4364
Langmuir 2008, 24, 4364-4369
Electrically Driven Motion of an Air Bubble on Hemispherical Oil/Water Interface by Three-Phase Boundary Reactions Masanori Satoh, Koichi Aoki,* and Jingyuan Chen Department of Applied Physics, UniVersity of Fukui, 3-9-1 Bunkyo, Fukui-shi, 910-8507 Japan ReceiVed NoVember 25, 2007. In Final Form: January 15, 2008 Our electrochemical cell consisted of a ferrocene-included hemispherical nitrobenzene (NB) droplet on the glassy carbon (GC) electrode which was immersed in the aqueous solution including sodium sulfate and sodium dodecyl sulfate (SDS). When an air bubble was injected near the boundary between the oil and the aqueous phase, it stayed at the top of the hemisphere on the boundary so that the lower half of the bubble was put in oil and the other half was in water. From the force balance of surface tension and buoyancy of the bubble, the bubble took an energetic minimum at the interface. It sank into the oil phase when ferrocene in the oil was electrochemically oxidized through the GC electrode by the three-phase boundary reaction. The electrochemical reduction caused the bubble to move back toward the aqueous phase. The motion of the bubble was synchronized with the redox reaction of ferrocene. The potential step oxidation showed such a rapid response that the motion could not be attributed to diffusion of ferricenium ion from the three-phase boundary to the bubble. Our idea of explaining the rapidity was the translational motion of the SDS layer along the boundary, which was driven by the difference in the surface concentration of SDS caused by the electrochemical generation of the ferricenium ion. The motion of the SDS layer was demonstrated by the shrinkage of the oil layer spread on the water surface when SDS solution was dropped on the oil layer. The spreading velocity was close to the velocity of propagating the oxidation of ferrocene to the bubble.
Introduction Electrode reactions at three-phase boundaries (TPB), at which an oil, a water, and an electrode phase meet together, occur when a redox species in either the oil phase or the aqueous one reacts at the electrode with the help of the other phase.1 A typical cell apparatus is composed of the oil droplet including only a redox species, which is located on an electrode in an aqueous solution including supporting electrolyte.2,3 The oil droplet often takes a hemispheric shape from the balance of its buoyancy in water and the surface tension with the electrode, as is shown in Figure 1A, and consequently, the TPB forms a ring from the top view. Although the oil phase contains a redox couple, no electrode reaction occurs at the oil/electrode interface because the reaction requires a counterion which could be supplied from the aqueous phase. TPB reactions may be partially indicated by electrode reactions of potentially electroactive solids which are located on an electrode.4 The other geometry of the TPB is a cylindrical microelectrode inserted into the oil/water (O|W) interface.5 Adsorption of a number of microdroplets on an electrode can also form the TPB to enhance the current owing to the large area of the boundary.6 The development of ionic liquids has extended the selection of the kinds of oil for the TPB reactions.7 * Corresponding author (
[email protected], fax +81 776 27 8494). (1) (a) Komorsky-Lovric, S.; Riedl, K.; Gulaboski, R.; Mirceski, V.; Scholz, F. Langmuir 2002, 18, 8000. (b) Gulaboski, R.; Mirceski, V.; Scholz, F. Electrochem. Commun. 2002, 4, 277. (c) Scholz, F.; Gulaboski, R.; Mirceski, V.; Langer, P. Electrochem. Commun. 2002, 4, 659. (2) (a) Scholz, F.; Komorsky-Lovric, S.; Lovric, M. Electrochem. Commun. 2000, 2, 112. (b) Hermes, M.; Scholz, F. Electrochem. Commun. 2000, 2, 845. (c) Lovric, M.; Scholtz, F. J. Solid State Electrochem. 1997, 1, 108. (3) (a) Chang, C.-L.; Lee, T.-C.; Huang, T.-J. J. Solid State Electrochem. 1998, 2, 291. (b) Gulaboski, R.; Mirceski, V.; Scholz, F. Electrochem. Commun. 2002, 4, 277. (c) Donten, M.; Stojek, Z.; Scholz, F. Electrochem. Commun. 2002, 4, 324. (d) Tasakorn, P.; Chen, J.; Aoki, K. J. Electroanal. Chem. 2002, 533, 119. (4) (a) Bond, A. M.; Marken, F.; Williams, C. T.; Beattie, D. A.; Keyes, T. E.; Forster, R. J.; Vos, J. G. J. Phys. Chem. B 2000, 104, 1977. (b) Bond, A. M.; Feldberg, S. W.; Miao, W.; Oldham, K. B.; Raston, C. L. J. Electroanal. Chem. 2001, 501, 22. (c) Zhang, J.; Bond, A. M. Anal. Chem. 2003, 75, 2694. (5) (a) Bak, E.; Donten, M.; Stojek, Z. Electrochem. Commun. 2005, 7, 483. (b) Bak, E.; Donten, M. L.; Donten, M.; Stojek, Z. Electrochem. Commun. 2005, 7, 1098.
