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 CH2Clz can 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.
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5170 The Journal of Physical Chemistry, Vol. 94, No. 12, 1990
Henglein and Gutierrez.
I 0
0
20
40
t
60
80
[SI
Figure 1. Relative viscosity of a poly(acry1amide) solution as a function of sonication time. Inset: Plot of 'to/o vs time.
the results obtained that the relative importance of the two kinds of reactions are different in the application of pulsed and continuous ultrasound, and may also depend on the intensity. We also report here on a comparative study of K I oxidation and polymer degradation by almost audible sound (20 kHz) generated by a commercial transducer, Le., under irradiation conditions which are often used in experiments in which biological cells are to be ruptured.
Experimental Section The decrease in the chain length of the polymer was followed by measuring the viscosity of the solution. Figure 1 shows a typical example. At times much longer than shown in the figure, the viscosity strives toward a limiting value; it is well-known that the mechanical degradation of polymers leads to a limiting chain ~ * ~ initial length below which no more chain scission O C C U ~ S . ~ The part of the viscosity-time curve can be approximated by a hyperbolaS5 In the case of continuous irradiation, the approximation is based on the formula
where vo is the relative viscosity before irradiation and kdo the "degradation constant" for continuous irradiation. The inset of Figure 1 shows that a plot of v o / t vs irradiation time to indeed yields a straight line, from the slope of which kdo can be calculated. Because of the linear relationship in the inset of the figure, one viscosity determination after irradiation is sufficient to obtain the degradation constant. Similarly, for pulsed irradiation we have 7 = TO( 1 / 1
+ kdt)
(3)
where kd is the degradation constant and t the irradiation time (eq 1) for pulsed irradiation. The equipment for irradiation at a frequency close to 1 M H z has recently been described.6 In order to achieve a high efficiency of uptake, the ultrasound was transmitted through the plane bottom of a glass vessel, the thickness of which was matched to the wavelength. In Figures 2-4, the hf power picked up by the transducer is given as a measure of the intensity of the sound produced. The relation between the hf power [W] and intensity [W/cm2] of our I-MHz equipment can be seen from Figure 2 in ref 6. A commercial 20-kHz sound generator (KLN system 582; horn diameter, 14 mm) was also used; 20 mL of solution was irradiated in a beaker (inner diameter, 30 mm), the distance between the horn and the bottom of the vessel being 24 mm. The intensity (4) (a) Schmid, G.; Paret, G.; Pfleiderer, H. Kolloid.-Z. 1951, 124, 150. (b) Henglein, A. Makromol. Chem. 1955, IS, 188. ( 5 ) Gebert, F. Angew. Chem. 1952, 64, 625.
(6) Gutierrez. M.; Henglein, A . J . Phys. Chem. 1990. 94. 3625.
L I
0
20
I
1
&O
60
F o -
80 hf-power [ w a t t s ]
100
Figure 2. Rate of iodine formation in the absence of polymer (0)and presence of high (u) and low ( 0 )molecular weight poly(acry1amide) as a function of hf power (the intensity was about 3 W/cm2 at the highest power applied; see Figure 2 in ref 6 for the relation between hf power
and intensity). I of the sound was determined by measuring the increase in temperature of the solution and calculating I in W/cm2 according to
I = CAT/tA (4) where C [J/(g "C)] is the heat capacity of the solution plus beaker, AT ["C] the temperature increase after irradiation time t [SI, and A [cm2] the square area of the horn. The I, yield from the iodide oxidation was determined spectrophotometrically ( t at 350 nm = 2.4 X IO4 M-' cm-' ). The concentration of KI was 0.2 M in all irradiation experiments. The poly(acry1amide) was a commercial sample (EGA-Chemie, average molecular weight: 5 X IO6). The polymer concentration in the solution was 3.75 g/L. In a few experiments (Figure 2). a poly(acry1amide) sample of much lower molecular weight (about 3 X IO5) was used. It was obtained by sonicating the solution of the high molecular weight sample (irradiation with the 20-kHz horn for 30 min at an intensity of I O W/cm2).
