J . Phys. Chem. 1990, 94, 1346-1351
1346
h
l
o
I
-0.03
/
0
-I /
0 51
01 3
,
-0.02
;
t
-
5
6
/
/
4 1/ T
c 0.00
( lO-'K-')
Figure 3. Plots of the obtained reorientational correlation times (0)and angular momentum correlation times ( 0 )at various temperatures under study. The relation of these two correlation times is given by eq 7 . The dashed and dotted curves are obtained from the nonlinear regression of the corresponding data.
important, without the S R relaxation term, the magnitude of the differential intensity ratio is rather sensitive to the variations of the ex, values but not to the variation of 7,. Without the CSA-DD cross-relaxation term, the calculated signal intensity of the 212, spin order vanishes. Thus, the variation of the differential intensity ratio in the relaxation processes of the 2I$, spin order demonstrates the importance of cross correlation in 13C-'H spin interactions. The measured AI,/Io values versus evolution time t at various temperatures are shown in Figure 2. The theoretical curves are also shown in the same figure for comparison. The best fitted curves for the temperature-dependent relaxation profile of two-spin order are obtained with eX2,= 35". Corresponding to this orientation, C , , = -8.14 kHz, C2, = -2.12 kHz, and C3, = -1.26 kHz are used in the calculations of relaxation profiles at various temperatures. The values of Oyi and Ox, utilized in this work agree well with eYi = 85' and Ox, = 33O obtained by Linder et al. from
the study of two-dimensional NMR powder spectra.' Our result indicates that u2, is nearly parallel to the C=O bond. In Figure 2, consistency of theoretical calculation with experiment is obtained at different temperatures. The decreases in the differential intensity ratio with increasing temperature indicate the effect of S R interaction. The temperature-dependent reorientational correlation times and angular momentum correlation times derived in this study are depicted in Figure 3. At 178 K, the obtained T, and rj are given by 14.8 and 5.4 X ps, respectively, and the effect of SR interaction on the relaxation of two-spin order is negligibly small. However, at 273 K, the obtained T, and rj are given by 1.4 and 3.3 X ps, respectively, and the effect of S R interaction is significant. The existence of this effect results in a 50% reduction of relaxation intensity. Without the S R relaxation term, the best fit of experimental data at 273 K may be obtained with T, = 2.7 ps and Ox, = 48O, which are essentially analogous to the results obtained previously by Jaccard et ale6 The discrepancy in Oxzr values demonstrates the important role of SR interaction in the relaxation of two-spin order. Conclusion It has been demonstrated that the cross correlation of DD and CSA interactions is responsible for the existence of the 2ZJ, spin order, which can be implemented to determine the tensorial orientation of CSA interaction. However, it is noted that certain inherent limitations do exist. The effect of S R interaction not only accelerates the relaxation but also significantly reduces the relaxation intensity. In applying this method, large I3C random field interactions may sequester two-spin order. Therefore, proper preparation of the sample by minimizing the effect of intermolecular spin interactions and making the measurements at temperatures as low as possible is required for the application of this method. Acknowledgment. Support of this work by grants from the National Science Council of the Republic of China is gratefully acknowledged.
Kinetics and Product Vibrational Energy Disposal Dynamics in the Reaction of Chlorine Atoms with D2S Jeanne M. Hossenlopp, John F. Hershberger, and George W. Flynn* Department of Chemistry and Columbia Radiation Laboratory, Columbia University, New York, New York 10027 (Received: June 12, 1989; In Final Form: August 28, 1989)
The reaction of chlorine atoms with D2S, forming DCI and DS, has been investigated by using time-resolved infrared diode laser absorption spectroscopic probing of both the D3SCland D3'C1 product. The rate constant obtained by using the pseudo-first-order method was found to be 3.2 (i0.3) X lo-'' cm3 molecule-I s-l. The vibrational energy distribution in the DCI fragment was also determined, with 33 (17)% of the product DC1 formed in u = 0,56 (i7)% in u = 1 and 1 1 (13)% in u = 2. These results are consistent with the known vibrational population inversion between the u = 0 and u = 1 states of DCI previously observed for this reaction. The advantage of using infrared absorption measurements, rather than infrared emission, to determine vibrational distributions is that the u = 0 population can be directly measured. The relative vibrational populations were modeled by using two different prior functions, both of which led to linear surprisal plots.
