J . Phys. Chem. 1985, 89, 5421-5427 in CDs. By using these values all parameters for the kinetic model can be estimated and they are listed in Table IV. These values for the kinetic parameters seem plausible because the ‘overall” equilibrium constant K has an order of magnitude similar to those reported for complex formation processes with inclusion compounds. The “overall” equilibrium constant calculated here as K = 1/(K43K21)are 6.5 X and 5.9 X for a-and y-CD, respectively. These are similar in order of magnitudes to those reported in the 1iterature.l It is not so surprising that a-CD has positive AV32 value. (The positive value means that an expansion process occurs between states 2 and 3.) According to X-ray studies by Saenger et al.13*15 and by Maclennan et al.,I4 a-CD is strained in its “empty” (uncomplxed hydrated) state and the energy is stored because of hydrogen-bond formation between OH groups of adjacent glucose units. However, ‘empty” /3- and y-CDs are not so strained. Therefore contribution of strain energy is important only for a-CD in complex f~rmation.’~ Taking this into account one may imagine that relieveing the strain energy gives rise volume increase between states 3 and 2. Comment on the Relaxation Process Associated with the Segmental Motion of Polysaccharides. As reported previ~usly,~ aqueous solutions of dextrans showed two ultrasonic relaxation
5421
processes in the megahertz frequency range, but solutions of glucose, maltose, and raffinose showed no relaxations. So, at that stage, we could not clarify the magnitude of the units of segmental motions which gave rise to the relaxation processes in polymer solutions. For the magnitude of the units of segmental motions now we can show that at least 6 glucose units bonded circularly with each other can be responsible for ultrasonic perturbation in the frequency range from 0.8 to 135 MHz. Ultrasonic relaxation spectra of aqueous solutions of a-CD resembles closely those of dextran solutions in relaxation frequencies and amplitudes. This supports our previous argument that the most likely origin of the ultrasonic relaxation process in dextran solutions is the exchange process of hydrated water molecules induced by a segmental motion of polymer chains. The resemblance further suggests that dextran may take on a helical structure consisting of 6 glucose units in solutions as highly hydrated amylose does in the crystalline state.25 Registry No. a-Cyclodextrin, 10016-20-3;8-cyclodextrin, 7585-39-9; y-cyclodextrin, 17465-86-0. (25) J. J. Cael, J. L. Koenig, and J. Blackwell, Carbohyd. Res., 29, 123 (1973).
Flow ESR and Static Studies of the Decomposition of Phenyl-Substituted Ethanes M. J. Manka,t R. L. Brown, and S. E. Stein* Chemical Kinetics Division, Center for Chemical Physics, National Bureau of Standards, Gaithersburg, Maryland 20899 (Received: February 25, 1985)
The thermal decomposition of 1,1,2,2-tetraphenyIethane(DD) was studied in high-temperature fluids by using both sealed tube and flow ESR techniques. In the sealed tube experiments its central C-C bond homolysis rate constant in tetralin solvent was 1015.92f0.13 exp(-(23 910 i 160)/1) S-I (473-550 K). Concentrations of diphenylmethyl radicals in equilibrium with DD were measured by ESR between 648 and 683 K. The equilibrium constant for the dissociation reaction was 106.69’0.66 exp(-(23 770 i 1020)/fl M. Combining this expression with the dissociation rate constant yields a recombination rate constant for diphenylmethyl radicals of 1.5 X lo9 M-’ s-I at 648 K. Bond homolysis of 1,1,2-triphenylethane (BD) was also studied in tetralin. Its rate constant was 1016~18*o.11 exp(-(29080 i 150)/TJ s-l (593-653 K). An analysis of the above data shows that the rate of BD dissociation is not strongly affected by release of steric energy. In contrast, the DD homolysis rate was increased by more than an order of magnitude through release of strain.
Introduction Bond homolysis is important in pyrolysis chemistry as a means of initial molecular breakup and as a source of free radicals. In addition, bond homolysis measurements can yield thermodynamic properties of free radicals’ and strained molecules2 not easily measured by other means. Therefore, as part of our program to study reactions occurring in aromatic thermolysis, we have been examining bond homolysis reactions of large polyaromatic molecules. The work reported here deals with the dissociation of the ethane C-C bond in phenyl-substituted ethanes. Early dissociation studies of phenyl-substituted ethanes involved pentaphenylethane3v4 and alkyl-substituted tetraphenylethane~.~ These reactions were easily studied at or near room temperature because of the weak ethane bond present. This weakness is presumably due primarily to the large amount of strain in these molecules. More recently, dissociation rates of phenylethane (ethylben~ene)~?’ and 1,l -diphenylethanes were measured in the gas phase, and the dissociation of 1,Zdiphenylethane (bibenzyl) has been examined in both the liquid”3 and gas phase.I3 Resonance stabilization energies, not strain, determine these relative rates. In fact, resonance stabilization energies of benzyl and diphenylmethyl radicals have been determined1v8J4from such rate ‘Guest Worker from the Chemistry Department of The Catholic University of America, Washington, DC 20064. Current address: SOH10 Research, 9101 E. Pleasant Valley Road, Independence, OH 44131.
