J . Phys. Chem. 1991, 95, 8741-8744 at 122 eV, which corresponds quite well to the graphite LDF density of states.36
5. Conclusions LDF atomization energies are significantly greater for icosahedral Clmand Cw, than for icosahedral Cm Both of these larger fullerenes have only slightly smaller HOMO-LUMO gaps and ionization potentials than Cbo. Cso has an electron affinity that is smaller than the electron affinities of Ciao and CZ4by 0.7 and 0.8 eV, respectively. Thus, we see no energetic barrier to the creation of these two larger Ih fullerenes. If these two larger molecules cannot be made in significant quantities by using methods similiar to those used to isolate c60, CT0,and Cg4,1-7despite the fact that laser vaporization sources can currently generate carbon clusters in this larger mass range,
8741
then it is likely that the isomerization energy associated with moving one of the 12 pentagons of carbon atoms around on the surface of fullerenes in at least the Clmto CZMsize range is quite low. If they can be made in quantity, then our photoelectron spectra should be a useful diagnostic.
Note: After we submitted this paper, MNDO calculations of the vibrational spectra of these three (and other) f~llerenes,~ have appeared and have been brought to our attention. Acknowledgment. These calculations were made using a grant of CRAY X-MP computer time from the U S . Naval Research Laboratory. This work was supportd in part by the Office of Naval Research (ONR) through the Naval Research Laboratory and through the ONR Chemistry Division Contract NOOO1491-WX-24154. ~
(36) Bianmni, A.; Hagstram, S.B. M.; Bachrach, R. Z.Phys. Rev. B 1977, 16, 5543.
(37) Bakowies, D.; Thiel, W. J . Am. Chem. Soc. 1991,113,3704; Chem. Phys. 1991, 151, 309.
Temperature Dependence of the Klnetlcs of the Reactlon BO
+ O2
C. T. Stanton,+ Nancy L. Garland, and H. H. Nelson* Chemistry Division/Code 61 IO, Naval Research Laboratory, Washington, DC 20375-5000 (Received: April 2, 1991; In Final Form: June 19, 1991)
+
The temperature and pressure dependenceof the rate constant for the reaction of BO O2is investigated in a high-temperature flow reactor. BO is generated by photolysis of BC12(0CH,) and detected by laser-induced fluorescence. Rate constants are obtained by monitoring the decay of the BO signal as a function of added O2pressure. The rate constant at room temperature is ( 1.94 0.18) X 1O-" cm3s-l and is found to be pressure independent between 20 and 200 Torr. The temperature dependence of the rate constant between 300 and 1000 K can be represented by the Arrhenius expression k(T) = (7.0 f 0.6) X cm3s-I exp[(0.51 f 0.08 kcal mol-I)/RT]. A mechanism involving formation of a BO3adduct with subsequent decomposition to BO2 0 is proposed to account for the observed negative temperature dependence.
*
+
Introduction There has been a recent resurgence of interest in the chemical reactions of small boron-containing radicals for several reasons. First, boron compounds, especially hydrides, oxides, and oxyhydrides, are extremely attractive systems for theoretical study because they have a small number of valence electrons. Calculations of heats of formation, reaction rate constants, and dimerization energies of boron species have been reported Second, there is a practical interest in the combustion of boron and boron-doped hydrocarbon fuels and propellants due to the potential for large energy release on combustion of these systems. The highest gravimetric and volumetric exothermicities are available from the combustion of elemental boron; however, this process is hampered by the presence of a boron oxide coating on the boron particles which inhibits oxygen transport to the elemental boron. One solution to this problem is to burn the boron as an additive in a system where there are sufficient radicals present a t lower temperatures to attack the oxide layer or in which the temperature is high enough for the oxide coating to vaporize. This is the situation that may be found, for example, in the combustion of boron-doped hydrocarbon fuels. A homogeneous combustion model for such a system of boron doped in hydrocarbon fuels has recently been published.6 The oxidation of boron proceeds through the sequence B
- - \-/ BO
BO2
8203
(1)
HOBO
'ONT/NRL Postdoctoral Research Associate. Present address: Code R13. Naval Surface Warfare Center, Silver Spring, MD 20903-5000.
