J . Phys. Chem. 1990. 94, 5164-5169
5164
are present for photooxidized films. A schematic representation of the effect of far-UV radiation on Kapton H films is given in Fieure 11. It is unresolved whether the photooxidized and unphotooxidized radicals exist simultaneously on the surface, or whether the former radicals are on the surface and the latter radicals are just beneath the surface. However, it is likely that other polyimides exhibit similar behavior. Recent XPS studies3I have demonstrated that fully cured polyimide films contain excess starting constituents, or their derivatives, within the sample depth of XPS. Hence, such films probably have significant heterogeneities in composition in the near-surface region, which would further complicate any detailed interpretation of the near-surface properties of these important polymers. Y
( 3 1 ) Lamb, R. N.; Baxter, J.; Grunze, M . , Kong, C. W.; tinertl, W. N. Langmuir 1988, 4. 249.
Further studies of the surface magnetism and motional dynamics of radiation-induced free radicals in polyimide films are in Droeress . .* in our laboratories.
Acknowledgment. We acknowledge an Arizona State Research Graduate Fellowship(M,A,G,), Mr, John McNerney of The Arizona Corporation for helpful discussions, Drs, Thomas Gray and Michael McKelvy of Arizona State for assistance with the X-ray and thermogravimetric studies respectively, Dr, James Anderson of Montana State ,.niver;ity for assistance with the xps work, and the Magnetism and Magnetic Resonance Facilityat Arizona State University and the Center for Research in Surface Science and Submicron Analysis at Montana State University for use of their facilities. This research was supported by the Arizona Instrument CorDoration and Arizona Siate Uniiersity. Registry No. Kapton H, 25036-53-7; (pyromellitic dianhydride) (4,4-diaminodiphenylether) (copolymer), 25038-81-7; gold, 7440-57-5.
Electrochemical and Electron Paramagnetic Resonance Studies of Carotenoid Cation Radicals and Dicatlons: Effect of Deuteration M. Khaled, A. Hadjipetrou,?and L. Kispert* Chemistry Department, Uniuersity of Alabama. Tuscaloosa, Alabama 35487 (Receiued: Nocember 9, 1989)
The oxidation process involving the transfer of two electrons for @-caroteneis confirmed by bulk electrolysis in a CH2C12 solvent and the observation of AE = 42 mV from cyclic voltammetric measurements. A similar process is also found to occur for P-apo-8’-carotenal and canthaxanthin. An additional cathodic peak between 0.2 and 0.5 V relative to SCE is shown to be dependent on the initial formation of dications followed by the loss of H+ as evidenced by a large isotope effect and most likely due to the reduction of a carotenoid cation. EPR evidence exists for the formation of radical cations by the reaction of diffusing carotenoid dications with neutral carotenoids. The rate of formation is consistent with the differences in the diffusion coefficients of the carotenoids deduced by chronocoulometric measurements, being fastest for canthaxanthin. The apparent decay half-life of 0-carotene (1.4 min) cation radical in CHzClzsolvent in the presence of excess &carotene increases an order to magnitude to 14.3 min upon deuteration.
Introduction Carotenoids are present in the chloroplasts of photosynthetic green plants.14 They serve as photoprotect devices by preventing the formation of damaging singlet oxygen and act as antenna pigments for the absorption of light energy in the spectral region where chlorophyll is not an efficient absorber. Understanding the photosynthetic process is essential to the development of artificial photosynthetic systems. An important component of artificial photosynthesis systems that would convert solar energy into chemical energy is light-driven electron-transport processes across a membrane. Recently, it was shown that the molecular triad molecules consisting of porphyrins covalently linked to both carotenoids and quinones (CPQ) can achieve photodriven electron transfers in good Excitation of the CPQ moiety yields a final charge-separated state C+-P-Q- with a lifetime of the order of microseconds. This suggests that carotenoids can play an active role in the photosynthetic electron-transport chain, with the carotenoid cation radical C+ as an integral part of the electrontransfer process. Carotenoid cation radicals have also been reported to occur at the photosystem I1 reaction It follows that a detailed knowledge of the carotenoid and their oxidation products is important to the overall understanding of these processes. To date,lOJ1an EPR, optical and electrochemical study have been carried out to characterize the physical properties of @-carotene(I), P-apo-8’-carotenal (11), and canthaxanthin (111) cation radicals. These carotenoids were selected for study because ‘Participant in a National Science Foundation summer 1989.
sponsored REU program.
