Sonoelectrochemistry: transient cavitation in acetonitrile in the neighbourhood of a polarized electrode

EISEVIER

Journal of Elecaoanalytical

Chemistry

399 (1995) 147-155

Sonoelectrochemistry: transient cavitation in acetonitrile in the neighbourhood of a polarized electrode Jiri Klima ‘, Claude Bernard, Chantal Degrand

*

Luboratoire d’Elecrrochimie Organique, CNRS URA 434, lJnicersit6 Blaise Pascal, 63177 AubiPre, France Received 22 March 1995; in revised form 15 May 1995

Abstract The voltammograms recorded with ultrasound at a stationary electrode present a sigmoidal shape and their limiting current is the sum of steady-state and transient components. A semi-quantitative description of the integrated transient component is proposed in the case of the one-electron reduction of methyl viologen in acetonitrile at a platinum disc electrode of small radius (250 pm> under the action of ultrasound (acoustic intensity = 1.4 W cm -*, i.e. acoustic pressure = 1.7 atm). With the help of the basic theoretical and experimental data provided by Neppiras, Plesset and Chapman, it can be estimated that transient cavitation involves gas- or vapour-filled bubbles of similar radius R, (160-200 pm) collapsing at the surface of the electrode. Jets of liquid of almost cylindrical shape develop, which repeatedly strike the electrode surface with a constant velocity (228 m s-‘) and submicrosecond duration. Hence 4.2 X 10m9 C are expected to be consumed in the first reduction step of methyl viologen (0.23 mM) when the largest collapsing bubbles (R, = 200 pm) are involved. The experimental result (4.2 X 10e9 C) is consistent with the above description. The voltammetric results show that the increase of the electrolytical current due to sonication is mainly given by the transient component. The consequences of the formation of violent jets striking the electrode surface are discussed. Keywords: Sonoelectrochemistry;

Cavitation;

Acetonitile

1. Introduction Sonochemistry which deals with the influence of ultrasound on chemical processes is a rapidly expanding field of research. Sonication, i.e. irradiation of the reaction mixture, with “power” ultrasound produces the cavitation phenomenon, i.e. the expansion and violent collapse of microbubbles within the solution. The violent compression during cavitation can result in an increase of temperature and pressure up to several thousand Kelvin and several hundred atmospheres and a large acceleration of mass transport [I]. A variety of reactions can be promoted by sonication in both homogeneous and heterogeneous mixtures [2-61. Sonoelectrochemistry can be defined, by analogy to sonochemistry, as the field of research dealing with the influence of power ultrasound on electrochemical pro-

* Corresponding author. ’Present address: J. Heyrovsky Institute, Academy of Sciences Czech Republic, Dolejskova 3, 182 23 Prague 8, Czech Republic.

of the

0022.0728/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDI 0022.0728(95)04197-4

cesses. According to this definition, sonoelectrochemistry is quite an old science since the first application of ultrasound to electrochemistry is sixty years old now [7], pioneering work in this field being performed during the 1930s [7-91. From this time ultrasound has been used as an auxiliary tool in different fields of electrochemistry (for a review see Ref. [lo]>. The first work was connected with lowering potentials at which gases are produced electrolytically. It was found that the depolarization effect of ultrasound can decrease the hydrogen and chlorine deposition potentials down to an equilibrium potential [8,9]. These studies have been reconsidered recently Ill]. Sonication was applied in electroplating [ 121 and improvements in the quality of electroplating in terms of better adhesion [131, higher hardness [13-171, brighter finish 115,181 and the possibility of utilization of higher current density [ 181, were described. Ultrasound was used to assist electropolymerization [ 19-211 and a considerable improvement of the mechanical properties of conducting thiophene polymer films was observed [21]. Ultrasonic agitation was applied for high-speed controlled potential coulometry [22], enhancement of the sensitivity of flow-cell electrochemical

