The Pennsylvania State University. The Graduate School. College of Engineering DEVELOPMENT AND APPLICATION OF THE REAXFF POTENTIAL FOR

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering DEVELOPMENT AND APPLICATION OF THE REAXFF POTENTIAL FOR HETEROGENEOUS CATALYSIS AND METAL OXIDATION: TOWARD THE DYNAMIC SAMPLING OF LARGE FREE ENERGY SURFACE A Dissertation in Mechanical and Nuclear Engineering by Chenyu Zou 2014 Chenyu Zou Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2014

2 The dissertation of Chenyu Zou was reviewed and approved* by the following: Adri C.T. van Duin Associate professor of the department of Mechanical Engineering Dissertation Advisor Chair of Committee Donghai Wang Associate professor of the department of Mechanical Engineering Michael Janik Associate professor of the Department of Chemical Engineering Lasse Jensen Associate professor of the Department of Chemistry Dan Haworth Professor of the Department of Mechanical Engineering Head of the Graduate Program of the Department of Mechanical Engineering *Signatures are on file in the Graduate School

3 ABSTRACT A ReaxFF force field has been developed to describe the complex catalytic chemical reactions on the surface of the iron/iron carbide Fischer-Tropsch (FT) catalysts. Based on fitting parameters against an extensive training set containing data obtained from both ab-initio calculations and experimental measurements, the ReaxFF potential can reproduce reasonably well the potential energy surface of a relevant Fe/C/H/O atomistic system. The force field is first validated by performing molecular dynamics (MD) simulations to describe the dissociative adsorption and desorption of hydrogen molecules on iron and iron carbide surfaces. It was found that the existence of carbon atoms at the subsurface sites tends to increase the hydrogen dissociation barrier on the surface, and also stabilizes the adsorbed surface hydrogen atom. We then used this force field to study the complex catalytic surface chemistry as one will typically encounter at the initial stage of the FT synthesis. By performing MD simulations using relevant atomistic systems, the carbon monoxide methanation and the hydrocarbon chain initiation processes were studied. It was found that the catalytic methanation initiates from the undissociated CO molecules absorbed on the surface of the catalyst. This process leads to the generation of surface absorbed CH x - groups which initiate the synthesis of methane and the hydrocarbon chain growth. Direct hydrogenation of the surface carbide was not observed in the simulation. Coordination analysis of the carbon atoms in the system shows that the surface carbon atoms tend to diffuse toward the subsurface sites. This diffusion indicates the tendency of the formation of iron carbide at elevated temperatures. Furthermore, MD simulations enable us to investigate the various reaction pathways of key intermediates under FT conditions. We found that the surface CH- groups can dissociate into surface carbon atoms or be further hydrogenated into CH 2 - groups. The latter is an important intermediate species in the synthesis of methane as well as the chain initiation. Results from the C-C coupling simulation suggested the preference of coupling between CH- and CH 2 - groups. These results agree with the available experimental iii

4 iv observations and ab-initio based study. This study demonstrates that the ReaxFF reactive potential can efficiently probe the catalytic heterogeneous interface, generate complex reaction networks, and hence improve our mechanistic understanding of heterogeneous catalysis. During catalytic surface reactions, the metal materials will also experience oxidation and corrosion under realistic working conditions at high temperature. In order to study the metal oxidation phenomenon, we have developed a new ReaxFF potential for the Ni/O system. The force field was validated by performing MD simulations of self-diffusion of nickel and the interstitial diffusion of oxygen. The predicted diffusivity and the activation energy achieved quantitative agreement with their respective published values. Furthermore, this force field enables us to study the effects of vacancies on the diffusion of interstitial oxygen and the successive initiation of internal oxidation. A new oxygen diffusion mechanism is proposed in which the oxygen atom diffuses via the movement of the oxygen-vacancy pair. In addition, our MD simulation results suggest that the voids at the grain boundaries can induce local oxygen segregation due to the strong oxygen-vacancy binding effect. This segregation is responsible for the formation of nickel oxide particles in subsurface voids. These results demonstrate that the ReaxFF MD study can contribute to bridging the gap between the QM calculations and the experimental observations in the study of metal oxidation.

5 v TABLE OF CONTENTS List of Figures... vii List of Tables... xi Acknowledgements... xii Chapter 1 Introduction Background Computational modeling... 3 Chapter 2 The ReaxFF reactive force field The Molecular Dynamics simulation method The ReaxFF reactive force field method... 7 Bond order and Bond energy (E bond )... 8 Valance angle energy (E val )... 9 Torsion angle energy (E tor )... 9 Lone pair Energy (E lp )... 9 Van der Waals Energy (E vawaals ) Coulomb energy (E coulomb ) The force field optimization scheme Chapter 3 Application to the Fischer-Tropsch (FT) synthesis Introduction Force field parameterization Iron-Iron interaction Iron-Carbon interaction Iron-Hydrogen interaction Iron/Carbon/Hydrogen interaction Iron/CO interaction Molecular Dynamics simulation Hydrogen dissociation on iron/iron carbide CO methanation Surface carbide hydrogenation Hydrogenation of the surface methylidyne (CH-) Hydrogenation of the surface methylene (CH 2 -) C-C coupling reaction Chapter Summary and Outlook Chapter 4 Application to nickel Oxidation Introduction Force field parameterization Nickel-Nickel interaction... 56

6 vi Nickel-Oxygen interaction MD simulations of diffusion and oxidation Nickel self-diffusion Interstitial oxygen diffusion Internal oxidation initiation Chapter Summary and Outlook Chapter 5 Conclusions Reference... 77

7 vii LIST OF FIGURES Figure 2-1 Flow chart for a generic molecular dynamics algorithm... 7 Figure 3-1. Comparison of the ReaxFF fit (right panel) of the Equation of State (EoS) for bcc and fcc bulk phases of iron with the corresponding QM data (left panel) for the bcc (FM), fcc (FM) and fcc(afmd) as obtained in Reference Figure 3-2. Energy correction upon bond dissociation in small iron clusters Figure 3-3. Energy corrections for small iron clusters after force field optimization Figure 3-4. Effect of the energy complement function on bcc/fcc iron equation of state Figure 3-5. ReaxFF fit for the EoS for Fe3C cementite Figure 3-6. Comparison of Fe 5 C 2 surface energies for seven low Miller indices obtained using QM and ReaxFF methods Figure 3-7. Graphical representation of the seven Fe 5 C 2 surfaces with low Miller indices: Panel A) surface (010)0.25; Panel B) surface (11-1)0.00; panel C) surface (110)0.00; panel D) surface (111)0.00; panel E): surface (11-1) 0.50; panel F); surface (110)0.50; panel G) surface (001) Figure 3-8. ReaxFF fit for binding energies of H atom at various sites on (a) Fe (100) and (b) Fe (110) surfaces Figure 3-9. ReaxFF fit for (a) Binding energies of H atom to different vacancies in bulk phase iron (b) H diffusion pathway from a (100) surface hollow site to a subsurface tetrahedral site (c) H diffusion pathway from a (110) surface 3-fold site to subsurface tetrahedral site (d) H diffusion pathway among two nearby subsurface tetrahedral sites in a FeH-bulk phase Figure Hydrogen dissociation pathway on a Fe(100) surface starting from a twofold site above the surface and ending to two neighbor four-fold hollow sites Figure Adsorption of the CH (four fold hollow site), CH 2 (four-fold hollow site) and CH 3 (two fold bridge site) groups on Fe bcc (100) surface Figure Hydrogenation of a carbon atom on the Fe (100), starting with the H atom and C atom at the hollow site and ending with CH- group at the hollow site Figure Hydrogenation of a CH- group on the Fe (100), starting with the H atom and the CH- group at the hollow site and ending with a CH 2 - group at the hollow site Figure 3-14.Hydrogenation of a CH 2 - group on the Fe (100), starting with the H atom and the CH 2 - group at the hollow site and ending with a CH 3 - group at the bridge site... 28