0022-3654/90/2094-5 164$02.50/0
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they are found in a variety of plants and vegetables, are readily available, and are easily purified. They provide a variation in ( 1 ) Goedheer, J . C. Annu. Reu. Planr Physiol. 1972, 23, 81.
( 2 ) Sauer, K . Bioenergetics of Photosynthesis; Academic: New 1975; pp 115-181.
1990 4merican Chemical Societl
York,
Carotenoid Cation Radicals and Dications conjugated chain length (13-10 double bonds) as well as possessing either one, two, or no carbonyl groups. The study reveals that the carotenoid cation lifetime depends on the host lattice matrix;I0 however, the reason remains undetermined. In addition, a second cathodic peak is also observedl0J' and attributed to the reduction of the monocation (R+). This peak is absent if the potential is after the first oxidation wave of canthaxanthin, suggesting that dication formation RH;+ is necessary for the second cathodic peak to be observed. Furthermore, a reaction mechanism has been proposed" in which H+ is lost from the carotenoid dication to form the monocation (RH+). Upon reduction, RH' is believed" responsible for the cathodic peak occurring between 0.2 and 0.5 V vs SCE. Although these results have been useful, it is still necessary (a) to determine what experimental conditions are required to stabilize the cation radicals and the dications, (b) to confirm the twoelectron process which has been suggested to occur for @-carotene, (c) to measure the relative diffusion coefficients for carotenoids so that the variation in diffusion-limited reaction rates can be understood, and (d) to establish whether a cation radical-dication equilibrium exists in solution for the oxidized carotenoids. To accomplish this, a more complete study as a function of solvent (CH2CI2and C2H,Cl2) has been carried out using EPR, chronopotentiometry, cyclic voltammetry, chronocoulometry, and bulk electrolysis techniques.
Experimental Section Appararus. A three-electrode weighing bottle cell and a platinum disk (area 0.02 cm2) and a platinum wire serving as the working and auxilliary electrodes, respectively, were used in all electrochemical techniques. A Ag/CI reference electrode, which was calibrated with a CH2C12solution of ferrocene, had a potential of 0.190 V vs S C E and was used as the reference electrode for the CH2CI2and C2H4CI2solvents. The distance that separated the three electrodes was kept to a minimum. All measurements were performed in a stationary solution inside a Vacuum Atmospheres Model HE-63P drybox under a N, atmosphere, at room temperature. A Bioanalytical Systems BAS 100 A electrochemical analyzer was used for cyclic voltammetry, chronocoulometry, square-wave voltammetry, and bulk electrolysis. All measurements were IR compensated. The electrochemical data were transferred to a JAMECO PC and stored on floppy disks. EPR measurements were recorded on a Varian E-12 spectrometer during in situ electrolysis, using a two-electrode, custom-designed Pyrex electrolytic flat cell, with a large platinum gauge electrode as the anode and a platinum wire as the cathode. Solutions were prepared in the drybox and excess solutions transferred to the EPR cell maintaining the highest N2 pressure in the drybox before sealing the flat cell assembly. It was found that as electrochemical oxidation was carried out, the higher pressure caused an internal convection or stirring of the solution in the flat portion of the cell maintaining an excess of carotenoid there throughout the experiment. If an excess of solution and N2 pressure were absent, it was then found necessary to remove the EPR flat cell from the cavity and manually stir the solution by (3) Renger, G.; Wolff, Ch. Biochim. Biophys. Acta 1977, 460, 47. ( 4 ) Chessin, M.; Livingston, R.; Truswtt, T. G.Trans. Faraday Soc. 1966, 62, 1519. ( 5 ) Seta, P.; Bienvenue, E.; Moore, A. L.; Mathis, P.; Bensasson, R. V.; Liddell, P.; Pessiki, P. J.; Joy, A,; Moore, T. A,; Gust, D. Nature (London) 1985. 316. 653. (6) Moore, T.A.; Gust, D.; Mathis, P.; Mailozq, J. C.; Chachaty, C.; Bensasson, R. V.; Land, E. J.; Doizi, D.; Liddell, P. A,; Lehman, W. R.; Memeth, G. A.; Moore, A. L. Nature (London) 1984, 307, 630. (7) Gust, D.: Moore, T. A.; Liddell, P. A,; Nemeth, G. A,; Makings, L. R.; Moore. A. L.; Barrett, D.; Pessiki, P. J.; Bensasson, R. V.; Raigee, M.; Chachaty, C.; De Schryver, F. C.; Van de Anweraer, M.; Halzwarth, A. R.; Connolly, J. S. J. Am. Chem. Soc. 1987, 109, 846. (8) Mathis, P.; Rutherford, A. W. Biochim. Biophys. Acta 1984, 767, 217. (9) Schenck, C. C.; Diner, D.; Mathis, P.; Satoh, K. Biochim. Biophys. Acta 1982, 680, 216. (IO) Grant, J. L.; Kramer, V. J.; Ding, R. S.; Kispert, L. D. J. Am. Chem. Soc. 1988, 110, 2151. ( I I ) Mairanovsky, V. G.; Engovatov, A. A,; loffee, N. T.; Samokhvalov, G. I . J. Electroanal. Chem. 1975, 66, 123.
