37
3.3.4.3. Rate Constants for Steps 14 and 15
The rate constants of step 14 decomposing into CO and step 15 into CO2 were calculated as shown in Figure 8. The rate constant of step 14 was significantly larger than step 15 at all temperatures, and thus CO formation was dominant within the proposed unimolecular decomposition pathways in Scheme 1.
As the other possible pathways responsible for CO2 formation, the produced CO and M10 might recombine to generate M13 through step 21, as shown in Scheme 2. The reverse reactions of step 14 and 15 are also considered as the CO and M10 recombination. When comparing the rate constant for step 21 with those of the reverse reactions, as shown in Figure 9, step 21 had a lower rate constant at all temperatures and was likely the minor reaction channel. CO2 formation routes remain unresolved theoretically, and further insight into this aspect is left to future work. Modified Arrhenius parameters for all steps (step 1 to 22) are given in Table S1 in the Appendix B for future research of reaction kinetic modeling. Additionally, the possible reaction steps for the H-addition reaction with resorcinol were depicted in Figure S2 in the Appendix B, and the corresponding Modified Arrhenius parameters are given in Table S2 in the Appendix B.
38
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Table 1: CBS-QB3 calculated activation energies Ea (kcal/mol) at 0 K for OH bond scission and H-abstraction reactions from the hydroxyl group by H atoms.
Ea Ea
Step 1 R → M1 + H 86.24 Step 19 R + H → TS1 → M1 + H2 10.56 Step 7 M3 → M11 + H 69.66 Step 21 M3 + H →TS7 →M11 + H2 6.70 Step 8 M1 → M6 + H 86.19 Step 20 M1 + H →TS8 →M6 + H2 8.67
42
SCHEME 1. Proposal of Reaction Pathways for CO and CO2 Formation during Resorcinol Pyrolysis.
Reaction Pathway 1: Step 1 → Step 2 → Step 3 → Step 4 Reaction Pathway 2: Step 1 → Step 2 → Step 5 → Step 6
Reaction Pathway 3: Step 1 → Step 2 → Step 3 → Step 7 → Step 14 Reaction Pathway 4: Step 1 → Step 9 → Step 12 → Step 13
Reaction Pathway 5: Step 1 → Step 8 → Step 10 → Step 11 → Step 14
Reaction Pathway 6: Step 1 → Step 2 → Step 3 → Step 7 → Step 15 → Step 16 → Step 17 Reaction Pathway 7: Step 1 → Step 8 → Step 10 → Step 11 → Step 15 → Step 16 → Step 17
43
SCHEME 2: Recombination of M10 and CO generating M13.
Resorcinol [syn-syn]
0 [kcal/mol]
Resorcinol [syn-anti]
-0.64508 [kcal/mol]
Resorcinol [anti-anti], R
-0.64571 [kcal/mol]
Figure 1. Optimized resorcinol structures at the B3LYP/6-311G(2d,d,p) level of theory.
Distances are measured in Å. Relative energies (kcal/mol) of the three resorcinol configurations at the CBS-QB3 level are also given with reference to the syn-syn configuration.
44
0 2 4 6 8 10 12
0 50 100 150 200 250
187.1
M10 + CO + 2H.
190.1
TS5 + 2H.
179.8
M6(Singlet) + 2H. 197.2
190.3
106.4
R
TS13 + 2H.
M11 + 2H.
M10 (Singlet) + CO + 2H.
TS11 + 2H.
TS10 + 2H.
M8 + 2H.
TS6 + H.
M3 + H.
triplet state singlet state doublet state
Relative Energy (kcal/mol)
Reaction Process
M1 + H.
TS3 + H.
M2 + H.
TS2 + H.
TS12 + H.
M5 + CO + H.
M4 + H.TS4 + H.
M7 + 2H.
TS9 + 2H.
M6 + 2H.
