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A fast moving nanometric interface: the example of acoustic cavitation
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
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
Potential (V) vs. Pt electrode
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
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
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
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
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.
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
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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