Introduction Gas-phase chlorine atoms play critical rols in atmospheric chemistry,' surface e t ~ h i n g , ~and J the production of chemical lasers! One important class of chlorine reactions is the abstraction of hydrogen atoms from a wide variety of precursors. The fundamental issues in these systems involve the determination of ~~
~~
~
~~
~
~~~~
(1) Molina, M. J.; Rowland, F. S . Nature 1974, 249, 810. (2) Ritsko, J . J.; Ho, F.; Hurst, J . Appl. Phys. Lett 1988, 53, 78. (3) Danner, D. A.; Hess, D. W. J . Appl. Phys. 1986, 59, 940. (4) Gross, R. W. F., Bott, J. F., Eds. Handbook of Chemical Lasers; Wiley: New York, 1976.
0022-3654/90/2094-1346%02.50/0
reaction rates as well as the characterization of the energy disposal dynamics in the reaction products. One well-studied example is the reaction of chlorine atoms with H2S where the primary reaction leads to the formation of HC1 CI + H2S ---* HCI + HS The rates of the primary and secondary reactions in this system have been obtained by a number of different experimental techn i q u e ~ . ~The - ~ distribution of internal energy in the products is ( 5 ) Clyne, M. A. A.; Ono, Y . Chem. Phys. Lett. 1983, 94, 597.
0 1990 American Chemical Society
Reaction of Chlorine Atoms with D2S also of interest. It is known that a population inversion is produced in the u = 1 vibrational state of HCLel2 This inversion has been exploited to produce a chemical laser used for fluorescence studies.I2 Vibrational energy distributions in chemical reaction products are often examined by laser-induced fluorescence (LIF), or by infrared fluorescence or multiphoton ionization when the molecules are not amenable to LIF probing. Ro-vibrational state-specific detection of HCI and DC1 has been demonstrated by using infrared emission" and multiphoton i o n i ~ a t i o n techniques. ~~'~ The relative yields of o' = 1 and u = 2 states have been determined for the reaction of C1 with both H2S and D2S by monitoring HCI/DCl infrared emission." The limitation of using IR emission is that the population in u = 0 must be inferred from a statistical analysis of the excited state (u L 1) populations. The use of multiphoton ionization provides high-sensitivity ro-vibrational resolution but is complicated by the spectroscopy of the intermediate states. In addition, the range of accessible rotational states when HC1 is probed via the E IZ+ intermediate state has been shown to be limited due to Franck-Condon factors.15 The focus of the work presented here is the investigation of the reaction rate and product vibrational state distribution in the reaction of C1 with D2S. This reaction serves as a good prototype for the application of new detection techniques since previous work on the product vibrational energy distributions" and a large number of kinetic studies on the analogous H2S reactionH provide a basis for comparison with the present results. The detection technique used here to determine the DC1 product vibrational distribution and primary reaction rate is time-resolved diode laser infrared absorption spectroscopy. Time-resolved infrared diode laser absorption spectroscopy has been applied with great success to the study of nonreactive collision dynamics. The amount of vibrational, rotational, and translational energy transferred to polyatomic probe molecules in collisions with translationally or internally excited transient species can be determined.16-20 The technique has been used to examine the product state distributions in photodissociation experiments,20-22 and rates of chemical reactions have also been studied by using time-resolved diode laser a b s ~ r p t i o n . In ~ ~the case of bimolecular chemical reactions, it should be possible to obtain nascent vibrational, rotational, and translational energy distributions in the reaction products. Unlike infrared fluorescence, all vibrational states can be directly probed by using diode laser absorption spectroscopy. The limitations on accessible rotational levels which have been found15 in some MPI experiments on HCI are also eliminated. The work reported here uses this powerful technique to directly determine, for the first time, the relative populations in all of the thermodynamically accessible vibrational states of ( 6 ) Clyne, M. A. A.; MacRobert, A. J.; Murrells, T. P.; Stief, L. J. J . Chem. SOC.,Faraday Trans. 2 1984,80, 877. (7) Nava, D. F.; Brobst, W. D.; Stief, L. J. J . Phys. Chem. 1985,89, 4703. (8) Lu, E. C. C.; Jyer, R. S.; Rowland, F. S. J. Phys. Chem. 1986, 90, 1988.