148

J. Klima et al./Journnl

of Electroanalytical Chemistry 399 (1995) 147-155

sensors [23] and variation of the convection rate of the solution at a glassy carbon electrode in hydrodynamic modulation voltammetry [24]. The electrochemical preconcentration of platinum was accelerated in anodic stripping voltammetry [25]. Sonication can increase the electrolytical current by activation of the electrode surface too. It was observed that it reduces the passivation of the electrode in aqueous solutions of methyl viologen and pyrrole [26] and in an acetonitrile solution of CI(CO), [27] and that glassy carbon electrodes were activated by ultrasonic pretreatment [28,29]. Focussed ultrasound of intensity up to 7.8 kW cm-* was used to investigate the processes influencing the electrochemical passivation and depassivation of iron [30]. Both ultrasonic agitation and electrode surface activation were utilized in electrosynthesis. Ultrasound was used to promote the electrochemical reduction of insoluble Se and Te powder to Se:-, Se*-, Tei- and Te*- anions in the synthesis of aliphatic [31] and organometallic chalcogenides 1321. The synthesis of aromatic seleno and telluro derivatives by an electrochemically induced S,, 1 reaction [33-371 and the electrochemical synthesis of polymethylsilane without solvent [38] were performed with sonication. The presence of ultrasound changed the product distribution in the anodic oxidation of carboxylic acids [10,39-421 and the cathodic reduction of aldehydes [43]. The electrochemiluminescence from &is-(2,2-bipyridine) ruthenium (II) and arylacetate was notably enhanced by simultaneous irradiation with power ultrasound [44--461. Edge effects were diminished, reproducibility and stability were increased, and a lower cell voltage was required. Recently sonication was shown to modify significantly the voltammograms recorded at a stationary electrode [26,47-501. They present a sigmoidal shape with an oscillatory behaviour and the average limiting current is high and does not depend on the scan rate up to 25 V s- ’ [49]. The limiting current I, of Fe(CN)z-/Fe(CN)zin water was studied by several groups [26,47-491 as a function of different parameters including the ultrasonic frequency and power and the separation distance between the working electrode and the ultrasonic horn. It was found that I, would correspond to 330-2830 rotations per second (rps) at a rotating disc electrode under laminar flow conditions [26,47-491. The effects of ultrasound are supposed to be brought about by acoustic cavitation and turbulence in the vicinity of the electrode surface, which involves pulsing and collapsing bubbles [ 10,26,47-501 which are associated with steady-state and transient components respectively, for the limiting current [49]. We have recently shown [51] with the help of a platinum electrode of small area and a solution of methyl viologen in acetonitrile, that the increase of the voltammetric current at a stationary electrode is caused predominantly by a number of individual current pulses. We ascribed the origin of these pulses to jets arising from the collapse of cavitation bubbles in the near vicinity or at the surface of the electrode. The aim of this work is a more

quantitative description of the individual pulses. In the first part of this paper we summarize the basic theoretical and experimental data on the collapse of a bubble in solution and in the neighbourhood of a solid boundary in the absence of sonication, and on ultrasonic cavitation in solution [52-541. We extend these data to the case of a bubble collapsing at the solid wall under the influence of ultrasound, and we apply these extended data to the determination of the size and shape of individual jets at the surface of an electrode immersed in acetonitrile. In the second part, we demonstrate semi-quantitatively with the help of a Pt-disc microcathode, that the individual current pulses result from the one-electron reduction of methyl viologen contained in the jets of solution striking the Pt disc when the electrode is immersed in a solution of this salt and polarized at a potential coresponding to its first reduction step.

2. Experimental Acetonitrile (Janssen Chimica, analytical grade), tetrabutylammonium-hexafluorophosphate (Fluka, electrochemical grade) and methyl viologen dichloride hydrate (Aldrich) were used without further purification. All measurements were performed using an electrochemical cell of cylindrical shape of internal diameter 13.5 mm with a flat bottom, as shown in Fig. 1. The cell was

us

Fig. 1. Sa~cture

of the electrochemical

cell with ultrasound.

