Assisted Ion Transfer at Organic Film-Modified Electrodes

Article pubs.acs.org/JPCC

Assisted Ion Transfer at Organic Film-Modified Electrodes François Quentel,† Valentin Mirčeski,*,‡,§ Maurice L’Her,† and Katerina Stankoska‡ †

UMR-CNRS 6521, Université de Bretagne Occidentale, 6, Avenue Victor Le Gorgeu, C.S. 93837, 29238 Brest Cedex 3, France Institute of Chemistry, Faculty of Natural Sciences and Mathematics, “Ss Cyril and Methodius” University, P.O. Box 162, 1000 Skopje, Republic of Macedonia § Faculty of Medical Sciences, University Goce Delčev, Štip, Republic of Macedonia ‡

ABSTRACT: An experimental and theoretical study of a complex electrochemical mechanism at three-phase and thin organic film-modified electrodes, where the coupled electron−ion transfer reaction is complicated by complexation reaction of the transferring ion, is reported. The transfer of monovalent and divalent cations across water|nitrobenzene interface, coupled with the complexation reactions with the ionophore valinomycin, is studied. Both types of electrodes are assembled of an edge plane pyrolytic graphite electrode modified with a nitrobenzene solution of lutetium bis(tetra-tert-butylphthalocyaninato) as a redox mediator and valinomycin as an ionophore. The reversible redox transformations of the redox mediator to either a monovalent hydrophobic anion or cation serve to drive the ion transfer across the liquid|liquid interface. In contact of the modified electrode with an aqueous electrolyte containing alkali or earth alkaline metal cations, significant partition of the aqueous electrolyte is taking place, due to the interfacial complexation of the cation with valinomycin. Thus, the thermodynamics and kinetics of the interfacial complexation−partition reaction at the liquid|liquid interface affect markedly the overall electron−ion transfer reaction at the modified electrodes under voltammetric conditions. Experiments are qualitatively compared with theoretical data collected by simulation of two different electrochemical mechanisms coupled with chemical reactions under conditions of square-wave voltammetry. It has been concluded that the overall electrochemical mechanism at three-phase electrodes can be described as a specific CrE reaction scheme, where Cr represents the reversible interfacial complexation−partition reaction of the transferring ion with valinomycin at the liquid|liquid interface.

1. INTRODUCTION In the past two decades, solid electrodes modified with redoxactive water immiscible organic liquids or solution of organic solvents1 emerged as a versatile tool to assess the charge transfer reactions across liquid|liquid (L|L) interfaces. Following the first experiments of Bard et al.2 in which a microelectrode was covered with a film of an organic solvent, Anson et al.3,4 developed thin-film electrodes (TFE) in which pyrolytic graphite was modified with a thin film of a waterimmiscible organic solvent containing a lipophilic redox probe. Thin-film electrodes have been broadly applied to study a variety of electrochemical phenomena ranging from ion and electron transfer kinetics across L|L interfaces,5−7 biomimetic studies,8−10 to preparation and electrochemical inspection of noble metal nanoparticles.11,12 Following the advances of thinfilm electrodes, a three-phase electrode (TPE) system has been developed, which appears in a variety of configurations, such as electrodes modified with randomly distributed microdroplets of redox-active organic liquids,13 or a paraffin-impregnated graphite electrode partly covered with a single droplet of an organic solvent containing a neutral lipophilic redox probe.14 Three-phase electrodes are extensively applied to study thermodynamics of ion transfers across the interface between water and a variety of solvents.15 The three-phase and thin-film electrodes paved the way to study the ion transfers across L|L interfaces by means of a conventional three-electrode configuration as well as to analyze the transfers of strongly hydrophilic ions that otherwise are difficult to be assessed by © 2012 American Chemical Society