measurements. Collectively, these studies have shown that large changes in the dissociative rate constant occur as the number of phenyl substituents is varied and that to predict accurate dissociation rates, both strain energies and resonance stabilization energies must be known. This paper presents results on the dissociation of 1,1,2-tri(1) McMillen, D. F.; Golden, D. M. Annu. Rev. Phys. Chem. 1982, 33, 493. (2) Ruchardt, C.; Beckhaus, H. D.; Hellmann, G.; Wiener, S.;Winiker, R. Angew. Chem., Int. Ed. Engl. 1911, 16, 875. (3) Bachmann, W. E.; Wiselogle, F. Y. J. Org. Chem. 1936, 2, 354. Bachmann, W. E.; Osbon, G. J . Org. Chem. 1940, 5, 29. (4) Coops, J.; Galenkamp, H.; Haantjes, J.; Luirink, K. L.; Nauta, W. T. Recl. Trau. Chim. Pays-Bas 1948, 67, 469. (5) Coops, J.; Nauta, W. T.; Ernsting, M. J. E.; Faber, A. C., Recl. Trau. Chim. 1940,59, 1109. ( 6 ) Benson, S. W.; ONeal, H. E. “Kinetic Data on Gas Phase Unimolecular Reactions”. Natl. Stand. Ref. Data. Ser. (US., Natl. Bur. Stand.) 1970, NSRDS-NBS 21. (7) Robaugh, D. A,; Stein, S. E. In?. J . Chem. Kine?. 1981, 23, 445. (8) Robaugh, D. A. Ph.D. Dissertation, W. Virginia University, Morgantown, WV, 1982. (9) Poutsma, M. L. Fuel 1980, 59, 335. (10) Brower, K. R. J. Org. Chem. 1980,45, 1004. (1 1) Cronauer, D. C.; Jewell, D. M.; Shah, Y. T.; Kucser, K. A. I d . Eng. Chem. Fund. 1978, 17, 291. (12) Miller, R. E.; Stein, S . E. J . Phys. Chem. 1981, 85, 580. (13) Stein, S . E.; Robaugh, D. A.; Alfieri, A. D. Miller, R. E. J . Am. Chem. SOC.1982, 104, 6567. (14) Rossi, M. J.; Golden, D. M. Int. J. Chem. Kinet. 1979, 2 2 , 969.
This article not subject to U.S. Copyright. Published 1985 by the American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985
Manka et al.
phenylethane (BD) and 1,1,2,2-tetraphenylethane(DD) and on the equilibrium between diphenylmethyl radicals and DD. Our results provide information on the amount of strain in these molecules and extend our predictive abilities for reactions of polyaromatic species. The self-recombination rate constant for diphenylmethyl radicals is also derived from the measurements. This, along with similar measurements for the benzyl r a d i ~ a l ' ~ . ' ~ provide the only available data for radical recombination reactions in high-temperature fluids.
pressure (5-10 torr). Biphenyl, bibenzyl, BD, and DD were recrystallized from ethanol. Diphenylmethane was purified by repeated freezing and decanting of the liquid phase at 22 OC. The purity of tetralin was greater than 99.6% while that of BD, DD, bibenzyl, and biphenyl was 99.9% as determined with the OV-101 column. A 0.1% impurity in DD was found to be tetraphenylethene but did not interfere with the homolysis reaction of DD. Fisher brand ACS grade toluene was used without further purification. ESR Studies. The apparatus used for the ESR measurements was modeled after that described by Livingston and Ze1des.l' Reactant solutions were pumped through a quartz reaction tube inserted along the axis of a cylindrical microwave cavity operated in the TEoll mode. This reaction tube was heated by a flow of hot air. The cavity was thermally isolated from the hot air by a quartz Dewar which surrounded the reaction tube. The axis of the cavity was horizontal. Because of the high temperatures used, the mixture had to be pressurized to keep the density high enough to obtain sufficient signal strength. This was accomplished by a high-pressure liquid chromatographic pump. The pressure was controlled by pinching in a large vice, a 1/16-in.-o.d.by 0.030-in.4.d. stainless steel tube held between a brass plate and a 2-in.-diameter brass cyclinder. An in-line filter upstream from this constriction prevented its blockage by small particles. While not providing automatic regulation, this arrangement proved satisfactory. Drifts in pressure were so minor that compensating adjustments could easily by made by changing the screw setting of the vice. Oxygen was removed from the reaction mixtures by purging with nitrogen. The mixtures were then conveyed to the pump and on to the reaction cell through stainless steel tubing. Teflon tubing was tried but proved to be too permeable to oxygen. The reaction tube, 30-cm-long overall, was constructed from high purity silica ground both inside and out to give 1.40-mm i.d. and a 4.70-mm 0.d. To join the reaction tube to the metal portion of the flow system, conventional static O-ring seals were used. Ejection of the tube by the fluid pressure from one seal was prevented by the opposition of the second seal at the other end of the tube. This method of construction made disassembly easy. The temprature was measured with chromel-constantan thermocouples in the hot air stream near the entrance and exit of the microwave cavity. These were calibrated with a thermocouple inside the reaction tube at the center of the cavity. During the calibrations, toluene surrounded the thermocouple at a pressure of 7900 kPa (1 140 psi). After the calibrations this internal thermocouple was removed. The ESR spectrometer is of conventional design with direct X-band detection by a single diode. This diode was designed for use in Doppler radar applications where low noise at low intermediate frequencies is important. It was therefore possible to use 10 kHz field modulation rather than the more usual 100 kHz. Microwave power incident on the cavity was approximately 0.3 mW. Magnetic field measurements were made with a proton resonance probe located to one side of the cavity. Determination of radical concentrations was made in the manner described by Zeldes and Livingston,I8wherein the radical spectrum is compared to its computer simulation. The specM deoxytrometer sensitivity was determined with a 3 X 1-oxy1 genated solution of 4-hydroxy-2,2,6,6-tetramethylpiperidineradicals in toluene. In contrast to Zeldes and Livingston who also used the simulation technique for the spectrum of this stable radical,'* we measured its signal intensity by a double integration. For the diphenylmethyl radical signals observed in the present work, we believe the concentration measurements to have an accuracy of &SO%. Concentrations of nonradical species were measured by gas chromatography on room temperature samples of reactant and product mixtures. An additional parameter required for the concentration measurements is the density of the reaction mixture at the temperature
