(56c) Reaction Path and Coverage Effects Analyses of Benzene Hydrogenation On Pd(111)

1           Introduction

Benzene hydrogenation is a key reaction in various industrially important processes such as hydrotreatment of petroleum feedstocks, caprolactam and adipic acid production, and also plays an important role in environmental protective technologies. Palladium catalysts are often employed for hydrogenation reactions because of their high activity and selectivity. The (111) surface  is normally chosen in fundamental studies to evaluate the catalytic performance in benzene hydrogenation [1-3] because of its abundance on supported industrial catalysts.

Micro-kinetic modeling allows to analyze catalytic surface reactions in detail, by incorporating the surface chemistry of all elementary reaction steps into a kinetic model [4]. The catalytic hydrogenation of benzene is a complex process. Even if only one single benzene adsorption site is considered, the hydrogenation of benzene can proceed via 13 different reaction paths. Performing an extended reaction path analysis based on the results of theoretical calculations allows to identify the most important reaction steps and surface intermediates. This may lead to simplification of the complex reaction network and can contribute optimizing the industrial catalytic process.

Periodic Density Functional Theory (DFT) calculations are usually performed at low to moderate coverage. However, these theoretical calculations can also be performed at higher surface coverages, enabling the modeling of coverage effects on the kinetics and thermodynamics of the adsorption and surface reaction steps. This feature is highly important for hydrogenation reactions, since in industry these are typically performed at high hydrogen pressures, and hence, at higher hydrogen coverages.

Three different techniques are employed to perform a reaction path analysis of the full reaction network of benzene hydrogenation from periodic DFT calculations at low coverage (θ_H=0.11). Additionally, the micro-kinetic model for benzene hydrogenation is also calculated at higher hydrogen coverages (θ_H  = 0.44 and 0.67), in order to evaluate the coverage effects on the simulated activities by comparison with experimental data.

2           Methodology

The adsorption energies, geometries and vibrational frequencies at 0 K are calculated from Periodic DFT calculation using the Vienna Ab initio Simulation Package (VASP 4.6) [5]. This program solves the Kohn-Sham equations of DFT by using pseudopotentials with the projector augmented wave method (PAW) and periodic boundary conditions by expansions of the wave function in terms of plane-wave basis sets for which a converged cutoff energy of 400 eV has been used.

The Nudged Elastic Band method [6] and Dimer method [7] are used to locate transition states on the potential energy surface. In addition, the harmonic oscillator approach (HO) is used to numerically calculate the vibrational frequencies of all species. In combination with statistical thermodynamics, the frequencies are used to calculate the kinetic and thermodynamic parameters of every reaction, and therefore to construct the micro-kinetic model.

In the periodic DFT calculations, one hydrocarbon molecule and one hydrogen atom are adsorbed on a (3×3) Pd(111) unit cell to evaluate the kinetics at low coverage, leading to a fractional coverage of θ_H = 0.11 and of q_HC= 0.11 for the hydrocarbon species. The effect of hydrogen coverage on the kinetics and thermodynamics is evaluated by increasing the number of hydrogen atoms to 4 and 6 atoms on the (3×3) unit cell, corresponding to  hydrogen coverages of 0.44 and 0.67.

Three tools are implemented in an in-house FORTRAN code for the reaction path analysis: Degree of Rate control (DRC) [8, 9], Sensitivity Analysis (SA) and Rate Of Production (ROP). The equations for the two first are shown below. The rate of production analysis identifies the most important reactions and/or species within the reaction network by calculating the net production rates for all intermediate species occurring in the network

 3           Results and discussion

The DFT results at 0 K for θ_H = 0.11 indicate that the hydrogenation of benzene to cyclohexane follows the same minimum energy path for the two preferred bridge30º and hollow-hcp0º adsorption sites of benzene on Pd(111). These two networks are defined as bridge-site and hollow-site networks, respectively. The minimum energy path is the one that runs from benzene to monohydrobenzene (BH), proceeding over cyclohexa-1,3-diene (13CHD), trihydro-1,2,3-benzene (123THB), cyclohexene (CHE) and cyclohexyl (c-hexyl) to cyclohexane (CHA). For both adsorption sites, the calculated kinetics and thermodynamics confirm this path to be potentially dominant at 450 K and indicate that the first surface reaction step has the largest activation energy. Hence, the first hydrogen addition could potentially be the step with the largest control on the rate of cyclohexane formation along the dominant reaction path, as already previously suggested by Morin et al. based from BEP relationships [10]. Furthermore, simulations of the activity for both networks indicate that the hollow-site is more reactive than the bridge-sitenetwork.

