Surface Acoustic Cavitation Understood via Nanosecond

E. Maisonhaute, P. C. White, and R. G. Compton*. Physical and Theoretical Chemistry Laboratory, UniVersity of Oxford, South Parks Road,. Oxford OX1 3Q...
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J. Phys. Chem. B 2001, 105, 12087-12091

12087

Surface Acoustic Cavitation Understood via Nanosecond Electrochemistry E. Maisonhaute, P. C. White, and R. G. Compton* Physical and Theoretical Chemistry Laboratory, UniVersity of Oxford, South Parks Road, Oxford OX1 3QZ, U.K. ReceiVed: June 26, 2001; In Final Form: August 29, 2001

The application of high intensity ultrasound to liquids leads to cavitation. In contrast to the homogeneous situation this is poorly understood close to a surface despite the implications for many biological, chemical, and physical applications. By using ultrafast electrochemical equipment and arrays of electrodes, we prove that the acoustic bubbles in the range of power ultrasound are hemispherical, not spherical as usually supposed, possessing a large range of possible diameters and oscillating at harmonics and sub-harmonics of the driving frequency (20 kHz). Most importantly, contrary to inferences made previously at much lower frequencies, no liquid microjet inside the bubble is observed.

Introduction There has been an increasing interest in cavitation studies over the past decade. On the one hand, bubble implosion in solution causes extremely high temperatures leading to sonoluminescence and sonochemistry effects.1-5 On the other hand, surface cavitation may have either positive effects such as cleaning properties and increased mass transport,6 or destructive ones such as those that cause erosion of pipes or damage to propellers, but also lead to medical applications.7 However, experimental data concerning the full characterization of the bubble behavior close to a surface are rare. The first photographic detection was carried out by Benjamin and Ellis,8 and then by Crum9 for an acoustic bubble driven at 60 Hz. Lauterborn also studied the collapse of laser induced bubbles and the resulting erosion that occurs.10 These experimental approaches revealed the presence of a microjet (cf. Figure 1) and have been successfully simulated first by Plesset and Chapman11 and later by Blake.12,13 However, the standard conditions useful for ultrasound applications in biology, chemistry, and physics use kHz or MHz frequencies, and so differ significantly from the above experiments. In fact, the RayleighPlesset equation describing the bubble behavior is highly nonlinear, and its numerical solution is very sensitive to the experimental conditions. An alternative method of monitoring bubble activity is to use indirect measurements. By applying an electrochemical perturbation during a limited time τ, a diffusion layer of length δ is created in the vicinity of the electrode. δ can be adjusted at will by varying τ between a few nanometers for nanosecond electrochemical perturbations and δSS, the steady-state diffusion layer imposed by the local hydrodynamic conditions (δSS ≈ r0 if no convection occurs, δSS < r0 otherwise, where r0 is the electrode radius14). For δ < δSS, δ and τ are related through the diffusion coefficient D: δ ≈ (Dτ)1/2. An event occurring at a distance h from the electrode surface will be detected provided h is smaller than δ. Adding an electroactive analyte to the solution then allows detection solely of the cavitation activity that affects the diffusion layer. First attempts to monitor the single bubble activity using microelectrodes were reported by Birkin, but these results were * Author to whom correspondence should be addressed. E-mail: richard. [email protected].

Figure 1. Schematic diagram showing the occurrence of a microjet when a bubble collapses close to a surface.

Figure 2. Experimental setup. The counter and reference electrodes are platinum wires.

either affected by the band-pass of the equipment,15-16 or very different from those we describe in this paper,17 perhaps partly because of erosion by sonication of the gold electrode used. Recently, some of us showed that electrochemical measurements could be performed down to a few tens of nanoseconds without distortions.18-19 In the following, we report experiments carried out in water, using the well-known Fe(CN)63-/Fe(CN)64electrochemical couple:

Fe(CN)63- + e h Fe(CN)64The experimental setup is described in Figure 2. We applied either a constant potential (chronoamperometry) or a potential triangular ramp (cyclic voltammetry). We demonstrate in this paper that employing ultrafast electrochemical equipment allows us to monitor the bubble activity in real time, to determine the bubble size, and to gain an insight into the bubble dynamics, disproving the presence of microjetting at the frequencies studied.