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 5165 inverting the cell. The constant current was supplied by a PAR voltage/current source. The magnetic field was measured with a Bruker EPR 035 M gaussmeter, and the microwave frequency was measured with a Model H / P 5245 L frequency counter. Materials. Unopened bottles of HPLC grade dichloromethane (CH2C12)and dichloroethane (C2H4C12)solvents from Aldrich were transferred under nitrogen to a round-bottom flask. The solvents were then degassed three times on a vacuum line to be certain of the absence of 0, and stored in the drybox. Tetra-nbutylammonium hexafluorophosphate (TBAHFP), polarographic grade, was used as supplied from Fluka. TBAHFP was kept inside an oven at 110 "C for 1 week and then stored inside the nitrogen atmosphere of the drybox. In all cases a solvent-supporting electrolyte solution was scanned over the solvent window to assure the absence of electroactive impurities. All carotenoids were purified on a column packed with silica gel (Davision Chemicals, Davisil 62). P-Carotene (I) (Sigma) was eluted with carbon tetrachloride (CCI,), @-apo-8'-carotenal (11) (Fluka) with a mixture of petroleum ether and acetone (20:1, v/v), and canthaxanthin (111) (Fluka) with a CCI, acetone mixture (20:1, v/v). Deuterated I 1 was extracted from 99% deuterated Scenedesmus obliquus algae grown at Argonne National Laboratory.', The purity of each compound was verified by thin-layer chromatography and UV-vis spectroscopy. All carotenoids were stored under N2 in the drybox. All glassware was washed in a KOH/EtOH bath, rinsed several times with distilled water, and dried in an oven at 110 "C. The glassware was removed just before use and cooled in a N2 or Ar atmosphere. A large series of experiments were carried out which showed that the purity of the solvent and the potential drop were the most important factors that affect the electrochemical peak-to-peak separation, AEp, for the oxidation and reduction waves of @carotene and the @-carotenecation radical. Previously,Ioa typical value of AEp was observed to be greater than 59 mV which suggested a complication in the electron-transfer mechanism. Our experiments show that failure to use degassed HPLC solvents in an inert atmosphere drybox caused the complication. For example, the AEp for @-carotene was always above 100 mV when dichloromethane or dichloroethane was taken from an old HPLC bottle. However, by using degassed HPLC solvents opened under N,, using IR compensation, and keeping the distance that separates the three electrodes to a minimum, we obtained a value of AEp = 42 mV of @-carotene. The value remained the same for both freshly purified and commercially received @-carotene. The value of AE,increased significantly if the distance between the electrodes were not kept to a minimum. To investigate the effect of water on the carotenoid electrochemistry, a solution of @-carotenewas left inside a freezer. Upon removal, CV's of the solution were taken out on the bench top where water was allowed to condense in the solution. The peak separation was observed to increase, and the cathodic and anodic id decreased. Upon thorough stirring of the solution, all peaks in the CV disappeared, suggesting that the carotenoid species had reacted with water leading to an electrochemical-inactive species.
