Microkinetic modelling of the formation of C1 and C2 products in the Fischer-Tropsch synthesis over cobalt catalysts

The heats of adsorption of different C₁ and C₂ molecules assumed to be present during the initial steps of the Fischer-Tropsch synthesis and activation energies for elementary steps envisioned to occur in the synthesis are calculated for Co by using the unity bond index-quadratic exponential potential (UBI-QEP) method. The preexponential factors for the elementary steps are calculated from transition-state theory, and the rate constants are calculated according to the Arrhenius equation. The activation barrier for hydrogenation of CO is found to be lower compared to hydrogen assisted dissociation of CO, which has a smaller activation barrier than direct dissociation of CO. The reaction steps with high activation barriers are eliminated. Based on this elimination two sets of elementary steps for formation of C₁ and C₂ alkenes and alkanes in the Fischer-Tropsch synthesis are established: one based on hydrogen assisted CO dissociation (carbide mechanism) and one based on CO hydrogenation (CO insertion mechanism). In addition, one mechanism of producing CO₂ from the water-gas shift reaction is proposed. The resulting mechanisms are combined and used in the microkinetic model, which are fitted to experimental results at methanation conditions (T = 483 K or 493 K, p = 1.85 bar and H₂/CO = 10) over a Co/Al₂O₃ Fischer-Tropsch catalyst. A good tuning is obtained by adjusting the C-Co and H-Co binding strengths. The microkinetic modelling based on these assumptions indicates that CO is mainly converted through hydrogenation of CO and that C₂ compounds are mainly produced by insertion of CO into a metal-methyl bond. Thus, from the surface coverages and reaction rates predicted by the microkinetic modelling the mechanism can be further reduced to only include the CO insertion mechanism. Hydrogenation of CHO to CH₂O is found to be the rate determining initiation step, and insertion of CO into a metal-methyl bond is found to be the rate determining step for chain growth. By using the UBI-QEP method for calculation of activation energies, the activation barriers for dissociation of CO and hydrogenation of surface carbon are found to be too large for the carbide mechanisms to occur. However, experimental data or another theoretical method is necessary in order to support or disprove the calculated activation energies in this work.     

Pomeron-Odderon interference effects in electroproduction of two pions

We study Pomeron-Odderon interference effects giving rise to charge and single-spin asymmetries in diffractive electroproduction of a pair. We calculate these asymmetries, originating from both longitudinal and transverse polarizations of the virtual photon, in the framework of QCD and in the Born approximation, in a kinematical domain accessible to HERA experiments. We predict a sizable charge asymmetry with a characteristic dependence on the invariant mass of the pair, which makes this observable very important for establishing the magnitude of the Odderon exchange in hard processes. The single-spin asymmetry turns out to be rather small. We briefly discuss future improvements of our calculations and their possible effects on the results. Received: 18 July 2002 / Published online: 25 October 2002     

Calculation of the Knight shift in palladium

The direct and the exchange core polarization (ECP) contributions of the conduction electrons to the Knight shift of palladium are evaluated. To obtain the wave functions for the conduction electrons and the partial densities of states at the Fermi surface a KKR energy band calculation was performed. The contributions of the core electrons to the Knight shift were determined by using the moment perturbation method (MP). Electron-electron interactions are taken into account by individual enhancement factors for thed ands electrons. The agreement between the theoretical results and the available experimental data is quite satisfactory.     

A cutting plane algorithm for a clustering problem

In this paper we consider a clustering problem that arises in qualitative data analysis. This problem can be transformed to a combinatorial optimization problem, the clique partitioning problem. We have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope. These theoretical results are utilized in this paper. We describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before. We discuss some details of the implementation of our code and present our computational results. We mention applications from, e.g., zoology, economics, and the political sciences.     

A note to the paper “An efficient algorithm for linear programming” of V Ch Venkaiah

In Venkaiah [1] an algorithm for solving linear optimization problems based on the idea of the projective algorithm of Karmarkar, is proposed. The essential simplification in the new algorithm is the use of a fixed projection operator. In this way the algorithm requires onlyO(n ² ) operations to obtain a sufficient exact solution. In this note it is shown that in some special cases the algorithm of Venkaiah yields a feasible solution that is far from the optimal one.     

Ab initio predictions of zeolite structures and Si NMR chemical shifts

A recent shell-model potential parameterized on ab initio data is used for predicting the all-silica structures of zeolites MFI, MEI, MTW, TON, FAU and of α-quartz. Cluster models are defined around each site and the ²⁹Si NMR shielding constants are calculated by ab initio techniques (GIAO-HF). Good agreement with observed ²⁹Si NMR chemical shifts is found. Comparison is made with shifts calculated for observed structures. The structures predicted by the ab initio shell-model potential prove as accurate as the observed ones when judged on the quality of the calculated ²⁹Si NMR spectra.