(9) Braithwaite, M.; Leone, S. R. J . Chem. Phys. 1978, 69, 839. (IO) Dill, B.; Heydtmann, H. Chem. Phys. 1978, 35, 161. (11) Agrawalla, B. S.; Setser, D. W. J . Phys. Chem. 1986, 90, 2450. (12) Coombe, R. D.; Pritt, Jr., A. T.; Pilipovich, D. Chem. Phys. Lert. 1975, 35, 349. (13) Arepalli, S.; Presser, N.; Robie, D.; Gordan, R. J. Chem. Phys. Lett. 1985, 118, 88. (14) Callaghan, R.; Arepalli, S.; Gordon, R. J . J . Chem. Phys. 1987, 86, 5273. (15) Rohlfing, E. A.; Chandler, D. W.; Parker, D. H. J. Chem. Phys. 1987, 87, 5229. (16) Hershberger, J. F.: Hewitt, A. S.; Flynn, G. W. J . Chem. Phys. 1987, 87, 1894. (17) Kreutz, T. G.; ONeill, J. A.; Flynn, G. W. J . Chem. Phys. 1987, 87, 4598. (18) Brady, B. B.; Spector, G. B.; Chia, L.; Flynn, G. W. J . Chem. Phys. 1987, 86, 3245. (19) ONeill, J. A.: Cai, J. Y.; Wang, C. X.; Flynn, G. W. J . Chem. Phys. 1988, 88, 6240. (20) Kreutz, T. A.; O'Neill, J. A.; Flynn, G. W. J . Phys. Chem. 1987, 91, 5540. (21) Holland, J. P.; Rosenfeld, R. N . Chem. Phys. Lett. 1988, 145, 481. (22) Holland, J. P.; Rosenfeld, R. N . J . Chem. Phys. 1988, 89, 7217. (23) Kreuger, H.; Weitz, E. J . Chem. Phys. 1988, 88, 1608.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1347 DCl produced in the reaction of D2S with C1. The rate of deuterium atom abstraction from D2S by CI has also been obtained.
Experimental Section The diode laser absorption technique has been described in detail in other publications.16-20 The basic experiment involves using a pulsed laser to initiate the reaction by forming C1 atoms in situ. The changes in IR absorption when the diode laser is tuned to a particular ro-vibrational transition of the product DCI are then followed in time. The general reaction scheme is shown below. S2Clz+ hv(340 nm) C1 + S2Cl (+ other products) (initiation)
-
-
+ D2S DCI(u=0,1,2;J) + DS DCl(u;J) + hv(-2100 cm-') C1
kr
-
DCI(u+l;J& 1)
(reaction)
(diode laser probing)
On the basis of the thermodynamics of the primary reaction," DC1 can be formed in vibrational levels u = 2 or lower. Chlorine atoms were produced by the 340-nm photolysis of S2C12. This chlorine atom precursor was chosen in order to minimize the contribution of secondary reactions to the measured yield of DC1.9*24325 Substituting C1, for S2CI2led to the production of large amounts of DC1 between laser pulses due to secondary chain reactions, consistent with the measured rate constant,26 1.4 X cm3 molecule-I S-I, for the reaction HS + Clz HCI + S + CI -+
This buildup of secondary products obscures the transient signals. Using S2C12as a C1 atom precursor eliminated this problem. The pulsed photolysis source was a Lambda Physik FL2002 dye laser pumped by an EMG 201 XeCl excimer laser. The dye laser power was approximately 15 mJ per pulse. The DCl products were monitored by a Laser Analytics continuous wave diode laser (v 2100 cm-I). The probe beam was copropagated with the photolysis laser through a 2-m absorption cell. Time-resolved changes in the transmitted IR intensity were obtained with an InSb detector which has a risetime of approximately 600 ns. Signals were averaged on a LeCroy 9400 digital oscilloscope and then stored in an IBM PC-AT. Signals obtained when the diode laser was slightly detuned from a particular DCI transition were averaged and subtracted from the on-resonance signals in order to eliminate contributions to the transient signals from thermal effects. The dye laser beam was also expanded with a telescope to minimize the thermal effects. The diameters of both the IR and UV beams were controlled by a 5-mm iris in front of the cell. D2S (MSD Isotopes, 97% D) was purified by three freezepump-thaw (FPT) cycles in liquid nitrogen. UHP argon (Spectra Gases, 99.999%) was used to relax the nascent rotational populations to a Boltzmann distribution and to help limit diffusive losses of chlorine atoms. S2C12(AIdrich, 95%) was first purified by three FPT cycles in liquid nitrogen, then three more FPT cycles in a chloroform/liquid N2 bath and finally vacuum distilled at 0 OC. The reaction was investigated at pressures ranging from 0.5 to 2 Torr, typically in a 1:l:lO mixture of S2CI2:D2S:Ar. All experiments were performed with the gases flowing rapidly through the cell and the reactants mixing just before entering the cell. There was no evidence of DCI buildup betweeen laser pulses until dye laser repetition rates were increased to several hertz. All experimental measurements were made with UV laser repetition rates of either 0.5 or 1.0 Hz.
-
Results The reaction of C1 + D2S leads to observable IR absorption signals from the u = 0, 1, and 2 levels of DC1. No molecules were (24) Krasnoperov, L. N.; Chesnokov, E. N.; Panfilov, V. N. Chem. Phys. 1984, 89, 297. (25) Chasovnikow, S . A.; Chichinin, A. I.; Krasnoperpov, L. N. Chem. Phys. 1987, 116, 91. (26) Nesbitt, D. J.; Leone, S. R. J . Chem. Phys. 1980, 72, 1722.
