Electrochemical Instability in the Transfer of Cationic Surfactant across

Dec 25, 2003 - The electrochemical instability has been shown to appear in the transfer of cationic surfactant ions across the 1,2-dichloroethane/wate...
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Langmuir 2004, 20, 875-881

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Electrochemical Instability in the Transfer of Cationic Surfactant across the 1,2-Dichloroethane/Water Interface Takuya Kasahara, Naoya Nishi, Masahiro Yamamoto, and Takashi Kakiuchi* Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan Received August 7, 2003. In Final Form: September 17, 2003 The electrochemical instability has been shown to appear in the transfer of cationic surfactant ions across the 1,2-dichloroethane/water interface. Cyclic voltammograms possess all fundamental characteristics that are predicted by the theory of electrochemical instability: the presence of the instability window, that is, the potential range where the interface becomes unstable, the location of the instability window around the standard ion transfer potential of surface-active ions, and the dependence of the width of the instability window on the concentration of the surfactant ions. Electrocapillary measurements clearly demonstrate that the interface becomes unstable, while the interfacial tension is positive, being higher than 20 mN m-1. The electrocapillary curve exhibits the discontinuities at both ends of the instability window, indicating the similarity between the electrochemical instability and the phase transitions induced by the temperature, pressure, and chemical potential. The results from voltammetry and interfacial tension measurements for cationic surfactants support the idea that the electrochemical instability, so far reported in the transfer of anionic surfactants across the liquid/liquid interface, is one of intrinsic properties of the two-phase systems where the partition of surface-active ions takes place.

Introduction The coupling of the partition and adsorption of surfaceactive ions between the two immiscible solutions can lead to the instability of the interface.1 Theoretical predictions based on this coupling agree with the experimental observation that the transfer of anionic surfactants is accompanied with chaotic currents that are associated with Marangoni-type movements of and emulsification at the interface.2,3 Turbulence, agitation, and other “even more bizarre”4 effects at liquid-liquid interfaces have long been known 5-8 and have been the subject of intensive studies in nonlinear physics and chemistry.9 Such interfacial turbulences have been mainly explained in terms of the instability driven by the difference in the chemical potentials of reactant species in the two phases; the transfer due to this driving force induces the Marangoni instability, leading to various forms of interfacial turbulences,4,9,10 in much the same way as that of the Be´nard instability.9 One notable feature of the electrochemical instability is that the system gets out of the unstable state by simply bringing the phase-boundary potential outside the instability potential window. Importantly, the system becomes stable even in the limiting current region where the net flow of ions is present. In cyclic voltammograms * Author to whom correspondence should be addressed. Tel.: (81)-75-383-2489. Fax: (81)-75-383-2490. E-mail: kakiuchi@ scl.kyoto-u.ac.jp. (1) Kakiuchi, T. J. Electroanal. Chem. 2002, 536, 63-69. (2) Kakiuchi, T.; Chiba, M.; Sezaki, N.; Nakagawa, N. Electrochem. Commun. 2002, 4, 701-704. (3) Kakiuchi, T.; Nishi, N.; Kasahara, T.; Chiba, M. ChemPhysChem 2003, 4, 179-185. (4) Sterling, C. V.; Scriven, L. E. AIChE J. 1959, 5, 514-523. (5) McBain, J. W.; Woo, T. M. Proc. R. Soc. London, Ser. A 1937, 163, 182-188. (6) Kaminski, A.; McBain, J. W. Proc. R. Soc. London, Ser. A 1949, 198, 447-454. (7) Lewis, J. B.; Pratt, H. R. C. Nature 1953, 171, 1155-1156. (8) Sherwood, T. K.; Wei, J. C. Ind. Eng. Chem. 1957, 49, 10301034. (9) Colinet, P.; Legros, J. C.; Velarde, M. G. Nonlinear Dynamics of Surface-Tension-Driven Instabilities; Wiley-VCH: Berlin, 2001. (10) Mendes-Tatsis, M. A.; de Ortiz, E. S. P. Chem. Eng. Sci. 1996, 51, 3755-3761.