.I. Klimn et d/Journal

of Electroanalytical

immersed in a larger glass tube of internal diameter 22 mm. A titanium ultrasonic horn (tip area 1 cm2> was situated at the bottom of this tube. Thermostated water (20 “C) flowing through this tube served as both cooling agent and coupling medium for the transfer of ultrasound from the horn to the cell. The working electrode (WE) was a platinum disc of diameter 0.50 mm (area 0.20 mm21 sealed in a glass tube wir,h a Torr Seal (Varian). A vertical position of the Pt disc was found to be the most suitable since it allows a free vertical movement of the bubbles formed near the surface, which otherwise would disturb the electrochemical measurements. The distance between the working electrode and the ultrasonic horn tip was ca 20 mm. A silver wire quasireference electrode (RE) was placed near the surface of the solution and a platinum wire counter electrode (CE) was wound around the glass tube of the working electrode. Although cavitation at the auxiliary electrode had no influence on the electrochemical measurements, its position near the surface of the solution was preferred. The electrochemical cell was capped by a Teflon stopper with holes for all of the necessary inputs, and filled with 10 ml of acetonitrile + water (9: 1) solution containing 0.1 M Bu,NPF, as the supporting electrolyte. The solution was bubbled with pure argon presaturated with acetonitrile in order to remove oxygen, saturate the solution with an inert gas and therefore increase the number of microbubbles and cavitation nuclei. Electrochemical experiments were performed using a digital electrochemical apparatus Sirius (ESII, Montpellier), the initial data acquisition of which is analogical, and so there is no loss of charge for an integrated signal of very snort duration (down to 1 ns). This apparatus was linked to a 386 personal computer.

2 .I. Ultrasonic calibration of the electrochemical

cell

A high intensity ultrasonic cell disrupter instrument (Sonic and Materials, Inc., Connecticut) operating at an ultrasonic frequency f of 20 kHz was used as the source of ultrasound. The calorimetric calibration inside the electrochemical cell and in the absence of electrodes was carried out with a thermocouple (Physitemp BAT-12). Its sensitivity was 2.5 X 10-l ’C (temperatures within the range 20-30 “C) and its response time was 10e2 s. The cell was filled with 5.0 g of acetonitrile thermostated at 20 “C (6.4 ml, i.e. a cylindrical liquid column of cross-section A= 1.43 cm* and height 4.5 cm). The temperature increase per second de/d t was measured after switching on the ultrasonic instrument at different output settings. No significant changes in d0/dt were observed when the distance between the tip of the thermocouple and the ultrasonic horn was moved from 20 to 35 mm and the measured de/d t values hold reasonably for the whole bulk [55]. The ultrasonic power P supplied in the electrochemical cell is

149

Chemistry 399 (199.5) 147-155

Table 1 Calorimetric

/s

I,,/w-? p/wlo-J g1/“es-l

calibration

Output setting [

20 25 30 35 40

of the ultrasonic

0.1 rto.03 0.l5f0.03 O.lSrtO.03 0.21 f 0.03 0.24kO.03

I.1 +0.4 1.6kO.4 2.0 + 0.4 2.4kO.4 2.7 i 0.4

0.77 f 0.28 l.lZkO.28 1.40 f 0.28 1.68f 0.28 1.89f0.28

P, power; I,,, intensity.

related to the temperature switching on sonication by:

increase

immediately

after

ld01

(1) where C is the heat capacity of acetonitrile (C, = 2.22 J g-’ K-+56]) an d m is the mass of acetonitrile (5 g). The temperature was measured every ca. 1.6 s and [do/d t], _ o was the slope of the linear part corresponding to the first four items of data. It was verified that the temperature decrease was definitely slower after turning off the ultrasonic probe than the temperature rise immediately after switching on. Therefore the calorimetric loss was not significant in the determination of [d8/dt], _ 0 and the main source of error in the determination of P was the ultrasound reproducibility. The ultrasonic intensity I, is the ratio P/A since the power is spread almost homogeneously to the whole cross-section A of the cell. Table 1 indicates the [d B/d t], _ O, P and I, values obtained for different output settings when the distance between the tip of the horn and the thermocouple was 20 mm. The output setting corresponding to about 30% of the maximum value delivered by the instrument was found to be well adapted for sonication and corresponded to an ultrasonic intensity I,, of about 1.4 X lo4 W m- 2. At the output settings above 40%, an intense cavitation phenomenon was observed at the tip of the horn and consequently only a small part of the ultrasonic energy was transferred to the electrochemical cell. The acoustic pressure amplitude PA is given by: P* = (2pcl,,)“1 where p is the liquid density ( p = 0.78 X 10” kg mm ’ for acetonitrile) and c the velocity of the sound in the liquid (1.3 X lo3 m SC’ for acetonitrile [57]). Therefore PA is ca. 1.7 X 10’ Pa (1.7 atml for the output setting 30%.