10.1021/jp012437e CCC: $20.00 © 2001 American Chemical Society Published on Web 11/09/2001

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Experimental Section Photographic Detection. Pictures and movies were taken directly through the ocular of a binocular loop with a Casio QV3000 digital camera. A Petri dish (8 cm diameter) was used, and the sonic horn had to be angled (around 60°) in order to immerse it in the solution and still allowing it to take pictures. The horn-to-surface distance was around 1 cm, and the camera was focused on the surface. Reagents. Chemical reagents used are as follows: K3Fe(CN)6 and KNO3 (Aldrich), and were used as received. Argon bubbling (Pureshield, BOC) was used to maintain a dry and inert atmosphere. Aqueous solutions were prepared using UHQ grade water of resistivity of not less than 18 MΩ cm (Elga, High Wycombe, Bucks, U.K.). Instrumentation. To monitor many electrodes at the same time, we used a home-built multiple potentiostat, which has a sub microsecond rise time. The potential was applied with a TTI TG1304 programmable function generator (Thandar), and the current were recorded with two Tektronix TDS3032 and TDS 220 oscilloscopes. Microelectrodes. Single microelectrodes of diameters ranging from 25 µm up to 0.5 mm were made by sealing platinum wires into soft glass, according to published procedure.20 Arrays of 29 µm electrodes were made in epoxy resin (MA2, PRESI). First, an epoxy plate (around 1 × 1 cm) was made and polished with PRESI P4000 abrasive paper. Then a droplet of epoxy was spread on half of it, and the microwires were positioned at the desired distance under a binocular loop. The epoxy was then allowed to cure for 1 h at 40 °C. Connecting wires were then soldered and the electrode length extended by attaching a glass tube with epoxy. More epoxy was then added to completely cover the wires and the connections. All electrodes were polished with PRESI papers and then with PRESI 0.3 µm alumina. Their sizes were evaluated from pictures taken through the binocular loop. An array of electrodes with different sizes was also made to record the steady-state current without dismounting the cell. Ultrasonic Equipment. We used a 1.3 mm diameter titanium ultrasound horn transducer system (Sonics & Materials, VCX400) instead of a microtip (3 mm) to minimize the error in the position of the electrode. The horn was calibrated according to a published procedure.21 Experimental Section Results and First Deductions Chronoamperometry at a Single Electrode. In these experiments we continuously reduce Fe(CN)63- into Fe(CN)64at the electrode surface, with the latter held at -0.8 V (vs Pt reference). Figure 3 shows typical chronoamperograms for a 29 µm platinum electrode, under sonication. We attribute the observed peaks to the appearance of a cavitational bubble in the vicinity of the electrode.22 The overall signal length varies from around 50 µs (1 acoustic cycle, transient cavitation) up to a few milliseconds (stable cavitation). By decreasing the horn to electrode distance (and thereby increasing the local acoustic pressure), we could see that transient cavitation events became more numerous (cf. Figure 3d). This transition has been already well described in homogeneous solution1,23,24 but is observed for the first time here at a surface. Hence, in the following experiments, we kept the horn-to-electrode distance and the ultrasound intensity constant (1 cm and 8.9 W cm-2, respectively). Remarkably, at times outside the occurrence of the peaks, the current is approximately constant, but is much greater than the spherical diffusion-limited current under silent conditions.

Figure 3. Chronoamperometric current obtained for the reduction of 50 mM K3Fe(CN)6 in a 0.1 M KNO3 water solution under sonication at 8.9 W cm-2. Electrode diameter: 29 µm. Horn-to-electrode distance: 1 cm (a,b,c) or 1.5 mm (d). Figures (a), (b), and (c) are different transients obtained under the same conditions.

Figure 4. Acoustic streaming steady-state current versus electrode surface under sonication at 8.9 W cm-2. Solution: 10 mM K3Fe(CN)6 in 0.1 M KNO3. Horn-to-electrode distance: 1 cm. Symbols: experimental values, obtained by averaging 3 independent measurements. Solid line: linear best fit.

