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A fast moving nanometric interface: the example of acoustic cavitation

A fast moving nanometric interface: the example of acoustic cavitation

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Time (μs)

Fig. 22 Chronoamperometirc current obtained for the reduction of K3[Fe(CN)6] (50 mM) in

aqueous KNO3 under ultrasound power of 8.9 WcmÀ2 at a 29 mm diameter platinum electrode.

Horn-to-electrode distances are 1.5 mm (d) and 1 cm (a, b and c). Reprinted with permission

from Ref. 163.



separation cavitation shifts from stable to transient (see Fig. 22d). It is

observed that the current in the transients, such as those shown in Fig. 22,

was approximately constant outside the occurrence of peaks but was much

greater than the spherical diffusion-limited current under silent conditions.

Furthermore, this current was found to be proportional to the electrode

area for a range of electrode diameters. This is attributed to macroscropic

acoustic streaming, which leads to a convection-dominant response. The

resulting diffusion layer was 8 mm for the conditions used. Since any peak

inducing a variation of more than 10% in the steadystate current would be

detected, this observation suggests that there is little or no cavitation

activity contribution in this steadystate current, which is consistent with

independent measurements of the diffusion layer behavior by differential

pulse voltammetry.171 Returning to the chronoamperograms, it is obvious

that the entire millisecond signal cannot be described as a single peak as

suggested elsewhere.172 Figure 22 shows that the signal 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 or 20 kHz

(Figs. 22c and 22a, respectively), leading to larger currents that can be up to

200 times higher than the steady-state diffusion-limited current under silent

conditions. Higher harmonics of the driving frequency can also be observed

(see Fig. 22b).

Next, ultrafast cyclic voltammetry was investigated. In Fig. 23, one

can see that the cavitation peak is preceded by a long depletion in the

voltammetric current, indicating the presence of an obstacle to the diffusion

layer growth.

Analogous behaviour was observed with scan rates as high as 104 V sÀ1.

This suggests that the bubble grows in the close vicinity of the electrode

22 | Electrochemistry, 2013, 11, 1–33



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Potential (V) vs. Pt electrode



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Fig. 23 Cyclic voltammograms recorded simultaneously ((a,c) and (b,d)) for two electrodes

separated by 206 mm. Conditions: K3[Fe(CN)6] (50 mM) in KNO3 (0.1 M), horn-to-electrode

distance 1 cm, electrode diameters 29 mm. Voltammograms under silent conditions (red) and

subject to 8.9 WcmÀ2 insonation (blue) are represented. Reprinted with permission from

Ref. 163.



surface: After the spike, the end of the voltammogram overlays with the

silent voltammogram, as does the back peak corresponding to the ferrocyanide reoxidation. This is proof that the diffusion layer structure returns

after the collapse occurs. Experiments with a single microelectrode show

thus that the cavitation activity is complex. Oscillations at harmonics of the

driving frequency are observed with cyclic voltammetry experiments proving that the bubble is in the close vicinity of at least a part of the electrode.

Due to the complexity of activity, the spatial dependence of a single cavitational event is difficult to assess since no theoretical model immediately

allows easy linking of the signal obtained to the space variables. For this

purpose microelectrode arrays were used. Multielectrode arrays allow a

direct visualization of the spatial extension of the bubbles. The chronoamperometric experiments presented above were repeated as before but

the current was simultaneously recorded on different electrodes of the array.

A typical array is shown in Fig. 24.

The appearance of cavitation peaks on the three electrodes is observed

almost simultaneously in Fig. 24a–c. Since it is unlikely that two independent bubbles appear at around the same time on different electrodes and

with the same peak shape and lifetime, it is inferred that the signals are

induced by the same bubble. Analogous synchronous events could be

recorded for distances as large as 0.8 mm using different electrode-toelectrode separations. Furthermore in Fig. 24d–f, where the interelectrode

distance is less than 5 mm, a signal is observed only on the middle electrode.

From geometrical considerations, we can estimate that the bubble size there

is less than 40 mm. This behavior suggests that a wide distribution of bubble

sizes is produced, including bubbles of sizes less than 40 mm. In all work

Electrochemistry, 2013, 11, 1–33 | 23



200 m



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Fig. 24 Top: exemple of microelectrode array. Bottom: Chronoamperometric current recorded simultaneously (a, b and c or d, e and f) on three electrodes using 50 mM K3[Fe(CN)6] in

aqueous KNO3 (0.1 M). Reprinted with permission from Ref. 163.



carried out, the same type of signal with nearly the same current amplification is observed, suggesting that in these type of experiments (20 kHz,

interfacial cavitation) the absence of a microjet, or if the microjet is present,

it is ineffective in controlling the magnitude of the electrode signal, since

different signals would be expected for electrode positions below the jet,

below the toroidal bubble and outside the bubble. Furthermore, cyclic

voltammetry experiments revealed that when cavitational activity is seen on

two different electrodes, generally both show a depletion in the voltammogram (see Fig. 24) either in the faradaic current or in the background

current. Since this depletion is attributed to blocking of the surface, the

24 | Electrochemistry, 2013, 11, 1–33



h/RB ratio, where h is the distance from the bubble centre and the electrode

and RB the bubble radius, must be less than 0.5. Bubbles are thus more

likely to be hemispherical or flatter rather than spherical shape as often

assumed.

