Ind. Eng. Chem. Res. 1992,31, 19-29 Simon, M.; Back, M. H. Kinetics of the Pyrolysis of Propylene. Part I. Can. J. Chem. 1970a,48,317. Simon, M.;Back, M. H. Kinetics of the Pyrolysis of Propylene. Part 11. Can. J. Chem. 1970b,48,3313. Tavernier, D.; Hosten, N.; Anteunis, M. Synthesis of cis1,2,3,4,4a,5,8,8a-Octahydronaphthaleneand cis-transoid-cis1,4,4a,5,8,8a,9,9a,lO,lOa-Decahydroanthracene. Synthesis 1979, 613. Watkins, K. W.; Olsen, D. K. Cyclization and Decomposition of
19
4-Penten-l-yl Radical in the Gas Phase. J. Phys. Chem. 1972,76, 1089. Wheeler, R. V.; Wood, W. L. The Mechanism of Thermal Decomposition of the Normal Olefins. J. Chem. SOC.1930,1819.
Received for review August 1, 1990 Revised manuscript received January 11,1991 Accepted January 21, 1991
New Method for Studying the Pyrolysis of VPE/CVD Precursors under Vacuum Conditions. Application to Trimethylantimony and Tetramethyltin Glenn D. Svoboda* and John
T.Gleaves
Department of Chemical Engineering, Washington University, One Brookings Drive, St. Louis, Missouri 63130-4899
P a t r i c k L. Mills Central Research and Development, Du Pont Company, Experimental Station, Wilmington, Delaware 19880-0262
The gas-phase pyrolysis reactions of trimethylantimony and tetramethyltin are studied under vacuum conditions. The experimental method is based upon introducing the organometallic precursor from either a high-speed molecular beam type pulse valve or a continuous feed source into a fixed-bed microreactor under high vacuum, and measuring the transient response or steady-state performance using a quadrupole mass spectrometer. Interpretation of the steady-state mass spectrometer cracking patterns shows that the pyrolysis results primarily in the formation of methane and ethane as stable gas-phase reaction products. Analysis of the transient response data shows that the pyrolysis behaves according to a first-order unimolecular reaction where the activation energies for trimethylantimony and tetramethyltin are 41.1 and 59.1 kcal/mol, respectively.
Introduction Pyrolysis of organic and inorganic compounds generally involves homogeneous gas-phase reactions and heterogeneous gas-solid catalyzed reactions which occur at elevated temperatures and either atmospheric or subatmospheric pressures (Boudart and Djega-Mariadassou, 1984;Spokes and Benson, 1967,1970).Experimental determination of fundamental kinetic and thermochemical parameters for the low-pressure gas-phase thermal decomposition of various organic compounds provided some of the first reliable data in the field (Colussi and Benson, 1977a,b; Golden et al., 1973, 1974; King et al., 1971; King and Goddard, 1975a,b;Stein et al., 1976). Concise overviews of the key experimental and theoretical developments during this period are provided in the authoritative papers of Benson and co-workers (Spokes and Benson, 1967; Golden et al., 1973). An emerging area where pyrolysis chemistry and kinetics are gaining increasing attention is vapor-phase epitaxy (VPE) and chemical vapor deposition (CVD). In these processes, decomposition of organometallic precursors is used to deposit thin films of selected metals and form unique solid lattice structures. These decomposition reactions often involve a variety of highly reactive gas-phase and surface-active intermediates during the solid film deposition and growth (Stringfellow, 1989). It is known, for example, that highly reactive organometallic intermediates are an important element in CVD processes for the deposition of silicon (Coltrin et al., 1984). Stable molecules,
* Author to whom correspondence should be addressed. 0888-588519212631-0019$03.00/0
such as SiH,, are converted by thermal pyrolysis or electron impact plasma into radicals, such as SM2or SM3,that react in the gas phase or on the growing film surface. As another example, the decomposition of organometallic precursors is used to produce group III-V and group II-VI semiconductors, such as those containing AlGaAs, HgCdTe, or ZnS (Dupuis, 1984;Ludovise, 1985;Stringfellow, 1989). Very little is known about the reaction pathways and reactive intermediates of these processes. Typical precursor molecules, such as Me& ASH, EbGa, and EtJn, are thought to form free radicals by homolysis of metal carbon bonds or metal hydrides and olefins by elimination reactions under pyrolysis conditions on a hot deposition surface. From the study of these systems and others provided in detail elsewhere (Stringfellow, 1989), it is evident that some differences exist between pyrolysis of organometallic precursors and more conventional hydrocarbon pyrolysis. A particularly noteworthy one in the case of pyrolysis of organometallic precursors is the presence of homogeneous gas-phase reactions coupled with heterogeneous surface reactions where the latter type contribute to the growing solid lattice. Recent work on the pyrolysis of MqIn and PH3 in either pure form or as binary mixtures on SiOz (Stringfellow et al., 1987)using D2 as the carrier gas has led to a number of useful conclusions on the probable reactive intermediates and reaction pathways for this system. It was shown, for example, that the pyrolysis of binary mixtures of Me31n and PH3 at elevated temperatures involves both homogeneous gas-phase and heterogeneous surface reactions where an unstable Me31n-PH3 adduct is a key intermediate and CH, and InP are stable products. It is not 0 1992 American Chemical Society
20 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992
unreasonable to expect that similar information can be obtained for other organometallic systems using well-defined experimental investigations. Most of the detailed investigations on the kinetics and mechanisms of hydrocarbon pyrolysis cited above, as well as more recent studies on pyrolysis of organometallic precursors, were based upon the analysis of steady-state performance data. Since being first introduced in the late 1960s, the very-low pressure pyrolysis (VLPP) system of Benson and co-workers (Spokes and Benson, 1967) has been extensively utilized to obtain rate measurements on fast unimolecular reactions, very fast bimolecular reactions, and very fast heterogeneous reactions (cf. Colussi et al., 1977; Islam and Benson, 1984; King et al., 1971; King and Goddard, 1975a,b). The working concept is based upon introduction of a steady flow of the hydrocarbon reactant into an isothermal reaction zone maintained at high vacuum so that Knudsen conditions exist in the system. This condition eliminates or significantly reduces secondary reactions both within and external to the pyrolysis zone. In contrast, the experimental system used by Stringfellow et al. (1987) employed a reaction zone maintained near atmospheric pressure. It would appear that this approach would result in the promotion of secondary reactions since the reactant gas would exist in the continuum regime. The advantages and disadvantages of the VLPP system of Spokes and Benson (1967) and the atmospheric pressure system of Stringfellow et al. (1987) as well as other similar systems have not been clearly examined, especially in the context of studying the kinetics and mechanisms of organometallic VPE/CVD systems. The use of transient response techniques provides an alternate approach for studying the kinetics and mechanisms in lieu of steady-state or steady-flow methods. Although the use of concentration and temperature input transients have been widely used to examine fundamental surface chemistry of heterogeneous catalysis systems (cf. Christoffel, 1989), they have not been applied to study fast pyrolysis kinetics. When compared to steady-state analysis of rate data, transient response techniques have greater potential for providing unambiguous data on reaction mechanisms since the pseudo-steady-state approximation may not be valid during the time scale of the imposed transient. In addition, if the concentration transient can be imposed on a time scale which is smaller than the relaxation time of the governing sequence of elementary steps, then it may be possible to discriminate between the kinetic parameters which describe these steps. This may not be the case using steady-state rate data since several plausible reaction mechanisms often cannot be clearly discriminated from one another in a statistical sense. Hence, it would appear that studying the kinetics and mechanisms of pyrolysis systems using transient response methods may provide useful insights and data that cannot be readily obtained using conventional steady-state methods. The primary objective of this work is to demonstrate a new method for studying the pyrolysis of VPE/CVD precursors under vacuum conditions based upon a pulsed transient response technique. This work represents a novel application of the TAP (temporal analysis of products) reactor system which, until now, has been used to study the mechanistic aspects of gas-phase heterogeneous catalyzed systems (Gleaves et al., 1988a,b, 1990). Besides demonstrating the utility of using transient response methods to examine the pyrolysis of typical organometallic precursors, such as trimethylantimony and tetramethyltin, another objective is to elucidate a possible decomposition
mechanism for these precursors on quartz particles and to determine kinetic parameters for the overall decomposition processes.