1348
Hossenlopp et al.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 v)
.-
L
5
0.06
1
1
/d
.
.
.
0
, 100
.
, 200
. , 300
.
,
400
.
i
500
Time (microseconds) 0.35
L v)
/
a.
-100
-.-
120 1
Transient Signal
b.
n
C
3
v = l Transient Signal
2
1
0
3
4
D2S Concentration (molecules cm-3 x 10-15) Figure 3. A pseudo-first-order reaction rate plot is shown. The corrected rise rates were obtained for different DzS pressures while probing the transition D35CI(~= 1,J=3) + hv(2077.339 cm-l) DCI(o=2,J=4). The straight line is a least-squares fit to the points. The rate constant determined from this plot is 3.2 (& 0.3) X IO-” cm3 molecule-’ s-l.
-
-100
0
100
200
300
400
500
Time (microseconds) Figure 1. (a) Time-resolved infrared absorption signal for DCI u = 2
-
level. The transition probed was D35Cl(u=2,J=5)+ hv(2041.254 cm-I) D35Cl(u=3,J=6). The signal was obtained in a 1 : I : l O mixture of S,CI,:D,S:Ar at 1.2 Torr total pressure. The smooth curve indicates the fit to the signal decay which was extrapolated to time t = 0 in order to obtain AI for use in eq I . (b) Time-resolved infrared absorption signal for DCI 11 = 1 level. The transition probed was: D35Cl(u=1,J=3)+ hu(2077.339cm-’) D35Cl(u=2,J=4). The signal was obtained in a 1:l:lO mixture of S,CI2:D2S:Arat 1.2 Torr total pressure. The smooth curve indicates the fit to the signal decay which was extrapolated to time t = 0 in order to obtain AI for use in eq 5 .
-
I
I
decrease, followed by a slow rise. Absorption signals are a measure of the population difference between the two levels that are being probed. The observation of negative absorption signals, or gain, is consistent with the fact that this reaction is known to produce a population inversion between the u = 1 and v = 0 states.+I2 The increase in absorption at later times is due to the collisional relaxation from the u = 1 and u = 2 states. The rate of increase in infrared absorption in the u = 0 state is comparable to the decay rate observed in v = 1 and v = 2 transient signals. A. Rate Constant. The rate of the C1 + D2S reaction should be pseudo first order in D2S concentration9 due to the very small concentration of photolytically produced chlorine atoms. The bimolecular rate constant k, for the primary reaction is determined, using the pseudo-first-order method, from the rise of DC1 absorption signals in the u = 1 state, properly corrected for diffusion and vibrational quenching. Because of the small diode laser beam diameter, diffusion and vibrational relaxation contribute about equally to the observed decay of absorption from the u = 1 level. Since the reaction rate is substantially faster than these two processes, their effect can be removed by subtracting the long time decay portion of the signal from the total signal, leaving just the contribution of reaction to the time-dependent absorption curves. To accomplish this, the decay portion of signals measured for the transition DCl(o=1;5=3) hv DCl(u=2;J=4)
+
i.u
-+
is fit to a single exponential. The fitted decay curve, extrapolated back to time t = 0, is then subtracted from the experimental data, and the rising portion of the difference curve is fitted to a single exponential, giving the rate of DCI production. The rate of DCI production is plotted as a function of D2S concentration in Figure 3. For each D2S concentration, signals were obtained with dye laser repetition rates of 0.5 and 1.0 Hz. The S2CI2concentration was also varied by a factor of 2 for signals measured at 1.6 X 1015 and 3.2 X l O I 5 molecules/cm3 of D2S concentrations. The rate constant for the reaction is found to be 3.2 (i0.3) X 10-I’ cm3 molecule-I s-’, independent of S2CI2concentration. The one standard deviation uncertainty in the rate constant plot slope is calculated considering both the scatter in the corrected rise rates and the uncertainty in the D2S concentration measurements. The fact that the overall rate constant can be obtained from the rate of appearance of any DCI(u) quantum state can be seen by considering a simple kinetic reaction step. CI + D2S DCl(u) + DS rate constant k,
-100
0
100
200
300
400
500
T i m e (microseconds) Figure 2. Time-resolved infrared gain/absorption signal for DCI u = 0 level. The transition probed was D3’Cl(u=0,J=7) + hv(2165.754 cm-l) D3’CI(u=1.J=8). The signal was obtained in a 1:l:lO mixture of S2C!,:D,S:Ar at 1.2 Torr total pressure. An exponential fit to the rising portion of the signal was extrapolated to f = 0 to obtain Si and to t = m to obtain Sr.
