J. Phys. Chem. 1987, 91, 3041-3047
304 1
Polymerization of Styrene Initiated by Ultrasonic Cavitation P. Kruus,* D. McDonald, and T. J. Patraboy Department of Chemistry, Carleton University, Ottawa, Ontario K l S 5B6, Canada (Received: February 19, 1986; In Final Form: January 21, 1987)
The polymerization rate of styrene as initiated by intense ultrasound has been studied as a function of temperature and reaction medium. The initiation rate varies only slightly with the bulk temperature down to 48 OC. Below this temperature, the polymerization rate drops significantly, and colored compounds with structures based on dimers and trimers of styrene are increasingly observed. This latter reaction has a mechanism which results in an apparent negative activation energy when bulk temperature is considered. The addition of a high vapor pressure hydrocarbon liquid increases the initiation rate and suppresses the formation of the colored compounds. The results are consistent with previous experiments on the darkening of other aromatic liquids and the polymerization of methyl methacrylate. They can be explained on the basis of a model describing the collapse of cavitation bubbles and subsequent chemical reactions.
Introduction The initiation of polymerization in styrene monomer by intense ultrasound was reported in 1983.' Subsequent studies2 indicated that, at lower temperatures, the application of intense ultrasound to styrene monomer resulted preferentially in the formation of colored compounds (CCs) rather than polystyrene. The appearance of CCs had been noted earlier in studies of nitrobenzene3 and other aromatic compound^.^ The addition of hexane to the styrene monomer resulted, however, in the formation of more ~ no quantitative explanation of these polymer and less C C S , but effects had been possible. A model of the initiation of the polymerization with ultrasound was developed from the results of experiments using pure methyl m e t h a ~ r y l a t e . ~Further experiments were initiated on styrene in order to obtain quantitative relations for this rate and thus to test the more general validity of this model. The experiments were also broadened in scope to include systems other than pure monomer. A number of additives under a variety of conditions were used in order to try to find optimum conditions for the formation of polystyrene and to understand the reasons behind the appearance of CCs. Experimental Section Reagents. Styrene monomer (Dow Chemical Canada, 99.4%) was purified either by vacuum distillation ( 8 5 Torr at 65 OC) or by passing it through a commercially prepared column (Scientific Polymer DTR-7) in order to remove the inhibitor (p-tert-butylcatechol, 12 to 50 ppm). Prior to both treatments the monomer was dried over anhydrous sodium sulfate for 30 min. Samples passed through the column were also degassed under vacuum for about 5 min. Purified monomer was used immediately without atmospheric exposure. The method used to purify the monomer had no noticeable effect on the rates of polymerization obtained. Hence no further checks were made on the purity of the styrene monomer. Linde prepurified grade argon and ultrahigh purity grade (U.H.P.) nitrogen were passed through an oxygen scavenger (Fisher-Ridox R-30) prior to their use. The following chemicals were used as the hydrocarbon additives: reagent grade n-hexane (Fisher H-301), n-heptane (Fisher H-350), n-octane (Fisher 0-3980), n-nonane (Fisher 0-0953), n-hexadecane (0-3035), toluene (Fisher T-289),cyclohexane (Fisher C-55 2 ) , mesitylene (Eastman), 1,7-0ctadiene (Aldrich 0-0250-l), and (1) Kruus, P. Ultrasonics 1983, 201. (2) Dupont, L. A.; Kruus,P.; Patraboy, T. J. In Ultrasonics International 83; Butterworth: London, 1983; p 502. (3) Donaldson, D. J.; Farrington, M. D.; Kruus, P. J . Phys. Chem. 1979, 83, 3 130. (4)Diedrich, G.K.;Kruus,P.; Rachlis, L. M. Can. J . Chem. 1972, 50,
1743. (5) Kruus, P.; Patraboy, T. J. J. Phys. Chem. 1985, 89, 3379.