0 86.2
134.9 132.5
140.4 141.1
120.7 120.3 125.2 123.4 172.4
189.9 165.7
152.8 230.1
222.6 230.5
Figure 2. PES diagram calculated at 0 K with the CBS-QB3 level of theory for the formation of CO without H-abstraction. (Reaction Pathway 1: R → M1 + H → TS2 + H → M2 + H → TS3 + H → M3 + H →TS4 + H → M5 + CO + H; Reaction Pathway 2: R → M1 + H → TS2 + H → M2 + H → TS5 + H → M4 + H → TS6 + H → M5 + CO + H; Reaction Pathway 3: R → M1 + H → TS2 + H → M2 + H
→ TS3 + H → M3 + H → M11 + 2H → TS13 + 2H → M10 + CO + 2H; Reaction Pathway 4: R → M1 + H → M6 (Singlet) + 2H → TS9 + 2H → M7 + 2H → TS12 + 2H → M10 (Singlet) + CO + 2H; Reaction Pathway 5; R → M1 + H → M6 + 2H
→ TS10 + 2H → M8 + 2H → TS11 + 2H → M11 + 2H → TS13 + 2H → M10 + CO + 2H).
45
0 2 4 6 8 10 12 14
0 50 100 150 200 250
222.6
230.1 230.5
140.4 TS2 + H.
195.6 243.5
199.0 225.6 175.4 227.5
190.3
120.7 132.5
134.9 172.4
86.2
M14 + CO2 + 2H.
TS16 + 2H.
M13 + 2H.
TS15 + 2H.
M12 + 2H.
TS14 + 2H.
M3 + H.
TS3 + H.
M2 + H.
M11 + 2H.
TS11 + 2H.
M8 + 2H.
TS10 + 2H.
M6 + 2H.
M1 + H.
triplet state doublet state
Relative Energy (kcal/mol)
Reaction Process
R 0
Figure 3. PES diagram calculated at 0 K with the CBS-QB3 level of theory for the formation of CO2 without H-abstraction. (Reaction Pathway 6: R → M1 + H → TS2 + H → M2 + H → TS3 + H → M3 + H → M11 + 2H → TS14 + 2H → M12 + 2H
→ TS15 + 2H → M13 + 2H → TS16 + 2H → M14 + CO2 + 2H; Reaction Pathway 7; R → M1 + H → M6 + 2H → TS10 + 2H → M8 + 2H → TS11 + 2H → M11 + 2H → TS14 + 2H → M12 + 2H → TS15 + 2H → M13 + 2H → TS16 + 2H → M14 + CO2 + 2H).
46
0.5 1.0 1.5 2.0 2.5 3.0 3.5
-140 -120 -100 -80 -60 -40 -20 0 20
ln(k[1/s])
1000/T (1/K)
Step 1 Step 7 Step 8 Step 9
Figure 4. High-pressure limiting rate constants for Step 1, 7, 8 and 9 in the temperature range of 300 – 1500 K. (Step 1: R → M1 + H; Step 7: M3 → M11 + H; Step 8: M1 → M6 + H; Step 9: M1 → M6 (Singlet) + H).
TS1 TS7 TS8
Figure 5. Optimized structure of transition state at B3LYP/6-311G(2d,d,p). (TS1, TS7 and TS8 for H abstraction of step 1, 7 and 8, respectively). Distances are measured in Å.
47
0.5 1.0 1.5 2.0 2.5 3.0 3.5
20 40 60
ln(k[cm3 /mol/s])
1000/T (1/K)
Step 19 Step 20 Step 21
Figure 6. High-pressure limiting rate constants for Step 19, 20 and 21 in the temperature range of 300 – 1500 K. (Step 19: R + H → TS1 → M1 + H2, Step 20: M1 + H →TS8
→M7 + H2, and Step 21: M3 + H →TS7 →M10 + H2).
0.5 1.0 1.5 2.0 2.5 3.0 3.5 -100
-80 -60 -40 -20 0
ln(k[1/s])
1000/K (1/K)
Step 2 Step 8
Figure 7. High-pressure limiting rate constants for Step 2 and 8 in the temperature range of 300 – 1500 K.
48
0.5 1.0 1.5 2.0 2.5 3.0 3.5
-30 -20 -10 0 10 20 30
ln(k[1/s])
1000/K (1/K)
Step 14 Step 15
Figure 8. High-pressure limiting rate constants for Step 14 and 15 in the temperature range of 300 – 1500 K.
0.5 1.0 1.5 2.0 2.5 3.0 3.5
-20 0 20 40
ln(k[cm3 /mol/s])
1000/T (1/K)
Step 21
Reverse of Step 14
Figure 9. High-pressure limiting rate constants for Step 21 and reverse reaction of step 14 in the temperature range of 300 – 1500 K.
49
Chapter 4: Theoretical Study on the Kinetics of Thermal Decomposition of Guaiacol and Catechol