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Detailed balance in multiple-well chemical reactions
James A Miller1, Stephen J Klippenstein, Struan H Robertson
1Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969, USA. jamille@sandia.gov
Physical Chemistry Chemical Physics : PCCP
|February 12, 2009
Summary
This study examines detailed balance in chemical kinetics, finding that rate constants from master equation solutions rarely satisfy it exactly. However, discrepancies are practically negligible in combustion and atmospheric chemistry.
Area of Science:
- Chemical Kinetics
- Theoretical Chemistry
Background:
- Reactions with multiple potential wells are crucial in combustion and atmospheric chemistry.
- Accurate theoretical rate constants require solving time-dependent, multiple-well master equations.
Purpose of the Study:
- To investigate the extent to which detailed balance is satisfied by rate constants derived from master equation solutions.
- To explore conditions for chemical equilibrium and the relationship between detailed balance and Wegscheider conditions.
Main Methods:
- Solving time-dependent, multiple-well master equations.
- Analyzing the "near-Boltzmann" distribution approximation in reaction wells.
- Examining necessary and sufficient conditions for systems to evolve to chemical equilibrium.
Main Results:
- Rate constants obtained from master equation solutions are unlikely to satisfy detailed balance exactly.
- The "near-Boltzmann" distribution offers insight into deviations from detailed balance.
- Quantitative measures for "near-Boltzmann" distributions were proposed.
Conclusions:
- While exact detailed balance is improbable, the observed deviations in rate constants are vanishingly small.
- The findings have implications for the accuracy of theoretical models in chemical kinetics, particularly for combustion and atmospheric processes.
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