J . Phys. Chem. 1990, 94, 1881-1883 then exhibit increasing efficiency with rise in temperature, is still to be resolved. Such a minimum in the temperature variation of collision efficiency is well-known from earlier shock tube studies of energy transfer.I9] In any case, it is evident that eq 111 (eq 3 here) when used with eq I1 and 111 in KS does not provide "part of a coherent picture of energy transfer in unimolecular reactions" as stated there. ~
~~~~~
(19) Lambert, J. D. Vibrational and Rotational Relaxation in Gases; Clarendon Press: Oxford, 1977.
1881
Conclusion In recent years, high-temperature systems such as flames and combustion have come into increasing prominence. The importance of using the correct relationship between ( and ( AE)d for high-temperature systems becomes all the more evident. The relation must include both the correct temperature and energy dependence as provided by eq 4.
Acknowledgment. D.C.T. thanks the Department of Energy (Division of Chemical Sciences, Office of Basic Energy Sciences, Grant DE-FG02-87ER13700) for their support.
Flash Photolysis Resonance Fluorescence Investigation of the Gas-Phase Reactions of Hydroxyl Radicals with Cyclic Ethers Philippe Dagaut,+ Renzhang Liu, Timothy J. Wallington,t and Michael J. Kurylo* Chemical Kinetics Division, Center for Chemical Technology, National Institute of Standards and Technology Uormerly National Bureau of Standards), Gaithersburg, Maryland 20899 (Received: May 15, 1989; In Final Form: August 22, 1989)
Absolute rate constants were measured for the gas-phase reactions of hydroxyl radicals with a series of dioxanes and other cyclic ethers by using the flash photolysis resonance fluorescence technique. At 298 K, the rate constants obtained (in units of cm3 molecule-l s-l) were as follows: 1,3-dioxane, (9.15 f 0.43); 1,4-dioxane, (10.9 f 0.5); 4-methyl-1,3-dioxane, (1 1.3 f 0.6); trimethylene oxide, (10.3 f 0.6); tetrahydropyran, (13.8 f 0.7); and oxepane (15.4 f 1.3) where the errors expressed are 20 derived from the statistical analysis. Kinetic data for 1,3-dioxaneand 1,4-dioxane,reactions 1 and 2, over the temperature range 240-440 K were used to derive the Arrhenius expressions: k l = (9.4 f 0.2) X exp[(lO i 60)/a cm3 molecule-I s-l; k2 = (8.3 f 2.2) X exp[(lO f 90)/7'l cm3 molecule-' s-l. These results are compared to our earlier measurements for aliphatic ethers and are discussed in terms of reaction mechanisms and the prediction of reaction rates for such compounds from group reactivity values.
Introduction As part of a continuing laboratory effort to examine trends in the gas-phase reactivity of hydroxyl radicals, we have conducted detailed kinetic measurements on a series of simple alcohol^,^-^ and ethers4-' from which we have developed a group reactivity scale useful for rate constant predictions. More recently, these studies have been extended to difunctional oxygenates* and pol yet her^,^ thereby allowing us to revise and extend this group reactivity tabulation. In the present study we have examined the reactions of OH radicals with cyclic ethers, a class of compounds for which very few data are available in the literaturelo despite the fact that such compounds may play an important role in atmospheric chemistry due to their release during industrial production, use as solvents, and combustion of practical fuels. We report herein the results of our flash photolysis resonance fluorescence (FPRF) investigations of the gas-phase reactions of OH radicals with 1,3-dioxane, 1 ,Cdioxane, 4-methyl- 1,3-dioxane, trimethylene oxide, tetrahydropyran, and oxepane. Rate constants for all of these cyclic ethers were determined at 298 K; while for 1,3-dioxane and 1,4-dioxane, reactions 1 and 2, the temperature dependencies of the rate constants were studied over the range 240-440 K.
Experimental Section The apparatus and experimental methodology used in these studies have been described in detail in many previous publications (see, for example, ref 1 and 2) and do not require further elaAuthor to whom correspondence should be addressed. 'Present address: CNRS, CRCCHT, 1C Ave. de la Recherche Scientifique, 4507 1 Orldans Cedex 2, France. *Present address: Ford Motor Company, Scientific Research Laboratory, P.O. Box 2053, Dearborn, MI 48121.