This quasi-steady-state current is proportional to the electrode area for electrodes diameters ranging from 25 µm to 0.4 mm (cf. Figure 4) and is attributed to macroscopic acoustic streaming.25 The resulting diffusion layer has a thickness of 8 ( 2 µm. Since any peak inducing a variation of more than 10% in the steady-state current would be detected, this result reveals that in our mild conditions, there is no cavitation activity contribution in this steady-state current. This is consistent with independent measurements of diffusion layers by differential pulse voltammetry.26 However, it is also obvious that the entire millisecond signal cannot here be described as only a single peak, as suggested elsewhere.17 It comprises many thinner spikes, whose rise time can be less than one microsecond. In some cases, these narrow spikes can be periodic, with a frequency of 10 (Figure 3a) or 20 kHz (Figure 3b) leading to larger currents that can be as high as 200 times more than the steady-state diffusion-limited current under silent conditions. Higher harmonics of the driving frequency can also be observed (cf. Figure 3c). These features reveal strong bubble oscillations in the sound field, and a varying lifetime. Harmonics and sub-harmonics of the driving frequencies have been mentioned in the literature.23 Cyclic Voltammetry. The use of a time-limited electrochemical perturbation is of interest as it allows the diffusion layer to grow over a distance δ ≈ (Dτ)1/2. The voltammetric time scale is given by τ ) RT/FV, where R ) 8.314, T is the temperature, and V the scan rate. For example, V ) 1000 V s-1 gives δ ≈ 0.15 µm. Relatively short diffusion layers can then easily be achieved. In Figure 5a and 5b, one can see that the cavitation peak is preceded by a long depletion in the voltam-

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Figure 6. Picture of an array made out of five 29 µm electrodes. The current on each electrode can be monitored independently.

Figure 5. Cyclic voltammograms recorded simultaneously (a and b, or c and d) for two electrodes separated by 206 µm. Solution: 50 mM K3Fe(CN)6 in 0.1 M KNO3. Horn-to-electrode distance: 1 cm. Electrode diameters: 29 µm. Circles: voltammogram under silent conditions (scan rate 2800 V s-1). Solid line: voltammogram under sonication at 8.9 W cm-2. (c) and (d) were recorded outside the electroactivity of Fe(CN)63- (background current).

metric current, indicative of an obstacle to diffusion layer growth. Analogous behavior was observed with scan rates as high as 104 V s-1 (δ ≈ 50 nm). In our opinion, this clearly demonstrates that the bubble grows in the close vicinity of the electrode surface. Moreover, the cavitation activity surprisingly does not “spread over” the diffusion layer: after the spike, the end of the voltammogram overlays with the silent voltammogram, as does the back peak, corresponding to the ferrocyanide reoxidation (note that Fe(CN)64- is only produced at the electrode surface when E, the applied electrode potential, is below Eeq, the equilibrium potential). This is supplementary proof that the diffusion layer structure returns after the collapse occurs. On the other hand, a surprising feature occurred when we used a solution containing no electroactive species, or when the scan range was outside the electroactivity of the analyte (cf. Figure 5c and Figure 5d). Whereas no signals whatsoever were observed when the potential was kept constant, we could see cavitation spikes with the same characteristics as above when a potential scan was applied. Our interpretation is that no double layer charging peak is observed at constant potential because sonication cannot remove the double layer, since the electrostatic attraction between the electrode surface and the ions of opposite charge in solution is too strong. Using the simple Helmholtz model to describe the double layer, the attractive force between the two plates of the Helmholtz capacitor is F ) CSAU/d, where CS is the capacitance per surface area, A the electrode area, d the distance between the plates, and U the tension applied. This corresponds to a pressure of P ) CSU/d, and using standard parameters (CS ) 0.2F.m-2 and d ) 0.2 nm) we reach pressures of the order of 1 GPa. Therefore very high energies are needed to remove the double layer. As the potential varies, the charge on the electrode is changing and ions from the solution are needed to compensate this extra charge. When a bubble partially blocks the surface, double layer charging is prevented and hence a depletion in the current is observed. Upon bubble collapse, the charge is recovered over a short time, giving a sharp current peak. More precisely, the bubble is able to block the surface if there are not enough ions in the thin liquid layer between the bubble wall and the electrode. This implies layer thicknesses of at most a few nanometers.

Figure 7. Chronoamperometric current recorded simultaneously (a, b and c or d, e and f) on three electrodes. Solution: 50 mM K3Fe(CN)6 in 0.1 M KNO3. Horn-to-electrode distance: 1 cm. Electrode diameters: 29 µm. Sonication at 8.9 W cm-2. Inter-electrode distance: 104 µm (a,b, and c) or less than 5 µm (d,e, and f).

