Molecular microkinetics simulations

In this section, we will present results of microldnetics simulations based on elementary reaction energy schemes deduced from quantum chemical studies. We use an adapted scheme to enable analysis of the results in terms of the values of elementary rate constants selected. For the same reason, we ignore surface concentration dependence of adsorption energies, whereas this can be readily implemented in the simulations. We are interested in general trends and especially the temperature dependence of overall reaction rates. The simulations will also provide us with information on surface concentrations. In the simulations to be presented here, we exclude product readsorption effects. Microldnetics simulations are attractive since they do not require an assumption of rate-controlling steps or equilibration. Solutions for overall rates are found by solving the complete set of PDFs with proper initial conditions. While in kinetic Monte Carlo simulations these expressions are solved using stochastic techniques, which enable formation 

In order to base a kinetic model on molecular quantum chemical data, one needs to have a molecular mechanistic model of the reaction. Accuracy of quantum chemical data is not high enough to be kinetically predictable (order of 10 kj mol , whereas kinetics requires 1 kJ mol ), but this accuracy is usually large enough to discriminate between different mechanistic options. 

We have based our reaction energy scheme on the Ciobica et al. [29]. proposal that CHjjjg monomers become incorporated in the growing reaction chain. We allow only for olefin formation, which is the primary product of the FT reaction of the metals Co or Ru. 

The growing hydrocarbon chain is of the alkenyl CH-CH-R type that is terminated by addition of a hydrogen atom to the primary C atom, but becomes an intermediate for chain growth when H is added to the secondary atom. 

Beyond a critical temperature where a has still a high value, we observe rapid convergence of a with chain length. In simulations with a low cutoff of hydrocarbon chain length, the kinetics data relevant to FT can be simulated as long as low-temperature data are ignored. This chain length-cutoff-dependent behavior provides a new interpretation to previous kinetic Monte Carlo simulations [4]. 

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We will quantify the rate ratios of Figure 16.1. In Section 16.4 and the following, a molecular reaction energy diagram will be introduced that enables deduction of the lumped kinetic parameters of Scheme 16.1 from microkinetics simulations. 

Single-event microkinetics describe the hydrocarbon conversion at molecular level. Present day analytical techniques do not allow an identification of industrial feedstocks in such detail. In addition current computational resources are not sufficient to perform simulations at molecular level for industrial feedstock conversion. These issues are addressed using the relumping methodology. 

Microkinetic modeling assembles molecular-level information obtained from quantum chemical calculations, atomistic simulations and experiments to quantify the kinetic behavior at given reaction conditions on a particular catalyst surface. In a postulated reaction mechanism the rate parameters are specified for each elementary reaction. For instance adsorption preexponential terms, which are in units of cm3 mol"1 s"1, have been typically assigned the values of the standard collision number (1013 cm3 mol"1 s 1). The pre-exponential term (cm 2 mol s 1) of the bimolecular surface reaction in case of immobile or moble transition state is 1021. The same number holds for the bimolecular surface reaction between one mobile and one immobile adsorbate producing an immobile transition state. However, often parameters must still be fitted to experimental data, and this limits the predictive capability that microkinetic modeling inherently offers. A detailed account of microkinetic modelling is provided by P. Stoltze, Progress in Surface Science, 65 (2000) 65-150. 

In previous papers by the authors [9,10], the temperature-programmed desorption of N2 from an iron-based catalyst has been studied experimentally. The microkinetic analysis of these results is based on the kinetic simulation of ammonia synthesis by Stoltze and Nprskov [22-24] using the approach by Dumesic and Trevino [2]. On Fe single crystal surfaces it was possible to detect a di-molecular precursor labelled a-N2 — forN2 dissociation... 

The microkinetic interpretation of the origin of these different patterns may be confirmed by molecular dynamics (MD) simulations. As an example. Fig. 11 presents the result of an MD study with methane in a cation-free zeolite of type LTA [117,118]. By increasing the Lennard-Jones distance a between the methane molecules and the oxygen of the zeolite lattice one is able to simulate the influence of a reduction of the window diameter on the dif-... 

Microkinetic modehng assembles molecular-level information obtained from quantum chemical calculations, atomistic simulations and experiments to quantify the kinetic behavior at given reaction conditions on a particular catalyst surface. In a postulated reaction mechanism, the rate parameters are specified for each elementary reaction. For instance, adsorption pre-exponential terms, which are in units of cm mol s have... 

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