3. Basic theoretical cavitation 3.1.

Collapse

and experimental

of a bubble

in solution

data on transient

under

u constant

external pressure

The collapse of an empty spherical cavity of initial radius R, in a liquid of density p under a constant

150

J. Klima et al./Journal

of Electroanalytical

Chemistry 399 (1995) 147-155

external pressure P, was studied by Rayleigh in 1917 [53]. Neglecting the surface tension and viscosity he derived the following equation for the instant bubble radius R:

(3) Solving

this equation

3.2. Formation solution

he obtained

and collapse

the total collapse

of a bubble

time T

in a sonicated

In the case of ultrasonic cavitation, there is first expansion up to a radius R, of some starting nucleus which is usually a microbubble of initial radius R, filled with gas and vapour, and then the collapse of this expanded bubble occurs. Rayleigh’s equations (Eqs. (3) and (4)) were modified to this more general case by Noltingk and Neppiras [58,59]. Neglecting the compressibility and viscosity of the liquid, Rq. (3) can be written in the form: 2

R!$+;;

2 1 =-

1

(5)

P

where AP is the overpressure, i.e. the difference between the external pressure of the liquid P, and the internal pressure of gas and/or vapour in the bubble Pg. AP = P, - Pg

(6)

Pressure P, is the sum of the external ambient pressure P,, the pressure P, = 2 u/R due to the surface tension u, and the ultrasonic pressure P, = P,sin2_rrfr where PA is the acoustic pressure amplitude. + PAsin 2 nfr

(7)

The initial internal gas pressure PgO inside the initial microbubble of radius R, without sonication is in equilibrium with the external pressure P, of the liquid, i.e. Pg,, = P,, = P, + 2u/R,

(8)

The instantaneous internal pressure Pg in the bubble under sonication should be obtained with the help of an equation of state. Eq. (5) has been solved numerically under different experimental conditions and with different approximations by many authors (for a review see, for example, Ref. [52]). If the acoustic pressure amplitude PA is larger than the internal pressure within the bubble, i.e. P,, > P, + 2u/R,

0.25

0.50

0.75

IXf

2. Schematic representation of expansion and collapse of gas- or vapour-filled bubbles under transient conditions.

Fig.

AP

P, = P, + P, + P,, = P, + 2u/R

0

(9

a negative pressure is formed in the rarefaction phase (the minimal P, value is P, + (2u/R) - P,>, and so the bubble starts a fast expansion as shown in Fig. 2. The underpressure is changed to overpressure in the subsequent compression phase and the expansion of the bubble ceases

at time t, when the maximum radius R, is reached. Then the expansion is changed to a compression which can result in a violent bubble collapse. The dependence of R, on the initial bubble radius R, was illustrated by Neppiras [52] for gas bubbles in water under the atmospheric pressure (P, = lo5 Pa> sonicated with an ultrasonic frequency f = 15 kHz and an acoustic pressure amplitude PA = 4 X IO5 Pa. For R, smaller than ca. 0.2 pm, no negative pressure is formed because the pressure due to the surface tension P, = 2 u/R, is larger than PA - P,, and consequently the bubble oscillates with a small amplitude around its average radius R, and no cavitation occurs. For R, 2 0.2 pm, condition (9) is fulfilled and the bubble radius can expand up to R, which is approximately proportional to the acoustic pressure amplitude PA, inversely proportional to the ultrasonic frequency f and the density p of the liquid. RM N P,/fP

(10)

R, depends to some extent on R,. First it increases rapidly with increasing R, values to reach ca. 400 pm for R, = 0.7 pm. Then, it increases only slightly according to the approximate equation: RM -R,+430pm

when R, > 10 p,m

(11)

Clearly R, does not exceed ca. 500 pm in water when f = 15 kHz and PA = 4 atm as R, does not exceed ca. 70 pm. The maximal radius R, is reached at a time tM which is almost independent of R, (tM = 46 f 0.5 ps in the R, range l-70 pm when PA = 4 X lo5 Pa and f = 15

