Parameterising Rate Coefficients

While the results of trajectory calculations provide an accurate testing ground for more approximate theories, and, in the parameterised form developed by Su, Chesnavich and Bowers [25,26], a widely applied means of calculating capture rate coefficients for these more complex interactions, they provide less insight into reaction mechanisms and rate coefficient determinants than more analytic approaches. The simplest approach is provided by phase space theory (PST) which assumes an isotropic potential between the reactants [31]. The centrifugal term in the effective potential in (3.2) can be expressed in terms of the orbital angular momentum quantum number, , for the collision, so that the equation for Vejf (Rab) becomes ... 

An important part of specifying a chemical reaction mechanism is providing accurate parameterisations of the rate coefficients. In liquid phase and in atmospheric kinetics, the temperature dependence of rate coefficient k is usually described by the Arrhenius equation ... 

The Troe equation and the similar SRI equation (Stewart et al. 1989) can accurately represent the fall-off region only for single-well potential energy surfaces (Venkatech et al. 1997). For more complicated elementary reactions, the difference between the theoretically calculated rate coefficient and the best Troe fit can be as high as 40 %. A series of fitting formulae for the parameterisation of the fall-off curves are discussed in Zhang and Law (2009, 2011). In some mechanisms, the pressure dependence is given by the so-called log p formalism [see e.g. Zador et al. (2011)] ... 

We have already discussed the fact that significant uncertainties can exist in the parameterisation of gas kinetic models and in theoretical calculations of rate coefficients of relevance to gas-phase chemistry. In many applications within gas-phase chemistry, however, the basic structure of the model is reasonably well known or can be suggested using mechanism constructirui protocols such as those... 

Cumene is cracked in a recycle reactor over commercial H-ZSM5 extrudates. A Thiele modulus approach is used to determine the diffusion coefficient and the intrinsic rate constant. The results are compared to those obtained from pulse experiments. A linear model for diffusion, adsorption and reaction rate is applied for reactants and products. In contrast to literature it is argued that if the Thiele modulus is greater than five, the system becomes over parameterised. If additionally adsorption dynamics are negligible, only one lumped parameter can be extracted, which is the apparent reaction constant found from steady state experiments. The pulse experiment of cumene is strongly diffusion limited showing no adsorption dynamics of cumene. However, benzene adsorbed strongly on the zeolite and could be used to extract transient model parameters which are compared to steady state parameters. 

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