Results The cyclic voltammogram for canthaxanthin (111) in CH2CI2 is given in Figure 1A. Analysis of the spectrum (Table I) indicates that 111 , undergoes . a reversible electron transfer as ic4/ial 0.9 while I c 3 / l a 2 0.7. Peaks and have been previous'yIOshown to be due to the first and second oxidation wave with peaks 3 and 4 corresponding to the reduction peaks. Bulk electrolysis experiments indicate that two electrons are transferred, confirming the assignment of peak 2 as the second oxidation wave. The identity of the species belonging to peak 5 is not known for certain; however, it has been suggested that it is due to the reduction wave for the carotenoid cation formed by the loss of H+ from the carotenoid dication." This mechanism is consistent with the observation that peak 5 does not appear if the CV is stopped at
-
*
-
(12) Strain, H. H.; Thomas, M. R.; Crespi, H. L.; Blake, M. I.; Katz, J. J. Ann. N . Y . Acad. Sei. 1960, 84, 617.
5166
Khaled et al.
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 Apocarotenal
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Figure 1. Cyclic voltammograms (CV) and Osteryoung square-wave voltammograms (OSWV) for canthaxanthin in CH2C12 and C2H,C12 with 0.08 M TBAHFP as the supporting electrolyte. Scan rate 100 mV/s. (A) CV, (B) CV to first anodic peak, (C) OSWV to the first anodic peak, (D) OSWV to the second anodic peak, and (E) OSWV in C2H,C12. The 500-nA scale and the 5-pA scale are given for (A), ( 9 ) and (C)-(E), respectively. TABLE I: Peak Potentials (mV)/Currents (lod A ) vs Ag/AgCI Reference Electrode ~
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+0.850 V vs Ag/AgCl (Figure IB) before the dication (second peak) is formed. In recording OSWV spectra, it is noted that the absence of any weak peaks (Figure 1C) upon scanning from 0.8 to 0 V confirms the absence of peak 5 even at low concentrations. However, if the scan is started at 1.00 V and scanned to 0 V, peak 5 does appear (Figure 1 D). The intensity increases if the scan is started at 1.300 V (Figure IE). A somewhat different observation was observed for the OSWV spectra recorded for P-apo-S’-carotenal (11) in CH2C12(Figure 2). I n Figure 2A-C, no peak 5 occurs when the initial scan voltage starts at 0.600 V or lower (beginning tail of the first oxidation line) and scans to lower voltage. However, if the initial scan voltage starts at 0.7 V (maximum of first oxidation line), then a small peak appears at 0.18 V, which increases in intensity as the starting voltage is increased to +1.000 V. The second oxidation peak overlaps the first, so only at scan voltages below 0.6 V is only a one-electron transfer present. Bulk electrolysis experiments for I 1 and 111 showed that two electrons were transferred in both cases, and analysis of the CV’s in Figures 1A and 2G shows that reversible electron transfer occurs for both carotenoids. Reversible electron transfer is also observed for @-carotene(Figure 3); however, an OSWV spectrum (Figure 3B)
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Figure 3. CV’s and OSWV for @-carotenein CH2C12 with 0.08 M TBAHFP as the supporting electrolyte. Scan rate 100 mV/s. (A) CV, (B) OSWV scanning from high potential (1300 mV) to a final of -500 mV.
of p-carotene scanning from 1.300 to 4 . 5 V showed not only peak 5 near 0.0 V but extra peaks at 0.85 and 1.1 V. These extra peaks disappear at high scan rates but are always present at slower scan rates for purified 1. Thus far, the identity of the species responsible for these peaks remains unknown, but studies are under way to identify them. The current measured for peak 5 of @-caroteneas a function of the starting potential for the OSWV spectrum is given in Figure 4. As the starting potential is increased from 0.40 to 0.90 V, the current increases from 0.16 X lo-’ to 9.13 X IO-’ A (listed in the center of Figure 4). Carrying out the same experiment for deuterated /3-carotene (C,D,,) indicate only a small increase in current (listed on the right of Figure 4) from 1.43 X IO-’ to 1.87 X IO-’ A when the starting voltage is changed from 0.50 to 0.900 V. This remarkable difference upon deuteration was also observed when the carotenoid radical cation was formed by a constant current pulse left on for 1 (Figure 5A), 5 (Figure 5B), and 9 min (Figure 5C) (start of a I-min scan). A general decrease in intensity is observed. However, an increase in EPR signal occurs 2 min after the current pulse is turned off (Figure 5D). This increase in EPR signal is also observed for deuterated @-carotene
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 5167
Carotenoid Cation Radicals and Dications p-Carotene Initial > Final E. C u r r e n t (10-7)
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Figure 6. Current pulse on and EPR recorded ( A ) after 2 min for deuterated p-carotene. The current pulse is turned off and EPR spectra recorded after (B) 0, (C) 6, and (D) 17 min (start of a I-minscan). An increase in signal occurs up to (C) and then the signal decreases.