Figure 1. Illustration (A) of a hemispherical oil droplet including an air bubble mounted on an electrode in salt-included aqueous solution, and interpretation (B) for the TPB reaction of ferrocene (Fc) in the oil phase. Supporting ions, M+ and A-, form a double layer at the water/electrode interface.
Impregnation of solids with oil has enhanced the usage and dispersion technique of the oil material.8 Most of the TPB reactions have varied with the measurement time, such as potential scan rates and the number of potential cycles, because supporting electrolytes transfer between the two phases2,9 to mix and extend the area of the reacting surface. The (6) (a) Banks, C. E.; Davies, T. J.; Evans, R. G.; Hignett, G.; Wain, A. J.; Lawrence, N. S.; Wadhawan, J. D.; Marken, F.; Compton, R. G., Phys. Chem. Chem. Phys. 2003, 5, 4053. (b) Wadhawan, J. D.; Evans, R. G.; Banks, C. E.; Wilkins, S. J.; France, R. R.; Oldham, N. J.; Fairbanks, A. J.; Wood, B.; Walton, D. J.; Schroeder, U.; Compton, R. G. J. Phys. Chem. B 2002, 106, 9619. (c) Giovanelli, D.; Davies, T. J.; Jiang, L.; Jones, T. G. J.; Compton, R. G. Phys. Chem. Chem. Phys. 2004, 6, 3889. (d) Wadhawan, J. D.; Wain, A. J.; Kirkham, A. N.; Walton, D. J.; Wood, B.; France, R. R.; Bull, S. D.; Compton, R. G. J. Am. Chem. Soc. 2003, 125, 11418. (e) Davies, T. J.; Brookes, B. A.; Compton, R. G. J. Electroanal. Chem. 2004, 566, 193. (f) Davies, T. J.; Wilkins, S. J.; Compton, R. G. J. Electroanal. Chem. 2006, 586, 260. (7) (a) Marken, F.; McKenzie, K. J.; Shul, G.; Opallo, M. Faraday Discuss. 2005, 129, 219. (b) Marken, F. Electrochim. Acta 2005, 50, 2315. (c) Ghanem, M. A.; Marken, F. Electrochem. Commun. 2005, 7, 1333. (d) Bonne, M. J.; Reynolds, C.; Yates, S.; Shul, G.; Niedziolka, J.; Opallo, M.; Marken, F. New J. Chem. 2006, 30, 327. (8) (a) Niedziolka, J.; Opallo, M. Electrochem. Commun. 2004, 6, 475. (b) Opallo, M.; Saczek-Maj, M. Electrochem. Commun. 2001, 3, 306. (c) Shul, G.; Opallo, M. Electrochem. Commun. 2005, 7, 194. (9) (a) Samec, Z.; Marecek, V.; Weber, J. J. Electroanal. Chem. 1979, 103, 11. (b) Girault, H. H. Modern Aspects of Electrochemistry, Bockris, J. O. et al., Eds.; Plenum Press: New York, 1993; Vol. 25, pp 1-62.
