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Temperature effect on quenching of CH(A2Δ)
Chemical Physics 230 Ž1998. 317–325
Temperature effect on quenching of CHž A2D / Congxiang Chen ) , Fei Wang, Yixin Chen, Xingxiao Ma Department of Chemical Physics, UniÕersity of Science and Technology of China, Hefei, Anhui 230026, China Received 13 October 1997
Abstract The quenching rate constants of CHŽA2D . radicals by alcohol, alkane, O 2 , and C 2 H 4 molecules over the temperature range 297–653 K have been measured using laser photolysis of CHBr3 at 266 nm to produce CHŽA. radical and time-resolved fluorescence measurements. Under the simultaneous effects of multiple attractive potentials and repulsive barrier, the temperature dependence of the quenching process of CHŽA2D . is discussed qualitatively based on a modified collision complex model. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction The monovalent carbon radicals known as carbines are of interest in practical systems, such as combustion, discharge, and atmospheres of planets, where they play the role of very reactive radicals w1,2x. Methylidyne ŽCH. is the simplest member of the family of carbines and has attracted the attention of experimentalists and theoreticians. At room temperature, the quenching of electronically excited CHŽA2D . has been extensively studied. The quenching rate constants of CHŽA,B,C. by alcohol, alkane, CS 2 , O 2 , Ar, ŽC X 3 . 2 CO, CF3 COO X, C X Cl 3 Ž X s H and D. were previously measured w3–5x in our laboratory. But the study of the temperature dependence of quenching of CH is relatively insufficient. Crosley’s group at SRI has previously developed a method to study the quenching of electronically excited CH at temperature above 1000 K by laser flash heating using a pulsed CO 2 laser w6x. )
Corresponding author.
Heinrich et al. w7x modified the SRI method. After the CO 2 laser pulse, the heated parent molecules were photolyzed by a ArF laser to generate the electronically excited molecule CHŽA.. The temperature of the system depends on the delay time between the two lasers. At different delay time D t, they measured the dispersed CHŽA–X. fluorescence spectra. The temperature was derived by the comparison of the measured and the simulated spectra assuming the equilibrium Boltzmann distribution was reached. They measured the quenching rate constants from room temperature up to 1000 K with rather large temperature uncertainties, say, below 1000 K the error is "50 K and above 1000 K the error is "100 K. In addition, the number density of the quencher was determined by solving a nonlinear differential equation based on a one-dimensional, instationary equation of continuity w8x. Earlier, they also investigated the temperature dependence of the quenching in the low temperature range 240–420 K w9x by using a resistive wire heater or cooling by passing methanol from a cryostat.
0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 0 3 0 - 5
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C. Chen et al.r Chemical Physics 230 (1998) 317–325
Crosley concluded w10x that the temperature dependence of quenching of CHŽA. is different from those of NHŽA., OHŽA. and PHŽA.. He pointed out that an activation barrier exists on the reaction coordinate between collision partners. In our previous work w4x, we have modified the collision complex model by adding an activation barrier as adjustable parameter to the effective potential to interpret the quenching of CHŽA. by alkane molecules. In this work, an electric furnace was used to heat the reactor and a precise temperature controller was used to control the temperature of the system. The quenching rate constants of CHŽA2D . by alcohol, alkane, O 2 and C 2 H 4 molecules were measured over the temperature range 290–653 K. In addition, the modified collision complex model was used to estimate the value of the activation barrier and a discussion on this model is presented.
2. Experimental The experimental arrangement is similar to that described in previous work w3x. Some modifications were made in this work. The reactor used in this work was different from that in w3x and was described in reference w11x. Briefly, the parent molecule CHBr3 and quenching molecules were slowly flowing into the reactor. The total pressure was kept at 26 " 2 Torr Ž1 Torr s 133 N my2 .. The preparation of gases and control of flow velocity were similar to those in the previous work w3,4x. The parent molecule CHBr3 Ž0.2% in Ar. and the quenching molecules Ž5–10% in Ar. were stored in 10 l reservoirs prior to experiments. The quadrupled YAG laser at 266 nm was focused by a lens with a focal length of 50 cm and irradiated into the center of the reactor. CHŽA2D . radical was produced by laser photolysis of CHBr3 at 266 nm. The fluorescence emitted from CHŽA. was transmitted through an interference filter Žwavelength 430 " 10 nm. and was observed by a photomultiplier ŽGDB56, Beijing.. It means that the whole emission of CHŽA–X. was recorded here. The time-resolved output of photomultiplier was taken to a fast digital storage oscilloscope ŽPM 3311, Philips. interfaced to a microcomputer. The time-resolved signals were averaged over 30 laser shots. Before
analyzing the time-resolved signals, so as to derive the fluorescence decay rate constants, a small background signal was subtracted from the gross one to get the net value. The reactor was described elsewhere w11x. The temperature in the reactor could be automatically controlled from room temperature to 700 K by a calibrated thermocouple equipped with a temperature controller ŽDWT 702, Shanghai.. The reactor was heated by a resistive wire heater furnace. The temperature accuracy in the reactor was within "18C. 2.1. Materials Ar Ž99.999% Wuhan., O 2 Ž99.999% Beijing. and C 2 H 4 Ž99.999% Wuxi. were taken from cylinders without further purification. C 2 H 5 OH, n-C 3 H 7 OH, n-C 4 H 9 OH, n-C 5 H 12 , n-C 6 H 14 , n-C 7 H 16 and CHBr3 were all AR grade, carefully degassed, vaporized into reservoirs and mixed with the bath gas Ar before use.
3. Results Typical CH ŽA –X . fluorescence and their semilogarithmic plots are illustrated in Fig. 1. The exponential nature of the decay is demonstrated by semilogarithmic plot. First-order rate coefficients were derived from the Fig. 1 with some points disregarded which were deviated from the straight line mainly due to the generation process of the
Fig. 1. Typical signals and their semilogarithmic plots of CHŽA–X. for collision process CHŽA.qC 5 H 12 . ŽwC 5 H 12 x s 3.84=10 14 molecule cm3 ..
C. Chen et al.r Chemical Physics 230 (1998) 317–325
electronically excited CH radicals. It means that the decay of the fluorescence is mainly due to the quenching process. Under the same conditions, the first-order decay rate constants were plotted vs. the concentrations of added quencher as illustrated in Fig. 2. The slop of the straight line is the second-order quenching rate constant k. The quenching rate constants k and quenching cross sections sex , the later were derived by the relation sex s krÕ where Õws Ž8 kTrpm .1r2 x is the average relative kinetic velocity, are summarized in Tables 1–3 for the quenching of CHŽA. by alkane, alcohol, O 2 and C 2 H 4 over the temperature
319
Fig. 2. Typical plot of first-order rate constant for quenching of CHŽA. as a function of C 5 H 12 at temperature 413 K.
