Geometric investigation of association/dissociation kinetics with an application to the master equation for CH3 + CH3 ↔ C2H6

Journal of Physical Chemistry A

Volumn 106, Issue 24, 2002, Pages 5860-5879

  Davis, Michael J ^a   Klippenstein, Stephen J ^b  

^a ARGONNE NATIONAL LABORATORY   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASSOCIATION KINETICS; LINEAR MASTER EQUATIONS;

EIGENVALUES AND EIGENFUNCTIONS; GEOMETRY; KINETIC ENERGY; ORGANIC COMPOUNDS; PHASE SPACE METHODS; RATE CONSTANTS;

DISSOCIATION;

EID: 0037141793     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp014136a     Document Type: Article

References (56)

1. Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific: Oxford, U.K., 1990.
2. Holbrook, K. A.; Pilling, M. J.; Robertson, S. H. Unimolecular Reactions, 2nd ed.; Wiley: Chichester, U.K., 1996.
3. Robertson, S. H.; Pilling, M. J.; Baulch, D. L.; Green, N. J. B. J. Phys. Chem. 1995, 99, 13452.
4. Barker, J. R. Chem. Phys. 1983, 77, 301.
5. Shi, J.; Barker, J. R. Int. J. Chem. Kinet. 1990, 22, 187.
6. Bedanov, V. M.; Tsang, W.; Zacharian, M. R. J. Phys. Chem. 1995, 99, 11452.
7. Gates, K. E.; Robertson, S. H.; Smith, S. C.; Pilling, M. J.; Beasley, M. S.; Maschhoff, K. J. J. Phys. Chem. A 1997, 101, 5765.
8. Vereecken, L.; Huyberechts, G.; Peeters, J. J. Chem. Phys. 1997, 106, 6564.
9. Tsang, W.; Bedanov, V.; Zachariah, M. R. Ber. Bunsen-Ges. Phys. Chem. 1997, 491.
10. Venkatesh, P. K.; Dean, A. N.; Cohen, M. H.; Carr, R. W. J. Chem. Phys. 1997, 107, 8904.
11. Frankcombe, T. J.; Smith, S. C.; Gates, K. E.; Robertson, S. H. Phys. Chem. Chem. Phys. 2000, 2, 793.
12. Blitz, M. A.; Beasley, M. S.; Pilling, M. J.; Robertson, S. H. Phys. Chem. Chem. Phys. 2000, 2, 805.
13. Knyazev, V. D.; Tsang, W. J. Phys. Chem. A 2000, 104, 10747.
14. Barker, J. R. Int. J. Chem. Kinet. 2001, 33, 232.
15. Barker, J. R.; Ortiz, N. F. Int. J. Chem. Kinet. 2001, 33, 246.
16. Miller, J. A.; Klippenstein, S. J. J. Phys. Chem. A 2001, 105, 7254.
17. Klippenstein, S. J.; Harding, L. B. J. Phys. Chem. A 1999, 103, 9388.
18. Klippenstein, S. J.; Wagner, A. F.; Dunbar, R. C.; Wardlaw, D. M.; Robertson, S. H. Variflex, version 1.0; 1999.
19. Davis, M. J.; Skodje, R. T. J. Chem. Phys. 1999, 111, 859.
20. Davis, M. J.; Skodje, R. T. Z. Phys. Chem. 2001, 215, 233.
21. Skodje, R. T.; Davis, M. J. Phys. Chem. A 2001, 105, 10356.
22. Fraser, S. J. J. Chem. Phys. 1988, 88, 4732.
23. Roussel, M. R. A Rigorous Approach to Steady-State Kinetics Applied to Simple Enzyme Mechanisms. Ph.D. Thesis, University of Toronto, Toronto, Canada, 1994 and references cited therein.
24. Roussel, M. R.; Fraser, S. J. Chaos 2001, 11, 196 and references cited therein.
25. Maas, U.; Pope, S. B. Combust. Flame 1992, 88, 239.