8 Figure 3-15.Hydrogenation of a CH 3 - group on the Fe (100), starting with the H atom at the hollow site and the CH 3 - group at the bridge site and ending with a CH 4 molecule Figure Adsorption of a CO molecule on Fe bcc (100) surface at three different sites (1F on-top site, 2F bridge site, 4F hollow site), Fe bcc (211) surface and Fe bcc (310) at two different configurations ( -1 stands for the down configuration, 1 stands for the up configuration, title in consistency with reference 62 ) Figure MD simulation setups for two cluster systems of (I) iron and (II) cementite Figure Iron hydride cluster after 250 ps and H 2 exposure at: A, 500 K; B, 600 K; C, 750 K. Yellow dots: Fe; White dots: hydrogen Figure Iron carbide hydride cluster after 250 ps and hydrogen exposure at: A, 500 K; B, 600 K; C, 750 K. Yellow dots: Fe; White dots: hydrogen; Green dots: carbon Figure 3-20 MD simulation setup for system I: an iron slab with gas phase CO and H Figure 3-21 Graphic representation of system I after 2 ns: panel A) system side view and panel B) slab top view Figure 3-22 surface CH X O- species population analysis in system I Figure 3-23 surface hydroxyl and water species population analysis in system I Figure 3-24 surface CH X - species analysis for system I Figure 3-25 graphic representation of the pre-treatment process of system II: panel A) the iron slab is pre-covered with carbon atoms and placed in the gas phase CO molecules; panel B) CO molecules adsorbed on the surface of the slab; panel C) the slab with surface adsorbed CO molecules was then extracted; panel D) the O atoms were artificially removed; panel E) the remaining structure underwent a surface annealing process; panel F) the resulted slab after the surface annealing was placed in a H2 gas phase environment Figure 3-26 coordination analysis for the carbon atoms in system II before and after exposure to H2 molecules Figure 3-27 MD simulation setups for system III: an iron slab (pre-covered with CHspecies randomly at hollow site) with gas phase H2 molecules Figure 3-28 final configuration of system III after 2 ns: panel A) system side view and panel B) slab top view Figure 3-29 population analysis of reactant and major products in system III Figure 3-30 MD simulation setups for system IV: an iron slab (pre-covered with CH 2 - groups randomly at hollow site) with gas phase H2 molecules viii

9 ix Figure 3-31 final configuration of system IV after 2 ns: panel A) system side view and panel B) slab top view Figure 3-32 population analysis of reactant and major products in system IV Figure 3-33 panel A) MD simulation setups for system V: an iron slab (pre-covered with C-, CH-, CH 2 - and CH 3 - groups randomly; panel B) final configuration of system V after 2 ns Figure 3-34 population analysis for the pre-covered groups in system V Figure 3-35 population analysis for major products resulting from C-C coupling in system V Figure 4-1 Comparison of the predicted EOS between QM (Panel A) and ReaxFF (Panel B) for five different crystal structures of nickel Figure 4-2 ReaxFF fit for the nickel vacancy migration pathway. Color code, blue: nickel atom; green: vacancy Figure 4-3 ReaxFF fit for the EOS of NiO Figure 4-4 Comparison of the oxygen diffusion pathway. Panel I-A: O-T jump without a first neighbor vacancy; Panel I-B: O-O jump without a first neighbor vacancy; Panel II-A: O-T jump with a first neighbor vacancy; Panel II-B: O-O jump with a first neighbor vacancy. Color code, blue: nickel atom; red: oxygen atom; green: vacancy Figure 4-5 Ni self-diffusion coefficient predicted from ReaxFF MD simulations in comparison Figure 4-6 Extrapolation of the diffusivity versus V.C. at: 1500 K (Panel A) and 1000 K (Panel B) Figure 4-7 Oxygen diffusivity with and without a nearby vacancy in comparison with first-principle predictions and experimental measurement Figure 4-8 System snapshots during the MD simulation of oxygen diffusion at 1500 K. Panel A: initial configuration; Panel B: configuration at 875 ps. color code, blue: nickel atom; red: oxygen atom; pink: vacancy; hopping direction indicated by gray arrow Figure 4-9 Comparison of the two oxygen diffusion mechanisms. Panel A: vacancymodified interstitial diffusion mechanism; Panel B; vacancy-oxygen pair diffusion mechanism. color code, blue: nickel atom; red; oxygen atom; green: vacancy. TS: transition state. *: data point not included in the training set Figure 4-10 Effect of an interstitial oxygen atom on the vacancy-mediated self -diffusion of nickel... 68

10 x Figure 4-11 Oxygen diffusivity at 1500 K as a function of V.C. value in nickel Figure 4-12 Cross section view of the system initial configuration for oxidation simulation. color code, blue: nickel atom; red: oxygen atom; yellow : void region Figure 4-13 system snapshots during the internal oxidation simulation at: A: 0 ps; B: 50 ps; C: 200 ps.color code: transparent blue: nickel atom; red: oxygen atom Figure 4-14 Number of oxygen atoms in the core region (5 Å radius to the center of the simulation box) as a function of simulation time Figure 4-15 Comparison of the atomic charge on the nickel atoms between the initial and final configuration as a function of distance to the center of the structure... 72

11 xi LIST OF TABLES Table 3-1 Effect of energy compensation functional on the surface energy of Fe bcc (all numbers are with units: kcal/mol) Table 3-2 Energy barriers from DFT for the coupling reactions... 49

12 xii ACKNOWLEDGEMENTS I express my deepest gratitude to Dr. Adri C.T. van Duin for his significant guidance through my PhD research and study. He has offered me valuable suggestions and walked me through all stages of my graduate research. Without his support, encouragement, and edification, the success towards my thesis research will be impossible. Secondly, I thank Dr. Donghai Wang, Dr. Michael Janik and Dr. Lasse Jensen for agreeing to be my committee members. They have provided valuable input to my PhD research and this dissertation. I sincerely acknowledge Dr. Sumathy Raman for her constant support and education. Her broad knowledge of chemistry and general science has helped and guided me through my research, career and life. I thank all my lab mates for their kindness and patience for my endless questions. Together we have been going through a wonderful journey in the microscopic world of materials and molecules. As the only child of my family, I bear great appreciation for the support from my family for their loving considerations and great confidence in me all through these years of my graduate study abroad. My deepest appreciation and love goes to my wife, Jie. I cannot ever forget how her tender care and trusting eyes helped me walk though the wanderest night and the toughest time. I will always love you, my dear.

13 Chapter 1 Introduction 1.1 Background Advances in many engineering disciplines require rapid synthesis and fabrication of advanced materials, and evaluation of their performance under realistic working conditions. Requirements for these advanced materials, based on their applications, include but not limited to: good catalytic performance for reaction engineering applications; good mechanical properties for structural and load bearing applications; good material integrity with resistance to corrosion and oxidation; good electrical and magnetic properties with low specific weight. As a realistic alternative to brute force synthesis and fast screening through enormous amount of material candidates, atomistic level understanding of the synthesis of the materials, and their degradation processes under realistic working conditions contribute to the rational design of these advanced materials. Novel catalysts design requires atomistic level understanding of the active sites of the catalyst, detailed reaction networks, and mechanisms for catalyst deactivation; Novel structural materials design requires atomistic level understanding of the oxidation, corrosion and degradation processes. These understandings not only improve our fundamental knowledge, but also serve as guidance in searches of novel materials. In heterogeneous catalysis, reactants (typically in gas or liquid state) adsorbs on to the surface of the catalysts (typically in solid state), undergo a series of complex chemical reactions, forms the intermediates and products, and desorb from the surface. Though widely used in the industry for the production of chemical species for decades, many of these catalytic processes

14 2 consist of a chemical reaction network so complex that a thorough understanding has yet been achieved. Fischer-Tropsch (FT) synthesis is among the many poorly understood heterogeneous catalytic processes. FT synthesis 1 consists of a series of chemical reactions that transform a mixture of two simple molecules, hydrogen and carbon monoxide, into a variety of hydrocarbons ranging from small molecules such as methane to heavy hydrocarbon compound. Though its practical applicability strongly depends on the price of crude oil 2, its effectiveness of producing sulfur-free fuels as well as organic chemicals of industrial importance has long been attracting the petroleum industries attention. In this process, metals such as iron, nickel or cobalt are used as catalysts. Initially proposed by Fischer and Tropsch 3 In 1906, FT synthesis has been widely used for nearly a century. Despite its long history, a detailed and precise reaction mechanism is still missing. Such a mechanism will improve our understanding of the synthesis such as the product selectivity 4-5, which depends on temperature, mixture composition and the catalysts chosen. Improving the performance of the catalysts such as selectivity and reactivity requires a complete understanding of the detailed reaction networks at an atomistic level. Such understanding will provide valuable information for efficient catalyst screening and facilitate rational catalyst design. One of the key mechanisms related to long-term degradation of metal catalyst performance is oxidation. Metal and alloy oxidation is another research area where atomistic level mechanism for the growth of oxide scale is needed. Besides catalytic applications, Nickel-based super-alloys are widely applied in the energy industry 6-8 under extreme conditions such as high temperatures in conjunction with a corrosive environment. They are typically used in load-bearing applications at a temperature in excess of 80% of their melting temperature. Compared to other metals, these materials exhibit good mechanical strength and resistance to corrosion at high temperatures 9. Although such nickel-based super-