0022-3654/91/209S-8741$02.50/0
One of the key reactions in this sequence is the reaction of BO with molecular oxygen BO 02 BO2 + 0 (2)
+
+
Reliable modeling of boron combustion requires an accurate characterization of the temperature and pressure dependence of the rate constants for this and other elementary reactions which lead from B to B203. There have been two reports of the room temperature rate constant for reaction 17,*Llewellyn, Fontijn, and Clyne7 investigated the feasibility of using flow tube techniques to study reactions of boron oxide radicals. BO for this study was generated by the reaction of BCI, with N and 0 atoms produced in a microwave discharge. This method was used to avoid the problem of dimer (B202) formationlo which plagued other BO production techniques. However, it resulted in low fluxes of BO and cor( I ) Page, M. J . Phys. Chem. 1989, 93, 3639. (2) Page, M.; Adams, G.; Binkley, J. S.; Melius, C. F. J . Phys. Chem. 1987, 91, 2675. (3) Curtiss, L. A,; Pople, J. A. J . Chem. Phys. 1988, 89, 614. (4) Dewar, M. J. S.; Jie, C.; Zoebisch, E. G . Organometallics 1988, 7,513. (5) Harrison, J. A.; Maclagan, R. G . A. R. Chem. Phys. Lett. 1988,146, 243. (6) Yetter, R. A,; Rabitz, H.; Dryer, F. L.; Brown, R. C.; Kolb, C. E. Combust. Flame 1991.83, 43. (7) Llewellyn, I. P.; Fontijn, A.; Clyne, M. A. A. Chem. Phys. Lett. 1981, 84, 504. (8) Oldenborg, R. C.; Baughcum, S. L.; Winn, K. R. Submitted to J . Phys. Chem. (9) Oldenborg, R. C.; Baughcum, S.L. Aduances in Laser Science I; AIP Conference Proceedings 146; Stwalley, W. C., Lapp, M., Eds.; AIP New York, 1986; p 562. (10) Scheer, M. D. J . Phys. Chem. 1958, 62, 490.
0 1991 American Chemical Society
8742 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
Stanton et al.
reaction tube. A smaller flow of the buffer gas is directed over the optical windows to prevent clouding. Finally, the BO photolytic Pump t + Baratron precursor, diluted with the remaining buffer gas, enters the chamber through a water-cooled, insulated, movable inlet which serves to minimize thermal decomposition of the precursor. Direct determination of the gas temperature in the reaction zone is achieved by measuring the rotational temperature of CH radicals generated by the photolysis of CHBr3 or CHBrCI2. These temperatures are derived from excitation scans of the B2Z- X211 (0,O)band. All temperature measurements are made after a minimum 5 ps delay following photolysis to insure thermalization of the CH radicals. The reported temperatures are an average of the temperatures derived from 3-4 separate spectral scans. BO radicals are generated by the 193-nm photolysis of diI chloromethyl borate (BC12(OCH3))using the output of a Lambda Buffer Gas/Reactant inlet Physik EMG 201MSC excimer laser. The photolysis beam is directed through a 1-cm aperture, focused with a 50 cm focal \ Precursor length S1 lens, passed through a 6-mm-diameter iris and directed Figure 1. Schematic diagram of the high-temperature reactor used in through the cell. Photolysis laser energies range from 10 to 25 this work. The double-lined arrows indicate the path of the laser beams. mJ/pulse. The BO radicals are probed by laser-induced fluorescence (LIF), exciting the A211 X2Z+ (5,O) band near respondingly large uncertainties in the measured rate constant. 339 nm, using a Lambda Physik excimer-pumped dye laser An appreciable loss of BO on the injector and walls of their flow (EMG 102/FL2002) operating with PTP in dioxane. Typically reactor further complicated the kinetic measurements. Llewellyn we excite the 416 transition at -339.0 nm. Probe laser pulse et aL7 report a pressure-independent rate constant for reaction energies are typically 20-40 pJ. The pump and probe laser beams 2 of (4.4_+,42)X 10-I2 cm3 s-I over the range of 1.9-5.5 Torr. enter and counterpropagatethrough the cell via 12.5-cm-long arms In a more recent study of reaction 2, Oldenborg, Baughcum, equipped with optical ports. The resulting BO fluorescence is and Winn8produced BO by a two-step process; photolysis of BCI3 collected at 90' to the laser paths with a two-lens telescope and produced B atoms which subsequently reacted with O2to generate imaged through an iris onto a filtered photomultiplier tube (PMT) BO. This method avoids the problems of BO loss on the walls (RCA C3 1000M). A narrow-band interference filter (Corion encountered by Llewellyn et aL7 but produces BO with a high level P10-365-R; Xo = 365 nm; fwhm = 12 nm) was used to transmit of internal excitation. Oldenborg et aL8 estimate that only 1.5% fluorescence from the (5,l) band and to reduce scattered light of the BO is initially produced in