0022-3654/87/209 1-3041$01.50/0
isopropylcyclohexane (Aldrich 1-2,190-4). These chemicals were degassed by at least two freeze-pump-thaw cycles prior to use. Samples were brought back to atmospheric pressure by using U.H.P. grade nitrogen. Reagent grade naphthalene (Record Chemical) was used without further treatment. Reagent grade cyclohexene (Eastman 1043) was first washed with distilled water to remove the sodium hydroxide inhibitor. It was then dried with sodium sulfate and treated in the same fashion as the other hydrocarbon additives. The ethylbenzene (Aldrich E-1,250-8) used was 99% pure. It was further purified by vacuum distillation at 100 Torr and 74
OC. Apparatus and Methods. The apparatus and methods for ultrasonic irradiation used in these experiments were essentially the same as those described in ref 5. The total volume of liquid used at the start of an experimental run was from 0.2 to 0.4 L. An argon flow rate of at least 0.15 L m i d was found to be necessary in order to get reproducible results. Lower gas flow rates made the cavitation noise harsher and louder, and resulted in less polystyrene and more CC formation. The temperature was monitored by a thermocouple in a well in the reaction vessel. After the first few minutes of a run, the temperature could be controlled to within f0.5" from the highest temperatures down to 14 O C , and to f2O a t the very lowest. Polymerizations in neat styrene were carried out as previously described5 at an acoustic intensity of 21 f 1 W cm-2 (60 W total). The intensity was checked regularly by cavitating a sample of liquid in a Dewar flask and recording the temperature as a function of time. A check on the intensity was also carried out on styrene and ethylbenzene at lower temperatures to ensure that increases in viscosity did not affect the intensity of ultrasound introduced. The power delivered remained the same at these lower (down to -25 "C) temperatures. A weighed portion (approximately 3 g) of the sample, which was removed to follow the course of the polymerization, was analyzed for its absorbance (vs. a neat styrene reference) at several wavelengths between 308 and 315 nm. The remainder of the sample (approximately 6 to 10 g) was injected into a 20-fold excess of methanol. The precipitated polymer was then filtered, dried, and weighed. For polymerizations with hydrocarbon additives, a weighed amount of the additive was added to a known mass of styrene. Vigorous bubbling of argon provided adequate mixing of monomer and additive before the reaction was started. In these experiments, the absorbance analysis was done vs. a sample of the mixture withdrawn before the insonation was started. The procedure followed for these experiments was otherwise identical with that followed for the neat polymerization. One such experiment took about 4 h to carry out, 8 h when inhibitors were removed by distillation rather than chromatography. Ultrasonic irradiation of ethylbenzene was carried out at five temperatures between -15 and 45 "C, and the rate of darkening as measured by the maximum absorbance in the range 310 to 325 0 1987 American Chemical Society
3042 The Journal of Physical Chemistry, Vol. 91, No. 11, I987
Kruus et al.
TABLE I: Data from Irradiation of Styrene with Intense Ultrasound run no.
1-4 5
6 I 8 9-12 13-14 15 16 17 18 19 20 21 22 23 24 25 26 21 28
29 30 31 32 33 34 35
additive none none none none none none noneh none none n-hexane n-hexane n-hexane n-heptane n-octane n-nonane n-hexadecane n-hexadecane cyclohexane cyclohexane cyclohexane cyclohexane ipchJ ipc' 1,7-0ctadiene cyclohexane toluene naphthalene mesitylene
xa 0.0 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.066 0.088 0.125 0.226 0.238 0.205 0.062 0.152 0.018 0.032 0.065 0.104 0.050 0.285 0.152 0.102 0.419 0.051 0.099
Tbb
61.4 57.8 53.2 48.2 45.6 42.0 42.0 34.0 14.5 42.0 42.0 34.0 42.0 53.2 59.0 42.0 61.4 42.0 42.0 42.0
42.0 42.0 42.0 53.2 42.0 42.0 59.0 59.0
p,'
40.9 34.7 27.9 21.8 19.1 15.9 15.9 10.3 3.1 37.1 44.2 50.5 46.5 42.5 39.0 15.0 35.8 22.2 27.1 38.6 52.2 15.8 15.1 36.3 39.5 36.7 35.0 34.9
PIP
R,C
Rdf
0.122 0.105 0.086 0.068 0.060 0.051 0.051 0.0335 0.0108 0.118 0.140 0.164 0.148 0.130 0.117 0.048 0.108 0.070 0.086 0.123 0.166 0.050 0.048 0.111 0.125 0.117 0.105 0.105
16.5 15.1 11.7 9.9 6.7 5.0 5.0 2.30 0.61 9.4 10.0 6.1 8.1
1.15 1 .oo 1.20 1.66 2.13 2.35 2.23 2.91 4.20 0.93 0.66 0.40 0.32 0.27 0.36 2.64 0.60 1.63 1.24 0.70 0.51 1.86 1.63 0.69 1.03 1.50 0.66 1.14
10.0
1.4 3.78 5.1 7.3 9.3 9.1 9.5 5.3 5.9 1.2 7.9 6.8 14.7 15.4
Rid 5.6 6.0 4.78 4.71 2.56 1.85 1.83 0.66 0.28 6.4 7.2 4.78 4.82 3.48 3.21 1.04 4.82 3.92 6.3 6.0 6.6 2.05 2.57 4.43 4.59 3.33 5.3 5.9
Mole fraction of additive. bTemperature in Celsius, f0.5 OC. CTotalvapor pressure in Torr, f6%. dVapor pressureftemperature. CPolymmol s-l). *Monomer vacuum distilled. erization rate (IO-' L1l2s-I), 16%. fDarkening rate at 312 nm (lo4 L'/2 s-I), *4%. 8Initiation rate Isopropylcyclohexane.