Results and Discussion Effect of Poly(acry1amide) on the Yield of 12. Figure 2 shows the rate of iodine formation as a function of the hf power picked up by the quartz transducer. The experiments were carried out with a 0.2 M K I solution in the absence and presence of poly(acrylamide), both the high and low molecular weight samples being used in the latter case. Under all conditions, the curve obtained passes through a maximum with a rather steep decrease at higher intensities. The maximum has been observed previously and is attributed to a change in the cavitation conditions.6 The bubbles coalesce at higher intensities to form larger bubbles in which the adiabatic compression does not produce temperatures as high as in the smaller, resonating bubbles. In the presence of the high molecular weight polymer the viscosity of the solution was strongly increased ('tobeing 8.2). It is remarkable that this effect did not affect the shape of the curve for iodide oxidation in a noteworthy manner. However, the iodine yield was slightly greater in the presence of poly(acrylamide), the effect being practically the same for the samples of high and low molecular weight. We attribute this to a chemical interference of the polymer with the oxidation of iodide. The degradation and also the thermal decomposition of the polymer3 produces organic radicals which in the presence of air form peroxy radicals. The latter then contribute to the oxidation of I- ions. In the following experiments in which the degradation and oxidation yields are compared the solution contained both KI and the polymer; Le., the two processes occurred under the same cavitation conditions. Effects of viscosity and chemical interaction are thus eliminated and the observed phenomena are only due to the different dependences of the two processes on the cavitation conditions.
The Journal of Physical Chemistry, Vol. 94, No. 12, 1990 5171
Chemical Effects of Ultrasound
1.2
hf-power I w a t t s l
10
0
40
80
120
140 1.0
r
1
0 0 1 V '
Y
O.? 0.6
W
O.I 0.2
c
= 2 0 10-2
0
10"
T Is1
Figure 5. Reduced yields of iodine formation and polymer degradation as functions of pulse length T for two on/off ratios R. hf power: 25 W.
"0
40
80
120
140
hf-power I w a t t s l
Figure 3. Rate of iodine formation and specific rate of degradation as functions of hf power for continuous and pulsed irradiation. The on/off ratio was 1:100, different pulse lengths. Solution: 0.2 M KI and 5 X IO-* M poly(acry1amide) (high molecular weight).
-k I -
.^
1.0
._
0.5
1
"0
I
I 20 40 60
I
I
80 100 120 140
hf-power [ w a t t s ]
Figure 4. Yield ratio k&'/rate of I2 formation as a function of hf power (from the data in Figure 3).
Pulsed Ultrasound. Figure 3 shows the yields of iodine formation and polymer degradation at various hf powers for both continuous and pulsed irradiation. The on/off ratio was 1:lOO and pulse trains of different pulse lengths were used. It is seen that the iodine yield maximum is shifted to lower intensities with decreasing pulse length. This effect has been observed previously and discussed in terms of the "activation" and "deactivation" of the irradiated liquid with respect to chemically effective cavitation. A pulse needs time to activate the liquid, Le., to form gas bubbles. If this time is shorter than the pulse length, chemical effects do not occur. The bubbles disappear during the interval between the pulses mainly by coalescence. If the time of disappearance is longer than the interval, the subsequent pulse finds the system still activated and is chemically more effective than a pulse arriving after a much longer time. The specific rate of degradation under continuous irradiation reaches its maximum at 100 W and the subsequent decrease is very gentle in contrast to the steep decrease in the I2 yield. The polymer degradation, thus, has an intensity dependence significantly different from that of the iodide oxidation. This is further illustrated by Figure 4 where the ratio of the polymer degradation yield to I- oxidation yield is plotted vs the hf power. The ratio was formed by dividing k$ (lower plot in Figure 3) by the I2 rate (upper plot). The higher the intensity of the ultrasound the more favored is the degradation of the polymer. In other words, the degradation of the polymer occurs relatively efficiently under conditions where the gas bubbles coalesce. It is concluded that