10.1021/la703675e CCC: $40.75 © 2008 American Chemical Society Published on Web 02/27/2008
Air Bubble on Oil/Water Interface
use of the supporting electrolyte, sodium sulfate, insoluble to the oil phase, has allowed us to keep the steady-state current for the TPB reactions.10 This concept is based on the restriction of forming a double layer only to the water/electrode interface (Figure 1B), which penetrates the oil phase to cause the electrode reaction. Evidence for the TPB reaction is both the exhibition of the steadystate current and the proportionality of the current to the length of the TPB.10a However, it is not easy to obtain the obvious evidence because of local motion of the boundary during the redox reaction,10a formation of emulsions around the TPB,10b and convection caused by the redox reaction.10c The apparatus for the TBP has been formed by mounting an oil droplet on an electrode surface in aqueous solution by means of a syringe. The oil in a syringe is sometimes mixed with air bubbles to yield a bubble-mingled oil droplet, as is shown in Figure 1A. Air bubbles are always located on the O|W interface near the top of the hemispherical droplet. They do not float to be expelled from the solutions, owing to their buoyancy. The fact that they stay on the interface may be explained in terms of the surface tension of the water/air (W|A), which acts on the bubbles downward, being larger than that of the O|A and the buoyancy. In the preliminary experiment, we have found motion of an air bubble depending on surfactants and electrode potentials, probably because of response to a subtle change in the surface tension of the O|W interface. The air bubble is predicted to be a measure of the environment of the TPB. Bubble motion in liquids has relevance in engineering subjects such as froth flotation, foam fractionation, waste treatment, aeration of water reservoirs, bubble columns, gas-liquid reactors, and mass transfer mechanism in fluidized beds with bubble rise. The fundamental concept is based on capillarity or the YoungLaplace equation,11 and has been applied through a change in the surface energy to effects on chemical reactions,12 bubble formation,13 bubble rise,14 coalescence of bubbles,15 and oscillation of bubbles.16 In these examples, a causal force for the motion acts directly on bubbles. The present air bubble on the O|W interface, in contrast, is located far from the TPB, and hence it is necessary to take into account the long-distance force acting on the bubble. This report is devoted to investigating the static and dynamic behavior of the air bubble on the O|W interface in the context of the TPB reaction of ferrocene. The force balance of the air bubble at the O|W interface will be formulated in terms of the interfacial tensions and the buoyancy. It will be (10) Aoki, K. K.; Tasakorn, P.; Chen, J. J. Electroanal. Chem. 2003, 542, 51. (b) Chen, J.; Sato, M. J. Electroanal. Chem. 2004, 572, 153. (c) Aoki, K.; Satoh, M.; Chen, J.; Nishiumi, T. J. Electroanal. Chem. 2006, 595, 103. (11) Adamson, A. W. Physical Chemistry of Surfaces, 3rd ed.; John-Wiley and Sons: New York, 1976; pp 4-15. (12) (a) Sanfelda, A.; Sefianeb, K.; Beniellic, D.; Steinchen, A. AdV. Colloid Interface Sci. 2000, 86, 153. (b) Loubie`re, K.; He´brard, G. Chem. Eng. Proc. 2004, 43, 1361. (c) Teschke, O.; Souza, E. F. Chem. Phys. Lett. 2007, 447, 379. (d) Ashokkumar, M.; Grieser, F. J. Phys. Chem. B 2005, 109, 19356. (13) (a) Tsuge, H. Hydrodynamics of bubble formation from submerged orifices. In Encyclopedia of Fluid Mechanics, Cheremisinoff, N. P., Ed.; Gulf Publishing: Houston, 1986; pp 191-232. (b) Sadhal, S. S.; Ayyaswany, P. S.; Chuang, J. N. Transport Phenomena with Drops and Bubbles; Springer-Verlag: New York, 1997; pp 311-402. (c) Lee, J.; Kentish, S.; Ashokkumar, M. J. Phys. Chem. B 2005, 109, 14595. (14) (a) Krzan, M.; Zawala, J.; Malysa, K., Colloid Surf., A 2007, 298, 42. (b) Malysa, K.; Krasowska, M.; Krzan, M. AdV. Colloid Interface Sci. 2005, 114, 205. (c) Kemiha, M.; Olmos, E.; Fei, W.; Poncin, S.; Li, H. Z. Ind. Eng. Chem. Res. 2007, 46, 6099. (d) Liao, Y.; McLaughlin, B. J. J. Colloid Interface Sci. 2000, 224, 296. (15) (a) Sunartio, D.; Ashokkumar, M.; Grieser, F. J. Am. Chem. Soc. 2007, 129, 6031. (b) Sunartio, D.; Ashokkumar, M.; Grieser, F. J. Phys. Chem. B 2005, 109, 20044. (c) Oolman, T. O.; Blanch, H. W. Chem. Eng. Commun. 1986, 43, 237. (d) Lee, J.; Kentish, S.; Ashokkumar, M. J. Phys. Chem. B 2005, 109, 5095. (e) Zahradnik, J.; Fialova, M.; Linek, V. Chem. Eng. Sci. 1999, 54, 4757. (16) (a) Kamath, V.; Prosperetti, A., J. Acoust. Soc. Am. 1989, 85, 1538. (b) Blake J. R.; Gibson, D. C. Annu. ReV. Fluid Mech. 1987, 19, 99. (c) Klaseboer, E.; Khoo, B. C. J. Appl. Phys. 2004, 96, 4808.