other electrochemical techniques. An important advantage of TPEs is the easiness in detecting of the type of the ion transfer reaction across the L|L interface, which is of particular importance for mechanistic studies of complex electrochemical processes. In the present communication, we report on the study of complex electrode mechanisms at TPEs and TFEs in which the transferring cation is involved in an additional complex formation chemical reaction. The aim of the work is to inspect the effect of complexation reactions of the transferring ion on the response of the TPEs and TFEs16 under voltammetric conditions, as well as to inspect the ability of these modified electrodes to probe the thermodynamics and kinetics of complex interfacial chemical processes. Both type of electrodes are assembled by using lutetium bis(tetra-tert-butylphthalocyaninato) (LBPC) as a redox mediator due to its possible oxidation as well as reduction to highly hydrophobic redox states to induce the transfer reactions of strongly hydrophilic anions and cations.16,17 The interfacial complex forming reaction is exemplified by using valinomycin (val) as a cation complexing agent. Valinomycin is a well-known ionophore for K+ ion transport across biological cell membranes,18 or liquid membranes, very selective against Na+. This complexing agent has also been used for building selective electrodes.19,20 Finally, Received: July 8, 2012 Revised: August 29, 2012 Published: August 29, 2012 22885

dx.doi.org/10.1021/jp3067603 | J. Phys. Chem. C 2012, 116, 22885−22892

The Journal of Physical Chemistry C

Article

Figure 1. Typical net SW voltammograms of LBPC at three-phase electrodes in the absence (solid line) and presence (dashed line) of 5 mmol/L valinomycin in the organic phase. The aqueous phase contains 0.5 mol/L chloride salt of Na+, K+, Li+, and Ca2+. Parameters of the potential modulation are as follows: SW frequency f = 12 Hz; amplitude Esw = 50 mV; and potential step ΔE = 1 mV.

Square-wave voltammograms29 were recorded using an Autolab instrument (Eco-Chemie, Utrecht, Netherlands). A saturated calomel electrode was used as a reference and a platinum wire as the auxiliary electrode. All experiments are performed in a thermostatic cell at 25 ± 0.1 °C. 2.2. Capillary Electrophoresis. Capillary electrophoresis measurements have been conducted with a CIA apparatus (Waters), the supporting electrolyte being composed of UV CAT 2 (Waters), and 18-crown-6 (Aldrich) for the measurement of K+; a 20 kV voltage was applied to the capillary column (length, 60 cm; diameter, 75 μm). The extraction experiments were carried in vials with screw-tops. Aqueous solutions (1.5 mL of 1 mM) of KCl, KClO4 and KPF6 were added to 1.5 mL of 1 mM valinomycin solution in nitrobenzene. After vigorous shaking, the vials were placed in a water bath at 25 °C for 12 h. After centrifugation, the concentration of K+ remaining in the aqueous phase was measured by capillary electrophoresis.

valinomycin-facilitated ion transfer across a variety of L|L interfaces,21−25 including room temperature ionic liquids,26 has been frequently studied by voltammetry.

2. EXPERIMENTAL SECTION 2.1. Voltammetry. LBPC was synthesized and purified according to the procedure already described.27,28 All other chemicals were of high purity and used as received. Potassium ionophore (valinomycin) was purchased from Fluka. LBPC was dissolved in water-saturated nitrobenzene (o). A disk electrode of highly oriented pyrolytic graphite (0.32 cm2) has been used. Before modification of the electrode surface with the organic solution, graphite was abraded with SiC paper (600), sonicated for 30 s in water, rinsed with pure water and acetone, and dried in air. For preparation of three-phase electrodes, 0.2 μL of the nitrobenzene solution was deposited on the graphite electrode with the help of a micropipet, covering partly the electrode surface. The organic solution contained the redox probe and the ionophore, and no supporting electrolyte was added to the organic phase. For experiments with thin-film electrodes, 1 μL of the organic solution was layered on the electrode surface, completely covering the graphite surface. Both aqueous and organic phases contain supporting electrolytes with a common K+ cation. The electrolyte in the organic phase was 5 mmol/L potassium tetrakis(4-chlorophenyl) borate (KTPBCl). Nitrobenzene-saturated water (w) (Millipore Q) was used to prepare all aqueous solutions.