Experimental Section Apparatus. All experiments were conducted using the TAP reactor system which has been described in detail elsewhere (Gleaves et al., 1988a,b). Only the key features relevant to this application are given here. The principle components of the TAP system include (i) a gas feed system that supplies reactants to two highspeed pulse valves and a continuous-flow valve, (ii) a microreactor which can be used in either an open tubular or a packed tubular mode, (iii) three interconnected vacuum chambers that house the microreactor valve assembly and the quadrupole mass spectrometer (QMS) detector, and (iv) a dedicated Hewlett-Packard Series 9000 Model 360 computer workstation that provides a user-friendly interface between various supporting instruments along with real-time display of the experimental results. A diagram of the overall system and the various integrated components is given in Figure 1. The TAP microreactor, valves for introduction of the gas pulses, and solenoid valve for introduction of a continuous flow of reactant gas are located in the reactor vacuum chamber with vacuum being supplied from a Varian 10-in. oil diffusion pump. The ionization head of the UTI l00C quadrupole mass spectrometer is located in the detector vacuum chamber where the latter two chambers can be fully isolated using a special-purpose shutter valve. This arrangement permits the microreactor to be removed and replaced within a few minutes while maintaining the QMS under full vacuum. Primary vacuum in the combined differential-detector chambers is provided by a Varian 6411. oil diffusion pump with a liquid nitrogen trap and gate valve, with secondary vacuum being supplied from a Varian 450 L/s turbomolecular pump. Typical background pressures in the reactor vacuum chamber and the detector chamber are in the range of 5 X lo-' to 1 X Torr and 1 X lo* to 1 X lo-* Torr, respectively. The pulse valves are similar in concept to molecular beam valves available from Newport Corp. (Newport, 1984) with various modifications that provide optimal performance and simplified tuning procedures. The valve interior is divided into two separate chambers by a small stainless steel bellows. The front and back chambers contain the reactant gas and an inert backing gas, respectively. A pressure difference is maintained between the rear and front chambers using a modified Moore dome-loaded differential pressure control valve. The gas pressure in the front chamber is controlled using either pneumatic or electronic pressure controllers where the set point can be maintained between ca. 10 and 1000 Torr. The pulse intensity (i.e., the moles or molecules introduced per pulse) can be varied by changing the pressure in the front chamber or by either increasing or decreasing the ratio of the valve open-to-closed time using the pulse beam valve driver electronic controls. The TAP microreactor that was developed for this work is shown in Figure 2. The reactor had an overall length of 42.2 mm with an inner diameter of 5.6 mm and was constructed of Inconel. Heat was supplied by a radiant furnace with a tantalum wire heater element mounted in a boron nitride holder. The reactor temperature was monitored using two type K thermocouples located at 12.7 and 25.4 mm from the reactor inlet. A third type K thermocouple was situated in a side-entering thermowell at a distance of about 21 mm from the inlet. This thermocouple was used as the control point for the reactor PID
Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 21
Gas Manifold
Figure 1. Principal components of the TAP reactor syatem.
'
O-ring
---
I_
1c
2 ) ,I
1
Bed 3 8 1Length cm
v
Mounting Flange
Figure 2. Schematic of the TAP mimoreador used in the pyrolysis experiments.
temperature controller. In a typical organometallic pyrolysis experiment, the reactor was packed to a depth of 38.1 mm with 425-600-pm quartz granular particles. Materials. Trimethylantimony (Me&%) and tetramethyltin (Me&) were obtained from Strem Chemicals in electronic grade with a minimum purity of 99.999% and 98%, respectively, and were used as received without any further pretreatment. Neon, oxygen, argon, carbon dioxide, and krypton were selected as nonreacting gases and were used to verify that the gas transport in the reactor was controlled by Knudsen diffusion. They were obtained from commercial sources in standard size cylinders in research purity grade and were used as received without any further pretreatment. Binary gas mixtures of Me3Sb or Me,Sn and argon or krypton were used as feed gases for both steady-flow and pulsed transient experiments. These were prepared by blending the gases in a sample cylinder using predetermined partial pressures to a given total pressure. Quartz granules were used as an inert reactor packing to provide a heat-transfer media and to provide a surface for the organometallic deposition. They were obtained from a commercial source in rod form and subsequently crushed and screened to various size fractions. The 4256oowm size fraction was used in this work and was loaded
into the reactor with intermittent tamping to the bed depth mentioned above. TAP Experiments. Experiments were conducted using both the scan and pulse modes of operation (Gleaves et al., 1988a.b). In a typical scan experiment, a continuous flow of a binary gas mixture containing the organometallicprecursor and argon was introduced to the reactor, and the mass spectrum of the product gas was measured between m / e = 1 and m/e = 200 at various increasing temperatures. Scan experiments were used only to identify characteristic fragments of suspected reaction products, such as unreacted Me3& or Me,Sn, methane, and ethane. This mode of operation is similar to the one employed in the VLPP system described by Spokes and Benson (1967). It represents a steady-state experiment with a time resolution in which the mean residence time can be controlled from to 1s. Data obtained from this mode of operation could be used to obtain steady-flow kinetic data. This exercise is outside the scope of the present work. In a typical pulsed mode experiment, one of the pulse valves was filled to a fixed pressure of 50 Torr using one of the nonreacting gases or a binary gas mixture containing the selected organometallic precursor and krypton. The reactor temperature was set to a desired value and the pulse valve driver intensity and duration were adjusted to ensure that Knudsen conditions existed in the reactor. The QMS was then set to an appropriate amplifier range and mass center for a given m / e value. The latter was chosen to he unique for a particular species. The pulse valve driver and reactant pressure were adjusted to produce approximately 1 X lo', to 1 X loi5 molecules/pulse for Knudsen flow conditions, at a rate of 1 pulse/s for 100-200 pulses. The raw output signal from the QMS was sampled at a minimum time increment of 10 ps over a minimum sampling period of 0.1 s to produce a maximum of loo00 points per input pulse. Subsequent pulses were signal averaged to improve the signal to noise ratio and plotted in real time every 10 pulses. The final signal-averaged pulse, produced upon completion of 100-200pulses, was written to a hard-disk fde for subsequent use in further data reduction procedures and modeling.