5422
Experimental Section Bond Homolysis Studies. Bond homolysis studies of DD and BD were performed in sealed Pyrex glass tubes over the temperature ranges 199-277 and 320-380 OC, respectively. Various amounts of DD and BD were added to tetralin, an effective high-temperature radical trap, in amounts ranging from 0.02 to 1.O%. Tetralin was also sometimes used as an internal standard since its concentration changed little in the course of a reaction. In most cases, however, biphenyl was added to the reaction mixture as an internal standard in amounts comparable to DD and BD. Pyrex glass reaction tubes were prepared by first rinsing the tubing with an H F solution, then with distilled water, and finally with methanol. The tubing was dried and cut into 15-cm lengths. Each tube was sealed at one end and dried with a flame. To avoid decomposition of the reactant while sealing the tube, the reaction mixture was added to the bottom of the tube with a disposable pipet. The amount added to each tube was in the range 0.4-0.6 mL. The reaction mixture was cooled in liquid nitrogen, evacuated (1 X 10-3 torr), and sealed by using a flame. Reaction tubes were heated to the reaction temperature in a fluidized bath of aluminum oxide particles. The bath temperature was monitored with a chromelalumel thermocouple to a precision of fO.l OC. The thermocouple was placed in the bath at a depth near the center of the reaction mixture. The temperature during a run fluctuated no more than f 0 . 5 "C and its homogeneity in the sample region of the bath was better than f l OC. At the higher temperatures the time required for the sample to reach the reaction temperature was found to be about 30 s. This was determined from plots of the extent of decomposition vs. time at short reaction times. All reactions were assumed to occur in the liquid phase since it comprised at least 80% of the total volume and vapor pressure calculations of BD indicated that less than 0.4% of it was in the gas phase. A similar calculation for DD indicated that less than 0.1% was in the gas phase. After reaction, each sample mixture was analyzed at least twice by using temperature programmed gas chromatography. A Hewlett-Packard Model 5880A gas chromatograph equipped with flame ionization detectors (FID) was used with a Hewlett-Packard Model 7671A automatic sampler. A sample volume of 1 FL was injected directly onto a 1.83-m long, 4-mm-i.d. glass column packed with 10% OV-101 coated 80/100 mesh Chromosorb WAW or into a split injection system with a 25-m SE-30 WCOT capillary column. Peak areas were determined by electronic integration. Instrument response factors were calibrated with known mixtures of toluene, biphenyl, diphenylmethane, bibenzyl, BD, DD, and tetralin. Mass spectrometry was used to identify the recombination products. Mass spectrometric peaks obtained in each case correspond to the masses of the recombining radicals. The identity of 1,l'-ditetralin was further confirmed by comparing retention times and mass spectra of this product with those of a sample of this compound prepared independently (by heating di-tert-butyl peroxide in tetralin at 425 K). All compounds were obtained commercially and underwent further purification of our laboratory. BD and DD were obtained from Farchan Labs. Tetralin and diphenylmethane were obtained from Wiley Organics and Aldrich Chemical, respectively, and biphenyl and bibenzyl were obtained from Eastman Kodak. Tetralin was washed with concentrated sulfuric acid and then distilled with a spinning band distillation column at reduced (1 5) Lehni, M.; Schuh, H.; Fischer, H. Inf. J. Chem. Kinef. 1979,11, 705. (16) Zeldes, H.; Livingston, R. Fuel 1982, 61, 1254.
(17) Livingston, R.; Zeldes, H.; Conradi, M. S . J . Am. Chem. SOC.1979, 101, 4312. Livingston, R.; Zeldes, H. Rev. Sci. Instrum. 1981, 52, 1352. (18) Zeldes, H.; Livingston, R. J . Mugn. Reson. 1981, 49, 84.
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985 5423
Decomposition of Phenyl-Substituted Ethanes
TABLE I: Results of Bond Homolysis Studies of 1,1,2,2-Tetraphenylethane (DD) in Tetralin wt %
temp, K
DD
548
0.50 0.10 0.02
550
0.21
541
0.21
525
0.21
512
0.21
498
0.21
472
0.21
re1 concn'
reaction time, s
[DHlr
[TTI,
[DTI,
PDI,
[Ib
120 240 120 240 120 230 330 10 40 100 280 580 300 600 1200 300 600 1200 2400 4800 7200 15000 7200 14400 29760 61200 9 1200 179700 360000
0.150 0.283 0.167 0.328 0.167 0.332 0.460 0.033 0.073 0.170 0.449 0.781 0.243 0.477 0.803 0.082 0.150 0.300 0.561 0.903 0.487 0.847 0.179 0.321 0.521 0.934 0.132 0.266 0.485
0.080 0.139 0.419 0.477 1.992 2.018 2.252 0.084 0.135 0.149 0.239 0.343 0.358 0.426 0.551 0.169 0.207 0.256 0.345 0.463 0.439 0.553 0.208 0.28 1 0.370 0.490 0.224 0.230 0.351
0.065 0.114 0.052 0.087 0.037 0.055 0.070 0.007 0.020 0.044 0.111 0.182 0.062 0.111 0.171 0.023 0.039 0.067 0.109 0.168 0.086 0.127 0.03 1 0.048 0.074 0.119 0.016 0.026 0.047
0.891 0.800 0.890 0.793 0.896 0.794 0.73 1 0.989 0.959 0.894 0.723 0.549 0.864 0.732 0.547 0.950 0.908 0.8 19 0.687 0.488 0.7 18 0.559 0.898 0.832 0.714 0.505 0.921 0.852 0.738
0.892 0.801 0.890 0.793 0.898 0.804 0.734 0.980 0.954 0.893 0.721 0.533 0.850 0.713 0.529 0.948 0.906 0.8 17 0.672 0.477 0.715 0.534 0.895 0.8 19 0.706 0.490 0.926 0.854 0.735
kdrCs-' 9.23 X lo4 9.68 x 10-4 9.43 x 10-4
1.09 x 10-3 5.31 x 10-4
1.54 X lo4 4.17 x 10-5
1.14 x 10-5 8.57 x 10-7
'All concentrationsare relative to the initial amount of DD. b [ l is the extent of reaction 1 based on appearance of products and is calculated from the expression [DD],/([DD], ([DH], + [DT],)/2). eRate constant. Each rate constant is the slope of the plot of In vs. reaction time.