3. RESULTS AND DISCUSSION 3.1. Valinomycin-Assisted Cation Transfer at ThreePhase Electrodes. Three-phase electrodes prepared with LBPC as a redox probe exhibit two well-defined voltammetric responses due to the coupled electron and ion transfers: LBPC(o) + X−(w) ⇄ LBPC+(o) + X−(o) + e

(1)

LBPC(o) + M+(w) + e ⇄ LBPC−(o) + M+(o)

(2)

Electrochemical reactions 1 and 2, occurring in the absence of valinomycin, are represented by the net SW voltammograms (full lines in Figure 1). Both oxidation and reduction of LBPC 22886



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are one-electron electrode reactions, yielding chemically stable and strongly hydrophobic cationic and anionic forms of the lutetium bisphthalocyanin, thus being accompanied by the ingress of an anion (eq 1) or of a cation (eq 2) from the aqueous to the organic phase, respectively. If the time of the electrochemical experiment is sufficiently long (i.e., low frequency of SWV), both electrochemical reactions appear reversible, with formal potentials given by eqs 3 and 4 for the oxidation (ox) and reduction (red) reactions, respectively:16 ⊖′ Ec⊖′(ox) = E LBPC + Δw → oϕX⊖′ − − + /LBPC

+

Table 2. Potential Shift of the Net SW Voltammograms for the Reduction of LBPC at the Three-Phase Electrodes due to 5 mmol/L Valinomycin Added to the Organic Phasea M+ +

Na K+ Li+ Rb+ Cs+ Mg2+ Ba2+ Ca2+

RT ln(c X*−(w)) F

RT * )/2 ln(c LBPC F

a

(3)

⊖′ w → o ⊖′ − + Δ Ec⊖′(red) = E LBPC/LBPC ϕ M+ +

RT * +(w)) ln(c M F

ΔEp = Ep(val) − Ep (V) 0.381 0.370 0.419 0.288 0.340 0.363 0.417 0.424

All other conditions are the same as for Figure 1.

Figure 2, its peak potential is a linear function of the standard potential of the anion transfer (Δw→oφ⊖ X−′). Moreover, for a

RT * )/2 ln(c LBPC (4) F For the meaning of symbols see Table 1. As already demonstrated,16 this experimental system provides a partic−

Table 1. List of Symbols symbol

definition

A β βh c*i Di Δw→oφ⊖ i ′ ΔE Esw E⊖ c ′ E⊖′ F f I K k R T

electrode surface area homogeneous equilibrium constant heterogeneous equilibrium constant bulk concentration of species i diffusion coefficient of species i formal potential of ion transfer from water to organic phase step potential height of the potential pulses (amplitude) formal potential of an electrochemical reaction formal redox potential Faraday constant frequency of the potential modulation electric current apparent equilibrium constant rate constant gas constant thermodynamic temperature

Figure 2. Dependence of the net SW peak potential for the oxidation (1) and reduction (2) of LBPC at three-phase electrodes on the standard potential of anion transfer in the absence (rhombus) and presence (circles) of 5 mmol/L valinomycin in the organic phase. The aqueous phase contains 0.05 mol/L potassium salts of the following anions: Cl−, Br−, NO3−, SCN−, ClO4−, PF6−, IO3−, BrO3−, ClO3−, and the triflate− (trifluoromethanesulfonate) anion. All other conditions are the same as for Figure 1.

ularly wide potential window for studying ion-transfer reactions across a L|L interface; more specifically, it is about 1 V for the water|nitrobenzene interface. As shown in Figure 1, in the presence of valinomycin in the organic phase (dashed lines), the position of the voltammetric peak attributed to the oxidation process (eq 1) remains almost unaltered for almost all studied cations. At the same time, a strong shift toward more positive potentials is observed for the reduction process. This implies that the lipophilicity of the cation is increased by the complexation with valinomycin. As illustrated by Figure 1 and Table 2, the assisted cation transfer is not limited to potassium. Valinomycin also facilitates the transfer of other alkali and earth alkaline metal cations. The peak potential of the reduction process shifts linearly with the logarithm of the valinomycin concentration with a slope close to 60 mV for all monovalent and 30 mV for the divalent species. Interestingly, only in the presence of valinomycin, the reduction process of LBPC also becomes sensitive to anions present in the aqueous phase. As shown by line 2 (circles) in