of anionic surfactants, however, emulsion particles formed within the instability window give irregular current spikes, making the observation of the stable state in the limiting current region difficult, which necessitated potential-step chronoamperometry for demonstrating that the interface is stable in the limiting current region.3 To further elucidate the properties of the electrochemical instability, we studied in this work the transfer of alkylammonium ions across the interface between 1,2dichloroethane (DCE) and water (W) using cyclic voltammetry, potential-step chronoamperometry, and electrocapillarity measurements. The results clearly demonstrate that the transfer of cationic surfactants also induces the electrochemical instability predicted theoretically,1 revealing unique properties of the electrochemical instability associated with the interfacial transfer of cationic surfactants. Experimental Section Tetrapentylammonium tetraphenylborate (TPnATPB) used as a supporting electrolyte in the DCE phase was prepared from tetrapentylammonium iodide (98%, Tokyo Kasei Kogyo) and sodium tetraphenylborate (99.5%, Dojindo Lab), as described elsewhere.11 Tetrapentylammonium chloride (98%, Tokyo Kasei Kogyo), lithium chloride monohydrate (99.9%, Wako Chemical Industries), and magnesium chloride (pro analysis, Merck) were used without further purification. Decylamine (98%, Tokyo Kasei Kogyo) was dissolved in the aqueous solution of 0.1 mol dm-3 LiCl and 0.01 mol dm-3 HCl. DCE (99.5%, Wako Chemical Industries) was washed with W three times before use. Reagentgrade sorbitan monooleate (Wako Chemical Industries) was used as received. The electrochemical cell employed in the present study is

5 mM TPnACl 100 mM 10 mM MgCl2 TPnATPB Ag AgCl Wref DCE 0.1 M LiCl + 10 mM HCl a mM decylammonium ion AgCl Ag W

10.1021/la035452e CCC: $27.50 © 2004 American Chemical Society Published on Web 12/25/2003

(Cell I)

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where M ≡ mol dm-3, Wref is the aqueous phase for the reference of the potential in DCE, W is the aqueous phase containing ionic surfactant, and TPnACl stands for tetrapentylammonium chloride. The potential of the right-hand side of the Ag/AgCl electrode with respect to the left is denoted as E and the current carried by the positive charge from W to DCE is taken to be positive. Electrochemical measurements were made with a fourelectrode configuration.12 The area of the flat polarized interface used for cyclic voltammetry and chronoamperometry was 0.16 cm2. A platinum electrode was used as a counter electrode in each of the W and DCE phases. Ag/AgCl electrodes were used as reference electrodes in Wref and W. The solution resistance was compensated for with a positive-feedback method. The interfacial tension, γ, was determined from a video image of a pendant drop.13,14 A pendant drop of the DCE solution was formed in the W phase from a glass tube of 1-mm inner diameter. The potential across the interface was controlled by four electrodes with the positive feedback for IR compensation, as was the case of the flat DCE/W interface. To record the electrocapillary curves, the potential was applied stepwise by 25 mV from 100 to 500 mV. The shape of a drop was extracted from a video image (720 × 480 pixels) of the drop taken with a charge-coupled device camera (771 × 492 resolution) using a homemade software for video-image processing.15 A theoretical curve obtained by numerically solving the Bashforth-Adams equation16,17 was fitted to the experimental shape of the drop using SALS, a versatile software for nonlinear least-squares regression analysis,18 as described elsewhere.19 The densities of DCE and W were assumed to be the same as those of pure DCE and W. All measurements were made at 25 °C.

Results Cyclic Voltammetry. Figure 1 shows cyclic voltammograms for the transfer of decylammonium (DA+) ions across the DCE/W interface recorded at four different values of the scan rate (v), 10, 20, 50, and 100 mV s-1 when a ) 1 in Cell (I). The solid line in each panel shows that the abnormally large current in the middle of the applied potential reproducibly appeared, as has been observed in the transfer of alkanesulfonates and alkyl sulfates.2,3 The broken line in each panel shows the voltammogram recorded when the DCE phase contained 3 mmol dm-3 sorbitan monooleate, which suppresses the convective motion of the solutions that is responsible to the current augmentation and irregular current spikes in the transfer of anionic surfactants.3 The presence of this nonionic, noncoordinating surfactant as a stabilizer restores the shape of the voltammograms to those known for electrochemically reversible reactions. The midpoint potential, Em, is then readily determined to be 200 mV for the transfer of DA+ ions. The current augmentation in the absence of sorbitan monooleate started in the vicinity of Em, and the sharp rise in the current followed. This abnormally large current is similar to that appearing in the transfer of anionic surfactants and suggests the convective motion of the (11) Nishi, N.; Yamamoto, K. I. M.; Kakiuchi, T. J. Phys. Chem. B 2001, 105, 8162-8169. (12) Samec, Z.; Marecˇek, V.; Koryta, J.; Khalil, M. W. J. Electroanal. Chem. 1977, 83, 393-397. (13) Girault, H. H.; Schiffrin, D. J.; Smith, B. V. D. J. Electroanal. Chem. Interfacial Electrochem. 1982, 137, 207-217. (14) Girault, H. H. J.; Schiffrin, D. J.; Smith, B. D. V. J. Colliod Interface Sci. 1984, 101, 257-266. (15) Kasahara, T. Master Thesis, Kyoto University, Kyoto, Japan, 2003. (16) Bashforth, F.; Adams, J. C. An attempt to test the theories of capillary actions; University Press: Cambridge, 1883. (17) Adamson, A. W. In Physical Chemistry of Surfaces; John Wiley and Sons: New York, 1976; Chapter 1. (18) Nakagawa, T.; Oyanagi, Y.; In Recent Developments in Statistical Inference and Data Analysis; Matusita, K., Ed.; North-Holland: Amsterdam, 1980; p 221. (19) Kakiuchi, T.; Nakanishi, M.; Senda, M. Bull. Chem. Soc. Jpn. 1988, 61, 1845-1851.