+
and pressure in the reaction tube. This can obtained from the compressibility 2 through the relation p = P M / ( Z R T )where M is the average molecular weight of the mixture. The mixture compressibility was calculated from the Redlich-Kwong equation of state.19 Mixture flows were normally about 0.6 mL/min, giving a mixture residence time in the microwave cavity of roughly 3 s at 650 K. The reaction mixture used for the equilibrium constant measurements consisted of 98 mL diphenylmethane, with benzene added to make the total volume 200 mL. To this was added 10 mL of di-tert-butyl peroxide as the radical initiator. On reaching the hot part of the reactor, the peroxide dissociates into tert-butoxy radicals which rapidly abstract a hydrogen atom from the diphenylmethane (DH) to give diphenylmethyl radicals (Ds).~O These combine to form DD. Because this compound is relatively insoluble in benzene at room temperature, direct generation in the hot reactor was used to maximize its concentration and thus that of the radical. As will be seen, this method had one drawback. A computer modeling calculation showed that equilibrium between diphenylmethyl radicals and DD was established in less than 0.01 s. Since the equilibrium dimer concentration was 500-1000 times greater than that of the radical, its concentration in the product mixture could be used to calculate directly its concentration in the hot reaction chamber. All product concentrations were measured relative to the D H concentration, which being in great excess remained unchanged by the reaction. The amount of di-tert-butyl peroxide used yielded a concentration of DD which was too high to remain in solution in the product mixture at room temperature. Toward the end of the series of measurements discussed later, precipitation of the dimer caused blockage of the downstream constriction. This produced a sudden and potentially dangerous increase in the system pressure arising from large quantities of gas generated by the decomposition of tert-butoxy radicals into methyl radicals and acetone. A significant amount of such decomposition must have occurred since (19) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. 'The Properties of Gases and Liquids", 3rd ed.; McGraw-Hill: New York, 1977. (20) Manka, M.J.; Stein, S.E. J . Phys. CRem. 1984, 88, 5914.
only about 45% of the peroxide resulted in DD product. For this to happen, most of the methyl radicals must have decayed through recombination with themselves or with D. rather than through hydrogen abstraction from DH. Experiments were also performed on similar mixtures in which toluene (BH) replaced benzene. In this system, benzyl radicals (B.) are generated in addition to diphenylmethyl radicals. Under the conditions used, the benzyl radical concentration was not high enough to give an observable ESR signal. The product mixture contained the additional recombination products bibenzyl (BB) and BD. In this system the left-hand side of hydrogen exchange reaction D. BH = D H B. is favored. Much of the B- generated by the radical initiator is rapidly converted into D. which in turn recombines to form DD. As in the benzene system, the DD = 2D- equilibrium is established quickly. However, the final equilibrium favors BD and especially BB as products. Computer modeling calculations indicated that this initially formed DD will slowly decompose and appear eventually as BD. Because of this, the DD concentration could be decreasing throughout passage of the fluid through the reactor. In this case its value measured in the products would be an unknown fraction of its value in the reactor. Therefore, without more detailed experiments, this system was considered unsuitable for measuring the diphenylmethyl radical-DD equilibrium.
+
+
Results Dissociation of I ,I ,2,2- Tetraphenylethane. Results of bond homolysis experiments of DD studied in the temperature range 472-550 K in an excess of tetralin are shown in Table I. All concentrations given are relative to the initial DD concentration. They are consistent with the following mechanism: DD D. + D. (1)
-
D-
+ TH D H + T. D- + T- DT T.+ T. TT
-
+
-+
(2)
(3) (4)
Compound symbols not previously identified are tetralin (TH),
5424
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985
Manka et al.
TABLE I 1 Results of Bond Homolysis Studies of 1,1,2-Triphenylethene (BD) in Tetralin temp, K 653
time, s 300 600 900 300 600 900 900 1800 3600 3600 7200 14400 2 1600 43200 86400
0.10 633
1 .oo
613
I .oo
593
1.oo
re1 concnQ
reaction
wt % BD 1 .oo
[BHlr 0.174 0.319 0.462 0.195 0.367 0.483 0.153 0.271 0.480 0.131 0.237 0.416 0.158 0.289 0.512
WHI, 0.170 0.306 0.448 0.166 0.326 0.452 0.138 0.248 0.43 1 0.116 0.218 0.424 0.137 0.258 0.453
[TTI r 0.128 0.151 0.143 0.217 0.225 0.201 0.210 0.142 0.135 0.101 0.2 18 0.122 0.139 0.119 0.094
tsb
PBIr 0.853 0.685 0.545 0.834 0.674 0.548 0.862 0.747 0.544 0.877 0.772 0.570 0.860 0.734 0.536
kd,cs-'
0.832 0.687 0.545 0.822 0.660 0.540 0.856 0.742 0.544 0.877 0.772 0.576 0.854 0.729 0.526
6.71 x 10-4 6.90 x 10-4 1.68 x 3.83 x 10-5 7.43 x 10"
"All concentrations are relative to the initial amount of BD. * E s is the extent of reaction 5 based on appearance of products and is calculated from the expression [BD],/([BD], + ([BH], + [DH],)/2). CRateconstant. Each rate constant is the slope of the plot of In E5 vs. reaction time.