Langmuir, Vol. 24, No. 8, 2008 4365
demonstrated that the electrode reaction varies the surface tension at the O|W interface to cause surface convection. Experimental Section The glassy carbon working electrode was fabricated with a GC20S rod (Tokai Carbon, Tokyo), 3 mm in diameter, by covering the side with a shrinkable poly(tetrafluoroethylene) tube, so that the end of the tube was flush with the electrode surface. The electrode surface was polished with alumina powder and was sonicated in water. The electrochemical cell was a plastic spectroscopic cell (10 × 10 × 40 mm3), the bottom of which was drilled and plugged with the working electrode. The inserted working electrode was sealed with poly(tetrafluoroethylene) tape against a leakage of aqueous solution. The electrode was mounted so that the surface was in the horizontal direction and was directed upward. The aqueous solution, 0.15 mM SDS and 0.5 M Na2SO4 (M: mol dm-3) was filled in the cell. A nitrobenzene droplet was mounted on the surface of the electrode by inserting a microsyringe into the aqueous solution. An air bubble was injected on the top of the surface of the oil droplet by using a microsyringe. Photographs of the oil droplet and the air bubble were taken with the video microscope, Scopeman (Moritex, Tokyo), from the side of the cell. Diameters and amounts of the oil droplet were evaluated from the image analysis on the computer monitor. The reference electrode was Ag|AgCl in 3 M NaCl solution. The counter electrode was a platinum coil. The potentiostat was a µ-Autolab (Eco Chemie). Nitrobenzene (Wako, GR grade) was distilled and dehydrated with molecular sieves for a day. Ferrocene (Wako, GR grade) was sublimed and crystallized. It was used as an electroactive species at the TPB reaction. Na2SO4 and SDS were commercially available without purification. An electric synchronization circuit for the light-emitted diode was homemade. The potential step signal generated from the potentiostat was passed through a comparator with an adjustable threshold voltage by use of some operational amplifiers.
Results and Discussion Air Bubble Trapped on O|W Interface. Air bubbles were commingled accidentally into the nitrobenzene droplet at the injection. A bubble less than 0.04 mm in diameter was moving spontaneously on the hemispherical O|W interface, probably due to the Brownian motion. When a potential of 0.5 V vs Ag|AgCl was applied between the electrode and the aqueous phase, the bubble motion stopped suddenly on the boundary. Figure 2 shows photographs of the air bubble deliberately injected near the oil phase. The bubble injected into the oil phase floated through the oil and stayed on the O|W interface, although it was subjected to the buoyancy from both the phases. The stay on the boundary may be ascribed to the surface tension at the W|A interface in the bubble, which acts on the bubble in the gravitational direction, prevailing over the surface tension at the O|A interface. The addition of the surfactant (SDS) to the aqueous phase shifted the bubble position upward. This is the evidence of the contribution of the surface tension to the bubble staying at the W|O interface. In order to change the size of the air bubble, we injected air of a given volume on the oil O|W interface. A larger bubble stayed at a higher position at the interface or at a larger ratio of the water-excluded volume by the bubble to the oil-excluded volume. The buoyancy obviously increases in proportion to the volume of the bubble, whereas the W|A surface tension does in proportion to the water-contacting surface area of the bubble. Thus, the former force prevails over the latter as the size increases. As a result, the bubble stays upward on the boundary as the bubble size increases.
4366 Langmuir, Vol. 24, No. 8, 2008
Satoh et al.