26. Maas, U.; Pope, S. B. Proc. Combust. Inst. 1992, 28, 103.
27. Maas, U.; Pope, S. B. Proc. Combust. Inst. 1994, 25, 1349.
28. Davis, M. J. J. Chem. Phys. 2002, 116, 7828.
29. Brau, C. A. J. Chem. Phys. 1967, 47, 1153.
30. Brau, C. A. J. Chem. Phys. 1967, 47, 3076.
31. Hogarth, W. L.; McElwain, D. L. S. J. Chem. Phys. 1975, 63, 2502.
32. Hogarth, W. L.; McElwain, D. L. S. Chem. Phys. 1977, 19, 429.
33. Lim, C.; Truhlar, D. G. J. Phys. Chem. 1983, 87, 2683
34. Benson, S. W. The Foundations of Chemical Kinetics; McGraw-Hill: New York, 1960.
35. Perko, L. Differential Equations and Dynamical Systems; Springer-Verlag: New York, 1996.
36. Pilling, M. J.; Seakins, P. W. Reaction Kinetics; Oxford University Press: Oxford, U.K., 1995.
37. For an example where eigenvalues are explicity defined, Hanning-Lee, M. A.; Green, N. J. B.; Pilling, M. J.; Robertson, S. H. J. Phys. Chem. 1993, 97, 860. This case involves bimolecular terms but becomes pseudo-first order because one of the species is in excess.
38. See, for example, the discussion in chapter 2 of ref 1.
39. Mallard, W. G. NIST Chemical Kinetics Database, and reference cited therein.
40. Glänzer, K.; Quack, M.; Troe, J. Chem. Phys. Lett. 1976, 39, 304.
41. Glänzer, K.; Quack, M.; Troe, J. In Sixteenth Symposium (International) Combustion; 1977, p, 949.
42. Hippler, H.; Luther, K.; Ravishankara, A. R.; Troe, J. Z. Phys. Chem. NF 1984, 142, 1.
43. Slagle, I. R.; Guttman, D.; Davis, J. W.; Pilling, M. J. J. Phys. Chem. 1988, 92, 2455.
44. Walter, D.; Grotheer, H.-H.; Davies, J. W.; Pilling, M. J.; Wagner, A. F. In Twenty-Third Symposium (Int.) Combustion; 1990, p 107.
45. Hwang, S. M.; Rabinowitz, M. J.; Gardiner, W. C. Jr. Chem. Phys. Lett. 1993, 205, 157.
46. Davidson, D. F.; DiRossa, M. D.; Chang, E. J.; Hanson, R. K.; Bowman, C. T. Int. J. Chem. Kinet. 1995, 27, 1179.
47. Du, H.; Hessler, J. P.; Orgren, P. J. J. Phys. Chem. 1996, 100, 974.
48. Wagner, A. F.; Wardlaw, D. M. J. Phys. Chem. 1988, 92, 2462.
49. Smith, S. C.; Gilbert, R. G. Int. J. Chem. Kinet. 1988, 20, 307.
50. Hessler, J. P.; Ogren, P. J. J. Phys. Chem. 1996, 100, 984.
51. For example, eq 31 in ref 3.
52. This form of the master equation has been used elsewhere; see ref 11 and Miller, J. A.; Klippenstein, S. J.; Robertson, S. H. Proc. Combust. Inst. 2000, 28, 1479.
53. Expressions such as this have been used elsewhere; see, for example, ref 11.
54. The assumption of an equilibrium constant for the master equation has been discussed in Smith, S. C.; McEwan, M. J.; Gilbert, R. G. J. Chem. Phys. 1989, 90, 4265
55. Jeffrey, S. J.; Gates, K. E.; Smith, S. C. J. Phys. Chem. 1996, 100, 7090 and references therein.
56. Frankcombe, T. J.; Smith, S. C. Faraday Discuss. 2001, 119, 159.