J. Chem. SOC., Faraday Trans. I, 1989, 85(4), 843-853 Determination of the Kinetics of Facilitated Ion Transfer Reactions across the Micro Interface between Two Immiscible Electrolyte Solutions Jane A. Campbell, Alan A. Stewart and Hubert H. Girault* Department of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, Scotland The transfer of K' from water to dichloroethane assisted by dibenzo-18- crown-6 has been studied at a liquid-liquid interface supported at the tip of a micropipette. The apparent electrochemical rate constant and apparent charge-transfer coefficient have been determined by analysis of the quasi- reversible steady-state wave observed. A kinetic model is proposed and the true electrochemical rate constant for the complexation reaction is thereby calculated.Since the first investigation of the kinetics of ion transfer across the interface between two immiscible electrolyte solutions (ITIES) by Gavach et al.,' who studied the transfer of tetra-alkylammonium ions from water to nitrobenzene by chronopotentiometry, much work has been dedicated to this topic. The main conclusion of the results hitherto obtained*-' for simple ion transfer and facilitated ion transfer' is that these reactions are fast and therefore difficult to measure. The standard electrochemical methodology for studying quasireversible charge transfer circumvents mass-transport limitations either by rapid variation of the electrode potential (e.g. Chronoamperometry, a.c. polarography, a.c. impedance and fast-sweep voltammetry) or by enhancing the rate of arrival of the reactants (e.g.rotating-disc, wall- jet and microelectrodes). To date the published investigations of the kinetics of ion transfer have relied only on the first category of techniques, and the purpose of the present paper is to show that, in the case of facilitated ion transfer, data can also be obtained by enhancing the diffusion using a microITIES. The main problem with electrochemical measurements at liquid-liquid interfaces resides in the low polarity of the organic phase. The consequently large iR drop is usually either compensated by positive feedback or decreased by the use of concentrated supporting electrolyte. The effect of analogue compensation is to introduce, by definition, a large amount of noise, which limits the accuracy of current acquisition and hence makes techniques such as cyclic voltammetry non-ideal.Furthermore, in this particular case, 100 % analogue compensation is never achieved, and the residual iR drop also contributes to the peak shift observed. Alternatively, the use of a concentrated supporting electrolyte in the organic phase causes significant ion-pairing effects between the transferring ion and the supporting electrolyte counter-ion. Such interactions complicate the determination of the data sought, and investigations in dilute media are to be preferred. The difficulties just described render most of the techniques used so far inherently inaccurate, as reviewed recently by Samec.' According to this author the most reliable method is a.c. impedance, i.e.measurement of the charge-transfer resistance. However, as shown in ref. (9), full semi-circles are difficult to obtain, and the accuracy of the measurement is heavily dependent on the reliability of the curve-fitting algorithm employed. 843 FAR I 29844 Ion Transfer across Interfaces More generally, all transient techniques require relatively sophisticated instru- mentation, including a potentiostat with a fast rise time and high-speed transient recording equipment. However, the accuracy of these techniques at liquid-liquid interfaces is intrinsically limited at short times by the low impedance of the double layer, in parallel with the faradaic processes. An entirely different experimental approach to the study of ion-transfer reaction kinetics is to increase the rate of mass transport of the reactants to the interface.Taylor and Giraultl' showed that micro-liquid-liquid interfaces supported at the tip of the micro-pipette can be used to provide a spherical diffusion pattern similar to that observed at solid microelectrodes. l1 This enhanced mass transport produces a steady- state current when the transferring species enters the pipette, whereas classical linear diffusion behaviour is observed when the ion exits from the pipette. Consequently a theory similar to that employed at solid-state microelectrodes may be applied in the special case of facilitated ion transfer, where both the rate of arrival of the reactants and