In the present work, the barrier energies (Eb) of CH4 formation and C–C coupling and the mechanism of Fischer–Tropsch synthesis (FTS) on different cluster sizes of cobalt were investigated. Three cobalt clusters with 10, 18, and 30 atoms (Co-10, Co-18, and Co-30) were used for comparison of the results. The Eb, transition state, and reaction energy (DEr) were analyzed by using density functional theory (DFT) calculations. The results showed that CH4 was produced more easily on the small cluster (Co-10) than on the other two clusters. The Eb values for the Co-10, Co-18, and Co-30 clusters were 1.62, 2.53, and 2.44 eV, respectively. The Eb values for dissociation of CO on the three clusters Co-10, Co-18, and Co-30 were 1.64, 0.93, and 1.81 eV, respectively, and the minimum Eb was related to the Co-18 cluster. Also, the tendency towards chain growth increased with increasing cobalt cluster size. The results showed that the mechanism of the FTS reaction was dependent on the particle size of the cobalt clusters. It can be concluded that the Co-10 cluster followed the CO insertion mechanism and the Co-18 cluster followed the carbide mechanism in the FTS reaction. Also, the Co-30 cluster followed both mechanisms (CO insertion and carbide mechanisms) in the FTS reaction. DFT results showed that as the cobalt cluster size increased, the olefin/paraffin ratio in the FTS reaction products enhanced.

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