15 3 alloys have been extensively studied for many decades, there is still significant discussion regarding the fundamental oxidation mechanism of these materials 10. An atomistic level understanding of the diffusion processes of different elements during the alloy oxidation contributes to the design of these materials and the prediction of their performance in environment relevant to the advanced energy systems. 1.2 Computational modeling In the past few decades, quantum mechanics (QM) based ab initial computational methods have become a key tool in evaluating the atomistic details that molecules and condensed materials undergo. These calculations can determine the thermodynamic properties of materials and the kinetic parameters of chemical processes based on fundamental knowledge of the electronic structures. In heterogeneous catalysis, Density Functional Theory (DFT) based electronic structure calculations have been widely used to study the energetics of adsorption, dissociation and surface reactions of reactants and intermediates; in metal oxidation, similar methods are used for the study of diffusion of impurities in metal crystal matrix. Such calculations provide valuable atomistic level understanding, some of which are difficult to obtain using experimental techniques. These calculations aim at exploring the potential energy surface of a relevant atomistic system. With this knowledge at hand, one can further describe the complete chemical processes by utilizing the transition state theory and ab initio thermodynamics. This approach allow us to translate our knowledge of the potential energy surface to the free energy surface, on which the chemical processes is taking place under realistic conditions. However, for many complex heterogeneous catalytic processes such as the FT synthesis, a complete list of reaction mechanisms is difficult to obtain due to the large number of species

16 4 involved. On the other hand, the structural complexity of the state-of-art catalyst adds additional difficulties to the application of the ab initio calculations due to the size limitations. In metal oxidation, First-principle calculations have difficulties describing the diffusion and oxidation phenomena at grain boundaries because a large number of atoms are required to model the complex local environment of grain boundaries. The length scale of such a model is beyond the capability of QM methods within reasonable computational cost. Furthermore, most of the QM calculations explore the potential energy surface of a particular system at 0 K. Thus, the dynamics of a system containing multiple atoms at high temperature such as the metal oxidation process are largely unaccounted for. Firstprinciple molecular dynamics methods 11 have been employed to address this issue. However, the system scale and the time span of these simulations are highly restricted (~100 atoms and several picoseconds, respectively) due to the time-consuming electronic structure calculations. How can we explore the large free energy surface associated with large atomic systems? An alternative to trying to solve the Schrödinger s equation from first principles in the ab initial calculations, Empirical potentials can be built to describe the potential energy surface. These potentials contain parameters to be optimized against data from higher level of theory (i.e. ab initio results) or experiments. The purpose of developing the empirical potential is to reproduce the potential energy surface with reasonable accuracy, while maintaining significantly lower computational cost while applied to simulate large systems. By solving the Newton s equation of motion of an ensemble of particles, one can infer thermodynamic properties of substances using traditional non-reactive potential, or to explore the free energy surface by analyzing the trajectories of the particles using advanced reactive potential. These techniques

17 5 save computational powers at the cost of fitting the parameters in the empirical energy functional. Various potentials have been developed for different kinds of applications in the past decades. In this dissertation, we employed the ReaxFF reactive force field method 12 to study the metal material behavior under catalytic and oxidative environment. In ReaxFF, the empirical energy functional is based on the bond order concept This concept allows smooth transition between bonded and non-bonded systems (transition state description), which is a crucial improvement compared with non-reactive empirical potentials. These non-reactive potentials typically utilize harmonic type of potential with at most higher order correction terms from Tyler s expansion, and are only accurate around the equilibrium bond length and hence their description is confined within a well on the free energy surface. While useful for investigation of thermodynamic properties, they cannot be used to describe the transition state connecting two wells on the free energy surface and hence much insight of the systems is missing. Compared to the early generation of reactive potential 13-14, ReaxFF features the nonbonded interactions, including van der Waals and Coulomb terms calculated between each pair of atoms. These features make this method transferable among covalent, ionic and metallic systems. A detailed description of the energy functional in the method will be provided in the next chapter.

18 Chapter 2 The ReaxFF reactive force field 2.1 The Molecular Dynamics simulation method In empirical molecular dynamics, interaction of N particles is governed by the classical Newton s equation of motion: d dt r 2 i mi i, 2 = F, i = 1 N (1) Where, the force, in a general conservative field, is the gradient of the energy functional: Fi = iu ( r1, r2,..., rn ), i = 1, N (2) Generally the potential energy functional depends on the coordinates of the atoms only. As introduced above in chapter I, a large number of energy functionals have been developed for a wide range of molecules and materials. The equations of motion are then numerically integrated to predict the positions of the particles as a function of time. Information concerning system properties are calculated by averaging the properties over a number of MD iterations. Many integration algorithms are available; in this study, the velocity Verlet algorithm was used as employed in the ReaxFF code: 2 dt 4 ri ( t + dt) = ri ( t) + dtvi ( t) + ai ( t) + ο( dt ) (3) 2 3 v ( t + dt) = v ( t) + [2a ( t) + a ( t + dt)] + ο( dt ) (4) i i i The algorithm has advantages over predictor-corrector algorithm in terms of the energy conservation and time reversibility. In the algorithm the coordinates of all the atoms are updated i

19 7 first followed by the updating of the velocities as can be seen from equation (3) and equation (4). The overall algorithm has 3 rd order accuracy with respect to the time step. A typical molecular dynamics simulation algorithm is demonstrated in Figure 2-1. Figure 2-1 Flow chart for a generic molecular dynamics algorithm 2.2 The ReaxFF reactive force field method When a chemical system is studied through an empirical MD approach, the Schrödinger s equation is replaced by the Newton s equation to reduce the complexity by freezing the electronic degrees of freedom. Instead of solving the motion of the nuclei from first principle, empirical potentials are constructed to describe the interaction of the nuclei. The energy functional in ReaxFF consists of the following major energy terms:

20 E E sys under = E + E + E + E + E + E + (5) bond + E over val + E pen tol + E coa lp + E vdwaals coulomb C + E triple + E 2 conj + E H-bond The essential energy functional terms will be discussed in the following section. It is worth mentioning here that the terms in equation (5) are the general terms included in the studies of all chemical systems. Other minor correction terms maybe also included when some special systems are studied. For a more detailed description of the full set of the ReaxFF energy functionals, readers are referred to Bond order and Bond energy (E bond) ReaxFF employs the bond-length/bond-order and bond-order/bond-energy relationships. Bond orders are calculated from interatomic bond lengths using the following equation (6): r ' ij r be2 ij r σ π ππ p pbe4 ij pbe6 BOij = BOij + BOij + BOij = exp[ pbo 1( ) ] + exp[ pbo3( ) ] + exp[ pbo5( ) ] σ π ππ (6) r r r 0 ReaxFF distinguishes the bond order contributions from the sigma bond, pi bond and double pi bond. The exponential terms on the right hand side of the above equation correspond to the empirical functional of the uncorrected bond order with respect to the three type of bonds, respectively. The results from the equation (6) is then modified using a over coordination penalty scheme 12 to calculate a corrected bond order all connection dependent energy functionals. 2 E bond e ij be1 ij 0 BO ij, which is further used for the calculation of σ σ σ pbe π π ππ ππ = D BO exp[ p (1 ( BO ) ) D BO D BO ] (7) e ij e ij 0 In the above equation (7), D, p be1, p be2, σ e π De and ππ D e are bond parameters to be optimized.