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Figure 1. Cyclic voltammograms for the transfer of DA+ ions across the DCE/W interface in the absence (solid lines) and presence (dotted lines) of 3 mmol dm-3 sorbitan monooleate in W. Initial concentration of DA+ ions in W: 1 mmol dm-3. Scan rates: 10 (a), 20 (b), 50 (c), and 100 (d) mV s-1. The vertical line in each panel indicates the location of the midpoint potential of DA+ ion transfer.

solution in the vicinity of the interface. The abnormal current subsided when the potential was made sufficiently positive, 350-400 mV, and returned to the level of the diffusion-limited current. The potential region where the current becomes abnormal thus exists as the potential window, which was less clearly identified in the case of cyclic voltammograms for the transfer of alkanesulfonates and alkyl sulfates.2,3 The instability window becomes wider with increasing v: 130 mV at 10 mV s-1 (Figure 1a), 200 mV at 100 mV s-1 (Figure 1d), and 270 mV at 500 mV s-1 (voltammograms not shown). The abnormal current starts to appear earlier and last longer on the potential axis in the forward scan. Interestingly, the widening of the window with v is more pronounced at the positive end of the window, while the negative end moves a small amount away from Em. In the reverse scan, the sudden increase in the abnormal current always started at the potential that was 20-30 mV more negative to the point of the cessation of the abnormal current in the forward scan. The current becomes normal in the vicinity of the midpoint potential in the reverse scanning. The width of the instability window is narrower on the reverse scan. The potential window in the reverse scan also tends to become wider with v. Unlike the case of the instabilities exhibited in the voltammetry of the transfer of alkane sulfonates and alkyl sulfates,2,3 irregular current spikes did not appear on the voltammograms. Because the current spikes correspond to the fusion of emulsion particles to the electrochemical interface,20,21 the absence of those current spikes probably indicates the absence of the emulsification even within the instability window. Effect of the Surfactant Concentration on the Width of the Instability Window. Figure 2 compares two cyclic voltammograms for the transfer of DA+ ions recorded when a ) 0.5 and 2 at v ) 20 mV s-1. The increase in the bulk concentration of DA+ ions significantly widens the instability window from 60 mV at a ) 0.5 to 200 mV at a ) 2. The width and the location of the instability (20) Kakiuchi, T. Electrochem. Commun. 2000, 2, 317-321. (21) Nakawaga, M.; Sezaki, N.; Kakiuchi, T. J. Electroanal. Chem. 2001, 501, 260-264.

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Figure 2. Effect of bulk concentration of DA+ ions in W on the width of the instability window. Initial concentration of DA+ ions in 2 (a) and 0.5 (b) mmol dm-3. Scan rate: 20 mV s-1.