Table 1 Quenching rate constants and cross sections of CHŽA2D . by O 2 and C 2 H 4 . Unit of k is 10y1 1 cm3 moleculey1 sy1 and those of sex and scf are 10y2 nm2 TrK
O2 k
sex
scf
297 323 353 383 413 443 473 503 533 563 593 300 300 298 300 450 500 600 700 750 800 850 900 950 1300 243 273 296 415
2.27 " 0.11 2.23 " 0.09 1.98 " 0.05 2.20 " 0.09 2.01 " 0.06 1.94 " 0.05 1.88 " 0.07 2.01 " 0.07 2.15 " 0.18 2.14 " 0.03 1.84 " 0.06 1.7 " 0.2 2.76 " 0.52 a 1.6 " 0.1 1.5 " 0.1 1.5 " 0.1 1.8 " 0.2 1.7 " 0.1 1.9 " 0.1 2.1 " 0.1 2.1 " 0.1 2.1 " 0.1 2.3 " 0.1 2.1 " 0.1 4.7 " 0.5 1.95 " 0.08 1.86 " 0.06 1.85 " 0.07 1.5 " 0.1
2.74 " 0.26 2.59 " 0.20 2.20 " 0.18 2.35 " 0.19 2.07 " 0.12 1.93 " 0.10 1.88 " 0.13 1.87 " 0.13 1.95 " 0.32 1.83 " 0.08 1.58 " 0.10 2.05 " 0.48 3.33 " 1.25 1.94 " 0.24 1.81 " 0.24 1.48 " 0.20 1.68 " 0.37 1.45 " 0.17 1.50 " 0.16 1.60 " 0.15 1.55 " 0.15 1.50 " 0.14 1.60 " 0.14 1.42 " 0.14 2.72 " 0.58 2.61 " 0.21 2.35 " 0.15 2.14 " 0.50 1.51 " 0.21
52.72 51.09 49.43 47.86 46.38 44.94 43.55 42.19 40.86 39.56 38.30 52.47 52.47 52.63 52.47 44.61 42.32 38.00 34.03 32.19 30.45 28.81 27.27 25.83 18.21 56.42 54.22 52.72 46.28
a
Ref. w3x. Ref. w14x. c Ref. w9x. b
P
Ref.
0.052 0.051 0.045 0.049 0.045 0.043 0.043 0.044 0.048 0.046 0.041 0.039 0.063 0.037 0.034 0.033 0.040 0.038 0.044 0.050 0.051 0.052 0.058 0.055 0.149 0.046 0.043 0.041 0.033
This work This work This work This work This work This work This work This work This work This work This work w13x w3x w14x w7x w7x w7x w7x w7x w7x w7x w7x w7x w7x w6x w9x w9x w9x w9x
C2 H4 k
sex
23.4 " 0.8 27.0 " 1.5 27.2 " 0.7 28.4 " 0.6 28.9 " 0.9 28.4 " 0.8 32.1 " 1.0 31.2 " 0.9 32.5 " 1.3 33.8 " 0.5 19.0 " 1.0 b
26.65 " 1.82 29.41 " 3.27 28.45 " 1.46 28.60 " 1.21 28.11 " 1.75 26.73 " 1.51 29.30 " 1.82 27.66 " 1.60 28.04 " 2.24 28.41 " 0.84 22.45 " 0.24
21.0 " 0.6
24.86 " 1.42
21.7 " 0.4 c
28.49 " 1.05
C. Chen et al.r Chemical Physics 230 (1998) 317–325
320
Table 2 Quenching rate constant and cross section of CHŽA2D . by alkanes TrK
289 297 323 353 383 413 443 473 503 533 563 593 623
C 5 H 12
C 6 H 14
k
sex
scf
3.10 " 0.18
41.0 " 4.8
58.15
3.47 " 0.20 3.77 " 0.08 3.74 " 0.13 3.87 " 0.06 4.03 " 0.08 4.39 " 0.04 4.48 " 0.11 4.63 " 0.13 5.15 " 0.11 5.18 " 0.16 5.60 " 0.14
43.4 " 5.0 45.1 " 1.9 42.9 " 3.0 42.8 " 1.3 43.0 " 1.7 45.3 " 0.8 44.9 " 2.2 45.0 " 2.5 48.7 " 2.1 47.8 " 3.0 5.04 " 2.5
58.76 59.49 60.30 61.15 62.01 62.85 63.68 64.47 65.23 65.95 66.64
C 7 H 16
k
sex
scf
k
sex
scf
3.96 " 0.19 4.21 " 0.12 4.87 " 0.11 4.90 " 0.27 5.21 " 0.13 5.50 " 0.11 5.62 " 0.31 6.23 " 0.15 6.45 " 0.14 6.70 " 0.16 6.92 " 0.19
51.3 " 4.9 52.6 " 3.0 58.2 " 2.6 56.2 " 6.2 57.6 " 2.9 58.7 " 2.4 58.0 " 6.4 62.4 " 3.0 62.7 " 3.4 63.4 " 3.0 63.8 " 3.5
87.84 87.73 87.77 87.91 88.11 88.35 88.60 88.86 89.12 89.38 89.63
6.11 " 0.12 6.22 " 0.23 5.98 " 0.22 6.06 " 0.18 6.23 " 0.16 6.48 " 0.35 6.63 " 0.16 6.73 " 0.25 6.83 " 0.22 6.80 " 0.284 6.89 " 0.23 7.19 " 0.28
80.2 " 3.2 80.8 " 6.0 74.7 " 5.5 72.4 " 4.3 71.5 " 3.7 71.6 " 7.7 70.7 " 3.4 69.5 " 5.2 68.6 " 4.4 66.1 " 5.4 65.2 " 4.4 66.3 " 5.2
120.8 120.6 119.6 118.7 117.8 117.1 116.6 116.0 115.5 115.2 114.8 114.5
Unit of k is 10y1 0 cm2 moleculey1 sy1 and those of sex and scf are 10y2 nm2 .
range 290–653 K. The uncertainty shown in these tables represents two times of the standard deviation of the least square fitting in Fig. 2. The dependences of the quenching rate constants of CHŽA2D . by some molecules on temperature are shown in Figs. 3–6 which are presented by the formal equation
are shown in the figures. The resulting values of A, n, and E are listed in Table 4. It is seen that the temperature dependence can not be fitted well to Arrhenius relation for the most of collision partners. The quenching of CHŽA2D . by O 2 molecule at room temperature has been extensively studied w3,12–16x. But the temperature dependence was seldom studied w6,7,9x. The rate constants vs. temperature is shown in Fig. 3 where those of w12,15,16x are
k s AT n exp Ž yErRT . except for C 2 H 4 . The fitting lines of this equation Table 3 Quenching rate constants and cross sections of CHŽA2D . by alcohols TrK
C 2 H 5 OH
C 3 H 7 OH
k
sex
scf
285 289 297 323 353 383 413 443 473 503 533 563 593 623 653
3.52 " 0.30
45.5 " 3.9
54.96
3.62 " 0.28 3.68 " 0.30 3.33 " 0.32 3.24 " 0.24 3.33 " 0.24 3.17 " 0.20 2.92 " 0.14 2.96 " 0.16 3.52 " 0.26 3.59 " 0.28 3.73 " 0.42 4.13 " 0.36
45.9 " 3.5 44.7 " 3.6 38.7 " 3.7 36.1 " 2.7 35.8 " 2.6 32.9 " 2.1 29.3 " 1.4 28.8 " 1.6 33.3 " 2.5 33.0 " 3.5 33.4 " 3.8 36.1 " 3.1
54.01 51.80 50.37 49.51 49.02 48.82 48.81 48.94 49.16 49.46 49.80 50.18
C 4 H 9 OH
k
sex
scf
4.68 " 0.17
61.2 " 4.5
76.52
4.47 " 0.21 4.24 " 0.21 4.15 " 0.21 4.01 " 0.14 3.90 " 0.20 3.96 " 0.13 4.12 " 0.12 4.29 " 0.25 4.44 " 0.30 4.97 " 0.27 5.67 " 0.34
55.9 " 5.2 50.7 " 5.0 47.6 " 4.8 44.6 " 3.1 41.6 " 4.3 40.9 " 2.7 41.2 " 2.4 41.5 " 5.8 42.0 " 5.7 45.8 " 5.0 51.0 " 6.1
75.19 74.52 74.14 73.94 73.87 73.90 73.99 74.13 74.29 74.47 74.66
Unit of k is 10y1 0 cm2 moleculey1 sy1 and those of sex and scf are 10y2 nm2 .