the probed level, v" = 0. With from the probe laser. The PMT output is captured by a gated vibrational relaxation occurring on the same time scale as reaction, integrator (Stanford Research Systems Model 250) and digitized the measured BO v" = 0 decay is the sum of production terms and stored by a microcomputer. involving relaxation by O2 and the buffer gas, Ar, and loss by Temporal profiles of the radical concentration are obtained by reaction with 02.After analyzing their decays using a model varying the time delay between the photolysis and probe lasers. incorporating the effects of vibrational relaxation, Oldenborg et A minimum probe laser delay of 5 ps is used to allow the emission aL8 report a pressure-independent rate constant of (2.3 f 0.2) X from excited-state photoproducts to decay and to allow the BO lo-" cm3 s-I over the range 10-250 Torr. The large difference radicals to rotationally and translationally thermalize. A digital between this value and that reported by Llewellyn et ah7 cannot delay generator (SRS DG-535) provides trigger pulses to the lasers be explained by the different pressures used, however, as reaction and the gated integrator; the time delay is controlled by commands 2 was found to be pressure-independent in both studies as had from the computer. Twenty points of baseline and 500 points of been expected for a simple atom-transfer reaction. Oldenborg signal, each an average of 3-10 laser shots, are collected for each and Baughcum have also reported in a conference proceedings decay measurement. that the rate constant for reaction 2 "decreases with increasing Experiments are performed under pseudo-first-orderconditions temperature in a non-Arrhenius fa~hion".~ with at least a 5 times excess of reactant over radical precursor. We report here a measurement of both the pressure and temIn the absence of added reactant, the disappearance of BO is due perature dependence of the rate constant for the reaction of BO to diffusion from the viewing region and reaction with the pre+ 02. Our measurements are made using a laser photolysis cursor and other photolysis products. When reactant O2is added, technique which produces BO directly, primarily in v" = 0. This the temporal profile measured is well approximated by a single method avoids the problems associated with both previous room exponential decay over 2-3 lifetimes. temperature measurements of this important rate constant. The Dichloromethyl borate was synthesized following the method results from this study allow us to resolve the discrepancy between of Gerrard and Lappert.13 Trimethyl borate (B(OCH3),) is slowly the two reported measurements of the rate constant for reaction dropped under vacuum into a slight excess of liquid BCI3 (1 :2 2 and to predict the value at combustion temperatures. molar ratio) maintained at 210 K using a CHC13/liquid nitrogen Experimental Section slush. The mixture is warmed to room temperature and the excess BC13 is pumped off. The resulting BC12(0CH3)is transferred The kinetic measurements are made in a high-temperature under vacuum to a glass saturator and stored in the refrigerator reactor, Figure 1, based on a design of Marshall and Fontijn" until use. During use, the precursor is held in the saturator at which we have described in detail recently.12 Briefly, it consists 0 OC and entrained in a buffer gas flow before entering the reaction of a 5-cm4.d. mullite reaction tube heated by four banks of Sic cell. Typical flow conditions, measured with calibrated Tylan mass resistance heating elements. This assembly is surrounded by a flowmeters and/or controllers, are 2-7 sccm buffer gas through 2.5-cm layer of zirconium oxide insulation and a stainless steel, the saturator, 60 sccm of buffer gas directed at the windows, and water-cooled vacuum housing. Four ports in the vacuum chamber 0-130 sccm of the reactant O2mixed with 400440 sccm of buffer and reaction tube allow optical access for the pump and probe gas. In an initial set of experiments at room temperature, He, laser beams and observation of fluorescence. The majority of the N2, Ar, and an N2/SF6 mixture were used as buffer gases at total buffer gas and the reactant enter the vacuum chamber from the pressures from 10 to 200 Torr. The temperature dependence bottom and are heated by wall collisions as they flow up the measurements were carried out at a total pressure of 50 Torr using Ar as the buffer gas. He (Air Products, 99.995%), N2 (Air
-
'
-
( 1 1) Marshall, P.; Fontijn, A. J. Chem. Phys. 1986, 85, 2637. (12) Garland, N. L.; Stanton, C. T.; Fleming, J. W.; Baronavski, A. P.; Nelson, H. H. J . Phys. Chem. 1990, 94,4952.
