Unraveling the Effects of Pore Size and Diamine Functionalization on CO2 Diffusion in Metal-Organic Frameworks using Machine-Learning Interatomic Potentials

M2(dobdc) (dobdc4- = 2,5-dioxido-1,4-benzenedicarboxylate; M = Mg, Mn, Fe, Co, Ni, Cu, Zn), commonly referred to as M-MOF-74, and its variants have been extensively studied for their outstanding CO2 capture performance. In particular, diamine-functionalized M2(dobpdc) (dobpdc4- = 4,4’-dioxidobiphenyl-3,3’-dicarboxylate), an extended analogue of M2(dobdc), has demonstrated exceptional CO2 selectivity under humid conditions owing to its unique cooperative CO2 capture mechanism. Despite these advantages, its CO2 diffusion behavior—a critical parameter for practical applications—remains poorly understood. Here, we systematically investigate the effects of pore size and diamine functionalization on CO2 diffusion in Mg2(dobpdc). By employing machine-learning interatomic potentials (MLPs), we achieve quantum-level accuracy within classical molecular dynamics (MD) simulations, enabling the examination of large-scale systems comprising over 4,000 atoms on nanosecond timescales. To elucidate the CO2 diffusion behavior, we compare Mg2(dobpdc) with its smaller-pore counterpart Mg2(dobdc) and larger-pore analogue Mg2(dotpdc) (2,5-dioxido-1,4-terephthalate). Four distinct diamines–m-2 (N-N'-methylethylenediamine), m-2-m (N,N’-dimethylethylenediamine), e-2 (N-ehylethylenediamine), and e-2-e (N,N’-diethylethylenediamine)–are appended to Mg2(dobpdc) and Mg2(dotpdc) to evaluate their influence on CO2 diffusion. The developed MLPs exhibit root mean square errors (RMSEs) of less than 5 meV/atom for energies and 0.3 eV/Å for forces, compared to density functional theory (DFT) calculations, with MLP-optimized lattice parameters deviating from DFT values by no more than ±2%. For bare MOFs, our MLPs accurately predict CO2 binding enthalpies and the localized CO2 feature near open Mg sites, consistent with experimental observations. This results in low diffusion coefficients (2.0 x 10-11 m2/s – 3.1 x 10-10 m2/s) at low CO2 uptake. For Mg2(dobpdc) and Mg2(dotpdc), which possess larger pore sizes than Mg2(dobdc), the diffusion coefficients increase with increasing CO2 uptake. This trend is attributed to the saturation of Mg sites, which reduces interactions between free CO2 molecules and Mg ions. At one CO2 per Mg, the diffusion coefficients are calculated as 2.1 x 10-9 m2/s and 3.7 x 10-9 m2/s for Mg2(dobpdc) and Mg2(dotpdc), respectively. Diamine functionalization further enhances CO2 diffusion (0.8 x 10-9 m2/s ~ 13.2 x 10-9 m2/s) by reducing access to open Mg sites and introducing complex interactions between diamine units and CO2 and between ammonium carbamate units and CO2. However, at high CO2 loadings, steric hindrance caused by functionalized diamines decreases the diffusion coefficients (1.6 x 10-9 m2/s ~ 6.1 x 10-9 m2/s), particularly in Mg2(dobpdc) due to its smaller pore size relative to Mg2(dotpdc). These findings provide valuable insights into the interplay between pore architecture, functionalization, and CO2 diffusion in bare and diamine-functionalized MOFs. Our results not only deepen the understanding of CO2 capture mechanisms but also provide a framework for designing next-generation materials optimized for carbon capture applications.