22 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992
,MI ?-----%
I66
7.5
15.0
22.5
0
Time, sec x 100
' ' ' ' 1! 0 ' ' ' ' ' ' ' Atomic Mass Units
' ' '
'
4""""'!"'"""!'"""'!"''""'i so
0.0
10
'
'
150 ! ' '
'
'
'
'
'
'
' 21 0
Figure 4. Normalized transient response obtained from a typical Knudaen regime Me3Sb pyrolysis pulsed experiment. Conditions: inlet gas composition = 90 mol % Me3Sb-10 mol % krypton; T = 625 OC; packing = quartz granules; d, = 425-600 pm; L = 38.1 mm. Peak identification: A, m / e = 84, krypton parent; B, m / e = 151, Me3Sb fragment; C, m / e = 28, ethane fragment; D, m / e = 16, methane parent.
150
200
Atomic Mass Units
Figure 3. Mass spectra of a 85 mol % Me3Sb-15 mol % argon mixture from a scan experiment. (a) T = 300 OC. (b) T = 650 OC. Conditions: packing = quartz granules; d, = 425-650 pm; L = 38.1 mm; Q, = 5 sccm (approximately).
With the above pulse intensity and a typical reactor loading of 2 g of relatively nonporous quartz granules having a total surface area of 0.1 m2/g, a single pulse would deposit approximately O.OOO1 monolayers of metal species assuming 100% conversion. As a result, the amount of metal deposited during a data collection sequence involving 100-200 pulses would amount to &2% of the total surface area depending upon the actual conversion obtained. Scan Mode Results Mass Spectra Interpretation. Mass spectral data obtained from scan mode experiments in which a binary mixture containing ca. 85 mol % Me3Sb and 15 mol % argon was introduced to the reactor at a constant flow rate are compared in Figure 3a and Figure 3b corresponding to reactor temperatures of 300 and 650 "C, respectively. The results given here span the range of m l e = 1 to m l e = 200 since no other fragments were detected outside this range. The fragmentation patterns at 300 "C (Figure 3a) show that key fragments occur at m l e = 166,151,136,121,28, and 15 for Me3Sbat m / e = 40 and 20 for argon. This same fragmentation pattern is observed at significantly lower temperatures (e.g., 25 "C) which indicates that the decomposition of Me3Sb is insignificant between 25 and 300 "C. Independent experiments showed the onset of Me3Sb pyrolysis to occur at about 475 "Cfor the conditions used here. Since the above m / e values can be uniquely assigned to Me3Sb, the additional fragmentation patterns which appear at 650 OC (Figure 3b) can be assigned to various Me3Sb pyrolysis products. Additional inspection of the fragmentation patterns given in Figure 3b shows that the pyrolysis of Me3Sb is nearly complete since the parent peaks corresponding to the two major Me3Sb isotopes at m / e = 168 and 166 and
other primary fragments at m l e = 151,136, and 121 are nearly absent. At high Me3Sb conversions,the fragments between m l e = 26-30 can be assigned to ethane, while those between m / e = 12-16 can be assigned to methane. Trace amounts of hydrogen and C3'swere also detected. Peaks at m l e = 16 and 28 are seen to have the greatest relative intensity which agrees with the fragmentation patterns given in standard references (Stenhagen et al., 1969; Heller and Milne, 1978) for methane and ethane, respectively. From these results, it can be concluded that the decomposition of Me3Sb results primarily in the formation of methane and ethane as stable gas-phase products. As discussed later, the reaction pathways which lead to these products probably include methyl radicals as proposed intermediates. Verification of the existence of these radicals and other similar species under the steady-flow and pulsed transient conditions used here requires special experimental hardware and lies outside the scope of this work. Steady-flow pyrolysis scans for Me4Sn are similar to those given above for Me3Sb so that only a brief summary is given here. The fragmentation patterns for the MelSn (not shown) reveal that the key fragments occur at m l e = 165, 150, 135, 120, 28, and 15. These patterns remain constant until a temperature of about 600 "C which corresponds to the onset of pyrolysis. At a temperature of 750 "C, the pyrolysis of the precursor is nearly complete. Fragments between m l e = 26-30 associated with ethane and m / e = 12-16 associated with methane are present. This behavior is similar to that observed for MeaSb and suggests that the pyrolysis of these types of molecules occurs through a reaction pathway where the corresponding alkane and the coupled alkyl radicals are stable gas-phase reaction products. Pulsed Mode Results Qualitative Interpretation. Figure 4 shows the normalized transient responses for the pyrolysis of Me3Sb obtained from pulse experiments using a temperature of 625 "C. The transient responses for the pyrolysis of Me3Sb are based upon a fragment peak for Me3Sb at m l e = 151, a parent peak for krypton at m / e = 84, a fragment peak for ethane a t m / e = 28, and a parent peak for methane at m / e = 16. Other relevant experimental details are given in the figure caption. The transient responses for Me4Sn are similar and are not shown. The observed differences in the shapes of the transient responses indicate that each response curve can be uniquely associated with a particular species. The transient
Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 23 response of krypton a t mle = 84 provides a convenient reference for the remaining species since it is inert and does not contribute to the reaction sequence. If the primary mechanism of transport for the gas pulses in the reactor voids is due to Knudsen diffusion, it can be shown that the mean residence time is directly proportional to the square root of the gas molecular weight (Gleaves et al., 1988a),assuming that the pulse does not undergo exchange with the surface or chemical reaction. The transient responses in Figure 4 clearly do not follow this behavior since the species having the highest molecular weight, such as Me3Sb and krypton, have responses which emerge before those species having lower molecular weights, such as ethane and methane. The order in which the transient responses for the various species appear in Figure 4 relative to krypton is indicative of the Me3Sb reaction network. In the case of Me3Sb, the earlier emergence of Me3Sb and its narrow width relative to krypton, ethane, and methane indicates that Me3Sbis pyrolyzed to form ethane and methane. The greater width and larger mean residence time of methane compared to that of ethane suggest that it is either formed in series from ethane or through a different, slower reaction pathway. The steady-state and transient response data given above provide the basis for several postulated mechanisms which explain the formation of the observed stable products and the metal deposition on the quartz particles. Here, a free-radical-type mechanism is proposed in which the given organometallic precursor undergoes a homolytic cleavage to form methyl radicals which can recombine on the surface to form ethane or decompose to form carbon and atomic hydrogen. Methyl radicals can also combine with surface-bound atomic hydrogen or abstract a hydrogen from an alkyl radical to form methane. Recombination of methyl radicals in the gas phase is disregarded due to the existence of Knudsen conditions in the reactor. If Me3Sb is chosen as the precursor and CH3decomposes on the quartz surface, then one possible mechanism would involve the following steps where M denotes a surface site on the quartz particles. x(CHJ3Sb -!?+ x ( C H , ) ~ S+~xCH3