boration in this report. Each of the cyclic ethers used as a reactant had a manufacturer's stated purity of at least 98% and was further purified by repeated freeze-pump-thaw cycles followed by fractional distillation. The argon diluent gas used in preparing the reaction mixtures had a stated purity of 199.998% and was taken directly from the cylinder. As in our other recent FPRF hydroxyl radical investigations, the initial OH concentration was estimated from a comparison of the present apparatus and flash lamp geometries and operating conditions with those of previous experiments in this laboratory and with similar systems used by other workers.">l2 The conclusion that lolo I[OH], I10" molecules cm-3 assured that pseudo-first-order kinetic conditions with respect to the OH decay were maintained throughout the reagent concentration range of (0.9-11.1) X 1013 molecules ~ m - ~ . (1) Wallington, T. J.; Kurylo, M. J. J . Phys. Chem. 1987, 91, 5050. (2) Dagaut, P.; Wallington, T. J.; Liu, R.; Kurylo, M. J. J. Phys. Chem. 1988, 92, 4375. (3) Wallington, T. J.; Kurylo, M. J. Znt. J . Chem. Kinet. 1987,19, 1015. (4) Wallington, T. J.; Dagaut, P.; Liu, R.; Kurylo, M. J. Enuiron. Sci. Technol. 1988, 22, 842. (5) Wallington, T. J.; Dagaut, P.; Liu, R.; Kurylo, M. J. Znt. J . Chem. Kinet. 1988, 20, 541.
( 6 ) Wallington, T. J.; Liu, R.; Dagaut, P.; Kurylo, M. J. Znt. J . Chem. Kinet. 1988, 20, 41. (7) Liu, R.; Wallington, T. J.; Dagaut, P.; Kurylo, M. J. Acta PhysXhim. Sin. 1989. 5. 210. (8) Dagaut, P.; Liu, R.; Wallington, T. J.; Kurylo, M. J. J. Phys. Chem. 1989. 93. 7838. (9) Dagaut, P.; Liu, R.; Wallington, T. J.; Kurylo, M. J. Znt. J. Chem. ~
Kinet.,in press. (10) Atkinson, R. Znt. J . Chem. Kinet. 1987, 19, 799. (11) Wallington, T. J. Znt. J . Chem. Kinet. 1986, 18, 487. (12) Witte, F.; Urbanik, E.; Zetzsch, C. J . Phys. Chem. 1986, 90, 3251.
This article not subject to U S . Copyright. Published 1990 by the American Chemical Society
1882 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
1200
r
Dagaut et al. TABLE 11: Chemical Structure of the Cyclic Ethers in Table I
I 1 -
I
i 800
c
Y
I
Y
7
Y v
1,4-dioxane
1,3-dioxane
h
400
1
H,C'
0 C ' H,
I
I
H2C,CH.0
trimethylene oxide
I
c H3 0 0.0
. 1 .o
I ---.-
2.0
A-i
4-methyl-I,3-dioxane
0 C ' H,
HC ,'
3.0
P( 1,3-dioxane), mTorr
Figure 1. Plot of (k'" - k,) vs 1,3-dioxane concentrationat 298 K: (0) 25, (A) 30, ( 0 )40, and (0)50 Torr. The line corresponds to a linear
oxepane telrahydrcpyran
least-squares analysis. TABLE I: Measured and Predicted Rate Constants from the Present Work k(298 K), cm3 molecule-' SKI
reactant 1.3-dioxane 1,4-dioxane 4-methyl-1,3-dioxane trimethylene oxideC tetrahydropyran oxepane
tetrahydrofurand 1 ,3,5-trioxanec
measured (9.15 f 0.43) (10.9 f 0.5) (11.3 f 0.6) (10.3 f 0.6) ( 1 3.8 f 0.7) (15.4 f 1.3) 16.1 1.9
predicted GRa SARb 18.0 45.8 18.0 26.4 53.8 13.5 3.2 22.5 17.4 27.0 18.8 18.0 12.8 13.5 93.5
tetrahydrofuran
1,3-trioxane
TABLE 111: Rate Constants Measured for the Reaction of l,3-Dioxane ( k I ) and 1,4-Dioxane ( k 2 ) with Hydroxyl Radicals between 240 and 440 K
temp, K 240 298 350 400 440
aCalculated by using the CH2 group reactivity in linear aliphatic ethers. bCalculated by using the structure activity relationship of ref 10. 'Also named oxetane. dSee ref 13. 'See ref 14.
ki(T)' (10.0 f 0.51 '(9.15 f 0.43)
k2(V
0.8) (10.9 f osj (9.55 f 0.58) (9.68 f 0.83) (10.4 f 0.9) (1 1.8 f
(10.6 f 0.2) (9.65 f 0.31) (9.72 f 1.18)
"Expressed in units of cm3 molecule-l resent 20 from a least-squares analysis. 20.0
Results
r
-
s-l.