21 9 Valance angle energy (E val ) is given by: The valance angle energy formed by three atoms i, j, k with atom j being the center atom E val 2 = f ( BO ) f ( BO ) f ( ) p {1 exp[ p ( Θ Θ ) ]} (8) 7 ij 7 jk 8 j val1 val 2 0 ijk It is clear that the valance angle energy not only depend on the angle formed by the three atoms but also depend on the bond order contributions from the two bonds in the group (contained in the functional f 7, which can be found in 12 ). The equilibrium bond angle Θ0 depends on the sum of the pi bond orders of the central atoms in the valence angle. Also p val1 and p val2 are angle force constant parameters to be optimized. Torsion angle energy (E tor ) The Torsion angle energy formed by four nearby atoms i, j, k and l is given by: E tor 1 V 2 2 = f 10 exp{ p ( BO tol1 ij, BO ( BO π jk jk, BO kl 1+ f )sin Θ 11 ( j ijk, 1 sin Θ jkl[ V1 (1 + cosωijkl ) )) }(1 cos 2ω ijkl ) + V3(1 + cos3ω 2 k ijkl )] (9) The torsion angle energy depends on the three bond orders of the bonds forming the dihedral angle (contained in the functional f 10, refer to reference 12 ). Lone pair Energy (E lp ) The number of long pairs is equal to the sum of bond orders around the atomic center subtracted from the the total number of elections in the outer shell. The long pair energy penalty is given by:

22 10 E lp lp p lp 2 i = (10) lp 1+ exp( 75 ) i The term lp i is the sum of the long pairs. Van der Waals Energy (E vawaals ) The distance corrected Morse potential is employed to account for the van der Waals interactions. The shielded interaction is included in the energy functional to avoid excessively high repulsion between bonded atoms and atoms forming a valence angle. E vdwaals f13( rij ) 1 f13( rij ) = Tap * Dij{exp[ α ij (1 )] 2exp[ α ij (1 )]} (11) r 2 r vdw vdw The Tap is a specific functional form 12 designed to avoid discontinuities when charged species enters or exits the cut-off radius. Coulomb energy (E coulomb ) A shielded Coulomb-potential is employed for the orbital overlap between atoms at close distance. Charges on the atoms are calculated using the geometry dependent Electronegativity Equalization Method (EEM, 15 ). E coulomb qiq j = Tap * C * (12) [ r + r ] 3 ij 3 3 ij The non-bonded interactions (van der Waals and Coulomb) is calculated between each pair of atoms in the system regardless of connectivity with a distance cut-off of 10 Å and are shielded for excessively high repulsion at short distance. In addition to these functionals, extra energy terms are included in the functional form for atoms in specific chemical environment.

23 11 Examples of such energy terms include the energy term for stabilizing the two double bonds sharing a center atom in a valence angle, the three-body conjugation energy term for stabilizing the NO 2 group, the four-body conjugation energy term for stabilizing aromatics, a triple bond stabilization energy term for carbon monoxide and a penalty energy term for correcting the overestimated binding energy of C 2 dimer 16 from the original potential. These energy terms ensures the transferability of a force field when extended to describe the corresponding chemistry as mentioned above. By training against extensive set of data from QM predictions and experiments, the ReaxFF potential aim at reproducing the energetic (thermodynamics as well as reaction barriers) of relevant materials close to QM accuracy while maintaining orders of magnitude lower computational expenses compared to the ab-initio methods when applying to large systems (~ 1000 atoms on a single process or ~10 6 atoms in a parallel simulation environment). 2.3 The force field optimization scheme The accuracy of any MD simulations primarily depends upon the quality of the potentials. Before applying to large scale practical systems, it is necessary to validate the force field results against available experimental data or ab initio calculations for a wide range of representative small systems. ReaxFF force fields are typically parameterized against an extensive training set, which usually consists of equation or states, heats of formation of bulk phases, surface energies, diffusion pathways, bond dissociation energies, angle distortion energies, and transition state calculations. The parameterization procedure employed in our force field development is a successive one-parameter search technique 17. The error function to be minimized in the procedure is defined as follows:

24 N X Error = ( i= 1 i, QM X σ i i,re axff ) 2 12 (13) Where X i,qm is the quantum mechanics determined value and X i,reaxff is the ReaxFF calculated value. The term σ i is the weight assigned to each training point in the training set. The data as the training targets are a collection from literature and work from the project collaborators. A typical target for a ReaxFF force field is to reproduce the DFT reaction energies within 2 kcal/mol and the DFT predicted reaction energy barriers within 5 kcal/mol.

25 Chapter 3 Application to the Fischer-Tropsch (FT) synthesis Introduction FT synthesis 1 is an important industrial process that converts a mixture of hydrogen and carbon monoxide into varieties of hydrocarbons. Its effectiveness of producing sulfur-free fuels as well as organic chemicals of industrial importance has attracted the petroleum industries attention. Though widely used for nearly a century 3, it suffers from lacking a detailed and precise reaction mechanism. Experimental observations demonstrate that the process has a strong dependence upon the choice of the catalysts in terms of the product selectivity 4-5. Iron-based catalysts regenerate H 2 from H 2 O through water-gas-shift (WGS) reaction and hence allow the use of feed gas with low H 2 content. In the meantime, iron favors oxygenated hydrocarbons and suffers from the accumulation of surface carbide which intends to deactivate the catalysts. In contrast, Nickel-based catalysts avoid the formation of inactive surface carbon species but suffer from relatively high price and high methane selectivity 4. The complexity of the reaction mechanism has led to a larger number of experimental measurements identifying possible reaction intermediates and chemical kinetics modeling Key observations concerning the methanation process from early experimental studies confirmed that methylidyne (CH-), methylene (CH 2 -) and methyl (CH 3 -) groups are all intermediates during a methanation process on Fe 22 and Ni 23. Furthermore, polymerization of these CHx- groups, especially reactions involving surface CH 2 - groups, contributes to the chain growth to higher hydrocarbons.

26 However, there are various chain growth mechanisms 3, 34 that 14 have been proposed, among which the carbene mechanism proposed original by Fischer and Tropsch 3 and developed by Maitlis 35 and Dry 36 is the currently most widely accepted one due to its capability of accounting for several current experimental observations 28, One of the many differences between the carbene mechanism and another titled oxygenate mechanism lies in the sequence of carbon hydrogenation and CO dissociation. van der Laan and Beenackers in their review 39 in 1999 stated that: it is uncertain if the monomer (CH 2 -) formation proceeds via hydrogenation of dissociated or undissociated CO. There are several other distinctions between the two mechanisms in illustrating the chain initiation and propagation details. Even so, Davis 40 suggested that the elementary reactions of these mechanisms may occur simultaneously during a real FT process, taking into account its complexity. In the meantime, there is argument regarding the detailed schemes of the carbene mechanism about how the surface CH X - groups are polymerized. Brandy and Pettit 18 proposed in 1980s the alkyl polymerization scheme, where CH 2 - is added to alkyl chains. However, Maitlis et.al argued against this scheme with an alkenyl polymerization scheme, where CH 2 - is added to alkenyl chains. Whichever is considered, CH 2 - is an intermediate of primary importance due to its relatively high reactivity and mobility on the surface of the catalysts. Besides many experimental studies and kinetics models, theoretical investigations especially Density Functional Theory (DFT) based ab initial calculations have been employed to verify and confirm the experimental observations in an FT process. These quantum mechanics based computational studies enable us to acquisite information concerning thermal dynamics properties and potential energy surfaces which are not easily accessible via experimental approach. For instance, reference show the studies of interaction between adsorbed CH X - groups and Cobalt while reference focus on Ruthenium and Gold 48 as catalysts. Some later literatures carried out similar investigations on iron and iron carbide 54 surfaces.