Experiments with a single microelectrode show that the cavitation activity is complex. Oscillations at harmonics of the driving frequency are observed, and cyclic voltammetry experiments prove that the bubble is in contact with at least a part of the electrode. However, due to this complexity the spatial dependence of a single cavitational event is difficult to assess, since no theoretical model allows easy linking of the signal obtained to the space variables. For this purpose, we used microelectrode arrays, to which we turn next. Multielectrode Arrays. Building arrays allow us to have a direct visualization of the spatial extension of the bubbles. The experiments in the previous sections were repeated as before, but the current was recorded simultaneously on different electrodes of the array (up to 3 electrodes were monitored at the same time). A typical array is shown in Figure 6. Figure 7a-c shows typical chronoamperograms obtained for an array of three 29 µm electrodes, with an inter-electrode distance of 103 µm. The appearance of cavitation peaks on the three electrodes is there observed almost simultaneously. Since it is very unlikely that two different bubbles appear at around the same time on different electrodes, and given the same peak shape and lifetime, we attribute the signals on the different electrodes to the same bubble. Synchronous events could be recorded for distances as large as 0.8 mm using different electrode-to-electrode separation. Conversely, in Figure 7d-f, for which the inter-electrode distance is less than 5 µm, a signal is observed only on the middle electrode, which reveals that

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Figure 8. Probability to observe a chronoamperometric signal simultaneously on two electrodes separated by a gap g. (a) Experimental probability. Solution: 50 mM K3Fe(CN)6 in 0.1 M KNO3. Horn-toelectrode distance: 1 cm. Electrode diameters: 29 µm. Sonication at 8.9 W cm-2. (b) Theoretical expression of P(g/RB), considering a single bubble radius RB.

the bubble size is there less than 40 µm. We suggest that this behavior proves we are dealing with a wide distribution of bubble sizes. Note that the same kind of signal (spikes) with nearly the same current amplification is obtained on all the electrodes. This rules out the possibility of having a microjet, since different signals would be expected for electrode positions below the jet, below the toroidal bubble, and outside the bubble. Or, at least, if a microjet is present then it must have no significant effect on the electrode signal. Microjetting is thus unlikely to play a predominant role in the action of 20 kHz ultrasound as applies to biological, chemical, and electrochemical interfaces. A statistical analysis can be made: noting g, the electrodeto-electrode separation, and choosing to trigger the scope on one electrode (called E1), we decided to register the probability Pexp(g) of simultaneously having an event on an electrode E2 separated by g from E1. First, the maximum peak height was estimated for E1. Then, the scope was triggered on E1 at a level half of the maximum peak height. We decided that an event occurred on E2 when its current exceeded half the trigger level. The current is usually far above or far below this limit, hence the precise position of the limit does not significantly change the results. The probability Pexp(g) corresponding to 4 different distances is given in Figure 8a and will be discussed below. Using the cyclic voltammetry experiment described previously, it is easily possible to observe whether there is a depletion in the diffusion layer during the bubble expansion. Generally, when cavitational activity is seen on two different electrodes, both show a depletion in the voltammogram (cf. Figure 5), either in the Faradaic current or in the background one. Since this depletion is attributed to a blocking of the surface, the bubbles must have γ values of less than 0.5 at maximum size (γ ) h/RB, where h is the distance from the bubble center and the electrode and RB the bubble radius). Bubbles are thus hemispherical rather than spherical, or even flatter, in contrast to the assumptions made in the past. Photographic Detection. Direct detection of bubbles formed in solution by sonication with a 10 kHz transducer has been published by Leighton.24 However, to our knowledge, no similar work is available for cavitation at a surface. Since electrochemical results show that the bubble lifetime can reach several milliseconds, we have attempted to film them directly through a binocular loop, with a basic digital camera. The whole movie is available upon request, and 3 pictures are presented in Figure 9. Bubbles appear as poorly defined shadows on the pictures. The camera takes one picture every 67 ms, so no precise description of the bubble movement can be obtained. This simple experimental setup nevertheless allowed the detection of many different bubble sizes, ranging from 15 µm up to 0.6 mm, in agreement with the electrochemical measurements.

Maisonhaute et al.

Figure 9. Photographic detection of the cavitational bubbles (8.9 W cm-2).