oscillating or collapsing bubbles still produce strong shear forces in the liquid even under conditions where their adiabatic compression temperature is not very high. Under pulse conditions, the degradation yield passes through a maximum a t lower intensities with decreasing pulse length as observed for the iodine yield. However, the comparison between the two yields again shows that polymer degradation is favored at high intensities. In Figure 5, a comparison is made between the two processes by plotting the reduced rates as functions of pulse length for two on/off ratios, keeping the hf power at 25 W. The yields decrease more rapidly with decreasing pulse length as the on/off ratio decreases. In both cases, however, the decrease of the polymer degradation is less pronounced than that of the iodine oxidation. It is concluded that the yield of polymer degradation depends less critically on the formation of gas bubbles during the pulse and their disappearance in the interval than the yield of iodide oxidation. The present conclusions point in the same direction as the previous ones which were drawn from the observation of the dependence of degradation yield on the nature of the gas in the cavitation bubble^.^ As already mentioned in the Introduction, the nature of the gas was found to have little influence, although the compression temperatures were quite different for the various gases used. This shows again that high temperatures are not required to generate effective shear forces in the vicinity of cavitation bubbles, which cause main-chain scission in dissolved macromolecules. 20-kHz Horn Experiments. The intensities produced by the horn were much greater than in the above 1-MHz quartz experiments. In fact, the lowest intensity of the horn was roughly the same as the highest one in the experiments with the quartz transducer. However, the effects of the two kinds of sonication cannot be compared by simply regarding the intensities involved. In the case of the 1-MHz irradiation, a field of standing waves is readily formed in the irradiation liquid, the dimensions of which were greater than half a wavelength. It is well-known from luminescence experiments that the chemical action of ultrasound having intensities of only a few W/cm2 mainly occurs in the antinodes of pressure in the standing wave field. In the case of audible sound this effect can also be seen if the length of the irradiated liquid is matched to the wavelength of the sound.la However, in experiments with the horn in the 20-40 kHz range, one usually does not attempt this matching. At the high sound intensities involved in horn irradiations, good yields are also obtained under unmatched conditions. Under these conditions, there is strong coalescence of the cavitation bubbles, Le., conditions exist which are similar to the ones at the highest intensities between 2 and 3 W/cm2 applied in the 1-Mhz quartz irradiation experiments (Figure 3). Figure 6 shows the yield of iodine formation and the specific degradation rate, kdo,as functions of the 20-kHz sound intensity. In both cases, the yield increases the same way with intensity. The M-I, i.e., even greater ratio kdO/rateof I2 formation is 5 X than in the 1-MHz experiments of Figures 3 and 4. Thus, it is again found that polymer degradation is very much favored under
J . Phys. Chem. 1990, 94, 5172-5179
5172
irradiation conditions are the most favorable ones to minimize free-radical side effects. Under the horn conditions, mechanical destruction of large structures is by far the favored process, oxidations occurring relatively seldom as compared to irradiations with higher frequency ultrasound.
intensity Iwatts/cm21
Figure 6 . Sonication of a solution containing both KI and poly(acry1amide) with 20-kHz ultrasound of a commercial horn. Yield of I, formation and specific rate of degradation, kdo, as functions of sound in-
tensity. sonication conditions where the gas bubbles coalesce. The sonication conditions in Figure 6 were comparable to what is usually the case in the application of commercial horns to degrade large structures mechanically, such as in the destruction of cell membranes and the formation of vesicles in certain tenside solutions. In these experiments, a certain number of free radicals, which may oxidize the structures or may form Hz02,is generated; this could be a disturbing factor in subsequent experiments with the biological material. Our experiments show that the horn
Final Remarks Although the theories about the mechanical degradation of polymers’ and cavitation* are well developed, there has never been a theoretical prediction as to the relation between the temperature in the cavitation bubbles and the mechanical shear forces produced by the cavitation bubbles. On the basis of the existing theories one could not expect to encounter the effects, which are described in the present paper, i.e., vastly different dependencies of freeradical reactions and mechanical degradation on the intensity of the ultrasound and the nature of the cavitation gas. Our findings may perhaps contribute to the exploration of the effects from the point of view of the current theories. Acknowledgment. We gratefully acknowledge the assistance by Mrs. H. Pohl and Mr. A. Maulitz. Registry No. Poly(acrylamide), 9003-05-8; potassium iodide, 768 111-0. (7) See, for
example: Basedow, A. M.; Ebert, K. H. Adc. Polym. Sci.