J. Klima et al./Journal

kHz) and inversely Ref. [52] indicates i.e.:

151

of Electroanalytical Chemistry 399 11995) 147-155

proportional to f. Moreover Fig. 23 of that I, varies only slightly with PA,

(‘2) holds approximately. Collapse occurs while the acoustic pressure P, is near its peak and the total collapse time r is given by Eq. (13) considering a constant overpressure Al’: I/‘2

(13) The bubble collapses very rapidly to a very small microbubble in so far as the sphericity of the bubble is not disturbed by some external influence. The bubble-wall velocity can overcome the velocity of sound at the final phase of collapse, due to a large acceleration, and the resulting change of the bubble volume is very fast. For instance r= 4 X 10m5 s when R, = 400 pm and AP = 105 Pa (1 atm), and the bubble radius decreases from 0.5R, to the final microradius in the last 10% period of the collapse history i.e. within 4 ps. Consequently the gas compression is almost adiabatic and temperatures of several thousand Kelvin as well as pressures of several hundred atmospheres can be reached. This process, called transient cavitation, is believed to be responsible for the chemical effects in homogeneous sonochemistry. Even a small disturbance of the spherical symmetry during the bubble expansion and/or during the initial phase of the collapse (such as the proximity of another bubble or a solid particle or another inhomogenity in the vicinity of the bubble), results in a large disturbance of the bubble shape in the last phase of the collapse. It can thus result in disintegration of the original bubble to several very small microbubbles, the internal pressure of which eventually being too large to be overcome by the acoustic pressure Pat since 2o/R can increase dramatically. However the alternating acoustic pressure P, causes these microbubbles to oscillate around their average radii. If the concentration of dissolved gas in the liquid is high enough (e.g. in the case of nearly gas-saturated solution) the diffusion of gas into the bubble in the negative half-cycle

of pressure (Fig. 2, low internal pressure, larger surface, thinner diffusion layer) occurs more readily than the diffusion outward from the bubble to the solution in the compression phase (larger gas pressure, but smaller bubble surface and thicker diffusion layer). This results in an increase of the amount of gas and/or vapour in the bubbles and consequently of their average radii, a process called rectified diffusion. The corresponding increase of the bubble radii results in a decrease of the surface tension pressure P, which enables the bubble expansion and collapse, i.e. cavitation after some time of stable oscillations. 3.3.

Collapse

spherical

under

a constant

external

pressure

of a

bubble initially in contact with a solid boundary

When a bubble collapses in the vicinity of a solid boundary, which is the case in sonoelectrochemistry where the solid boundary is the electrode surface, the spherical symmetry of the system is lost. Hindrance to the motion of the liquid from the side adjacent to the boundary results in the deformation of the bubble, and then the formation of a jet of liquid directed toward the solid boundary (Fig. 3). The existence of such jets was demonstrated experimentally by Benjamin and Ellis [60] by a series of photographs. The gas or vapour compression in the bubble collapsing at the solid boundary is much smaller and slower compared with the case of unperturbated collapse, as the bubble disintegrates long before a large compression. That is why the adiabatic heating-up of the gas is negligible and cannot result in apparent chemical effects. Consequently the influence of ultrasound on heterogeneous processes is mainly brought about by the effects of the jets of liquid on the solid boundary properties and their contribution to the mass transport. Plesset and Chapman studied numerically the problem of the collapse in water of a spherical vapour-filled cavity initially in contact with a solid wall when the external overpressure AP is constant 1541. Computation gives the velocities of the jet of liquid at various stages of the collapse and the bubble shapes as sketched in Fig. 3. Neglecting the pressure P, due to the surface tension, the

Fig. 3. Evolution of the shape of a bubble collapsing near a plane solid wall. The time intervals from initiation collapse time) are: (A) 0, (B) 79, (C) 92 and (D) 100. From Ref. [53].

of collapse (expressed

in % of the total

J. Klima et al./Journal

152

authors calculated that, once the jet in formed, u of its tip remains fairly constant (i.e. there is tion) until it reaches the solid boundary. The does not depend on the bubble radius R, and

of Electroanalytical Chemistry 399 (1995) 147-155

cylindrical shape contained inside the gasvapour-filled muff (Fig. 3(D) and Fig. 4(A)).