given type of the aqueous electrolyte and the valinomycin concentration c*val(o) ≥ 10 mM, the peak potential of the reduction process is almost independent of the concentration of the aqueous electrolyte, revealing clearly the reductive electrochemical mechanism follows a different reaction pathway than described by eq 2. For the sake of comparison, it is worth mentioning that the oxidative process is insensitive to valinomycin for all studied anions. As shown by line 1 in Figure 2, the dependence Ep versus Δw→oφ⊖ X−′ for the latter process is identical regardless of the presence of valinomycin, implying that the electrochemical mechanism still undergoes according to eq 1 and its peak potential is defined by eq 3. As indicated by literature data,22,26 valinomycin is capable of interfacial cation complexation, causing a significant extraction of the aqueous cation in the organic phase as soon as the modified electrode is immersed into the aqueous electrolyte (eq 5). 22887


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of LPBC at the TFE recorded in contact with KCl aqueous solution is depicted by the full line in Figure 3. The

(5)

The latter heterogeneous reaction at equilibrium conditions is associated with an equilibrium constant, βh, which is related to the homogeneous stability constant of the complex formation in the organic phase, β, through the standard potential of the cation transfer, Δw→oφ⊖ M′+ , as follows: βh = βexp[(F/RT)Δw→oφ⊖ ′ + ]. However, to maintain the charge neutrality of the M organic phase, the interfacial cation complexation reaction has to be accompanied by the anion transfer to the organic phase, causing extraction of the aqueous electrolyte: M+(w) + val(o) + X −(w) ⇄ Mval+(o) + X −(o)

(6)

The latter complexation−partition equilibrium is associated with the equilibrium constant defined as βh,p = βexp[(F/ w→o ⊖ RT)(Δw→oφ⊖ φX−′)]. Hence, in the presence of M′+ − Δ hydrophilic anions in the organic phase, the reduction of LBPC is expected to be accompanied by expulsion of the anions from the organic phase, as the latter is energetically the most favored process: LBPC(o) + X−(o) + e ⇄ LBPC−(o) + X−(w)

Figure 3. Typical net SW voltammograms of LBPC at thin-film electrodes in the absence (solid line) and presence (dashed line) of 18 mmol/L valinomycin in the organic phase in contact with 0.5 mol/L aqueous KNO3 electrolyte. Besides 0.5 mmol/L LBPC and valinomycin, the organic phase contains 5 mmol/L KTPBCl as an organic electrolyte. All other conditions are the same as for Figure 1.

(7)

with the formal potential defined as: ⊖′ w → o ⊖′ − + Δ Ec⊖′ = E LBPC/LBPC ϕX − −

+

RT ln(c X*−(w)) F

RT ln(c X*−(o)) F

electrochemical mechanisms of the oxidation and reduction of LBPC are described by eqs 10 and 11, respectively:

(8)

As dictated by reaction 6, the following condition holds: c*X−(o) =c*Mval+(o), which reflects the charge neutrality of the organic phase prior to the voltammetric experiment. Thus, by substituting in eq 8 and taking into account the definition of the stability constant of reaction 5, the formal potential of the reduction process in the presence of valinomycin is defined as follows: w → o ⊖′ ⊖′ − + Δ Ec◦′(val. ) = E LBPC/LBPC ϕX− + Δw → oϕ M⊖′+ RT RT * ) + ln β + ln(c val(o) F F

LBPC(o) + K+(o) ⇄ LBPC+(o) + K+(w) + e

(10)

LBPC(o) + K+(w) + e ⇄ LBPC−(o) + K+(o)

(11)

