5.57� 10�4. T=298.15 K.

Reproduced from [J. A. Ortuno, C. Serna, A. Molina and E. Torralba, Electroanalysis, 2009, 21,

2297] with permission of [ John Wiley and Sons].

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potential difference (69 mV per �CH2�CH2� unit) is observed between each two

consecutive homologues. These findings may be useful for predicting ionic liquid

cations lipophilicity.

The concentration of the target ion directly influences the value of the peak

current of the response. To show this, the experimental SWV voltammograms for

the ionic liquid cation HxMIm+ for several concentration values, together with the

plot of peak current vs. HxMIm+ concentration are depicted in Fig. 6.

As can be seen, a linear relationship is obtained within the concentration range

studied with a regression coefficient of 0.999, which reflects the potentiality of SWV

for the performance of voltammetric ion sensors.

2.1.2. Cyclic staircase voltammetry (CSCV) and cyclic voltammetry (CV). Cyclic

voltammetry is the most widely used technique for acquiring qualitative information about

electrochemical processes. It is extremely powerful, offering a rapid global characterization

of the system under study. It has also proved to be very useful for the study of ion transfer

across bulk, supported or polymer composite membranes.7,14,20,83 Most of the references

relative to this technique use numerical methods to solve the mass transport problem

associated with its application, which can be very cumbersome. Recently, simple explicit

expressions for the application of CV to the study of the ion transfer in membrane systems

of one polarized interfaces have been used based on the transposition of the theory already

developed for electrode/solution interfaces30

The dimensionless current for CSCV is given by:

c ¼ Iffiffiffipp

zFAc�Xz

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFRT

DWXzv

q ¼ffiffiffiffiffiffiffiffiffiffiRT

FDE

r Xpj¼1

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðp� j þ 1Þ

p 1

1þ gJj�1� 1

1þ gJj

� � !ð25Þ

where v = DE/t is the sweep rate, Ji is given by eqn (17) for i Z 1 and J0 = 0, and

other symbols are as given in the Notation. When the absolute value of the pulse

Table 1 Standard ion transfer potentials obtained from SWV

Cation type R DwMf0

Xþ=mV

C4H9 �24.2C6H5 �53.2C6H13 �93.2C8H17 �162.5

C4H9 �35.2

C4H9 �51.5

Reproduced from [J. A. Ortuno, C. Serna, A. Molina and E. Torralba, Electroanalysis, 2009,

21, 2297] with permission of [John Wiley and Sons].

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amplitude tends to zero (|DE|o 0.01 mV in the practice) this equation holds for CV,

as depicted in Scheme 3.

In this case, the applied potential wave-form behaves as a continuous function of

time in the way

EðtÞ ¼ Einitial þ vt for t Er

EðtÞ ¼ Efinal � vt for t4Er

ð26Þ

with Er being the reversal potential.

Taking into account the following relationship for the time elapsed between the

beginning j-th pulse at the end of the p-th pulse tj,p.

tj;p ¼ ðp� j þ 1Þt ¼ Ep�jþ1 � Einitial

vð27Þ

Fig. 6 Background-subtracted SWV recordings obtained for solutions of HxMIm+ of

different concentrations. Esw: 50 mV, Es = 10 mV and t = 0.3 s. The concentrations

(in mM) are shown on the curves. Inset: linearity plot of the peak current vs. concentration.

Reproduced from [J. A. Ortuno, C. Serna, A. Molina and E. Torralba, Electroanalysis, 2009,

21, 2297] with permission of [John Wiley and Sons].

Scheme 3 Evolution of the potential perturbation from Staircase Voltammetry to LinearSweep (or Cyclic) Voltammetry. Reproduced from [A. Molina, C. Serna, J. Gonzalez,J. A. Ortuno and E. Torralba, Phys. Chem. Chem. Phys., 2009, 11, 1159] with permission of[Royal Society of Chemistry].

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where Zi is given by eqn (17) and Zin

Zinitial ¼zF

RTðEinitial � DW

Mf00XzÞ ð28Þ

and introducing eqn (17), (27) and (28) in eqn (25) one obtains for the direct scan,

c ¼Xpj¼1

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðZp�jþ1 � ZinitialÞ

q 1

1þ gJj�1� 1

1þ gJj

� �0B@

1CA ð29Þ

the current corresponding to the reverse scan is obtained by taking into account

eqn (26).

Representative cyclic voltammograms for the application of CV to the study of the

ion transfer at supported liquid PVDF membrane are depicted in Fig. 7.

This figure shows that it is possible to study the transfer of highly hydrophilic ions

having a polarizable and a non-polarizable interface in series, by choosing conditions

in which the mass transfer of the target ion through the polarizable interface is limited

by the ion transfer reaction taking place at the non-polarizable one.23

2.2. Two polarized interfaces systems

In these kinds of systems the polarization phenomenon is effective at the two

interfaces involved. Specifically, in membrane systems comprising two ITIES, this

behaviour is achieved when the membrane contains a hydrophobic supporting

electrolyte and the sample aqueous solution, the inner one contains hydrophilic

supporting electrolytes, and there is no common ion between any of the adjacent

phases. In this case, the potential drop cannot be controlled individually and the

processes taking place at both interfaces are linked to each other by virtue of the

same electrical current intensity. Systems of two polarized interfaces have shown a

series of peculiarities that can be profitable when studying ion transfer processes.

Indeed, they provide a potential window about twice that of one polarized interface

systems, the signals of cations and anions with similar standard ion transfer potential

Fig. 7 Cyclic voltammograms for the transfer of hydrophilic cations across the o-NPOE/water

interface. Scan rate = 50 mV s�1. Reproduced from [S. M. Ulmeanu, H. Jensen, Z. Samec,

G. Bouchard, P-A. Carrupt and H. H. Girault, J. Electroanal. Chem., 2002, 530, 10] with

permission of [Elsevier].

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values appear widely separated when these systems are used and when the half wave

potential of the ions in these systems is influenced by their concentration.

2.2.1. Multipulse voltammetry

2.2.1. (a) Normal pulse voltammetry. When NPV is applied to liquid membrane

systems of two polarized interfaces the current response can be characterized by the

following expression24

I ¼ zFA


Xz

pt

rc�XzgðZÞ ð30Þ

where g(Z) is the function that contains the dependence on the applied potential for

this kind of membrane systems

gðZÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffil2e2Zþ8leZp

�leZ4

Z ¼ zFRTðE � E00

MÞE00M ¼ Dw

Mf00Xz � Dw

Mf00

Rz0

9>>=>>; ð31Þ

and

l ¼2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDW 0

Rz0DMXz

qDW

Xz

c�Rz0

c�Xz

ð32Þ

when the target ion, Xz, and the ion which is transferred simultaneously across the inner

interface, Rz0, have the same signs (and, for simplicity, the same charge z =z0), and

l ¼2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDM

Rz0DMXz

qDW

Xz

c�Rz0

c�Xz

ð33Þ

when the target ion and the ion which is transferred simultaneously across the inner

interface have opposite signs (and, for simplicity, z = �z0).Fig. 8 shows the Normal Pulse Voltammograms corresponding to the transfer of a

target cation X+ from water to a plasticized polymeric membrane in a system of one

and two L/L polarized interfaces (dashed and solid line, respectively).

From these curves it is immediately noted that the response of the two polarized

interfaces system appears distorted and shifted towardsmore positive potentials in a similar

way to that corresponding to a non-reversible process in a system with one polarized

interface. This distortion is caused by the unequal distribution of the applied potential

between the outer and inner interfaces, as depicted in Fig. 8b. It is worth highlighting that

the displacement observed for the response of the two polarized interfaces system can be

tuned by varying the nature or the concentration of the supporting electrolyte at which

Rz0 belongs (M or W0). This constitutes an extra advantage of this kind of membrane

systems when, for example, locating the response in the potential window available.60

2.2.2. (b) Double differential pulse voltammetry and double multi pulse voltammetry.

Taking into account that the first potential pulse duration is much longer than the

second t1 c t2, the following simple expression for the response in DDPV is obtained

for systems of two polarized interfaces.25

IDPV ¼ zFA


Xz

pt2

sc�Xz gðZ2Þ � gðZ1Þ½ ð34Þ

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Fig. 8 (a) Normalised current-potential curves corresponding to a system with two polarized

interfaces (solid line) and to a system with one polarized interface (dashed line). (b) IN/EM (solid

line), IN/Eout (dashed line) and IN/(�Einn) (dotted line) curves. E00

Xþw1 =XþM

¼ �224 mV,

E00

Rþw2 =RþM

¼ �304 mV, Dw1

Xþ ¼ Dw2

Rþ ¼ 10�5 cm2 s�1, Dm1

Xþ ¼ 10�8 cm2 s�1, C�Xþ ¼ 0:1 mM,

c�Rþ ¼ 50 mM, T = 298.15 K. Reproduced from [A. Molina, C. Serna, J. Gonzalez,

J. A. Ortuno and E. Torralba, Phys. Chem. Chem. Phys., 2009, 11, 1159] with permission of

[Royal Society of Chemistry].

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where g(Zj) is given by

gðZjÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffil2e2Zjþ8leZjp

�leZj4

Zj ¼ zFRTðEj � E00

MÞ

)ð35Þ

with j = 1,2, l given by eqn (32) or (33) and E00M given by eqn (31).