27 15 However, while these calculations allow the exploration of catalysts properties on an atomistic and electronic scale (Reference 55 is an example of how QM calculations contribute to revealing the catalyst dependence of the product selectivity), one Major defect of these DFT studies is that they are addressing situations at 0K and thus lack the capability to evaluate the effect of elevated temperatures. On the other hand, description of a realistic system involves a variety of macro-scale properties such as chemical kinetics and reaction dynamics and hence requires the system size and time scale well beyond the capability of current DFT based QM calculations. In this Chapter, we seek to develop a ReaxFF description of the Fe/C/H/O system and hence to investigate the reaction networks in the FT synthesis under realistic reaction conditions. The force field parameters were trained to reproduce an extended set of QM descriptions of properties of matter (e.g. heats of formation, equation of state, binding energy, reaction pathway etc). Based on the force field parameters, we examined the CO methanation and the C-C coupling process on the Fe (100) surfaces using ReaxFF reactive dynamics (RD) simulation method. Results of these RD simulations provided key information concerning these heterogeneous catalytic processes and proved to be useful in revealing the complexity of FT synthesis. Force field parameterization Iron-Iron interaction In order to correctly describe the iron bulk and the corresponding surface energies in different chemical configurations, we trained the iron-iron interaction to reproduce not only the iron crystal at ambient conditions, but also the bulk phase under compression and expansion conditions. In our current force field parameters, the energy of the optimized bcc bulk phase iron

28 16 is 3.17 kcal/mol lower than the fcc bulk phase iron, compared with a value of 3.64 kcal/mol from DFT prediction. The bulk lattice constant predicted by ReaxFF is 2.84 Å, compared with 2.86 Å and 2.83 Å from DFT data, using ultra-soft pseudo-potentials (USPP) 56 and plane-augmented waves (PAW) potentials 57 respectively. The experimental value is 2.86 Å. Figure 3-1. Comparison of the ReaxFF fit (right panel) of the Equation of State (EoS) for bcc and fcc bulk phases of iron with the corresponding QM data (left panel) for the bcc (FM), fcc (FM) and fcc(afmd) as obtained in Reference 58 Figure 3-1 compares the relative energies of bulk bcc iron upon compression and expansion as determined from DFT and ReaxFF. The force field parameters weree trained against the QM derived equations of state for ferromagnetic (FM) bcc and fcc bulk phases and the antiferromagnetic double-layer (AFMD) phase of iron. The DFT results for fcc-fm show a double well, related to a low-spin transition to a high-spin state, as described in detail by Jiang and Carter 58. Since ReaxFF does not include a magnetic term, the parameters were fit against the lowest- parameters energy magnetic bcc and fcc phases at all volumes. This figure shows that our current successfully reproduce the variation of the energies of bcc and fcc bulk phase around the equilibrium region and for small external stresses. In high stress situations, there is a larger difference between QM and ReaxFF but they are acceptable as long as ReaxFFF can recognize these structures as energetic undesirable and avoid them in typical chemical environment. This also indicates that our current force field parameters may be less accurate to predict the material properties under extreme mechanical environment with high stress. Also, The ReaxFF bcc (100)

29 17 and (110) surface energies are 14.5 kcal/mol and 9.96 kcal/mol respectively, which compare well to the values of kcal/mol and 9.78 kcal/mol obtained from DFT calculations 59. The existing ReaxFF description 60 of iron can reproduce many aspects of the metal properties including: bcc and fcc bulk phase equation of state, bcc (100) and (110) surface energies and small iron cluster atomization energies. However, ReaxFF tends to underestimate the atomization energy of the iron dimer. This deficiency couldn t be remedied via the optimization of the iron related ReaxFF parameters without sacrificing the ReaxFF performance for bulk phases. In this study, we constructed an empirical function serving as an energy compensation for the iron-iron bond in the ReaxFF description. The function is expected to stabilize the Fe dimer while having minor effect on all the other iron systems. We constructed the following empirical equation: Param3 Param2 boa E = Params1* boa *exp[1 ] (14) abo(1) + abo(2) 2 Where, Boa is the bond order of an iron-iron bond; Abo (i), i=1, 2 are the total bond order of the i th atom sharing the bond with bond order boa. The three parameters (denoted as Params1, Params2, and Params3) are additions to the original force field. The second term in equation (14) insures that the energy compensation diminishes to zero upon bond dissociation. The third exponential term insures that the functional diminishes as the coordination number of any iron atom sharing the corresponding iron-iron bond increases. This property is important since the modification primarily serves to stabilize the iron dimer, while maintaining little effect on the species containing iron atom with high coordination numbers. Figure 3-2 shows the behavior of the function upon bond dissociation with some rough values of the three parameters:

30 18 Figure 3-2. Energy correction upon bond dissociation in small iron clusters The X axis of Figure 3-2 describes the ratio of the actual value of the bond order during a bond dissociation process over that at equilibrium. The process is artificially designed so that all the bonds in one cluster are stretched simultaneously at the same rate till the corresponding bond order diminishes to zero. The figure shows that the function indeed has the two properties as expected: 1. the energy compensation diminishes upon bond dissociation; 2. the energy compensation diminishes as cluster grows bigger. Figure 3-3 shows how the energies are corrected for small iron clusters in the ReaxFF training set. Figure 3-3. Energy corrections for small iron clusters after force field optimization

31 Figure 3-4 shows how the function affects the equation of state of iron bcc and fcc bulk phase iron. The modification is negligible as expected. Table3-1 shows a side effect of the 19 function on the surface energies. The modified potential and re-parameterized force field underestimate the stability of both the surfaces. Nevertheless, the new description maintains the preference of (100) surface as the more stable surface. Thus in conclusion, the function is behaving correctly and effectively. Figure 3-4. Effect of the energy complement function on bcc/fcc iron equation of state Table 3-1 Effect of energy compensation functional on the surface energy of Fe bcc (all numbers are with units: kcal/mol) Surface QM ReaxFF old ReaxFF new Bcc(110) Bcc(100) At the current force field development stage, these modifications are not integrated in the general parameter set describing the FT process, which still focus on the interaction of hydrocarbon molecules with the metal surfaces. However, such integration will be necessary when it comes to describing the interaction involving Fe clusters. Iron-Carbon interaction During a FT synthesis the iron surface is transformed into a carbide surface as a result of carbon monoxide adsorption and dissociation on the surface and carbon atom migrating to the

32 20 subsurface. At equilibrium the catalyst is transformed to an iron carbide phase while the resulting oxygen is eliminated as water. Thus it is important to include in the training set structures and energetic data for bulk iron carbide and different corresponding surfaces. The heat of formation of Fe 3 C (cementite) predicted by ReaxFF is 5.94 kcal/mol, compared to 4.14 kcal/mol from QM prediction and 4.37 kcal/mol from experimental measurements. Figure 3-5 shows the EoS for cementite predicted by ReaxFF and DFT based calculation. Figure 3-5. ReaxFF fit for the EoS for Fe3C cementite Figure 3-6 shows a comparison of seven low Miller index Fe 5 C 2 surface energies between ReaxFF and DFT data. The graphical representation of the seven surfaces is demonstrated in Figure 3-7. These results indicate that we have good agreement describing iron carbide species between ReaxFF and QM predictions.

33 21 Energy(kcal/mol) QM ReaxFF Figure 3-6. Comparison of Fe 5 C 2 surface energies for seven low Miller indices obtained using QM and ReaxFF methods

34 22 A B C D E F G Figure 3-7. Graphical representation of the seven Fe 5 C 2 surfaces with low Miller indices: Panel A) surface (010)0.25; Panel B) surface (11-1)0.00; panel C) surface (110)0.00; panel D) surface (111)0.00; panel E): surface (11-1) 0.50; panel F); surface (110)0.50; panel G) surface (001)0.00 Iron-Hydrogen interaction Figure 3-8 shows the hydrogen binding energies at different sites of Fe bcc (100) and Fe (110) surfaces and for three different surface coverages. We observe that ReaxFF provides a good agreement with DFT data particularly for the case of binding at the most stable bridge and hollow sites but underestimates the adsorption energies at the top sites on both (100) and (110)

35 23 surfaces. This limitation is however not problematic as the adsorption at the top sites on both surfaces is not stable and the adsorbed H 2 molecule at such sites will quickly move to the nearby bridge or hollow sites which provide stable local minima. 0.8 Binding energy (ev) QM ReaFF -0.6 (a) Top 11% Bridge 11% Hollow 11% Top 25% Bridge 25% Hollow 25% Bridge 100% Hollow 100% Binding energy(ev) (b) Top 25% Short bridge 25% Long bridge 25% 3-fold 25% QM ReaxFF Figure 3-8. ReaxFF fit for binding energies of H atom at various sites on (a) Fe (100) and (b) Fe (110) surfaces To ensure our force field provides an accurate description of the C/H/Fe system, structures describing the hydrogen interacting with bulk phase metal were also included in our fitting analysis and the corresponding results are indicated in Figure 3-9. Panel a) indicates the binding energies of hydrogen absorbed at Fe bulk vacancy sites, while panels b) to d) show three hydrogen diffusion pathways. The iron hydride heat of formation predicted by ReaxFF is 1.73 kcal/mol, which is in good agreement with the QM value of 1.89 kcal/mol.