1-tetralyl radicals (T.), the cross recombination product (DT), and the recombination product 1,l'-ditetralin (TT). Disproportionation reactions involving 1-tetralyl radicals were not included in this mechanism due to the slowness of these reactions relative to recombination.20 At sufficiently high concentrations of DD, the measured dissociation rate constant decreased with increasing DD concentration. This is due, presumably, to the recombination of the diphenylmethyl radicals, the reverse of reaction 1. At these high concentrations of diphenylmethyl radials, recombination effectively competes with H-atom abstraction from tetralin. Therefore, homolysis rate constants for DD were always determined at sufficiently low DD concentrations where the measured rate constants were independent of its concentration. Evidence that recombination was unimportant was confirmed by the fact that the concentration of 1,l'-ditetralin (TT) was always much greater than the cross-recombination product of 1-tetralyl and diphenylmethyl radicals (DT). Rate constants for reaction 1 were obtained from plots of In El vs. reaction time, where E1
= [DDl,/~[DDl, + ( P H I , + [DT1,)/21
This gives the extent of reaction based on the appearance of products. It agrees well with the observed [DD], which gives the extent of reaction based on disappearance of reactants. An Arrhenius plot of rate constants is shown in Figure 1. A least-squares linear regression of this data gives k l = 1015,92*0.13 exp((-23910 f 160)/T] s-I
(I)
Error limits shows here and in (11) and (111) reflect only the precision of the measurements and not their absolute accuracy. Dissociation of 1,1,2-Triphenylethane. The thermal decomposition of BD in tetralin was studied in the temperature range 593-653 K. The following mechanism was used to interpret the results: BD -.+ B* De (5)
+
Be
+ TH
De
+ TH B. + T. D. + T. B. + B. T- + T-
-.+ -.+
BH
+ T.
(6)
DH
+ T.
(2)
+
-.+
-.+
BT
(7)
DT
(3)
BB
(8)
TT
(4)
The compound symbol not previously identified is the crosscombination product (BT). Disproportionation reactions involving 1-tetralyl radicals were again not included in the above reaction mechanism because of their slowness relative to recombination.20 To avoid competition between the recombination of diphenyl-
-2.5r -3.5
I\ t
\
-5*51 -
\
l#
1, 1, 2,2-tetraphenylethane
-
1
1
1
1
1
1
1
1
I
l
l
1
I
J
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985 5425
Decomposition of Phenyl-Substituted Ethanes
I, 1,2-triphenylethane 1, 1, 2,2-tetraphenylethane 1.60
1,70
iooo/r PK)
1.50
Figure 2. Plot of dissociation rate constant vs. inverse temperature for 1,1,2-triphenyIethane in excess tetralin.
TABLE III: Species Concentrations and Equilibrium Constants from Flow ESR Experiments for the Dissociation of 1,1,2,2-Tetraphenylethane (DD) in Benzene-Diphenylmethane Solvent Mixture mixture concn, M K, = [D*]*/ temp, density," K g/mL IDHl lDHl ID.1 DDl, M 648 0.440 1.40 5.78 x 5.7 x 10" 5.62 x 1O-Io 649 0.440 1.40 5.55 X 5.7 X 10" 5.85 X 1.32 5.76 X 8.2 X 10" 1.17 X 660 0.418 683 0.371 1.17 4.88 X 1.4 X 4.02 X 683 0.371 1.17 4.26 X IO-' 1.2 X 3.38 X "Density calculated for a system pressure of 7.9 MPa.
ization to form DD, presumably via a radical-catalyzed neophyl rearrangement,21was much faster than homolysis. Dissociation products were primarily diphenylmethane and DD. Only trace amounts of toluene and triphenylmethane could be observed. Conversion of 1,1,1,Ztetraphenylethane to DD was at least 300 times faster than its dissociation a t 560 K. Equilibrium Studies. The equilibrium constant K, for the equilibrium between diphenylmethyl radicals and DD was determined over the temperature range 648-683 K. Table I11 gives the concentrations of diphenylmethane, DD, and diphenylmethyl radicals in the hot reactor at the different temperatures, as determined by ESR and end product analysis. Also given is the pressure and density of the mixture and the concentration equilibrium constant, K,, defined as the ratio [D-I2/[DD] at equilibrium. A van't Hoff plot of log K, vs. inverse temperature is shown in Figure 3. A least-squares analysis gives K, = 106.69*0.66 exp(-(23 770 f 1020)/T) M
(111)
The self-recombination rate constant of diphenylmethyl radicals is obtained from the ratio of the dissociation rate constant and the equilibrium constant. At 648 K the dissociation rate constant k l for DD, obtained by using eq I, is 0.84 s-l and the equilibrium M. These values yield a recombination constant is 5.7 X rate constant of 1.5 X lo9 M-' s-l. (21) Crimmons, T.F.; Murphy, W. S.; Hauser, C. R. J. Org. Chem. 1966,
31, 4273.
(22) Lankamp, H.; Nauta, W. T.; MacLean, C. Tetrahedron Lett. 1968, 2, 249.
1.55
iooo/r PK) Figure 3. Plots of equilibrium constant for diphenylmethyl radicals and 1 , I ,2,2-tetraphenylethane vs. inverse temperature in benzene-diphenylmethane solvent mixture.