As for the one polarized interface system, these equations can also be used to

characterize the response provided by DMPV for reversible processes, in such a way

that advantage can be taken of the faster potential-time perturbation of this

modality of DPV.76

By numerical fitting of eqn (34), the following peak parameters, EpeakDDPV and IpeakDDPV

are obtained25

EpeakDDPV(mV) C E1/2

M + 13.0 (36)

IpeakDDPV ’ zFA


Xþ

pt2

sc�Xz8:91� 10�3DE ð37Þ

and for the half peak width,

W1/2DPV (mV) C 131 + 2.43 � 10�3 DE (38)

where E1/2M is the half-wave potential for systems of two polarized interfaces, given by

E1=2M ¼ DW

Mf00Xþ þ

RT

zFln

1

l

� �ð39Þ

with l given by eqn (32) or (33) (depending on whether the target ion and theion transferred coupled with it have the same or opposite sign) and DE isexpressed in mV.

To compare the DDPV responses of liquid membrane systems of one and

two polarized interfaces, Fig. 9 shows the DDPV curves corresponding to both

systems (dashed and solid lines, respectively) for two different values of the pulse

amplitude DE.As can be seen, the DDPV peaks obtained for the two polarized interfaces system

are shifted 13 mV with respect to those obtained with the system of a single polarized

one, in agreement with eqn (36). Moreover, the IDDPV �Eindex curves for the two

polarized interfaces system are lower (around 40–45%) and wider than those of the

single polarized interface system (W1/2DPV C 131 mV versus the 90 mV observed when

only one interface is considered).

Fig. 10 shows the background corrected experimental DDPV (or DMPV) curves

corresponding to four different drugs (in their protonated form) obtained for a pulse

amplitude of DE = 50 mV together with that of TBA as reference ion. The values of

the standard ion transfer potential obtained by theoretical/experimental fitting are

given in the inset.

As can be appreciated, the fitting of the experimental data to the theoretical

equations is fairly good in all cases, and hence, the broadness and baseness of the

signal of the two polarized interfaces system are barely detrimental in obtaining

standard ion transfer potential values.25,27,30

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2.2.1. (c) Square wave voltammetry. SWV current corresponding to two polarized

interfaces systems has the form27

Isw ¼ I2p�1 � I2p ¼ IdðtÞX2p�1j¼1ðgðZj�1Þ � gðZjÞÞ

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2p� j þ 1p � 1ffiffiffiffiffiffiffiffiffiffiffiffiffi

2p� jp

� �"

þgðZ2p�1Þ � gðZ2pÞi ð40Þ

where g(Zi) is given by eqn (35) for i Z 1 and g(Z0) = 0; and Id(t) has the same form

as that corresponding to a single polarized interface system (eqn (23)).

In order to show the distribution of the applied potential between the outer and

inner interfaces in SWV, the potential-time waveform used in this technique is

depicted in Scheme 4. The applied potential, E, (black line), and the outer (Eout, dark

grey line) and inner (Einn, grey line) have been plotted.

It can be seen that in the central part of the cyclic sweep, the outer potential, Eout,

follows the same trend as the applied potential, E, such that in this zone the outer

interface presents a behaviour similar to that of a system with a single polarizable

interface. Concerning the inner interface, Einn is quite sensitive to the external

polarization at both extremes of the cyclic sweep, becoming independent of the

Fig. 9 Normalized IN,DPV � (Eindex � E1/2M ) curves for systems of one and two polarized

interfaces (dashed and solid lines, respectively). The values of DE are on the

curves. E00

Xþw1=Xþ

M

¼ �200 mV, E00

Rþw2=Rþ

M

¼ �350 mV, DE = 40 mV, t1 = 12.5 s, t2 = 0.25 s,

Dw1

Xþ ¼ Dw2

Rþ ¼ 10�5 cm2 s�1, DMXþ ¼ 10�8 cm2 s�1, c�Xþ ¼ 0:1 mM, c�Rþ ¼ 50 mM, T = 298.15

K. Reproduced from [A. Molina, C. Serna, J. A. Ortuno, J. Gonzalez, E. Torralba and A. Gil,

Anal. Chem. 2009, 81, 4220] with permission of [American Chemical Society].

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potential in the central zone of the same. In the inset we can see how the potential

pulses are distributed unequally between both outer and inner interfaces27

For comparison of the SWV responses provided for systems of one and two

polarized interfaces, Fig. 11 shows the |Isw|/E curves corresponding to the direct and

to the reverse scans (solid line and empty circles, respectively) for both kinds of

membrane systems, calculated for Esw = 50 mV by using eqn (40).

As can be appreciated, in line with what is observed for DDPV or DMPV, the curves

corresponding to the system with two polarized interfaces are lower and wider than those

corresponding to the system of a single polarized one. Moreover, the peaks obtained when

two polarized interfaces are considered are shifted 8 mV with respect to those obtained for

the system with a single polarized one, which implies that the half wave potential for the

system with two polarized interfaces can be easily determined from the peak potential by

Epeak(mV) C E1/2M � 8 (41)

for�Esw = 50 mV (with the upper sign for cations and the lower one for anions),whereas Epeak = E1/2 when only one interface is considered, regardless of the squarewave potential. It is interesting to note that the |Isw|/E curves corresponding to thedirect and reverse scans for both systems of one and two polarized interfaces aresuperimposable, which indicates that the ion transfer processes taking place at boththe outer and inner interfaces are reversible. Thus, SWV can be used as an excellenttool for analyzing the reversibility of charge transfer processes.

Regarding the influence of the ionic concentration on the SWV response for this

kind of membrane system, the major difference encountered between the behavior of

the SWV signal in systems of one and two polarized interfaces is, that the increase of

this variable causes a shift of the peak potential toward more positive values through

Fig. 10 Background subtracted DPV recordings obtained for 1 � 10�4 M solutions of: (black

circles) imipramine, (white triangles) clomipramine, (white squares) verapamil and (black

diamonds) tacrine. Solid lines correspond to the theoretical DPV curves. DE = 50 mV, t1 = 12.5 s,

t2 = 0.25 s, and AffiffiffiffiffiffiffiffiffiffiDw1

Xþ

qin cm3 s�1/2: (a) Vr, 0.72 � 10�4, (b) Im, 0.93 � 10�4, (c) Cm, 1.04 � 10�4

and (d) Tc, 1.11 �10�4. T= 298.15 K. [A. Molina, C. Serna, J. A. Ortuno, J. Gonzalez, E. Torralba

and A. Gil, Anal. Chem. 2009, 81, 4220] with permission of [American Chemical Society].

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Scheme 4 Potential-time waveform of SWV in a system of two polarized interfaces (black line)and its distribution between the outer and inner interfaces (dark grey and grey line,respectively). Reproduced from [A. Molina, J. A. Ortuno, C. Serna, E. Torralba andJ. Gonzalez, Electroanalysis, 2010, 22, 1634] with permission of [John Wiley and Sons].

Fig. 11 Theoretical |Isw|/(E � E1/2) curves corresponding to the direct and reverse scans of the

square wave (solid lines and empty circles, respectively) for a system with one and two

polarizable interfaces. Ein = �450 mV, Efin = 450 mV, DEs = 10 mV, Esw = 50 mV, t = 1s,

A = 0.081, Dwof

00Xþ ¼ �50 mV, Dw

of00Rþ ¼ �150 mV, c�Xþ ¼ 0:5 mM, c�Rþ ¼ 50 mM,

Dw1

Xþ ¼ Dw2

Rþ ¼ 10�5 cm2 s�1,DMXþ ¼ 10�8 cm2 s�1. T=298.15K.Reproduced from [A.Molina,

J. A. Ortuno, C. Serna, E. Torralba and J. Gonzalez, Electroanalysis, 2010, 22, 1634] with

permission of [John Wiley and Sons].

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an increase of E1/2M in the two polarized interfaces system, as well as the increase in

the peak current already observed for the system of a single polarized interface.

Therefore, SWV can be used as a very good analytical tool for the determination of

ion concentration in both kinds of membrane systems.27

Fig. 12 shows the experimental (black points) and theoretical (solid grey line)

SWV voltammograms corresponding to the transfer of a series of ions distributed

into a range of potential over 1200 mV, which constitutes one of the widest potential

windows seen in the literature, together with that recently obtained by Cousens and

Kucernak.17 The standard ion transfer potentials of the different ions presented in

Fig. 12 are shown in the first column of Table 2.

Fig. 12 Experimental SWV obtained for 5 � 10�4 M solutions of several ions (shown on the

curves). Theoretical curves are given by solid lines. Esw = 50 mV, Es = 10 mV, t = 0.3s and

AffiffiffiffiffiffiffiffiffiffiDw

Xþp

in cm3 s�1/2: (a) TMA+, 5 � 10�4; (b) TEA+, 4.9 � 10�4; (c) TPA+, 4.5 � 10�4;

(d) TBA+, 3.8 � 10�4; (f) SbCl6�, 3.3 � 10�4; (g) AuCl4

�, 4.9 � 10�4; (h) Pic�, 3.7 � 10�4.