(1)
x(CH3)?Sbkf_ xCH3Sb + xCH3
(2)
x C H ~ S ~ xSb(s) + x C H ~
(3)
k3
+
3x - 22 4
CH,+M-
k4
3x - 22 4
C(S) +
9~ - 62 9~ - 62 H+M-CH3 + 4
4
k6
3(3x - 22)
9X - 62 4
H
+M
(4)
CHI
+M
(5)
22CH3 M -% 2C2H6 + M (6) Addition of eqs 1-6 yields the following overall reaction for the pyrolysis of Me3Sb: x (CH3)BSb
k
The mechanism for the pyrolysis of Me4Sn can be developed in an analogous fashion. Due to the similarity between this mechanism and the one shown above for Me3Sb, the details of the individual steps are not given. Addition of the individual steps yields the following overall
reaction for the pyrolysis of Me4Sn:
k
X(CH~)~S~ 1 2 -~62 xSn(s) CH4 + z C ~ H + ~4x 4- 22 C(s) (8) 4
+
-
In eqs 1-7, the stoichiometric coefficients are written in variable form since the production of methane, ethane, and surface species per mole of Me3Sb reacted was not quantitatively determined for a given set of pyrolysis conditions. One approach for assessing whether or not the proposed mechanism given in eqs 1-6 is plausible would involve a detailed analysis of the mass balance for the gas and solid phases. For example, a knowledge of the amount of precursor deposited on the surface in the form of metal and carbon-bearing species, along with the relative amounts of methane and ethane formed, would provide the data needed for identifying the stoichiometric coefficients. The gas-phaae and solid-phase product ratios could change over a given temperature range as a result of a change in the mechanism, or because of the relative change of the rate of methyl radical recombination to form ethane to that of methyl radical combination with hydrogen to form methane. A detailed analysis of the product formation and its implications on the mechanism is a topic for future study. In addition, the overall reactions given above in eqs 7 and 8 assume that the form of surface carbon is elemental carbon. It is well-known that other carbon-containing species can exist on these surfaces, such as various hydrocarbons and other similar species. Precise identification of these species would require use of various surface spectroscopic and other sophisticated analytical techniques, and is also a topic for future research. Quantitative Interpretation. Quantitative interpretation of the Me3Sb and MelSn transient response data can be performed using a mathematical model that accounts for the transport-kinetics interactions that occur during the passage of a gas pulse from the reactor inlet through the reactor to the mass spectrometer. Initial efforts on modeling of the TAP reactor transient responses where the primary objective was to compare model-predicted responses for a few basic types of mechanisms that describe heterogeneous catalyzed systems are given by Gleaves et al. (1988a). These models assumed that homogeneous gas-phase reactions, such as those that might occur during pyrolysis, were absent. In addition, the inlet gas pulse was assumed to be an ideal Dirac 6 function so that deviations of the gas pulse that occur outside the reaction zone, such as between the pulse valve and the reactor inlet, were not accounted for. In addition, the boundary condition at the reactor exit assumed zero gas concentration which yielded inferior agreement between the model predictions and experimental results when compared to those obtained using a zero-flux boundary condition as described below. Before setting forth these new TAP modeling equations, a few comments on the transport-kinetics interactions that occur in the TAP reactor are in order. The modes of gas transport that can occur during a pulsed TAP transient experiment include Knudsen diffusion, molecular diffusion, pressure diffusion, and viscous flow. At moderate to high inlet gas puke intensities (e.g., 1 x 1016to 1 x 1Ol9 molecules/pulse), a model that incorporates these four modes of gas transport along with suitable reaction and surface kinetics may be necessary to obtain an accurate description of the TAP transient responses. By using an appropriate constitutive equation for the gas transport, such as the Dusty Gas Model (Mason et al., 19671, the effect of the
24 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992
inlet gas pulse intensity on the relative contribution of the fluxes associated with each mode of gas transport can be quantified (Svoboda et al., 1992). It can be shown that when low inlet gas pulse intensities are used (e.g., 1 X 1014 to 1 X 1015molecules/pulse), Knudsen diffusion is the controlling mechanism for gas transport. Experimental verification of the result is shown in a later section by using inert gases of various molecular weights and by varying system parameters, These results provide the basis for the modeling equations developed below. Knudsen Diffusion Model. The modeling equations given below describe the mass conservation of a species A during a typical pulsed reaction experiment. The key model assumptions are (1)molecular and pressure diffusion and convective flow of the gas are negligible, (2) the gas pulse temperature is constant over the reaction zone, (3) linear, reversible adsorption and first-order irreversible reaction can occur on the reactor packing, (4) first-order irreversible reaction can occur in the gas phase, and (5) the packing is nonporous. With these assumptions, eqs 9 and 10 describe the mass conservation of component A in the gas phase and on the reactor packing surface. ka%Ag + k d ( 1 - %)As - krgtbAg (9)
The initial and boundary conditions are t = 0: Ag=A,=O, OlzlL
(11)
>0
(12)
z = o 2
= L:
-De*
= X(t), t
A,=O, t > O
(13)
Here, A, and A, denote the concentration of species A in the reactor voids and on the packing surface, respectively, where the latter is based upon the packing volume. de^ denotes the effective Knudsen diffusion coefficient for transport of species A, k, and k d are the adsorption and desorption rate constants, and k,, and k,, denote the first-order rate constants for gas-phase and surface reaction, respectively. The initial condition given by eq 11 specifies that the reactor voids and packing surface are initially free of species A. The boundary condition at the reactor inlet (z = 0) given by eq 12 states that the flux of A at the inlet is described by a nonideal pulse forcing function X ( t ) . The boundary condition at the reactor exit (z = L)given by eq 13 assumes that the exit concentration is zero, whose justification is explained in detail by Svoboda et al. (1992). The model-predicted transient response can be obtained by evaluating the flux at the reactor exit. Solution Method and Parameter Estimation. The solution of eqs 9 and 10 subject to the initial and boundary conditions given by eqs 11-13 provides the model-predicted concentration of A in the gas phase A,(z,t) for an assumed set of model parameters P = [ha k d k, k, DeAIT. The bed porosity t b can be determined from independent measurements of the packing weight in the reactor wp, apparent packing density p and empty reactor volume VI using the relationship 1 - wp/pp/Vr. One technique for relating the model-predicted transient response at the reactor exit to an experimental forcing function involves the application of the Laplace transform method which is described in standard texts on the subject (cf. Jenson and Jeffreys, 1977). The model-predicted output response can be related to the input forcing function by use of an impulse response, E(t,P),which results