k
sex
scf
4.57 " 0.34 4.96 " 0.42 4.03 " 0.36 4.25 " 0.22 4.15 " 0.32 4.78 " 0.14 5.15 " 0.24 4.76 " 0.32 4.70 " 0.28 5.34 " 0.32 5.36 " 0.54 5.54 " 0.22 5.93 " 0.54
61.0 " 4.5 63.0 " 5.3 49.0 " 4.4 49.6 " 2.6 46.6 " 3.6 51.9 " 1.5 54.1 " 2.5 48.5 " 3.6 46.5 " 2.8 51.4 " 3.1 50.3 " 5.1 50.7 " 2.0 53.0 " 4.8
88.25 88.03 88.00 88.10 88.27 88.49 88.73 88.98 89.24 89.50 89.75 90.00 90.24
C. Chen et al.r Chemical Physics 230 (1998) 317–325
Fig. 3. The dependence of the quenching rate constant of CHŽA2D . by O 2 molecule on the temperature. Full circles this work, triangles: Ref. w9x; squares: Ref. w7x; open circle: Ref. w6x.
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Fig. 5. The dependences of the quenching rate constants of CHŽA2D . by alkane molecules on temperature T where full circles for n-C 5 H 12 ; full squares for n-C 6 H 14 ; full triangles for n-C 7 H 16 .
not included. This work and Ref. w9x show that in the lower temperature region, the rate is decreased with increasing temperature. But in the higher temperature region, it is suggested w7x that the rate is increased with increasing temperature. In the overview for all data listed in Table 1, it can be seen in Fig. 3 that the rate data are slightly decreased and then increased with increasing temperature. The quenching of CHŽA. by C 2 H 4 was seldom studied w9,14,16x. Over the temperature range 243– 593 K, the results of previous and this work listed in Table 1 indicate that the quenching rate constant is monotonously increased with increasing temperature as shown in Fig. 4. To the best of our knowledge, the study on the quenching of CHŽA2D . by alkane and alcohol molecules is not extensive. At room temperature, the investigations of quenching by alkane molecules in which the number of carbons is from 1 to 7 were
carried out by some groups w3,13,14x. But, the temperature dependence of the quenching rate has not been studied except for C 2 H 6 w9x. In this work, the temperature dependences of quenching rate constants of CHŽA2D . by n-C 5 H 12 , n-C 6 H 14 and n-C 7 H 16 were measured. The results are listed in Table 2 and shown in Fig. 5. At room temperature, the rate data for n-C 5 H 12 and n-C 6 H 14 in this work are in coincidence with our previous work w3x. But for n-C 7 H 16 the rate constant in this work is 30% more than that in Ref. w3x. For n-C 5 H 12 and n-C 6 H 14 , the quenching rate constants are monotonously increased with increasing temperature although for n-C 7 H 16 , the datum is slightly decreased at lower temperature and then increased at higher temperature if without the consideration of the data in Ref. w3x. The investigation of the CHŽA2D . quenching by alcohol at room temperature was performed in our
Fig. 4. Rate constant k on a logarithmic scale for the quenching of CHŽA2D . by C 2 H 4 as a function of the inverse of the temperature T.
Fig. 6. The dependences of the quenching rate constants of CHŽA2D . by alcohol molecules on temperature T where triangles for C 2 H 5 OH, squares for n-C 3 H 7 OH and circles for n-C 4 H 9 OH.
C. Chen et al.r Chemical Physics 230 (1998) 317–325
322
Table 4 Rate parameters A, n, E for the quenching rate constants fitting to k s AT n expŽy Er RT . Quencher
A r10y1 0 cm3 moleculey1 sy1
n
ErkJ moly1
C 2 H 5 OH C 3 H 7 OH C 4 H 9 OH C 5 H 12 C 6 H 14 C 7 H 16 C2 H4 O2
Ž0.21"1.1.=10y6 Ž0.65"3.5.=10y7 Ž0.53"2.7.=10y4 Ž2.4"6.0.=10y3 0.23"0.60 0.85"1.4 Ž4.9"2.6.=10y10 Ž0.82"2.0.=10y4
2.4"0.7 2.6"0.7 1.7"0.7 1.2"0.3 0.6"0.4 0.6"0.2 0 1.4"0.4
y7.9"2.4 y8.6"2.4 y4.8"2.4 y1.6"1.2 0.82"1.2 y1.4"0.79 2.0"0.3 y5.0"1.4
previous work w5x. In this work, we measured the temperature dependences of the quenching rate constants of CHŽA2D . by C 2 H 5 OH, n-C 3 H 7 OH and n-C 4 H 9 OH listed in Table 3 and shown in Fig. 6. In this work, the rate data are 40% smaller than those in Ref. w5x. Notice, in this work, the whole emission of CHŽA–X. was observed while in previous work w3,5x the signal was mainly from QŽ0,0. branch of CHŽA– X. and the time-resolved signal is much stronger than that observed before. In Fig. 6, it is clearly shown that the quenching rate constants are decreased in low temperature region and increased in high temperature region with increasing the temperature.
4. Discussion The quenching rate data and cross sections of CHŽA2D . by the molecules studied in this work have been listed in Tables 1–3. It appears to be difficult to fit the temperature dependences to Arrhenius relation or simple collision complex model w17x. Generally, in Arrhenius relations the reaction barrier is the controlling factor, while in the simple collision complex model the multiple attractive potential is the controlling factor. As concluded in Refs. w4,6x, the quenching of CHŽA. by some molecules is usually controlled by the simultaneous effects of the multiple attractive potentials and the repulsive barrier on the collision complex formation.
According to the complex model, following processes are responsible for the quenching process: CH Ž A . q M | w CHM x
)
™ CH Ž X . q M ™ products
electronic quenching reaction
where M denotes the quencher. The multiple attractive potentials and reaction barrier for the formation of complex wCH M x ) will control the overall quenching process. Hence, the temperature dependences studied in this work are not especially attributed to chemical or physical quenching process. The multiple attractive potentials between CHŽA. and quenchers include dipole–dipole, dipole– quadrupole, quadrupole–quadrupole, dipole–induced dipole and dispersion interaction, respectively. The specific expressions for the interactions in terms of the molecular parameters were given in Refs. w18,19x. For the formation of a collision complex between the collision partners, there exists an activation barrier Ea on the reaction coordinate. We modified the effective potential Veff Ž r . by adding an activation barrier Ea to the sum of the centrifugal and the attractive multiple potentials. Therefore, the effective potential could be expressed as: Veff Ž r . s Eb 2rr 2 y C3rr 3 y C4rr 4 y C6rr 6 y C8rr 8 q Ea where Ea is the activation barrier and others are the same as in Ref. w17x. Using the average orientation calculation method w17x, we calculated the complex formation cross section scf listed in Tables 1–3 where some previous work is included for comparison. The parameters used in the calculation are listed in Table 5. In the calculation process, we prescribed a radius limit for the distance between the collision partners in the collision process. In the collision complex model described in w17x, the volumes of the collision partners are not considered. It was found that with increasing the relative translational energy, the critical distance R between the collision partners at which the collision complex is formed will be decreased. It is unreasonable, when the translational energy increases to a sufficient value, the distance
C. Chen et al.r Chemical Physics 230 (1998) 317–325 Table 5 Parameters used in the calculation of complex formation cross sections
CHŽA. C 5 H 12 C 6 H 14 C 7 H 16 C 2 H 5 OH C 3 H 7 OH C 4 H 9 OH O2
na ŽDebye.
qa ŽA3 .