nm was determined. For the run at 45 "C, the ethylbenzene was evaporated off the solution which had been irradiated for 6 h. The mass of the remaining dark, high molecular weight material remaining was then determined in order to get an estimate of the absolute rate of formation of the CCs. Some UV/visible spectral studies were carried out on colored compounds. Runs were carried out on pure styrene at -10 OC for 60 min and at -25 OC for 35 min. At these bulk temperatures essentially no polymer was formed. After irradiation, the styrene was removed by low-temperature vacuum distillation and the nonvolatile product dissolved in ethylbenzene. These solutions were then spotted on preparative thin layer chromatography plates precoated with aluminum oxide. The plates were subsequently developed in the dark by a two-dimensional process. Initially, a mixture of 20:l hexane:methanol was used. The plates were then rotated to 90' and developed with either a 4:4:1 diethyl ether: methano1:water mixture or a 1:l acetonitri1e:diethylether mixture. Several bands were observed on the plates upon examination under long-wavelength UV light. These spots were removed and eluted with either Caledon Spectral grade methanol or Fisher C-552 cyclohexane. The UV and fluorescence spectra of these spots were then recorded on a PE 202 UV/visible spectrophotometer and a PE 204-S fluorescence spectrophotometer. Molecular weight determinations of polymer samples were done at the National Research Council Polymer Laboratory by gel permeation chromatography using 2 wt % solutions in tetrahydrofuran and a column packed with micro-Styragel. Some preliminary studies of the molecular weight distribution of the colored compounds were also carried out with GPC at the Canadian Customs Laboratories, Consumer and Corporate Affairs, Canada. The solvent used was again tetrahydrofuran; the method used is described in detail in ref 10. Densities of several of the liquid mixtures were determined at room temperature with an Anton Paar densitometer. Vapor pressures were determined for many of the solutions at several controlled temperatures with an available liquid-vapor equilibrium apparatw6 (6)Kruus, P.;Hayes, A. C. Can. J. Chem. 1985.63, 3403.
Results Densities and Vapor Pressures. In treatment of the primary experimental data, knowledge of the density and the vapor pressure is required. Densities of pure materials were taken from ref 7-9. Where data did not exist at the temperatures used in this work, values at 20 or 25 O C were used. This would have only a small effect on the accuracy of the resulting value for the mixture since temperatures were not far from 25 OC, and since additives where data did not exist at the temperature of the experiment were present in small amounts (less than 5%). Densities of mixtures were calculated by assuming ideal mixing. This assumption was tested by experimentally determining the densities of eight of the solutions (runs 19-22,24, 28, 30, and 33 in Table I.) In no case was the deviation from ideality greater than 5%. Vapor pressures of mixtures were calculated by using van Laar solubility parameters." The data for pure materials at various temperatures were obtained from ref 12. For mixtures which are expected to follow the van Laar theory poorly,I3 the vapor pressure was determined experimentally at the appropriate temperature (runs 19-22 and 28). The Margules equation was used to obtain the vapor pressures for runs 17 and 18 from the data for run 19, and for runs 25-27 from the data for run 28. Calculation of Conversions. Conversions for neat polymerizations were calculated as beforee5 When a hydrocarbon was added, conversions were corrected for the presence of the additive as follows: cor = P/(S@rn) (1) (7)West, C. J.; Hull, C . International Critical Tables; McGraw-Hill: New York, 1933. (8). Weast, W. C., Ed. Handbook of Chemistry and Physics, 57th ed; Chemical Rubber Co.: Cleveland, 1976. (9) Boundy, R. H.,Boyer, R. F., Eds Styrene: Its Polymers, Copolymers and Derivatives; Inhold: New York, 1952;p 54. (10) Taymaz, K.J . Liq. Chromatog., accepted for publication. (1 I ) Hildebrand, J. H.; Scott, R. L. The Solubility of Nonelectrolytes, 3rd ed; Dover: New York, 1964. (12)Boublek, T.;Fried, V.; Hala, E. The Vapour Pressures of Pure Substances; Elsevier: New York, 1973. (13) Weber, H. C.; Meissner, H. P. Thermodynamics for Chemical Engineers, 2nd d ; Wiley: New York, 1957.
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987 3043
Ultrasound-Initiated Polymerization of Styrene
r
0
I
0
r
/
I 20
I
I
I
40
I 60
L
I
L
80
0
I
I
I
I
I
40
20
0
Time I min
I
I
60
80
I
Time / min
Figure 1. Corrected conversion (polymerization) vs. time for run 9 in Table I.
Figure 2. Corrected absorbance at 312 nm vs. time for run 9 in Table I.