-
detected in the L; = 3 level. Typical transient absorption signals are shown in Figures 1 and 2. Probing DC1 molecules formed in either the = 2 or L; = 1 states, as shown in Figure 1, a and b, leads to transient absorption signals with an initial rise which is due to the formation of DCI in the chemical reaction. This is followed by decay at later times caused primarily by collisional quenching of the vibrational states being monitored. The timedependent absorption from the u = 0 state exhibits an initial
-
The time-dependent behavior of the C1 concentration for such a reaction is [CII = [CUOexp(-w)
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1349
Reaction of Chlorine Atoms with D2S where [CI], is the initial CI concentration and y = [D2S]C,k, = k,[D2S]. Thus k, = E&,,the sum of the reaction rate constants for all quantum states u, controls the rate of loss of [CI]. Using the same reasoning
TABLE I: Vibrational Population Data”
transition v = 2 R(2) u = 2 R(5)
[DCUU)I = (k”/7)[C1IO[D,SI(1 - e?‘)
+
8.0
u=2av u = 1 R(3) u = 1 R(5)
u = 1 R(7)
-
SiISf
6.3 7.5 5.7 6.7 i 0.95 38 38 29 23 38 33 33 f 5.8
u = 2 R(7)
Thus, the amplitude of [DCI(v)] depends on the microscopic rate constant k,, but the overall growth rate depends only on k,, the total reaction rate constant. E. Relative Populations. The relative populations of the three vibrational levels u = 0, 1, 2 can be obtained from the transient absorption signals properly corrected for the transition moment^.^' For u = 2 transitions DCI(v=2;J) hu DCI(u=3;J+l)
re1 No 6.1
v=lav v = 0 R(6)
D35C1
v = 0 R(7)
D”CI
0.1 1 0.13 0.23
Equation 1 gives the relative yield of molecules in ( u = 2; J), N(u=2;J). Terms, such as the absorption path length, which are N(u=2;J)
a
[(AI/Io)uI / [XAR(m))’I
held constant in all experiments and thus do not influence relative yields, are not explicitly shown in this expression. In eq 1, Io is the total IR intensity at frequency u. AI is the change in the amount of IR intensity transmitted following the reaction, but prior to vibrational relaxation. XJis a rotational state dependent term given by ( J l)/(W 1) for R-branch transitions and J / ( U + 1) for P-branch lines. R ( m ) is the transition matrix element. The value of AI was determined by extrapolating, back to time r = 0, a double-exponential fit to the decay of the absorption signals. Extrapolating the rising exponential part of the signal to time t = leads to similar values for AI since the overall decay rate is very small. A double-exponential fit to the decays more accurately represents the observed data than a single-exponential fit. Thus, to obtain accurate amplitudes at t = 0, the doubleexponential fit is best. When growth rates rather than amplitudes are extracted, however, a single-exponential fit to the decay is sufficient to give good accuracy for the growth rates. In the case of harmonic oscillator behavior, R2 is proportional to (u l).27 A more accurate approach is to use the form of the matrix element derived from spectroscopic data which will account for anharmonicity and ro-vibrational coupling. The matrix elements which were used here are those obtained by Oba et al. from IR emission experiments2* Their analysis uses the spectroscopic emission data to obtain an RKR potential and a dipole moment function (truncated Taylor series expansion about the equilibrium internuclear separation). The resulting matrix elements are expressed as a power series expansion shown in eq 2 where m = ( J 1) for R-branch transitions, and (-J)for P-branch transitions.
+
+
+
+
R ( m ) = a,
+ a2m + a3m2+ a4m3
(2) From the appropriate values of ai for each transition, given in ref 28, and eq 1 and 2, the relative yield of each (v = 2; J) state probed by the diode laser was calculated. The relative yield for total u = 2 state production is determined by dividing the result of eq 1 by the fraction,f,, of u = 2 molecules in the particular J state being monitored.
f~= ((25 + 1) exp(-hcB,J(J
+ I)/kT)I/qrot
(3)
In eq 3, h is Planck’s constant, c is the speed of light, k is the Boltzmann constant, T is the rotational temperature, and E2 is the rotational constant for the u = 2 state. The value of B, for DCI containing each of the chlorine isotopes was determined29 Y,,, and Y2,, by using the values of the Dunham coefficients, Yo,, determined by Guelachvili et aL30 B” = Yo, + Y,,(u+ 1/2)
+ Y2,(u + 1/2)2
0.1 1
(1)
(4)
(27) Penner, S. S. Quantitative Molecular Spectroscopy and Gas Emissivifies; Addison-Wesley: Reading, MA, 1959. (28) Oba, D.; Agrawalla, B.S.; Setser, D. W. J . Quant. Spectrosc. Radiat. Transfer 1985, 34, 283. (29) Herzberg, G. Spectra ofDiatomic Molecules, 2nd ed.;Van Nostrand Reinhold: New York, 1950.