the velocity no accelerajet velocity is given by:

(14)

P LH -PC"

holds approximately, where c is the velocity of sound in the liquid. This pressure and its duration are estimated to be ca. 2000 atm and 0.1 ps under the above experimental conditions. The pressure rapidly decreases to a lower value (ca. 80 atm) called the stagnation pressure P,:

L, N R,/2

(19) TRj11 N

(20)

-

200

(21)

“28

Morever, it is reasonable to assume that the flow of liquid does not stop suddenly at time rj but is maintained as long as the gas- and/or vapour-filled muff of inner radius rj is not destroyed (Fig. 4(B)). Extrapolation of the Plesset and Chapman simulations indicates that its outer wall merges into its inner wall (Fig. 4(C)) at time rjf close to l.5rj, assuming that speed u is constant up to rjr. The total length Ljf and volume Vjf of the jet of liquid involved in the collapse are:

(16)

which has a duration approximately equal of the jet (i.e. the length of the jet divided and can be a source of damage to the solid The time r from the beginning of the moment when the jet reaches the wall (Fig.

(18)

Plesset and Chapman’s simulations [54] stopped at the moment when the jet touched the wall since afterwards the approximation of uncompressibility of the liquid is no longer valid. Nevertheless we can use the data obtained by extrapolation of their results for semiquantitative conclusions. In the first approximation we can suppose that the duration of the jet of liquid of volume V, is 7j = Lj/u, i.e. we assume that its speed remains constant as long as it strikes the surface. Taking into account Eq. (14), duration rj is given by:

(15)

PS - ;pu*

ri N R,/lO

vj- 7rrfLj

The tip velocity is much smaller than the bubble-wall velocity at the end of collapse for a bubble in solution, for which a large acceleration is involved. Indeed Eq. (14) indicates that u = 128 m s -’ in water when AP = lo5 Pa (1 atm). However, a jet of liquid of such speed produces a very high initial pressure when it strikes the solid boundary. This pressure of very short duration is called liquid hammer pressure P,, and

and/ or

to the duration by its velocity) wall. collapse to the 3) is given by:

Ljr - cmjr - 1 .5Lj

(22)

l/2

(17)

J L. Jf VJf - rrr.‘

It is only slightly longer than the time derived from Eq. (13) for a spherical bubble collapsing in solution, because most of the time is consumed early in the collapse while the bubble is nearly spherical Computation gives also the radius rj and the length Lj and therefore the volume Vj of the jet of liquid of about

Fig. 4. Expected simulations).

collapse

history

of the jet beyond

the moment

pressure

of a

When the bubble is not initially in contact with the wall a similar jet is formed, but its length and duration are

t=ca1,5r,

T,

B

A

(23)

l.5Vj

3.4. Collapse under a constant external spherical bubble near a solid boundary

t=ca

t=0

-

when the jet touches

C the wall (from

the extrapolation

of Plesset and Chapman’s

J. Klima et al./Journal

shorter [54]. Moreover the movement of the jet is impeded by the bulk solution before it reaches the solid surface. Consequently, the effect of thk jet on the solid boundary and the mass transport are lower than in the case of a bubble collapsing in contact with the wall.

Table 2 Characteristics of the jets initiated by bubbles collapsing at the electrode surface in acetonitirle when the amplitude of the acoustic pressure PA is 1.7atm and the acoustic frequency 20 kHz

Velocity c/m s- ’ Liquid hammer pressure P,, Stagnation pressure P, /atm Radius r, /pm

4. Results and discussion 4.1. Collapse of bubbles in contact with an electrode immersed in a sonicated acetonitrile solution Under our experimental conditions, transient cavitation occurs in acetonitrile + water (9: 1) solution ( p = 0.80 X lo3 kg m- ‘) with an ultrasound of frequency f = 20 kHz and acoustic pressure amplitude PA = 1.7 X lo5 Pa (1.7 atm). Therefore the maximum possible radius is ca. 200 pm and R, is estimated to lie within the range 160-200 pm for the most part of the bubbles. These values were obtained from Eq. (10) and with the data provided by Neppiras [52] on the sizes of gas bubbles collapsing in water (R, = 400-500 pm when f= 15 kHz, p= lo3 kg mm3, PA = 4X lo5 Pa). Plesset and Chapman’s simulations [54] correspond to a bubble in contact with a solid wall collapsing under a constant external overpressure A P. An alternating pressure P,_ = P, + P,sin27rft is involved in our case (N.B. pressure P, due to the surface tension is neglected) and therefore an approximate average value should be used during the collapse time, i.e. a value between t, and t, + 7.

