Modification of 2D Graphene Membranes for Biogas Enrichment Using Machine-Learning Force Fields

Abstract

The present project explores the use of grazynes, two-dimensional (2D) carbon allotropes nanoengineered with nanopores, as an innovative solution for separating CO₂ and CH₄ in biogas. This is achieved by performing substitutions of the hydrogen atoms originally located at the pore sites with different halogens (F, Cl, and Br). The system is assessed through theoretical simulations using Density Functional Theory (DFT), employing the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional, and including dispersive interactions via the Grimme D3 method (PBE-D3). The analysis focused on the diffusion of CO₂ and CH₄ through the pores of various halogenated grazynes. Adsorption energies and penetration energy barriers for both molecules were calculated, revealing that CO2 exhibits low adsorption and diffusion barriers, while CH₄ shows also low adsorption energies, but with significantly higher barriers. This implies that fluorinated grazynes are promising candidates for biogas upgrading. However, chlorine and bromine substitutions increase the atomic radius at the pore, reducing permeability and making these materials unsuitable for gas separation. Subsequently, diffusion rate constants were computed using Transition State Theory (TST), confirming that only fluorinated grazynes present large enough rate constants (k), indicating effective gas permeation, while chlorinated and brominated grazynes yield values close to zero, highlighting their poor performance as separation membranes. Thus, CO₂ could be largely selectively separated when using defective [1],[2]{2}-tetrafluorograzyne, specially when goes through various penetration cycles. The [1],[2]{2}-fluorograzyne and [1],[2]{2}-o-difluorograzyne were subjected to further study via Molecular Dynamics (MD) simulations using Machine-Learning Force Fields (ML-FF). Although the force field exhibited low training errors, the MD trajectories displayed chemically unrealistic behaviour, e.g. bent CO₂, implying that the model had not been exposed to a sufficiently diverse training set. Thermodynamic plots showed a sudden increase in temperature and energy during the simulation, which confirms that the system adopted unrealistic atomic configurations. Therefore, the force field must be trained with more data to ensure accurate and reliable MD-MLFF results.