T = 298.15 K. Reproduced from [A. Molina, J. A. Ortuno, C. Serna, E. Torralba and

J. Gonzalez, Electroanalysis, 2010, 22, 1634] with permission of [John Wiley and Sons].

Table 2 Comparison between the standard ion transfer potentials obtained from the fit of theSWV voltammograms of Fig. 12 and those previously reported

Dwmf

0Xz=mV

Xz

Ratio NPOE/PVC NPOE

2/1 4/110 NPOE2 NPOE84

TMA+ 139 � 1 120 140 111

TPA+ �100 � 1 �106 �92 �90TBA+ �221 � 1 �230 �242SbCl6

� 178 � 2

AuCl4� 51 � 2

Reproduced from [A. Molina, J. A. Ortuno, C. Serna, E. Torralba and J. Gonzalez,

Electroanalysis, 2010, 22, 1634] with permission of [John Wiley and Sons].

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The comparison of the standard ion transfer potentials obtained in this work with

those previously reported for membranes with different ratios PVC/NPOE2,10,84

shows that the PVC content in the organic phase, even at relatively high values, does

not significantly affect the values of the standard ion transfer potential with respect

to the solvent (2-nitrophenyl octyl-ether) alone. Besides, it is extremely interesting to

note the huge differences shown between the peaks corresponding to the square wave

voltammograms of the ions TMA+ and SbCl6� (approximately 800 mV), which

contrast with the nearly 40 mV that separate them in the standard ion transfer

potentials table (Table 2). This huge peak separation is mainly due to the great

difference between the formal potentials of the ions transferred at the inner interface,

and it provides this system with a high resolving power for the study of species with

opposite charge but with similar standard ion transfer potential, as compared to the

system with a single polarizable one27 This feature is extremely interesting when

analyzing salt transfer processes, as will be shown below.

2.2.2. Cyclic staircase voltammetry and cyclic voltammetry. As for single polarized

interface systems, an explicit analytical equation for the CV response for systems with

two L/L polarizable interfaces is derived from that corresponding to CSCV when the

pulse amplitude DE approaches zero:24

c ¼ Iffiffiffipp

zFAc�Xz

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFRT

DWXzv

q ¼ffiffiffiffiffiffiffiffiffiffiRT

FDE

r Xpj¼1

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðp� j þ 1Þ

p ðgðZjÞ � gðZj�1ÞÞ !

ð42Þ

or

c ¼Xpj¼1

1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðZp�jþ1 � ZinitialÞ

q ðgðZjÞ � gðZj�1ÞÞ

0B@

1CA ð43Þ

where g(Zi) is given by (35) with i Z 1 and g(Z0) = 0, Zi is given by eqn (17), Zinitial byeqn (28) and other symbols are given in the Notation. The current corresponding to

the reverse scan is obtained by taking into account eqn (26).

In line with what is observed for other techniques, the CV response for the ion

transfer at two polarized interfaces systems is lower and broader than that of single

polarized interface ones;22 and this feature has been attributed to different polarization

rates at the outer and inner interfaces.26

In Fig. 13 the cCV/E curves for a system of two polarized interfaces are depicted

by taking as the abscise the applied potential E (solid line), and the outer Eout and

inner Einn interface potentials (dashed and dotted lines, respectively).

From these curves it is clear that the difference between peak potentials for the

cCV/EM curve (DEp = 88 mV) is equal to the sum of those obtained from the cyclic

voltammograms plotted versus Eout and Einn (61 and 27 mV, respectively). The

different voltammetric responses obtained at outer and inner interfaces are the result

of the different potential drops at each. This feature is confirmed by the inset, in

which the time evolution of Eout (dashed line), Einn (dotted line) and EM (solid line)

are plotted. As can be seen, with the exception of the extreme regions, the time

variation of Eout is similar to that of E (although shifted towards more positive

potentials), such that a voltammogram similar to those of a single water/organic

interface is obtained (with DEp D 60 mV). In contrast, Einn remains almost constant

for the central part of the sweep (thus presenting a behaviour similar to that of a non

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polarizable interface). This constant value causes a sharp fall in the current

(see cCV/Einn curve) and, therefore, a narrow response (DEp = 27 mV).24,26

2.3. Coupling voltammetric techniques: Study of salt transfer processes

The coupling of different voltammetric techniques is extremely helpful for a fast,

effective and complete analysis and characterization of the system under study. One

innovative and interesting example is the combination of NPV, LSV and SWV

providing physical insights of the salt transfer processes.30 Indeed, Linear Sweep

Voltammetry (LSV) and SWV can complement each other effectively to distinguish

whether two successive ion transfers correspond to ions of opposite sign (like the

constituents of a Rz+Yz� salt) or to ions of equal sign, even though two voltammetric

peaks of the same sign are observed for both kind of transfers in both LSV and SWV

techniques. The use of NPV helps to interpret the experimentally observed behaviour.

Fig. 14 shows the theoretical NPV voltammograms (Fig. 14a), together with the

experimental and theoretical LSV voltammograms (dotted and solid lines,

respectively, Fig. 14b), and the experimental and theoretical SWV voltammograms

(circles and lines, respectively, Fig. 14c), corresponding to the transfer of the ionic

Fig. 13 cCV/EM (solid line), cCV/Eout (dashed line) and cCV/(�Einn) (dotted line) curves.

DE = 10�4 mV and v = 0.01 V s�1. Insert Figure: time evolution of the potentials EM (solid),

Eout (dashed) and (�Einn) (dotted). Reproduced from [A. Molina, C. Serna, J. Gonzalez,

J. A. Ortuno and E. Torralba, Phys. Chem. Chem. Phys., 2009, 11, 1159] with permission of


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Fig. 14 Theoretical NPV voltammograms (a), experimental (dotted lines) and theoretical (solid lines)

LSV voltammograms (b), and experimental (circles) and theoretical (lines) SWV voltammograms (c),

obtained for a 2.5� 10�4M solution of BMPyrTFSI bymaking two different and independent sweeps

in opposite directions: from negative to positive potentials (indicated by dash arrows, Ein = �0.7 V,

Efin=0.5 V) and vice versa (indicated by solid arrows,Ein=0.5 V,Efin=�0.7 V). Theoretical curvesin (a) were calculated by using the optimal E

1=2M;Xz and A

ffiffiffiffiffiffiffiffiffiDw

Xz

pobtained from the fitting of (c):

E1=2M;BMPyrþ ¼ 311 mV, E

1=2M;TFSI� ¼ �494 mV, A

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDw

BMPyrþ

q¼ 5:9� 10�4 cm3 s�1=2, A

ffiffiffiffiffiffiffiffiffiffiffiffiDw

TFSI

p¼

6:24� 10�4 cm3 s�1=2 and t = 1s. Theoretical curves in (b) and (c) were calculated by taking

E1=2M;Xz and A


Xz

pas adjustable parameters. (b): DE = 0.01 mV, v = 5 mV/s. (c): Esw = 50 mV,

Es = 10 mV, t= 0.3 s. T= 298.15 K. Reproduced from [A. Molina, J. A. Ortuno, C. Serna and E.

Torralba, Phys. Chem. Chem. Phys., 2010, 12, 13296] with permission of [Royal Society of Chemistry].

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liquid salt BMPyrTFSI from water to the solvent polymeric membrane in a membrane

system of two polarized interfaces. A similar plotted is depicted in Fig. 15, but showing

the theoretical NPV, LSV and SWV responses (Fig. 15a–c, respectively) of two ions of

opposite sign (solid lines) and with the same sign (dashed lines).

Through NPV (Fig. 14a and 15a), it is easy to distinguish if two successive ion

transfers correspond to ions of opposite sign, as occurs with the anion and the cation

in the case of a salt, giving rise to two waves of different sign (Fig. 14a), or ions of the

same sign which could be present in the sample, which gives two waves of the same

sign (Fig. 15a). However, more powerful and easily applicable techniques like LSV

(Fig. 14b and 15b) or SWV (Fig. 14c and 15c) are highly desirable.

Regarding the LSV and SWV voltammograms corresponding to the salt transfer

(Fig. 14b and c), it is clear that the two peaks which appear in each scan of both figures

correspond to the transfers of the anion and the cation. However, as these two peaks do

not have different current signs it could seem difficult to determine if they correspond to

ions with the same or opposite charge. The use of LSV makes it easy to distinguish both

situations easily, since in the case of opposite charged ions a large current fall is observed at

the beginning of the experiment and the current tends to zero between both ion transfer

processes (Fig. 14b); while when the transfer of two equal sign ions is considered, the initial

current is null and the current between both ion transfer processes is always different form

zero, since it tends to the limit current value of the first ion transfer (Fig. 15b).

Fig. 14a (NPV) and 14b (LSV) are the key for the physical explanation of the

SWV voltammograms given in Fig. 14c since, due to the subtractive character of

SWV technique (Isw = I2p�1 – I2p), the morphology of its signal makes it difficult to

discern between the two kinds of ion transfer considered. This indicates that, in spite

of the high resolution and great selectivity of SWV, LSV is more suitable for

distinguishing the ion transfer of the two constituting ions of a salt, and both

techniques can complement each other in an excellent way.

Systems with two L/L polarized interfaces are more advantageous for the analysis

of the transfer of the two ions constituting a salt than those with a single polarized

one, since the voltammetric signals of the ions are much more separated in these kind

of systems.27,30

3. Chronopotentiometry

Although current driven ion transfer through solvent polymeric membranes of ion

selective electrodes has provided innovative applications such as pulstrodes,85 back-

side calibration chronopotentiometry,86 substrate ions release for potentiometric

biosensing of enzymes87 and reverse current pulse method to restore uniform

concentration profiles in ion-selective membranes,88,89 the study and characterization

of the corresponding signal of the ion transfer driven by current fluxes has been

scarcely tackled, even less so when these current fluxes vary with time. Given the great

versatility that current fluxes show for studying charge transfer processes,90,91 this

shortage of application might be due to a lack of theory.