(13) Gerrard, W.;Lappert, M. F. J. Chem. Soc. 1955, 3084.
Kinetics of the BO
+ O2 Reaction
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 8743
t' 14
I5
2 8 c,
IO
12
I3
17
I8
16
I5
14
9
13
I
0
/
8 7 6 I2
I1
IO
0.0
0.4
1.2
0.0
0, Pressure (Torr)
"
340.0
I
1
339.8
339.6 339.4 339.2 Wavelength (nm)
339.0
-
Figure 2. Laser-induced fluorescence excitation spectrum of A211 X22+ ($0) band of the BO radical produced from the photolysis of (BCI,(OCH,)) with photolysis pulse energies of 15 mJ. I
I
I
Figure 4. Plot of the pseudo-fint-order disappearance rate constants for BO as a function of O2pressure at 967 K. The symbols are measured decays and the solid line is the result of a linear least-squares fit to the measured values. TABLE I: Pressure and Buffer Cas Dependence of the Room TemPerature Rate Constant for the Reaction BO + O? total press., Torr buffer gas kbi f lo, cm3s-I
17 42 45 46 47 50 60 68 111
195
He Ar
He NZ Ar Ar
25% SFs, 75% Nz N2
N2 He
1.98 f 0.21 2.14 f 0.23 1.88 f 0.17 1.80f 0.21 2.57 f 0.29 1.95 f 0.18 1.60f 0.17 1.95 f 0.18 2.14 f 0.20 1.88 f 0.19
TABLE II: Temperature Dependence of the Bimolecular Rate Constant for the Reaction of BO Ol kh f 10, kbi f lo, T f 1 u, K cm3s-I T f lo, K cm3s-l 294 f 6 1.94f 0.18 878 f 52 1.04 f 0.10 394 f 14 1.23 f 0.12 921 f 60 0.79 f 0.07 1.22 f 0.11 967 f 125 1.10 0.10 433 f 15 0.96 f 0.08 994 f 76 0.87 f 0.11 493 f 25
+
0
50
100
150
-
reaction time (ps) Figure 3. Plot of the BO A211 XzZ+ LIF intensity as a function of time in the presence of 154 mTorr of O2at 967 K. The points are the measured intensities and the solid line is a nonlinear least-squares tit to
the data. Products, 99.998%), Ar (Air Products, 99.995%), SF, (Matheson, 99.99%), and O2 (Matheson, 99.98%) were as received. Results and Discussion Photolytic Production of BO. Photolysis of BC12(OCH3fwith laser pulse energies in the range 10-25 mJ results in the clean production of BO, primarily in u" = 0. An excitation spectrum of the A2U-X22+ (5,O) band of BO produced in this manner is shown in Figure 2. The spectrum is assigned by using line positions reported in the 1iterat~re.I~Under these photolysis conditions, we have determined the degree of vibrational excitation in the product BO by recording an LIF excitation spectrum of the A211-X22+ (0,l) band and attempting to record a spectrum of the ( I ,2) band. From the estimate of our sensitivity for these bands, derived using the Franck-Condon factors reported by Lizst and Smith,Is we can calculate the ratio BO(u=O):BO(u=l) to be 27:l. BO(u=2) could not be detected but from an estimate of the signal to noise ratio in our measurement we can derive a lower limit to the ratio BO(u=O):BO(u=2) to be 50. At higher photolysis pulse energies, new spectral features are observed in this wavelength region. The use of N2as the buffer gas appears to increase the intensity of these features. A preliminary analysis of these bands, using combination differences, (14) Coxon, J. A.; Foster, S.C.;Naxakis,S. J . Mol. Specrrosc. 1984, 105,
A6 5 .--.