0.14 av 0.14 i 0.05
“The relative N, and Si/S, values were calculated assuming an effective rotational temperature of 375 K. The listed uncertainties are one standard deviation from the mean. The rotational partition function, qrot,is calculated by using the Euler-MacLaurin e~pansion.~, Calculation of the relative u = 1 populations from the u = 1 u = 2 absorption is similar to the calculation of N(u=2). However, the light absorbed in the u = 1 u = 2 transition is proportional to the population difference between u = 1 and u = 2:
-
-
Thus to obtain N(v=l;J) from an R-branch transition, N(u= 2;J+1) must be subtracted. The contribution of the u = 2 level to these signals is determined from the results of eq 1. The relative vibrational population, N(v=2)/N(u= l), obtained from this analysis depends upon the rotational temperature used in the calculations. However, the individual results of eq 1 or 5 should not depend upon which particular rotational level was probed, assuming a Boltzmann rotational distribution. An effective rotational temperature can be found by measuring IR absorption signals at a number of different J levels for each vibrational state. In the case of the u = 2 level, eq 1 is calculated as a function of temperature for each rotational level. The effective rotational temperature is that which leads to the smallest deviation among the values of N(u=2) determined from the set of rotational states probed. The same procedure is repeated for the u = 1 level, using eq 5 and the appropriate N(v=2) values. Transient absortion signals were obtained for J = 2, 5, and 7 in the u = 2 level and J = 1, 3, 5, and 7 in u = 1 using a 1:l:lO S2C12:D2S:Armixture at 1.2 Torr total pressure. Both vibrational levels exhibited an effective rotational temperature at 375 K. The values for N(u=2) and N(v= 1) determined from the experimental data, assuming the 375 K rotational temperature, are listed in Table I. The average value of N(v=2)/N(u=l) is equal to 0.20 (*0.05), where the error is one standard deviation. The only other reported value for this reaction is that of Agrawalla and Setser, who determined, from infrared fluorescence measurements, that N(u=2)/N(u= 1) was approximately 0.4, with an uncertainty of 20% in the relative values. The nascent u = 0 population can be determined from the diode laser absorption signals by considering a simple two-level system. The lower state is designated by ( u = 0,J) and the upper state by (u = 1, J*). The contribution to the signals from spontaneous emission can be ignored on the time scale of these experiments. The initial signal, Si,is proportional to the population difference, (30) Guelachvili, G.; Niay, P.; Bernage, P. J . Mol. Spectrosc. 1981, 85, 271. (31) McQuarrie, D. A. Statistical Thermodynamics; Harper and Row: New York, 1973.
1350
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990
corrected for the specific rotational levels being probed, between the upper and lower states, v,.N(u=l) -fJN(u=O)]. Negativegoing signals, Le., gain, are observed due to the population inversion between the c = 0 and u = 1 levels. If all of the population in L' = 1 and c = 2 is quenched into u = 0, then the final signal following the slow rise, Sf,is proportional to the total number of DCI molecules, N,,,. The initial and final signals were determined from a single-exponential fit of the slow rise portion of the absorption signal as shown in Figure 2. The initial signal amplitude is found by extrapolating the fit back to t = 0 and the final signal amplitude is similarly determined at t = a. The signal dependence on the transition matrix element, IR frequency, and Io is the same for the S , and Sfportions of the curves, allowing these terms to be eliminated from the analysis. Equation 6 gives the ratio of initial to final signal. This type of analysis is identical with that performed for diode laser probes of halogen atoms produced photolytically from many different p r e c ~ r s o r s . ~ ~ - ~ ~ Si/Sf = V ~ * d u = 1- )f ~ N ( u = O )/l V~Ntota11 (6) The fraction of molecules, P,in each vibrational state is simply P(u=k) = N(u=k)/N,,,,,. Using eq 6 and the fact that the sum of P(u=k) over the three available vibrational levels must be equal to 1, the final expressions for the fraction of molecules in each state are given by eq 7-9. First, we solve eq 8, using the exP(u=O) = IcfJ*/fJ)P(o=1)1- S,/Sf (7) P ( u = l ) = 11 S i / S f l / V p / f J 1 + N ( u = 2 ) / N ( u = I ) ) (8) P(u=2) = ( N ( u = 2 ) / N ( u = l ) ] P ( u = l ) (9) perimentally determined &/Sfand the ratio N ( u = 2 ) / N ( u = l ) which was determined by probing the u = 1 and u = 2 levels. The values of S,/Sfused here are listed in Table I. Knowing the N(u=2)/N(u=l)ratio allows P(u=2) to be calculated from P(u=l) (eq 9). The value of P ( u = l ) is also used to determine P(c=O) as shown in eq 7. The relative DCI vibrational state populations determined in this way from time-resolved diode laser absorption spectroscopy are 33 ( f 7 ) % u = 0,56 ( f 7 ) % u = 1, and 11 ( f 3 ) % u = 2. The uncertainties are determined for the final results by propagating an uncertainty of one standard deviation in the measured A I / I o values through eq I , 5, and 6-9.