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Figure 4. OSWV spectra for 0-carotene (Cd0HS6,left) in CH2CI2when scanning from ( A ) 300 to 0 mV, (B) 400 to -300 mV, (C) 500 to -300 mV, (D) 600 to -300 mV, and (E) 900 to -300 mV. Note the large A to (E) 9.13 X A after the increase in current ( A ) 0.16 X dication is formed. The vertical scale for (A)-(D) is given in Figure 4D. The increase in current for deuterated @-carotene(C4,,DS6) is given on the right in each spectrum.
C.
D.
TABLE 11: Half-Life (minutes) of the @-CaroteneRadical Cation; Formation. Diffusive Growth. and Decav in C H 4 X after constant current pulse off carotenoid formation growth decay 0-carotene C40H56 0.27 ( I > 11, consistent with the observed radical cation formation and decay rates after the current is turned off. For instance, the largest increase in radical concentration occurs for 111 (Figure 7b) while the apparent rate of decay is largest for I1 and smallest for 111, the larger diffusion coefficient of 111 providing a competitive mechanism for the formation of radical cations. The appearance of an increase in the EPR detected radical cation concentration is most apparent for the oxidation of canthaxanthin (111) and deuterated @carotene. I n the case of 111. the diffusion rate is large enough and the decay rate of the cation radical slow enough to allow the detection of the radical cation formation. In the case of deuterated @-carotene,the observed increase in the radical cation concentration after the constant is turned off is a result of the decreased rate of deuteron loss from the dication to form a cation. Thus, there is a competition between loss of available dication concentration via eq 1 and the loss of dication concentration via eq 2. When the rate of (1) is slowed upon deuteration, formation of radical cations via eq 2 is enhanced. The order of magnitude decrease in the radical cation decay rate upon deuteration is unusually high for C-H vs C-D bond breakage in the dication, suggesting that the decay of carotenoid radical cations also involves a C-H bond breakage. The decay mechanism of the carotenoid radical cation is not known and is still under study. Canthaxanthin in both solvents has a larger D value than the other two carotenoids. A possible reason may be that canthaxanthin and P-apo-8'-carotenal both have local dipole moments. After their dications are formed, a positive charge in the middle of the chain is predicted by an AM1 calc~lation.'~The negative ion of the supporting electrolyte ion will move toward the dication
-
( 1 5 ) Bradford. E.; Hollis, K.; Kispert, L D
Unpublished results
J . Phys. Chem. 1990, 94, 5169-5172 formed to solvate it. For canthaxanthin it will be more difficult for the dication to be solvated since local dipole moments occur at both ends. Therefore, the electrostatic interaction of canthaxanthin dications will be greater than @-caroteneand fl-apo8’-carotenal dications.
Conclusion The proposed oxidation processes involving the transfer of two electrons are now confirmed by bulk electrolysis and the observation of PE = 42 mV from CV measurements for @-carotene. Similar processes were also found to occur for apocarotenal and canthaxanthin. The relative diffusion coefficients for the carotenoids were larger in CHzC12than in C2H4CI2with canthaxanthin the larger. EPR evidence exists for the formation of radical cations by reaction of carotenoid dications with neutral carotenoids. The
5169
cyclovoltammetric peak at around 100-300 mV was dependent on the formation of dications followed by the loss of H+, a faster process for C40H56 than for CmDS6. The appearant half-lifes of the carotenoid radical cations in the solvent CH2Clzcan be as long as 2 min and are dependent on the carotenoid diffusion coefficients. A considerable increase in the apparent half-life (- 14 min) of CmDs6*+occurs because the reaction of C40D56with C D 2+ via electron transfer replenishes the concentration of C40D56 ?+ .
*
Acknowledgment. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Science, Department of Energy, under Grant DE-FG05-86ER13465. We thank John Howell of BAS for many useful discussions and Mike Wasielewski at Argonne National Laboratory for supplying the deuterated 0-carotene.
