Evidence for the emission of ‘alkali-metal–noble-gas’ van der Waals molecules from cavitation bubbles

Ultrasonics Sonochemistry 8 (2001) 151±158 www.elsevier.nl/locate/ultsonch

Evidence for the emission of Ôalkali-metal±noble-gasÕ van der Waals molecules from cavitation bubbles Francßoise Lepoint-Mullie a, Nicole Voglet a, Thierry Lepoint a,*, Rudi Avni b a

Institut Meurice, CERIA, Chemistry Department, 1 Avenue Emile Gryzon, 1070 Brussels, Belgium b NRC Negev and BG University, P.O. Box 9001, Beer-Sheva 84190, Israel Received 29 November 1999; accepted 14 February 2000

Abstract Visible emission spectra in the vicinity of resonance lines of alkali metals were recorded from acoustically cavitating aqueous and 1-octanol solutions (acoustic frequency: 20 kHz; solutes: Ar (or Kr), NaCl, RbCl or rubidium 1-octanolate). The maximum intrabubble density deduced from line shift data was 5  0:7  1026 m 3 , i.e. 18  2 amagats. It is demonstrated that (i) the emission from alkali metals arose from the gas phase of bubbles, (ii) the blue satellite and line distortions were induced, respectively, by B2 R‡ ±X2 R‡ and A2 P)X2 R‡ transitions of Ôalkali-metal/rare-gasÕ van der Waals molecules and (iii) excitation/de-excitation mechanisms are chemiluminescent in essence. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 33.20K; 33.70; 47.55B; 78.60M Keywords: van der Waals molecules; Sonoluminescence; Acoustic cavitation; NaAr; RbAr; RbKr

1. Introduction Acoustic cavitation consists of the creation, the growth, the non-linear oscillation and the violent collapse of bubbles in a liquid traversed by an intense acoustic wave. Collapsing bubbles emit a faint UV± visible light [1±3]. This phenomenon, which is well known in the case of organic [4±6] and aqueous [7] solutions, involves both bubble clouds and single bubbles either maintained in levitation in a resonant acoustic setup [8,9], or generated by means of sparks [10] and lasers [11]. Although the details of the atomic and molecular excitation/emission processes remain to be fully characterised, there is much evidence that this luminescence is associated with the ®nal instant of collapse [12,13]. The hot±spot model (which describes the almost adiabatic compression of the intracavity gas and vapour and assumes a uniform intracavity pressure) is supported experimentally. For example, in a recent study Giri and Arakeri [14] measured the ¯ash duration (t) associated with Ar bubbles in NaCl aqueous solutions. They found that t is in the range of tens of ns and is in agreement with the predictions of a state-of-the-art *

Corresponding author. Tel.: +32-2-526-7356; fax: +32-2-526-7301.

model developed by Kamath et al. [13]. However, in the case of aqueous solutions containing air, Matula et al. [15] measured a much shorter ¯ash duration (<1 ns) in contrast with the predictions of the hot±spot model [13]. This renews the interest in the possible formation of an inward pressure waves [16] and/or shock waves [17,18] as triggering mechanisms for the emission of light from cavitation bubbles. Beside the identi®cation of the macroscopic triggering mechanisms and the microscopic processes, the question of the participation of the liquid phase immediately adjacent to the bubble±liquid interface still remains open, as is emphasised in Ref. [9]. In the present paper, we focus on the detection and origin of the spectral features associated with the emission of rubidium and sodium during the insonation of aqueous solutions of RbCl or NaCl (2 M) on the one hand, and of 1-octanol solutions of rubidium 1-octanolate (0.5 M) (dissolved gases: Ar or Kr) on the other. We analyse whether the alkali metal species emit in the gas or the liquid phase. This concern corresponds to the necessity to clarify earlier contradictory analyses. On the one hand, Sehgal et al. [19] provide an indication in favour of the existence of Ôalkali-metal/rare-gasÕ exciplexes (typically, the existence of di€use bands at 554 and 740 nm attributed to Na±Ar and K±Ar, respectively). However, these authors do not provide a direct

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evidence of the existence of these exciplexes. On the other hand, Flint and Suslick [5], who have studied sonoluminescence in primary alcohols, note that the width and positions of potassium lines are independent of both solvent vapour pressure and inert gas (Ar/He) ratio. Arguing that the intensity of cavitational heating is dependent on both of these parameters (the hot±spot model), in order to explain this apparent paradox, these latter authors hypothesise that the emission from K arises in the liquid phase. 1 Our second objective is to identify the mechanisms of atomic and molecular excitation/de-excitation.