This section focuses on the theoretical development and experimental application

of two of the most used current-time functions in chronopotentiometry: the

exponential current flux and the constant current.

3.1. Ion transfer driven by exponential and constant current fluxes.

The use of an exponential current flux of the form I(t) = I0ewt (see Notation for

symbol definitions) is a powerful tool in the characterization of electrode processes

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Fig. 15 Theoretical NPV voltammograms (a), and theoretical LSV (b) and SWV (c) voltammograms

obtained, respectively, for the successive transfer of two ions with opposite charge (R+Y�, solid lines)

and of two cations (R+R0+, dashed lines). c�Yþ ¼ c�Y� ¼ c�R0þ ¼ 2:5� 10�4 M, E1=2M;Rþ ¼ 311 mV,

E1=2M;Y� ¼ �494 mV, E

1=2M;R0þ ¼ �494 mV. (a): A


Rþp

¼ 5:9� 10�4 cm3 s�1=2, AffiffiffiffiffiffiffiffiffiffiDw

Y�p

¼6:24� 10�4 cm3 s�1=2, A

ffiffiffiffiffiffiffiffiffiffiDw

R0þp

¼ 6:24� 10�4 cm3 s�1=2, t = 1 s. (b): AffiffiffiffiffiffiffiffiffiDw

Rþp

¼ 7:8�10�4 cm3 s�1=2, A

ffiffiffiffiffiffiffiffiffiffiDw

Y�p

¼ 6:6� 10�4 cm3 s�1=2, AffiffiffiffiffiffiffiffiffiffiDw

R0þp

¼ 6:6� 10�4 cm3 s�1=2, DE =

0.01 mV, v = 5 mV/s, Ein = �0.75 V, Efin = 0.5 V. (c): AffiffiffiffiffiffiffiffiffiDw

Rþp

¼ 5:9� 10�4 cm3 s�1=2,

AffiffiffiffiffiffiffiffiffiffiDw

Y�p

¼ 6:24� 10�4 cm3 s�1=2; AffiffiffiffiffiffiffiffiffiffiDw

R0þp

¼ 6:24� 10�4 cm3 s�1=2, Esw = 50 mV, Es =

10 mV, t = 0.3 s, Ein = �0.75 V, Efin = 0.5 V. T = 298.15 K. Reproduced from [A. Molina,

J. A. Ortuno, C. Serna and E. Torralba, Phys. Chem. Chem. Phys., 2010, 12, 13296] with permission of


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since it presents important advantages over the application of a constant current,

such as enabling the time window to be changed easily by using different values of I0and/or w, or by allowing a stationary response which is simpler to analyze.90,91

When an exponential current flux of the form I(t) = I0ewt is applied to drive the

ion transfer of a target ion Xz in a single L/L polarized interface system, the

expressions for the interfacial concentrations can be written as28

cWXzð0; tÞc�Xz

¼ 1�NsFðOÞ ð44Þ

cMXzð0; tÞc�Xz

¼


Xz

DMXz

sNsFðOÞ ð45Þ

where O = wt (see Notation for other definitions). In the case of a system of two

polarized interfaces, as well as eqn (44) and (45), the interfacial concentrations at the

inner interface need to be considered

cW0

Rz0 ðd; tÞc�Xz

¼ffiffiffiffiffiffiffiffiffiDW

Xz

DW 0

Rz0

sNsFðOÞ ð46Þ

cMRz0 ðd; tÞ ¼ c�

Rz0 ð47Þ

where it is supposed for simplicity that |z| = |z0|.

Assuming that the ion transfers behave in a nernstian way, the E � t responses

corresponding to the application of this current flux to both kinds of membrane

systems given by eqn (T3.1) and (T3.2) of Table 3 are derived. The corresponding

expressions for the E � t curves when a constant current flux is applied are also

shown in Table 3 (Eqs. (T3.3) and (T3.4))). They can be easily derived from the

previous ones just by making w - 0.35

E1/2 and E1/2M in the table are, respectively, the voltammetric half-wave potential

and the voltammetric half-wave membrane potential for the system of one and

two polarized interfaces (eqn (20) and (39)). The transition times, te.c and tc.c,corresponding to the application to both kind of membrane systems of the

exponential and constant current fluxes are given- the former by the following

non-explicit expression

FðOtÞ ¼1

Nsð48Þ

Table 3 Expressions for the transient E-t responses corresponding to ion transfer driven by anexponential and a constant current-time flux in membrane systems with one and two polarizedinterfaces (see Notation for symbol definitions)

One polarized interface system Two polarized interfaces system

EðtÞ ¼ E1=2 þ RTzF

ln NsFðOÞ1�NsFðOÞ

� �(T3.1) EðtÞ ¼ E

1=2M þ RT

zFln 2 NsFðOÞ½ 2

1�NsFðOÞ½

� �(T3.2)

EðtÞ ¼ E1=2 þ RTzF

ln t1=2

t1=2c:c �t1=2

� �(T3.3)

EðtÞ ¼ E1=2M þ RT

zFln 2 t

t1=2c:c �t1=2

� �(T3.4)

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with Ot = wt, and the latter by the Sand0s equation92

t1=2c:c ¼ p1=2Ns

ð49Þ

3.2. Reciprocal derivative chronopotentiometry (RDCP)

In Reciprocal Derivative Chronopotentiometry (RDCP) the inverse of the derivatives

of the E � t or E � I curves are plotted vs the potential E (with E being the measured

potential and I the applied current). The signal thus built presents a peak-shaped

feature from which it is possible to obtain accurate thermodynamic information of the

process under study, since ohmic drop and capacitative effects scarcely influence the

peak because these are obtained from the central part of the E � t curve. Hence, it is

much more useful than the traditional S-shaped potential-time curves.93–95

The expressions for the transient reciprocal derivative chronopotentiometric

dt/dE � E and dI/dE � E curves corresponding to the uptake of a target ion Xz in

a membrane system of one and two polarized interfaces during the application of an

exponential or a constant current can be obtained by differentiating the corresponding

E � t expressions.35 In the particular case of the application of a constant current the

peak coordinates can be obtained analytically, and are given by.

Epeak ’ E1=2 þ 0:693 RTzF

dtdE

�peak’ 0:296 zF

RTtc:c

)ð50Þ

for the system of a single polarized interface, and

Epeak ’ E1=2M þ 1:31 RT

zFdtdE

�peak’ 0:227 zF

RTtc:c

)ð51Þ

for that of two L/L polarized ones. Evidently, expressions for the dI/dE � E responses

cannot be derived in this particular case.

Fig. 16 and 17 display the theoretical and experimental dt/dE – E curves

corresponding to the transfer of a series of tetraalkylammonium cations and

tricyclic catamphiphilic drugs from water to a solvent polymeric membrane driven

by an exponential current flux of the form I(t) = I0ewt (Fig. 16) and by a constant

current (Fig. 17) in a system of one (Fig. 16a and 17a) and two (Fig. 16b and 17b)

polarized interfaces. As can be seen, a very good fitting between theoretical and

experimental data is attained in all cases.

Regarding Fig. 16 and 17, it can be seen that for both kinds of membrane systems

quite well-defined peaks are obtained for any of the target ions considered.

Furthermore, the peaks obtained with both kinds of current fluxes are even

narrower than those obtained with some of the more powerful voltammetric

techniques like SWV or DPV, in such a way RDCP shows a higher resolution.

It is noteworthy that the wide range of potentials that the system of two polarized

interfaces provides makes the registration of the chronopotentiogram of the highly

lipophilic ion THexA+ possible (white triangles in Fig. 16b and 17b) as well as the

determination of its standard ion transfer potential to NPOE/PVC membranes.

Table 4 shows the standard ion transfer potentials for the different ions assayed in the

two kinds of systems, obtained when the ion transfer is driven by an exponential

current-time flux (first and second columns, ðDWMf0

XþÞ and by a constant one (third and

fourth columns, ðDWMf0

Xþ ;c;cÞ, together with those reported using voltammetry.27,42

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The values of the standard ion transfer potentials presented are in acceptable

agreement with those previously reported by using voltammetry, showing the

reliability of the procedure for the determination of standard ion transfer potentials.

A comparison of the values of the standard ion transfer potentials obtained with

both kinds of membrane systems for each kind of current flux reveals that the data

Fig. 16 Experimental dt/dE � E curves obtained for 10�3 M solutions of different ions in a

membrane system of one and two polarized interfaces (a and b, respectively) when an

exponential current-time flux of the form I(t) = I0ewt is applied to drive the ion transfer. Solid

lines correspond to the theoretical curves. I0 = 12 mA, w = 0.05 s�1, T = 298.15 K, and

AffiffiffiffiffiffiffiffiffiDw

Xz

pin cm3 s�1/2: (a): TBA+, 4.6 � 10�4 (’); TPA+, 5.2 � 10�4 (K); Im+, 4.7� 10�4 (m);

Cmp+, 4.6 � 10�4 (J). (b): TBA+, 3.8 � 10�4 (’); TPA+, 3.9 � 10�4 (K); THexA+, 5.0 �10�4 (n); Im+, 5.2 � 10�4 (m); Cmp+, 4.8 � 10�4 (J). Reproduced from [E. Torralba,

J. A. Ortuno, C. Serna, J. Gonzalez and A. Molina, Electroanalysis, 2011, 23, 2188] with

permission of [John Wiley and Sons].

