J . Phys. Chem. 1990, 94, 2314-2311
2374
TABLE VI: Regions of Existence of Symmetric and Unsymmetric Oscillations and Stable Steady States“ coupling
low medium
high
low [Br-] high [Br-] low [ M A ] high [ M A ] low [ M A ] -high [MA] sym SS only sym osc + sym SS only unsym osc sym SS sym osc + sym SS only unsym SS unsym SS sym SS only sym osc only sym SS only
+
‘The exact limits of the various regions are given in the text. This table is only qualitative. Unlike the above case, in this report we deal with situations where the single CSTR has either one single steady state, stable (region D in Figure 1) or unstable (region E), or three unstable steady states (region F). The single CSTR will, therefore, oscillate or be in a single stable state. The report shows that, even in this situation, the obvious symmetric solution is not the only one, and an unexpected unsymmetric solution, oscillating as well as stable, can coexist with the symmetric ones. In Table VI the various regions of existence of the symmetric and unsymmetric solutions are qualitatively shown. It is seen that the system containing two identical CSTRs can, depending on constraints and initial conditions, be in the following states: (a) stable symmetric steady state, (b) symmetric oscillations, (c) coexistence of symmetric and unsymmetric steady states, (d) coexistence of symmetric oscillations and unsymmetric stable steady state (broken symmetry), and (e) coexistence of symmetric and unsymmetric oscillations. The latter differ from the former in phase, in amplitude, and in period. On the other hand, no unsymmetric oscillations were found to coexist with the symmetric steady state. All the initial conditions tried (even those with p = 2 ) ended in either of the two stable
states. While this paper was being written, the work of Crowley and Epstein” appeared. In that work two similar, but not identical, BZ oscillators were coupled and the results compared to calculations of two coupled Oregonators (without flow). Their experimental results corroborate the predictions given in this paper, in particular the coexistence of the symmetric and either unsymmetric oscillations or steady state and the lengthening of the period of the unsymmetric oscillations toward their “end” when they collapse to the unsymmetric steady state. Another feature of the oscillations, whether symmetric or unsymmetric, is that they “end” at a Hopf bifurcation, with a period increase obeying a power law with the distance to the Hopf. In all cases the final change of period T with the relative distance with different from the Hopf A obeys the relationship T = values for a. The same relationship between A and r holds for a single with similar a’s: a small a when [MA], is decreased and a large one when [Br-1, is increased. The particular exponent depends on the position of the bifurcation but not on the symmetry of the oscillation. The ‘‘Hopf‘ behavior, namely, small oscillations with period depending on the imaginary part of the vanishing real part eigenvalue, is observed only temporarily. This behavior is rather unexpected and indicates that something else may be hidden in the dynamics of the system. As has been mentioned earlier, we were unable to determine the nature of the Hopf bifurcations (super- or subcritical) nor were we able to continue beyond it by AUTO. In all cases the computation approached the Hopf to within -0.1%; it is therefore quite possible that the oscillations “end” not at the Hopf but at another such as saddle-loop, homoclinic, global b i f ~ r c a t i o n which , ~ ~ is located very near the Hopf. The possibility that the period does not go infinite, but just to a very high value near a supercritical Hopf bifurcation, cannot be excluded. It is quite possible that in the high dimensionality of the problem ( 2 X 5 = 10 dimensions) rather unexpected behaviors can be manifested.
Kinetics and Mechanisms of the C02 Laser Induced Decompositions of CFCI, and CF2CI2 R. N. Zitter,? D. F. Koster,**tT. K. Choudhury,f§ and A. Cantonitsl Department of Physics and Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, Illinois 62901 (Received: April 17, 1989; In Final Form: August 22, 1989)
The kinetics and reaction mechanisms of the decomposition of CFCI, and CF2CI2induced by a continuous C 0 2 laser are examined and compared with previous results for CF3CI. All three compounds clearly exhibit two temperature regimes, with similar reaction mechanisms in the low-temperature regimes and significantlydifferent mechanisms in the high-temperature regimes.
Introduction Fluorine-containing compounds have often been used for studies of CO, laser induced gas-phase chemical reactions because they typically have strongly absorbing infrared band frequencies matching those of CO, lasers. However, few of the reported investigations have been devoted to careful examination of decomposition kinetics and mechanisms, while standard pyrolytic techniques do not span the temperature range available with lasers. Furthermore, laser excitation can induce reactions far from gas cell walls to avoid the complications of wall reactions with fluorine and highly reactive radicals. ‘Department of Physics. *Department of Chemistry and Biochemistry. Present address: Department of Chemistry, The Catholic University of America, Washington, DC 20064. Present address: California Laboratories, Carlsbad, CA 92008.