window in Figure 2a are very similar to those of Figure 1c at v ) 50 mV s-1. The concentration effect in Figure 2 qualitatively agrees with the theoretical prediction1 and reflects the fact that the increase in the bulk concentration of the surfactant ions increases the surface coverage, depending on the form of a particular adsorption isotherm as well as the magnitude of the adsorption coefficient.1 In the interfacial transfer of alkanesulfonates and alkyl sulfates, the instability window is wider than that in the present case. For example, the width when the aqueous phase contains 0.5 mmol dm-3 dodecanesulfonate is more than 150 mV from chronoamperometry measurements; in voltammetry, the current once disturbed because of the electrochemical instability seldom subsides in the limiting current region.3 Because both DA+ and dodecanesulfonate have similar midpoint potentials, the difference in the width of the window is likely to reflect the difference in their intrinsic surface activities; a dodecanesulfonate ion is more surface-active than a DA+ ion. Potential-Step Chronoamperometry. To further confirm the presence of the instability window, we also conducted potential-step chronoamperometry measurements (Figure 3). The potential was stepped from E ) 50 mV to E ) 100 (a), 150 (b), 200 (c), 250 (d), 300 (e), 350 (f), 400 (g), 450 (h), and 500 (i) mV. The solid line in each panel is a trace recorded without sorbitan monooleate in DCE. An irregular current increase was seen only when the potential was stepped to 250, 300, and 350 mV, which are within the instability window observed voltammetrically (cf. Figure 1). The broken line in each panel shows the trace recorded when DCE contained 3 mmol dm-3 sorbitan monooleate, showing the current-time transients expected for a reversible charge transfer across the planar interface, where the diffusion predominates the mass transport in the adjacent solution phases. This potential-step experiment again demonstrates that the interface becomes unstable only in the limited range of the potential encompassing the standard ion-transfer potential, or Em, of the surface-active ion, as has been shown for the transfer of anionic surfactants.3 More importantly, from the comparison of the results in Figure 3 with those in Figure 1, we conclude that an unusually large convection current appears no matter how the potential is brought into the instability window, in

Figure 3. Potential-step transients for transfer of DA+ ions across the DCE/W interface in the absence (solid lines) and presence (dotted lines) of 3 mmol dm-3 sorbitan monooleate in W. Initial potential, 50 mV; second potential, 100 (a), 150 (b), 200 (c), 250 (d), 300 (e), 350 (f), 400 (g), 450 (h), and 500 (i) mV.

accordance with our earlier finding in the transfer of anionic surfactants.3 The width of the instability window from chronoamperometry is about 100 mV, which is comparable to but slightly narrower than that seen in cyclic voltammograms, in which the width was 130 mV at v ) 10 mV s-1. Electrocapillarity. Another notable feature of the electrochemical instability is that the interface should become unstable, even when γ has a positive, finite value. To confirm this prediction, we measured γ as a function of E. The electrocapillary curves obtained are shown in Figure 4. When a ) 0, the shape of the electrocapillary curve (open circles, curve 1) is parabolic, as has been reported at several different types of the liquid-liquid interfaces.13,19,22-28 The electrocapillary maximum, that is, the point of zero charge (pzc), in the absence of DA+ ions is located at 269 mV in the present system. This means that the pzc is 69 mV more positive than the halfwave potential for the DA+ ion transfer, 200 mV. The maximum value of the interfacial tension, 29.2 mN m-1, (22) Gros, M.; Gromb, S.; Gavach, C. J. Electroanal. Chem. 1978, 89, 29-36. (23) Kakiuchi, T.; Senda, M. Bull. Chem. Soc. Jpn. 1983, 56, 13221326. (24) Girault, H. H. J.; Schiffrin, D. J. J. Electroanal. Chem. 1984, 179, 277-284. (25) Kakiuchi, T.; Kobayashi, M.; Senda, M. Bull. Chem. Soc. Jpn. 1987, 60, 3109-3115. (26) Kakiuchi, T.; Usui, T.; Senda, M. Bull. Chem. Soc. Jpn. 1990, 63, 2044-2050. (27) Allen, R. M.; Kontturi, K.; Williams, D. E. Electrochem. Commun. 2000, 2, 703-706. (28) Samec, Z.; Lhotsky´, A.; Ja¨nchenova´, H.; Marecˇek, V. J. Electroanal. Chem. 2000, 483, 47-56.