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provided for the system of two polarized interfaces are, in general, more consistent. Thus,

the system with two polarized interfaces seems to be better suited to this kind of studies.

Moreover, the corresponding standard variation values obtained indicate that this system

displays a slightly better repeatability. No great differences are found between the results

from the application of the exponential current flux and that of the constant one, merely

that the application of the exponential current provides slightly better detection limits.35

Fig. 17 Experimental dt/dE � E curves obtained for 10�3 M solutions of different ions in a

membrane system of one and two polarized interfaces (a and b, respectively) when the ion

transfer is driven by a constant current flux. Solid lines correspond to the theoretical curves.

I0 = 15 mA, T= 298.15 K, and AffiffiffiffiffiffiffiffiffiDw

Xz

pin cm3 s�1/2: (a): TBA+, 5.3 � 10�4 (’); TPA+, 4.6 �

10�4 (K); Im+, 5.8 � 10�4 (m); Cmp+, 5.2 � 10�4 (J). (b): TBA+, 3.6 � 10�4 (’); TPA+,

3.1 � 10�4 (K); THexA+, 3.5 � 10�4 (n); Im+, 3.7 � 10�4 (m); Cmp+, 3.4 � 10�4 (J).

Reproduced from [E. Torralba, J. A. Ortuno, C. Serna, J. Gonzalez and A. Molina,

Electroanalysis, 2011, 23, 2188] with permission of [John Wiley and Sons].

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In spite of the goodness that chronopotentiometry and RDCP shows for ion

transfer studies and the potentiality these kinds of studies have, the treatment of

the experimental data has proved to be rather cumbersome, especially for the

compensation of the IR term in current fluxes variable with time. Moreover, the

spoilage of the membrane system when current fluxes are applied to drive the ion transfer

seems to be somewhat quicker than for the application of potential perturbations, so

further investigation and improvements in these points are still needed.

3.3. Stationary behaviour

The use of programmed currents of the form I(t) = I0ewt allows a steady state

behaviour to be attained even under planar diffusion conditions. In this steady state

situation the E–t and RDCP responses simplify notably and can be characterized

analytically. Moreover, under steady state conditions the chronopotentiometric

IN–E responses are analogous to the voltammetric ones, so identical information

can be obtained from them and their derivatives28

In Table 5 the expressions for the stationary chronopotentiometric E � t and

reciprocal derivative chronopotentiometric dt/dE � E and dI/dE � E curves

corresponding to the uptake of a target ion Xz from the sample solution to the

membrane in a system of one and two polarized interfaces are gathered, and this

transfer is driven by an exponential current-time flux of the form I(t) = I0ewt28

IN(t) in Table 5 represents the normalized applied current

INðtÞ ¼ I0ewt=I0e

wte:c ¼ hðtÞ ð52Þ

for systems of a single polarized interface, and

INðtÞ ¼ I0ewt=I0e

wte:c ¼ gðtÞ ð53Þ

Table 4 Standard ion transfer potentials for the different ions assayed (mV). The differentmembrane systems and current fluxes used are indicated by square brackets and subscripts,respectively. Reproduced from [E. Torralba, J. A. Ortuno, C. Serna, J. Gonzalez and A.Molina, Electroanalysis, 2011, 23, 2188] with permission of [John Wiley and Sons]

Ion Dwmf

0Xz ;e:c

a Dwmf

0Xz ;e:c

b Dwmf

0Xþ ;c:c

a Dwmf

0Xz ;c:c

b Dwmf

0Xz

c

TPentA+ �355 �358 �388 �354 �365THexA+ — �472 — �440 —

Im+ �161 �130 �150 �135 �163Cmp+ �213 �172 �193 �170 �175a Data obtained using the single polarized interface system. b Data obtained using the two

polarized interfaces system. c Data obtained using voltammetry.

Table 5 Expressions for the stationary E-t, dt/dE-E and dI/dE-E curves corresponding to iontransfer driven by an exponential current-time flux in membrane systems with one and twopolarized interfaces

One polarized interface system Two polarized interfaces system

EssðtÞ ¼ E1=2 þ RTFln IN ðtÞ

1�IN ðtÞ

� �(T5.1) EssðtÞ ¼ E

1=2M þ RT

zFln

2I2NðtÞ

1�IN ðtÞ

� �(T5.2)

dtdE

�ss¼ zF

wRTð1� hðtÞÞ (T5.3) dt

dE

�ss¼ zF

wRT1�gðtÞ2�gðtÞ

h i(T5.4)

dIN ðtÞdE

� �ss¼ dðhðtÞÞ

dE¼ zF

RTgeZðtÞ

ð1þgeZðtÞÞ2(T5.5) dIN ðtÞ

dE

� �ss¼ dðgðtÞÞ

dE¼ zF

4RTðleZðtÞÞ2þ4leZðtÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðleZðtÞÞ2þ8leZðtÞp � leZðtÞ� �

(T5.6)

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for those of two polarized ones, where h(t) is the function that contains the

dependence with the measured potential in a system of a single polarized interface

(analogous to that given in eqn (12)) and g(t) in a system of two polarized interfaces

(analogous to that given in eqn (31)). These stationary dt/dE and dI(t)/dE responses

present sigmoidal-shaped and peak-shaped features, respectively, and both of them

can be characterized analytically. Specifically, the dt/dE � E responses can be

characterized by a half-wave potential (E1/2chrono for systems of a single polarized

interface or E1/2M,chrono for systems of two polarized ones), and by a limiting dt/dE

value (yplateau), and the dIN/dE � E responses by a certain peak coordinates

(Epeak, ypeak) and a half-peak width (W1/2, see Table 6).

As can be seen, the stationary RDCP responses are quantitatively related with the

voltammetric half-wave potential in the case of systems of a single polarized

interface and with the voltammetric half-wave membrane potential in the case of

systems of two polarized ones, and therefore they can be used to quantify the

lipophilicity of the ions studied, so avoiding numerical fitting.

Regarding the dIN/dE � E curves, the peak parameters shown in Table 6 are

identical to those obtained from the derivatives of the IN � E voltammetric curves

obtained in NPV (with E being the measured potential for chronopotentiometric

techniques and the applied potential for the voltammetric ones), with the

voltammetric normalized current, IN,24,74 given by

IN ¼ I=zFA


Xz

pt

rc�Xz ð54Þ

Moreover, the shift of 13 mV of the potential peak of the these curves with respect

to the voltammetric half-wave membrane potential in the system of two polarized

interfaces resembles the behaviour previously reported when Differential Pulse

Voltammetry was applied to these kinds of membrane systems.11,25,28

Fig. 18 depicts the theoretical E � t (Fig. 18a) and (dt/dE)–(E � E1/2) (Fig. 18b)

curves corresponding to the application of an exponential current flux of the form

I(t) = I0ewt to a system of two polarized interfaces for a fixed value of the exponent

w and different values of I0 (solid lines), together with the corresponding stationary

E � t and RDCP curves (black dots). The values of Ot (= wt) corresponding to each

value of I0 are shown on the curves.

From Fig. 18a it can be observed that, as the value of Ot increases (i.e. as I0diminishes) the potential time curves corresponding to the transient state (solid lines)

tend to overlap at smaller time values with those of steady state (dotted lines).

Moreover, when comparing those curves with those provided for the system of a

single polarized interface, it is found that for a given Ot the chronopotentiogram of

Table 6 Characteristic parameters of the stationary dt/dE vs E curves and peak coordinates ofthe stationary (dIN/dE) vs E ones for systems of one and two polarized interfaces

One polarized interface Two polarized interfaces

dt=dE � EE

1=2chrono ffi E1=2

yplateau ¼ zFwRT

�dt=dE � E

E1=2M;chrono ffi E

1=2M þ 25ðmVÞ

yplateau ¼ zF2wRT

(

dIN=dE � EEpeak ¼ E1=2

ypeak ¼ zF4RT

W1=2 ffi 90ðmVÞ

8<: dIN=dE � E

Epeak ffi E1=2M þ 13ðmVÞ

ypeak ffi 0:7 zF4RT

W1=2 ffi 131ðmVÞ

8><>:

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the system of two polarized interfaces covers a wider range of potential than that

corresponding to the system of a single polarized one, which constitutes an

advantage for this kind of membrane system.28

Regarding Fig. 18b, it can be noted that as Ot increases, the RDCP curves (solid

lines) become higher and wider, until they show a plateau for Ot values at which the

steady state condition is attained practically from the beginning of the experiment.

