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MARGULIS et al.
ization of maleic acid, the efficiency of the laser- four orders of magnitude higher than the energy yield of
induced spark was found to be ~7 times higher than the sonochemical redox reactions [6, 9]. It is believed that
efficiency of the multibubble cavitation. Note that the such reactions may occur under the action of high-energy
chemical action of the multibubble cavitation is associ- particles or products formed under their action (mole-
ated with electrical breakdowns inside the bubbles in cules, ions, electrons, radicals, excited species, etc.).
their deformation and splitting [5].
According to estimates [12] the total energy of pho-
tons emitted by a laser-induced spark was estimated at
~6 × 10–6 of the energy absorbed by the spark. In the
single-bubble cavitation, the energy yield of photons at
22°ë is equal to 4.7 × 10–7 and, at 3°ë, 3.6 × 10–6 [13]
(see table). In the multibubble cavitation, the efficiency
of conversion of acoustic energy into luminous is very
low, 10–11–10–12 [6, 9, 14].
The laser-induced spark and the single-bubble cavi-
tation exhibit much the same energy yields of NO–2 and
efficiencies of conversion of absorbed energy into lumi-
nous. In both cases, the temperature of equilibrium
plasma is equal to ~104 K. Thus, it is believed that these
processes are similar in nature.
The chemical action of a single bubble was consid-
ered in [13]. It was concluded that the chemical action
is associated with the heating of the vapor–gas mixture
in the bubble to ~104 K in its compression during the
period of acoustic vibration. Energy yields of NO–2 ions
and OH radicals in pulsations of a single bubble in air-
saturated water at a sound pressure amplitude of 1.5 atm
and a US wave frequency of 52 kHz were determined.
At 22°ë, the maximum radius of the cavitation bubble
Rm = 28.9 µm, and amounts of NO–2 ions and OH radi-
cals formed in one period (N) were found equal to 3.7 ×
106 and 6.6 × 105, respectively. At the expansion stage,
the cavitation bubble accumulates the acoustic field
energy, and the total energy accumulated by the bubble
is determined by the relation
ACKNOWLEDGMENTS
The authors are grateful to S.V. Egerev for providing
a high-power laser.
E1 = (4πR3m /3)(ph + pac – ps),
(7)
This work was supported by the Russian Foundation
for Basic Research (project no. 03-02-16232) and the
“State Program for Support of Scientific Schools”
(grant no. NSh-1176-2003-2).
where ph = 1 atm is the hydrostatic pressure, pac is the
sound pressure averaged over the period of fast com-
pression (pac ≈ 0.3 atm), and ps is the saturated vapor
pressure (ps ꢀ ph). The energy yield of the product is
K = N/(6.02 × 1023E1).
(8)
REFERENCES
Substituting numerical values gives KNO– = 4.4 ×
1. Yu. P. Raizer, Gas Discharge Physics (Nauka, Moscow,
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2
10–10 mol/J (related to the acoustic energy), and
KOH = 7.8 × 10–11 mol/J. At 3°ë, the bubble is com-
pressed to a higher degree (Rm = 30.5 µm) because of a
lower vapor pressure, which prevents its collapse, and
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period of laser irradiation are equal to 9.9 × 106 and
8.2 × 105, respectively; that is, KNO– = 1.06 × 10–9 mol/J
2
(related to the acoustic energy), and KOH = 8.8 ×
10–11 mol/J (see table).
After 60 min of exposure of 25 ml of a 25% maleic
acid solution saturated with n-butyl bromide to the
focused laser beam with a pulse energy of 140 mJ and
a pulse interval of 1.2 s, 0.19 g (1.64 × 10–3 mol) of
fumaric acid was formed (with allowances made for its
solubility in 25 ml of water, 0.15 g (1.1 × 10–3 mol)).
Thus, we obtained the stoichiometric amount of
fumaric acid, which corresponds to the chain reaction
mechanism. The energy yield of the reaction was found
to be four to five orders of magnitude higher than those
for redox reactions in the irradiation with a focused
laser beam, which is an extra argument in supports of
the chain reaction mechanism (see table). Note that the
energy yield of the ultrasonically initiated chain reac-
tion of stereoisomerization of maleic acid into fumaric
acid in the presence of alkyl bromides is also three to
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RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 80 No. 6 2006