1 Application of the ReaxFF reactive force fields to nanotechnology Adri van Duin, Weiqiao Deng, Hyon-Jee Lee, Kevin Nielson, Jonas Oxgaard and William Goddard III Materials and Process Simulation Center, California Institute of Technology

2 Contents - ReaxFF: background, rules and current development status - Ni-catalyzed nanotube growth - Validation of the all-carbon ReaxFF potential - Building the Ni/NiC potential - Testing the Ni-cluster description: magic number clusters - Study of the initial stages of nanotube formation

3 Time Distance ÅngstromKilometres years QC ab initio, DFT, HF Electrons Bond formation MD Empirical force fields Atoms Molecular conformations MESO FEA Design Grains Grids Hierarchy of computational chemical methods ReaxFF Simulate bond formation in larger molecular systems Empirical methods: - Allow large systems - Rigid connectivity QC methods: - Allow reactions - Expensive, only small systems ReaxFF: background and rules

4 System energy description 2-body multibody 3-body4-body

5 -To get a smooth transition from nonbonded to single, double and triple bonded systems ReaxFF employs a bond length/bond order relationship. Bond orders are updated every iteration. - Nonbonded interactions (van der Waals, Coulomb) are calculated between every atom pair, irrespective of connectivity. Excessive close-range nonbonded interactions are avoided by shielding. - All connectivity-dependent interactions (i.e. valence and torsion angles) are made bond-order dependent, ensuring that their energy contributions disappear upon bond dissociation. - ReaxFF uses a geometry-dependent charge calculation scheme that accounts for polarization effects. Key features

6 General rules - MD-force field; no discontinuities in energy or forces even during reactions. - User should not have to pre-define reactive sites or reaction pathways; potential functions should be able to automatically handle coordination changes associated with reactions. - Each element is represented by only 1 atom type in the force field; force field should be able to determine equilibrium bond lengths, valence angles etc. from chemical environment.

7 Current status ‘Finished’ ReaxFF force fields for: - Hydrocarbons (van Duin, Dasgupta, Lorant and Goddard, JPC-A 2001, 105, 9396) (van Duin and Sinninghe Damste, Org. Geochem.2003, 34, Si/SiO 2 (van Duin, Strachan, Stewman, Zhang, Xu and Goddard, JPC-A 2003, 107, 3803) - Nitramines/RDX (Strachan, van Duin, Chakraborty, Dasupta and Goddard, PRL 2003,91, Al/Al 2 O 3 (Zhang, Cagin, van Duin, Goddard, Qi and Hector, PRB in press) Force fields in development for: - All-carbon materials - Transition metals, metal alloys and metals interacting with first row elements - Proteins - Magnesium hydrides

8 Ni-catalyzed nanotube growth Longer nanotube Concept: grow nanotubes from buckyball building blocks - Exothermic reaction - Huge activation barrier - Probably needs catalyst

9 Validation of the ReaxFF all-carbon potential QC-data taken from hydrocarbon training set: - Single, double and triple bond dissociation - C-C-C, C-C-H and H-C-H angle bending - Rotational barriers around single, double and aromatic C-C bonds - Conformation energy differences - Methyl shift and H-shift barriers - Heats of formation for a large set of strained and unstrained non-conjugated, conjugated and radical hydrocarbons - Density and cohesive energies for diamond, graphite, cyclohexane and buckyball crystals - All-carbon ReaxFF should also work for hydrocarbons

10 CompoundE Ref (kcal/atom)E ReaxFF Graphite0.00 a 0.00 Diamond0.8 a 0.52 Graphene1.3 a _10 nanotube2.8 b _0 nanotube2.84 b _8 nanotube2.78 b _2 nanotube2.82 b 2.82 C 60 -buckyball11.5 a 11.3 a : Experimental data; b : data generated using graphite force field (Guo et al. Nature 1991) - ReaxFF gives a good description of the relative stabilities of these structures Relative energies for all-carbon phases All-carbon data added to the hydrocarbon training set

11 - Even-carbon acyclic compounds are more stable in the triplet state; odd-carbon, mono and polycyclic compounds are singlet states - Small acyclic rings have low symmetry ground states (both QC and ReaxFF) - ReaxFF reproduces the relative energies well for the larger (>C6) compounds; bigger deviations (but right trends) for smaller compounds - Also tested for the entire hydrocarbon training set; ReaxFF can describe both hydro- and all-carbon compounds

12 C-C distance (Å) Energy (kcal/mol) - ReaxFF gives good energies for key structures in buckyball growth -Training set includes all hydrocarbon cases used for ReaxFF CH

