The Single Event Concept

Beyond a number of assumptions and thermodynamic constraints a substantial reduction of the number of parameters to be determined from a set of experimental data is only possible by modeling the rate parameters. The modeling is based upon transition state theory, it makes use of the single event concept introduced by Froment and co-workers [Baltanas et al., 1989 Vynckier and Froment, 1991 Park and Froment, 2001 Feng et al., 1993 Svoboda et al., 1995 De Wachtere et al., 1999 Martinis and Froment, 2006 Kumar and Froment, 2007 Froment, 2005] and of the Evans-Polanyi relationship for the activation energy [1938]. 

The standard entropy that enters into the frequency factor of the rate coefficient contains electronic, translational, vibrational and rotational contributions  

The latter can be split into internal and external contributions, but both consist of an intrinsic term (5° ) and a term containing the symmetry number, a, that reflects the structure of the species  

To account for the effect of n chiral centers, a global symmetry number, gi ext int is defined, so that the change in standard entropy due to symmetry changes associated with the transformation of the reactant into the activated complex is written  

When the symmetry contribution (2.4.3.1-3) is factored out, equation (2.4.3.1-1) for the rate coefficient of a monomolecular elementary step e.g., becomes 

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Whereas the single event concept accounts for the effect of the structure on the frequency factor of an elementary step the linear free energy type relationship of... 

The single event concept and the Evans-Polanyi relationship drastically reduce the number of independent rate coefficients and thus enable addressing the complex problems encountered in industrial processes. 

The carbon number of the paraffin feed can extend up to 100. The reaction network has to be generated by computer as indicated in Sections 2.4.1 and 2.4.2. The reduction of the number of kinetic parameters is performed using the single event concept and the Evans-Polanyi relationship. 

The single-event microkinetic concept ensures the feedstock independence of the kinetic parameters [8]. Present challenges in microkinetic modelling are the identification of catalyst descriptors accounting for catalyst properties such as acidity [10,11] and shape selectivity [12,13]. 

Tullis (Ref 26) investigated both of these approaches to a single event FAE and proposed a concept best described as a one-step automatic two-event FAE. Here the second-event explosive is replaced by a very highly hypergolic oxidizer under the implosive dispersal mode. The technique is a one-step process since only one explosive charge need be detonated. The mechanism, however, proceeds via two events as the explosive charge causes a dual dispersal ... 

The rate constants for isomerization steps are similar in the forward and the reverse directions. For convenience, we choose to parameterize the kinetic model in terms of the forward rate constants. In this respect, we use the concept of single-event rate coefficients developed by Froment (127). According to Froment, the rate constant for a particular step is obtained by multiplying a single-event rate coefficient by the number of single events, ne, possible for the reactant. The expression for ne is... 

The concept of single-events lies upstream from the notion of elementary step. 

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