We have reported’ a detailed study of the decomposition kinetics and mechanisms of CF3CI induced by a continuous (CW) C 0 2 laser. Similar studies of CFCI, and CF2Clzare presented here and form an interesting basis for comparison. For all three compounds, the data show two distinct temperature regimes, with reaction pathways that are dominant in one regime but not the other. The reaction mechanisms are similar in the “low”-temperature regimes but differ significantly at higher temperatures.
Experimental Details The techniques employed here are the same as those described elsewhere.’-3 Briefly, a laser beam of diameter 1.6 mm is absorbed ( I ) Zitter, R. N.; Koster, D. F.; Choudhury, T. K . J. Phys. Chem. 1989. 93, 3167. ( 2 ) Zitter, R. N.; Koster, D. F.; Cantoni, A,; Pleil, J. Chem. Phys. 1980, 46. 107.
OQ22-3654/9Q/2094-2314~02.50/0 0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 6,1990 2375
Kinetics of the Decompositions of CFCI, and CF2CI2 in a reaction cell of diameter 22 mm and length I O cm that is equipped with a crossarm for infrared diagnostics. The rates of product formation are obtained by observing the growths of their characteristic absorption bands in real time. Only initial rates corresponding to small product concentrations are used for data. The rate constants k for product formation, calculated from the data according to established procedure^,^*^ are defined as k = [A]-' d[B]/dt, where [A] and [B] are respectively the reactant and product concentrations. Temperatures T are c a l ~ u l a t e dfrom ~~ measurements of the laser-induced optical absorptions of the reactants, together with tabulated values4 of their thermal conductivities. The laser frequencies used are in near-resonance with reactant absorption band centers, and beam powers ranged from that 3 to 9 W. With these techniques, it has been sh0wn~3~ Arrhenius plots of k vs T I provide accurate values of activation energies, regardless of laser frequency or reactant pressure. Arrhenius preexponential factors, however, change with frequency and pressure as a result of the laser-induced difference between vibrational and translational temperatures and hence do not represent truly thermalized values. Accordingly, the following text ignores preexponential factors, and the focus is on activation energy values.
Initial Reaction The initial reaction step in each of the compounds C F Q , CFCI,, and CF2C12is CI elimination. This has been amply demonstrated by molecular beam experiments5-* employing detection of fragments by mass spectrometry and/or chemical scavengers. Fluorine atom or CI2 elimination is negligibly small, except perhaps at the extremely high intensities of focused pulsed TEA C 0 2 laser beams, which exceed the intensities of the present work by a factor of lo8 or more. CFJCI It is desirable to summarize some of the results previously obtained] for this compound: I . At temperatures below about 1480 K in the laser beam, the only carbon-containing product detected is the haloethane C2F6, with production characterized by an activation energy of 86.0 kcal/ mol. 2. At higher temperatures, the activation energy for CzFs production becomes 55.0 kcal/mol, and now the halomethanes CF4 and CF2CI2are detected, produced at equal rates with an activation energy of 86.2 kcal/mol. The concentrations of the latter products become dominant over CzF6at the highest temperatures used. 3. A satisfactory account of these results involves a rather lengthy set of reactions: CF3CICF3 CI
+ CF3
-
CF2Cl
+ CF3CI
CI
+ CF3CI
CF2CI
+
+ CI
+ CF3CI
CF3
CF3
+ CI
('41)
C2F6
(-42)
Cl2
+ CF2Cl CFzClz + CF3 C12 + CF3
CF4
-
+ CI
+
CFzCl2
(A3) ('44)
0 trans-CFCICFCI 0 cis-CFCICFCI
10 h
r
b 0
I
v)
z
5.5
('47)
(3) Zitter, R. N.; Koster, D. F.; Cantoni, A.; Ringwelski, A. Chem. Phys. 1981, 57, 1 I . (4) Touloukien, Y. S.; Liley, P. E.; Saxener. S. C. Thermophysical Properties of Matter. Thermal Conductiuity of Nonmetallic Liquids and Gases; Plenum: New York, 1970; Vol. 3. ( 5 ) Hudgens, J. W.J . Chem. Phys. 1978, 68, 777. ( 6 ) Sudbo, A. S.;Schulz, P. A.; Grant, E. R.; Shen, Y. R.; Lee, Y. T. J . Chem. Phys. 1978, 68, 1306. (7) Subdo, A . S.;Schulz, P. A,; Grant, E. R.; Shen, Y. R.; Lee, Y. T. J . Chem. Phys. 1979, 70, 912. (8) Morrison, R. S.: Loring, R. F.; Farley, R. L.; Grant, E. R. J . Chem. Phys. 1981, 75, 148.