Quoted errors rep ----
1
At the radical concentrations estimated above, the intensity of the OH fluorescence is directly proportional to the OH concentration and the following integrated first-order rate expression can be used to determine the kinetic parameters:
F, = F,, exp{-k'Yt - to))= Froexp(-(k,
+ k,[Rl)(t - to))
(I)
where Froand F, are the OH radical fluorescence intensities at times to and t, respectively, kistis the total first-order decay rate, ko is the first-order rate constant for OH removal in the absence of reactant (attributed to diffusion out of the viewing zone and reaction with possible impurities in the argon diluent gas), and k , is the bimolecular rate constant for the reaction of OH with the reactant, R . At every reactant concentration, a value of kist was determined by nonlinear least-squares fit of the OH fluorescence decay curve to eq I. A corresponding ko value was similarly determined (for the various conditions of total pressure, flow rate, and temperature) in the absence of reactant gas and ranged from 25 to 50 s-I at T 5 298 K, increasing to 50-80 s-l at higher temperature. These ko values were reproducible to within I O s-l for a given set of experimental conditions and represented a small contribution to most of the kist measurements, which ranged as high as 1000 s-I in the presence of reactant. k, was then determined from linear least-squares analyses of plots of (klSt - k,) versus ether concentration. In all experiments, exponential decays of the resonance fluorescence signal were observed over at least three half-lives and the measured decay rates exhibited a linear dependence on the reactant concentration. The data statistics in Figure 1, for 1,3dioxane at 298 K, are typical of those for all of the reactants over the 25-50-Torr total pressure range. A value of kl(298 K) = (9.15 i 0.43) X lo-'* cm3 molecule-' s-l, obtained from a linear least-squares analysis of these data, is indicated by the line drawn in the figure. Unless specified differently, all quoted errors are 2 standard deviations and do not include our estimated 5-10%
70
7.0
,-
6.0
J
}
1
5.0 1 2.0
I
2.5
3.0
3.5
4.0
-1 4.5
1 OOO/T. K-'
Figure 2. Arrhenius plot for the reaction of hydroxyl radicals with 1,3-dioxane (0)and 1,4-dioxane (A). The solid and dashed lines correspond to the Arrhenius equations given in the text for k , and k,,
respectively. additional uncertainty for systematic errors in such experiments. Variation of the flash energy (and hence [OH],) by a factor of 3 and of the reaction mixture residence time by a factor of 4 resulted in no change in any of the measured rate constants. Thus, the results appear to be free from complications due to secondary reactions involving either reaction products or photofragments. The complete set of room-temperature (298 K) rate constants measured in the present work are given in Table I along with recent results for tetrahydrof~ran'~ and 1,3,5-trioxane.14 The chemical structure of each of these compounds is given in Table 11. The results obtained for reactions 1 and 2 over the temperature range 240-440 K are presented in Table 111. Arrhenius plots for these (13) The rate constant presented is an average of the three measurements for tetrahydrofuran summarized in ref 6 . (14) Zabarnick, S . S . ; Fleming, J. W.; Lin, M . C. Int. J . Chem. Kinel. 1988, 20, 117 .
The Journal of Physical Chemistry, Vol. 94, No. 5 , 1990 1883
Reactions of Hydroxyl Radicals with Cyclic Ethers
/ /
I
N
-b I ?
/'
J 0
0
1
2
3
Number of
4
5
6
I
7
CH2 Groups
Figure 3. Rate constants for the reactions of O H with cyclic ethers as a function of the number of C H 2 groups in the reactant molecule: 1,3,5-trioxane ( 0 ) ;1,3-dioxane (A);1,4-dioxane (V);tetrahydropyran (+); oxepane (m); trimethylene oxide (0);and tetrahydrofuran (A). The solid line is a linear least-squares fit to the solid points and corresponds to a C H I group reactivity of 2.6 X cm3 molecule-' s-l. The dashed line corresponds to the C H 2 group reactivity previously determined for linear aliphatic ethers (4.5 X cm3 molecule-l s-I).