A UV-enhanced CCD matrix (1024  256) cooled with liquid N2 and coupled to a CCD interface (SpectrumOneâ ) was used as a detector. This instrument was purchased from Jobin±Yvon Horiba. The calibrations were carried out with an Oriel 50 W QTH-lamp (6337) in the case of the apparatus function, and with a hollow cathode Rb lamp (inner gas: Ne, P845 Photron) for the wavelength.

3. Results and discussion 3.1. The site of emission

2. Experimental section The acoustic part of the set-up consisted of a Undatim Ultrasonics sonoreactorâ driving a Ti-horn (frequency: 20.2 kHz; tip diameter: 14 mm) immersed in 10 4 m3 of solution ®ltered continuously via a peristaltic pump in order to remove Ti dust (Fig. 1). The acoustic pressure measured by calorimetry was 0.66 MPa. Demineralised water, Ar (99.99%, BOC), Kr (99.995%, Air Products), NaCl and RbCl (>99.8%, Acros), 1-octanol (rein, Merck) and Rb (99.6%, Aldrich) were used without further puri®cation. The solutions were maintained at 10  1°C by external cooling, and were submitted to continuous bubbling during the experiments. Photons were collected through a quartz window by a 1000 lm diameter multimode silica optical ®bre and passed through a focusing adapter including (in the case of experiments with Rb) a red ®lter (cut-o€ wavelength: 650 nm, Coleman) before they entered an HR 250 monochromator (focal length: 250 mm, f =4:1) equipped with a 1200 gr/mm holographic grating (linear dispersion: 3 nm/mm).

Sonoluminescence (SL) emission spectra were recorded in the vicinity of the resonance lines (2 P±2 S transitions) of the alkali metals at a resolution of 0.24 nm and a repeatability on the position of the lines equal to 1 pixel, i.e. 0.07 nm. Fig. 2 illustrates the SL spectra of aqueous solutions containing NaCl (Fig. 2a) or RbCl (Fig. 2b), both with Ar as the dissolved gas.

Fig. 1. Experimental setup.

1

It must be emphasised that, in the case of more recently studied sonoluminescent systems involving volatile metal compounds [such as Fe(CO)5 or Cr(CO)6 ], SuslickÕs group has shown clearly that the emission of metal species arises from bubble interior. See, for e.g. Ref. [6].

Fig. 2. (a) Na SL spectra associated with a 2 M NaCl aqueous solution saturated with Ar. (b) The same as in (a) but for Rb (dissolved salt: RbCl). The resolution was 0.24 nm and the repeatability of the position of the lines was 0.07 nm (1 pixel).

F. Lepoint-Mullie et al. / Ultrasonics Sonochemistry 8 (2001) 151±158

153

Table 1 Summary of shifts associated with the Rb resonance lines in the case of luminescence in water and 1-octanola Transitions in Ar gas 2

Shift

H2 O 1-octanol

a

H2 O 1-octanol

Transitions in Kr gas 2

P3=2 ± S1=2

2

P1=2 ± S1=2

2

(cm )

(nm)

(cm )

(nm)

(cm 1 )

0.41 0.58

6.7 9.5

0.56 0.67

8.9 10.6

1.59 0.98

26.1 16.1

2.22 1.40

35.1 205.1

(m 3 ) (amagats)

´ 10

15.7 20.2

26

1

P1=2 ±2 S1=2

(nm)

26

1

P3=2 ±2 S1=2

(cm )

4.2 5.4

1

2

(nm)

´ 10 Density

2

(m 3 ) (amagats)

5.0 5.6

18.7 20.9

± ±

± ±

Densities are obtained by means of the shifts (on the basis of Ref. [22]).