36 Binding energy (ev) QM ReaxFF Fe2H oct fixed Fe2H oct opt Fe16H oct fixed Fe16H oct opt Fe54H oct fixed Fe128H oct fixed bcc[100]tetr_sub (a) Energy (ev) (b) (c) (d) QM ReaxFF Distance from hollow site (Å) Distance from 3-fold site (Å) Distance from tetrahedral site (Å) Figure 3-9. ReaxFF fit for (a) Binding energies of H atom to different vacancies in bulk phase iron (b) H diffusion pathway from a (100) surface hollow site to a subsurface tetrahedral site (c) H diffusion pathway from a (110) surface 3-fold site to subsurface tetrahedral site (d) H diffusion pathway among two nearby subsurface tetrahedral sites in a FeH-bulk phase The dissociative adsorption process of a hydrogen molecule on the Fe bcc (100) surface is investigated. Figure 3-10 shows one of the hydrogen dissociation pathways as predicted by ReaxFF. A H 2 molecule was initially placed above the iron surface in between two forth fold hollow sites and oriented perpendicular to the iron-iron bond. Using a bond restraining technique, we gradually force the hydrogen molecule to get dissociative chemisorbed to the two hollow sites. The energy barrier found in this case is nearly 4 kcal/mol and the reaction energy is kcal/mol. A similar dissociation pathway was found using DFT based method 61 with an energy barrier of 3.87 kcal/mol and a reaction energy of about -15 kcal/mol. Note that this dissociation

37 pathway was not included in the training process, and the reasonable agreement found between ReaxFF and QM method indicates the versatility of the ReaxFF parameters. 25 Product TS Reactant Figure Hydrogen dissociation pathway on a Fe(100) surface starting from a two-fold site above the surface and ending to two neighbor four-fold hollow sites Iron/Carbon/Hydrogen interaction As mentioned above in the introduction section, methylidyne (CH-), methylene (CH 2 -) and methyl (CH 3 -) groups are all intermediates during the initial methanation and the chain propagation process. It is thus essential for the force field to correctly describe the interaction of these small hydrocarbon groups with the metal surface. Figure 3-11 displays how the current field reproduces the binding energies of these three groups on Fe bcc (100) surfaces.

38 26 Figure Adsorption of the CH (four fold hollow site), CH 2 (four-fold hollow site) and CH 3 (two fold bridge site) groups on Fe bcc (100) surface The synthesis of methane is investigated as described in Figure 3-10 to Figure The carbon atom initially sitting at the hollow site goes through a series of hydrogenation process and eventually forms a methane molecule. Product TS Figure Hydrogenation of a carbon atom on the Fe (100), starting with the H atom and C atom at the hollow site and ending with CH- group at the hollow site

39 27 In the hydrogenation process of a carbon atom (shown in Figure 3-12), the hydrogen and carbon atom were placed at two nearby hollow site corresponding to their most stable adsorption position. Using a bond restraint technique, the hydrogen atom was gradually forced to migrate towards the carbon atom through a local minimum (corresponding to a bridge adsorption site) before overcoming the main barrier. The energy barrier of this case is 21 kcal/mol compared with the QM value 16.6 kcal/mol 49. The reaction is over all endothermic with reaction energy of 3 kcal/mol. Reactant Product TS Figure Hydrogenation of a CH- group on the Fe (100), starting with the H atom and the CHgroup at the hollow site and ending with a CH 2 - group at the hollow site Figure 3-13 shows the hydrogenation process of a CH- group. It is initially placed at a hollow site with a hydrogen atom sitting at a nearby hollow site. With the same bond restraint technique, a CH 2 -group was formed through the combination of the CH- group and the H atom. In this case the reaction has a barrier of 13kcal/mol compared with 16 kcal/mol resulted from DFT study. This second hydrogenation process is predicted by ReaxFF to be exothermic of 5 kcal/mol compared with the DFT prediction of endothermic of 10 kcal/mol. This discrepancy indicates necessary further optimization of the force field parameters. Again, a small intermediate

40 energy barrier was observed during this process corresponding to the transition from the hydrogen hollow adsorption site to its bridge adsorption site. 28 TS Product Reactant Figure 3-14.Hydrogenation of a CH 2 - group on the Fe (100), starting with the H atom and the CH 2 - group at the hollow site and ending with a CH 3 - group at the bridge site In Figure 3-14 the third hydrogenation process is demonstrated. The reaction energy barrier is about 9 kcal/mol, which agrees well with the quantum prediction of 7 kcal/mol. The over all process is exothermic with reaction energy of about -12 kcal/mol. In this case, we didn t observe an intermediate energy barrier as in the previous two cases. This might due to that during the process, the CH 2 - group and the H atom proceeds towards the bridge site simultaneously and combined above the site.

41 29 TS Product Reactant Figure 3-15.Hydrogenation of a CH 3 - group on the Fe (100), starting with the H atom at the hollow site and the CH 3 - group at the bridge site and ending with a CH 4 molecule The formation process of a methane molecule is shown in Figure The energy barrier of this reaction is 17 kcal/mol compared with the QM calculation of 12.5 kal/mol. Iron/CO interaction CO is one of the crucial reactants in the FT process; as such it is necessary for the force field to reproduce the binding energies of CO on the Fe surfaces. Figure 3-16 shows the binding energy determined by ReaxFF and the comparison with QM predictions at different adsorption sites on three different types of iron surfaces from bcc structures.

42 30 Figure Adsorption of a CO molecule on Fe bcc (100) surface at three different sites (1F ontop site, 2F bridge site, 4F hollow site), Fe bcc (211) surface and Fe bcc (310) at two different configurations ( -1 stands for the down configuration, 1 stands for the up configuration, title in consistency with reference 62 ). As a staged summary, the current force field parameters are capable of describing certain primary phenomena in a FT synthesis environment. Next we will perform molecular dynamics simulations to further validate the description of the force field. It is worth mentioning that before the finalization of any empirical method, the study will go through a trial, modification and retrial approach. Any unexpected phenomena in the validation stage will lead to a further modification of the empirical potentials.

43 31 Molecular Dynamics simulation Hydrogen dissociation on iron/iron carbide As an initial validation of the force field parameters, the adsorption and desorption process of gas phase hydrogen molecules on Fe and Fe carbide are investigated. Two systems are set up as demonstrated in Figure Figure MD simulation setups for two cluster systems of (I) iron and (II) cementite Figure 3-18 shows the iron hydride cluster at 500 K, 600 K and 750 K after 250 ps as indicated in panels A, B, and C respectively. Since 750 K is higher than a typical FT synthesis temperature range (470 K~620 K), we only performed simulations at this temperature for force field validation purposes. Compared to 500 K case, where the surface and the cluster maintained the original shape, we begin to observe cluster deformation at 600 K and 750 K. The active sites including the bridge and hollow sites for hydrogen dissociation are still recognizable. This figure also shows that most of the gas phase hydrogen molecules dissociated at the four-fold hollow sites, indicating that these sites are more stable than the top and bridge sites. We also observed dissociated hydrogen atoms adsorbed at bridge sites (as pointed by black arrow), in agreement with previous QM results 61 which indicate that bridge sites are stable for atomic hydrogen.