(15) Lizst, H.S.:Smith, W . H.J . Quanr. Specrrosc. Radial. Transfer 1971, 1 1 , 1043.
*
721 f 40
1.10f 0.10
reveals that these features definitely do not belong to BO but the identity of the carrier remains uncertain. Further investigations of these spectral features are underway. For the present study it is sufficient to note that none of the new spectral features overlap the line used for the kinetics studies and our kinetics measurements are not affected by the presence of this unidentified species. BO O2 Reaction. Pseudo-first-order rate constants are measured by monitoring the disappearance of BO in the presence of added 02.Figure 3 shows a typical BO decay measured a t 967 K in the presence of 154 mTorr of 02.The second-order bimolecular rate constant is derived from the slope of a plot of the measured first-order rate constants versus O2pressure. This is illustrated by the data in Figure 4 which were also obtained a t 967 K. These measurements are repeated as a function of temperature to obtain the Arrhenius parameters. In order to investigate one possibility for the difference between the two previous measurements of k2,',* we measured the room temperature rate constant at total pressures from 17 to 195 Torr using a variety of buffer gases. These data are listed in Table I. As can be seen, there is no significant variation of the measured rate constant with total pressure or buffer gas. A weighted average of these values gives a room temperature rate constant of (1.94 f 0.18) X cm3s-'. This value is in excellent agreement with that reported by Oldenborg et a1.* of (2.3 f 0.2) X lo-" cm3 s-l. The close correspondence between our result obtained in a system where there is no possibility of vibrational relaxation interfering with the reaction rate constant measurement and that of Oldenborg et a1.8 confirms that they have successfully accounted for vibrational relaxation in their system.
+
8744 The Journal of Physical Chemistry, Vol. 95, No. 22, 1991
Stanton et al. transition states similar to the recent work of McEwen and Golden'8 on the reaction of ?err-butyl radical + HI. These calculations result in qualitative agreement with our measured results. The calculations show a slight negative temperature dependence for the observed loss of BO which results from the rate of BO3*decomposition into products (BO2 0)increasing more slowly with temperature than the rate of decomposition back to reactants (BO 02). That is, the ratio of these two processes exhibits a negative temperature dependence. The RRKM calculations predict complex lifetimes of a few picoseconds at even the lowest levels of excitation which result in no pressure dependence of the observed rate constant up to several atmospheres at room temperature in agreement with our measurements. The qualitative agreement obtained is not unique to this particular geometry and erlergy of the BO3 adduct. All that is required is a loose entrance channel transition state and a tighter exit channel transition state. In addition, we are able to obtain agreement with our measured temperature dependence using either a small barrier to the back reaction, BO2 0, as illustrated in Figure 6 or no barrier and a somewhat tighter transition state. Therefore, a more quantitative model for this reaction will require detailed calculationsof the potential energy surface for this system. This interpretation is in good agreement with that suggested for the reaction of A10 with O2by Fontijn.I9 In the case of A10 + 02,the overall reaction is more nearly thermoneutral. Thus, the A103complex is even more likely to dissociate back to reactants than is the BO3 intermediate in the BO O2reaction. This results in a lower A factor for the A10 + O2reaction, (2.3 f 0.6) X IO-" cm3 s-I,I9 than found in this study for BO 02,(7.0 f 0.6)X cm3 s-'.