In all the experiments (whatever be the solvent and the dissolved gas), the lines of the alkali metals exhibited asymmetry towards the red zone of the spectra. The lines were broadened, red-shifted and accompanied by a blue satellite. Table 1 summarises the shifts for the two components of the Rb doublets in the case of aqueous and 1-octanol solutions. As indicated in a comparison of Fig. 2a and b, the position of the blue satellites in relation to the blue resonance lines depended on the alkalimetal type. The line asymmetry, line shift, line broadening and the presence of blue satellites accompanying the resonance lines are reminiscent of the disturbances produced by foreign neutral atoms on atomic emitters when the density of the foreign gas is no longer negligible [20±22]. This problem is very well documented from both the experimental and the theoretical points of view. It involves absorption and emission [22], and is analysed in terms of classical, semi-classical, and quantum-mechanical models (see Ref. [23] for a detailed discussion). Disturbances caused to atomic emitters by foreign neutral atoms explicitly imply a gas phase. Considering the introduction of the present paper, the site of emission from alkali metal in SL must therefore be ascertained. In this respect, the emission of the blue Rb resonant line satellite is an unambiguous test. Drummond and Gallagher [24] and Carrington and Gallagher [25] have studied the spectral ¯uorescence features of Rb vapour diluted in various noble gases and have demonstrated that the position of the blue satellite changes with the nature of the noble gas (Fig. 3a). In these experiments, Rb±Rg van der Waals (vdW) molecules are the main emitters. Here, Rg denotes a rare-gas atom. The term ÔvdW moleculeÕ denotes a molecule in which two species are loosely bonded together by intermolecular forces [26,27]. As shown by the Gallagher group [24,25], the ground and excited states (in particular B states) of Rb± Ar or Rb±Kr are signi®cantly di€erent so that the B±X transitions can be distinguished clearly (Fig. 4). If the emission from alkali metal associated with the bubble collapse arises in the intracavity gas phase, the

Fig. 3. (a) Portion of the gas-phase ¯uorescence (GPF) spectra associated with the B2 R‡ ±X2 R‡ transition of Rb±Kr (upper curve) and Rb±Ar (lower curve) vdW molecules. The blue line (2 P3=2 ±2 S1=2 ) transition is not represented (After Drummond and Gallagher [24]). (b) Part of the SL spectra (water/RbCl/Kr (upper spectrum), Ar (lower spectrum)) allowing a direct comparison with the GPF spectra in Fig. 3a. (c) The same as in (b) but with 1-octanol and rubidium 1-octanolate. The numbers reported in the ®gures correspond to the k k0 di€erence measured in GPF experiments, with k as the wave number associated with the maximum intensity of the blue satellite and k0 the reference attributed to the maximum intensity of the blue line.

Fig. 4. (a) The Rb±Ar potential curves vs. internuclear distances, (b) the same as in (a) but for Rb±Kr. The data are from Drummond and Gallagher [24]. We do not represent the A1=2 curve for reasons of clarity.

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substitution of Ar by Kr in cavitation experiments should induce a shift of the Rb blue satellite, as in gasphase ¯uorescence (GPF) experiments (Fig. 3a). Fig. 3b (SL in water) and c (SL in 1-octanol) show that this is so. In order to illustrate the fairly good agreement between GPF and cavitation experiments, the relative positions of the maximum intensity of the satellites in relation to the Rb blue line in GPF experiments are reported on SL spectra. It can be concluded that, for both the organic and the aqueous media, alkali-metal species are emitting in the gas phase of collapsing bubbles. This test also con®rms that the blue satellite is not due to the 23 Pg ±13 R‡ u transition of Rb2 (604 nm) [28], which was not detected in our cavitation experiments. In comparison with the GPF experiments and the potential curves (Fig. 4), it is possible to attribute the blue satellites to B2 R‡ ±X2 R‡ transitions of Ôalkali-metal/rare-gasÕ vdW molecules. On the other hand, the line asymmetry and the broadening towards long wavelengths is due to A2 P±X2 R‡ transitions of Ôalkali-metal/rare-gasÕ vdW species. Because of spin±orbit coupling, asymmetry and broadening involve both components of the alkali-metal doublets. The present direct observations are important because (1) they are the ®rst evidence (as far as the authors are aware) of intracavity gas participation in the act of light emission even though the atomic lines of the gas are not detectable and (2) the techniques for the diagnosis of light (the link between line shift and foreign gas density, or the analysis of the line pro®le) may be envisaged additionally in order to estimate some of the characteristics of the intracavity luminescent medium. Since what we collected was time-averaged spectra, only average intracavity density estimations were carried out. We added the experimental shifts associated with Rb resonance lines (experiments with Ar) to the appropriate Ôline shift vs. relative densityÕ graph given by Chen and Takeo [22, Fig. 3], and obtained an average intracavity density of …5  0:7†  1026 m 3 , i.e. 18  2 amagats for Rb (Table 1). With this density, the interparticle (ArAr) distance in the intracavity medium was 1.5 nm during SL emission (vs. 4.2 nm for Ar in NTP conditions). The intracavity SL medium can safely be assumed to be a gas. 3.2. Atomic and molecular excitation/de-excitation mechanisms Given the analogies between GPF and cavitation experiments (the same type of emitting species, rare-gas densities > 1026 m 3 ), we propose the Carrington and Gallagher mechanism for the formation/excitation/deexcitation of Ôalkali-metal/rare-gasÕ vdW species: [25]