Figure 2. An air bubble injected deliberately into the O|W boundary, where the oil phase was nitrobenzene and the aqueous phase was composed of 0.5 M Na2SO4 (A) without SDS and (B) with 0.015 mM SDS.
We shall derive an equation for the dependence of the location of the air bubble on the interfacial tensions and the size. The spherical air bubble with the radius a staying at O|W interface is supported by the balance of the surface tensions with the buoyancy. We consider the unit cylindrical cell normal to the interface so that it surrounds the air bubble, as is shown in Figure 3A. Letting the distance between the top of the bubble and the O|W interface be x, and the zenith angle of the sphere to the interface be θ, the geometrical relation between x and θ is given by x ) a - a cos θ. The partial surface areas of the bubble in contact with the water phase and the oil phase (Figure 3B) are expressed, respectively, by
Sw )
∫0
So )
∫θπ (2πa sin φ)a dφ ) 2πa2(1 + cos θ)
θ
(2πa sin φ)a dφ ) 2πa2(1 - cos θ)
Figure 3. Model (A) of the spherical air bubble located on the W|O boundary, which includes the three surface tensions at the W|A, O|A, and W|O interfaces, and the surface areas (B) of the three interfaces.
There are three interfaces in the cylinder, i.e., W|O, W|A, and O|A interfaces. Since the areas of three interfaces vary with x, the three surface energies in the cylinder depend on x. The area of the W|O interface (Figure 3B) is
Swo ) πa2 - π(a sin θ)2 ) πa2 cos2 θ Letting the surface energies at the W|A, the O|A, and the W|O interfaces be γw, γo, and γwo, respectively, the total surface energy in the cylinder is given by
Figure 4. Dependence of the sum of the surface energies inside the cylinder on the rising distance of the air bubble.
U ) γwSw + γoSo + γwoSwo )
by
πa2[2γw(1 - cos θ) + 2γo(1 + cos θ) + γwo cos2 θ] When cos θ is substituted for x through cos θ ) 1 - x/a, U is replaced by
U ) πa2[2γwx/a + 2γo(2 - x/a) + γwo(1 - x/a)2] (1) The surface energy, U, is a quadratic function of x, of which the variation with x/a is shown in Figure 4. When the bubble is in the oil (x < 0), the energy is U0 ) πa2(γwo + 4γo), controlled by γo. The energy for the bubble in the water (x > 2a) is U2a ) πa2(γwo + 4γw), controlled by γw. There is a minimum energy at x ) a(γwo + γo - γw)/γwo for 0 < x < 2a. Therefore, the bubble is stabilized at the W|O interface against the buoyancy.
The force by the surface energy in the x-direction is expressed
fs ) -
∂U ) -2πa[γw - γo - γwo(1 - x/a)] ∂x
(2)
This force is balanced with the buoyancy force, fb. Letting the water-excluding volume of the bubble and the oil-excluding volume be Vw and Vo, respectively, and the densities of water and oil be dw and do, respectively, we have the expression for the buoyancy
fb ) (Vodo + Vwdw)g
(3)
The volumes of the water phase and the oil phase are given by
Vw )
a π π(a2 - z2) dz ) x2(3a - x) ∫a-x 3
Air Bubble on Oil/Water Interface
Vo )
Langmuir, Vol. 24, No. 8, 2008 4367
∫-aa-x π(a2 - z2) dz ) π3 [4a3 - x2(3a - x)]
Equating eqs 2 and 3 with the help of Vw and Vo, we have
[
]
a2gdo x2 x 4 - 2 3 - (1 - dw/do) ) 6 a a γw - γo - γwo(1 - x/a) (4)
(
)
Figure 5. Dependence of y on 1 - x/a in the 0.009 mM SDS aqueous solution and the NB droplet, where y has been defined by eq 5. Values of x and a were varied by controlling the injector.
