Density Functional Theory Simulation of Rhodium Nanoframes and Carbon Nanotube–Graphene Pillars | Learning | Beckstein Lab

As part of his applied project for his Professional Science Master’s in Nanoscience at ASU, Ben Folsom constructed theoretical models for recently synthesized hollowed rhodium nanoframes¹ and covalently bonded carbon nanotube–graphene pillars² based on the TEM images provided in the source publications. These models were used to test whether a combination of the two systems would lead to physisorbtion. Modeling and stability testing was performed in Quantumwise’s ATK³ using the REBO⁴ and EMT⁵ force fields for the pillars and frames, respectively. The density functional theory (DFT) package SIESTA⁶ was used for additional relaxations and calculating the combined frame–pillar system energies along several z-displacement points.

Z-Displacement Mapping. The frame–pillar system at 3 ? separation. A transparent grey isosurface is shown for an electron density of ? = 0.031 eV/?.

Modeling Pillars

Several factors were considered in re-creating Zhu’s experimental results.² These included step height distance in the tube–graphene interface region, chiralities of the tubes, and the structure of the truncated outer “sheath”.
When relaxed with SIESTA, the junction area steps were found to have an interlayer structure resembling the sp3 bonding seen with adatom-covered graphite surfaces.⁷ Though all the TEM images of the tube diameters matched a zigzag (M,0) chirality, conductive (3*x,0) and semiconductive (3*x1,0) chiralites showed a marked difference in response to uniaxial bending in classical MD simulations of a 0.1 ns duration.

Carbon Nanotube–Graphene Pillars. (a) A (12,0) carbon nanotube–graphene pillar. (b) TEM image of the NGP base region, seen from below through a SiO2 substrate. Image taken from Zhu, Y. et al. Nat. Commun. 3, 1225 (2012). Copyright 2012 Macmillan Publishers. (c) (12,0) pillar model as seen from above. Base graphene layer is omitted.

Modeling Rhodium Nanoframes

The slight concavity and bulbous edges of the rhodium frames were the primary characteristics we attempted to re-create. Originally, models were constructed using structures derived from {100} face-centered cubic facets, since this is where rhodium is deposited experimentally before corrosion etching (from a bromide-ion–coated palladium cube with only said facets exposed). None of these models were stable, however, and it was found that frames derived from a simple cubic structure relaxed to a shape closely resembling the dimensions of those seen in the TEM images.

Rhodium Nanoframes. (a) through (d): TEM images of the etched rhodium nanoframes. Image taken from Xie, et al. Angew. Chem. Int. Ed. 51, 102–10270 (2012). Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. (e) through (h): Candidate models for the rhodium nanoframe. Only (g) was stable.

Energetics of Nanoframe Positioned along CNT Pillar

Self-consistent field calculations of interaction energies were taken by centering the frame over the pillar then lowering it incrementally until the frame reached covalent-bonding distance from the pillar’s step edges. Each of these measurements required 1422 CPU hours (20 self-consistency cycles * 256 cores * 1000 seconds per cycle) on XSEDE’s Stampede supercluster⁸, reaching the project’s maximum allocation. Further calculations would be expected to reach <1 eV precision at 3000 CPU hours each. Though the resulting error margins leave the likelihood of binding affinity ambiguous, all benchmarking and test calculations showed a trend of the total energy lowering consistently on a large scale (400–800 eV) to a point of minimal fluctuation (± 30 eV). As the final calculations were cut off in this lowering phase, it is expected that more precise calculations would trend toward the lower error limits.
An energy maximum was observed at the point where the bottom edges of the frame were centered around the pillar’s outer “sheath”, indicating the chosen frame and pillar were too tight a fit to be energetically favorable for binding. An energy minimum was observed at the point where the nearest separation of a rhodium and carbon atom was ~3.5 ?, which agrees with other DFT studies involving graphene adsorption.^9,10 The complete project report is available as a PDF download.

Results for Nanoframe-Pillar System. Interaction energies for the nanoframe–pillar system along x- and z-displacements.

References

1. ^a Xie, S. et al. Synthesis of Pd-Rh Core-Frame Concave Nanocubes and Their Conversion to Rh Cubic Nanoframes by Selective Etching of the Pd Cores. Angew. Chem. Int. Ed. 51, 10266–10270 (2012).
2. ^{a b} Zhu, Y. et al. A seamless three-dimensional carbon nanotube graphene hybrid material. Nat. Commun. 3, 1225 (2012).
3. ^a ATK ToolKit. 12.2. 0. QuantumWise A/S.
4. ^a Brenner, D. W. et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter 14, 783 (2002).
5. ^a Jacobsen, K. W., Norskov, J. K. & Puska, M. J. Interatomic interactions in the effective-medium theory. Phys. Rev. B 35, 7423–7442 (1987).
6. ^a Soler, J. M. et al. The SIESTA method for ab initio order-N materials simulation. J. Phys. Condens. Matter 14, 2745 (2002).
7. ^a Odkhuu, D., Shin, D., Ruoff, R. S. & Park, N. Conversion of multilayer graphene into continuous ultrathin sp3-bonded carbon films on metal surfaces. Sci. Rep. 3, (2013).
8. ^a Gordon, S. I. Advancing Computational Science Education through Xsede. Comput. Sci. Eng. 15, 90–92 (2013).
9. ^a Hamada, I. & Otani, M. Comparative van der Waals density-functional study of graphene on metal surfaces. Phys. Rev. B 82, 153412 (2010).
10. ^a Amft, M., Sanyal, B., Eriksson, O. & Skorodumova, N. V. Small gold clusters on graphene, their mobility and clustering: a DFT study. J. Phys. Condens. Matter 23, 205301 (2011).