6.5
7.0 x l o s 4
l/T ( K ' ) Figure 1. Arrhenius plots of product formation in the decomposition of CFC1, a t 50 Torr. T h e laser frequency is 1078 cm-'.
CFC13 At ''low'' temperatures, the dominant carbon-containing product is the haloethane CFCI2CFCI2,and its production as illustrated in the Arrhenius plots of Figure 1 is characterized by an activation energy E, of 77.4 kcal/mol. The cis and trans isomers of CFClCFCl are also produced at nearly equal rates with an identical E, of 98.2 kcal/mol, but these compounds are virtually absent compared with CFClzCFC12at the lowest temperatures employed. At high temperatures, the E, for CFCI2CFCl2production is only 28.0 kcal/mol, and now the cis and trans isomers of CFClCFCl are produced with an E, of 77.2 kcal/mol. The isomers are the dominant products at the high end of the temperature range. The same overall results are seen at laser frequencies and reactant pressures other than the ones used for Figure 1, and each of the E, values quoted here is the average obtained from all the Arrhenius plots, with an estimated net error of f 0 . 3 kcal/ mol. The reaction path of CFCI, in the low-temperature regime is entirely similar to that exhibited by CF3C1, namely, elimination of CI followed by the formation of the appropriate haloethane as the dominant carbon-containing product. In the high-temperature regime, however, the reaction pathways must be entirely different, simply because CF3C1gives the five-atom product molecules CF4 and CF2C12,while CFCI3 produces the six-atom cis and trans isomers of CFCICFCI. To explain the results observed for CFCI,, we postulate the following set of reactions: CFCI3 -+ CFCl2 CI (B1)
+
CFCl2
('45) (A61
6.0
CFC12 CFCl
+ CFCl2 CI + CI
+ CFC13*
+ CFCl
-
-+
-
+
CFC12CFCI2 C12
CFClCFCl
C1 + CFCI,
-
C1,
033)
+ CI + CFC13
CFCl
(B2)
(cis and trans)
+ CFC12
(B4)
(B5) (B6)
In particular, reaction B4 is introduced here to account for CFCl production and the subsequent formation of the CFClCFCl isomers because alternate routes appear to be untenable. First, molecular beam experiments have shown that CI2elimination from CFCI3does not occur. A second possibility is the reaction of CFCI, with C1 to give CFCl and CI,, but this would hardly compete with the reverse o f ( B l ) which represents an enthalpy change that is 79 kcal/mol smaller. A third possibility is the reaction of two CFCI, radicals to give CFCl and CFCI,, but again this is ener-
2376 The Journal of Physical Chemistry, Vol. 94, No. 6, 1990 getically unfavorable compared to the competing reaction B2, whose enthalpy change is less by 58 kcal/mol. By contrast, reaction B4 is plausible. As written, (B4) symbolizes the collision of a CFC12 radical with a vibrationally excited CFCI, molecule, which donates the energy required for the indicated dissociation. This is a plausible mechanism because from thermochemical data9 the enthalpy change in the dissociation (BI) is calculated as 7 7 kcal/mol, which means that CFC13 molecules can absorb up to this amount of energy from laser photons before dissociating, while the energy required for the dissociation shown in (B4) is similarly calculated as only 59 kcal/mol. In fact, molecular beam experiments do show some secondary dissociation of CFC12 into CFCl and C1, and of course (B4) could also occur via a series of collisions rather than a single step. We characterize the above reactions (Bi) with the rate constants k, and activation energies Ei. As noted above, E , and E4 are expected from thermochemical calculations to have the respective values 77 and 5 9 kcal/mol. If specie concentrations are represented by the symbols A = [CFCI,],X = [CFC12], Y = [CI], and Z = [CFCI], then in the standard steady-state approximation where residual concentrations are constant in time, one has the relations k l A - 2 k 2 Y - k4AX k , A - 2k3P
+ k6AY = 0
+ k4AX-
k6AY= 0
k 4 A X - 2k5Z2 = 0
(1) (2)
(3)
while the product formation rates are given by d[CFCI2CFCl2]/dt = k2XZ
(4)
d[CFClCFCl]/dt = k S Z 2 (cis and trans)
(5)
d[Cl,]/dt = k 3 P
+ k6AY
(6)