Qb Ž10y26 ecu.cm 2 .
IP a Žev.
0.78 c 0.10 0.05 0.10 1.69 1.66 1.66 0.00
3.30 9.99 11.9 13.7 10.49 10.15 10.04 1.58
2.29 c 2.6 3.0 3.5 0.65 1.50 2.00 0.39
8.25 10.4 10.2 9.9 5.11 7.61 8.88 12.06
a
Ref. w20x. Ref. w21x. c Ref. w22x. b
becomes much shorter than the sum of the radiuses of CH and quencher. Hence, in our calculation, we introduced a R 0 which approximately equals to the sum of the radiuses of the collision partners and limited the distance r between the collision partners which could not be smaller than R 0 when the relative translational energy is sufficient high. The critical radiuses R 0 for all quenching systems are listed in Table 6. On the basis of the collision complex model, the quenching cross section sex is the production of the complex formation cross section scf and a probability P by which the quenching will occur during the residence time of the complex, i.e., sex s Pscf . At the different temperatures, as for the same quencher, the value of P should be similar to each other. In our calculation of scf , we adjusted the activation barrier Ea in order to get the similar P for different temperature and a given quencher. The values of Ea derived are listed in Table 6 as well. Because of the immaturity of the model for the transition state and
323
experimental uncertainty, we could not get the same P but a value range as listed in Table 6. Based on the modified collision complex model, if the multiple attractive potential is the controlling factor, the temperature dependence of the complex formation cross section, therefore the quenching cross section is a monotonous decrease. On the other hand, if the activation barrier is the controlling factor, the temperature dependence is a monotonous increase. Over the temperature range in this work, as shown in Tables 2 and 3, the quenching of CHŽA. by alcohol and alkane molecules is controlled by both factors although the activation barrier for n-C 7 H 16 is very small. The quenching probability for these organic molecules is 0.6–0.8 or 0.6–0.7 which seems reasonable. In the quenching of CHŽA. by O 2 , the temperature dependence measured in this work is a monotonous decrease. Combining this results with those of previous work listed in Table 1, it is shown that the quenching rate constant decreases first and then increases with increasing temperature. By using the modified collision complex model we calculated the complex formation cross section. It is found the quenching probability P is very small P s 0.05. The quenching of CHŽA. by C 2 H 4 was an exceptional result. It shows nearly the Arrhenius dependence. The pre-exponential factor and the activation barrier are listed in Table 4. It is shown in Tables 2 and 3 that the quenching rate constants of CHŽA. generally increase with increasing the number of carbon atoms contained in alcohol and alkane molecules. The activation barrier has the contrary trend. To our best knowledge, the reaction mechanism has not been observed experimentally. For the collision between CH and saturation hydrocarbon molecules, Cooper et al. w23x suggested that for all the states of CH except for the C state, the rate constants increase with increasing the number of C–H bonds, as would be expected if the
Table 6 Activative barrier Ea , radius of complex R 0 and quencher probability EarkJ moly1 R 0rnm P
C 2 H 5 OH
C 3 H 7 OH
C 4 H 9 OH
C 5 H 12
C 6 H 14
C 7 H 16
O2
3.6 0.48 0.6–0.8
1.7 0.52 0.6–0.8
1.0 0.56 0.6–0.7
2.4 0.53 0.6–0.7
1.2 0.56 0.6–0.7
0.24 0.59 0.6–0.7
7.8 0.25 0.05
324
C. Chen et al.r Chemical Physics 230 (1998) 317–325
collisional removal of CH was largely by chemical reaction. Berman and Lin w24x, and Nokes and Donovan w14x pointed out that the insertion of the CHŽX. or CHŽA. radical into a C–H bond occurs, yielding an energetic or electronically excited adduct when CHŽX. or CHŽA. collides with carbon hydride compounds. We made an ab initio calculation on the reaction of CHŽX. with CH 4 w25x and concluded that a two-step mechanism Žabstraction–addition path. exists. From the viewpoint of the reaction which is thought to proceed either via abstraction or insertion followed by the rapid decomposition of the adduct the collision cross section and the activation barrier correlating with the bond energy of the attacked bond are important for the formation of adduct. Because there is an OH group in alcohol molecule, resulting in much stronger polarity than that of alkane molecule and the induction of the OH to weaken the C–H bond, the multipole attractive forces between CH and alcohol are stronger than those between alkane and CH, and the reaction barrier between CH and alcohol is lower than that between CH and alkane. Therefore, the quenching cross section of CHŽA. by alcohol should be larger than that by the corresponding alkane molecule. For the quenchers of both alcohol and alkane, it is noticed that the activation barrier decreases with increasing the number of carbon atoms contained in these quenchers. In the case of C 2 H 4 as a quencher, the temperature dependence is nearly consistent with the Arrhenius correlation which suggests that the reaction mechanism is probably different from those of CHŽA. with alkane and alcohol, e.g., addition reaction might take place. The quenching rate constant of CHŽA. by O 2 is smaller than those by alkane and alcohol by one order of magnitude. For the quenching process of the electronically excited CH radical, the total available energy of the complex is mainly contributed by CHŽA., because the energy of CHŽA. is much greater than that of the quencher. Therefore, it can be considered that the total available energies of complexes are similar. During the residence time of the complex, the energy will be redistributed among its internal degrees of freedom. For given total energy, the density of states of complex and quenching product species increase with increasing numbers of atoms in the complex. When the complex dissociates
to form quenching products or reactants, CHŽA. and quencher, the probability P of forming quenching products will be higher for a larger quencher. O 2 molecule is the smallest and simplest molecule studied in this work. Hence, both the quenching cross section and the probability P are the smallest. This explanation could be used to interpret the dependences of the quenching cross sections of CHŽA. on the number of atoms contained in alcohol and alkane molecules as well.
Acknowledgements We appreciate financial support by the National Natural Science Foundation Committee of China.
References w1x W.C. Gardiner, Jr., Combustion Chemistry, Springer, Berlin, 1984. w2x K.H. Becker, J. Lobel, Atmospharische Spuhrenstoffen und ihr physikalisch-chemisches Verhalten, Springer, Berlin, 1985. w3x C. Chen, X. Wang, S. Yu, Q. Lu, X. Ma, Chem. Phys. Lett. 197 Ž1992. 286. w4x C. Chen, Q. Ran, S. Yu, X. Ma, J. Chem. Phys. 99 Ž2. Ž1993. 1070. w5x C. Chen, Y. Sheng, S. Yu, X. Ma, J. Chem. Phys. 101 Ž7. Ž1994. 5727. w6x N.L. Garland, D.R. Crosley, Chem. Phys. Lett. 134 Ž1987. 89. w7x P. Heinrich, F. Stuhl, Phys. Chem. 199 Ž1995. 105. w8x U. Ganzer, Gasdynamik, Springer, Heidelberg, 1988. w9x R.D. Kenner, S. Pfannenberg, P. Heinrich, F. Stuhl, J. Phys. Chem. 95 Ž1991. 6585. w10x D.R. Crosley, J. Phys. Chem. 93 Ž1989. 6237. w11x Q. Li, S. Yu, C. Chen, X. Ma, J. Chem. Phys. 101 Ž7. Ž1994. 5700. w12x W. Bauer, B. Engelhardt, P. Wiesen, K.H. Becker, Chem. Phys. Lett. 158 Ž1989. 321. w13x P. Heinrich, R.D. Kenner, F. Stuhl, Chem. Phys. Lett. 147 Ž1988. 575. w14x C.J. Nokes, R.J. Donovan, Chem. Phys. 90 Ž1984. 167. w15x F.L. Tabares, U.A. Gonzalez Urena, J. Photochem. 21 Ž1983. 281. w16x C.J. Nokes, G. Gilbert, R.J. Donovan, Chem. Phys. Lett. 99 Ž1983. 491. w17x P.W. Fairchild, G.P. Smith, D.R. Crosley, J. Chem. Phys. 79 Ž1983. 1795. w18x J.O. Hirschfelder, C.E. Curtis, R.B. Bird, Molecular Theory
C. Chen et al.r Chemical Physics 230 (1998) 317–325 of Gases and Liquids, Wiley, London, 1954, pp. 22–30, 949–951, 968–970, 984–987. w19x A.D.Q. Buckingham, Rev. Chan. Soc. Lond. 13 Ž1959. 183. w20x D.R. Lide, CRC Handbook of Chemistry and Physics, 71st ed., CRC, Boca Raton, FL, 1991. w21x D.E. Stogryn, A.P. Stogryn, Mol. Phys. 11 Ž1966. 371.