where +,, is the weight fraction of monomer in the mixture, P the weight of precipitated polymer collected on a fine porosity glass frit, and S the weight of sample removed and injected into methanol (approximately 6 to 10 g). A correction for the liquid volume which was irradiated was required since sampling reduced the volume by up to 40% over the course of a run. The correction was applied by using a reciprocal square root volume dependence as in ref 5. The calculated density and total weight at a given time were used to calculate the liquid volume at that time. The total sample weights removed were used for correction purposes although only a part of the sample was actually precipitated. In order to check the volume dependence, two series of experiments (at two temperatures) were carried out with identical acoustic intensity (21 W cm-2) in neat styrene, but with different monomer volumes. Plots of uncorrected conversion vs. time were linear, with correlation coefficients better than 0.99. A plot of the logarithm of the slopes of these plots vs. the logarithm of the average monomer volume for data at 42 OC (runs 9-14) has a slope of -0.3 f 0.1, while that for 61.4 O C (runs 1-4) has a slope of -0.5 f 0.1. This suggests that the expected reciprocal square root volume dependence used in the correction is reasonable. A typical plot of the corrected conversion vs. time is given in Figure 1. The slopes of such plots yield the overall polymerization rates listed in Table I for all the experiments. The reproducibility of six runs with identical conditions (rups 9-14) is within 5.4%, and for runs 1-4 within 3.7%. The accuracy of the polymerization rates listed is thus estimated to be better than 6%. Absorbance Calculations. The absorbance at 312 nm was used for all rate calculations. When a hydrocarbon was added, the observed absorbance was corrected for the dilution effect of the additive. This correction was applied as follows:
Wavelength 1 nm
A series of experiments were performed using neat styrene at 42 O C and an acoustic intensity of 21 W cm-2, and different monomer volumes. Plots of the absorbance vs. insonation time were linear with correlation coefficients better than 0.99. A plot of the logarithm of the slopes of such plots vs. the logarithm of the average monomer volume present during the insonation has a slope of -0.41 f 0.01. This again indicates a reciprocal square root dependence; the volume correction method was thus identical with that used for the conversion studies. The plots obtained (see Figure 2 for a sample plot) were all linear. Points at t = 0 were not considered in calculating the slopes, as it took of the order of 5 min for the temperature to stabilize. The rates obtained from such plots are given in Table I. The reproducibility in the darkening rate of five runs with identical conditions is 3.3%. The accuracy of the rates listed in Table I is thus taken to be *4%. This is somewhat better than
,
280W
,
,
I
30000
/
,
I
I
Wave number
I
I
,
I
40000
35000
I
42000
1 cm-’
Figure 3. Fluorescence intensity and absorbance for 1,l-diphenylethyleneI5 (-) compared to those for a spot from the TLC of the colored compound obtained on ultrasonic irradiation of styrene (- - -). Exciting wavelength 265 nm in cyclohexane solution.
the 6% reproducibility obtained in experiments on the darkening of nitr~benzene.~ The absolute rate of formation of CCs for ethylbenzene was determined from the mass of the residue (1.83 g of a dark brown liquid with specks of black solid) from a 6-h run to be 8 X lo-’ mol of ethylbenzene s-’. Ethylbenzene rather than styrene was used for this determination in order to avoid the presence of any polystyrene in the residue left after evaporation. Recent experimental data on the pyrolysis of ethylbenzene is also a~ai1able.l~ Molecular Weights. Molecular weight determinations were carried out for the polymers obtained from nine of the runs listed in Table I. No dramatic trends were noted. The highest molecular weight noted was for run 1 (number average 225000, weight average 455000) and the lowest for run 9 (number average 126000, weight average 186 000). The polymers from the other runs tested had values intermediate to these (runs 6, 18, 19, 21, 26, 28, and 32). In the case of the low-temperature runs, where the product was primarily CCs, a number of peaks were observed in the region where dimers and trimers of styrenes would be expected. Analysis of UVI Visible and Fluorescence Spectra. The UV/visible spectra obtained in these runs did not alter noticeably as the reaction proceeded. They exhibited a maximum in the 3 10-320-nm range with a long tail extending into the visible region. (14) Robaugh, D. A.; Tsang, W.; Fahr, A,; Stein, S . E. Ber. Bunsen-Ges.
Phys. Chem. 1986, 9 0 , l l .
3044
Kruus et al.
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987
0
/” /
I ’ 0
I
I .04
I
I
I
.08
1 .12
I
I .16
L
pv Tb -1 / Torr K-l Figure 4. Logarithm of the concentration-correctedinitiation rate vs. vapor pressure/bulk temperature. The numbers refer to runs in Table I: methyl methacrylate points from ref 6 ; ( 0 )runs with pure styrene.