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Figure 4. Electrocapillary curves in the absence (O, curve 1) and presence (b, curves 2, 2′, and 2′′) of 1 mmol dm-3 DA+ ions. Data shown as (*, curve 3) are obtained when DCE contains 3 mmol dm-3 sorbitan monooleate. The two vertical dashed lines indicate the limits of electrochemical instability.

is slightly greater than the values reported for the DCE/W interface without containing electrolytes,14,19 27.9 and 28.3 mN m-1, and may reflect the negative adsorption of the supporting electrolytes, LiCl and TPnATPB, at the interface, as has been observed at the nitrobenzene/W interface.23 The interfacial tension data when a ) 1 are plotted as filled circles in Figure 4. At the negative end of the potential where no ion transfer takes place, the difference in two electrocapillary curves is probably within the experimental error and is, hence, negligible. With shifting the potential to the positive side, the difference becomes greater and clearer (curve 2). The interfacial tension is significantly lower in the presence of DA+ ions even at E ) 100 mV, where the transfer of DA+ ions is not discerned in the voltammogram (cf. Figure 1), indicating that the adsorption of DA+ ions precedes the ion transfer. The gradual deviation from the upper electrocapillary curve with E accords with the model of potential-dependent adsorption of ionic species, assuming the linear variation of the adsorption Gibbs energy with E,1,11 which is a modification of Grahame and Parson’s model of specific adsorption of ions on mercury.29 A further increase in E causes the break in the lower capillary curve around E ) 210 mV, which is close to the midpoint potential of DA+ ion transfer. Then, up to E ) 350 mV, the γ values are well below the curve expected from the extrapolation using the data points in the range E < 210 mV (curve 2′). At E ) 375 mV, γ jumps about 3 mN m-1 up, close to the upper electrocapillary curve (curve 2′′). The difference between the upper and the lower data points (O and b) between E ) 375 and 500 mV is in fact less significant, indicating that the adsorption of DA+ ions in this potential range is very weak. There are three notable features in the electrocapillary curve in the presence of DA+ ions. First of all, in the potential range where the interface becomes unstable, the global interfacial tension, that is, the interfacial tension measured from the shape of a pendant drop, is higher than 23 mN m-1, far above 0 (curve 2′). From video imaging, kicking motion was sometimes observed during the electrocapillarity measurements, although emulsification was not visible and the movement of a pendant drop was less vigorous than that under the linear sweep of E in cyclic voltammetry. The electrocapillary curve in the presence of DA+ ion transfer, thus, clearly demon(29) Grahame, D. C.; Parsons, R. J. Am. Chem. Soc. 1961, 83, 12911296.

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strates that the electrochemical instability takes place when the global interfacial tension is large and positive. This does not, however, preclude the possibility that γ at a certain small portion of the interface becomes close to 0 due to the electrochemical instability. Second, the region of E limited by the two break points in the lower curve in Figure 4 roughly corresponds to the instability potential window deduced from voltammetry, especially the one at v ) 10 mV s-1, and also that from chronoamperometry. According to the theory of electrochemical instability, the instability should appear when the curvature of an electrocapillary curve is positive.1 Actually, this positive curvature is never realized in real systems because the system escapes from the unstable state by dissipating energy. The break points in the lower electrocapillary curve are, therefore, likely to correspond to the points where the curvature of a hypothetical electrocapillary curve becomes positive. Third, in the instability window, the interfacial tension stayed almost constant around 23 mN m-1. If the mechanical motion of the pendant drop shakes off adsorbed DA+ ions to restore the stable state, the interfacial tension would increase to the point close to the upper electrocapillary curve in the instability window. Lower values actually seen within the instability window suggest that DA+ ions do adsorb at the interface even within the instability window. The addition of sorbitan monooleate in DCE further lowered the interfacial tension. When DCE contained 3 mmol dm-3 sorbitan monooleate, the interfacial tension decreased down to 15 mN m-1 in almost the entire range of the applied potential (curve 3 in Figure 4). This is interesting because the stabilization of the interface is realized by further lowering γ, which might seem to be counterintuitive. This fact indicates that the stabilization is achieved not by changing the value of γ but by decreasing the dependence of γ on E. If the instability is first initiated by the local inhomogeneity of the potential drop across the interface, the strong dependence of γ on E is expected to cause a greater difference in γ locally, which can lead to a strong driving force for the Marangoni movement of the interfacial zone. Instability in the Transfer of Other Cationic Surfactants. We also measured the transfer of alkylammonium ions having different alkyl chain lengths. The abnormal increase in the current was not observed in the transfer of nonylammonium ions and octylammonium ions even when the concentration in W was 2 mmol dm-3. On the other hand, the irregular increase in the current reproducibly appeared in the transfer of dodecylammonium and tetradecylammonium ions, as exemplified in Figure 5a for the dodecylammonium ion transfer. The addition of sorbitan monooleate in DCE did not effectively suppress the instability-driven convection in this case. It seems that the surface activity of alkylammonium ions having alkyl chains longer than the decyl moiety is higher than those having shorter alkyl chains. Because the transfer of octyl sulfates and octanesulfonates across the DCE/W interface induces the electrochemical instability in cyclic voltammograms,3 the surface activity of alkylammonium ions is weaker than the corresponding alkyl sulfates and alkanesulfonates. This weaker surface activity of DA+ ions is reflected in the decrease in γ in Figure 4, where the magnitude of the depression is on the order of 5 mN m-1, which contrasts to the greater depression of γ by alkanesulfonate ions.15 To illustrate that the electrochemical instability of cationic surfactants is not limited to alkylammonium ions, Figure 5b displays a voltammogram for the transfer of