two dioxanes appear in Figure 2, and the Arrhenius equations resulting from a linear least-squares analysis of the data and corresponding to the lines drawn in the figure are expressed as k, = (9.4 f 0 . 2 ) X exp[(lO f 6 0 ) / T j cm3 molecule-' s-l and k2 = (8.3 f 2.2) X
exp[(80 f 90)/Tj cm3 molecule-'
s-I
Discussion The rate constants determined in the present study are the first to be reported for these cyclic ethers. Thus, our discussion will focus on the derivation of reactivity values for the hydrocarbon groups in these compounds and the comparison of these values with those for the same groups in linear aliphatic oxygenates (a complete tabulation of which may be found in ref 8). In Table I we have also listed the rate constants calculated at 298 K for the cyclic ethers by using the CHI group reactivity (GR) value determined from our analysis of rate constants for aliphatic ethers,' (4.5 f 0.5) X lo-'* cm3 molecule-' s-I. As can be seen, use of this G R value results in an overestimation of every rate constant, especially those for six-member rings or larger. This is seen more graphically in Figure 3 where we have plotted the rate constants vs the number of CH2 groups for four-member (trimethylene oxide), five-member (tetrahydrofuran), six-member ( 1,3-dioxane, 1 ,Cdioxane, 1,3,5-trioxane, and tetrahydropyran), and seven-member (oxepane) ring cyclic ethers. The solid line in the figure is a linear least-squares fit to the six- and sevenmember-ring data (solid points) and corresponds to a CH2 group cm3 molecule-' s-I. reactivity in these cyclic ethers of 2.6 X The dashed line corresponds to the (70% larger) C H 2 reactivity in linear aliphatic ethers. This difference in CH2 reactivity is consistent with that observed between aliphatic and cyclic alkanes.1° It is further apparent from this plot that there is no increase in CH, group reactivity within the cyclic ethers due to
the presence of a second or even a third ether function. This result may be contrasted with our recently reported 25% increase in the reactivity of CH2 groups positioned between two ether functions in linear aliphatic polyethers. Also listed in Table I are the rate constants predicted from the structure activity relationship (SAR) developed by Atkinson.Io As can be seen from a comparison with the measured values, significant revision of the SAR formulation derived from simpler aliphatic compounds is required for the cyclic ethers. The reason for the higher reactivity of CH, groups in four- and five-member-ring cyclic ethers (trimethylene oxide and tetrahydrofuran, plotted as open points in Figure 3) is not immediately apparent. While one might anticipate structural effects on bond energies to play an important role, the 70% higher O H rate constant for tetrahydrofuran than for 1,Cdioxane is particularly puzzling, since the latter has twice as many weak (Y C-H bonds. This difference in reactivity between these two compounds has been noted in both the gas (OH and O(3P)'s) and solution (SO4-, NO3, H , and O H ) phases as summarized in ref 16 and appears t o be amplified as one goes to less reactive attacking species. From the present rate constant determination for 4-methyl1,3-dioxane, we can use the CH, reactivity in cyclic ethers derived above to estimate a group reactivity value for C H in a cyclic ether. To do this, we must assume that the reactivity of the CH3 group in 4-methyl- 1,3-dioxane is equal to that previously determined for CH3 groups (Y to a tertiary carbon atom adjacent to an ether cm3 molecule-' s-').'-~ Thus, we derive a function (0.7 X C H reactivity in cyclic ethers of 2.8 X lo-', cm3 molecule-' s-I (a little more than half of that calculated for a C H group in linear aliphatic ethers9). The derived Arrhenius parameters for the reactions of 1,3- and 1,4-dioxane (Le., values of E / R that are statistically indistinguishable from one another and from zero) are consistent with those we have reported for other ethers. Such small "inverse" temperature dependencies of reactions occurring through direct hydrogen atom transfer can be attributed to zero or near-zero activation energies associated with abstraction from weak C-H bonds coupled with the anticipated temperature dependence of the preexponential factor in the Arrhenius expression. Finally, using the present results and an assumed average tropospheric O H concentration of lo6 ~ m - we ~ , can calculate reactive lifetimes with respect to O H in the troposphere ranging from 18 to 30 h for the cyclic ethers of the present study. Thus, reaction with O H is the dominant atmospheric sink for these compounds since solar phot~lysis'~ of most oxygenated organics and their reactions with O3or NO3'* are considerably slower.
Acknowledgment. The research described herein was conducted at the National Institute of Standards and Technology (formerly the National Bureau of Standards) with the partial support of the National Aeronautics and Space Administration under Interagency Agreement W-15,816. Registry No. THF, 109-99-9; hydroxy radical, 3352-57-6; 1,3-dioxane, 505-22-6; 1,4-dioxane, 123-91-1; 4-methyl-l,3-dioxane, 1120-97-4; trimethyl oxide, 503-30-0; tetrahydropyran, 142-68-7; oxepane, 592-90-5; 1,3,5-trioxane, 110-88-3. (15) Liu, R.; Dagaut, P.; Huie, R. E.; Kurylo, M. J., to be submitted for publication. (16) Huie, R. E.; Clifton, C. L. Int. J . Chem. Kine?.,in press. (17) Calvert, J.; Pitts, J. N., Jr. Photochemistry; Wiley: New York, 1966. (18) Atkinson, R.; Carter, W. P. L. Chem. Rev. 1984, 84, 437.