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w22x G.C. Lie, J. Hinze, B. Liu, J. Chem. Phys. 57 Ž1972. 625. w23x J.L. Cooper, J.C. Whitehead, J. Chem. Soc. Faraday Trans. 88 Ž1992. 2323. w24x M.R. Berman, M.C. Lin, Chem. Phys. 82 Ž1933. 435. w25x Z. Yu, C. Chen, M. Huang, Can. J. Chem. 71 Ž1993. 512.
Temperature effect on quenching of CHž A2D / Congxiang Chen ) , Fei Wang, Yixin Chen, Xingxiao Ma Department of Chemical Physics, UniÕersity of Science and Technology of China, Hefei, Anhui 230026, China Received 13 October 1997
Abstract The quenching rate constants of CHŽA2D . radicals by alcohol, alkane, O 2 , and C 2 H 4 molecules over the temperature range 297–653 K have been measured using laser photolysis of CHBr3 at 266 nm to produce CHŽA. radical and time-resolved fluorescence measurements. Under the simultaneous effects of multiple attractive potentials and repulsive barrier, the temperature dependence of the quenching process of CHŽA2D . is discussed qualitatively based on a modified collision complex model. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction The monovalent carbon radicals known as carbines are of interest in practical systems, such as combustion, discharge, and atmospheres of planets, where they play the role of very reactive radicals w1,2x. Methylidyne ŽCH. is the simplest member of the family of carbines and has attracted the attention of experimentalists and theoreticians. At room temperature, the quenching of electronically excited CHŽA2D . has been extensively studied. The quenching rate constants of CHŽA,B,C. by alcohol, alkane, CS 2 , O 2 , Ar, ŽC X 3 . 2 CO, CF3 COO X, C X Cl 3 Ž X s H and D. were previously measured w3–5x in our laboratory. But the study of the temperature dependence of quenching of CH is relatively insufficient. Crosley’s group at SRI has previously developed a method to study the quenching of electronically excited CH at temperature above 1000 K by laser flash heating using a pulsed CO 2 laser w6x. )
Corresponding author.
Heinrich et al. w7x modified the SRI method. After the CO 2 laser pulse, the heated parent molecules were photolyzed by a ArF laser to generate the electronically excited molecule CHŽA.. The temperature of the system depends on the delay time between the two lasers. At different delay time D t, they measured the dispersed CHŽA–X. fluorescence spectra. The temperature was derived by the comparison of the measured and the simulated spectra assuming the equilibrium Boltzmann distribution was reached. They measured the quenching rate constants from room temperature up to 1000 K with rather large temperature uncertainties, say, below 1000 K the error is "50 K and above 1000 K the error is "100 K. In addition, the number density of the quencher was determined by solving a nonlinear differential equation based on a one-dimensional, instationary equation of continuity w8x. Earlier, they also investigated the temperature dependence of the quenching in the low temperature range 240–420 K w9x by using a resistive wire heater or cooling by passing methanol from a cryostat.
0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 0 3 0 - 5
318
C. Chen et al.r Chemical Physics 230 (1998) 317–325
Crosley concluded w10x that the temperature dependence of quenching of CHŽA. is different from those of NHŽA., OHŽA. and PHŽA.. He pointed out that an activation barrier exists on the reaction coordinate between collision partners. In our previous work w4x, we have modified the collision complex model by adding an activation barrier as adjustable parameter to the effective potential to interpret the quenching of CHŽA. by alkane molecules. In this work, an electric furnace was used to heat the reactor and a precise temperature controller was used to control the temperature of the system. The quenching rate constants of CHŽA2D . by alcohol, alkane, O 2 and C 2 H 4 molecules were measured over the temperature range 290–653 K. In addition, the modified collision complex model was used to estimate the value of the activation barrier and a discussion on this model is presented.
2. Experimental The experimental arrangement is similar to that described in previous work w3x. Some modifications were made in this work. The reactor used in this work was different from that in w3x and was described in reference w11x. Briefly, the parent molecule CHBr3 and quenching molecules were slowly flowing into the reactor. The total pressure was kept at 26 " 2 Torr Ž1 Torr s 133 N my2 .. The preparation of gases and control of flow velocity were similar to those in the previous work w3,4x. The parent molecule CHBr3 Ž0.2% in Ar. and the quenching molecules Ž5–10% in Ar. were stored in 10 l reservoirs prior to experiments. The quadrupled YAG laser at 266 nm was focused by a lens with a focal length of 50 cm and irradiated into the center of the reactor. CHŽA2D . radical was produced by laser photolysis of CHBr3 at 266 nm. The fluorescence emitted from CHŽA. was transmitted through an interference filter Žwavelength 430 " 10 nm. and was observed by a photomultiplier ŽGDB56, Beijing.. It means that the whole emission of CHŽA–X. was recorded here. The time-resolved output of photomultiplier was taken to a fast digital storage oscilloscope ŽPM 3311, Philips. interfaced to a microcomputer. The time-resolved signals were averaged over 30 laser shots. Before
analyzing the time-resolved signals, so as to derive the fluorescence decay rate constants, a small background signal was subtracted from the gross one to get the net value. The reactor was described elsewhere w11x. The temperature in the reactor could be automatically controlled from room temperature to 700 K by a calibrated thermocouple equipped with a temperature controller ŽDWT 702, Shanghai.. The reactor was heated by a resistive wire heater furnace. The temperature accuracy in the reactor was within "18C. 2.1. Materials Ar Ž99.999% Wuhan., O 2 Ž99.999% Beijing. and C 2 H 4 Ž99.999% Wuxi. were taken from cylinders without further purification. C 2 H 5 OH, n-C 3 H 7 OH, n-C 4 H 9 OH, n-C 5 H 12 , n-C 6 H 14 , n-C 7 H 16 and CHBr3 were all AR grade, carefully degassed, vaporized into reservoirs and mixed with the bath gas Ar before use.
3. Results Typical CH ŽA –X . fluorescence and their semilogarithmic plots are illustrated in Fig. 1. The exponential nature of the decay is demonstrated by semilogarithmic plot. First-order rate coefficients were derived from the Fig. 1 with some points disregarded which were deviated from the straight line mainly due to the generation process of the
Fig. 1. Typical signals and their semilogarithmic plots of CHŽA–X. for collision process CHŽA.qC 5 H 12 . ŽwC 5 H 12 x s 3.84=10 14 molecule cm3 ..