+
+
Discussion The reaction rate, 3.2 ( f 0 . 3 ) X IO-" cm3 molecule-I s-l, obtained from these measurements is smaller than the average value of -6 X IO-Il cm3 molecule-' s-' reported for the reaction of chlorine atoms with H2S.- This is expected due to the deuterium isotope effect for chemical reaction rates. For the analogous reactions with fluorine atoms, the ratio of H2S/D2Sreaction rates has been found" to be 1.4, similar to the behavior found here for the chlorine reaction. The pseudo-first-order behavior of this system is demonstrated by the absence of any S2CI, concentration dependence of the signal rise times. The use of diode laser absorption as a probe of relative vibrational populations provides a direct measurement of all accessible states. In contrast, infrared emission experiments require the application of a statistical model to obtain an estimate of the relative u = 0 population. One commonly used technique, surprisal analysis, compares the experimentally determined vibrational distribution, Pcf,), with an expected, or prior, statistical distrib ~ t i o n . ~ The ' variablef, is the ratio of the DCI vibrational state energy to the total average available energy, E , / ( E ) . The prior distribution, Pocfo), is a statistical distribution for the product (32) Tiemann, E.; Kanamori, H.; Hirota, E. J . Chem. Phys. 1988, 88, 2457. (33) Hess, W. P.; Leone, S. R. J . Chem. Phys. 1987, 86, 3773. (34) Hess. W . P.:Naaman, R.; Leone, S. R. J . Phys. Chem. 1987, 91, 6085. ( 3 5 ) Hess, W. P.;Kohler, S. J.; Haugen, H. K.; Leone, S. R.J . Chem. Phys. 1986,84, 2143. (36) Haugen, H. K.; Weitz, E.; Leone, S. R. J . Chem. Phys. 1985, 83, 3402. (37) Levine, R.D.; Bernstein, R. B. Molecular Reaction Dynamics and Chemical Reacfiuity; Oxford University Press: New York, 1987.
Hossenlopp et al. No DS Vibrational Excitation
a.
,
- 8
0.0
0.2
0.4
0.6
0.8
fV
All Internal Degrees of Freedom
b. - 3
0.0
0.2
0.4
0.6
0.8
fv
Figure 4. (a) Surprisal plot, assuming no DS vibrational excitation for PO(fu). The straight line is a least-squares fit to the data with the equation y = -0.83 + 4.6fu and a correlation coefficient of 0.99. (b) Surprisal plot with all possible reaction product internal energy states included in the calculation of PO(fu).The straight line is a least-squares fit to the data with the equation y = -0.75 + 4.0hand a correlation coefficient of 0.98.
vibrational state populations. A surprisal analysis consists of a plot of In [Pcf,)/P"(f,)] versus the reduced variablef,. Assuming that the dynamical factors which control relative product state yields are the same for all vibrational levels, the surprisal plot based on IR emission results can be extrapolated to obtain the relative u = 0 population. The surprisal plots used to obtain an earlier estimate" for the u = 0 population from the IR emission results were based on a model for the prior distribution which assumed that the DS fragment had no vibrational excitation. The average available energy, ( E ) ,for the system is estimated by eq 10," where AH is the reaction enthalpy, E, is the activation energy, and 3kT is the translational energy. ( E ) = -AH
+ E, + 3kT = 5281 cm-'
(10)
The DCI harmonic oscillator vibrational energy is assumed to be 2100 an-'. Treating the DS fragment as though it only could accept rotational or translational energy allows the prior function to be approximated by eq 11.38 This model, as well as the next
u=o
one to be described here, assumes that the rotational constant, B, is independent of vibrational state and therefore does not appear in the prior function. The statistical analysis of the infrared fluorescence data of ref 11, based on eq 11, led to an estimate of 23% u = 0, 54% u = 1, and 23% u = 2 for the relative vibrational energy disposal in the DCI fragment. A surprisal plot, using this model with the present infrared absorption results, is shown in Figure 4a. In this case, no extrapolation is necessary since the relative u = 0 population is experimentally determined. Another model includes the possibility of DS vibrational excitation. The number of possible combinations of populated vibrational levels in DCI and DS is limited by the total available (38) Bogan, D. J.; Setser, D. W. J . Chem. Phys. 1976, 64, 586.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1351
Reaction of Chlorine Atoms with D2S energy. After integration of the total density of states over all rotational and translational degrees of freedom, a prior function can be expressed simply as shown in eq 12 where f,' is defined
- fu/)5/2 C(1 (1
P"cf,') =
(12)