44 32 (a) (b) (c) Figure Iron hydride cluster after 250 ps and H 2 exposure at: A, 500 K; B, 600 K; C, 750 K. Yellow dots: Fe; White dots: hydrogen Figure 3-19 shows in panels A, B and C the iron carbide hydride cluster at 500 K, 600 K, and 750 K after 250 ps, respectively. In this case, we can see that the cluster and the surface are substantially deformed, especially at high temperature (750 K), and the original (100) surface is hardly recognizable. This suggests that cementite clusters with exposed (100) surface is not very stable, particularly at temperatures in excess of 750 K. (a) (b) (c) Figure Iron carbide hydride cluster after 250 ps and hydrogen exposure at: A, 500 K; B, 600 K; C, 750 K. Yellow dots: Fe; White dots: hydrogen; Green dots: carbon Next we will use the developed force field to study the FT synthesis. In the MD simulations addressing a heterogeneous catalytic process as complex as FT synthesis, an MD model with which one expects to capture all the detailed process as well as the crucial intermediates and products will require a enormous system running for an extremely long simulation time. In order to overcome the length and time scale restraint, we constructed in this study five different systems (vide infra) to address the different stages of the real process and the

45 33 corresponding intermediates. Although some of these artificial systems distinct from the real FT environment, we believe they reveal key information regarding the surface reaction pathways of different species in the real process and hence contribute to the understanding of the detailed mechanism. These studies aim to reveal shortcomings in the current ReaxFF description after resolving these shortcomings we aim to use massively parallel ReaxFF simulations 63 and Parallel Replica MD-methods 64 to increase both size- and timescales. In all the 5 systems, a bcc iron slab consists of 486 atoms was placed in a 25.56*25.56*40 periodic box with its (100) surface facing the z direction. All the five systems underwent MD simulations for 2ns. In the graphical representations of all the five systems in this paper, yellow dots represent Fe atoms; white dots represent H atoms; green dots represent C atoms; red dots represent O atoms. CO methanation CO provides a carbon source for hydrocarbons in a FT process. The well accepted carbene mechanism indicates that the high carbon number species initiate from the adsorption and dissociation of CO molecules on the surface of the catalysts followed by the C atom hydrogenation and polymerization. In the meantime, O atoms also get hydrogenated and form water. hydrogenation of the C atoms to produce CH 2 - is limited to the surface carbide and is slower than that of O atoms and hence is rate limiting 36. The first system addresses this process of CO adsorption and hydrogenation. The aforementioned bcc iron slab (486 atoms) with its (100) surface exposed to 20 CO molecules and 200 H 2 molecules was placed into the Å* Å*40 Å periodic box. More H 2 molecules than in reality were provided so that sufficient events of hydrogenation were obtained. A graphic

46 representation of the system is shown in Figure 3-20 (at the beginning of the simulation, system side view) and Figure 3-21 (after 2 ns: panel A) system side view; panel B) slab top view). 34 Figure 3-20 MD simulation setup for system I: an iron slab with gas phase CO and H 2 A B CH 3 - HCO- HCOH- H 2 O CH 4 Figure 3-21 Graphic representation of system I after 2 ns: panel A) system side view and panel B) slab top view

47 35 In Figure 3-21, the products (CH 4 and H 2 O) and some of the intermediates (CH 3 -, HCO-, HCOH-) are highlighted by black circles. At the end of the simulation, 4 carbon atoms out of the 20 were released as methane molecules while 8 of them formed surface carbide species. The rest 8 carbon atoms formed a variety of intermediate species; 13 oxygen atoms out of the 20 were released as H 2 O molecules. Figure 3-22 shows the population analysis of the surface CH X O- species in system I. All the CO molecules were hydrogenated prior to their dissociation. The number of the CHOmolecules resulted from the first hydrogenation of CO molecules reached its maximum after 200 ps. This species could get further hydrogenated into CH 2 O-. Figure 3-22 suggests that CHO- and CH 2 O- are both important intermediates during the initiation of CO molecules. Furthermore, the decrease of the number of the CHO- species doesn t match the increase of that of the CH 2 O- species, which suggests that other than the further hydrogenation to form CH 2 O-, there are other reaction channels for CHO-, among which the C-O bond cleavage is a primary one. This dissociation process will lead to the formation of CH- group and surface O atom (if CHO- is structured as H-C-O-) or the formation of surface carbide and HO- group (if CHO- is structured as COH-). In the meantime, the formation of the CH 3 O- species is rare. The CH 2 O- species will mainly go through a dissociation channel compared to further hydrogenation into CH 3 O- due to the weak C-O bond in CH 2 O-. Also, the products will again depend on the initial structure of the CH 2 O-. Further details regarding these pathways and products will require a quantitative analysis and isomer structure analysis, which are not addressed in this study.

48 36 Figure 3-22 surface CH X O- species population analysis in system I Next, the population analysis of the surface hydroxyl group and water is provided in Figure 3-23 surface hydroxyl and water species population analysis in system I After the C-O bond dissociation (at whatever stages of the hydrogenation), the released HO- groups will react with a surface adsorbed H atom to form H 2 O. The oscillation of the number of the H 2 O molecules indicates that they can go through the dissociation and reformation channel into and from the surface OH- and H- species. This reaction channel is important for the watergas shift reaction when iron is employed as the catalyst in a FT process. In our simulations we do

49 37 not see any water molecule desorbs from the iron surface, which indicates that the ReaxFF Fesurface binding energy may be too high we aim to improve this description by comparing with dispersion-corrected DFT-results for water-binding. Finally, we examine the population of CHx- groups, including the C atoms, as shown in Figure Figure 3-24 surface CH X - species analysis for system I The final system configuration in the simulation indicates that the carbon atoms formed from the C-O bond cleavage in the COH- molecules will migrate into the subsurface and further into the bulk phase to form stable carbide species. Also, comparison among Figure 3-22 and Figure 3-24 shows that the number of CH X - groups are less than the other species (CH X O-, HOand H 2 O), indicating that the formation of these CH X - species maybe the rate limiting step, which agrees with the carbene mechanism. As a staged summary, in addition to the carbene mechanism, our RD simulation results indicate that the CO molecules can dissociate in a hydrogen assistant way. These observations agree with the initial stage of the oxygenate mechanism proposed in 1950s 65. Although different from the well accepted carbene mechanism, the oxygenate mechanism also have experimental evidences and the advantages in highlighting the importance of oxygen containing species in

50 38 the hydrocarbon chain initiation and propagation. Theoretically, when the carbon atom in the CO molecule is attacked by the hydrogen atom, the C-O bond interaction may get weakened and hence the dissociation energy barrier is decreased. This offers another dissociation pathway of CO molecules on the catalysts surface in addition to the description in the carbene mechanism. We aim to perform an analysis of the ReaxFF energies with recent DFT results for the pathways identified here and will use this comparison to improve, where necessary, the ReaxFF description. Surface carbide hydrogenation Surface carbon atoms resulting from the direct CO dissociation will migrate into the subsurface and further into the catalyst bulk phase to form surface carbide and bulk carbide species. The early time carbide mechanism explained the formation of the hydrocarbons as the formation of metal carbide followed by the hydrogenation of the carbide 3. Although It was proved inconsistent with thermodynamics data 73, later development revived this carbide theory with a requirement that the carbide species should be restricted to the surface layer since the bulk carbide is relatively more stable. We attempt to examine the direct hydrogenation of surface carbide by constructing a system II: the iron slab was pre-treated in the following way. One carbon atom was artificially placed at each hollow site on the Fe (100) surface. The slab with its (100) surface covered with carbon atoms was then exposed to CO gas phase molecules for 2ns at 800K. In the process, CO molecules absorbed on the surface while the pre-covered carbon atoms diffused into the sub surface layer and further into the bulk phase (they may also stay on the surface). After this process, we extracted the slab from CO gas phase and manually removed all the O atoms in the adsorbed CO molecules on the surface. The remaining structure then underwent a surface annealing process (equilibrated at 300K for 2.5 ps; then slowly heated up to 500K at a rate of

51 39 80K/ps; equilibrated at 500K for 2.5 ps; cooled down to 300K at a rate of 80K/ps; again equilibrated at 300K for 2.5 ps) to reach thermal equilibration. These pre-treatments have four objectives: 1. Imitate the possible CO dissociation in a real FT process by manually removing all the O atoms. 2. Without the employment of an iron-carbide slab directly, the property of bare iron surface as catalyst is maintained to a certain level. 3. Saturate the iron bulk phase with carbon atoms and hence maintain more surface carbide to increase the possibility of the direct hydrogenation. 3. Address the problem of carbon accumulation arises from employing iron as the catalyst in the FT process. A graphic representation of the pre-treatment process is shown in Figure A B C D E F Figure 3-25 graphic representation of the pre-treatment process of system II: panel A) the iron slab is pre-covered with carbon atoms and placed in the gas phase CO molecules; panel B) CO molecules adsorbed on the surface of the slab; panel C) the slab with surface adsorbed CO molecules was then extracted; panel D) the O atoms were artificially removed; panel E) the remaining structure underwent a surface annealing process; panel F) the resulted slab after the surface annealing was placed in a H 2 gas phase environment Subsequently, the annealed slab was exposed to H 2 gas phase at 800K for 2 ns. However we didn t observe the direct hydrogenation of surface carbon species to form the CH- groups in