the rate of departure of the products is enhanced. This can be achieved experimentally by, for example, using an excess of the concentration of the ion to be transferred inside the pipette together with a low concentration of the ionophore outside the pipette.Theory When the concentration of the transferring ion in the aqueous phase is in excess relative to the ionophore in the organic phase, the observed current for facilitated ion transfer is equal to the rate of departure of the complexed ion. In the case of spherical diffusion this reads as where the subscripts C and CI refer to the ionophore and complexed ion, respectively, the superscripts b and 0 refer to bulk and surface concentrations and where F is the Faraday constant, D the diffusion coefficient, A the area of the microITIES and r the radius of the tip of the pipette. The observed limiting current for the case where the initial concentration of the complexed ion is zero in the organic phase is given by Also, the kinetic expression for the current is + i = zi FA(kaPp - iapp GI) (3) -+ 4- where k,,, and k,,, are the apparent forward and reverse electrochemical rate constants.By substituting eqn (1) and (2) into eqn (3) we have -+ t i = zi FACE[k,,,( 1 - i/id) - kapp tilid] (4) where is the ratio Dc/DcI. Note that the concentration of the ion, C;, does not appear in eqn (3). This is because in the present case the ionic concentration in the pipette is taken to be orders of magnitude greater than that of the ionophore. The complexation reaction Corg + Iwater + CIow can be compared to a reduction reaction at an electrode, and is therefore pseudo-first- order.J .A . Campbell, A . A . Stewart and H. H . Girault 845 t c reaction coordinate mi x e d solvent layer u I I ' I , 4 O I I I I I I I I I I I I I I I +- ; I I I (2) (1) I' aqueous d i f f u s e 7 ' organic d i f f u s e *I layer I layer distance Fig. 1. (a) Simple representation of potential energy of Gibbs-energy changes during an ion- ionophore reaction at an ITIES. (b) Schematic Galvani potential distribution across an TTIES. The potential dependence of electrochemical rate constants for charge-transfer reactions across a liquid-liquid interface has been the cause of many discussions.12 However, the present situation is distinct from a classical non-assisted ion transfer in that the reaction coordinate does not correspond to the position of the ion with respect to the plane of the interface.As shown in fig. 1, the reaction can be modelled according to the transition-state theory. However, the initial and final positions (1) and (2) in fig. 1 correspond to positions just outside the back-to-back double layer, and consequently the rate constants kapp and k,,, correspond to a global transfer and not to the elementary complexation-reaction step occurring somewhere in the mixed-solvent layer between positions (1) and (2). -+ t 29-2846 Ion Transfer across Interfaces In the apparent standard case where the activation energy barrier is symmetrical and the concentration of the ionophore is equal to that of the complexed ion (i.e. at the boundary of the space-charge region assumed to be thin compared to the diffusion layer), the equilibrium is described by the equality ( 5 ) -+ t kapp c"c = kapp C"c* Hence the apparent standard rate constant k,Opp can be classically defined as + kip, = zap, = k,,, = Zexp (- AG",RT). (6) In the apparent standard case the Galvani potential difference between the two phases is defined as the formal potential A:@"'.The formal potential for facilitated ion transfer is related to the standard potential for ion transfer of the species i, A@: (= - AGY, J z i F, where AG; is the Gibbs energy of transfer) by where K , is the complexation constant in the organic phase and y is the activity coefficient. When the potential is varied from the formal potential, e.g. by making the oil phase more negative us. water, the Gibbs energy of the uncharged ionophore remains unchanged and that of the complexed ion is lowered by an amount zi F(AZ 0 - A: 0"').The activation energy barrier for the ion transfer to the oil phase, AG,, is itself lowered by a fraction of this Gibbs-energy difference : -+ AG, = AG; - a,,, zi F(A: 0 - A: 0"') (8) + whereas the activation energy barrier for the reverse process, AGA, is increased according to t AG, = AG: + (1 - a,,,) zi F(Ai 0 - A: 0"'). (9) From eqn (8) and (9) it can be shown that the reverse rate constant is related to the forward rate constant by t Consequently eqn (4) can be more generally