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ion transfer can be treated as electrochemically reversible.11 The adsorption also seems to be faster than the mass transport under the same condition. We can then assume the Nernst equation and an adsorption isotherm for the surface concentrations:

∆φ ) ∆φ0i +

cO i (x ) 0) RT ln W ziF c (x ) 0)

(1)

i

and

BRi cRi (x ) 0) ) f (θi)

Figure 5. Cyclic voltammograms for transfer of dodecylammonium ions (a) and C8mim+ ions (b) across the DCE/W interface in the absence (solid lines) and presence (dotted lines) of 3 mmol dm-3 sorbitan monooleate in W. Initial concentrations of dodecylammonium ions and C8mim+ ions in W: 0.5 and 1 mmol dm-3, respectively. Scan rate: 20 mV s-1. +

1-octyl-3-methylimidazolium ions (C8mim ) across the DCE/W interface. The abnormal current was reproducibly observed. Because C8mim+ and its analogues have been used as typical cationic species that can form roomtemperature molten salts, especially for two-phase extraction30-35 and two-phase organic synthesis by combination with hydrophobic anions,36-38 the instability shown in Figure 5 may have technological implications.

(2)

where ∆φ is the phase-boundary potential, ∆φ0i is the standard ion-transfer potential of ion i, zi is the signed unit of electronic charge on ion i, cRi (x ) 0) is the surface concentration of i in the phase R (R ) the oil phase, O, or the aqueous phase, W), BRi is the adsorption coefficient of i for the adsorption from the phase R, θi is the surface coverage of i, and f (θi) is a function of the surface coverage of i, θi. We numerically solved in a way similar to that reported elsewhere39 the one-dimensional diffusion equations for the diffusion of i in W and O, with these boundary conditions and the condition for the continuity of the flux at the interface in the presence of adsorption,

DW i

|

∂cW i ∂x

-

x)0

|

∂Γi ∂cO i ) DO i ∂t ∂x

x)0

(3)

where DRi and cRi are the diffusion coefficient and the concentration of i in R (R ) W or O), Γi is the adsorbed amount of i, and x is the distance along the axis normal to the interface at which x is taken to be 0 and is directed toward the bulk of the W phase. In the calculation, we assumed for simplicity that the adsorption of i from both sides of the interface can be described by the Langmuir adsorption isotherm:

Discussion Scan-Rate Dependence of the Width of the Instability Window. The concept of the electrochemical instability1 is based on thermodynamic arguments. The effect of time-invariant properties of the system, as exemplified by the effect of the bulk concentration on the instability, can be dealt with within this framework. However, the dependence of the width of the potential window on v is outside of the equilibrium consideration and needs to be considered separately. The ion transfer across the DCE/W interface is fast in comparison with the mass transfer at least at the planar interface in the conventional time scale of longer than microseconds; the (30) Dai, S.; Ju, Y. H.; Barnes, C. E. J. Chem. Soc., Dalton Trans. 1999, 1201-1202. (31) Visser, A. E.; Swatloski, R. P.; Reichert, W. M.; Griffin, S. T.; Rogers, R. D. Ind. Eng. Chem. Res. 2000, 39, 3596-3604. (32) Chun, S.; Dzyuba, S. V.; Bartsch, R. A. Anal. Chem. 2001, 73, 3737-3741. (33) Dietz, M. L.; Dzielawa, J. A. Chem. Commun. 2001, 2124-2125. (34) Visser, A. E.; Swatloski, R. P.; Reichert, W. M.; Mayton, R.; Sheff, S.; Wierzbicki, A.; Davies, J. H., Jr.; Rogers, R. D. Chem. Commun. 2001, 135-136. (35) Visser, A. E.; Swatloski, R. P.; Reichert, W. M.; Mayton, R.; Sheff, S.; Wierzbicki, A.; Davies, J. H., Jr.; Rogers, R. D. Environ. Sci. Technol. 2002, 36, 2523-2529. (36) Dupont, J.; de Souza, R. F.; Suarez, P. A. Z. Chem. Rev. 2002, 102, 3667-3692. (37) Branco, L. C.; Afonso, C. A. M. Chem. Commun. 2002, 30363037. (38) Lourenco, N. M. T.; Afonso, C. A. M. Tetrahedron 2003, 59, 789794.