Rate Constantfor Benzyl-Diphenylmethyl Recombination. To determine the rate constant for the combination of benzyl with diphenylmethyl radicals, we heated mixtures of toluene and diphenylmethane containing di-tert-butyl peroxide at 423 and 473 K. The product ratio [BD]/( [BB] [DD1)'I2 equals k5/(Flk-8)1/2. Its observed value was 1.7 f 0.2 with no noticeable difference for the two temperatures. Using the experimental value 7.7 X lo9 M-' s-' derived by Zeldes and Livingston16 for the bibenzyl reaction, our value of 1.5 X 10 M-' S-I for the DD reaction, and the observed value for the above ratio, we get 5.8 X lo9 M-' s-l for the benzyl-diphenylmethyl recombination.
Discussion As the number of phenyl groups replacing hydrogen atoms in ethane increases, its central C-C bond strength decreases. Both strain in the reactant molecule and resonance stabilization energy in the radical products can contribute significantly to this bond strength reduction. Triphenylmethyl radicals are so sterically hindered that head to head recombination to form hexaphenylethane is apparently not possible' and pentaphenylethane readily dissociates at only 80 0C.3,4Strain undoubtedly plays a significant role in weakening the bond in these molecules. On the other hand, for ~henylethane,~,'1,l-diphenylethane,* and 1,Zdiphenylethane,I2J3resonance stabilization of the products appears to be the key factor in the bond weakening. The results of our present measurements allow us to examine the question of strain energy in BD and DD. We can do this by comparing the observed bond homolysis rate constants for these molecules with those predicted for hypothetical "strain-free" reactions. Strain-free dissociation rate constants for BD and DD can be estimated by making appropriate corrections to the equilibrium constant for the dissociation of bibenzyl in which there is no apparent strain. In the following thermochemical kinetics analysis we use (23) Benson, S. W. "Thermochemical Kinetics", 2nd ed.; Wiley: New York, 1976. (24) ONeal, H. E.; Benson, S. W. Int. J . Chem. Kinet. 1969, 1, 221. ONeal, H. E.; Benson, S. W. "Free Radicals"; Kochi, J. K., Ed.;Wiley: New York, 1973; Vol. 11. (25) Cox, J. D.; Pilcher, G. 'Thermochemistry Organic and Organometallic Compounds"; Academic Press: New York, 1970.
5426
The Journal of Physical Chemistry, Vol. 89, No. 25, 1985
TABLE IV: Thermodynamic Data Used To Estimate Hypothetical Strain-Free Rate Constants for BD and DD Homolysis AH,, so Si0,b species kcal/mol cal/(mol K) uo cal/(mol K) 59.5d 6.1 61.7 ethyl 25.9' (28.3)g isopropyl 18.2'(21.2)9 68.8d 9.2 73.2 n-butane -30.15' 74.121 9.2 79.9 82.121 27 X 1 88.7 2-methylbutane -36.92' 2,3-dimethyl-42.49' 87.421 81 X 2 97.5 butane 9
"The total symmetry number, u, is the product of the internal and external symmetry number. bSio= So + R In (a) - R In (g,), where g, is the electronic degeneracy, and R = 1.9872 cal/(mol K). 'Reference 1 . dReference 24. eReference 25. fReference 26. gReference 29. W. Tsang's values.
methodsz3 commonly used for gas-phase reactions. They are expected to be quite reliable in the present high temperature, nonpolar environment^.^^ The simplest way to carry out this analysis would be to equate activation energies directly to reaction enthalpies and to derive AS from measured A factors. However, as is well-known in the analysis of gas-phase homolysis data,6 relatively minor temperature-dependent measurement errors can greatly perturb Arrhenius parameters. This, coupled with the uncertainties in possible activation energies for recombination make this simple approach unreliable. We therefore hesitate in deriving absolute bond strength and activation entropies from measured Arrhenius parameters, and will stay as close as we can to our measured relative rate constant values which we regard as quite accurate. The concentration equilibrium constant K, is the ratio of the dissociation rate constant kd to the recombination rate constant k,. Expressing the equilibrium constant in terms of enthalpies AH,and entropies AS, of reaction gives the following relationship between dissociation rates In
(kd/kdR)
- In ( k , / k , R ) = In ( K , / K , ~ ) =
-(AG, - A G C R ) / R T
= (AH, - A H c R ) / R T+ (AS,- A S C R ) / R
s-l
TABLE V Rate Data Used To Estimate Hypothetical Strain-Free Rate Constants for BD and DD Homolysis reaction reaction k,. SKI no. n-butane 2(ethyl) 1016 exp(-41300/ T)" 9 2-methylbutane 2-isopropyl + 1OI6 exp(-40350/ 10 ethyl 2,3-dimethylbutane exp(-38200/7Ja 11 2( 2-isopropyl) isopropylbenzene I-phenylethyl 10'' * exp(-35880/7JC 12 + methyl 1,l-diphenylethane exp(-34020/7Jd 13 diphenylmethyl + methyl
- -
(V)
(26) Stull, D. R.; Westrum, E. F.; Sinke, G . C. "The Chemical Thermodynamic of Organic Compounds"; Wiley: New York, 1969. (27) Tsang, W. 'Shock Waves in Chemistry"; Lifshitz, A,, Ed.; Marcel Dekker: New York, 1981. (28) Robaugh, D. A.; Stein, S. E., unpublished. ( 2 9 ) Tsang, W. Int. J . Chem. Kinet. 1969, I , 245. (30) Stein, S . E. J. Am. Chem. SOC.1981, 103, 5685.
