Molecular Modeling of Microporous Carbon Electrode Material
Microporous materials / Carbon electrode / CO2 adsorption / Molecular Dynamic simulation / Monte-Carlo simulation
Nanoporous materials are used in a variety of applications and market opportunities are still expanding. Important applications areas are, for example, gas storage, clean energy production and storage, catalysis and filtration . Carbide-derived carbons (CDCs) form a class of porous materials with exceedingly interesting properties. Their specific surface area is very high and the porosity can be very well controlled and fine-tuned . Experimentally, CDCs are typically synthesized by treating metal or metalloid carbides with halogens, commonly chlorine. The carbon matrix rearranges through the etching process in a microporous structure containing mainly sp2-hybridized carbon. CDCs posses an amorphous structure. The structure is a very fundamental property which in turn affects other properties, like for example reactivity. Such systems can be difficult to characterize completely only by experimental means. Computational approaches can provide valuable insights and help to gain a fundamental understanding of processes at the nanoscale. Prerequisite is the availability of a suitable model of the amorphous structure. In this case study, we show how to generate a realistic model of microporous carbon using molecular dynamics (MD) simulations.
Starting from a SiC carbide precursor, we have applied a pseudo mimetic approach using quenched molecular dynamics (QMD) similar to the methodologies described in Refs. [3-5]. SiC exists in different polytypes. 4H-SiC belongs to the most important one and was used as starting structure for the simulations. The crystal structure was build using MAPS  according to the parameters published by Melinon . Based on the unit cell, a 20x20x6 supercell was created. MD simulations were performed using MAPS LAMMPS plugin together with the SiC Tersoff potential . After a 50 ps NVT MD simulation at room temperature, the structure was equilibrated over 200 ps at 2500 K in the NPT ensemble. Afterwards, the system was cooled down back to room temperature over 1 ns in an NPT simulation. Then, all silicon atoms were removed and the carbon matrix was equilibrated over 200 ps in the NVT ensemble. Additional simulations were performed for confirming the validity of the chosen approach: (1) The simulation set-up was varied to study the influence of simulation parameters on the final structure. (2) The cell size was increased for validating that the system size was chosen large enough for relaxation of the carbon matrix into a porous structure. (3) The influence of the initial structure was investigated by using the crystal structure of two other common polytypes (6H-SiC and 3C-SiC) for building the simulation box.
Furthermore, we have simulated CO2 adsorption isotherms using Monte Carlo (MC) methods for comparison with experimental data. MAPS Towhee plugin was used for this purpose. Parameters for CO2 were taken from Ref.  and for carbon from Ref. . A simulation box containing 600 CO2 molecules was pre-equilibrated at 273 K and various pressures in the range of 3.48 – 98.1 kPa by running NPT MD simulations for 500 ps before performing 10,000,000 NPT MC moves for final equilibration at 273 K and the respective pressure. For the calculation of the isotherms, the number of adsorbed CO2 molecules was obtained from a series of Gibbs-NPT MC simulations at different pressures each consisting of 1,000,000 steps.
For analyzing the results, MAPS analysis functionality, Zeo++ , and polypy  were used.
Results and Discussion
1. Modeling Porous Carbon Structure
The structure of microporous CDC was obtained by running a set of MD simulations on a SiC-based simulation cell mimicking the experimental procedure. After heating and quenching, Si was removed and the carbon matrix was allowed to equilibrate to form the porous structure. The final structure is shown in Fig. 1.
Figure 1: Modeled structure of microporous carbon. Carbon atoms are shown in CPK representation.
The maximum pore size was obtained as 9.7 Å and the pore size distribution ranges between 3.2 Å and 9.7 Å demonstrating that we have indeed created a microporous structures, i.e. the pore size is < 20 Å by definition. The values are in line with experimental data . The apparent density was found to be 0.97 g/cm3 which also agrees well with experimental findings . For estimating the hybridization, the number of neighbors was determined for each carbon atom while taking the local geometry into account as well which means that carbon atoms with two or three bond partners and enclosing an angle of 120°±20° were considered as sp2-hybridized and carbon atoms with three or four bond partners and a deviation of 10° or more from planarity were counted as sp3-hybridized. In this way, 84 % of the carbon atoms were determined to be sp2-hybridized and 16 % sp3-hybridized, which agrees nicely with experimental results obtained from EELS spectroscopy . The ring size analysis revealed that the majority of carbon atoms (65 %) forms 6-membered rings, 2 % 5-membered rings, and 33 % are incorporated in 7-membered rings. Thus, the structural analysis shows an overall good agreement with experimental data.
Additional simulations were performed to validate the model structure further. The carbon matrix was equilibrated for only 200 ps. In order to check the convergence of the simulation, the simulation time was extended to 10 ns. The maximum pore size reduced only slightly by about 0.3 Å. For analyzing the stability of the porous structure, a 30 ns MD run was performed in the NPT ensemble so that the volume was allowed to relax. The simulation cell did not collapse as one could have expected, but maintained the porous structure. The density increased in the final structure to 1.1 g/cm3 and the maximum pore size reduced to 8.9 Å demonstrating that the simulation set-up is capable to produce stable microporous structures. Variations of the simulation parameters such as quench rate or temperature had no or only minor influence on the structural properties. However, we observed a rather large impact when removing the Si atoms right from the beginning of the simulation protocol. Such a more or less purely theoretical approach can give additional insights and allows to investigate aspects that are experimentally not accessible. In this case, we can gain information whether the structure depends only on the carbon matrix or on the metal or metalloid atom as well. A larger maximum pore size of about 12.7 Å was found and the amount of sp2 hybridization was reduced in favor of sp3 hybridization. This approach thus shows that the presence of the metal atoms influences the final carbon structure and can be applied for tuning the model properties.