As both oxidative and reductive mechanisms are coupled with the K+ ion transfer, in the presence of valinomycin, both reduction and oxidation net SW peaks shift equally toward more positive potentials, proportional to the strength of complexation of K+ ions (dashed line in Figure 3). A detailed study revealed that the electrochemical mechanisms could be even more complex compared to TPEs, due to the more complex ionic composition of the experimental system with film electrodes. The overall electrochemical behavior depends critically on the concentration ratio between valinomycin and K+(o). For c*val(o) < c*K+(o), only a fraction of K+(o) is complexed, and no significant salt extraction from the aqueous phase is taking place. Thus, K+(o) remains the transferring ion for both electrochemical reactions 10 and 11. However, for cval(o) * > c*K+(o), in parallel to the complexation of K+(o), an interfacial complexation takes place according to eq 6, causing extraction of the aqueous electrolyte into the organic film. Hence, similar to the mechanisms at TPEs, the expulsion of the aqueous anion from the organic to the aqueous phase is expected to be associated with the reduction of LBPC, whereas the opposite anion transfer would take place in the course of the oxidative mechanism. To check out this assumption, the effect of the aqueous KCl(w) concentration on the position of both oxidative and reductive net SW peaks was studied for a series of valinomycin concentrations that varied from 6 to 22 mM. The condition c*val(o) > c*K+(o) was satisfied in each experiment, as c*K+(o) = 5 mM. In all cases, the dependence of Ep versus log(c*KCl(w)) is a line with a slope of about 30 mV, for both oxidative and reductive mechanisms. These results imply strongly that K+ remains the

(9)

According to eq 9, the formal potential is a linear function on the standard potential of both anion and cation transfer, which agrees with experimental findings (Figures 1 and 2). In addition, eq 9 predicts a linear dependence of the formal potential on the logarithm of the valinomycin concentration, while the intercept of the line should enable estimation of β, providing the standard redox and ion transfer potentials are known. Finally, the formal potential should not depend on the concentration of ions in the aqueous electrolyte. As previously mentioned, this was experimentally found for cval(o) * = 10 mM, in an aqueous solution of KCl over the concentration interval from 0.05 to 1 M. However, for c*val(o) < 10 mM, a negative slope was found with the values being −14.5, −17.1, and −41 mV for cval(o) * = 7.5, 5, and 2 mM, respectively. This indicates that eq 9 can provide only qualitative and approximate description of the system. 3.2. Valinomycin-Assisted Cation Transfer at Film Electrodes. The assisted cation transfer can also be studied by using the thin-film electrode configuration3−7 for which the electrode is fully covered with a thin film of the organic solvent containing the redox probe, while K+, the transferring ion, is present in both liquid phases, establishing the potential difference across the L|L interface. A typical SW voltammogram 22888



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all species, without electrochemical kinetic constrains. By assuming that the reductive current is positive, solutions for the surface concentrations of electroactive species are given in a form of the following convolution integrals:29

transferring ion for both electrochemical mechanisms, which is the main difference compared to the mechanisms observed at TPEs. Obviously, the homogeneous complexation reaction within the organic phase prevails over the heterogeneous interfacial complexation−partition reaction 6. The value of the slope (≈ 30 mV) of the dependence Ep versus log(c*KCl(w)) is a half from the thermodynamic value of 59 mV found in the absence of valinomycin, which might be a consequence of the influence of the kinetics of the homogeneous complexation reaction in the organic phase. In accord with these findings is the evolution of the quasireversible maximum (QRM), measured in contact with a 0.05 M aqueous solution of KCl, presented in Figure 4. In the

ci(0, t ) = ci* −

ci(0, t ) =

∫0

t

∫0

t

I (τ ) FA Di

I (τ ) FA Di

1 π (t − τ ) 1

π (t − τ )

dτ (12)

dτ (13)

where i is the symbol for the species appearing in eq 2. More specifically, eq 12 is valid for LBPC(o) and M+(w), which are present in the system at the beginning of the voltammetric experiment represented by their bulk concentrations, whereas the solution to eq 13 is pertinent to LBPC−(o) and M+(o), as these species are absent at the beginning of the experiment. The surface concentrations are related through the Nernst equation of the following form: cLBPC(o)(0, t)cM+(w)(0, t) = exp(φ)cLBPC−(o)(0, t)cM+(o)(0, t), where φ = F/RT(E − w→o ⊖ E⊖ ′ ϕM′+ ). − − Δ LBPC/LBPC As the experiment is conducted with lower concentration of the redox form compared to the transferring ion, that is, c*LBPC ≪ c*M+(w), the overall current is controlled by the flux of the redox species. A typical simulated voltammogram is depicted in Figure 5A. Under conditions of SWV, the net peak potential depends on the concentration ratio cM * +(w)/cLBPC * as well as the ratio of the diffusion coefficients of the redox species and the transferring ion in the organic phase. The net SW peak potential (Ep) is defined by eq 4 only if the diffusion coefficients of all the electroactive species are equal. For DLBPC(o) = DLBPC−(o) ≠ DM+(o), the peak potential is defined as follows:

