Statistical rate theory

Onsager s reciprocal rules are valid for systems that are sufficiently close to global equilibrium. It is crucial to determine under what conditions the assumption of linearity will hold. Onsager s reciprocal rules hold if the flows and forces are independent of one another and are identified from the rate entropy production or dissipation function. 

As long as the entropy changes are large, Eq. (6.269) cannot be linearized. For example, chemical reactions and interfacial transport between two phases yield large entropy changes. Statistical rate theory leads to well-defined coefficients that can be measured or controlled and hence the criteria for linearization may be explicitly expressed. 

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Upson J B, Beiderhase T W, Molina L T and Molina M J 1999 Production of HCI in the OH + CIO reaction laboratory measurements and statistical rate theory calculations J. Phys. Chem. A 103 6540-51... 

Statistical rate theories have been used to calculate rate constants for gas-phase Sn2 reactions.1,7 For a SN2 reaction like Cl" + CH3Clb, which has a central barrier higher than the reactant asymptotic limit (see Figure 1), transition state theory (TST) assumes that the crossing of the central barrier is rate-limiting. Thus, the TST expression for the SN2 rate constant is simply,... 

A simplified approach is statistical rate theory (transition state theory) with the help of which the overall rate constant k(T) may be obtained from potential energy surface (PES) in a single jump averaging out all of the intermediate details. It is generally not possible to extract microscopic details such as energy-dependent cross sections from conventional kinetics experiments. The preferable approach is to calculate microscopic quantities from some model and then perform the downward averaging for comparison with measured quantities. 

Statistical rate theories often are also formulated using variational principles. Like the adiabatic principle, variational principles are intuitive and have to be proven (or disproven) by comparison with true dynamical treatments. As SACM in the previous chapters has been shown to give identical results with trajectory calculations at high temperature for the considered simple reaction system, differences between SACM and VTST would speak against the latter. The charge-dipole system, because of its simplicity, can be used particularly well for a quantitative comparison between SACM and VTST and, hence, for a quantitative test of VTST. 

The lowest-lying potential energy surfaces for the 0(3P) + CH2=C=CH2 reaction were theoretically characterized using CBS-QB3, RRKM statistical rate theory, and weak-collision master equation analysis using the exact stochastic simulation method. The results predicted that the electrophilic O-addition pathways on the central and terminal carbon atom are dominant up to combustion temperatures. Major predicted end-products are in agreement with experimental evidence. New H-abstraction pathways, resulting in OH and propargyl radicals, have been identified.254... 

As for most applications of statistical rate theory, the most difficult aspect is the characterization of the transition state. As discussed above, if the E0 value determined from a TCID experiment corresponds to the bond energy of AB+, then the transition state must be a loose one. In such a case, it is generally appropri-... 

On the other hand, from statistical rate theory, we have... 

Comparing these statistical rate theory equations, with Eqs. (6.283) and (6.284), we obtain the following phenomenological coefficients... 

Equations (6.299) and (6.300) show that Onsager s reciprocal rules hold. The Js eq and Jweq have a microscopic definition represented by perturbation matrix elements and a macroscopic definition represented by the equilibrium exchange rate. As long as the criteria of linearization are satisfied, the statistical rate theory may be used to describe systems with temperature differences at an interface besides the driving forces of pressure and concentration differences. 

FURTHER SUCCESSFUL APPLICATIONS OF THE NEW THEORETICAL DESCRIPTION OF ADSORPTION/DESORPTION KINETICS BASED ON THE STATISTICAL RATE THEORY... 

It is shown how the new approach to adsorption/desorption kinetics based on the Statistical Rate Theory can be successfully applied to describe the kinetics of dissociative gas chemisorption on solids. 

The breakthrough came at the beginning of the eighties of the 20" century with the new theoretical approach called the Statistical Rate Theory (SRT), linking the rate of adsorption/desorption kinetics to the chemical potentials of the molecules in the bulk and the adsorbed phases. [4]... 

The Statistical Rate Theory (SRT) is based on considering the quantum-mechanical transition probability in an isolated many particle system. Assuming that the transport of molecules between the phases at the thermal equilibrium results primarily from single molecular events, the expression for the rate of molecular transport between the two phases 1 and 2 , R 2, was developed by using the first-order perturbation analysis of the Schrodinger equation and the Boltzmann definition of entropy. 

Ward C.A. and Hndlay R.D., Statistical rate theory of interfecial transport. IV. Predicted rate of dissociative adsorption, J. Chem. Phys. 76 (1982) pp.S624-5631. 

Ward C.A. and Elmoseli M.B., Molecular adsorption at a well defined gas-solid interphase Statistical rate theory approach. Surf. Sci. 176 (1986) pp.4S7-47S. 

Elliott J.A.W. and Ward C.A., Statistical Rate Theory and the Material Properties Controlling Adsorption Kinetics. In RUDZINSKI W., STEELE W.A., ZGRABLICH G.. (eds.) Equilibria and Dyrutmics of Gas Adsorption on Heterogeneous Solid Surfaces (Elsevier New York, 1997), pp.285-333. 

Rudzinski W. and Panczyk T., The Kinetics Of Isothermal Adsorption On Enetgetically Heterogeneous Solid Surfaces A New Theoretical Description Based On The Statistical Rate Theory Of Inter cial Transport, J. Phys. Chem. B. 104 (2000) pp.9149-9162. 

Panczyk T. and Rudzinsld W., Kinetics of Multi-Site-Occupancy Adsorption on Heterogeneous Solid Sur ces A Statistical Rate Theory Approach, J. Phys. Chem., 106(2002) pp.7846-7851. 

Rudzinski W., Borowiecki T., Dominko A., and Panczyk T., New Method of Estimating the Solid Surface Energetic Heterogeneity from TPD Spectra Based on the Statistical Rate Theory of Inter cial Transport, Langmuir, 13 (1997) pp.3445-3453. 

Various quantum-mechanical theories have been proposed which allow one to calculate isotopic Arrhenius curves from first principles, where tunneling is included. These theories generally start with an ab initio calculation of the reaction surface and use either quantum or statistical rate theories in order to calculate rate constants and kinetic isotope effects. Among these are the variational transition state theory of Truhlar [15], the instanton approach of Smedarchina et al. 

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