f (θi) )

θi 1 - θi

(4)

and further assumed that the adsorption Gibbs energy R from the phase R, ∆G0,R ad,i ) -RT ln Bi , linearly varies with 1,40 E, as reported previously 0,O 0,O,Q ) ∆Gad,i + ziFβi(E - E0) ∆Gad,i

(5)

0,W 0,W,Q ) ∆Gad,i - ziF(1 - βi)(E - E0) ∆Gad,i

(6)

0,O 0 where ∆G0,O,Q ad,i is ∆Gad,i at the reference potential, E , that has been taken to coincide with the standard ion transfer potential in the present calculation. Figure 6a shows the variation of the dimensionless adsorption of i with E on the forward and reverse scans of E for the parameters: βi ) 0.5, B0i ) 1, Γm(ziFv/RT)1/2/ 0 R 1/2 0 [(DW)1/2 bcW i ) ) 5 , and zi ) 1, where Bi is Bi at E ) E , b W Γm is the maximum adsorption of i, and c is the bulk concentration of i in W. The adsorption in the forward scan is always higher than those in the reverse scan. If the threshold level demarcating the stability-instability of the system resides at a value of Γ indicated as the horizontal dashed line in Figure 6a, the range of E above

(39) Kakiuchi, T. J. Colloid Interface Sci. 1993, 156, 406-414. (40) Kakiuchi, T. J. Electroanal. Chem. 2001, 496, 137-142.

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Figure 7. Effect of the scan rate on the adsorption. Γm(ziFv/ RT)1/2/[(DW)1/2 bcW i ] ) 1 (curve 1), 1.1414 (curve 2), 2.2361 (curve 3), and 3.1628 (curve 4). See text for other values of the parameters used for calculation. The dashed line represents a threshold level, as is shown in Figure 6. Other parameters for calculation are the same as those for Figure 6.

Figure 6. (a) Dependence of adsorption on E for forward and reverse scans. The dashed line represents a threshold level, assumed for illustration, for the electrochemical instability of the interface. (b) Flux of i on the W side of the interface in the absence (dashed line) and presence (solid line) of adsorption. The parameters used for calculation are the same as those for part a.

this line is wider in the forward scan than that in the reverse scan. This semiquantitatively explains the difference in the width of the potential range where the voltammograms showed abnormal current in the forward and reverse scans. Figure 6b illustrates the flux of i on the W side of the interface for the same conditions as calculated in Figure 6a. Unlike the ion transfer in the absence of the adsorption, the flux is generally different from the ion transfer current, or “faradaic” current, because the charging current is inherently involved in the process. For comparison, the voltammogram in the absence of adsorption is shown as the dashed line. The effect of v on the width of the instability window is illustrated in Figure 7, where βi ) 0.5, B0i ) 10, Γm(ziFv/RT)1/2/[(DW)1/2 bcW i ] ) 1 (curve 1), 21/2 (curve 2), 51/2 (curve 3), and 101/2 (curve 4). The latter four values may be understood either as the change in the relative magnitude of v by the factor of 1, 2, 5, and 10, respectively, or as the change in the relative magnitude of Γm by 1, 21/2, 51/2, and 101/2, experimentally. The interesections of these curves with the dashed line, a hypothetical threshold level, shift to the positive direction of E with v. This qualitatively agrees with the experimental trend of widening the instability window with v, though the actual shift of the edge of the window is greater than that calculated. For a better agreement, a more realistic adsorption isotherm allowing for the strong lateral interaction seems to be required. Range of Instability. Figures 6 and 7 illustrate that the instability condition is realized under the current flow, which is different from the thermodynamic equilibrium. An implication of the assumptions made in eqs 1 and 2

for the surface concentrations of i is that the thermodynamic instability may be violated only right at the interface; the instability does not affect the states outside of the interfacial region. Because the thickness of the DCE/W interface having a γ value of more than 20 mN m-1 is on the order of 1 nm,41 it is expected, generally, that the region where the stability condition may be violated is comparable to this thickness, whereas the Marangoni effect causes the hydrodynamic turbulence of the entire solution. On the other hand, the hypothetical negative capacitance, or more realistically, very small values of the qW, in the instability window mean that the unstable region can extend over the thickness of the double layer, which is again about the same order of magnitude in the ionic strengths employed in the present study. Comparison of the Electrochemical Instability with the Phase Transition. From the electrocapillary equation in the form