Chemical Effects of Continuous and Pulsed Ultrasound: A Comparative Study of Polymer Degradation and Iodide Oxidation Arnim Henglein* and Maritza Gutierrez Hahn- Meitner-Institut Berlin GmbH, Bereich Strahlenchemie, 1000 Berlin 39, FRG (Received: November 7 , 1989; In Final Form: February 7 , 1990)
The oxidation of iodide and main-chain degradation of poly(acry1amide) were studied under continuous and pulsed 1-MHz ultrasound irradiation of aqueous solutions containing both solutes simultaneously. The ratio of the rates of degradation to oxidation strongly increases with the intensity of the ultrasound. In the intensity range where the coalescence of cavitation bubbles causes the oxidation yield to diminish, the degradation is little affected. It is concluded that strong shear forces (producing fast degradation) are still generated in the vicinity of oscillating or collapsing gas bubbles when the temperature reached in the adiabatic compression phase of the bubbles is not high (Le., little oxidation occurs). A high ratio of polymer degradation to iodide oxidation was also found in the irradiation with intense 20-kHz ultrasound from a commercial generator (horn diameter 14 mm). I t is concluded that free-radical side effects, such as oxidations, are relatively unimportant when 20-kHz ultrasound is used to mechanically rupture large structures.
Introduction Both the mechanical main-chain degradation of dissolved macromolecules and the redox reactions on dissolved substances, which occur when intense ultrasonic waves pass through liquids, have been known for several decades.’ In both cases, cavitation is needed to initiate the processes, and cavitation generally occurs when the solution contains a gas. However, the mechanism of the two kinds of chemical effects is quite different: redox reactions are initiated by free radicals formed by the thermal decomposition of solvent or solute molecules in compressed cavitation bubbles. Temperatures of several thousand kelvin can be reached in the adiabatic compression phase of such bubbles.2 On the other hand, main-chain degradation is caused by hydrodynamic shear forces appearing in the vicinity of oscillating or collapsing cavitation bubbles. As a consequence of these different mechanisms, the dependencies of the yields of the two types of chemical reactions on the irradiation conditions differ. In a recent paper, the influence of the dissolved gas has been studied.j While redox reactions occur ( I ) (a) Henglein. A. Ultrasonics 1987, 25, 6 . (b) Suslick, K. S . , Ed. Ultrasound, Its Chemical, Physical and Biological Effects, VCH: Weinheim, FRG, 1988. ( c ) Mason, T. J.; Lorimer, J. P. Sonochemisrry, Theory, Applications and Uses of Ultrasound in Chemistry; Ellis H o r w d : Chichester, U.K., 1988. (d) Basedow, A. M.; Ebert, K. H. Adu. Polym. Sei. 1977, 22, u3.
with appreciable yields only in the presence of a mono- or diatomic gas (in which especially high temperatures are reached upon adiabatic compression), the yield of macromolecule degradation depends little on the nature of the gas and can still be large in the presence of a polyatomic gas, such as N 2 0or C2H4 (see Figure 2 in ref 3). In other words, the degradation process depends much less on the cavitational conditions than the free-radical reactions. In the present paper, the degradation of poly(acry1amide) in aqueous solution under the influence of pulses of ultrasound was investigated. Pulse trains were applied, which deposited as much sound energy in the irradiated liquid as continuous irradiation, and the yields were compared. In order to deposit the same amount of energy, the time for pulse irradiation was longer than for continuous irradiation t = to(1
where to is the time of continuous irradiation and R = T / T o is the on/off ratio ( T , length of pulse; To,length of interval). The solution also contained potassium iodide and air. Under these circumstances, both macromolecule degradation and iodide oxidation occur simultaneously and the dependencies on pulse conditions can be compared with each other. The results are of interest with respect to the chemical effects occurring in medical applications of ultrasonic pulses. Both types of reactions. Le.. redox Drocesses and mechanical main-chain scission, may occur in b i o b i c a l objects. It is concluded from I
(2) (a) Noltingk, B. E.:Neppiras, E. A. Proc. Phys. Sot. 1950, B63, 674. (b) Neppiras, E. A . Phys. Rep. 1980, 61, 159. (c) Flynn, H. G. In Physical Acoustics: Principles and Methods; Mason, B. W. P., Ed., Academic Press: New York, 1964; Vol. I .
+ 1/R)
.
(3) Henglein, A.; Gutierrez, M. J. Phys. Chem. 1988, 92, 3705.
0022-3654/90/2094-5 169$02.50/0 0 I990 American Chemical Society