13 Angle bending in C 9 - ReaxFF properly describes angle bending, all the way towards the cyclization limit

14 c-axis (Å)  E (eV/atom) diamond graphite Diamond to graphite conversion Calculated by expanding a 144 diamond supercell in the c-direction and relaxing the a- and c axes QC-data: barrier eV/atom (LDA-DFT, Fahy et al., PRB 1986, Vol. 34, 1191) -ReaxFF gives a good description of the diamond-to-graphite reaction path

15 Applications of all-carbon ReaxFF: buckyball+nanotube collisions Impact velocity: 6 km/sec (1500K) Impact velocity: 9 km/sec (2500K)

16 Side impact -Materials are too stable, extremely high impact velocities are required to start reaction - Catalyst required to lower reaction barriers

17 Transition metal catalysis: Ni 1: ReaxFF and QC EOS for Ni bulk phases -ReaxFF gives a good fit to the EOS of the stable phases (FCC, BCC, A15) -ReaxFF properly predicts the instability of the low-coordination phases (SC, Diamond)

18 Icosahedron FCC Liquid Amorphous solid MD-iterations Energy/atom (kcal) Testing the force fields for Ni magic number clusters

19 Temperature (K) Energy/atom (kcal) Icosahedron FCC Liquid Amorphous solid MD-heatup/cooldown simulations heatup cooldown - ReaxFF gets the right trend for fcc/icosahedron transition - ReaxFF heat of melting converges on Ni bulk melting temperature (1720K)

20 Ni-C bond breaking in H 3 C-Ni-CH 3 Bond length (Å) Energy (kcal/mol) Ni-C bond breaking in Ni=CH 2 2. Results for Ni-C interactions

21 Ni-C bond breaking in Ni(CH 3 ) 4 Bond length (Å) Energy (kcal/mol) Ni dissociation from 5-ring compound Energy (kcal/mol)

22 Bond length (Å) Ni dissociation from 6-ring compound Energy (kcal/mol) Ni dissociation from benzene Energy (kcal/mol)

23 Ni dissociation from benzyne Energy (kcal/mol) Bond length (Å) C-Ni-C angle bending in benzyne/Ni complex Angle (degrees) Energy (kcal/mol)

24 Angle (degrees) Energy (kcal/mol) C-Ni-C angle bending in H 3 C-Ni-CH 3

25 Ni-assisted C 2 -incorporation reactions - ReaxFF Ni can describe the binding between Ni and C - A similar strategy has been used to make ReaxFF descriptions for Co/C and Cu/C, allowing us to compare their catalytic properties

26 R 12 = 1.45 Å R 12 = 1.49 Å Influence adsorbed Ni on buckyball reactions - ReaxFF predicts that buckyball C-C bonds get substantially weakened by adsorbed Ni-atoms - Might lower buckyball coalescence reaction activation barrier ReaxFF-minimized buckyball ReaxFF-minimized buckyball+2 Ni

27 Energy (kcal/mol) Reaction coordinate Low-T ReaxFF restraint MD-simulation Influence adsorbed Ni on reaction barrier - Ni-atoms lower reaction barrier - Overall reaction becomes exothermic due to formation of Ni-Ni bonds - May explain Ni catalytic activity

28 Influence Ni on initial stages of buckyball growth MD NVT-simulation (1500K); 5 C 20 -rings, 10 C 4 -chains (blank experiment) t=0 ps. t=125 ps. - C 4 reacts with rings to form long acyclic chains - No branching

29 MD NVT-simulation (1500K); 5 C 20 -rings, 10 C 4 -chains and 15 Ni-atoms t=0 to t=125 ps. t=125 to t=750 ps.

30 A closer look at the 750 ps. product - Ni-atoms help create cage-structures ps. product has no internal C-C bonds - Ni-atoms leave ‘finished’ material alone and move away to defect and edge sites - Total simulation time: 4 days on 1 processor - Future work: Co, Fe

31 Metal-catalyzed nanotube growth - Start configuration: 20 C 6 -rings, 5 metal atoms on edge - NVT simulation at 1500K - Add C 2 -molecule every 100,000 iterations Inital configuration

32 - Ni-atoms can grab C 2 - monomers and fuse them as new 6-membered rings

33 Metal-catalyzed nanotube growth Results after 2,000,000 iterations Metal=Ni Metal=Co Metal=Cu No metal -Ni and Co lead to greatly enhanced ring formation. Cu is far less active.

34 Conclusions - ReaxFF has proven to be transferable to transition metals and can handle both complex chemistry and chemical diversity - The low computational cost of ReaxFF (compared to QC) makes the method highly suitable for screening heterogeneous and homogeneous transition metal catalysts