1977, 22. 83.
Extraction of Polymer Properties from Oligomer Calculations C.X.Cui,+ Miklos Kertesz,*,t and Y . Jiang’ Department of Chemistry, Georgetown University, Washington, D.C. 20057 (Received: August 17, 1989; In Final Form: January 22, 1990)
Relationships between the electronic structures of oligomers and polymers are discussed. On the basis of these relationships, the band structures, energetics, and geometries of polyacetylene, polyethylene, polyyne, and polyphenylene have been extracted from the calculations on octatetraene, butane, octatetrayne, and tetraphenylene, respectively, and are generally in agreement with those calculated by energy band theory on the basis of periodic boundary conditions. The total energies per repeat unit of the above polymers can reach the accuracy of 0.1 kcal/mol for tetramer calculations. A derivation of the corresponding finite difference method is given. A new process is proposed, which determines the k vector of a polymeric orbital corresponding to a molecular orbital of an oligomer in an optimal and unique way. The effect of terminal group on the oligomer is analyzed, and the limitations of the oligomer approach for the case of systems with more than one alternative ground state are also pointed out.
Introduction When studying the properties of polymers, one might start to build up the polymer from monomers, dimers, and so on1,*while one also wants to make a connection between clusters (molecular orbitals) and solids (crystal orbital and energy band theory).2 It has been known that many chemical and physical properties of polymers can be extracted from the experimental and theoretical results on the corresponding oligomers, and therefore some intrinsic reltionships between oligomer and polymer should e x i ~ t . ’ , ~ - ~ Concerning theoretical calculations of the electronic structures of solids and clusters, some researchers have tried to use the cluster approach instead of band theory by looking at the solid as a large and, conversely, others have taken the energy band of a solid as a starting point for cluster calculation^.^ The latter approach is based on the similarity of Wannier’s functions and
’
Permanent address: Institute of Theoretical Chemistry, Jilin University, Changchun, PRC. ‘Camille and Henry Dreyfus Teacher-Scholar. 1984-1 989.
0022-3654/90/2094-5 I 72$02.50/0
molecular orbital^.^,' Although it seems that the two groups try to establish two different approaches, both have to deal with the same problem, that is, the relationships between finite and infinite systems. The first step toward the understanding of the above relationships might be to find out how the energy levels of oligomers are related to the energy bands. However, relatively less attention (I)(a) Hoffmann, R. Angew. Chem., Int. Ed. Eng. 1987, 29, 871. (b) Baetzold, R. C.: Hamilton, J. F. Prog. Solid State Chem. 1984, 15, 1 . (c)
Kertesz, M. Adu. Quantum Chem. 1982, 15, 161. (2) (a) Proceedings of Third International Meeting on Small Particles and Inorganic Clusters; Benneman, K. H., Koutecky, J., Eds.; Surf. Sci. 1985, 156. (b) Messmer, R. P. SurJ Sci. 1981, 106, 225. (c) Gavezzotti, A,; Simonetta, M. Ado. Quantum Chem. 1980, 12, 103. (d) Messmer, R. P. In The Nature ofthesurface Chemical Bond Rhodin, T. N.. Ertl, G . , Eds.; North-Holland: Amsterdam, 1979. (e) Messmer, R. P. In Semiempirical Methods in Electronic Structure Calculation Part B Application; Segal, G . A,, Ed.; Plenum: New York, 1977. (f) Burdett, J . K. In Strucrure and Bonding in Crysral; O’Keefe, M., Navrotsky, A,. Eds.; Academic: New York. I98 1 ; Vol. I , p 264 ff. (g) Koutecky, J . Chem. Rec. 1986. 86, 539.
C 1990 American Chemical Society