C. Chen et al.r Chemical Physics 230 (1998) 317–325
electronically excited CH radicals. It means that the decay of the fluorescence is mainly due to the quenching process. Under the same conditions, the first-order decay rate constants were plotted vs. the concentrations of added quencher as illustrated in Fig. 2. The slop of the straight line is the second-order quenching rate constant k. The quenching rate constants k and quenching cross sections sex , the later were derived by the relation sex s krÕ where Õws Ž8 kTrpm .1r2 x is the average relative kinetic velocity, are summarized in Tables 1–3 for the quenching of CHŽA. by alkane, alcohol, O 2 and C 2 H 4 over the temperature
319
Fig. 2. Typical plot of first-order rate constant for quenching of CHŽA. as a function of C 5 H 12 at temperature 413 K.
Table 1 Quenching rate constants and cross sections of CHŽA2D . by O 2 and C 2 H 4 . Unit of k is 10y1 1 cm3 moleculey1 sy1 and those of sex and scf are 10y2 nm2 TrK
O2 k
sex
scf
297 323 353 383 413 443 473 503 533 563 593 300 300 298 300 450 500 600 700 750 800 850 900 950 1300 243 273 296 415
2.27 " 0.11 2.23 " 0.09 1.98 " 0.05 2.20 " 0.09 2.01 " 0.06 1.94 " 0.05 1.88 " 0.07 2.01 " 0.07 2.15 " 0.18 2.14 " 0.03 1.84 " 0.06 1.7 " 0.2 2.76 " 0.52 a 1.6 " 0.1 1.5 " 0.1 1.5 " 0.1 1.8 " 0.2 1.7 " 0.1 1.9 " 0.1 2.1 " 0.1 2.1 " 0.1 2.1 " 0.1 2.3 " 0.1 2.1 " 0.1 4.7 " 0.5 1.95 " 0.08 1.86 " 0.06 1.85 " 0.07 1.5 " 0.1
2.74 " 0.26 2.59 " 0.20 2.20 " 0.18 2.35 " 0.19 2.07 " 0.12 1.93 " 0.10 1.88 " 0.13 1.87 " 0.13 1.95 " 0.32 1.83 " 0.08 1.58 " 0.10 2.05 " 0.48 3.33 " 1.25 1.94 " 0.24 1.81 " 0.24 1.48 " 0.20 1.68 " 0.37 1.45 " 0.17 1.50 " 0.16 1.60 " 0.15 1.55 " 0.15 1.50 " 0.14 1.60 " 0.14 1.42 " 0.14 2.72 " 0.58 2.61 " 0.21 2.35 " 0.15 2.14 " 0.50 1.51 " 0.21
52.72 51.09 49.43 47.86 46.38 44.94 43.55 42.19 40.86 39.56 38.30 52.47 52.47 52.63 52.47 44.61 42.32 38.00 34.03 32.19 30.45 28.81 27.27 25.83 18.21 56.42 54.22 52.72 46.28
a
Ref. w3x. Ref. w14x. c Ref. w9x. b
P
Ref.
0.052 0.051 0.045 0.049 0.045 0.043 0.043 0.044 0.048 0.046 0.041 0.039 0.063 0.037 0.034 0.033 0.040 0.038 0.044 0.050 0.051 0.052 0.058 0.055 0.149 0.046 0.043 0.041 0.033
This work This work This work This work This work This work This work This work This work This work This work w13x w3x w14x w7x w7x w7x w7x w7x w7x w7x w7x w7x w7x w6x w9x w9x w9x w9x
C2 H4 k
sex
23.4 " 0.8 27.0 " 1.5 27.2 " 0.7 28.4 " 0.6 28.9 " 0.9 28.4 " 0.8 32.1 " 1.0 31.2 " 0.9 32.5 " 1.3 33.8 " 0.5 19.0 " 1.0 b
26.65 " 1.82 29.41 " 3.27 28.45 " 1.46 28.60 " 1.21 28.11 " 1.75 26.73 " 1.51 29.30 " 1.82 27.66 " 1.60 28.04 " 2.24 28.41 " 0.84 22.45 " 0.24
21.0 " 0.6
24.86 " 1.42
21.7 " 0.4 c
28.49 " 1.05
C. Chen et al.r Chemical Physics 230 (1998) 317–325
320
Table 2 Quenching rate constant and cross section of CHŽA2D . by alkanes TrK
289 297 323 353 383 413 443 473 503 533 563 593 623
C 5 H 12
C 6 H 14
k
sex
scf
3.10 " 0.18
41.0 " 4.8
58.15
3.47 " 0.20 3.77 " 0.08 3.74 " 0.13 3.87 " 0.06 4.03 " 0.08 4.39 " 0.04 4.48 " 0.11 4.63 " 0.13 5.15 " 0.11 5.18 " 0.16 5.60 " 0.14
43.4 " 5.0 45.1 " 1.9 42.9 " 3.0 42.8 " 1.3 43.0 " 1.7 45.3 " 0.8 44.9 " 2.2 45.0 " 2.5 48.7 " 2.1 47.8 " 3.0 5.04 " 2.5
58.76 59.49 60.30 61.15 62.01 62.85 63.68 64.47 65.23 65.95 66.64
C 7 H 16
k
sex
scf
k
sex
scf
3.96 " 0.19 4.21 " 0.12 4.87 " 0.11 4.90 " 0.27 5.21 " 0.13 5.50 " 0.11 5.62 " 0.31 6.23 " 0.15 6.45 " 0.14 6.70 " 0.16 6.92 " 0.19
51.3 " 4.9 52.6 " 3.0 58.2 " 2.6 56.2 " 6.2 57.6 " 2.9 58.7 " 2.4 58.0 " 6.4 62.4 " 3.0 62.7 " 3.4 63.4 " 3.0 63.8 " 3.5
87.84 87.73 87.77 87.91 88.11 88.35 88.60 88.86 89.12 89.38 89.63
6.11 " 0.12 6.22 " 0.23 5.98 " 0.22 6.06 " 0.18 6.23 " 0.16 6.48 " 0.35 6.63 " 0.16 6.73 " 0.25 6.83 " 0.22 6.80 " 0.284 6.89 " 0.23 7.19 " 0.28
80.2 " 3.2 80.8 " 6.0 74.7 " 5.5 72.4 " 4.3 71.5 " 3.7 71.6 " 7.7 70.7 " 3.4 69.5 " 5.2 68.6 " 4.4 66.1 " 5.4 65.2 " 4.4 66.3 " 5.2
120.8 120.6 119.6 118.7 117.8 117.1 116.6 116.0 115.5 115.2 114.8 114.5
Unit of k is 10y1 0 cm2 moleculey1 sy1 and those of sex and scf are 10y2 nm2 .
