Nanoporous carbons are an emerging class of materials with important applications in energy storage. In particular, the ability of graphitic carbons to intercalate ions is exploited in commercial Li-ion batteries where the anode is (typically) made of graphite and Li ions become electrostatically bound to the carbon host as the battery is charged: electrons are stored in the graphitic matrix as part of an electron-ion pair. When the battery discharges, these electrons are injected into the external circuit (providing power) and the Li ion is released into the electrolyte traveling to the cathode, usually made of a transition-metal oxide, where it also intercalates. This cycle repeats itself as the battery is charged and discharged, with the Li ion traveling back and forth between the anode and cathode.
Li is relatively scarce on the Earth’s crust and the mid-to-long term supply of Li needed to cover the rapidly increasing demand for Li-ion batteries is in jeopardy. The Li-intercalation process could in principle also be applied to more Earth-abundant ions, like K and Na, thus providing a reduction in the cost of ion batteries and ensuring future supply of raw materials. These are required to scale up the use of ion batteries and to make it affordarble for domestic and industrial applications. Unfortunately, Na and K do not intercalate in graphite as favorably as Li does, with Na-intercalated graphite deemed thermodynamically unstable, and in all cases incurring strong dimensional changes between charge and discharge. These dimensional changes pose risks to the mechanical stability of the material and the device containing it, with the associated safety concerns.
Nanoporous carbons are an obvious alternative to graphite for ion intercalation because the pores, interstitial voids between disordered graphitic planes, can be made within a range of sizes, all larger than the usual interplanar spacing in graphite. Thus, nanoporous carbons can in principle accommodate larger ions, including Na and K, which motivates their study and structural characterization. However, as is often the case with amorphous and disordered materials, experimental characterization can be challenging, since common characterization techniques employed to characterize crystals cannot be used. In the case of nanoporous carbons, experimental characterization of pore sizes and shapes is very complicated.
With this background in mind, we decided to study the microscopic structure and mechanical properties of nanoporous carbon using state-of-the-art atomistic modeling techniques based on machine learning interatomic potentials. These techniques provide, for the first time, the required combination of accuracy and computational efficiency to study nanoporous carbons where the size of the simulation box does not constrain the size of the pores that can be studied. Our results are now published in Chemistry of Materials:
Y. Wang, Z. Fan, P. Qian, T. Ala-Nissila, M.A. Caro; Structure and Pore Size Distribution in Nanoporous Carbon. Chem. Mater. (2022). Link to journal’s website. Open Access 
PDF from the publisher.
We started out by training a Gaussian approximation potential (GAP) for carbon based on the database developed by Deringer and Csányi [Phys. Rev. B 95, 094203 (2017)]. This new potential [10.5281/zenodo.5243184] achieves better accuracy and speed than the earlier version and can accurately predict the defect formation energies in graphitic carbon.
Getting the relative formation energies right is critical for obtaining the correct topology of the complicated network of carbon rings within curved graphitic sheets. In particular, the relative abundance of 5-rings and 7-rings will determine the curvature and thus pore morphology in the material.
With this new potential, we carried out large-scale simulations of graphitization with the TurboGAP code developed in our group, using a melt-graphitize-anneal protocol, akin to that by de Tomas et al. [Carbon 109, 681 (2016)], but now with larger systems (more than 130,000 atoms) and the accuracy provided by the new GAP.
With these simulations we managed to generate realistic nanoporous carbon structures within a wide range of mass densities (0.5 to 1.7 g/cm3), and characterized in detail their short-, medium- and long-range order. For instance, these simulations reveal hexagonal motifs to be the dominant structural block in these materials (as expected) followed by 5-rings, then 7-rings and, in much smaller quantities, larger and smaller ring structures, with almost no density dependence for the most common motifs.
The pore sizes, the main target of this study, show clearly defined unimodal distributions determined by the overall mass density of the material. This means that the pore sizes and morphologies are relatively homogeneous for a given sample.
Finally, a useful result of our study is a library of nanoporous carbon structures freely available to the community and amenable to future studies on the properties of this interesting and important class of carbon materials.
This study would have not been possible without the hard work and dedication of our PhD student Yanzhou Wang and the help of the other coauthors, as well as the support provided by the Academy of Finland and the CPU time and other computational resources provided by CSC and Aalto University’s Science IT project.