In these conditions, the RDCP curves of the system of two polarized interfaces

exhibit a half-peak width approximately twice that of those of a single polarized one

Fig. 18 Solid lines: Theoretical (E � E1/2)�t (a) and RDCP ((dt/dE)–(E � E1/2), b) curves

corresponding to the application of a current flux of the form I(t) = I0ewt to a system of two

polarized interfaces for different values of I0. Black dots: Theoretical (E � E1/2)–t and RDCP

((dt/dE)–(E � E1/2)) curves corresponding to the steady state situation. The values of the

Ot(= wt) parameter corresponding to each value of I0 are shown on the curves. Stationary

curves for Ot = 0.3 are not shown. White square marks the coordinates of the chronopotentio-

metric half - wave membrane potential. c�Xþ¼ 1:5 mM, DWMf00

Xþ¼ 100 mV,

DW1

Xþ ¼ 10�5 cm2 s�1, DMXþ ¼ 10�8 cm2 s�1, w = 1 s�1, T = 298.15 K. I0 = 0.01, 0.1, 1, 10

and 50 mA. Reproduced from [A. Molina, E. Torralba, J. Gonzalez, C. Serna and J. A. Ortuno,

Phys. Chem. Chem. Phys., 2011, 13, 5127] with permission of [Royal Society of Chemistry].

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and their height is half that of the system of a single polarized interface (see Table 6).

It is also interesting to note that for systems of two polarized interfaces the

chronopotentiometric half-wave membrane potential is shifted 25 mV with respect

to that of the voltammetric one, as indicated in Fig. 18b (see also Table 6).

3.4. Current reversal chronopotentiometry (RCP)

In RCP a constant or variable with time current flux is applied and then reversed

when the corresponding transition time is reached with no re-establishing of the

equilibrium, and the E � t curves corresponding to the direct and reverse charge

transfer processes are plotted vs the potential.96,97

The uptake and stripping transition times corresponding to the application of the

two successive currents of opposite sign, tu and ts, are equal for both kind of

membrane systems, and are given by29

t1=2u ¼ p1=2Ns

ð55Þ

and

tstu

� �1=2

¼ 1

3ð56Þ

3.5. Cyclic reciprocal derivative chronopotentiometry (CRDCP)

CRDCP is considered one of the most powerful chronopotentiometric techniques,

since it is analogous to CV under current-controlled conditions. Thus, it provides the

same information as CV, but the mathematical treatment is simpler. It allows the

evaluation of thermodynamic, kinetic and analytical parameters for both direct and

reverse processes from the peak coordinates and, furthermore, the ratio of heights

and half-peak widths for both direct and reverse processes provide very simple and

reliable criteria for analyzing the reversibility.94,95,98,99

Fig. 19 shows the theoretical and experimental E � t and dt/dE � E curves

corresponding to the uptake and stripping of a series of tetraalkylammonium cations

from water to a solvent polymeric membrane when RCP (Fig. 19a) and CRDCP

(Fig. 19b) are applied to a system of one polarized interface.

As can be seen from Fig. 19a, a fairly good fit is obtained for both uptake and

stripping when RCP is applied. However, neither the beginning nor the end of the

chronopotentiogram is well-defined for both the uptake and stripping due to the non

desirable effects which appear in these zones. Hence, the application of techniques

with peak shaped responses like those plotted in Fig. 19b seems more attractive for

improving the reliability of the results.

The theoretically predicted features of the dt/dE � E curves are confirmed by the

experimental recordings presented in Fig. 19b, and the agreement between

theoretical and experimental data is better in the peak region than at the bottom

of the peak. In line with that observed from RDCP, the CRDCP uptake and

stripping peaks are narrower than those provided by the more powerful

voltammetric techniques like SWV or DDPV.

4. Facilitated ion transfer

Facilitated ion transfer is widely used in nature and in artificial membranes for

ion-selective sensors and metal ion separations. It is observed, for instance, in cases

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like the transfer of highly hydrophilic ions from water to an organic phase.100–108

Electrochemical studies on the facilitated transfer of various ions across L/L interfaces

have been extensively reported in the literature, with ion transfer followed by

complexation or ion-pair formation being one of the mot encountered examples.107

Facilitated ion transfer process can take place at ITIES according to an ACT

(Aqueous complexation followed by transfer) or a TOC (Transfer followed by

organic complexation) mechanism, represented in Fig. 20.

Fig. 19 Experimental E � t and dt/dE � E curves (a and b, respectively) obtained for 0.7 �10�3 M solutions of TBA+ and TPrA+ (black and white circles, respectively) when RCP and

CRDCP with constant current are applied to a system of a single polarized interface. Solid lines

correspond to the theoretical curves. I0 = 5 mA, T = 298.15 K and the following values of

AffiffiffiffiffiffiffiffiffiDw

Xz

p: (a) TBA+, 6.35 � 10�4 and TPrA+,8.4 � 10�4 cm3 s�1/2, (b) TBA+, 5.9 � 10�4 and

TPrA+,7.8� 10�4 cm3 s�1/2. Reproduced from [E. Torralba, A. Molina, J. A. Ortuno, C. Serna

and J. Gonzalez, J. Electroanal. Chem, 2011, 661, 219] with permission of [Elsevier].

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The TOC or EC mechanism, is based on the assumption that the facilitated ion

transfer reaction occurs via the diffusion of the ion from the aqueous phase to the

organic one, and that the chemical complexation with the ligand occurs once the ion

has crossed the interface. In contrast, in the ACT mechanism the ligand is partitioned

between the aqueous and the organic phases first. Then, aqueous complexation occurs

and, finally, the complex is transferred to the organic phase. The ACT mechanism is

rather less frequent than TOC, and has been less studied. In this section we focus on

the more frequent TOC mechanism and its variants.

Depending on the kind of kinetic control observed when an electrochemical

perturbation is applied to the TOC or EC mechanism, it can be split into four sub-

categories:

(a) TkinOCkin (EkinCkin): when the ion transfer is kinetically controlled (not reversible)

and the chemical complexation is disturbed by the electrochemical perturbation at the

surroundings of the interface. This implies the existence of a reaction layer in the organic

phase adjacent to the interface, with thickness comparable to the diffusion layer.

(b) TkinOCrev (EkinCrev): when the ion transfer is slow and the equilibrium

complexation is restored very quickly. In this situation the thickness of the reaction

layer is negligible.

(c) TrevOCkin (ErevCkin): when the ion transfer behaves as reversible, and

the chemical complexation is disturbed.

(d) TrevOCrev (ErevCrev): when the ion transfer behaves as reversible and

the complexation equilibrium is very quickly restored.

The first situation (a) is the most general for a TOC mechanism and the rest

should be deduced as particular cases of it. The last variant of the TOC mechanism

(d) is called TIC (Transfer by interfacial complexation) and does not consider kinetic

effects at all, yet a large proportion of references on facilitated ion transfer

assume this.

Fig. 20 Schematic view of the TOC and ACT mechanisms. kf and kb: forward and backward

kinetic constants of the ion transfer, k1 and k2: forward and backward kinetic constants of the

complexation reaction.

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4.1. Normal pulse voltammetry and chronoamperometry

When the homogeneous chemical reaction is kinetically controlled and the ion

transfer is reversible (case c), the ion transfer facilitated by complexation in the

organic phase (TOC mechanism) in membrane systems of one and two polarized

interfaces can be characterized, respectively, by the following I � E � t responses60

I

Id¼ geZð1þ KÞ

1þ Kdr=dþ geZð1þ KÞ ð57Þ

and

I

Id¼ 1

4

lð1þ KÞ1þ Kdr=d

� �2

e2Z þ 8lð1þ KÞ1þ Kdr=d

eZ

" #1=2� lð1þ KÞ1þ Kdr=d

eZ

8<:

9=; ð58Þ

In these equations, K is the equilibrium stability complexation constant under

pseudo-first order assumption, Id is given by eqn (13), Z is given by eqn (14) for the

former system and by eqn (31) for the latter; g and l are given, respectively, by

eqn (15) and (32) (or (33) depending on the signs of the ions transferred); drrepresents the reaction layer thickness

dr ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiDM=k

pð59Þ

d the diffusion layer one

d ¼ffiffiffiffiffiffiffiffiffiffiffiffipDMtp

ð60Þ

and other symbols are as defined in the Notation. The half-wave potentials for the

two kinds of membrane systems have, respectively, the forms

E1=2 ¼ DWMf00

Xz þRT

zFln

1

g

� �þ RT

zFln

1þ Kdr=d1þ K

� �ð61Þ

and

E1=2M ¼ E00

M þRT

zFln

1

l

� �þ RT

zFln

1þ Kdr=d1þ K

� �ð62Þ

eqn (57)–(62) simplify strongly if it is assumed that the complex formation and

dissociation are at equilibrium even when current is flowing, i.e. (k1 + k2)t c 1 or

dr { d. This assumption has been widely used in systems of a single polarized

interface103 and leads to the TIC mechanism (TrevOCrev), which involves a single

step occurring at the L/L interface and does not consider kinetic effects at all.

XZ(W) + L(M)$ XLZ(M)

Under total equilibrium conditions (te) the expression for the current and

half-wave potential for the system of one and two polarized interfaces become.