Figure 4. Quasireversible maximum for the oxidation (triangles) and reduction (circles) of LPBC at film electrodes in the absence (solid lines) and the presence of 22 mmol/L valinomycin (dashed lines), recorded in contact with 0.05 mol/L aqueous KCl electrolyte. Besides valinomycin, the organic phase contains 0.5 mmol/L LBPC and 5 mmol/L KTPBCl. All other conditions are the same as for Figure 1.

⊖′ w → o ⊖′ − + Δ Ep = E LBPC/LBPC ϕ M+ +

−

absence of valinomycin, the position of the QRM measured by the reduction and oxidation of LBPC is identical, as the transfer of K+ across the liquid interface is the rate-limiting step for both electrochemical reactions.5,6 In the presence of valinomycin, the position of the maximum measured with both oxidation and reduction of LBPC is again equal, implying the two electrochemical reactions involve the same type of ion transfers. The position of the maximum is shifted slightly toward higher frequency compared to the absence of valinomycin, revealing that the kinetics of the K+ transfer reaction is increased in the presence of valinomycin. 3.3. Theoretical Consideration of Valinomycin-Assisted Cation Transfer at Three-Phase Electrodes. The foregoing thermodynamic analysis presented in Section 3.1 can provide only a qualitative description of the electrochemical mechanism for the valinomycin-assisted cation transfer. Under voltammetric conditions, the situation at TPEs is expected to be more complex as, in the simplest case (e.g., reaction 2), the fluxes of four species are joined together. Hence, simulation of the experiment is required for getting insight into the electrochemical mechanism and understanding of the voltammetric behavior. In the absence of a facilitating agent, the reduction mechanism (eq 2) joins together four electroactive species. In a first approximation, we assume that the system is controlled by the mass transfer under semi-infinite diffusion conditions for

* ) RT (c LBPC RT + ln ln F F 2

RT * +(w) ln c M F D M+(o) DLBPC(o)

(14)

The application of this equation is however limited as the precise knowledge on the diffusion coefficients is yet missing, which implies that the usage of eq 4 for estimation of thermodynamic parameters might be a source of an error. The difference between the diffusion coefficients of the transferring ion in the aqueous phase and the redox probe is irrelevant, as the current response is controlled by the flux of the species in the organic phase only. In the presence of valinomycin, two different mechanisms are plausible at TPEs. The first one includes electrochemical ion transfer from the aqueous to the organic phase, followed by complexation in the organic phase: M+(o) + val(o) ⇄ Mval+(o)

(15)

It is a sort of ECr mechanism at TPEs. This is equivalent to an ECr mechanism at a solid electrode/solution interface, where the electrochemical step is represented by eq 2, with Cr being the follow-up chemical step (eq 15). However, if valinomycin is capable of interfacial complexation of the cation, causing extraction of the aqueous electrolyte prior to the electrochemical reaction, the overall electrochemical mechanism follows a very specific CrE reaction scheme, where Cr refers to the preceding complexation−extraction reaction 6, followed by electrochemical reaction 7. 22889