M ‡ 2Rg ! M±Rg …A2 P1=2

or 3=2 ; v; J†

‡ Rg


M ‡ 2Rg ! M±Rg B2 R1=2 ‡ Rg M±Rg …A2 P1=2

…1† …2†

or 3=2 ; v; J†

2

! M±Rg…X R1=2 ; v00 ; J00 † ‡ hm

…3†

M±Rg …B2 R1=2 ; v; J† ! M±Rg…X2 R1=2 ; v00 ; J00 † ‡ hm

…4†

M±Rg …v; J† ‡ Rg ! M±Rg …v0 ; J0 † ‡ Rg

…5†

M±Rg …v; J† ‡ Rg ! M ‡ 2Rg

…6†

M ‡ Rg ! M ‡ Rg ‡ hm

…7†

Scheme 1. Mechanism for the excitation/de-excitation of M±Rg vdW molecules according to Ref. [25]. The signs v and J denote vibrational and rotational levels and * denotes electronically excited states. Reactions (1) and (2) are recombinations. The reactions leading to bound radiation are (3) (the A±X transitions, which give a red asymmetry in the broadened spectral features) and (4) (the B±X transition, which corresponds to the blue satellite). Reactions (5)±(7) represent relaxation, dissociation and free±free molecular radiative processes, respectively.

In the present section, we test the fundamental processes of our suggestion in relation to the Giri and ArakeriÕs SL kinetic data [14]. We used the rate coecients and collision cross-sections reported in the literature for the gas-phase reactions in order to calculate the collision frequency, and thus to estimate the relative importance of the di€erent reactions reported in Table 2. The experimental constrains with which we were confronted were the emission of 106 photons per ¯ash and a ¯ash rise time of SL of 30 ns [14]. 3.2.1. Electronic excitation of M The excitation of M in the gas phase (the ®rst part of Scheme 2) requires the mechanical addition of alkalimetal salts to collapsing bubbles since the vapour pressure of these salts is too small for their evaporation to be plausible (for example: Pvap …NaCl† ˆ 1 mmHg at T 1200 K). Sonochemical experiments reveal that beside the intracavity phase, a part of the initially liquid phase adjacent to the bubble±liquid interface is involved (the two-site sonochemistry model) [12]. This corresponds to the ablation of either a shell of liquid around a collapsing bubble or of the tip of one or several inward jet(s) (or even droplets formed via surface-wave distortions) [13,29]. The relative importance of the ways of adding non-volatile solutes can be found in Ref. [13]. Fluid-mechanics-based arguments in favour of the formation of a single inward jet are reported in Refs. [30,31] (see also Ref. [32] for an introduction).

Table 2 Possible excitation/de-excitation reactions of alkali metal atoms and the (alkali-metal/rare-gas) vdW species in SLa Cross-sections (backwards reaction) (nm2 )

Reference

Methods of measurement

Rate coecients

M…2 P † ‡ Rg ˆ M…2 S† ‡ Rg (i)

10 4 < rNa=Ar < 5  10 2  10 5 < rRb=Ar < 10 0 < rNa=e < 0:3 0 < rRb=e < 0:8 0:015 < rNa=H2 O < 0:03 rRb=H2 O  0:04 ± ± ±