Ite

Id¼ geZð1þ KÞ

1þ geZð1þ KÞ ð63Þ

E1=2 ¼ DWMf00

Xþ þRT

zFln

1

g

� �þ RT

zFln

1

1þ K

� �ð64Þ

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and

It:e

Id¼ 1

4ðlð1þ KÞ2Þe2Z þ 8lð1þ KÞeZh i1=2

�lð1þ KÞeZ�

ð65Þ

E1=2M ¼ E00

M þRT

zFln

1

l

� �þ RT

zFln

1

1þ K

� �ð66Þ

eqn (64) and (66) constitute an equivalent of the Deford-Hume Equation for planar

diffusion in systems of one and two L/L polarized interfaces, respectively.109

Fig. 21a and b show (solid lines) the concentration profiles of the different species

involved in the ion transfer facilitated by complexation in the organic phase in a

membrane system of a single polarized interface, in limiting current conditions

(Fig. 21a), and for a potential applied of 50 mV (Fig. 21b) for two different values of

the stability constant (shown on the curves). The dotted lines correspond to the

concentrations profiles of a simple ion transfer in the same conditions. Fig. 21c

shows the I/E curves corresponding to the facilitated ion transfer at the two stability

constants selected (solid lines), together with those obtained with the te

approximation (dashed lines) and that corresponding to a simple ion transfer

process (dotted lines). A vertical dashed line indicates the potential chosen for

Fig. 21b.

One of the conclusions obtained from this Figures is that the application of

intermediate potentials is highly desirable in studying this kind of facilitated ion

transfer, since, limiting current conditions give rise to concentration profiles of the

ion X+independently of the kinetic of the complexation reaction (compare the

concentration profiles of the ion X+in the aqueous phase for the facilitated ion

transfer with those of the simple ionic transfer in Fig. 21a and b). Another important

point is the comparison between the current/potential curves obtained with and

without considering the kinetics of the complexation reaction. Thus, from Fig. 21c it

can be observed that as the stability constant increases, the kinetic effects gain

importance, and the te curves (obtained with the Matsuda’s treatment) differ from

those obtained when considering the kinetics. Hence, it is important to consider

these effects.60

Fig. 22a shows the variation of DE1/2 (eqn (67)) with the dimensionless kinetic

parameter w(= (k1 + k2)t) for different values of the stability constant K (shown on

the curves) for a system of a single polarized interface, with DE1/2 being the shift of

the half-wave potential of the facilitated ion transfer (c*L a 0) with respect to that

corresponding to a simple ion transfer process (c*L = 0)110 (see eqn (67)). In Fig. 22b

the plots exp(zFDE1/2/RT) versus 1=ffiffitp

for a fixed value of K and different values of

k are presented.

For a given value of the stability constant, DE1/2 values shift to more negative

potentials as w increases (Fig. 22a), since the transfer is being favoured by the

increasingly fast metal-complex interconversion causing a decrease in the Gibbs

energy of ion transfer The higher the equilibrium constant, the more stable the

complex and the easier the ion transfer. Consequently, a more accentuated

displacement to less positive potentials is observed as K increases. On the

contrary, the DE1/2 obtained by using the te approximation is not affected by the

kinetic, so the te treatment cannot be used for small values of w and higher values K.

The curves given in Fig. 22a can be used as working curves, from which for a given

time of the experiment, k(=w/t) can be immediately obtained once the stability

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Fig. 21 (a) and (b): Solid lines: Concentration profiles corresponding to the ion transfer facilitated

by complexation in the organic phase in a membrane system of a single polarized interface for two

different values of K (shown on the curves), obtained under limiting current conditions (a) and for a

potential applied of 50 mV (b). Dotted lines: Concentration profiles corresponding to a simple ion

transfer. (c): I/E curves of the facilitated ion transfer obtained from the dkss and te approximations

(solid and dash-dotted lines; respectively) at the same K values as used in (a) and (b) (shown on

the curves), and I/E curve corresponding to a simple ion transfer process (dotted line). te and

dkss curves corresponding to K = 0.7 are overlapped. DwMf00

Xþ ¼ 0 mV, c�Xþ ¼ 1 mM,

DW1

Xþ ¼ 10�5 ¼ 10�5 cm2 s�1, DMXþ ¼ 10�8 cm2 s�1, t = 1 s, w = 500, A = 0.081 cm2, T =

298.15 K. Reproduced from [A. Molina, E. Torralba, C. Serna and J. A. Ortuno, J. Phys. Chem. A,

2012, Doi: 10.1021/Jp2109362] with permission of [American Chemical Society]

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constant K is known. The variation in the dimensionless kinetic constant can

be attained by varying the time of the experiment and also by changing the

ligand concentration.

The plots given in Fig. 22b are very useful for the complete characterization of the

coupled chemical complexation. The representation of exp(zFDE1/2/FT) with 1=ffiffitp

is

Fig. 22 (a): Evolution of DE1/2 with w (= kt, being t = 1s) in a system of a single polarized

interface for different values of K (shown on the curves), obtained by using the dkss

approximation (dashed lines) and the te approximation (dash-dotted line). (b): Linear plots

of exp(zFDE1/2/FT) versus 1=ffiffitp

for the system of a single polarized interface for K = 50 and

different values of k(shown on the curves). DwMf00

Xþ ¼ 0 mV, c�Xþ ¼ 1 mM,

DW1

Xþ ¼ 10�5 cm2 s�1, DMXþ ¼ 10�8 cm2 s�1, A = 0.081 cm2, T = 298.15 K. Reproduced from

[A. Molina, E. Torralba, C. Serna and J. A. Ortuno, J. Phys. Chem. A, 2012, Doi: 10.1021/

Jp2109362] with permission of [American Chemical Society].

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linear, and the values of the slope and the intercept can be used to obtain k and K of

the complexation reaction, as can be seen in the equation inserted in Fig. 22b

DE1=2 ¼ E1=2ðc�L 6¼ 0Þ � E1=2ðc�L ¼ 0Þ ¼ RT

Fln

1þ K=ffiffiffiffiffiffipwp

1þ K

� �ð67Þ

These equations are also applicable for characterizing the coupled chemical

complexation in liquid membrane systems of two polarized interfaces, since the

kinetic dependence of the half-wave potential is the same for both kinds of

membrane systems (see eqn (61) and (62)).60

4.2. Cyclic voltammetry

The first theory for cyclic voltammetry of facilitated ion transfer across ITIES was

developed by Homolka et al.111 Its main conclusion was to relate the peak-to-peak

separation with the complexation stoichiometry. Nevertheless, this treatment, like

the majority of subsequent ones, was based only on pure thermodynamic principles

and ignored the kinetics of the complexation reaction. Gulaboski et al.107 were the

first to suggest that the kinetic effects due to the chemical complexation should be

taken into account; since neglecting these effects, could lead to misinterpretations

and incorrect values of the estimated parameters in the experiments.

Fig. 23 shows the simulated cyclic voltammograms for the facilitated ion transfer

reaction of an ion M+2 for different values of the ligand concentration, obtained by

Gulaboski et al. in reference.

Two distinctive features in the evolution of the cyclic voltammograms with the ligand

concentration can be observed when kinetic effects of the complexation reaction are

considered. First, the peak currents are sensitive to the ligand concentration’s decreasing

when the concentration increases; second, the mid-peak potentials remain practically

invariable when varying the ligand concentration, suffering just a slight shift toward

positive values as the concentration increases. This has been attributed to opposite

effects of the kinetics and thermodynamics of the complexation reaction.107

Fig. 23 Simulated cyclic voltammograms for facilitated ion transfer reaction of the M2+ ion

obtained by increasing the ligand concentration in the organic phase, in the presence of kinetic

effects due to the chemical complexation reaction. Scan rate v = 20 mV/s, potential increment

dE = 4mV, T = 298 K, the value of the real complexation constant in the simulations K0 =

108 mol dm3, k0f = 101.2 mol�1 cm3 s�1, D= 5 � 10�6 cm2 s�1. The concentration of the ligand

is c(L)/mol dm�3 = 0.00001(a), 0.0001(b) and 0.001(c). Reproduced from [R. Gulaboski,

E. S. Ferreira, C. M. Pereira, M. N. Cordeiro, A. Garau, V. Lippolis and A. Silva, J. Phys.

Chem. C 2008, 112, 153 ] with permission of [American Chemical Society].

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The effect of the charge of the free metal ion (as well as that of the complex) in the shape

of the cyclic voltammograms and in the mead-peak potential when a TIC mechanism is

considered is depicted in Fig. 24 for a 1 : 1 and 1 : 4 stoichiometry complexes.

As can be seen, the charge of the metal ion and that of the complex modifies the

fluxes across the interface, and then the current. The more positive the charge of

the ions, the more the transfer wave shifts towards high potentials. A variation of the

mid-peak potential proportional to 2.303 RT/zF with the slope and the intercept

given in Fig. 24c is obtained. The plot offfiffiffipp

gðstÞ vs z3/2given in Fig. 24d, whereffiffiffipp

gðstÞ is the current obtained by using the classical Nicholson and Shain

procedure, helps to interpret the observed behaviour.112

5. Ion transfer reactions at nanoscopic and microscopic Liquid/

Liquid interfaces

5.1. General scope

In the last thirty years the manufacturing and use of micrometer and nanometer-sized

electrochemical interfaces, microelectrodes andmicro-ITIES have been widely extended.

Fig. 24 Influence of the charge of the free ion on the voltammograms obtained when a unique

complex of 1 : 1 or 1 : 4 stoichiometry can be formed in the organic phase. (A) and (B) Currentffiffiffipp

gðstÞ vs. ðDwof

0 � Dwof

0Mzþ Þ for a 1 : 1 and, respectively, 1 : 4 stoichiometry; (C) Half-wave

potential Dwof

1=2MLþ vs. 2.303RT/zF; (D) Maximum forward peak current as a function of z3/2.