Let the left-hand side be y
y≡
[
a2gdo x2 x 4 - 2 3 - (1 - dw/do) 6 a a
(
)
]
(5)
of which values can be calculated for known values of x and a. Equation 4 provides a general criterion regarding whether air bubbles stay on the W|O boundary or float: for example, gas floatation for x > 2a, and a stay for 0 < x < 2a.17 The criterion depends on which is stronger, the difference in the surface energies or the buoyancy. We changed the size of the air volumes by controlling the injector, and read x and a from photographs of different air volumes. We calculated y from x, a, do, and dw by eq 5, and plotted y against 1 - x/a in Figure 5. Smaller bubbles take smaller values of y or smaller values of x/a. A linear relation was found, supporting eq 4. The slight concave shape of the plot may be ascribed to the deformation of the air bubble from a sphere, i.e., the larger curvature of the W|A interface than that of the O|A interface because of γw > γo. According to eq 4, the slope of the line is -γwo, and the intercept is γw - γo. The numerical values of the slope and the intercept in this plot are γwo ) 1.29 mN m-1 and γw - γo ) 0.90 mN m-1. Since SDS is accumulated at the W|O and W|A interfaces, we had better represent γwo, γw, and γo by γwSo, γwSa, and γoa, respectively, where the subscript S denotes SDS. Values of the three interfacial tensions are quite different from available data, e.g., γwa ) 72 mN m-1 and γoa ) 43.3 mN m-1 because of the contribution of SDS. We can estimate only γwSa ) γoa + 0.90 ) 44.2 mN m-1. We have assumed in the above analysis that the air bubble took on a spherical shape. This assumption may not always be correct because of the difference between γwSo and γwSa. However, the maximum deviation of the diameter of the bubble from a spherical shape was one pixel of the diameter of 200 pixels, which was less than the errors involved in the fitting process. Electrochemical Drive of Air Bubble. Ferrocene was added to the oil phase for an electroactive species at the TPB reaction. The hemisphere of the oil droplet was formed on the GC electrode in the 0.5 M Na2SO4 + 0.15 mM SDS aqueous solution into which the reference and the counter electrodes were inserted. The voltammogram (Figure 6) at the GC electrode showed the anodic current without hysteresis. The steeply increasing current at 0.40 < E < 0.55 V is relaxed slightly at E > 0.55. We regard the relaxed current for 0.55 < E < 0.8 V as a limiting current, although it has no plateau. A plateau appeared more clearly without adding the surfactant under the same conditions except for SDS.10 The current values were independent of scan rates from 5 to 25 mV s-1, and hence can be regarded as the steady state. They showed proportionality with the radius of the droplet, implying proportionality with the circumference of the circle on the oil/electrode interface. Therefore, the current should be controlled by diffusion at the thin ring electrode.10a The current (17) Adamson, A. W. Physical Chemistry of Surfaces, 3rd ed.; John-Wiley and Sons: New York, 1976; pp 464-474.
Figure 6. Voltammogram of 10 mM Fc in the hemispherical oil droplet in 0.15 mM SDS + 0.5 M Na2SO4 aqueous solution at the GC electrode with the scan rate of 10 mV s-1. The oil droplet was 1.13 mm in diameter, and the air bubble was 0.60 mm in diameter. The thin arrows denote the direction of the potential scan.
has been thought to be due to the oxidation of ferrocene at the TPB to the ferricenium ion without the transport of counterions through the O|W interface,10 because the anion, sulfate, in the aqueous solution cannot be dissolved in the oil. Ferricenium ion thus generated is expelled to the aqueous phase in order to keep electric neutrality in the oil phase. Expelled ferricenium ion to the aqueous phase was reduced at 0.22 V at the backward scan. When an air bubble was injected on the top of the oil hemisphere, it was all in the water phase (x ) 2a), i.e., the bottom of the bubble being in contact with the top of the oil hemisphere. When the potential was shifted to the positive, the bubble sank into the oil. The motion of the bubble was recorded with the digital video camera, being synchronized with the electrode potential scan. Variation of the position of the bubble with the potential is shown in Figure 6, together with the voltammogram. The bubble moved down monotonically into the oil as the anodic current flowed. It stayed in the quasi-limiting current domain so that half of the bubble was in the oil. When the potential was returned to the initial value, the bubble was headed to the initial location. However, the final location at 0.0 V was lower than the initial one, as the current was lower at E < 0.2 V. The maximum moving distance of x (0.35 mm in Figure 6), ∆x, increased with an increase in the concentration of ferrocene, as is shown in Figure 7. The concentration dependence of ∆x is close to the dependence of the limiting current (Figure 7). Therefore, the motion should be caused by the oxidation of ferrocene. No motion was observed without ferrocene. A possibility of the motion is the convention of the oil bulk associated with the oxidation of ferrocene.10c The flow rate estimated from the motion of added carbon powder in the oil was 0.2 mm s-1, which would take 3 s to transfer from the boundary to the top of the oil (ca. 0.6 mm). However, the time scale is much longer than the experimental result. A reason for the motion of the bubble is predicted to be a change in the surface tension near the bubble, which may be caused by the ferricenium ion generated at the TPB. If the ferricenium ion reaches the bubble by diffusion from the TPB,
4368 Langmuir, Vol. 24, No. 8, 2008
Satoh et al.