[23] [23] [23] [23] [23] [23]

a, a, f f a, a,

± ± ± ± ± ± 1  10 1  10 5  10

M…2 P † ‡ e ˆ M…2 S† ‡ e (ii) M…2 P † ‡ H2 O ˆ M…2 S† ‡ H2 O (iii) H ‡ OH ‡ M ! H2 O ‡ M (iv) H ‡ H ‡ M ! H2 ‡ M (v) O ‡ O ‡ M ! O2 ‡ M (vi) De-excitation: (X ˆ Ar) Na ‡ Cl ‡ X ! NaCl ‡ X (vii) Na ‡ OH ‡ X ! NaOH ‡ X (viii) Na ‡ H2 O ! NaOH ‡ H (ix) Na ‡ OH ! NaOH ‡ X (x)

3 2

b, c, e b, c, d, e, f b, c, d, e b

± ± ± ±

3  10 5  10 8  10 ±

43 43 42

40

…U ˆ 30† …U ˆ 30† …U ˆ 100†

T 1 …U ˆ 30† T 1 …U ˆ 30† 17 exp… 22 000=T † …U ˆ 30† 40

Methods of measurement

Reference

Flames (T ~2000 K) Flames (T ~2000 K) Flames (T ~2000 K)

[33] [33] [33]

Flames (T ~3000 K) Flames Flames

[33] [33] [33]

a M represents an atom of a metal, Rg is a rare-gas atom, and X is a third-body. The sign * denotes electronically excited species. The signs v, v0 , J and J0 are related to vibrational and rotational levels. The source of information is in Ref. [23, Table VI.1] for the cross-sections and Ref. [33] for the rate constants (see also Ref. [34]). In the latter case, U represents the degree of uncertainty. The units for rate coecients are m3 molecule 1 s 1 for bimolecular processes and m6 molecule 2 s 1 for termolecular reactions. The methods of measurements are (a) ¯ame experiments, (b) the quenching of ¯uorescence, (c) photodissociation, (d) ¯uorescence, (e) kinetic lifetime measurements and (f) electron beam experiments.

p crP 2 : kB T

Scheme 2.

155

…8†

The addition of metal species from a liquid solution containing their salts to the hot and compressed bubble gas-phase closely resembles the projection into a ¯ame of metal species from salts solutions. We therefore suggest that alkali-metal salts released into a bubble undergo a homolytic cleavage so as to generate alkalimetal atoms. In this framework, excitation/de-excitation involves neutral species only. The possible physical excitation/de-excitation mechanisms of M are reported in Table 2 (reactions (i)±(iii)). For the calculation of the collision frequency, we assumed that backward and forward reactions are characterised by cross-sections of the same order of magnitude [23]. The collision frequency (z) can be calculated via Eq. (8) with P, T, kB , r and c as the pressure, the temperature, the Boltzmann constant, the collision cross-section and the mean speed, respectively:

zˆ

We adopted a rare-gas density of 5  1026 m 3 deduced from the line shift, the most favourable r of 0.01 nm2 and a mean T of 3000 K (in agreement with theoretical predictions and some experimental data [19]) (i.e. c ˆ 1300 m/s). We obtained z ˆ 9  109 s 1 , i.e. <300 two-body collisions during the rise time of the SL ¯ash (30 ns) between Ar and either Rb or Na.

F. Lepoint-Mullie et al. / Ultrasonics Sonochemistry 8 (2001) 151±158

Excitation processes

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Fig. 5. Logarithmic representation of the degree of ionisation (x) of Ar as a function of the temperature at two di€erent pressures. This calculation was carried out with the Saha equation [35] (the condition of local or complete thermodynamic equilibrium). The dashed curve corresponds to P ˆ 1000 atm and the continuous curve to P ˆ 50 atm. At T ˆ 3000 K, x ˆ 10 9 % (P ˆ 50 atm) and 2  10 10 % (P ˆ 103 atm).

The excitation by electronic impact (reaction (ii), Table 2) also appears to be of minor importance. As indicated in Fig. 5, the degree of ionisation of Ar calculated by the Saha equation [35] at various temperatures and pressures likely to exist in a bubble is very weak. The Saha equation holds for the thermodynamic equilibrium. As emphasised by Drawin if the intracavity medium is out of equilibrium, the degree of ionisation will be even smaller than calculated by the Saha equation [36]. With degrees of ionisation much below 1% (i.e. with the electron density  5  1024 m 3 ) and for T ˆ 3000 K (electron velocity 3  105 ms 1 ), the frequency of Ôe /MÕ collision would be  7  1012 s 1 , i.e.  105 two-body collisions between electrons and alkali± metal atoms during the SL ¯ash rise time (30 ns). 2 Excitation with the conversion of the internal energy of a water molecule (reaction (iii)) can be discarded as well. The collision cross-section ranges between 0.015 and 0.04 nm2 . With a density in intracavity water of 1:6  1027 m 3 (6:6  109 molecules of water/[4p=3  3 …10 6 † ]) (see the end of the present section), zNa=water is 11 10 s 1 i.e. <3  103 two-body collisions during the SL ¯ash rise time. Similarly, the de-excitation of M* through processes (i)±(iii) is unlikely. This is in agreement with the fact that 2 P±2 S transitions are not dominant in SL spectra. 2