For both bridge-site and hollow-site networks, ROP analysis at actual conditions and coverages (450 K, P_H2 = 0.1 bar and P_benzene = 0.02 bar) agrees with the proposed dominant path from the calculated DFT rate coefficients, where the reactions along this dominant path contribute at least 90% to the net cyclohexane rate of formation. DRC and SA indicate that for the bridge-site network, the second hydrogen addition along the proposed dominant path is the kinetically most significant step, while for the hollow-sitenetwork it is the third hydrogen addition step. Clearly, inclusion of actual surface concentrations at reaction conditions is required to identify the step with the largest control along the dominant path, since the first step has the highest activation barrier.

Next, additional periodic DFT calculations were performed at higher hydrogen coverage (θ_H = 0.44 and 0.67) for the hollow-site dominant path obtained at θ_H = 0.11. For the 0.44 hydrogen coverage case, the calculated kinetics are much faster and lead to much higher simulated catalytic activities than for the θ_H = 0.11 case. These activities are in the same order of magnitude as experimentally observed at similar reaction conditions, e.g. 0.064 mmol_Benzene s^-1 kg_cat^-1 [11]. The reaction barriers calculated at a hydrogen coverage θ_H = 0.67 are even lower than for θ_H = 0.44. The very weak benzene adsorption calculated at θ_H = 0.67 leads however to a lower activity than using the kinetics obtained at θ_H = 0.44 coverage, since the simulated benzene coverages are too low. The activity using the kinetics obtained at θ_H = 0.67 remains faster than using those at θ_H = 0.11. 4      Conclusions

Benzene preferentially adsorbs at the bridge30º and hollow-hcp0º adsorption sites of Pd(111). At low hydrogen coverage, the dominant path of benzene to cyclohexane at these two sites proceeds through 1,3-cyclohexadiene and cyclohexene. The first hydrogen addition step is potentially the kinetically most significant step, due to its appreciable higher activation energy compared to the other elementary reaction steps of the dominant path. The reaction path analysis shows, however, that when surface concentrations are included for the simulation of activities, the second and third reaction steps along this dominant path are the ones controlling the rate of formation for the bridge-site and hollow-sitenetwork respectively. Therefore, it is required to include actual surface concentrations at reaction conditions to identify the step with the largest control on the net rate along the dominant path.

Inclusion of the effect of hydrogen coverage on the rate coefficients in the micro-kinetic model increases the rate of formation of cyclohexane, and the simulated activities using kinetics calculated at θ_H=0.44 are in the same order of magnitude as experimental observations.

Acknowledgements

The computational resources (Stevin Supercomputer Infrastructure) and services used in this work were provided by Ghent University, the Hercules Foundation and the Flemish Government – department EWI. Finally the authors thank IFPEN and the Fund for Scientific Research Flanders (FWO). References

[1] C. Morin, D. Simon, P. Sautet, J Phys Chem B, 108 (2004) 5653-5665.

[2] F. Mittendorfer, C. Thomazeau, P. Raybaud, H. Toulhoat, J Phys Chem B, 107 (2003) 12287-12295.

[3] M. Saeys, M.F. Reyniers, M. Neurock, G.B. Marin, J Phys Chem B, 109 (2005) 2064-2073.

[4] J.A. Dumesic, D.F. Rudd, L.M. Aparicio, J.E. Rekoske, A.A. Treviño, The Microkinetics of heterogeneous catalysis, American Chemical Society, Washington, D.C., 1993.

[5] G. Kresse, J. Furthmüller, Comput. Mat. Sci., 6 (1996) 15.

[6] G. Mills, H. Jonsson, G.K. Schenter, Surf Sci, 324 (1995) 305-337.

[7] G. Henkelman, H. Jonsson, Journal of Chemical Physics, 111 (1999) 7010-7022.

[8] C.T. Campbell, Journal of catalysis, 204 (2001) 520-524.

[9] C. Stegelmann, A. Andreasen, C.T. Campbell, J Am Chem Soc, 131 (2009) 8077-8082.

[10] C. Morin, D. Simon, P. Sautet, Surf Sci, 600 (2006) 1339.

[11] P. Chou, M.A. Vannice, Journal of catalysis, 107 (1987) 129-139.