(24) The begining of the collapse (t,> can be determined from Eq. (12) and the data provided by Neppiras in water (tM = 46 ps when PA = 4X lo5 Pa and f= 15 kHz), and conditions (PA thus t, = 29.6~s under our experimental = 1.7 X lo5 Pa and f = 20 kHz), which means that the maximum radius R, of the bubble is reached 7.9 ps before the acoustic pressure is at its peak (see Fig. 2. It occurs when tf= 0.75, i.e. t = 37.5 ps). A first estimation of‘the collapse time r is obtained with the help of Eq. (17) assuming that the acoustic pressure P, would be near its peak within the collapse period, i.e. AP = P, + PA = 2.7 X lo5 Pa

153

of Electroanalytical Chemistry 399 (1995) 147-155

(25)

Hence T would be ca. 9.7-12.2 ps for the bubbles with R, in the range 160-200 pm. Consequently, the jets strike the electrode surface 1.8-4.3 ps after the maximum acoustic pressure is reached. The corresponding average pressure P,_ has been calculated to be ca. 2.53 X lo5 Pa when R, = 160-200 pm. We obtained a more accurate value for T by introducing this new FL value in Eq. (17), i.e. the collapse times are

/atm

Length L,, /km Volume V,, /f m’ Duration T,, /+ms

R, = 160 p,rn

R,=2OOwm

228 2370 208 16 120 96 0.54

228 2370 208 20 150 187 0.68

10.1-12.6 ps when R, = 160-200 pm. The characteristics of the jets in acetonitrile under our experimental conditions are summarized in Table 2 for the two cases where the jets are initiated by the collapse at the electrode surface of small (R, = 160 pm) and large (R, = 200 pm) bubbles. 4.2. Voltammetric

behauiour

of methyl viologen

Methyl viologen (MV*+) is reduced in two reversible one-electron steps with the standard redox potentials EA = - 0.48 V and EA’= - 0.89 V vs. SCE in acetonitrile. MV*+ ‘+eMV+

‘+eMV

When methyl viologen is reduced with sonication, jets of acetonitrile containing MV*’ can strike the surface of the polarized electrode, which are accompanied by short pulses of faradaic current [51]. The approximate quantity of electricity consumed Q, during such microelectrolysis is given by Eq. (26) when the applied potential corresponds to the plateau of the first wave, and the corresponding current 1, is given by Eq. (27) assuming that the speed of the jet remains constant as long as the jet strikes the electrode surface, and that the flow of liquid directed towards the electrode surface is stopped when the gas- or vapour-filled muff surrounding the jet is destroyed (Fig. 4(C)):

Q,= FV,,C"

(26)

1,= Q/q

(27)

Current pulses 1, corresponding to individual jets can be observed when an electrode of small radius r is involved (r - R,). Therefore the voltammetric study of methyl viologen was performed at a stationary Pt electrode of area 0.2 mm*, i.e. of radius 250 pm. Voltammogram A of Fig. 5 corresponds to the first reduction step of methyl viologen at a concentration of 0.23 mM, with ultrasound. This voltammetric curve is characterized by fluctuations of large amplitude. The current repeatedly increases in individual pulses. The amplitude of these pulses are different but some maximum value