et:
from the modeling equations. The impulse response contains information regarding the transport and kinetics interactions in the reactor. Applying the Laplace transform method to eqs 9-13 yields the following expression for the model-predicted impulse response in the Laplace transfer domain at the reactor exit:
-DeA
d4(
7
The transport-kinetics model given in eqs 9-13 represents a particular type of linear dynamic model which has an impulse response of E ( t , P )where P denotes the vector of model parameters. A useful method for relating the normalized model-predicted impulse response at the reactor exit, E(t,P), to the normalized model-predicted output response at the QMS, y,(t), involves the convolution theorem (Jenson and Jeffreys, 1977). According to this theorem, the model-predicted output response can be obtained from applying a known normalized forcing function, x ( t ) , to the impulse response by evaluating the convolution integral y,(t) = S I0x ( t - 7 ) E(T,P)d7 + n(t)
(16)
In eq 16, n(t)is a function that accounts for random noise present in the system due to finite measurement errors. An approximation to the normalized input forcing function, x ( t ) , can be experimentally determined by removing the TAP microreactor and measuring the transient response of the system where the pulse intensity is identical to the one used when the microreactor is in place. The vector of model parameters is then determined by minimizing some user-defined measure of the error between the model-predicted output response y,(t) and the experimental output response y e @ ) . If one based upon mean-square relative errors is used at discrete time base points tj, then the objective function becomes N Q,
= Cwj[l - ~ r n ( t j ) / ~ e ( t j ) I ~ ;=l
(17)
In eq 17, N denotes the total number of time versus QMS response data pairs and the wj are the weights. Here, the weights w;were assigned a value of unity. Minimization of the above objective function was performed in this work using Marquardt's method (Seinfeld and Lapidus, 1974). Numerical Implementation. The solution of eq 16 can be efficiently performed using a combination of discrete Fourier transforms (DFT) and inverse discrete Fourier transforms (IDFT) which are implemented by the fast Fourier transform (FFT) as described by Brigham (1974). The model-predicted output response in the Fourier transform domain follows directly from eq 16 and is given by the DFT convolution theorem Y,(n) = X(n)*E(n,P)
(18)
where IN-1
X ( n ) = DFT(xj) = - C Tsxjexp
N
j=1
for n = 0, 1, ..., N - 1 (19) In eq 19, i = (-l)ll2 and T,= NAt is the sampling period.
Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 25 Table I. Comparison of Effective Knudsen Diffusion Coefficients
0.144
2
0.12-
gas krypton
5 ::0.10d u 0.08.-3 -
E
co:,
O.O6; 0.04-
i 0.02
0.00 0
4
8
12
16
20
24
Time, sec x 100
28
32
36
Figure 5. Comparison of a typical normalized experimental output response (points) for an inert gas with the model-predicted output response (solid line). Conditions: T = 708 OC; packing = quartz granules; d, = 425-600 pm; L = 38.1 mm.
The DFT of &,P) is obtained by substituting s = io in the Laplace-transformed expression E(s,P) in eq 14 and sampling at w, = 27rn/N for n = 0, 1, ..., N - 1. After multiplying X ( n ) and E(n,P) to form the complex product Y J n ) defined above by eq 18, the model-predicted output response in the time domain y,(tj) is then evaluated using the IDFT according to
argon 02 neon neon neon neon neon neon neon neon neon
temp, "C 400 400 400 400 400 200 250 300 350 400 400 400 400
mean d,, pm 230 230 230 230 230 195 195 195 195 195 275 327 390
DeA, cmz/s expta calcb 22.4 22.5 30.2 31.0 31.1 32.6 36.4 36.4 45.3 45.8 32.7 32.6 34.7 34.3 36.3 35.8 37.8 37.3 39.0 38.8 52.7 54.8 63.4 65.1 73.6 77.5
ec
0.4 2.6 4.6 0.0 1.1 0.3 1.2 1.4 1.3 0.5 3.8 2.6 5.0
"Obtained by parameter estimation using eq 20. bObtained from eqs 21 and 22 with T = l / e b . ODefined as 100 X abs[DeA(expt) - De~(c~c)l/De~(calc).
195 and 390 pm while the bed depth was fixed at 38.1 111111. Glass spheres were used as reactor packing in order to better characterize the bed tortuosity and porosity and their effect on the Knudsen diffusion coefficient. Experimentally determined Knudsen diffusion coefficients were compared to those calculated using the kinetic theory of gases (Hirschfelder et al., 1954) for Knudsen diffusion of a species in a porous medium
-(-)
DeA= t b 2 i 8RT Tb 3 TMA A significant advantage of this approach over others is that the number of operations associated with the FFT of a discrete sequence containing N elements is N log N as opposed to W for a conventional numerical Fourier transform. In addition, the numerical instabilities associated with a deconvolution approach are avoided. A detailed comparison of parameter estimation in linear tracer flow models using two independent approaches based upon convolution and deconvolution is available (Mills and Dudukovic, 1989). Nonreacting Gas Results. Figure 5 shows the result obtained for a typical inert gas when the normalized experimental output response is compared to the modelpredicted output response. For the case shown here, a krypton output response obtained in the Me4Sn experiments was used as an example. The reactor was packed to a depth of 38.1 mm with 425-600-pm crushed quartz particles and operated a t a temperature of 708 "C. The result shown in Figure 5 is based upon the assumption of negligible adsorption and desorption with no reaction (It, = k d = It,, = K,, = 0). Knudsen diffusion was experimentally confirmed by reducing the inlet gas pulse intensity until the resulting normalized output responses were constant. Inspection of Figure 5 shows that the agreement between the experimental and model-predicted transient responses is excellent. Use of other boundary conditions a t the reactor exit gives model-predicted responses which are in poor agreement with the experimental responses when graphically compared (Svoboda et al., 1992). In order to further validate the model, the experimental Knudsen diffusion coefficient was determined for other inert gases to verify the dependence of this parameter on gas molecular weight, temperature, and particle diameter. Gases used included neon, oxygen, argon, carbon dioxide, and krypton. The temperature was varied between 200 and 400 "C. The mean particle size was varied between
where i is the mean radius that exists in the voids of the packed bed. For spherical packing, or equivalent spherical particles, i is defined by p=-
2cb
3(1 - q,)rp
(22)