The spectrum for styrene is quite similar to those obtained for other aromatic compounds in previous ~ o r k . ~This , ~ , type ~ of spectrum is characteristic of polystyrene that has degraded by a thermal or a radiative process in the absence of 0 x ~ g e n . l ~ One of the thin layer chromatography spots (RFvalue of 0.26) was isolated and identified by UV and fluorescence spectroscopy as diphenylethylene (Figure 3).16 Another spot from the second plate gave spectra closely resembling those of 1,4- or 1,3-diphenyl-1 ,3-butadiene.I7
Discussion Calculation of Initiation Rates. The initiation rates Ri, listed in Table I were calculated from the experimental data for the rate of conversion, together with values for the termination and propagation rate constants taken from ref 18. The equation used to obtain the propagation and termination rate constants is In [kp/(2kt)1/2]= -3344.1/T + 6.16505 (3) The consistency of this relationship can be checked with a knowledge of a set of molecular weights by solving two equations with two unknowns. Using chain-transfer rate coefficients from EastmondI8 and data from runs 28 and 32, we obtained a value of kp/(2kt)1/2which agrees with that predicted by eq 3. This is, however, not possible for any set of two of the molecular weights determined, especially for cases where considerable CC formation (15) Hirt, R. C.; Searle, N. Z . Preprint SPE RETEC, Washington, DC, 1964. (Reproduced by Savides, C., et ai. In Stabilization of Polymers and Stabilizer Processes, Gould, R. F., Ed.; American Chemical Society: Washington, DC, 1986, Adv. Chem. Ser. No. 85.) (16) Berlman, I. B. Handbook of Fluorescence Spectra of Aromatic Molecules, 2nd e& Academic: New York, 1971. (17) Fox, R. B.; Price, T. R. In Stabilization and Degradation of Polymers, Allara, D . L., Hawkins, W. L., Eds.; 1978; Adv. Chem. Ser. No. 169. (18) Eastmond, G. C., Ed. Comprehensive Chemical Kinetics, Vol. 14a, Bamford, C. H., Tripper, C. F. H., Eds.; Elsevier: New York, 1976; pp 150-160.
(0)
was noted. A more complicated situation than simply normal chain-transfer reactions must therefore be involved in these cavitation-induced polymerizations. According to the model proposed in ref 5, the initiation rate Rin is given by
The meanings of the individual terms are given in ref 5. In this discussion, the assumed linear dependence of R,, with [Mol can be tested, since solutions rather than pure monomer were often used. A number of runs (12 in all) were made with solutions where, according to Raoult’s law, the vapor pressure was about 35 Torr. It was anticipated that the vapor pressure, rather than the bulk temperature, would keep the other factors in eq 4 constant (see next section). A correlation of In Rmvs. In [MI, for these 12 runs gives a slope of 1.2 f 0.3, while the value expected from eq 4 is 1. There are several assumptions made in this analysis. The assumption of ideal mixing in calculating styrene concentration would produce errors which are relatively small. However, subsequent measurements of vapor pressure showed that deviations from Raoult’s law are as great as 30%, although in most cases they are within 10%. In view of this, and a number of complicating effects introduced by the hydrocarbon additives (surface tension, chain transfer, possible chemical effects, etc.), the agreement with the predicted concentration dependence is good. Thus Figures 4 and 5 were drawn with Rin/[MIoand & / [ M I o as ordinates. TemperatureDependence. In such cavitation experiments, there are two different temperatures which must be considered. One is the bulk temperature (Tb),which is listed in Table I for this series of experiments. It is the proper temperature to consider for reactions taking place in the liquid phase, e.g. propagation and termination. The other temperature of importance is the temperature achieved on the collapse of cavitation bubbles (T,). It can reach
Ultrasound-Initiated Polymerization of Styrene
The Journal of Physical Chemistry, Vol. 91, No. 11, 1987 3045
t
-3.
0
.04
.08
Pv Tb-’
.12
-16
/ T o r r K-l
Figure 5. Logarithm of the concentration-correcteddarkening rate vs. vapor pressure/bulk temperature. The numbers refer to runs in Table I: runs with pure ethylbenzene; ( 0 )runs with pure styrene.
well over 1000 K in ultrasonic ~ a v i t a t i 0 n . l ~An estimate of Tc can be made by assuming either reversible (eq 5 ) or irreversible (eq 6 ) adiabatic collapse:5
Here P, is the vapor pressure in the cavity at the start of the collapse. It is assumed to be the equilibrium vapor pressure at Tb, but it is likely that the cavity also contains some argon from the microbubble which most probably was the nucleus for the cavity. The pressure Pa is the acoustic pressure a t the initiation of collapse, and P , the pressure at the end of the collapse, C, the heat capacity of the gas in the bubble, and g the ratio of specific heats. Since (g - 1 ) is for a vapor of styrene approximated well by R/C,,then these two equations differ in essence only through the factors Pa and P,. The temperature Tc is the more meaningful temperature to consider for reactions taking place in the collapsing cavitation bubble, i.e. gas-phase reactions. It is of course not a true thermodynamic temperature and can be estimated only very approximately through eq 5 and 6 . Activation energies based on Tccan be estimated from plots of the logarithm of the appropriate rate. vs. l / T c . In eq 6 , R is a constant, P , is likely to vary little with conditions, and C, varies relatively little as compared to P,. Figures 4 and 5, where the abscissa is P,/Tb, are thus, in essence, Arrhenius plots for reactions occurring in the collapsing cavity, from which activation energies can be obtained. It is noteworthy in Figure 4 that the initiation reaction is relatively independent of the chemical nature of the added hydrocarbon; the effect of vapor pressure predominates, as anticipated from previous experiment^.^ In the case of the darkening reaction (Figure 5 ) , chemical effects are more important. Two of the points lying above the pure styrene data (33 and 35) are (19) Fitzgerald, M. E.; Griffing, V.;Sullivan, J. J . Chem. Phys. 1956, 25, 926.