To evaluate if the initially chosen cell size is large enough to reflect the porous structure, a 2x2x2 supercell was built based on the original simulation box. Due to the larger cell size, we allowed the system to equilibrate over 5 ns in the NVT ensemble and over 10 ns in the NPT ensemble. The maximum pore size increased to 11.4 Å after NVT equilibration and reduced over NPT equilibration to 9.7 Å. The ring size distribution remained basically the same and the amount of sp2-hybridized carbon atoms reduced slightly by 9 % in favor of sp3 hybridization. However, the changes are rather moderate compared to the increase of the system size and further confirm the validity of our model.
Finally, for investigating the influence of the polytype on the structure, simulations were performed for a 6H-SiC-based and 3C-SiC-based cell. A significant influence on the final porous structure was not observed. Only in case of 3C-SiC, a somewhat smaller maximum pore size was found (9.0 Å).
2. CO2 Adsorption Isotherms
For additional comparison with experimental data, we simulated CO2 adsorption isotherms. Apart from the pure carbon backbone, also partially oxidized structures were considered containing 2 % and 5 % oxygen, respectively. The oxidized structures were created by adding oxygen in form of C=O groups at sp2 hybridized carbon atoms via scripting with MAPS. Fig. 2 shows the final structure of carbon containing 2 % oxygen with adsorbed CO2 molecules for a pressure of 98 kPa.
Figure 2: Partially oxidized porous carbon with adsorbed CO2 molecules obtained for a pressure of 98 kPa. Color code: carbon – black, C=O groups -orange, CO2 molecules – magenta.
The calculated adsorption isotherms are compared with the experimental measurement in Fig. 3.
Figure 3: CO2 adsorption isotherms for carbon models with different oxygen content. Experimental data  refer to TiC, while computed isotherms were obtained for carbon models based on 4H-SiC.
Overall, the simulated isotherms are in good accordance with the experimental findings. It should be noted the experimental data refer to TiC-based CDC, results for SiC-based CDC are, however, expected to be similar. The best agreement is found for the structure containing 2 % oxygen which is in line with experimental findings from XPS spectroscopy. The good agreement supports further the quality and validity of our structure model and confirms the chosen modeling approach.
We have presented a MD-based simulation approach for modeling the structure of microporous carbon. The structural properties were analyzed and compared to experimental results. In addition, CO2 adsorption isotherms were calculated for the pure carbon backbone and partially oxidized structures. Overall, a good agreement between simulations and experiment was found and the best agreement regarding the isotherms was obtained for the structure containing 2 % oxygen.
The work was done as part of the AktivCAPs project (grant no. 02E2-ESP077), a project supported by “Förderinitiative Energiespeicher” funded by the German Ministry of Education and Research. The responsibility for the contents of this publication lies with the author.
We would like to thank our collaborators Prof. Dr. B. Etzold and J. Landwehr at the Technical University Darmstadt for providing experimental data for comparison.
- Lu, G. Q. & Zhao, X. S., in: Series on Chemical Engineering: Volume 4, Nanoporous Materials: Science and Engineering, Lu, G. Q. & Zhao, X. S., Eds., Imperial College Press, 2004, Chapter 1: Nanoporous Materials - An Overview, 1-12.
- Chmiola, J.; Yushin, G.; Gogotsi, Y.; Portet, C.; Simon, P. & Taberna, P. L., Science, 2006, 313, 1760-1763.
- Palmer, J.; Llobet, A.; Yeon, S.-H.; Fischer, J.; Shi, Y.; Gogotsi, Y. & Gubbins, K., Carbon, 2010, 48, 1116 – 1123.
- Shi, Y., J. Chem. Phys, 2008, 128, 234707–234711.
- Schweizer, S.; Chaudret, R.; Low, J.; Subramanian, L. Comput. Mater. Sci., 2015, 99, 336 – 342.
- MAPS, Version 3.4, Scienomics, Paris, France, 2015, http://www.scienomics.com/.
- Melinon, P., in: Silicon Carbide - Materials, Processing and Applications in Electronic Devices, Mukherjee, D. M., Ed., InTech, 2011, Chapter: SiC Cage Like Based Materials, 23–52.
- Tersoff, J., Phys. Rev. B 1989, 39, 5566–5568.
- Harris, J. G.; Yung, K. H., J. Phys. Chem., 1995, 99, 12021–12024.
- Cheng, A.; Steele, W. A., J. Phys. Chem., 1990, 92, 3858–3866.
- Martin, R. L.; Smit, B. & Haranczyk, M., J. Chem. Inf. Model., 2012, 52, 308-318.
- polypy, 2014, http://sourceforge.net/projects/polypy/.
- Gogotsi, Y.; Nikitin, A.; Ye, H.; Zhou, W.; Fischer, J. E.; Yi, B.; Foley, H. C. & Barsoum, M. W., Nat. Mater., 2003, 2, 591-594.
- Urbonaite, S.; Wachtmeister, S.; Mirguet, C.; Coronel, E.; Zou, W.; Csillag, S.; Svensson, G.
- Carbon, 2007, 45, 2047 – 2053.
- Experimental data were kindly provided by the group of Prof. Dr. B. Etzold, Technical University Darmstadt.