Figure 9c also shows a cluster of bubbles, possibly resulting from fragmentation of an initial large bubble. This possibility has been considered by Blake,12 but had never been observed before. We notice also that in those conditions the bubbles can be detected on only one picture, proving that the lifetime is less than 70 ms, which is consistent with the electrochemical data. Full Discussion Various conclusions about interfacial cavitation emerge from the above. First, occurrence of a microjet leading to a toroidal bubble as seen by Crum9 at smaller driving frequency seems to be unlikely in our experimental conditions, since this would not be compatible with bubble lifetimes of several milliseconds under very turbulent conditions. Also, if the spikes were due to a microjet on the surface, it would be impossible to observe a nearly identical amplification at distances of more than 0.5 mm. Second, cyclic voltammetry experiments reveal that in order to observe a spike, there must first be a depletion in the voltammetric Faradaic peak or in the background current. Thus the bubble must cover the electrode surface. However, the current does not drop completely to zero, revealing that only a part of the bubble really touches the surface. Note that for the same conditions, the depletion seems to be more significant and happen more often in the Faradaic peak than in the background current. In our opinion, this is likely to be due to the surface roughness. AFM images of electrodes published previously reveal that a polished platinum electrode has roughness with pits and grooves of width and depth depending on the alumina particle sizes (around 0.3 µm) used in polishing.28 Furthermore, the bubble surface may also not be smooth. Since we attribute the depletion in the background current to contact with the surface, the magnitude of the depletion leads to the area of direct contact. From Figure 5c, we can estimate the depletions to be at most 50% of the total current. The array experiments reveal that the peak is due to the bubble wall freeing the electrode from the bubble and then flushing the electrode. Two effects may thus be considered: the bubble velocity (rate at which the surface is freed, of the order of 100 m s-1) and the distance h between the electrode and the bubble wall. A detailed model of the current spike will be given elsewhere, but in order to explain a current enhancement of 200 times the diffusion-limited current under silent conditions and a sub microsecond rise-time, h values of a few tens of nanometers have to be considered. h may be even smaller, allowing the bubble to prevent charging of the double layer. Moreover, a comparison with numerical solutions of the Rayleigh-Plesset equation under conditions where strong radius oscillations are possible (comparable to our work), reveals that most of the time the bubble radius is close to its maximum.13,23,24,27 This is consistent with our experimental data, which show a long depletion followed by a fast collapse and then another depletion. On the other hand, the peak width probably depends not only on h, but also on the time the diffusion layer is allowed to grow when the electrode surface

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J. Phys. Chem. B, Vol. 105, No. 48, 2001 12091 than RB (cf. Figure 10). Furthermore, the probability of finding B within a distance between r and r + dr from E1 is P1(r) ) (2πr dr)/(πRB2). Then, to record an event on E2, we must have R2 < RB, where R2 is the distance between B and R2. Therefore E2 needs to be on the arc of angle R. The probability P2 of recording an event on E2 for a given r is then P2(r) ) R/(2π). From basic geometry, we have

R ) 2arccos

Figure 10. Probability for a bubble of radius RB to cover two electrodes. Solid circle: bubble on the surface, covering E1. Dashed circle: position of the electrode E2 separated by a gap g. To observe a signal on both electrodes, E2 must be in the circle arc of angle R.

is freed from the bubble (upon collapse), before being covered again at a distance h′, possibly different from h. Another important parameter given by multielectrode experiments is the bubble size. They clearly show that the bubble may extend over diameters ranging from less than 15 µm up to 0.8 mm. These values contrast with the equilibrium bubble diameter in solution (300 µm). This is confirmed by the photographic detection. The statistical analysis of Figure 8a may be compared with the theoretical probability expression obtained for a single bubble (radius RB) appearing at a random position on the surface, but affecting the first electrode E1. The probability of observing a signal on an electrode E2 separated from E1 (cf. Figure 10) one by a gap g is (cf. appendix):

P(g/RB) )

∫0R πR2 2arccos B

B

(

)

r2 + g2 - RB2 r dr ) 2rg

∫01π2 arccos

(

( ) ( )

)

g 2 -1 RB u du g 2 u RB

u2 +

A numerical solution of P(g/RB) is given in Figure 8b. Clearly it does not exactly replicate the experimental behavior, and shows an overestimate for small distances, possibly due to the small bubble population and to the non isotropic nucleation of the bubbles. Here, the probability falls sharply around 200 µm, which reveals that the average diameter of the bubble distribution is probably around this value. Conclusions We show in this paper that at a surface, an ultrasonically created bubble grows and oscillates at harmonics of the driving frequency. Using microelectrode arrays, different bubble sizes up to 0.8 mm were observed. The shape of the bubble is hemispherical rather than spherical, and transient as well as quasi-stable cavitation is possible. More generally, this method may also be useful for characterization of cavitational bubbles appearing in other experimental conditions, as in pipes or propellers. Appendix Let us consider a single bubble radius. PRB starts from 1 when g , RB and goes to 0 for g g 2RB (center B of the bubble in the middle of [E1E2]). The oscilloscope is triggered on E1, then, each time we record a signal on E1, this means that r, the distance between E1 and B, the center of the bubble, is less