expressed as i i = z , F A C ~ k . , , [ ( 1 - ~ ) - ~ ~ e x p ( ~ ( A ~ ~ - - A ~ 0 " ' ) -+ from which the potential dependent rate constant for the assisted-transfer reaction can be obtained.In the case of an irreversible facilitated ion-transfer reaction, the reverse transfer can be neglected and consequently eqn (1 1) reduces to + i = zi FACE kapp (1 -t). Experimental The micropipettes were made from Kwik-Fil capillaries (1.5 mm o.d., 0.86 mm i.d., Clark Electromedical) pulled with a vertical pipette puller (Kopf 102, U.S.A.). The puller was adjusted to provide pipettes with a short shank and a fine tip, which were then polished on an optically flat glass of a pipette beveller (K. T. Brown, BV-10, U.S.A.).J. A. Campbell, A. A . Stewart and H . H . Girault 847 During polishing the resistance of the pipette was constantly monitored, as it decreases until a flat polish is obtained. Following this procedure, pipettes with circular sections can be made with external radii comprised between 5 and 50pm.Outside these limits, polishing becomes extremely difficult. Tetrabutylammonium tetraphenylborate (TBATPB) was prepared by mixing equi- molar aqueous solutions of TBABr (Fluka) and NaTPB (Aldrich), the precipitate being dried and recrystallized from acetone. Dibenzo- 18-crown-6 was used as supplied (Aldrich). The solvents consisted of doubly deionized water and AnalaR grade 1,2- dichloroethane. The voltage ramp was produced by a PPRI waveform generator (Hitek) and the current was measured by a home-made battery-powered current follower based on a high-input impedance FET operational amplifier (Burr Brown OAP 104). The electrochemical cell simply consisted of a glass U-tube in which the micropipette was immersed [see ref.(10) for further details]. The separation distance between the tip of pipette and the reference interface was within a 1 mm. During the experiment the tip of the pipette was monitored with a zoom microscope (Olympus, SZH, maximum magnification 384 x ) together with a colour video attachment (Sony, CCD camera, DXC-102). This constant observation was necessary to ensure that the interface remained located at the tip of the pipette. 10-1 mol dm-3 MgSO, I 1 mol dm-3 KC1 mol dmP3 TBATPB Results lop3 mol dm-3 TBACl The potential window containing the Kf ion transfer facilitated by DB18C6 across a water-1,2-dichloroethane interface supported at the tip of a micropipette is shown in fig. 2. The corresponding electrochemical cell is lo-’ mol dm-3 MgSO, mol dmP3 TBATPB I 1 O-* mol dm-3 KCl II 1 OP4 rnol dm-3 DB 18C6 mol (fm-3 TBACl I Steady-state properties are observed for Kf transferring out of and into the pipette.This behaviour is due to spherical-diffusion mass transport for the foward and return charge transfers and contrasts with typical behaviour observed12 for non-assisted ion transfer across micro-ITIES ( i e . peak-shape voltammogram for transfer out, steady-state wave voltammogram for transfer into the pipette). Steady-state voltammograms for this transfer have been analysed using the theory described above, and fig. 3 shows the result obtained when In kapp is plotted us. the applied potential difference A: 0 -A: 0O’. The linear relationship observed indicates that the ion transfer is quasi-reversible, with a standard rate constant, k:pF, equal to ca.2.0 x = 1. The potential-difference scales given in all the figures are real Galvani potential differences calculated after measurement of the potential of zero charge (taken to be equal to the zero Galvani potential difference). The potential of zero charge (P.z.c.) for the following cell -+ cm s-’, assuming that was measured at room temperature by the streaming method as described in ref. (16). The value measured herewith was - 136 mV. The accuracy of the value of kzPp measured depends chiefly on the exact determination of the formal potential, This difficulty is inherent to this type of study, and there are848 500 0 Ion Transfer across Interfaces I I I . I I -300 -1 00 0 100 A: @lmV Fig.2. Cyclic voltammogram for DB18C6-facilitated K' transfer at a micro ITIES for cell I. Scan rate 0.05 V s-l. -3 -4 -5 a T> 5 -6 -7 -8 -80 -40 0 LO 80 (A; @-A: @O')/mV Fig. 3. Plot of In k,,, us. A;@-A;Oo'. +J . A . Campbell, A . A . Stewart and H. H. Girault 849 Fig. 4. Cyclic voltammogram for cell (I) at large planar liquid-liquid interface used to evaluate the formal potential. Scan rates: 0.025, 0.049, 0.064 and 0.1 V s-l. Table 1. Values of kzpp and aaPp obtained for a range of formal potentials A t O0'/V