+
+
1.0
1.5
2.0 2.5 (10-3 KT
ut
3.0
3.5
Figure 5. Arrhenius plot for the measured bimolecular rate constants for the reaction BO + Oz. The vertical and horizontal error bars represent 2 0 errors in the rate constants and temperatures, respectively. The solid line is the result of a weighted linear least-squares fit to the data.
+
+
+
Figure 6. A schematic diagram of the reaction coordinate for the reaction of BO + O2 The energy and structure of the BO,intermediate are from a preliminary calculation of Saxe.16
The temperature dependence of this reaction between 300 and lo00 K was determined from a series of measurements at a total pressure of -50 Torr using Ar as buffer gas. The rate constants obtained are listed in Table I1 and displayed as an Arrhenius plot in Figure 5. A weighted linear least-squares fit of the data to the Arrhenius expression, k(7') = A exp(-EJRT), yields an A factor of (7.0f 0.6) X cm3 s-I and E,, = -0.51 f 0.08 kcal mol-'. Although the observed lack of a pressure dependence for the Mom temperature rate constant for this reaction led earlier workers to conclude that the mechanism for this reaction is a simple atom transfer, the Arrhenius parameters we report are diffioult to reconcile with this mechanism. We are able to rationalize the observed temperature dependence on the basis of a mechanism involving BO3 formation as suggested by Oldenborg and B a u g h c ~ m .This ~ mechanism is illustrated in Figure 6. In this scheme, the reaction proceeds through a loose transition state to formation of a BO3 adduct. This complex can either proceed to products through a second, more rigid transition state (with or without a small barrier to the reverse reaction, BO2 0) or dissociate back to reactants. We assume that complex stabiliaition is not important at the pressures appropriate to this study since the measured rate constant is independent of pressure. The energy and qualitative structure of the BO3 intermediate in this figure are based on the results of a preliminary SCF/CI calculation of Saxe.16 The relative energy has been previously reported by Oldenborg and Baughcum." Using this proposed mechanism, we have performed chemical activation, R R K M calculations using a vibrational model for the
+
(16) Saxe, P. Private communication. (17) Oldenborg, R. C.; Baughcum, S. L. Absrr. 1986 Contractors Meeting Combust. 1986, 57.
AFOSRIONR
Conclusion We have measured the temperature dependence of the rate of the reaction of BO + 02, a key reaction in the oxidation of boron. Our room temperature value and the lack of any pressure dependence of hlficawred rate constant confirm the recent results of Oldenborg et ala8 We propose that the reaction proceeds through a bound BO3 complex and have used this model to qualitatively explain the lack of pressure dependence and the observed negative temperature dependence. Our measurements extrapolate to -7.7 X 1O-I2 cm3 s-l for the rate constant for this reaction in the temperature range 2000-2500 K appropriate to boron combustion. It is, of coufse,possible that a direct aha" channel with higher activation energy may dominate the reaction at these temperatures. There are several other reactions of the BO radical that need to be investigated in order to develop a complete picture of the 'behavior of this radical in combustion systems. One of the most prominent of these is the reaction of BO + H2, for which there is a recent theoretical prediction of the rate constant as a function of temperature.' This reaction is under investigation in our laboratories. There have been several important discoveries, both theoretical and experimental, in the field of small, gas-phase boron species and their reaction chemistry in the past three years. Several of these impact heavily on the gas-phase boron combustion model that has been published.6 We are in the process of evaluating these new data and, if required, plan to update and extend this model. Acknowledgment. We thank Rich Oldenborg for providing copies of his manuscript prior to publication and for helpful discussions, S.C. Foster and J. A. Coxon for providing tables of rotational assignments for the BO spectrum, P.Saxe for providing details of his unpublished work, and the Office of Naval Research for the funding for this study. R e m NO. BO, 12505-77-0; 02,7782-44-7. (18) McEwen, A. B.; Golden, D. M. J . Mol. Srrucr. 1990. 224, 357. (19) Fontijn, A. Combust. Sci. Techno/. 1986,50, 151.