There are two routes to CI2 production, namely, (B3) and (B6), whose contributions appear on the right side of (6). As explained in detail in the analysis of the CF3CI reaction,, calculations based on tables of data for CI reactions show that (B6) predominates over (B3); i.e., k6A Y exceeds k3pby several orders of magnitude. Then algebraic combinations of (1) and ( 2 ) lead to the relations k 2 Y + k,AX = k6AY
(7)
kzXZ + k , P = k l A
(8)
where a term k 3 P has been ignored on the right side of (7). The terms on the left side of (7) represent respectively the production rates of CFCI2CFCI2and CFClCFCl (cis and trans). At low temperatures where the production of the ethane is dominant, we assume that k2$ is much greater than k4AX, in which case the above relations give d[CF2CICF2CI]/dt = k , A d[CFCICFCl] /dt = ( k l / 4 k 2 ) l / 2 k 4 A 3 / 2
(9) (10)
The Arrhenius plots in Figure 1 for the low-temperature regime show activation energies of 7 7 . 4 and 98.2 kcal/mol, respectively, for the product formation rates (9) and (IO). Since k2 represents a negligible activation energy, we deduce that E , = 7 7 . 4 kcal/mol
(11)
E, = 59.5 kcal/mol
(12)
These values are in good agreement with the enthalpy differences of 7 7 and 59 kcal/mol calculated for reactions BI and B4. At high temperatures, where CFClCFCl production predominates, we assume that the term k4AX in (7) is now much greater than k 2 P . which leads to the relations d[CFC12CFC12]/dt = k , A ( 1 + k3k42/k62)-' (9) Dever, D.F.; Grunwald. E. J . Am. Chem. SOC.1976, 98, 5055
(13)
Zitter et al. d[CFCICFCI] /dt = ( k l / 4 k 2 ) 1 / 2 k 4 A 3 / 2+( 1k 3 k 4 2 / k 6 2 ) - ' / 2 (14) To conform with experiment, we assume that k3k42/k62is much larger than unity, in which case the relations reduce to d[CFCI,CFCI,]/dr = k l k 6 2 A / k 3 k 4 2
(15)
d[CFClCFCl]/dt = k 6 A 3 / 2 ( k l / 4 k 2 k , ) 1 / 2
(16)
In this high-temperature regime, Arrhenius plots show activation energies of 36.6 and 77.2 kcal/mol, respectively, for the product formation rates (15) and (16). If we also use the activation energy values of E , and E4 obtained from the low-temperature regime, as given in (1 1) and ( 1 2 ) , then from (1 5) we obtain the value E6 = 39.1 kcal/mol
(17)
while (16), which does not depend on k4, provides the value
(18)
E6 = 38.5 kcal/mol
The consistency exhibited here tends to support the validity of our model. The reaction B6 characterized by this activation energy is a chlorine abstraction process. By comparison, the corresponding reaction for CF3CI, given earlier as (A6), has an activation energy of 3 1.3 kcal/mol.l It is important to notice that in Figure 1 the cis and trans isomers of CFClCFCl have identical activation energies in both temperature ranges, but their production rates are not quite equal. More precisely, the ratio of trans to cis concentrations has the value 1.3, and we find exactly the same ratio in a liquid mixture of the isomers as purchased commercially. Since there is little difference between the enthalpies of the isomers, the observed formation ratio is probably due to steric factors. In order to understand the differences in reaction pathways between CF3CI and CFCI, at high temperatures, where CF3CI produces methanes while CFCI, produces ethenes, we focus on the pivotal reactions A4 and B4. For (B4), its counterpart in the CF3C1 reaction would be the process CF3 CF3CI* CF2 F CF3CI
+
-+
+ +
where the required dissociation energy is donated by vibrationally excited CF3CI. However, this dissociation would require9 an energy of 97 kcal/mol, while the CF3CI cannot contain more than 86 kcal/mol before its own dissociation.' Accordingly, the above process would not occur. Conversely, the counterpart of (A4) in the reaction of CFCI, would be the fluorine abstraction process CFCI2 + CFCI, CF2Cl2 CCI3
-
+