kzpp/cm s-' - 0.050 9.92 x 10-4 0.92 -0.055 1.15 x 10-3 0.92 - 0.060 1.52 x 10-3 0.9 1 - 0.065" 1.96 x 10-3" 0.9 1 " - 0.070 2.46 x 10-3 0.90 -0.075 3.08 x 10-3 0.89 - 0.0080 4.46 x 10-3 0.87 a Values for the formal Galvani potential ob- tained by the mid-peak potential method.basically two ways to evaluate the formal potential. On the one hand, we could relate the potential scale to a real Galvani potential-difference scale using, for example, the TPATPB as~umption'~ or by measuring the potential of zero charge13 and then evaluating the formal potential from the standard potential and the dissociation constant according to eqn (7). In this approach the activity coefficients of the ionophore and complexed ion in the organic phase are required, and their approximation can lead to large inaccuracies. On the other hand, we can take the empirical approach based on8 50 Ion Transfer across Interfaces the measurement of the mid-peak potential of cyclic-voltammetry experiments at a large planar liquid-liquid interface extrapolated to zero sweep rate. The result of this approach is shown in fig.4. The value thus obtained using cell (I) is -201 mV (oil with respect to water) and compares with a value of apparent half-wave potential equal to - 236 mV (oil with respect to water) measured from a plot of In [(id - i)/z] us. potential difference. The formal Galvani potential difference, when related to the absolute Galvani potential scale established by the P.Z.C. measurement, is -65 mV (oil with respect to water). The importance of the determination of an accurate value of the formal potential is highlighted in table 1, where values of k& are calculated from eqn (1 1) for a range of different formal potentials. Discussion Before discussing the present results it may be worth explaining why the theory outlined here is not applicable to non-assisted ion-transfer reactions.In this case the Nernst diffusion layer thickness is not fixed inside the pipette, where linear diffusion takes place. Consequently eqn (1) no longer holds and the kinetic analysis fails. The results presented show that steady-state measurements are a powerful and straightforward route to kinetic information, especially for the determination of the apparent charge-transfer coefficient and the apparent standard rate constant, This, however, is not very informative about the process itself, as the real goal is the obtention of kinetic parameters for the rate-limiting step occurring somewhere in the mixed solvent layer separating the two diffuse layers. As recently shown15 for the case of simple ion transfer, the desired kinetic parameters can be obtained from the apparent measured values.A similar analysis is used here for the case of facilitated ion-transfer reactions. Let us consider that the complexation reaction occurs somewhere in the mixed solvent layer where k, and k, are the rate constants for the local reaction. Assuming again that the complexation reaction is pseudo-first-order (i.e. an excess of transferring ion) the real standard case for this local reaction is defined by -+ c c,* = c;, (13) where the superscript * refers to the local concentration at the plane of the reaction. These concentrations are related to the surface concentrations just outside the diffuse layer by c,* = c; (15) - z i F and c,*, = c;, exp ( RT (@* - Do)) where @* is the Galvani potential at the local plane where the complexation reaction occurs and @O is the Galvani potential in the bulk of the organic phase.Substituting eqn. (14) and (15) into (13) gives where A: @ is the Galvani potential difference between the water phase and the reaction plane. If we neglect mass transport and assume that the outside the diffuse layer obey the Nernst equation, in this surface concentrations case RT CE A:,@ = A","+-In- zi F C& it can be deduced thatJ . A . Campbell, A . A . Stewart and H. H. Girault 85 1 Note that in the real standard case the potential drop in the aqueous phase, A:@', is equal to the formal potential, i.e. the total Galvani potential difference for the apparent standard case when Cg = C&.At this point it is possible to define the real standard rate constant, k,", as and to express the true rate constant, k,, as - + t k," = k, = k, (19) (20) and similarly (21) where a is the classical charge-transfer coefficient defined for the local reaction. Because in the present case the reaction is pseudo-first-order, the local charge-transfer coefficient a is shifted to unity as the potential at which the activated state occurs coincides with the reaction plane defined above as @*. Eqn (20) and (21) thus reduce to e and k, = k,". (23) + These two equations can now be used to express the apparent rate constants kaPP and kapp by combining eqn (14) and (15) with eqn. (22) and (23), respectively: 4- -+ (A: @ -A: @') c k,,, = k," exp ($(A: @)). (24) We can now identify the apparent charge-transfer coefficient, aapp, introduced earlier in eqn (8) and (9) with @*-OW aapp = a o - m w * (26) Using eqn (18), eqn (24) and (25) can be rewritten as (aapp A:.