(0)
both for the case of aromatic additives, toluene and mesitylene, which are expected to darken by themselves. For the case of ethylbenzene, an absolute scale for the darkening can be obtained by noting that the absolute rate for the highest vapor pressure point is 8 X lo-’ mol s-’. In comparison, the initiation rates obtained are of the order of mol s-I. The specific absorbance of the styrene CC is likely to be similar to, but not identical with, that from ethylbenzene. This absolute rate of CC formation is of the same order of magnitude as that calculated from experiments reported in 1972,4 if those data are converted to the ultrasonic intensities used here (60 W acoustic here as compared to 6 W in 1972). For toluene, the absolute rate of CC formation was calculated to be 4 X mol of toluene s-’ by using those data. A wide variation of the specific absorbances of the CCs from different aromatic compounds was noted in ref 4 . No consideration has been made in Figure 5 for the dilution of styrene in the vapor phase. A plot of the darkening rate vs. the vapor composition, i.e. the partial pressure of styrene, for the 11 runs near 35 Torr total pressure shows IH)significant correlation. However, when plotted vs. mol fraction of styrene in the liquid, a correlation coefficient of 0.86 is obtained. This suggests that the “gas phase” reactions involve the liquid as well. This might be expected, as at the end of the cavity collapse, when the temperature is highest, the cavity is at its smallest. The liquid at the cavity surface would then have considerable effect on such reactions. Activation Energies. For the initiation reaction, two sets of activation energies can thus be estimated from Figures 4 and 6 . If a gas-phase reaction is assumed, E , is from Figure 4 about -1 kJ mol-’ for higher values of Pv/ Tb(Tb> 48 “C) and -27 kJ mol-’ for lower. These values are calculated by assuming a value of 123 J K-’ mol-’ for C,,and Pa = P, = 760 Torr. Even the relative values have a large degree of uncertainty, as the models on which they are based are not well refined. The variation of C,is relatively small when compared to the variation in P, and the accuracy of the model, and has thus been assumed constant. The value of
3046 The Journal of Physical Chemistry, Vol. 91, No. 11, 1987
1.1
1 2.9
I
I 3.1
Tb-l
,
I
10-3 .(-I
I
I
I 3.1
3.3
Figure 6. Arrhenius plots of Rh and Rd vs. the bulk temperature Tbfor runs with pure styrene. Data from runs 1-16 in Table I. shows the limits of uncertainty.
+
E, obtained from such an analysis is proportional to the value of P, chosen. As indicated in the discussion in the next section, this can be of the order of 10 atm or even greater. The activation energies for polymerization initiation in the liquid phase would from the data shown in Figure 6 be 100 kJ mol-' for Tb < 48 ' c and 12 kJ mol-' for Tb > 48 'c. The lowest temperature point was not considered in calculating these activation energies, as it was at the limit of detection of the polymer. These latter activation energies are the ones which seem more meaningful, i.e. the initiation reaction is probably controlled by steps occurring in the liquid. For the darkening reaction, = +6 kJ mol-', and Ea~iquid = -25 kJ mol-' after Figures 5 and 6. In this case, it is likely that the reaction occurs primarily in the gaseous phase. As indicated before, these activation energies are proportional to the value assumed for P,, and this could be at least an order of magnitude greater than the value of 1 atm assumed in the above calculations. Conditions on Collapse of Cavitation Bubbles. In the activation energy calculations above, P, was taken to be 1 atm. An estimate of the pressures attained in such a collapse can be obtained if data from the pyrolysis reactions of aromatic hydrocarbons is utilized. There seems to be good evidence from shock-tube and pyrolysis studies of aromatic hydrocarbons that the formation of soot in such reactions increases in the temperature range 1O2O2Oto 1800 K,2',22but then decreases. A high temperature is needed for the removal of the hydrogen (breaking of C-H bonds) which is responsible for the appearance of the soot. In the shock tube pyrolysis of ethylbenzene, this does not seem to occur until at least 1600 K.I4 The conditions in the reactions in the collapsing cavity resemble such shock tube experiments but are quite different from those in ordinary pyrolysis in that the cavity collapse occurs in a very short time, of the order of microseconds. Substituting these temperature values into eq 6 gives a range of 1.4 to 2.5 atm for P,. This means that the values of E , for the gaseous reactions given in the previous section should be magnified by a factor of the order of 2. At higher values of Pv/Tb, the value of T , would be less than 1000 K, and little darkening would be expected (see Figure 4). An eventual decrease in the darkening rate as T, increases above 1800 K is also observed here, as indicated by the ethylbenzene data. When Pv/Tb is 0.01 and P,,, is taken to be 2 atm, then the value of T , is estimated from the above to be close to 1800 K. The decrease in darkening rate at values of Pv/Tbless than 0.01 Torr K-' is thus consistent with the shock-tube and pyrolysis experiments. A pressure of this magnitude at the collapse of a cavitation bubble is of the correct order of magnitude, but i t - a n d therefore the Earns values-muld be considerably different. For example, (20) Brooks,C. T.; Peacock, S . J. J . Chem. SOC.,Faraday Trans. 1 1979,