52 40 this simulation. Though this might result from an insufficient simulation time or the imperfection of the force field potential, other explanations involve the coordination number of the surface carbon atoms and their stability as demonstrated in Figure Before hydrogenation, the three and five coordinated carbon atoms can potentially be hydrogenated. However, they only reflect a small amount of the total carbon atoms. Most carbon atoms are high coordinated after surface annealing. Furthermore, there is a clear trend of increase in the coordination number after the exposure to the H 2 molecules. This trend indicates that the carbon atoms were either migrating into the subsurface and bulk or extra stabilized by the surface deformation of the catalyst, both of which will increase the energy barrier of the direct hydrogenation. Figure 3-26 coordination analysis for the carbon atoms in system II before and after exposure to H 2 molecules QM calculation indicates that the hydrogenation of the carbon atom absorbed at the hollow site on the Fe (100) surface is approximately 14.6 kcal/mol 49. However, our RD simulation indicated that the stability of these surface carbon atoms maybe enhanced upon the deformation of the iron surface at elevated temperatures. A direct result is the increase of the energy barrier of the hydrogenation. This phenomenon may partly account for the surface deactivation arises from the carbon accumulation. Furthermore, this simulation proves the

53 41 capability of ReaxFF in capturing the elevated temperature effect in a complex heterogeneous catalytic environment and provides new configurations for DFT-studies, which, in turn, can be used to improve the ReaxFF description. Hydrogenation of the surface methylidyne (CH-) To study the CH-hydrogenation process in more detail, in system III we pre-covered the iron slab with about 40 surface CH- species and placed the slab in the simulation box with 200 hydrogen molecules. Every CH- group was manually placed in the hollow site, which is its most stable adsorption site on Fe (100) surface. The system configuration is shown in Figure 3-27 (initial system side view and slab top view) and Figure 3-28 (final system side view and slab top view after 2ns). In Figure 3-28, examples of products (CH 4 and C atom) and intermediates (CH 2 - and CH 3 -) are highlighted with black circles. The two primary reaction channels for CH- are: 1. further hydrogenation to form CH 2 -; 2. C-H bond cleavage to form surface C atom. In the latter case, as discussed in system II, the C atoms prefer to migrate into the subsurface and the bulk without any further hydrogenation.

54 42 Figure 3-27 MD simulation setups for system III: an iron slab (pre-covered with CH- species randomly at hollow site) with gas phase H 2 molecules. Figure 3-28 final configurationn of system III after 2 ns: panel A) system side view and panel B) slab top view

55 43 At the end of the simulation, thirty CH- species out of 40 were consumed. Twelve of the consumed CH- groups formed methane; Eleven dissociated to form carbide; Seven formed CH 3 - intermediates. The population analysis is shown in Figure Figure 3-29 population analysis of reactant and major products in system III Figure 3-29 suggests that the CH 2 - groups are consumed quickly to form CH 3 -, thus no accumulation of CH 2 - species is observed. This observation indicates that CH 2 - is an important intermediate of high reactivity. Furthermore, the hydrogenation of CH 3 - is the rate limiting step in the synthesis of methane. This observation is also supported by the DFT calculation: the barrier of the reaction CH H -> CH 3 - is about 7 kcal/mol, while the barrier of the reaction CH H-> CH 4 is about 20 kcal/mol. Hydrogenation of the surface methylene (CH 2 -) In order to further study the CH 2 - conversion reactions, in system IV the iron slab was pre-covered with about 72 surface CH 2 - groups and placed in a H 2 gas phase consisting of 200 molecules. The graphic representation of the system is shown in Figure 3-30 (initial system side view and slab top view) and Figure 3-31 (final system side view and slab top view).

56 44 Figure 3-30 MD simulation setups for system IV: an iron slab (pre-covered with CH 2 - groups randomly at hollow site) with gas phase H 2 molecules Figure 3-31 final configurationn of system IV after 2 ns: panel A) system side view and panel B) slab top view A population analysis is shown in Figure 3-32.

57 45 Figure 3-32 population analysis of reactant and major products in system IV In the simulation, around 90% of the CH 2 - groups were consumed before 200ps as demonstrated in Figure This result agrees with the experimental observation in that CH 2 - is a very reactive species. Furthermore, two of the major reaction channels for this species are: 1. further hydrogenation to form CH 4 via CH 3 - as the intermediate; 2. C-C coupling reaction to form a variety of C 2 species, among which, ethene and ethyne are predominant. In the meantime, C 2 H 3 -, C 2 H 5 - and C 2 H 6 did present in the simulation. The detailed pathway for the formation of these groups is not exactly clear. These species could be formed via the dissociation of ethene or the coupling reaction between CH 2 - and CH 3 -. The number of ethene molecules reached its maximum after about 200ps and then decreased, indicating the dissociation of ethene as the secondary reaction. The C 2 groups on the surface of the catalyst are important in the synthesis of higher hydrocarbons.

58 46 C-C coupling reaction In the simulations performed above, the slab together with its surface species was exposed to H 2 molecules and hence the hydrogenation process was favored. One major consequence of this preference is that any C-C coupling reaction maybe blanked out. In system V, we will focus the attention on the C-C coupling by pre-cover the surface with C, CH-, CH 2 - and CH 3 - gropus without H 2 gas phase molecules. The object of this simulation is to examine the preference of C-C coupling among these groups in the initiation of the chain propagation. This system is expected to contribute to the revealing of the detailed scheme of the carbene mechanism: whether it favors the alkyl polymerization scheme (where CH 2 - is added to alkyl chains) or the alkenyl scheme (where CH 2 - is added to alkenyl chains). The aforementioned iron slab was artificially pre-covered with 18 C atoms, 20 CHgroups and 19 CH 2 - groups sitting at different hollow sites and 12 CH 3 - groups sitting at different top sites. The adsorption sites were chosen as randomly as possible. One issue is worth mentioning: DFT calculation indicates that the energy barriers for C- C coupling reactions 51 are typically higher than the carbon hydrogenation 49. In order to examine the process in a relatively short simulation time, the temperature was increased to 1000K in this case. To avoid the possible C-H bond cleavage and focus the attention on the C-C coupling phenomena, the parameter in the force field describing the C-H σ bond dissociation energy was artificially increased from 169 kcal/mol to 300 kcal/mol. The objective is to prevent the C-H bond cleavage and to observe the reaction pathway of the entire CH X - groups. The slab was placed in vacuo and underwent RD simulation at 1000K for 2ns. The system configuration is shown in Figure 3-33, panel A):

59 47 Figure 3-33 panel A) MD simulation setups for system V: an iron slab (pre-covered with C-, CH-, CH 2 - and CH 3 - groups randomly; panel B) final configuration of system V after 2 ns. The final system configuration is shown in Figure 3-33 panel B) and the population analysis is shown in Figure 3-34 (reactants) and Figure 3-35 (products). Also, major intermediates are highlighted with black circles. Figure 3-34 population analysis for the pre-covered groups in system V

60 48 Figure 3-35 population analysis for major products resulting from C-C coupling in system V Figure 3-34 confirms that CH 2 - is of higher reactivity compared to the other 3 species. Seventeen out of 19 CH 2 - were consumed in the first 200ps. The observation agrees with the carbene mechanism in that the CH 2 - is an important building block in the chain propagation process. In contrast, there is no significant change in the number of the CH 3 - groups, as indicated by the blue curve in Figure Though CH 3 - group is highly mobile on the surface, it is less reactive with other groups compared to CH 2 - or even CH-, which is a very stable species at the hollow site on the surface. This might suggests that the essential reaction channel for CH 3 - is to form CH 4 via further hydrogenation by surface adsorbed H atoms. In the meantime, 4 out of 18 C atoms and 6 out of 20 CH- groups participate in the C-C coupling reactions. Our RD simulation indicates that the CH- and CH 2 - coupling to form a C 2 H 3 - group is of primary preference among varies coupling pathway as demonstrated by Figure Maximum number of the C 2 H 3 - groups reached 8, which is nearly twice the number of other possible C 2 species (4 for C 2 H 4, 3 for C 2 H 2, 2 for C 2 H-). C 3 species were also formed occasionally. These observations agrees with the alkenyl scheme version of the carbine mechanism proposed by Maitlis 41. QM data 51 also supports this scheme in a way that the energy barrier of