@ - A: O") As in ref. (12), we see that the apparent charge-transfer coefficient refers to the total Galvani potential difference between the two phases and not to the local interfactial potential drop. It represents the ratio of the potential drop between the locus of the activated state and the bulk aqueous phase to the total Galvani potential difference. By definition aapp is dependent on the applied potential difference and will be a function of the concentrations of the supporting electrolytes. The measured rate constant kZPp is defined for the equality852 Ion Transfer across Interfaces and is obtained when A@ = A@"'; it reads The apparent charge- transfer coefficient derived from following equation : was found to be 0.9.(30) fig. 3 by employing the (31) The true standard rate constant kt can therefore be calculated directly from eqn (30) using the value of the apparent standard rate constant computed from eqn (1 1) and inserting the corresponding value of aapp and the formal potential obtained by the graphical method described above. This calculation leads to a true standard rate constant of 2.5 x lop3 cm s-l. Another way to evaluate k," is by use of eqn (27) at the P.Z.C. for which the Galvani potential difference A: @ is defined to be zero. This second approach can only be used when the formal Galvani potential difference is small enough to provide accurate values of kapp at the P.Z.C.The analysis of the values obtained for these interfacial complexation reactions in comparison with the corresponding bulk reactions is beyond the scope of the present paper and will be discussed in a future publication on the mechanism of ion-ionophore reactions in heterogeneous media. To test the applicability of eqn (26) it is interesting to compare the apparent charge- transfer coefficient value thereby defined with the ratio A:@/A:@, where A:@ is the potential drop in the aqueous diffuse layer, which can be calculated for example using the Gouy-Chapman theory. Indeed for the 1 : 1 organic electrolytes used in the present experiment the Gouy charge is given by = - (8RTC0~")i sinh z=O whereas the aqueous charge for the 2:2 aqueous electrolyte is given by The electroneutrality of the interface allows us to calculate the potential drop in the aqueous diffuse layer, A:@.When the Galvani potential drop is equal to the formal potential (i.e. -0.065 V) A:@ was found to be equal to 2.2 mV. This leads to an apparent charge-transfer coefficient of 0.97. Given the inadequacy of the Gouy- Chapman theory in application to 2: 2 electrolytes and also that MgSO, is significantly ion-paired at such a high concentration in water, this calculated value of aapp compares relatively well with the measured value of 0.9 and justifies a posteriori the definition of aapp given by eqn (26). Conclusion The present work shows for the first time that the measurement of steady-state currents occurring during assisted ion transfer across a micro-liquid-liquid interface supported at the tip of a micropipette allows direct access to the apparent kinetic parameters of these processes.Furthermore, the accompanying kinetic theory proposed enables the calculaton of the true kinetic parameters corresponding to the local interfacial complexation reaction, and this without referring to any a priori model of the interface.J. A. Campbell, A . A. Stewart and H. H. Girault 853 We acknowledge the S.E.R.C. for supporting this work and for providing an Information Technology studentship to J. A. C . and a CASE award studentship in collaboration with Genetics International (U.K.) to A. A. S. The support of the Nuffield Foundation is also gratefully acknowledged. References 1 C . Gavach, B. d’Epenoux and E’. Henry, J . Electroanal. Chem., 1975, 64, 107. 2 T. Osakai, T. Kakutani and M. 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Electroanal. Chem., in press. 16 H. H. Girault and D. J. Schiffrin, J. Electroanal. Chem., 1984, 161, 415. Paper 8/01473F; Receied 15th April, 1988