where rp is the particle radius. The numerical values for the effective Knudsen diffusion coefficients obtained by matching the experimental and model-predicted transient output responses as described above are compared to those calculated from the kinetic theory of gases in Table I. If the DeA values calculated from eq 21 are used as the basis for evaluating the relative errors, then the results in Table I show that these are 5% or less with a mean error of 1.9%. The agreement between the two independently determined values for the Knudsen diffusion coefficient is very good and provides evidence for the assumed mechanism of gas transport in the bed voids. Additional verification that Knudsen diffusion is the dominant mechanism is provided in Figure 6. It follows from eq 21 that the experimental DeA values should have an inverse square-root dependence on the molecular weight, a square-root dependence on temperature, and a linear dependence on mean particle size. Consequently, a plot of Knudsen diffusion coefficients versus these parameters should result in a linear relationship. Figure 6 shows the experimental dependence of the Knudsen diffusion coefficients in Table I to these three parameters where the solid line is obtained from linear least squares. The data follow the linear dependence as required from eq 21. From these results, it is reasonable to conclude that the proposed model accurately describes the transport occurring within the reactor when the pulse intensity is sufficiently low. The above results suggest that the effective Knudsen diffusion coefficient for Me,Sb, Me4&, or any other reacting species can be obtained by multiplying the corre-
26 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 50 7
sition products in the bed voids can be described by the proposed transient Knudsen diffusion model, attention is now directed to cases where reaction occurs. Figure 7 compares the experimental normalized response for Me3Sb at m / e = 151 to the model predictions at temperatures of 399, 539, 568, 592, 614, and 633 "C,corresponding to fractional conversions of 0.0,0.31,0.51,0.71,0.84,and 0.92, respectively. The model predictions are based upon a reduced form of eqs 9 and 10 where adsorption and desorption on the quartz packing is neglected as well as first-order surface reaction (k, = kd = k,, = 0). This assumes that the surface remains inert during the course of an experiment. Hence, the primary mode of the organometallic pyrolysis is assumed to occur by first-order unimolecular decomposition. Figure 8 shows an Arrhenius plot of the various rate constants given in Figure 7 for Me3Sb and those obtained in the Me4% experiments. From the slope and intercept of the indicated lines, rate constants for the decomposition of Me3Sb (eq 23) and Me4Sn (eq 24) are, respectively
I
Inverse Square Root of Molecular Weight
In ( k / s - ' ) = (52.30 f 1.08) - (41.05 f 1.07 kcal/mol)/RT (23) In ( k / s - l ) = (64.14 f 0.92) - (59.05 f 0.87 kcal/mol)/RT (24)
80
. 70
-
60
-
50
-
40
-
Gas = Neon T =4OO"C
C
30
Mean Particle Diameter,
microns
Figure 6. Determination of the Knudsen diffusion coefficient dependence upon (a) the inverse square root of the gas molecular weight, (b) the square root of the temperature, and (c) the mean particle diameter.
sponding value for an inert gas, such as krypton, by the appropriate inverse square-root ratio of molecular weights. Using this approach for calculating the effective Knudsen diffusion coefficients of reactive species is attractive since the total number of unknown parameters is reduced. This leaves the kinetic and other rate parameters as the only unknowns. Pyrolysis Results. Having established that the transport of Me3Sb,Me4Sn, and the associated decompo-
These results are consistent with those summarized by Stringfellow (1989) using more conventional methods. They indicate that the pyrolysis of Me3Sb and Me4Sn for the conditions used here behaves according to a first-order unimolecular reaction where intrinsic kinetics is the controlling resistance. The pyrolysis mechanism described above by eqs 1-6 involves the homolytic cleavage of a metal-carbon bond with the formation of free radicals. This mechanism is consistent with that proposed by Sathyamurthy et al. (1950). It has also been proposed that decomposition can occur via an ethane elimination reaction (Waring and Horton, 1945). Transient experiments, such as those used in this work, can be used to distinguish between these two proposed mechanisms. The comparisons given above in Figure 7 between the model predictions and experimental results are based on the transient responses of the organometallic precursor reactant. An extension of this approach would consider the corresponding transient responses of gas-phase reaction products. If the reaction of interest occurs by initial elimination of ethane as proposed by Waring and Horton (19451, then such an extension should accurately predict the transient output response of the gas-phase product, ethane. Figure 9 compares the model-predicted response for ethane assuming an elimination reaction (solid line) with the experimental output response at 625 OC for Me3Sb pyrolysis. The inferior agreement between the responses, which was also obtained for Me4Sn, suggests that, for the conditions employed, ethane was not formed by a direct elimination reaction.
Summary and Conclusions The pyrolysis of Me3Sb and Me4Sn has been studied under both continuous flow and pulsed transient conditions using the TAP reactor system. A potentially attractive feature of this approach is that the characteristic time scale is on the order of tens of milliseconds so that the probability of detecting short-lived intermediates is increased when compared to other more conventional techniques having longer response times. Experiments in which the organometallic precursors are continuously introduced into the reaction zone show that
Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 27
a
0.10
T
= 399
'C
T X,
I0.08-
8
D,
= 592 ' C = 0.71 = 39.5 cm2/s
k,,
=
19.7
'.5
0.06 -
1.--
g 004 '
2
0.02 0.00
Time. sec x 100 0.10
b T
= 539
0
4
8
12
16
20
24
T
= = = =
28
Time, sec x 100
32
0.10
'C
L
I
X, De
0.08
k,,
0
a U
614 ' C 0.84 39.9 cm2/s 34.0 s.l
36
le
0.06
.-
5E 0.04 6
2
0.02
4
8
12- 16
20,--24 28
32
0.00
36
iime,secx iuu
0.101
4
8
12
16
20
24
Time, sec x 100
28
32
36
0.10 T
%
0
= = = =
X,
0.08-
De k,,
8 3 0.06a
568 ' C 0.51 39.0 cm2/s 9.14 s.'
T X,
0.08
I 0 a
8
a
'0
D,
= 633 ' C = 0.92 = 41.3 cmZ/s
k,
=
59.8
5.'
0.06
P.-
.-R
1 0.04E
1 0.04
2
z6
E
b
0.02 0.00
0
0.021
4
8
12
16
20
24
Time, sec x 100
28
32
36
0.00
0
& 4
8
12
16
20
24
28
32
Time, sec x 100 Figure 7. Comparison of the normalized experimental output responses (points) for MesSb with the model-predicted output responses (solid lines) for varying temperatures. Conditions: packing = quartz granules; dp = 425-600 pm;L = 38.1 mm.
the onset of pyrolysis for MesSb and MelSn occurs near 475 and 600 "C,respectively. The same species exceed 90% conversion a t 630 and 750 OC. By interpreting the mass spectra of the pyrolysis reaction products, it was shown that methane and ethane are the primary stable gas-phase products. Transient experiments, where a binary mixture of the organometallic precursor and krypton was introduced from a single pulse valve, yielded output responses for each major reaction product. Under Knudsen flow conditions, it was shown that the transient output responses for the reactant and products did not generally follow an inverse square-root dependence on the species molecular weight since kinetics and surface reaction processes were occurring. This behavior is different from the known behavior for inert, nonreacting species. For the conditions examined here, the transient response of the organometallic is followed by those for krypton, ethane, and methane, which is indicative of the pyrolysis reaction sequence.