as the sum of the DCI and DS vibrational energy divided by the total available energy. The prior function given by eq 12 must be evaluated for each of the energetically accessible combinations of DCI and DS vibrational populations. A final prior function, PO(fu),is then calculated for each of the three possible DCI vibrational levels by summing over all of the appropriate Pcf,'). For example, the u = 0 level of DCI is possible with DS levels of u = 0, 1, or 2 and, therefore, all three possibilities must be included in Pcf,). The reduced variablef, is, as in the previous model, the DCl vibrational energy divided by the total available energy. A surprisal plot derived from this model is shown in Figure 4b. Applying eq 12 to the infrared fluorescence data of ref 11 leads to an estimate of 30% u = 0, 49% u = 1, and 21% u = 2, slightly different from the results obtained by using eq 1 1. Note that the data fit a linear surprisal slightly better if the prior excludes the possibility of DS vibrational excitation (Figure 4a) than if the prior includes DS vibrational excitation (Figure 4b). This is in agreement with the experimental observation that the reaction does not produce vibrationally excited DS;" however, both plots fit a linear surprisal within experimental error. It has been well documented that the reaction studied here leads to a population inversion between the u = 0 and v = 1 states of the DCI product.*I2 The abstraction of a light atom, which is bonded to a heavy atom, by another heavy atom has been shown to lead to vibrational excitation in the new reaction product for a number of system^."^,^^ The relative u = 0 to u = 1 populations which we observe are consistent with those reported for other similar heavy-light-heavy systems.I0 The relatively linear surprisal plots support a model where the same set of dynamical constraints lead to the production of all three vibrational states in the DCI product. The value obtained in the present study for the ratio of the u = 1 to u = 2 populations, N ( v = Z ) / N ( u = l ) ,produced by the reaction is somewhat less than the value determined in previous emission experiments." However, the experimental data do overlap within two standard deviations, which is quite reasonable given the fact that two very different techniques were used to determine this ratio. Experimental values for the u = 0 population (39) Maylotte, D. H.; Polanyi, J. C.; Woodhall, K. B. J . Chem. Phys. 1972, 57. 1547.
could not, of course, be derived from emission experiments but are obtained from the present absorption experiments in a relatively straight forward manner. The fact that all vibrational levels in the product DCI can be described by a single rotational temperature in the present experiments does not imply that all three levels are produced with the same rotational energy as the result of reaction. Rather, the rotational levels within each u state are efficiently relaxed by the argon bath buffer gas, producing a single rotational distribution at the bath gas temperature. Note that the bath gas is extremely inefficient in causing changes of vibrational quantum number, so that total vibrational populations produced by reaction can still be accurately extracted. We had hoped, of course, to obtain nascent rotational and velocity distributions as well as vibrational distributions, but this was not possible given the overall sensitivity of the present apparatus and the spread of rotational population for the CI + D2S reaction. Such nascent distributions have, however, been recently obtained in a study of the reaction of CI atoms with perdeuteriocyclohexane.40
Conclusions The rate constant for the reaction of chlorine atoms with D2S, determined by time-resolved diode laser absorption probing of the DCl product using the pseudo-first-order method, is 3.2 (f0.3) X lo-" cm3 molecule-' s-l. This is consistent with the known reaction rate of CI with H2S. The relative vibrational populations for the DCI product have been determined to be 33 (f7)% v = 0,56 (f7)% u = 1, and 11 (f3)% u = 2. This is the first experimental determination of the relative populations in all three accessible vibrational states of the DCl in this reaction. The diode laser absorption probe technique is ideal for determining energy disposal in reactions not amenable to LIF probing since all of the energetically accessible vibrational states can be directly probed. Acknowledgment. The help of Yongsik Lee in some of the experimental measurements is greatly appreciated. This work was performed at Columbia University and supported by the Department of Energy under Grants DE-FG02-88-ER 13937 and DE-FG05-85-ER75213. Equipment support was provided by the National Science Foundation under Grant CHE-88-16581, the Joint Services Electronics Program ( U S . Army, U S . Navy, and the US. Air Force) under Contract DAAL03-88-(2-009, the Office of Naval Research, and the IBM Materials Research Program. (40) Hershberger, John; Hossenlopp, Jeanne; Lee, Yong-Sik; Flynn, George. Chemical Dynamics of the Reaction between Chlorine Atoms and Deuterated Cyclohexane, submitted for publication.