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Figure 5. Typical simulated SW voltammograms at TPE for the simple electron−ion coupled mechanism (A), ECr mechanism (B), and CrE mechanism (C). For (A) and (B), the current is normalized as Ψ = (I/FAc*LBPC√f); and for (C), as Ψ = (I/FAc*√f). The common conditions of the simulations are as follows: nEsw = 50 mV; ΔE = 1 mV; DLBPC(o) = DLBPC−(o) = 1 × 10−7 cm2 s−1; DM+(o) = 1 × 10−6 cm2 s−1; DM+(w) = 5 × 10−6 cm2 s−1. The conditions specific to (B) are as follows: log(β/mol L−1) = 10; cval = 10 mM; log(kf′/(mol−1 L s−1)) = log (kb/s−1) = 0.5; and f = 10 Hz. For * = 10 mM; and log(kf′/(mol−2 L2 s−1)) = log(kb/s−1) (C), a common diffusion coefficient is assumed D = 5 × 10−6 cm2 s−1; K′ = 0.18 mol−1 L; cval(o) = 5. The inset of (C) shows the theoretical variation of the net SW peak potential with log(c*val(o)), assuming log(β/mol L−1) = 10. Other conditions of the simulation corresponds to the experiments performed in 0.1 mol/L KCl(w) solution.

the forward and backward SW voltammetric components is virtually independent of the concentration of valinomycin. Hence, overall, the voltammetric behavior of the simulated ECr mechanism deviates from experimental observations. Considering the CrE mechanism, the solutions for the concentration of the transferring anion in the organic and aqueous phase are given by eqs 17 and 18, respectively.

Simulations of the ECr mechanism requires the solution for the surface concentration of M+(o):29 c M+(o)(0, t ) =

1 1+K +

∫0

t

K (1 + K )

I (τ ) FA D M+(o)

∫0

t

dτ π (t − τ )

I (τ ) FA D M+(o)

e−k(t − τ) π (t − τ )

dτ

c X−(o)(0, t ) =

(16)

K is the apparent equilibrium constant of complexation, defined as K = βcval(o) * , where β is the equilibrium constant of complexation reaction 15. As valinomycin is present in an excess in the organic phase compared to the redox probe, its equilibrium concentration is assumed to be constant in the course of the voltammetric experiment. The cumulative rate constant k is defined as k = kf + kb, where kf and kb are the forward and backward rate constants of reaction 15. kf (s−1) is the pseudo-first-order rate constant, related with the real rate constant kf′ (mol−1 L s−1) as follows: kf = kf′cval(o) * . Simulations of this mechanism show that the voltammetric features depend chiefly on the thermodynamic parameter K and on the chemical kinetic parameter ε = k/f, where f is the frequency of the SW potential modulation. In the real experiment, for a given SW frequency, both parameters K and ε are varied by altering the concentration of valinomicyn. The most striking voltammetric feature is the decrease of the reverse component of the SW response by increasing the valinomycin concentration, due to the loss of the M+(o) electroactive species in the complexation reaction (Figure 5B). The net peak potential depends linearly on cval(o) * , with a slope which, under most conditions, is different than 60 mV. In all experiments, the ratio of the peak currents of

K * c − K+1

∫0

t

I (τ ) FA D

e−k(t − τ) π (t − τ )

dτ (17)

K * c K+1

c X−(w)(0, t ) = c* − +

∫0

t

I (τ ) FA D

e−k(t − τ) π (t − τ )

dτ (18)

c* is the total concentration of the transferring anion defined as c* = c*X−(w) + c*X−(o). K = (c*X−(o))/(c*X−(w)) is the apparent equilibrium constant of reaction 6, which is related to the real equilibrium constant βh,p as K = βh,p(c*M+(w)c*val(o))/(c*Mval+(o)). For the sake of simplicity, in this derivation, it is assumed that all diffusion coefficients are equal. The solutions for the surface concentrations of the redox species are given by eqs 12 and 13. The cumulative rate constant k and the dimensionless chemical kinetic parameter ε are defined as for the ECr mechanism, with the main difference being in the definition of the forward rate constant, which reads as follows: kf = kf′c*val(o)c*M+(w). The complexity of this mechanism stems from the fact that the transferring anion X−(w) is both a reactant of the preceding chemical step (reaction 6) and a product of electrochemical 22890