Quantitative interpretation of the MeaSb and Me4Sn transient responses for the conditions given here can be performed by using a model that assumes Knudsen diffusion is the primary mechanism of transport in the bed voids. For the relatively inert quartz packing used here, surface adsorption and heterogeneous reaction are assumed to be insignificant. By using inert gases having various molecular weights and varying the inert packing diameter and bed temperature at a fixed bed length, Knudsen diffusion was confirmed and used to predict the Knudsen diffusion coefficient for the organometallic precursor under pyrolysis conditions. This method left the reaction rate constant for pyrolysis, k,, as the only unknown parameter. Comparison of the model-predicted transient output responses for MeaSb and Me4Sn with experimental output responses measured at different temperatures using a parameter estimation technique for k yielded rate forms consistent with literature values. Transient response techniques were shown to provide additional information
28 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 0 trimethylantimony A tetramethyltin 4-
?
3-
Y
-c
2-
1-
0 0 9
I
I
1 0
1 1
1 2
1 3
1000/T, 1IK Figure 8. Determination of the Arrhenius preexponential factors and energies of activation for MeaSb and MelSn pyrolysis. I
0.14,
I
k d = desorption rate constant first appearing in eq 9, s-l k , = fit-order reaction rate constant for gas-phase pyrolysis first appearing in eq 9, s-l k, = firsborder reaction rate constant for solid-phasecatalyzed pyrolysis first appearing in eq 10, s-l L = depth of the packed section in the reactor, cm M A= molecular weight of species A first appearing in eq 21, g mol-l n = index used to denote a particular sampled value of a function N = total number of data points, or total number of sampled function values P = column matrix of model parameter values Q, = gas flow rate, cm3 s-l r = mean radius between packing in the reactor defined by eq 22, cm = particle radius, cm = ideal gas law constant, J/(mol K) s = Laplace transform variable, t = time, s T = absolute temperature first appearing in eq 21, K T,= time-domain sampling period, s w, = weights assigned to sample j wp = packing weight, g x j = sampled value of the normalized experimental input response, s-l x ( t ) = continuous form of the normalized input response, s-l X ( t ) = continuous form of the input response first appearing in eq 12, mol cm-2 s-l y&j) = sampled value of the normalized experimental output response, s-l y&,) = sampled value of the normalized model-predicted output response, s-l Ym(n)= sampled value of the discrete Fourier transform of Ym(tj) y ( t ) = continuous form of the normalized output response,
2
S-1
z = reactor axial coordinate, cm 0
4
8
12
16
20
24
Time, sec x 100
28
32
36
Figure 9. Comparison of the normalized experimental output response (points) for ethane with the model-predictedoutput response (solid line) for an ethane elimination reaction. Conditions: T = 625 OC; packing = quartz granules; d, = 425-600 pm; L = 38.1 mm.
regarding the initial step of the MeaSb and MelSn pyrolysis, suggesting that the reaction proceeds via a freeradical process. The basic methodology used here should provide a useful starting basis for analyzing the kinetics and mechanisms of more complex pyrolysis reactions involving a broader range of compounds.
Nomenclature A, = concentration of species A in the gas phase, mol cm-3 A, = concentrationof species A on the surface of the reactor packing, mol ~ r n - ~ d p = particle diameter, cm DeA= effective Knudsen diffusion coefficient in the gas phase
based on the total reactor cross-sectional area, cm2s-l
E(c,P) = sampled value of the discrete Fourier transform of E(s,P) appearing in eq 18 E(s,P) = closed-form expression for the model-predicted Laplace transformed impulse response first appearing in eq 14, dimensionless E(t,P) = closed-form expression for the model-predicted time-domain impulse response f i t appearing above eq 16, S-1
i = (-1)lP j = summation index k , = adsorption rate constant first appearing in eq 9, s-l
Greek Symbols Cb = bed porosity, dimensionless X = eigenvalue defined by eq 15, cm-' p p = packing density, g cm-3 7 = integration variable in eq 16 7 b = bed tortuosity, dimensionless = objective function used for parameter estimation defined by eq 17, dimensionless u, = sampled value of the frequency, rad s-l Registry No. Meab, 59410-5;Me,Sn, 594-27-4;Sb,7440-36-0; Sn, 7440-31-5;CHI, 14-82-8;CzH6,74-84-0.
Literature Cited Boudart, M.; Djega-Mariadassou, G. Kinetics of Heterogeneous Catalytic Reactions; Princeton University Press: Princeton, New Jersey, 1984. Brigham, E. 0. The Fast Fourier Transform;Prentice Hall: Englewood Cliffs, NJ, 1974. Christoffel, E. G. Laboratory Studies of Heterogeneous Catalytic Processes; Elsevier, Amsterdam, 1989. Coltrin, M. E.; Kee,R. J.; Miller, J. A. A Mathematical Model of the Coupled Fluid Mechanics and Chemical Kinetics in a Chemical Vapor Deposition Reactor. J. Electrochem. SOC.1984, 131, 427-434. Colussi, A. J.; Benson, S. W. The Very Low-Pressure Pyrolysis of Phenyl Methyl Sulfide and Benzyl Methyl Sulfide and the Enthalpy of Formation of the Methylthio and Phenylthio Radicals. Znt. J. Chem. Kinet. 1977a, 9, 295-306. Colussi, A. J.; Benson, S. W. The Very Low-Preseure Pyrolysis of 2-Phenylethylamine and the Enthalpy of Formation of the Aminomethyl Radical. Znt. J. Chem. Kinet. 1977b,9, 307-316. Colussi, A. J.; Zabel, F.; Benson, S. W. The Very Low-Pressure Pyrolysis of Phenyl Ethyl Ether, Phenyl Allyl Ether, and Benzyl Ether and the Enthalpy of Formation of the Phenoxy Radical.