-dγ ) Sσ dT +

∑i Γi dµi + qW dE

where Sσ and qW are the excess surface entropy and the excess surface charge density in the aqueous phase; one can see that the transition between the electrochemically stable and unstable states is a counterpart of the phase transitions driven by the temperature and the chemical potential or, in the bulk phase, the pressure. In this respect, it would be interesting to examine the first derivative of γ with respect to E. The break points around E ) 210 and 370 mV in the electrocapillary curve in the presence of DA+ ion transfer (curve 2 in Figure 4) should result in the discontinuity in the excess surface charge density. Curves 1 and 2 in Figure 8 show qW values obtained from the slope of curves 1 and 2 in Figure 4, respectively. Curve 2 shows the jumps at E ) 210 mV (point B to C) and 370 mV (point D to E). Within the instability window, qW is small, having a slightly positive slope (point C to D). From an analogy with the van der Waals isotherm, one may deduce that the states in the region between A and B and that between E and F are thermodynamically unstable, though both satisfy the condition for the local stability of the interface.42 It would then be natural to (41) Benjamin, I. J. Chem. Phys. 1992, 97, 1432-1445. (42) Callen, H. B. In Thermodynamics and an introduction to thermostatistics; John Wiley & Sons: New York, 1985; Chapter 8.

Transfer of Cationic Surfactant

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macroscopically. More detailed measurements seem to be required for elucidating this point. Conclusions

Figure 8. Excess surface charge density in the aqueous phase as a function of E in the absence (curve 1) and presence (curve 2) of 1 mmol dm-3 DA+ ions in W, calculated from curves 1 and 2 in Figure 4. Curve 2 is a schematic illustration for the presence of two discontinuities in the curve.

postulate that, thermodynamically, the actual system should proceed from A, C, D, and F, satisfying the global stability conditions42 and that “supersaturated” states are experimentally seen in the regions between A and B and between E and F. In other words, if the applied potential is varied at an infinitesimally small scan rate the interface would be stable throughout the entire potential range. However, unlike the case of the van der Waals model, the energy of the system is a single-valued function of E (Figure 4) even in the presence of the DA+ adsorption. In this respect, there is no necessity for the system to jump from A to C and from D to F. The region between E and F is thermodyncamically undefined, at least in the macroscopic scale of the pendant drop employed in interfacial measurements. It is likely that in the region between C and D the interface is not laterally homogeneous (43) Ortiz, E. S. P.; de Marangoni. Phenomena in Liquid-Liquid Extraction. In Phase-Interface Phenomena in Multiphase Flow; Hewitt, G. W., Mayinger, F., Riznic, J. R., Eds.; Hemisphere Pub. Corp.: 1991; pp 555-562.

The electrochemical instability in the transfer of DA+ ions across the DCE/W interface is characterized by the abrupt current increase due to the instability in the vicinity of its half-wave potential, followed by its cessation in the limiting current region of the phase-boundary potential, resulting in the well-defined instability potential window. The confirmation of the electrochemical instability in the transfer of cationic surfactants is compelling to conclude that the electrochemical instability is a general consequence of the coupling of adsorption and the partition of surface-active ions. The electrochemical instability cannot be understood within the framework of the traditional model of interfacial turbulence that was first formulated by Sterling and Scriven4 and has been considered to be an archetypical model,43 in that (i) instability does not depend on the direction of ion transfer, (ii) the large differences in the density and the viscosity are not required for the turbulence, and (iii) the adsorption of surfactant plays a key role even when the interfacial tension is large and positive. The reproducible stability exhibited in the limiting current region under the current flow also is incompatible with the linear stability theory. All these characterize the uniqueness of the electrochemical instability. Acknowledgment. This work was partially supported by a Grant-in-Aid for Scientific Research (No. 14205120) and a Grant-in-Aid for Exploratory Research (No. 15655008) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan, and CREST of JST (Japan Science and Technology). The present work was conducted under the program the Center of Excellence for United Approach to New Materials Science, Kyoto University. LA035452E