Kruus et al. the value of P, could be either less than the equilibrium value assumed due to inadequate time for such equilibration during the bubble growth stage, or it could be larger, due to the presence of the gas (argon in most cases) present in the nucleation center around which the cavitation bubble developed. The values of T, and P, obtained by the above analysis are less than those obtained by S ~ s l i c k . ~The ~ conditions for the experiments may, however, be quite different. In those reported here, the presence of a sufficient flow of argon gas seems to be necessary for reproducible results. Lack of sufficient gas alters the reaction to one resembling one at a lower bulk temperature. This strongly suggests that the presence of the argon moderates the conditions in the collapse of the cavity in cases where polymerization is initiated. Possible Reaction Mechanism. Both of the reactions observed here have been observed previously. The results of the polymerization initiation are quite consistent with the results obtained with methyl methacrylateS (see, e.g., Figure 4). The activation energy obtained for the effective initiation reaction is low for both polymerization systems, of the order of 24 kJ mol-'. This is close to the value generally obtained for propagation reactions, 30 kJ mol-'. This seems reasonable, as some form of radical species must already be present from the cavity collapse. In ref 5, the initiation reaction was studied by using the radical scavenger DPPH. The disappearance of DPPH showed an effective negative activation energy considering the bulk temperature, and a value of E, = 8 kJ mol-' considering T, using the same assumptions as here, i.e. P , = 1 atm. Here, the corresponding value obtained is 6 kJ mol-'. This is additional support that the CCs are formed primarily in the gas phase on the collapse of the cavitation bubble, with hydrogen abstraction reactions resembling those in shock-tube pyrolysis. The darkening reaction was studied quite thoroughly by using nitrobenzene, where no high molecular weight polymers are f ~ r m e d .These ~ studies were all done at Tb = 20 'C, with the addition of various diluants to vary P, and Cp in eq 6. The value of E, obtained there with the same assumptions as here was 20 kJ mol-', as compared to 6 kJ mol-' here. These results again give support to the basic tenets of the proposed model. The formation of the CCs occurs actually under conditions quite similar to shock-tube experiments2' In those experiments, which also involve oxygen, the formation of CCs (soot) occurs only in a limited range of temperature, and not below 1000 K to any extent. Activation energies are ill-defined in such experiments. In other, more controlled pyrolysis reactions, the activation energies obtained are much greater than those obtained here. The rate of formation of toluene from the pyrolysis of ethylbenzene had an activation energy of 300 kJ mol-'.24 If the results are scaled up by assuming a value of P , of 10 rather than the factor 2 suggested, the E , obtained here is still less than 100 kJ mol-'. Some experiments suggest, however, that collapse pressures even greater than 100 atm are possible.23 These results suggest that the initial decomposition reaction observed here involves a bimolecular atom exchange type reaction. Such reactions are possible, as there is ample evidence of bimolecular reactions involving styrene.2s Figures 4-6 show that the initiation rate is inversely proportional to the darkening rate. This seems to be proof that the two reactions compete with each other. The simplest mechanism would consist of an initial fragmentation reaction on collapse of the cavity, followed by two competing reactions, formation of CCs and normal polymerization. Such a mechanism can explain the results if the rate constant for formation of CCs has a higher activation energy and a much higher preexponential factor than the rate constant for polymer initiation. Another explanation is that the CCs formed act as scavangers for the radicals which would otherwise initiate the polymerization \
75, 652. (21)
Wang, T. S.; Matula, R. A.; Farmer, R. C. Symp. ( I n t.) Combust.,
[Proc.], 18fh 1981, 1149. (22) Udseth, H. R.; Johnson, A. L.; Smith, R. D. Int. J . Mass Spectrom. Ion. Phys. 1983, 47, 6 3 .
(23) Suslick, K. S. "Organometallic Sonochemistry and Sonocatalysis", presented at the Royal Society of Chemistry Symposium, Warwick, 1986. (24) Davis, H.G. Int. J . Chem. Kine!. 1983, 15, 469. (25) Kopecky, K. R.; Hall, M. C. Can. J . Chem. 1981, 59, 3095.
J. Phys. Chem. 1987,91, 3047-3055 and essentially act as inhibitors. The structures of compounds such as 1,l-diphenylethylene which make up the CCs are similar to radical scavengers and inhibitors such as ptert-butylcatechol. Absolute values for their efficiencies as radical scavengers cannot be reasonably estimated until there is better knowledge of the amounts of the various compounds present in the CCs.