Figure 7. Variations of the maximum distance of the motion of the air bubble and the limiting current values with the concentration of ferrocene when the potential was cycled between 0.0 and 0.8 V.
Figure 9. Illustrations of (A) the flow caused by the local difference in the concentration of the surfactant and (B) the convergence of the surfactant at the air bubble as a result of the oxidation of ferrocene at the three-phase boundary. The arrows in (A) are the predicted velocity distribution. Figure 8. Time variation of the position of the air bubble when potential was stepped from 0.1 to 0.7 V, where the electrochemical conditions were the same as in Figure 6.
it takes 600 s for the oil droplet 0.8 mm in radius from the relation between the diffusion layer and the time. However, the x vs E curve in Figure 6 shows no recognizable delay from the voltammogram. Therefore, the diffusion is not responsible for the motion of the bubble. In order to estimate the delay of the motion from the oxidation, we applied the potential step for the oxidation of ferrocene (from 0.1 to 0.7 V) to the electrode while shooting a video. Unfortunately, we failed to trigger an onset of the video microscope by the potential step. Another method is to allow the video microscope to record the onset time of the potential step. We made such an electric circuit that a light diode was emitted immediately after the potential step. We identified the onset of the potential step as a brightly changed frame of the video movie. The time variation of x after the potential step is shown in Figure 8. The time, tm, from the potential step to the intersection with the extrapolated line was ca. 0.02 s. Since the video has an inherent delay of 0.033 s, which is the lapse time between two frames, the actual response time ought to be less than 0.053 s. This duration is much shorter than the diffusion time of the propagation of the ferricenium ion across the radius of the hemisphere. Our idea for the electrochemical drive is the translational motion of the O|W interface caused by the generation of ferricenium ion. We propose a model of driving the O|W interface by the local difference in surface tensions, as is illustrated in Figure 9A. When the surface concentration of the surfactant on the left of Figure 9A is higher than that on the right, the surface energy (tension) on the left is lower than that on the right. The force acts on the boundary in the left direction, and then the boundary gains the velocity to the left. The velocity should decay in the bulk obviously. When the boundary moves to the left, the surfactant is concentrated there and might be aggregated. However, the surface concentration is limited partly because of charge-charge repulsion of the surfactants and partly because of thermal dispersion. We apply this concept to the TPB reaction. The oxidation of ferrocene at the TPB is necessarily accompanied with charge neutrality by passing through the surfactant layer. The alkylsulfate ion of SDS may work as the electric neutrality
for the oxidation. Then, the concentration of SDS near the TPB becomes lower than that before the oxidation (see Figure 9B). The difference in the surface concentration of SDS ought to cause a flow from the TPB along the O|W interface. The SDSrich layer converges by the flow toward the top of the hemisphere from the ring TPB, and disperses SDS around the top to enhance the concentration of SDS near the air bubble. The enhanced concentration ought to push down the air bubble, as is demonstrated in Figure 2. It is necessary to justify experimentally the occurrence of the flow on the O|W interface by the local difference in concentrations. Our experimental apparatus for the justification is the colored oil spread on a water surface, onto which SDS aqueous solution is dropped, as is shown in Figure 10. We used ferroceneincluded silicone oil with 5 cSt for the colored oil, and spread it on the surface of 0.5 M Na2SO4 aqueous solution in a petri dish 15 cm in diameter. When 10 mM SDS solution was dropped on the yellow spread oil, the SDS drop spread on the aqueous phase in a concentric circle, excluding the oil phase, as is shown in Figure 10B,C. The exclusion can be explained as follows: The dropped SDS solution falls through the oil layer to be dissolved in the aqueous phase. It forms the interface of water|SDS|air at the fallen point. The interface has lower surface tension than the O|A or O|W interface, as has been demonstrated in Figure 5. Therefore, it is expanded in the concentric form toward the edge of the petri dish. As a quantitative measure of the concentric expansion, we evaluated the diameters, d, of the excluded oil, as is shown in Figure 10B. Figure 11 shows the time variation of the diameters, which increased with the time. The diameter reached the steady value at t > 0.6 s, partly because the expansion of the oil phase was blocked by the edge of the petri dish and partly because the expansion ran short of SDS owing to the dilution in the aqueous phase. Since the expansion occurred concentrically, the excluded area rather than the excluded diameter is expected to increase linearly with the time. We plotted the time variation of the excluded area in Figure 11. The linear relationship supports the rate-determining control of surface processes, implying a difference in the surface tensions of the oil film and the SDSspread water. The slope, i.e., area velocity, is 3.9 cm2 s-1, and the linear velocity at t ) 0 is 4.0 cm s-1. These values correspond
Air Bubble on Oil/Water Interface
Langmuir, Vol. 24, No. 8, 2008 4369
Figure 12. Variation of y with 1 - x/a for the data in Figure 6. The y-scale is the same as in Figure 5.