It should be noted that very weak degrees of ionisation are consistent with sonochemical results. Indeed, even though H(á) and HO(á) radicals resulting from water sonolysis [37] (and also alkyl radicals related to the decomposition of alkanes, halocarbons and organic compounds in general [38,39]) can be trapped in solutions, there is no trace of hydrated electrons [40] within a detection limit of 0.04 lM/min, at least [41].

Consequently, the only possible mechanism for the excitation of alkali metals in SL is chemiluminescence. Excitation reactions (iv)±(vi) in Table 2 are well precedented in the literature. The formation of radicals (H(á), OH(á) and R(á) with R ˆ alkyl) from water and nonaqueous media submitted to the acoustic cavitation is demonstrated in Refs. [37±42]. The reaction products (H2 and O2 ) are detected during the sonolysis of Ar sparged water, see for example Ref. [37]. The gas-phase excitation/de-excitation processes for alkali-metal atoms are well known [23,43]. Reactions (iv)±(vi) are exothermic (DH ˆ 5:2 eV (iv); )4.5 eV (v); )5.2 eV (vi)) [23] and may lead to the suprathermal excitation of alkali metals [44,45] (the ®rst levels of excitation (resonance lines) range as far as 2±2.5 eV). This latter aspect is considered in Section 4. The procedure for evaluating whether reactions (iv)± (vi) may be involved is based on the usual kinetic equation (9), which gives the link between the half lifetime (t1=2 ) of a species (M), the reaction rate coecient (k), the initial concentration in the gas phase ([M]0 ) and the reaction order (n). In our case, M ˆ Na (the concentration is expressed in m 3 ); n ˆ 3; kiv , kv and kvi (expressed in m6 molecule 2 s 1 ) can be found in Table 2. Equation (9) is given as t1=2 ˆ

2n …n

1

1 n 1

1†k‰MŠ0

;

…9†

where ‰MŠ0 ˆ NM =Vb and NM ˆ Vl ‰MŠl with Vb as the bubble volume during the SL emission, NM as the number of M atoms released in a bubble, Vl as the volume of liquid to be ablated and [M]l as the density of M in the liquid phase. After substitution Eq. (9) becomes Vl ˆ

 n 1 1=…n Vb 2 1 ‰MŠl …n 1†kt1=2

1†

…10†

so that the volume of liquid to be ablated is related to the kinetic data. When adopting the characteristics mentioned by Giri and Arakeri [14], i.e. a concentration of 1 M NaCl … ‰NaŠl ˆ 6  1026 m 3 ) and a SL ¯ash rise time of 30 ns, i.e. t1=2 (Na) 15 ns, we found Vl  0:05 Vb and ‰NaŠ0 ˆ 3  1025 m 3 since n ˆ 3 for reactions (iv)±(vi). In the typical case of a bubble with R ˆ 1 lm, Vl ˆ 2  10 19 m3 , i.e. 1:2  108 Na atoms and 6:6  109 molecules of water. If a shell of liquid surrounding a bubble is involved (the thickness ˆ r, the corresponding volume ˆ 4pR2 r), r will be 16 nm. This value, which corresponds to a shell of only 40 monolayers of water near the bubble±liquid interface, appears realistic for a process of evapouration/ablation. Moreover, the estimation that Vl is equal to 0.05Vb could be compatible with the loss of matter from the tip of an inward jet. In conclusion, reactions (iv)±(vi) may be the source of M*.

