Atomic Structure and Pore Size Distribution in Nanoporous Carbon

We study the structural and mechanical properties of nanoporous (NP) carbon materials by extensive atomistic machine-learning (ML) driven molecular dynamics (MD) simulations. To this end, we retrain a ML Gaussian approximation potential (GAP) for carbon by recalculating the a-C structural database of Deringer and Cs\'anyi [Phys. Rev. B 2017, 95, 094203] adding van der Waals interactions. Our GAP enables a notable speedup and improves the accuracy of energy and force predictions. We use the GAP to thoroughly study the atomic structure and pore-size distribution in computational NP carbon samples. These samples are generated by a melt-graphitization-quench MD procedure over a wide range of densities (from 0.5 to 1.7~g/cm$^3$) with structures containing 131,072 atoms. Our results are in good agreement with experimental data for the available observables, and provide a comprehensive account of structural (radial and angular distribution functions, motif and ring counts, X-ray diffraction patterns, pore characterization) and mechanical (elastic moduli and their evolution with density) properties. Our results show relatively narrow pore-size distributions, where the peak position and width of the distributions are dictated by the mass density of the materials. Our data allow further work on computational characterization of NP carbon materials, in particular for energy-storage applications, as well as suggest future experimental characterization of NP carbon-based materials.