Conclusions The two reactions observed here, darkening and normal polymerization, are the result of radicals formed in the fragmentation of styrene on the collapse of cavitation bubbles. At higher collapse temperatures,,the fragments are similar to those found in pyrolysis and give rise to colored compounds. Thus, the overall mechanism is quite complex. It is possible that it involves two reactions that compete for the products of an initial fragmentation reaction, but it is also possibly due to the inhibiting of the polymerization through radical scavenging by the polyaromatic colored compounds formed. The initial step must involve some bimolecular atom transfer, as the activation energies obtained are too low for a simple bond
3047
cleavage reaction expected in unimolecular gas-phase decomposition. When hydrocarbons are added to the styrene, their main influence on the reaction is not primarily chemical in nature but rather arises mainly from their influence on the vapor pressure. Results obtained in these styrene studies are consistent with previous results on the polymerization of methyl methacrylate and the darkening of nitrobenzene and other aromatic compounds. Acknowledgment. The authors thank Dr. S . Bywater of the National Research Council and Dr. K. Taymaz of Consumer and Corporate Affairs, Canada, for providing gel permeation data, Dr. G. Buchanan and Mr. K. Bourque of Carleton University for N M R data, Dow Chemical Canada Inc. for a supply of styrene monmer, and Dr. M. Goldenberg of CIBA-GEIGY Corp. for the suggestion of using chromatography to remove inhibitors from the monomer. The project was supported financially by the Natural Sciences and Engineering Council of Canada through a grant. Registry No. C6H5CH=CH2, 100-42-5; polystyrene, 9003-53-6.
Molecular Relaxation Dynamics and Structure of LiCiO, Solutions in 2-Methyltetrahydrofuran Heidrun Maaser: Meizhen Xu, Paul Hem",$
and Sergio Petrucci*
Weber Research Institute and Department of Chemistry, Long Island Center, Polytechnic University, Farmingdale, New York I 1 735 (Received: July 1, 1986; In Final Form: October 3, 1986)
Electrical conductance data in the temperature range +25 to -43 O C are reported and interpreted by the Fuoss-Kraus triple-ion theory. Theoretical expressions for the thermodynamicparameters for triple ions A W T and SoT have been derived. Comparison is made between the experimental figures of AW and ASoand the correspondingvalues calculated from the Bjerrum theory of ion pair formation. Comparison is also made between the experimental M O T and SoT and the values now calculated from theory. Both these tests give reasonable estimates of the ion pair separation distance d and of the ion to dipole separation distances a (in the triple ion.) Infrared spectra of the (infrared-active) 8, band of the perchlorate anion in the wavenumber band 550-700 cm-' reveal a complex spectral envelope which can be deconvoluted into three Gaussian-Lorentzian bands. One of them, centered at -625 cm-I, is assigned to the "spectroscopically free" ClO,- ion (that is, to the solvent-separated Li'S, CI04- and/or to the solvent-separated dimer (Li'S, C104--LifS, Clod-) where S is a solvent molecule), the perchlorate ion having Td symmetry. The other bands centered at 639 and 654 cm-' are presumed to be due to contact species, the C104having lower symmetry. The maximum band absorbances have been correlated to the electrolyte concentration by polynomial functions. Ultrasonic relaxation spectra in the concentration range 0.05-0.4M and frequency range 0.5-400 MHz are described by a single Debye relaxation function. Independence of the relaxation frequency on electrolyte concentration for c > 0.1 M and linearity of the maximum excess absorption coefficient of sound per wavelength p,,, on concentration identify the ultrasonic relaxation process as due to a first-order or pseudo-first-order process. The ultrasonic spectra are interpreted by the second step of the dimerization equilibrium 2M Me-M s M2, namely, by the scheme M-M M2 (k2,-2)where M is the monomeric ion pair, M-M a solvent-separateddimer or quadrupole, and M2 a contact dimer. Temperature dependence of the ultrasonic relaxation spectra allows for estimation of activation and thermodynamicparameters of the observed equilibrium. Microwave dielectricrelaxation spectra in the frequency range -0.8-90 GHz and concentration range 0.05-0.3M are interpreted by two Debye relaxation processes at 1.8 and 35 GHz, respectively. The one at lower frequency is attributed to the presence of the solute. Bottcher plots of the lower relaxation strength 4(t) vs. total concentration of electrolyte show a marked concave down curvature, revealing that not all of the electrolyte exists in dipolar form. Since K A E lo* M-I and the concentration of triple ions is small, no appreciable extent of free ions exists in solution as to cause the curvature of the Bottcher plot. The observed phenomenon is interpreted as evidence of the presence of dimer ion pairs or quadrupoles. M-M, the solvent-separated dimers, are the predominant species in solution, and previous theoretical work predicts that the ion pair components can rotate independently of each other. In fact, by approximating (Me-M) E c/2 and plotting the Bottcher relaxation strength function @(e) vs. c/2, one observes an approximately linear correlation.
(1) Delsignore, M.; Maaser, H. E.; Petrucci, S.J . Phys. Chem. 1984,88,
Colgate Palmolive, Piscataway, NJ 08854. *Miles Laboratories, Elkhart, IN 46514.
2405.
(2) Farber, H.; Irish, D. E.; Petrucci, S. J . Phys. Chem. 1983, 87,3515.
0022-3654/87/2091-3047$01.50/0 0 1987 American Chemical Society