Since neither CF2CI2nor CCI, is detected among the reaction products, the above process must be insignificant in comparison to the competing process (B4). Of course, the CI elimination in (B4) can occur in twice as many ways as the above-mentioned F abstraction, but it seems we must also presume that the activation energy for this F abstraction exceeds that of the C1 elimination, which is E4. Finally, we note that there are some differences between the present experimental results and those of Dever and G r ~ n w a l d , ~ who studied the decomposition of CFCI, by megawatt peak power pulses from a TEA CO, laser. These authors did not detect the presence of the haloethane C2F2C14,but this is not inconsistent with the present results, which show that the concentration ratio of this ethane to the cis- and trans-ethene isomers rapidly becomes very small with increasing temperature, and the temperatures produced by the TEA laser pulses should be quite high. In addition, Dever and Grunwald reported the formation of CF2==CCI2 at a concentration about one-third that of either the cis or trans isomers. We also observe the appearance of that compound at our highest laser power levels and prolonged exposure times, suggesting a secondary reaction following the formation of a primary stable product. The reaction mechanism proposed by Dever and Grunwald presumes CI2 elimination as the initial reaction step, but this is invalidated by the molecular beam experi men ts5-*
The Journal of Physical Chemistry, Vol. 94, No. 6,1990 2311
Kinetics of the Decompositions of CFCI, and CF2CI2 I
1000
d[CF3C1]/dt = (kl/k2)1/2k4A3/Z
where A represents the concentration of the reactant CF2CI2. Here we have assumed, as indicated by the data for this regime, that the production rate of CF2C1CF2CIgreatly exceeds that of either CF2ClCFC12or CFCl2CFCl2. We have also assumed, as in the analysis of the CF,CI and CFCI3 decompositions, that CI2 production by (C9) predominates strongly over (C3). A final assumption is that CI recombination by (C9) is much faster than by (C6), which is plausible because [CF2CI2]>> [CI] while the other quantities in (C6) and (C9) are of comparable magnitudes. Data for the low-temperature regime show the activation energies 83.3 and 102 kcal/mol, respectively, for the production rates (19) and (20) above. Then from the data we deduce that
CF,CICFCI, 100
r
g
(20)
10
fn
z
E , = 83.3 kcal/mol
(21)
E, = 60.2 kcal/mol (22) The value of El is in good agreement with the enthalpy difference of 83 kcal/mol for reaction C1. The value of E,, which characterizes the fluorine abstraction process (C4), may be compared to the value 58.7 kcal/mol obtained' for the corresponding process in CF,CI, shown earlier in the present work as (A4). In the high-temperature regime, the rate equations give the production rates
1
0.1
I
I
I
5.0
6.0
d[CF2CICF2CI]/dt = k2(kl /k4)2
7.0 x 1 0 . ~
(K1) Figure 2. Arrhenius plots of product formation in the decomposition of CF2CI2at 50 Torr. The laser frequency is 1078 cm-I. l/T
CFZC12 The essential features of the kinetics for product formation from the decomposition of CF2C12are displayed in the Arrhenius plots of Figure 2. The low-temperature regime indicates a predominant decomposition mechanism similar to that of CF3CI and CFCI,, namely, elimination of CI followed by the formation of the haloethane CF2C1CF2CI.At high temperatures, however, the pattern of products differs from that of either CF3CI or CFCI,; CF,CI becomes the dominant carbon-containing product formed, together with smaller quantities of CFCI,, CF2CICFCI2,and CFCl2CFCl2. In other words, the high-temperature regime shows a mix of methanes and ethanes but no ethenes. To explain the results, the set of reactions postulated is CFzClz CF2Cl
-+
CFzCl
+ CF2CI CI + CI
CFzCl
+ CF2C12
CFClz
+ CFzCl2 CFCl2
--+
CI
+ CFC12 CFC12 + CFCl2 CI + CF2C12
CF2CI
CF2ClCFzCl
+ --+
-+
+ CI
Cl2
(C1) (C2) (C3)
CF,CI
+ CFC12
(C4)
CFC13
+ CFzCl
(C5)
+
CFC13
(C6)
CF2ClCFCI2
(C7)
CFC12CFC12
(C8)
+ CF2Cl
(C9)
Cl2
As before, we denote the rate constants and activation energies associated with these reactions as ki and E,. In particular, E2, E,, and E, through E , characterize radical recombinations, and therefore are presumed to have values near zero. A steady-state equation analysis similar to that used for the other compounds gives, for the low-temperature regime, the product production rates d[CF,CICF,CI]/dt
= klA
(19)
(23)
d[CF,Cl]/dt = klA (24) provided that k9[C1]