J. Klima et al./ Journal of Electroanalytical

1.54

I, is reached repeatedly, which is not overcome and forms an envelope (curve e) with a plateau. The shape of this envelope does not depend on the potential scan rate and is similar to a voltammetric curve obtained at a rotating disc electrode. The limiting current would correspond to a rotation rate of ca. 1900 rps. One of the individual pulses is shown in Fig. (5)C and was obtained at a scan rate 100 times faster. The current first increases rapidly (in a few microseconds) up to a maximum value I, = 2.2 PA, then it decreases more slowly down. Integration of the hashed part of Fig. 4(C) indicates the consumption of 4.2 X 10e9 C during the pulse. This result is consistent with the collapse of a large bubble (R, = 200 pm> at the electrode surface, with formation of a jet of methyl viologen solution. Indeed the corresponding microelectrolysis is expected to consume 4.2 X 10e9C according to Eq. (26) and the data indicated in Table 2 for a large collapsing bubble (R, = 200 pm). The peak current value Zj expected from Eq. (27) is 13.8 mA. This value is much higher than the experimental pulse current value (Ihl = 2.4 PA). Obviously the electrochemical instrumentation is not able to respond to a very short current pulse (submicrosecond pulse) and indicates average values although the change is recorded accurately. Moreover it is possible that the velocity of the jet decreases as it strikes the solid wall, which would explain the tail-shaped pulse of Fig. 5(C).

0.8

I

I

0.2

0.4

,+ e

I

0.6

1

0.8

I

1.0

-E/V vs. SCE Fig. 5. Voltammograms of methyl viologen (0.23 mM) at a stationary Pt-disc microelectrode (radius 250 pm) in acetonitrile: (A) and (C) with ultrasound, and (B) without ultrasound. Scan rate: (A) and (B) 0.1 V s-’ ; (0 10 v s-‘.

Chemistry 399 (1995) 147-155

5. Conclusion The use of a microelectrode with a radius in the same range as the initial radius R, of the collapsing bubbles allows one to discriminate the transient component from the steady-state component of the limiting current in Fig. 5. In other words, the latter component can be reasonably ascribed to the current values corresponding to the lower envelope f in Fig. 4 and the former component to the current pulses comprised between envelopes e and f of Fig. 4. These current pulses involve collapsing bubbles at the electrode surface or in its vicinity. The limiting currents of the plateaus of curves e and f would correspond to 1900 rps and 45 rps, respectively, under laminar flow conditions. The limiting current of the first reduction wave of methyl viologen was equivalent to 340 rps under the same experimental conditions but with an electrode of larger area (16 mm2 instead of 0.2 mm2 [51]), with which the transient and steady-states current components could not be differentiated. The above results indicate that the increase of electrolytic current due to sonication is mainly originated from a series of local individual pulses resulting from jets of solution rather than from a decrease of the diffusion layer thickness due to stirring of the bulk solution. The electrochemical measurements confirm the theoretical calculations performed by Plesset and Chapman [54]. Their results can be applied not only to the case of bubbles collapsing under a constant pressure but also to the case of bubbles cavitating in an ultrasonic field. Extrapolation of their results beyond the time t, + T when the jet touches the surface allows one to calculate the volume and duration of the jet. The mechanism described here can explain the effects of ultrasound on different electrochemical processes described in the literature. In the case of electrochemical gas evolution [8,9,1 I], the microbubbles electrogenerated on the surface of the electrode can constitute cavitation nuclei, i.e. starting points for the expansion and collapse of bubbles, with formation of violent jets which can remove adsorbed gas and activate the surface. Similarly in electroplating [12- 181, removal of all the microbubbles and/ or impurities improves the quality of the deposited metal. The high liquid hammer pressure (Eq. (15)) and stagnation pressure (Eq. (16)) are responsible for the surface activation in the case of electrolyses performed in heterogeneous medium, i.e. the electrochemical reduction of selenium and tellurium as previously described by our group [31-371. Surface activation can modify the product distribution in electrolyses involving adsorption phenomena. This would explain the change of mechanism in the Kolbe reaction described by Mason et al. [10,39], since the same shift of mechanism from a single-electron-transfer to a two-electron transfer process was observed under sonication as well as when pyridine was added (strongly adsorbed pyridine prevents the adsorption of other molecules).

3. Klima ef al. / Journal of Electroanalytical Chemistry 399 (1995) 147- I55

Acknowledgements ‘This work was financially supported by the Centre National de la Recherche Scientifique (CNRS), RCgion Auvergne, ANVAR-Auvergne and SociCtC Biosonic (Villeneuve d’Ascq). One of the authors (JK) gratefully acknowledges financial support from the CNRS for his stay at the University Blaise Pascal.

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