Bayesian estimation of pore size distribution in porous carbon using a novel GCMC-based kernel incorporating surface roughness - Shotaro Hiraide; Naruaki Fuse; Kohei Yamamoto; Hideki Tanaka; Kazuyuki Nakai; Satoshi Watanabe (Carbon Trends)
Porous carbons play vital roles in adsorption-based applications, and their pore size distributions (PSDs) are crucial for performance. Kernel-based inversion of adsorption isotherms is the standard route to obtain PSDs, yet it still faces technical limitations. In this study, we address these issues by combining grand canonical Monte Carlo (GCMC) simulation with a Bayesian statistical framework. GCMC provides a thermodynamically rigorous description of adsorption, surpassing classical density functional theory (DFT). Building on these simulations, we construct a new kernel, termed rGCMC (roughness-integrated GCMC), which embeds energetic and geometric heterogeneities via patchwise offsets in a slit-pore model to effectively capture surface roughness. In parallel, we introduce a Bayesian inference scheme for PSD estimation. Comprehensive tests with synthetic data featuring known PSDs, atomistic carbon models, and real porous carbons reveal several key findings. Our Bayesian approach with second-order regularization (B2) produces PSD estimates accompanied by credible intervals and automatically selects the optimal regularization parameter—features that are lacking in the deterministic Tikhonov method commonly used for PSD estimation. The integration of the rGCMC kernel with the Bayesian method (rGCMC-B2) produces plausible PSDs without artificial valleys often appearing near 1 nm in traditional flat-wall kernels. Additionally, rGCMC-B2 exhibits enhanced performance relative to the widely utilized quenched solid DFT (QSDFT), particularly for estimating larger pore sizes. Collectively, these advancements significantly enhance both the accuracy and interpretability of PSD estimation, thereby facilitating more rational design of porous carbons for various applications.