nb
"Reference 27 *Obtained by interpolation of data given in ref 27 Reference 7 dReference 28
TABLE VI: Reaction Enthalpy and Entropy Differences Calculated from Observed Dissociation" and RecombinationbRate Constants according to Eq IV AH, - AHCR, ASc - SCR, AGJ573 K) - AGCR(573K), reaction kcal/mol cal/(mol K) kcal/mol BD -9.0 (-5.6)' -1.3 (2.7)' -8.3 (-7.1)' DD -19.3 (-12.5) 0.2 (5.4) -19.4 (-15.6) DD-BB -10.3 (-6.9) 1.5 (2.7) -1 1.2 (-8.5) "he dissociation rate for the reference reaction (bibenzyl) is given by eq V. Rates for BD and DD are given by eq I1 and I, respectively. *Recombination rates used were 7.7 X lo9, 5.8 X lo9, and 1.5 X I O 9 M-' s-I for bibenzyl, BD, and DD, respectively. They were assumed to be independent of temperature. Values estimated by thermodynamic methods for the hypothetical strain-free reactions using data shown in Table IV. T ~ a n g has * ~ published values of 28.3 and 21.2 kcal/mol for the heats of formation of ethyl and isopropyl radicals, respectively. These yield slightly smaller estimates for the AH, - AHcRdifferences. They are AH, - AHCR= -5.0 kcal/mol for the BD reaction and -1 1.3 kcal/mol for the DD reaction.
which applies to dissociation in excess liquid tetralin solvent. Inserting these quantities into (IV) and solving for kd, we get at T = 573 K
kd(BD,obsd)/kd(BD,calcd) = 1
(IV)
where the superscript R refers to the bibenzyl reference reaction. We assume that AC, - AC," = 0 so that the above expression applies at all temperatures. To get enthalpy and entropy differences we first estimate the effect of converting hydrogen centers to carbon by considering the dissociations of the analogous methyl-substituted ethanes, n-butane (for bibenzyl), 2-methylbutane (for BD), and 2,3-dimethylbutane (for DD). For this we use the thermodynamic data shown in Table IV. Intrinsic ent r o p i e ~were ~ ~ used to estimate entropy differences. Enthalpy differences so determined than have to be augmented by a resonance stabilization energy of 4.7 kcal/mol (1 kcal = 4.184 kJ)8 for a second phenyl group adjacent to the radical center. In the BD reaction there is one of these second phenyls, while in DD there are two. For the reaction enthalpy differences we estimate AH, - AHCRequals -5.6 kcal/mol for BD and -12.5 kcal/mol for DD. For the reaction entropy differences we estimate AS, - hSCR = 2.7 cal/(mol K) for BD and 5.4 cal/(mol K) for DD. For strain-free recombination rate constants we use krR(bibenzyl) = 7.7 x 109 M-1 s-1 ,16 k,(BD) = 2kIR, and k,(DD) = krR. For the bibenzyl dissociation rate constant k d R , we use the experimentalI3 expression kdR(bibenzyl) = 1016.58 exp(-33 620/T)
Manka et al.
and kd(DD,obsd)/kd(DD,cakd) = 6
(VI)
In the BD reaction the agreement between the observed rate and the predicted rate is an indication that strain is not a major factor in weakening the ethane bond in this molecule. In the DD reaction on the other hand, the much larger observed rate over the predicted rate is evidence that strain is a factor in the bond weakening. If the observed recombination rate constants for BD and DD are used in eq IV the difference between the observed and estimated rate for DD becomes even larger. With values of 7.7 X lo9, 5.8 X lo9, and 1.5 X lo9 M-I s-l for the recombination rate constants of bibenzyl, BD, and DD, respectively, eq IV gives kd(BD,obsd)/ kd(BD,calcd) = 2.7 and kd(DD,obsd) / kd(DD,calcd) = 29. Instead of using thermodynamic data one can also estimate these rate constants from rate data alone. We did this by taking appropriate differences in the free energies of activation for reactions 9-13 shown in Table v. The results are kd(BD,calcd) = kdR(BB)(klo/kg)a kd(DD,calcd) = kdR(BB)(klI / k 9 ) a 2 where cy = 2 k i 3 / k I 2 .Note the correction for reaction path degeneracy in reaction 12 which appears in a . At T = 573 K , this approach gives kd(BD,obsd)/kd(BD,caIcd) = 6 and kd(DD,obsd)/kd(DD,calcd) = 67. Because of its dependence on individual sets of experiments and the rather large temperature extrapolations required, this method is not expected to be as reliable as the thermodynamic approach. It does however support the conclusion
J . Phys. Chem. 1985, 89, 5427-5433 that the homolysis rates of phenyl-substituted alkanes cannot be accurately estimated without taking strain energy into consideration. The relationship given by eq IV was also used to calculate enthalpy, entropy, and free energy differences from observed dissociation and recombination rate constants. These results are given in Table VI along with the values estimated for the hypothetical strain-free reactions. Also given are the differences between the two reactions for each of these quantities. On going from BD to DD the observed change at 573 K in AGc - AGCRwas -1 1.1 kcal/mol. This is 2.6 kcal/mol greater than that estimated for the hypothetical strain-free reactions. At this temperature the enthalpy contribution to this free energy discrepancy is a factor of 5 larger than the entropy contribution. Attributing this to strain implies that the central C-C bond in DD contains roughly 3 kcal/mol more strain energy than that in BD. Ruchardt et aL2 have presented evidence that an appreciable fraction (0.4) of such strain energy released in a homolysis reaction remains in the transition state. This implies a positive activation energy for recombination. The equilibrium data shown in Figure
5421
3 is consistent with a zero activation energy. However, the uncertainty in this data is large. It could be consistent with an activation energy as large as 2 kcal/mol. We are thus unable to exclude the possibility that some strain may exist in the transition state in DD. Previous work on bibenzyl diss~ciation'~ has shown that the Arrhenius parameters for the reaction are considerably higher in liquids than in the gas phase, even though actual rate constants to not differ much. Arrhenius A factors measured in the present work for BD and DD are not quite as large as that for the liquid-phase bibenzyl reaction but are nevertheless still factors of 5-9 larger than that for the bibenzyl gas-phase reactions. The precise origin of these differences is not clear, but as in our previous studies they may be at least partly due to a viscosity (temperature)-dependent cage effect. Acknowledgment. This research was supported by the Gas Research Institute. We thank Dr. M. Mautner for his critical analysis of this work. Registry No. DD, 632-50-8; BD, 1520-42-9; diphenylmethyl radical, 4471- 17-4.