We apply eq 4 to the potential dependence of x in Figure 6, as has been done in Figure 5. Although eq 4 includes potential variations in γw, γo, and γwo, we neglect them for the time being. Figure 12 shows the variation of y with 1 - x/a for known values of a, dw, and do, where potentials are indicated numerically in the figure. The plot has actually a zero slope in comparison with the large slope in Figure 5. The value of the slope was positive, implying a negative value of γwo. This irrationality may be ascribed either to the potential dependence of both γw and γwo or to local variations of SDS concentration on the O|W interface. The potential dependence of surface tensions is well-known in the theory of the diffuse double layer.18 However, it may be a minor cause because no motion was found at the potential scan without ferrocene. In contrast, the concentration dependence was obvious from the upward shift of the air bubble at higher concentrations of SDS, and hence is more preferable than the potential dependence of surface tensions. This is indirect evidence of the local accumulation of SDS to the bubble.
Conclusion
Figure 10. Photographs of expansions of the ferrocene-including 5 cSt silicone oil spread on the surface of 0.5 M Na2SO4 aqueous solution (A) immediately after, (B) 0.07 s after, and (C) 0.13 s after 10 mM SDS was dropped on the spread oil surface. The excluded oil was almost a circle, in diameter d in (B).
Figure 11. Time dependence of the diameter (triangles) and the area (circles) of the concentrically expanding silicone oil after dropping 10 mM SDS on the water-floated oil surface.
to the common traveling period, 0.02 s, by dividing 4πro2 and ro, respectively, where ro is the radius of the oil droplet. The period is not inconsistent with the value (less than 0.052 s) obtained in Figure 8.
An air bubble injected in the oil phase stayed at the top of the hemispherical oil on the electrode, with a part of the bubble excluding the aqueous phase. The stay against the buoyancy is ascribed to the surface tension at the W|A interface of the bubble in the gravitational direction. The force balance was formulated by using the buoyancy and the surface tensions at the W|A, O|A, and W|O interfaces on the basis of the cylindrical cell model. There is a minimum energy for which the bubble is located at the W|O interface. The formulation may be helpful to discuss generally the stability of air bubbles accumulated at W|O interfaces or floatation. The small air bubbles were so sensitive to be driven even by the Brownian force. The air bubble was sunk toward the oil phase as ferrocene was oxidized at the TPB. Consequently, the potential dependence of going up or down was close to the voltammetric response of ferrocene. The response of the motion to the electrode reaction was much faster than the diffusion of ferricenium ion. As a possible fast process, we took into account the convection on the W|O interface, which is caused by the local difference in the surface concentration of the surfactant. This type of convection was demonstrated by the concentric exclusion of the colored oil layer spread on the water surface when SDS solution was dropped on the oil layer. Acknowledgment. This work was financially supported by Grants-in-Aid for Scientific Research (grants 18350041) from the Ministry of Education in Japan. LA703675E (18) Bard, A. J.; Faulkner L. R. Electrochemical Methods: Fundamentals and Applications; John-Wiley & Sons: New York, 2001; pp 540-541.
