The Generalized Rate Coefficient Formulae For Important Chemical Reactions In The Systems With Power-law Distributions

The calculations of reaction rate are important in studying the different processesin physics, chemistry, biology, engineering etc. There exist many theories of reactionrate, such as transition state theory, collision theory, barrierless reaction theory, andunimolecular reaction theory, all of which are based on the traditional statisticalmechanics and a Maxwell distribution whose form is exponential law holds in thewhole time. This exponential law form of reaction rate is usually called Arrheniusbehaviour. However, plenty of experimental results show non–Arrhenius behaviourand current theories can not be valid any longer. Therefore, providing correspondingtheortical description for non–Arrhenius behaviour becomes urgent. In this paper, thereaction rate theory with power–law distributions in nonequilibrium systems isstudied based on nonextensive statistical mechanics.Firstly, the generalized transtion state theory for an elementary bimolecularreaction is studied under the framework of power–law nonextensive statisticalmechanics. A generalized reaction rate formula with power–law distribution isobtained. It is shown that the reaction rate not only depends on a nonextensiveparameter but also on the reaction coordinate frenquency in the transition state. Theinflunce of nonextensive parameter on the rate is also discussed by theorticalderivation and numerical calculation. The example of F+H2is taken and the newtheory shows a better agreement with all the experimental results. In addition, thetunneling correction is considered into generalized transition state theory, which couldbe very important for the reactions in low temperature. Then the new theory is appliedinto reaction with most obivious tunneling correction, i.e. H+H2.Secondly, the generalized collision theory is studied based on power–lawnonextensive statistical mechanics. The reaction rate formula is obtained in theassumption that the system follows the power–law distribution. The generalizedcollision theory can effectively overcomes two important difficulties of the famousLindemann mechanism. The pre–exponential factors of F+H2, CO+O2, and CH3+CH3are calculated. What’s more, the reaction without barrier with power–lawdistribution is studied in the framework of Tsallis statistics.Thirdly, the generalized unimolecular reaction rate is studied. The two reaction rate formulae in high pressure limit and low pressure limit are got respectively withpower–law distributions. The decomposition of CH3CO and the isomerization ofCH3NC are taken as two examples and the generalized theoretical results presentconsistent with all the experimental results.