range 290–653 K. The uncertainty shown in these tables represents two times of the standard deviation of the least square fitting in Fig. 2. The dependences of the quenching rate constants of CHŽA2D . by some molecules on temperature are shown in Figs. 3–6 which are presented by the formal equation
are shown in the figures. The resulting values of A, n, and E are listed in Table 4. It is seen that the temperature dependence can not be fitted well to Arrhenius relation for the most of collision partners. The quenching of CHŽA2D . by O 2 molecule at room temperature has been extensively studied w3,12–16x. But the temperature dependence was seldom studied w6,7,9x. The rate constants vs. temperature is shown in Fig. 3 where those of w12,15,16x are
k s AT n exp Ž yErRT . except for C 2 H 4 . The fitting lines of this equation Table 3 Quenching rate constants and cross sections of CHŽA2D . by alcohols TrK
C 2 H 5 OH
C 3 H 7 OH
k
sex
scf
285 289 297 323 353 383 413 443 473 503 533 563 593 623 653
3.52 " 0.30
45.5 " 3.9
54.96
3.62 " 0.28 3.68 " 0.30 3.33 " 0.32 3.24 " 0.24 3.33 " 0.24 3.17 " 0.20 2.92 " 0.14 2.96 " 0.16 3.52 " 0.26 3.59 " 0.28 3.73 " 0.42 4.13 " 0.36
45.9 " 3.5 44.7 " 3.6 38.7 " 3.7 36.1 " 2.7 35.8 " 2.6 32.9 " 2.1 29.3 " 1.4 28.8 " 1.6 33.3 " 2.5 33.0 " 3.5 33.4 " 3.8 36.1 " 3.1
54.01 51.80 50.37 49.51 49.02 48.82 48.81 48.94 49.16 49.46 49.80 50.18
C 4 H 9 OH
k
sex
scf
4.68 " 0.17
61.2 " 4.5
76.52
4.47 " 0.21 4.24 " 0.21 4.15 " 0.21 4.01 " 0.14 3.90 " 0.20 3.96 " 0.13 4.12 " 0.12 4.29 " 0.25 4.44 " 0.30 4.97 " 0.27 5.67 " 0.34
55.9 " 5.2 50.7 " 5.0 47.6 " 4.8 44.6 " 3.1 41.6 " 4.3 40.9 " 2.7 41.2 " 2.4 41.5 " 5.8 42.0 " 5.7 45.8 " 5.0 51.0 " 6.1
75.19 74.52 74.14 73.94 73.87 73.90 73.99 74.13 74.29 74.47 74.66
Unit of k is 10y1 0 cm2 moleculey1 sy1 and those of sex and scf are 10y2 nm2 .
k
sex
scf
4.57 " 0.34 4.96 " 0.42 4.03 " 0.36 4.25 " 0.22 4.15 " 0.32 4.78 " 0.14 5.15 " 0.24 4.76 " 0.32 4.70 " 0.28 5.34 " 0.32 5.36 " 0.54 5.54 " 0.22 5.93 " 0.54
61.0 " 4.5 63.0 " 5.3 49.0 " 4.4 49.6 " 2.6 46.6 " 3.6 51.9 " 1.5 54.1 " 2.5 48.5 " 3.6 46.5 " 2.8 51.4 " 3.1 50.3 " 5.1 50.7 " 2.0 53.0 " 4.8
88.25 88.03 88.00 88.10 88.27 88.49 88.73 88.98 89.24 89.50 89.75 90.00 90.24
C. Chen et al.r Chemical Physics 230 (1998) 317–325
Fig. 3. The dependence of the quenching rate constant of CHŽA2D . by O 2 molecule on the temperature. Full circles this work, triangles: Ref. w9x; squares: Ref. w7x; open circle: Ref. w6x.
321
Fig. 5. The dependences of the quenching rate constants of CHŽA2D . by alkane molecules on temperature T where full circles for n-C 5 H 12 ; full squares for n-C 6 H 14 ; full triangles for n-C 7 H 16 .
not included. This work and Ref. w9x show that in the lower temperature region, the rate is decreased with increasing temperature. But in the higher temperature region, it is suggested w7x that the rate is increased with increasing temperature. In the overview for all data listed in Table 1, it can be seen in Fig. 3 that the rate data are slightly decreased and then increased with increasing temperature. The quenching of CHŽA. by C 2 H 4 was seldom studied w9,14,16x. Over the temperature range 243– 593 K, the results of previous and this work listed in Table 1 indicate that the quenching rate constant is monotonously increased with increasing temperature as shown in Fig. 4. To the best of our knowledge, the study on the quenching of CHŽA2D . by alkane and alcohol molecules is not extensive. At room temperature, the investigations of quenching by alkane molecules in which the number of carbons is from 1 to 7 were
carried out by some groups w3,13,14x. But, the temperature dependence of the quenching rate has not been studied except for C 2 H 6 w9x. In this work, the temperature dependences of quenching rate constants of CHŽA2D . by n-C 5 H 12 , n-C 6 H 14 and n-C 7 H 16 were measured. The results are listed in Table 2 and shown in Fig. 5. At room temperature, the rate data for n-C 5 H 12 and n-C 6 H 14 in this work are in coincidence with our previous work w3x. But for n-C 7 H 16 the rate constant in this work is 30% more than that in Ref. w3x. For n-C 5 H 12 and n-C 6 H 14 , the quenching rate constants are monotonously increased with increasing temperature although for n-C 7 H 16 , the datum is slightly decreased at lower temperature and then increased at higher temperature if without the consideration of the data in Ref. w3x. The investigation of the CHŽA2D . quenching by alcohol at room temperature was performed in our
Fig. 4. Rate constant k on a logarithmic scale for the quenching of CHŽA2D . by C 2 H 4 as a function of the inverse of the temperature T.
Fig. 6. The dependences of the quenching rate constants of CHŽA2D . by alcohol molecules on temperature T where triangles for C 2 H 5 OH, squares for n-C 3 H 7 OH and circles for n-C 4 H 9 OH.
C. Chen et al.r Chemical Physics 230 (1998) 317–325
322
Table 4 Rate parameters A, n, E for the quenching rate constants fitting to k s AT n expŽy Er RT . Quencher
A r10y1 0 cm3 moleculey1 sy1
n
ErkJ moly1
C 2 H 5 OH C 3 H 7 OH C 4 H 9 OH C 5 H 12 C 6 H 14 C 7 H 16 C2 H4 O2
Ž0.21"1.1.=10y6 Ž0.65"3.5.=10y7 Ž0.53"2.7.=10y4 Ž2.4"6.0.=10y3 0.23"0.60 0.85"1.4 Ž4.9"2.6.=10y10 Ž0.82"2.0.=10y4
2.4"0.7 2.6"0.7 1.7"0.7 1.2"0.3 0.6"0.4 0.6"0.2 0 1.4"0.4
y7.9"2.4 y8.6"2.4 y4.8"2.4 y1.6"1.2 0.82"1.2 y1.4"0.79 2.0"0.3 y5.0"1.4
previous work w5x. In this work, we measured the temperature dependences of the quenching rate constants of CHŽA2D . by C 2 H 5 OH, n-C 3 H 7 OH and n-C 4 H 9 OH listed in Table 3 and shown in Fig. 6. In this work, the rate data are 40% smaller than those in Ref. w5x. Notice, in this work, the whole emission of CHŽA–X. was observed while in previous work w3,5x the signal was mainly from QŽ0,0. branch of CHŽA– X. and the time-resolved signal is much stronger than that observed before. In Fig. 6, it is clearly shown that the quenching rate constants are decreased in low temperature region and increased in high temperature region with increasing the temperature.
4. Discussion The quenching rate data and cross sections of CHŽA2D . by the molecules studied in this work have been listed in Tables 1–3. It appears to be difficult to fit the temperature dependences to Arrhenius relation or simple collision complex model w17x. Generally, in Arrhenius relations the reaction barrier is the controlling factor, while in the simple collision complex model the multiple attractive potential is the controlling factor. As concluded in Refs. w4,6x, the quenching of CHŽA. by some molecules is usually controlled by the simultaneous effects of the multiple attractive potentials and the repulsive barrier on the collision complex formation.