On the trace displayed in Fig. 25b, a more quantitative interpretation was

possible. Here, the chronoamperometric trace was obtained for the reduction of [Ru(NH3)6]3 ỵ in aqueous solution.

We considered a simple model of bubble implosion close to a surface.

Firstly, we introduced the distance x0 between the disc electrode and the

bubble wall. We considered a potential sufficiently negative to ensure that

the concentration C of electroactive species at the electrode surface is zero.

Therefore diffusion of the electroactive species from the solution (C=C0)

toward the electrode (C=0) occurs. The model is described in Fig. 25a. At

time to0, the bubble grows and covers the electrode. Collapse occurs at

t=0 and bulk solution instantaneously replaces the bubble but the thin

layer (TL) above the electrode x0 is still fully electrolysed: the concentration

of the electroactive species in TL and the current are then both zero. After

the collapse, bulk solution instantaneously replaces the bubble above TL

and diffusion of the electroactive compound inside TL occurs. This model

neglects macroscopic streaming as this has been shown to correspond to

larger diffusion layers than are actually observed experimentally for the

transient, as opposed to the steady-state response. After a time t0 it is

believed that the bubble expands again, thus recreating another thin layer of

the same thickness x0. The electrode is then blocked again and the current

drops to zero within a time proportional to x02/(2D), where D is the diffusion coefficient of the redox system.

Theory based on this model was used to fit all the cavitation spikes shown

in Fig. 25. The peak height and width was matched with the working curve

data. This allowed values of x0 and t0 be theoretically deduced. Comparing



(a)



(b)



Current (µA)



X0



(c)



Time (µs)

Fig. 25 (a) Sketch of bubble evolution near a surface. (b) Single bubble cavitation chronoamperometric current recorded for [Ru(NH3)6]Cl3 (10 mM) in aqueous KNO3 (0.1 M) under

sonication at 20 kHz. Conditions: Horn-to-electrode distance 7 mm, insonation power

8.9 WcmÀ2, electrode diameter 32 mm. (c) Zoom on a single spike (circles) and simulation (line).

For simplicity reduction currents are here positive.



Electrochemistry, 2013, 11, 1–33 | 25



the experimental voltammograms with the simulations gave a very good fit

for several peaks whereas other peaks could not be described by the theory

developed. The peaks where the model is unsuccessful possibly result from

a different bubble/electrode distance x0 before and after the collapse,

although x0 would remain of the same order of magnitude in size. It is not

unexpected to observe such variations under the conditions used, since the

precise behaviour of the bubble results from a complex acoustic field

influenced by the presence of neighbouring bubbles as well as by the local

surface roughness. A large range of values for t0 are obtained, which reveals

that even in this apparent periodic signal a partially chaotic bubble behaviour exists. The experimental t0 values suggest that most of the time the

bubble covers the electrode, which is a similar conclusion to that of

Leighton based on simulations.173–175 Furthermore x0 values are shown to

range between 45 and 75 nm, which implies only small variations of x0 over

the whole chronoamperogram. These variations are consistant with the

quasi steady-state current observed between the spikes. This current is due

to a slow solution penetration in the bubble electrode gap that grows at

velocities of ca. 1 Â 10À4 m sÀ1. The presence of a thin layer of a solution

between the bubble wall and the surface is thus established and quantified.

The deduced values of t0 gave an average value of 0.2 ms. This gives an

average minimum wall velocity ranging from 160 to 320 m s À 1 depending

on the bubbles’ position. These extreme velocities are consistent with

Leighton’s simulations of acoustic bubbles oscillating in solution.173–175

Recently, Birkin et al. recorded simultaneously the cavitation activity with

electrochemical measurements and fast photographic recording.176 Though

the nanometric evolution of the interface can not be optically visualized,

recording of the bubble size, shape and position as a function of time may

be a first step to introduce more parameters in the simulation and unravel

the complex behaviour of these fast evolving triple boundaries interfaces.

5



Conclusions



This review highlights several fields of electrochemistry experiments onto

single systems which can provide unique information. The redox cycling,

pushed to its limits, already allows detecting currents due to single molecules. Here, the correlation analysis represents a new method to access to

the subtle behavior of the molecules in the solution and their interaction

with the electrodes. By combination with other (bio)electrochemical strategies, probably very competitive new generation sensors will arise. On the

other hand, the electrochemical detection of nanoparticles is a cheap and

rapid method to identify a solution mixture. In molecular electronics,

electrochemistry is a unique tool to make break junctions with unstable

metals. When single redox active molecules are in addition investigated, the

molecular energy levels control may give access to a very wide range of

responses. In this respect, coupling with spectroscopic tools is also a

promissing approach.177 Finally, we described how nanosecond electrochemistry allows to visualise an interface movement due to the flux created.

This strategy is also avaible for other fields more under focus such as

nanoparticles impacts on very small electrodes. There is no doubt that new

26 | Electrochemistry, 2013, 11, 1–33



features and inventions will appear in the near future, take advantage and

participate to the development of nanosciences and even more sensitive

instrumentation.

Acknowledgements

This work was supported by CNRS (programme e´change de chercheurs

CNRS/NSFC), Universite´ Pierre et Marie Curie and ANR (project RADE

JCJC 0810 01), NSFC (No. 21003110, 21211130097) and the Planned

Science and Technology Project of Zhejiang Province (No. 2011C37052).

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