(

)

r2 + g2 - RB2 2rg

Taking these two aspects into consideration, then probability of observing an event on E1 and E2 is, for a single bubble radius:

P(g/RB) )

∫0R

B

P1(r)P2(r)dr

Moreover, the entire expression of P(g) taking into account the bubble size distribution D(RB) is

P(g) )

∫0∞ D(RB)P(g/RB) dRB

Acknowledgment. We gratefully thank EPSRC for financial support, and P. Maisonhaute for lending his camera. References and Notes (1) Crum, L. A., Ed. Sonochemistry and sonoluminescence. NATO ASI series. Series C, Mathematical and physical sciences, 524, Dordrecht: London, 1999. (2) Mason, T. J. Sonochemistry; Ellis Harwood: Chichester, U.K., 1988. (3) McNamara, W. B.; Didenko, Y. T.; Suslick, K. S. Nature 1999, 401, 772. (4) Suslick, K. S. Science 1990, 247, 1439. (5) Doktycz, S. J.; Suslick, K. S. Science 1990, 247, 1067. (6) Compton, R. G.; Eklund, J. C.; Marken, F. Electroanalysis 1997, 9, 509. (7) Physical Principles of Medical Ultrasonics; Hill, C. R., Ed.; Ellis Harwood: Chichester (for Wiley: New York), 1986. (8) Benjamin, T. B.; Ellis, A. T. Philos. Trans. R. Soc. London 1966, A260, 221. (9) Crum, L. A. J. Physique 1979, 11, C8-285. (10) Philipp, A.; Lauterborn, W. J. Fluid Mech. 1998, 361, 75. (11) Plesset, M. S.; Chapman, R. B. J. Fluid Mech. 1998, 47, 283. (12) Blake, J. R.; Keen, G. S.; Tong, R. P.; Wilson, M. Philos. Trans. R. Soc. London A 1999, 357, 251. (13) Blake, J. R.; Hooton, M. C.; Robinson, P. B.; Tong, R. P. Philos. Trans. R. Soc. London A 1997, 355, 537. (14) Amatore, C. In Physical Electrochemistry: Principles, Methods and Applications; Rubinstein, I., Ed.; Marcel Dekker: New York, 1995. (15) Birkin, P. R.; Silva-Martinez, S. Anal. Chem. 1997, 69, 2055. (16) Birkin, P. R.; Delaplace, C. L.; Bowen, C. R. J. Phys. Chem. B 1998, 102, 10885. (17) Birkin, P. R.; Silva-Martinez, S. J. Electroanal. Chem. 1996, 416, 127. (18) Amatore, C.; Maisonhaute, E.; Simonneau, G. Electrochem. Commun. 2000, 2, 81. (19) Amatore, C.; Maisonhaute, E.; Simonneau, G. J. Electroanal. Chem. 2000, 486, 141. (20) Wightman, R. M.; Wipf, D. O. In Electroanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1989; 15. (21) Margulis, M. A.; Maltsev, A. N. Russ. J. Phys. Chem. 1969, 43, 592. (22) Klima, J.; Bernard, C.; Degrand, C. J. Electroanal. Chem. 1995, 399, 147. (23) Leighton, T. G. The acoustic bubble; Academic Press: London. (24) Leighton, T. G. Ultrasonics 1989, 27, 50. (25) Marken, F.; Akkermans, R. P.; Compton, R. G. J. Electroanal. Chem. 1996, 415, 55. (26) Del Campo, F. J.; Melville, J.; Hardcastle, J. L.; Compton, R. G. J. Phys. Chem. A 2001, 105, 666. (27) Leighton, T. G.; Walton, A. J.; Field, J. E. Ultrasonics 1989, 27, 50. (28) Akkermans, R. P.; Ming, W.; Fidel-Suarez, M.; Compton, R. G. Electroanalysis 1998, 10, 613.