Influence of the Hydrogen Uptake by the Support on Metal-Support Interactions in Catalysts. Comparison of the Rh/TiO, and Rh/SrTlO, Systems J. Sanz, J. M. Rojo, P. Malet,+ G. Munuera,+M. T. Blasco,t J. C. Conesa,*f and J. Soriat Instituto de Flsico-Qdmica Mineral. CSIC, Serrano I15 dpdo.. 28006 Madrid, Spain (Received: April 2, 1985)
Samples of Rh/Ti02 and Rh/SrTi03 catalysts subjected to thermal treatments under H2 and in vacuo have been examined by NMR, EPR, and quantitative adsorption techniques in order to ascertain the dependence of "SMSI effects" on hydrogen strongly adsorbed at high temperatures. Loss of H2 chemisorption capacity upon high-temperature reduction (monitored directly by NMR of metal-adsorbed hydrogen) occurs only in Rh/Ti02, and is accompanied by extensive incorporation of hydrogen in the support in form of hydride-type species. Both effects are reversed by high-temperature outgassing, while the amount of EPR-detected Ti3+increases. It is concluded that support-held hydrogen produces SMSI-type effects in Rh/Ti02 that cannot be explained by a conventional support reduction mechanism (generation of Ti3+ and anion vacancies) or by coverage of the metal with TiO, species migrating from the support. Electronic changes (rehybridization) induced in the small metal particles by interaction with highly reduced species generated at the support are proposed as a possible source of SMSI behavior that can be reversed by outgassing or oxidation more easily than coverage by TiO, entities.
Introduction Interest in the so-called strong metalsupport interaction (SMSI) in M / T i 0 2 systems ( M = Pt, Rh, Pd, or Ni) has been raised in recent years,',2 and though several hypotheses have been postulated3" to explain the origin of this effect, it remains still in doubt whether one or several of them will be able to account fully for the different phenomena observed. In previous works we have examined, with the aid of IR, NMR, and EPR techniques, the interaction of H2 with Rh/Ti02 and other similar systems.610 From these previous results we have concluded that at least three forms of hydrogen can be observed in Rh/Ti02 catalysts after reduction in H, a t T > 573 K. Thus, some of us6 observed in a previous work the reversible exchange of electrons between Rh (and Pt, Ru, and Pd) and the Ti02 support that generates Ti3+species, detected at 77 K by EPR. These Ti3+ species were in equilibrium with'a form of hydrogen weakly adsorbed on the metal (H,) and removable by pumping at 295 K. Further work with N M R and IR was able to show7,*
'
Departamento de Quimica General, Facultad de Quimica, Universidad de Sevilla, Sevilla, Spain. Instituto de Catilisis y Petrolecquimica, CSIC, Serrano 119, 28006 Madrid, Spain.
*
that spillover of protons to the support readily occurs under those mild conditions; at the same time 'H N M R allowed to differentiate this weakly adsorbed hydrogen from another form, H,, appearing as a 'H N M R line shifted to -120 ppm from the main line due to hydrogen on the T i 0 2 support. This second form of hydrogen, H,, bonded more tightly to the Rh particles, is retained by the (1) Tauster, S. J.; Fung, S. C.; Garten, L. R. J . Am. Chem. SOC.1978,100, 170. (2) See, e.g., papers 1-24 in: Imelik, B. et 11.
(3) (a) Meriaudeau, P.; Dutel, J.; Dufaux, M.; Naccache, C. In ref 2, p 95. (b) Santos, J.; Phillips, J.; Dumesic, J. A. J . Catal. 1983, 81, 147. (c) Resasco, D. E.; Haller, G. L. J . Catal. 1983, 82, 279. (4) (a) Short, D. N.; Mansour, A. N.; Cook Jr., J. W.; Sayers, D. E.; Katzer, J. R. J . Catal. 1983, 82, 299. (b) Belton, D. N.; Sun, Y. M.; White, J. M. J . Phys. Chem. 1984, 88, 1690. ( 5 ) Kelley, M. J.; Short, D. R.; Swartzfager, D. G. J . Mol. Catal. 1983, 20, 235. (6) Conesa, J. C.; Soria, J. J . Phys. Chem. 1982, 86, 1392. (7) Conesa, J. C.; Munuera, G.; MuAoz, A,; Rives, V.; Sanz, J.; Soria, J. Stud. Surf. Sei. Catai. 1983, 17, 149. (8) Conesa, J. C.; Malet, P.; Mufioz, A.; Munuera, G . ;Sainz, M. T.; Sanz, J.; Soria, J. Proc. 8th. Int. Congr. Catal., West Berlin, 1984, 1984, 5, 217. (9) Conesa, J. C.; Malet, P.; Munuera, G.; Sanz, J.; Soria, J. J . Phys. Chem. 1984, 88, 2986. (10) Sanz, J.; Rojo, J. M. J . Phys. Chem. 1985, 89, 4974.
I 0 1985 American Chemical Society 0022-3654/85/2089-5427$01.50/0 I
,
al. Stud. Surf. Sei. Cutal. 1982,