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L|L interface. As a consequence, there is an obvious change in the transferring ion (from a cation to an anion) that accompanies the reduction of the redox mediator, in the absence and the presence of the complexing agent, respectively. Such switching in the type of the ion transfer reaction can be easily detected by the simple analysis of the evolution of the response as a function of the type and concentration of the aqueous electrolyte. It is the thermodynamics and kinetics of the interfacial complexation−partition reaction at the L|L interface that controls the overall voltammetric properties of the TPEs. At TFEs, when both liquid phases contain the transferring ion, the ion transfer reaction remains the same regardless of the presence of the complexing agent in organic phase. When the concentration of the complexing agent is larger that the concentration of the transferring ion (at the same time the complexing ion) in the organic phase, the complexation reaction proceeds both as a homogeneous process within the organic phase as well as an interfacial complexation−partition reaction at the L|L interface, while the former prevails over the latter. Thus, the overall voltammetric behavior at TFEs is predominantly controlled by the properties of the homogeneous complexation reaction in the organic phase.

reaction 7. A representative voltammogram of this mechanism is depicted in Figure 5C. The overall voltammetric behavior can be partly rationalized on the basis of previous knowledge of the CrE mechanism in SWV.29 However, care must be taken for correct interpretation of the experimental parameters and their relation with the model variables K and ε. In general, the role of valinomycin and the aqueous electrolyte is complex, as both affect simultaneously the model variables K and ε. If the rate of the preceding chemical reaction 6 is fast (i.e., ε is large), the role of valinomycin will be manifested mainly through the thermodynamic parameter K. The net peak potential depends linearly on log(cval(o) * ) with a slope equal to 2.303(RT/F) and an intercept depending on βh,p. If the kinetics of reaction 6 affect the voltammetric response, the slope and intercept of the latter dependence can deviate from the thermodynamic value. It is important to note that the peak current of the backward SW component does not decrease by increasing c*val(o), being the main difference with the previous ECr mechanism (compare panels B and C in Figure 5). This provides a basis for a simple differentiation between the two reaction schemes. In addition, if the preceding chemical reaction is fast (log ε > 2), simulations confirm the validity of eq 9 that predicts the formal potential to be independent of the aqueous electrolyte concentration. As noted in Section 3.1, this was experimentally found for c*val(o) = 10 mM in the aqueous solution of KCl over the concentration interval from 0.05 to 1 M. However, for a sluggish chemical kinetics, the net peak potential shifts slightly toward negative potentials by increasing the aqueous electrolyte concentration. For instance, in simulations corresponding to experiments conducted in aqueous KCl solution and organic solution containing 7.5 mM valinomycin, the slope of the line Ep versus log(cKCl(w) * ) is −14 mV, assuming that kf′ = 10 M−2 s−1, kb = 10 s−1, and log β = 10. This agrees well with the experimentally found value of −14.5 mV. As a consequence of the short time scale of the SW potential pulses, the slow preceding chemical reaction cannot resupply the organic phase with the transferring anion. The inset of Figure 5C shows theoretically predicted variation of the net SW peak potential with log(cval(o) * ), assuming the constant of complex formation to be log β = 10. The other conditions of the simulations correspond to the experiments performed in 0.1 M KCl(w) solution. The slope and the intercept of the line are 0.059 and 0.164 V, respectively, being in a good agreement with the corresponding experimental values of 0.059 and 0.191 V. The control experiments with capillary electrophoresis give the value of the stability constant log β = 10.7, estimated according to the methodology of Makrliḱ et al.30 The two estimates are in mutual agreement, as well as in accord with most of the literature data.22

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS V.M. and K.S. gratefully acknowledge the Alexander von Humboldt foundation for the financial support from the Research Group Linkage Program 3.4-Fokoop-DEU/1128670 as well as the support of DAAD foundation through multilateral project “International Masters and Postgraduate Program in Materials Science and Catalysis” (MatCatNet).

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REFERENCES

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4. CONCLUSIONS It has been demonstrated that the response of both TPEs and TFEs under voltammetric conditions is particularly sensitive to the complexation reaction of the transferring ion. The overall mechanism in the presence of the cationic ionophore valinomycin is significantly different at TPEs and TFEs, implying the critical role of the ionic composition of the organic phase in determining the type of the ion transfer reaction across the L|L interface. Both experiments and modeling confirm clearly that the mechanism at the TPEs follows a CrE reaction scheme, involving an interfacial complexation−partition reaction of the transferring ion at the 22891



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Assisted Ion Transfer at Organic Film-Modified Electrodes

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