Ind. Eng. Chem. Res. 1992,31,29-37 Znt. J. Chem. Kinet. 1977,9,161-178. Dupuis, R. D. Metalorganic Chemical Vapor Deposition of 111-V Semiconductors. Science 1984,226,623-629. Gleaves, J. T.; Ebner, J. R.; Kuechler, T. C. Temporal Analysis of Products (TAP). A Unique Catalyst Evaluation System with Submillisecond Time Resolution. Catal. Rev.-Sei. Eng. 1988a, 30,49-116. Gleaves, J. T.; Ebner, J. R.; Mills, P. L. A Novel Catalyst Evaluation System for Temporal Analysis of Products with Submillisecond Time Resolution. In Catalysis 1987,Proceedings of the North American Meeting of the Catalysis Society; Ward, J. W., Ed.; Studies in Surface Science and Catalysis 38; Elsevier: New York, 1988b;pp 633-644. Gleaves, J. T.; Sault, A. G.; Madix, R. J.; Ebner, J. R. Ethylene Oxidation on Silver Powder: A TAP Reactor Study. J. Catal. 1990,121,202-218. Golden, D. M.; Spokes, G. N.; Benson, S. W. Very Low-Pressure Pyrolysis (VLPP); A Versatile Kinetic Tool. Angew. Chem., Znt. Ed. Engl. 1973,12,534-546. Golden, D. M.; Piszkiewicz, L. W.; Perona, M. J.; Beadle, P. C. An Absolute Measurement of the Rate Constant for Isopropyl Radical Combination. J. Am. Chem. SOC. 1974,96,1645-1653. Heller, S. R.; Milne, G. W. A. EPA fNIH Mass Spectral Data Base; National Bureau of Standards: Washington, DC, 1978. Hirschfelder, J. 0.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Cases and Liquids; Wiley New York, 1954. Islam, T. S.; Benson, S. W. Rates and Equilibria in the Reaction System Br + i-C4Hlq+ HBr + t-C4Hv The Heat of Formation of the t-Butyl Radical. Znt. J. Chem. Kinet. 1984, 16 (€9, 995-1008. Jenson, V. G.; Jeffreys, G. V. Mathematical Methods in Chemical Engineering; Academic Press: New York, 1977. King, K. D.; Goddard, R. D. Very Low-Pressure Pyrolysis of Cyclobutyl Cyanide. The Cyano Stabilization Enerav. -- Znt. J. Chem. K i i e t . i975a,3,109-123. King, K. D.; Goddard, R. D. Very Low-Pressure Pyrolysis (VLPP) of Alkyl Cyanides. I. The Thermal Unimolecular Reactions of Isopropyl Cyanide. J. Am. Chem. SOC.1975b, 97, 4504-4509. King, K. D.; Golden, D. M.; Spokes, G. N.; Benson, S. W. Very Low-Pressure Pyrolysis. IV. The Decomposition of i-Propyl Iodide and n-Propyl Iodide. Int. J. Chem. Kinet. 1971, 3, 411-426. Ludovise, M. J. Metalorganic Chemical Vapor Deposition of 111-V Semiconductors. J. Appl. Phys. 1985,58,R31-R55.
29
Mason, E. A.; Malinauskas, A. P.; Evans 111, R. B.; Flow and Diffusion of Gases in Porous Media. J. Chem. Phys. 1967,46,3199. Mills, P. L.; Dudukovic, M. P. Convolution and Deconvolution of Nonideal Tracer Response Data with Application to Three-phase Packed Beds. Comput. Chem. Eng. 1989,13,881-898. Newport Corporation Model BV-100Puked Molecular Beam Valve Instruction Manual for BV-1OOV Value and BV-1OOD Driver; Newport Corporation: Fountain Valley, CA, 1984. Sathymurthy, T. V.; Swaminathan, S.; Yeddanapalli, L. M. Kinetic Study of Thermal Decomposition of Tin and Silicon Tetramethyls. J. Indian Chem. SOC.1950,27,509-514. Seinfeld, J. H.; Lapidus, L. Mathematical Methods in Chemical Engineering, Vol. 3,Process Modeling, Estimation, and Identification; Prentice-Hall: Englewood Cliffs, NJ, 1974. Spokes, G. N.;Benson, S. W. Very Low-Pressure Pyrolysis. I. Kinetic Studies of Homogeneous Reactions at the Molecular Level. J. Am. Chem. SOC.1967,89,2525. Spokes, G. N.; Benson, S. W. Pyrolysis of Hydrocarbons in Knudsen Cells. In Recent Developments in Mass Spectroscopy; Ogata, K.; Hayakawa, T., Eds.; University of Tokyo Press: Tokyo, 1970;pp 1146-1152. Stein, S. E.; Benson, S. W.; Golden, D. M. Very Low-Pressure Pyrolysis (VLPP) of Hydrazine, Ethanol, and Formic Acid on Fused Silica. J. Catal. 1976,44, 429-438. Stenhagen, E.; Abrahamson, S.; McLafferty, F. Atlas of Mass Spectral Data; Interscience: New York, 1969. Stringfellow, G. B. Organometallic Vapor-Phase Epitaxy: Theory and Practice; Academic Press: San Diego, 1989. Stringfellow, G. B.; Buchan, N. I.; Larson, C. A. Reactions in OMVPE Growth of InP. In Materials Research Society Symposia Proceedings; Hull, R., Gibson, J. M., Smith, D. A., Eds.; Materials Research Society: Pittsburgh, 1987;Vol. 94,245-253. Svoboda, G. D.; Gleaves, J. T.; Mills, P. L. Fundamental Transport-Kinetics Models for Interpretation of TAP Reactor Transient Response Data. Rev. Sci. Znstrum. Manuscript in preparation, 1992. Waring, C. E.; Horton, W. S. The Kinetics of the Thermal Decomposition of Gaseous Tetramethyltin. J. Am. Chem. SOC.1945,67, 4Q-47.
Received for review June 17,1991 Accepted September 23, 1991
Detection and Identification of Free Radicals in Hydrocarbon Pyrolysis by an Iodine Trapping Method Peter H. Schmich, Hanns J. Ederer, and Klaus H. Ebert* Zmtitut fur Angewandte Physikalische Chemie and Sonderforschungsbereich 123, Universitat Heidelberg, I m Neuenheimer Feld 253, 0-6900Heidelberg, West Germany
A method for simultaneous determination of several free radicals in hydrocarbon pyrolysis is described. Propane pyrolysis was carried out in a quartz flow reactor in the temperature range of 960-1180 K and at a pressure of 30 Pa. Methyl, ethyl, vinyl, propyl, and allyl radicals were trapped in a matrix of frozen iodine at 77 K. After controlled warming up, the resulting alkyl iodides were analyzed in a quadrupole mass spectrbmeter. As natural iodine contains isotope 127 only, the radicals can be unequivocally identified. With this method semiquantitative measurements of free-radical concentrations are shown to be feasible. A reaction model was developed to evaluate the experimental results. It consists of 182 elementary reaction steps involving 25 different chemical species. The agreement between measured ahd calculated product distribution was reasonably good, though no attempt was made to adjust the model by fitting rate constants.
1. Introduction Species with radical character in chemical reactions have long been proposed and discussed, even in the nineteeth century by Bunsen, Kolbe, and Frankland. The first ex-
* T o whom correspondence should be directed a t Institut fur H e d Chemie, Kemforschungszentrum Karlsruhe, Postfach 3640, D-7500 Karlsruhe, West Germany. 0888-588519212631-0029$03.00/0
perimental proof of radicals (Paneth and Hofeditz, 1929) lies more than 60 years back. The advent of radical chemistry started in the 1930s when Rice, Kossiakoff, and Herzfeld (Rice, 1931, 1933; Rice and Herzfeld, 1934; Kossiakoff and Rice, 1943) were the first to formulate free-radical mechanisms for a number of reactions in the area of thermal disintegration of organic compounds. Formerly the decomposition of hydrocarbons was ex@ 1992 American Chemical Society