According to the complex model, following processes are responsible for the quenching process: CH Ž A . q M | w CHM x
)
™ CH Ž X . q M ™ products
electronic quenching reaction
where M denotes the quencher. The multiple attractive potentials and reaction barrier for the formation of complex wCH M x ) will control the overall quenching process. Hence, the temperature dependences studied in this work are not especially attributed to chemical or physical quenching process. The multiple attractive potentials between CHŽA. and quenchers include dipole–dipole, dipole– quadrupole, quadrupole–quadrupole, dipole–induced dipole and dispersion interaction, respectively. The specific expressions for the interactions in terms of the molecular parameters were given in Refs. w18,19x. For the formation of a collision complex between the collision partners, there exists an activation barrier Ea on the reaction coordinate. We modified the effective potential Veff Ž r . by adding an activation barrier Ea to the sum of the centrifugal and the attractive multiple potentials. Therefore, the effective potential could be expressed as: Veff Ž r . s Eb 2rr 2 y C3rr 3 y C4rr 4 y C6rr 6 y C8rr 8 q Ea where Ea is the activation barrier and others are the same as in Ref. w17x. Using the average orientation calculation method w17x, we calculated the complex formation cross section scf listed in Tables 1–3 where some previous work is included for comparison. The parameters used in the calculation are listed in Table 5. In the calculation process, we prescribed a radius limit for the distance between the collision partners in the collision process. In the collision complex model described in w17x, the volumes of the collision partners are not considered. It was found that with increasing the relative translational energy, the critical distance R between the collision partners at which the collision complex is formed will be decreased. It is unreasonable, when the translational energy increases to a sufficient value, the distance
C. Chen et al.r Chemical Physics 230 (1998) 317–325 Table 5 Parameters used in the calculation of complex formation cross sections
CHŽA. C 5 H 12 C 6 H 14 C 7 H 16 C 2 H 5 OH C 3 H 7 OH C 4 H 9 OH O2
na ŽDebye.
qa ŽA3 .
Qb Ž10y26 ecu.cm 2 .
IP a Žev.
0.78 c 0.10 0.05 0.10 1.69 1.66 1.66 0.00
3.30 9.99 11.9 13.7 10.49 10.15 10.04 1.58
2.29 c 2.6 3.0 3.5 0.65 1.50 2.00 0.39
8.25 10.4 10.2 9.9 5.11 7.61 8.88 12.06
a
Ref. w20x. Ref. w21x. c Ref. w22x. b
becomes much shorter than the sum of the radiuses of CH and quencher. Hence, in our calculation, we introduced a R 0 which approximately equals to the sum of the radiuses of the collision partners and limited the distance r between the collision partners which could not be smaller than R 0 when the relative translational energy is sufficient high. The critical radiuses R 0 for all quenching systems are listed in Table 6. On the basis of the collision complex model, the quenching cross section sex is the production of the complex formation cross section scf and a probability P by which the quenching will occur during the residence time of the complex, i.e., sex s Pscf . At the different temperatures, as for the same quencher, the value of P should be similar to each other. In our calculation of scf , we adjusted the activation barrier Ea in order to get the similar P for different temperature and a given quencher. The values of Ea derived are listed in Table 6 as well. Because of the immaturity of the model for the transition state and
323
experimental uncertainty, we could not get the same P but a value range as listed in Table 6. Based on the modified collision complex model, if the multiple attractive potential is the controlling factor, the temperature dependence of the complex formation cross section, therefore the quenching cross section is a monotonous decrease. On the other hand, if the activation barrier is the controlling factor, the temperature dependence is a monotonous increase. Over the temperature range in this work, as shown in Tables 2 and 3, the quenching of CHŽA. by alcohol and alkane molecules is controlled by both factors although the activation barrier for n-C 7 H 16 is very small. The quenching probability for these organic molecules is 0.6–0.8 or 0.6–0.7 which seems reasonable. In the quenching of CHŽA. by O 2 , the temperature dependence measured in this work is a monotonous decrease. Combining this results with those of previous work listed in Table 1, it is shown that the quenching rate constant decreases first and then increases with increasing temperature. By using the modified collision complex model we calculated the complex formation cross section. It is found the quenching probability P is very small P s 0.05. The quenching of CHŽA. by C 2 H 4 was an exceptional result. It shows nearly the Arrhenius dependence. The pre-exponential factor and the activation barrier are listed in Table 4. It is shown in Tables 2 and 3 that the quenching rate constants of CHŽA. generally increase with increasing the number of carbon atoms contained in alcohol and alkane molecules. The activation barrier has the contrary trend. To our best knowledge, the reaction mechanism has not been observed experimentally. For the collision between CH and saturation hydrocarbon molecules, Cooper et al. w23x suggested that for all the states of CH except for the C state, the rate constants increase with increasing the number of C–H bonds, as would be expected if the
Table 6 Activative barrier Ea , radius of complex R 0 and quencher probability EarkJ moly1 R 0rnm P
C 2 H 5 OH
C 3 H 7 OH
C 4 H 9 OH
C 5 H 12
C 6 H 14
C 7 H 16
O2
3.6 0.48 0.6–0.8
1.7 0.52 0.6–0.8
1.0 0.56 0.6–0.7
2.4 0.53 0.6–0.7
1.2 0.56 0.6–0.7
0.24 0.59 0.6–0.7
7.8 0.25 0.05
324
C. Chen et al.r Chemical Physics 230 (1998) 317–325
collisional removal of CH was largely by chemical reaction. Berman and Lin w24x, and Nokes and Donovan w14x pointed out that the insertion of the CHŽX. or CHŽA. radical into a C–H bond occurs, yielding an energetic or electronically excited adduct when CHŽX. or CHŽA. collides with carbon hydride compounds. We made an ab initio calculation on the reaction of CHŽX. with CH 4 w25x and concluded that a two-step mechanism Žabstraction–addition path. exists. From the viewpoint of the reaction which is thought to proceed either via abstraction or insertion followed by the rapid decomposition of the adduct the collision cross section and the activation barrier correlating with the bond energy of the attacked bond are important for the formation of adduct. Because there is an OH group in alcohol molecule, resulting in much stronger polarity than that of alkane molecule and the induction of the OH to weaken the C–H bond, the multipole attractive forces between CH and alcohol are stronger than those between alkane and CH, and the reaction barrier between CH and alcohol is lower than that between CH and alkane. Therefore, the quenching cross section of CHŽA. by alcohol should be larger than that by the corresponding alkane molecule. For the quenchers of both alcohol and alkane, it is noticed that the activation barrier decreases with increasing the number of carbon atoms contained in these quenchers. In the case of C 2 H 4 as a quencher, the temperature dependence is nearly consistent with the Arrhenius correlation which suggests that the reaction mechanism is probably different from those of CHŽA. with alkane and alcohol, e.g., addition reaction might take place. The quenching rate constant of CHŽA. by O 2 is smaller than those by alkane and alcohol by one order of magnitude. For the quenching process of the electronically excited CH radical, the total available energy of the complex is mainly contributed by CHŽA., because the energy of CHŽA. is much greater than that of the quencher. Therefore, it can be considered that the total available energies of complexes are similar. During the residence time of the complex, the energy will be redistributed among its internal degrees of freedom. For given total energy, the density of states of complex and quenching product species increase with increasing numbers of atoms in the complex. When the complex dissociates
to form quenching products or reactants, CHŽA. and quencher, the probability P of forming quenching products will be higher for a larger quencher. O 2 molecule is the smallest and simplest molecule studied in this work. Hence, both the quenching cross section and the probability P are the smallest. This explanation could be used to interpret the dependences of the quenching cross sections of CHŽA. on the number of atoms contained in alcohol and alkane molecules as well.
Acknowledgements We appreciate financial support by the National Natural Science Foundation Committee of China.
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