F. Lepoint-Mullie et al. / Ultrasonics Sonochemistry 8 (2001) 151±158

3.2.2. Formation of M±Rg* The formation of M±Rg species in SL indicates that the de-excitation reactions of M* (vii) and (viii) are of minor importance. At a typical temperature of 3000 K, reaction (ix) is slow (t1=2 (Na*) 320 ns with ‰NaŠ0 ˆ 3  1025 m 3 , see Section 3.2.1, and therefore negligible. In fact, as is generally the case at high gas densities (a situation encountered at the end of the bubble collapse), three-body reactions dominate two-body ones [23]. Terparticules reactions (vii) and (viii) are characterised by rate coecients kvii  kviii  10 43 m6 molecule 2 s 1 at T ˆ 3000 K (Table 2). If they coexist with reactions (1) and (2) without dominating them (their rate coecients [25,46] are also of an order of 10 43 m6 molecule 2 s 1 ), this means that M* is ÔdilutedÕ amongst the Rg atoms. This most probably explains why the spectral characteristics associated with the B2 R‡ ±X2 R‡ and A2 P±X2 R‡ transitions of Ôalkali-metal/ rare-gasÕ vdW molecules in SL are not a€ected by the presence of water or its debris although the concentration of water in a collapsing cavity may reach several mol per 10 3 m 3 (see the end of Section 3.2.1). Using Eq. (9) on the one hand and adopting t1=2 (Na*) 15 ns and k1  k2  10 43 m6 molecule 2 s 1 on the other hand, we deduced that the concentration of excited Na in a bubble ([Na*]0 ) is 3  1025 m 3 , i.e. a density 6 [Na]0 , which is the density of Na atoms injected into a bubble (Section 3.2.1). This result is satisfactory given the approximations in our calculation, and enables the suggestion to be made that reactions (1) and (2) are very likely for the production of M±Rg*. 3.2.3. Electronic deactivation of M±Rg* As reported by Carrington and Gallagher [25], the radiative rates in (3) and (4) are almost equal to the rate of spontaneous radiative recombination of M, i.e. 16 ns in the case of Na. This is in fairly good agreement with Giri and ArakeriÕs measurements. A summary of the reactions likely to lead to the emission of M±Rg in SL is given in Scheme 2, which shows the possible pathway leading to the excitation/deexcitation of alkali-metal (M) and M±Rg vdW species in SL. 4. Conclusions The present analysis made it possible to establish ®rmly that the site of the emission of alkali-metal species in multibubble SL is the intracavity gas phase, the average density of which is 5  1026 m 3 in the case of both organic and aqueous solutions insoni®ed at 20 kHz. The emitters detected are Ôalkali-metal/rare-gasÕ vdW molecules (B2 R‡ ±X2 R‡ and A2 P±X2 R‡ transi-

157

tions). The mechanism, which results from a combination of our spectroscopic data, Giri and ArakeriÕs kinetic data and gas-phase reaction rate coecients involves the sequence as follows: (i) the mechanical addition to a collapsing bubble of part of the surrounding ¯uid, (ii) the release of the salt molecules in the gas phase, (iii) the homolytic cleavage of salts, (iv) the electronic excitation of the metal atoms by means of three-body reactions (with 2H, 2O or O ‡ H as colliders), (v) the formation of electronically excited Ôalkali-metal/rare-gasÕ molecules via a three-body reaction with two rare-gas atoms as colliders and ®nally (vi) the bound radiation of these vdW molecules. As a matter of fact, SL is chemiluminescence. Another consequence of this study is that if an analysis of the line pro®le by standard diagnosis is carried out, special attention should be paid to the modi®cation of the Doppler component because of suprathermal reactions (the chemical excitation of the alkali-metal species). This situation is made more complex because of Dicke-narrowing. This latter modi®cation of the Doppler pro®le occurs when the density is no longer negligible, so that the mean free path between two successive collisions (radiating species/atoms belonging to the surroundings) cannot be considered as being much larger than the wavelength of the light emitted. Work is in progress in this direction.

Acknowledgements The authors are extremely indebted to Mr. J.-L. Domanchain and Mr. G. Nivez (Jobin Yvon Horiba) for their help, and also to Dr. M. Carleer (Laboratoire de Chimie Physique Moleculaire; Universite Libre de Bruxelles) for very useful discussions. T.L and F.L are very grateful to the Fonds National de la Recherche Scienti®que (Belgium) and the Fondation Agathon de Potter (Academie des Sciences de Belgique) for ®nancial support.

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