The input parameters are the following:Dw = 10-6, Kwj = 10�3, PL = 105, CLinit = 1, CMinit =

500. For the 1 : 1 stoichiometry, Ko1 = 1013, Ko

2 = Ko3 = Ko

4 = 10�3 and, for the 1 : 4

stoichiometry, Ko1 = Ko

2 = Ko3 = 104 and Ko

4 = 105. Reproduced from [F. Reymond, P. Carrupt

and H. H. Girault J. Electroanal. Chem 1998, 449, 49] with permission of [Elsevier].

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The main advantages associated with the reduction of the size of the interface are:

the fast achievement of a time-independent current-potential response (independent

of the electrochemical technique employed); the decrease of the ohmic drop; the

improvement of the ratio of faradaic to charge current, and the enhancement of the

mass transport. Their small size has played an important role in the electrochemical

expansion of the use of small sample volumes like microliter and even nanoliter,

which accounts for their good performance as sensors in living organisms.13,14,113,114

The first micro-ITIES was introduced by Taylor and Girault in 1986, who used a

glass micropipette which was pulled down to a fine tip of around 25 mm to support

the interface.13,14,113–115 For the uptake of ions into the pipette it is assumed that the

orifice is a disk; and therefore, the mass transport obeys the same mathematical

expressions as that for a microdisc electrode outside the pipette. So, the steady state

current corresponding to a disk microelectrode is

i = 4zFDrc*M (68)

whereD and c*M are the diffusion coefficient and concentration of the transferred species inthe solution outside the pipette and r the radius of the orifice. However, for a micropipettethe steady state current is 2.6 times higher than that given by eqn (68). This difference canbe attributed to a small amount of the filling aqueous solution which escapes from thepipette and forms a thin layer on its outer wall around the orifice. This results in animportant increase of the effective radius of the pipette, and a larger current can beobserved. Another factor is related with the very small thickness of the wall of the pipette,which is at most only some ten times greater than the orifice radius. The lower this wallthickness, the greater the enhancement of the diffusion transport. In contrast, for the egressof the ions enclosed within the confines of the pipette, linear semi-infinite diffusion, like thatcorresponding to a macro-ITIES, is considered. However, the quantitative analysis ofnon-steady state voltammetric data for this egress does not exactly obey this assumption,because the diffusion cannot be considered rigorously linear. These asymmetric diffusionfields give rise to asymmetric cyclic voltammograms.13,14,113 The smaller size of micro-pipette is advantageous for sensor applications, providing the possibility of studyingmicroenvironments as living cells, and can also be used as probe in scanning electro-chemical microscopy (SECM). Recently, Mirkin et al.116 have developed a nano-pipettewith the inside fluid motion electrochemically controlled by voltage variations. Volumesfrom attolitre to picolitre can be sampled or dispensed.

Campbell and Girault117 incorporated a micro-hole in a thin inert membrane. This

micro-ITIES has the advantage of symmetry of the diffusion fields on both sides of the

micro-orifice, which simplifies the theoretical treatment. Nevertheless, this advantage

is lost when the thickness of the membrane cannot be neglected. In this case it is

assumed that the microhole is cylindrical and filled with the organic phase, so, a planar

L-L interface separates the aqueous and organic phases. Converging diffusion outside

of the orifice and practically linear diffusion inside of the pore are assumed, with the

solution depending on the location of the interface inside the hole.114,118 This problem

can be rigorously treated by transposing the theory developed for microdiscs and

recessed microdiscs, which shows that the Cottrellian current decays for deep recess

microdiscs, showing that at short times linear diffusion dominates, while at long times,

the current tends to steady state value. This steady state response decreases as the

recess depth (thickness of the membrane) increases.119,120

In summary, although the construction of micro-ITIES is, in general, simpler than

that of microelectrodes, their mathematical treatment is always more complicated

for two reasons. First, in micro-ITIES the participating species always move

from one phase to the other, while in microelecrodes they remain in the same phase.

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This leads to complications because in the case of micro-ITIES the diffusion

coefficients in both phases are different, which complicates the solution when non-

linear diffusion is considered. Second, the diffusion fields of a microelectrode are

identical for oxidized and reduced species, while in microITIES the diffusion fields

for the ions in the aqueous and organic phases are not usually symmetrical.

Moreover, as a stationary response requiresffiffiffiffiffiffiDtp

� r0 (where D is the diffusion

coefficient, r0 is the critical dimension of the microinterface, and t is the experiment

time), even in L/L interfaces with symmetrical diffusion field it may occur that the

stationary state has been reached in one phase (aqueous) and not in the other

(organic) at a given time, so a transient behaviour must be considered.

Microdroplets (spheres or micro-hemispheres) are also of great interest in several

scientific fields, because they are efficient elements of storage for the transport of many

liquid species like neurotransmitters, pheromones, etc. They are present in micelles in

emulsion media, in phase transfer catalysis and in liquid phase separations. Also, they can

be used to biomimic the biphasic electrochemistry of a plethora of species.121 A wide

variety of electrochemical phenomena are suggested as occurring within microdroplet

environments. Based on this, considerable efforts have been devoted to understanding

electrochemistry in tiny environments and cells. The theoretical treatment of ionic

transfers in microdroplets is similar to that of an ionic transfer occurring at a mercury

microelectrode when amalgamation occurs, which is more complicated than when both

species are soluble in the electrolytic solution.122

5.2. Weakly supported Liquid/Liquid microinterfaces

All the previous considerations have been made assuming that both aqueous and organic

solutions contain a high amount of supporting electrolyte and that the current flux

through the external circuit can be expressed by eqn (68). The purposes of the addition of

supporting electrolyte are to increase the conductivity, reduce the ohmic polarization and

make the ionic migration negligible. Nevertheless, an excess of electrolyte may not be

adequate when it interacts with reactants, the organic solvent has a low permittivity, the

ion transfer proceeds in a non supported medium or the ions under study have very

positive standardGibbs energies (i.e. very hydrophylic ions like Li+, Na+, F�, or SO42�).

In these cases the migration cannot be ignored as a transport mode of ions and, the

Nernst–Plank equation together with the mass conservation yield to,

@ci@t¼ rJi ¼ Dir rci þ

ziF

RTcirf

� �ð69Þ

A usual approximation is the electroneutrality assumption,Pzici = 0 (70)

which might not be applicable in a narrow region close to the electrode surface.

The set of eqn (69)–(70) for the i participating species and the boundary value

problem, lead to the potential and concentrations profiles and the voltammetric

response. This cumbersome equation system can only be numerically solved.

However when small sized L/L interfaces are used, eqn (69) can be drastically

simplified by assuming the steady state assumption, so losing their time-dependence.

Oldham123 obtained the stationary voltammetric response of a Nernstian charge

transfer process at spherical microelectrodes, showing that they are very tolerant to

low levels of supporting electrolyte because, the ionic content is enriched near

microelectrode surface. The Oldham’s equations were transposed to microITIES by

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Wilke.31 Important restrictions apart, these equations can only be applied to micro-

holes when the depth of the hole is much smaller than the diameter of the interface

(quasi-hemispherical inlaid interface). Recently, Girault et al.32 have used this

methodology for determining standard Gibbs ion transfer energies of very hydro-

philic and lipophilic ions using a microhole drilled into a very thick film of

polyamide. In order to study other more useful L/L microinterfaces, further

theoretical methodologies should be developed.

Notation, Functions and Variables

Xz target ion.Rz0 ion that is transferred through the inner interface to assure

electroneutrality.z charge number of the target ion.z0 charge number of the ion transferred at the inner interface.W sample aqueous solution or outer solution.M organic phase or membrane.W0 inner aqueous solution or inner solution.F Faraday constant.R molar gas constant.T working absolute temperature.A area of the interface.gpi activity coefficient of the ion i phase p (p = W, M, W0).Dp

i diffusion coefficient of the of the ion i phase p (p = W, M, W0).c*i initial concentration of the ion i.DWMf0

i standard ion transfer potential of the ion i.

DWMf00

i formal ion transfer potential of the ion i ¼ DWMf0

i þ RTFln

gMigWi

� �� DE pulse amplitude in DDPV.Ein Base potential in SWVDEs potential step of the staircase in SWVEsw square wave amplitude in SWVt pulse duration in multipulse chronoamperometry and SWV.v sweep rate in CSCV and CV.I0 current amplitude.w exponent of the applied current.te.c transition time corresponding to the application of an exponential

current flux.tc.c transition time corresponding to the application of a constant

current flux.tu uptake transition time in RCP and CRDCP.ts stripping transition time in RCP and CRDCP.k1 forward kinetic constant of the complexation reaction.k2 backward kinetic constant of the complexation reaction.K stability constant of the complex under pseudo-first order

assumption. ¼ k1k2¼ c�

XLzðMÞ

c�Xz ðMÞ

� �k sum of the kinetic constants of the chemical reaction (= k1 + k2).

FðOÞ ¼ 1

2ffiffiffiffiwp eOerfð

ffiffiffiffiOpÞ

Ns ¼2I0

zFAc�Xz


Xz

p

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Acknowledgements

The authors greatly appreciate the financial support provided by the Direccion

General de Investigacion Cientıfica y Tecnica (Project Numbers CTQ2011-27049/

BQU and CTQ2009-13023/BQU), and the Fundacion SENECA (Project Number

08813/PI/08). Also, E. T. thanks the Ministerio de Ciencia e Innovacion for the grant

received.

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