D-BJH: The Intrinsic Model for Characterizing the Pore Size Distribution of Porous Materials.

A novel approach, the differential Barrett-Joyner-Halenda model (D-BJH), is proposed to address the limitations of the traditional BJH model in determining the pore size distribution (PSD). This method integrates multilayer adsorption and capillary condensation processes using advanced numerical techniques, notably, a Galerkin-based framework for solving the differential BJH equations. The D-BJH model offers a precise analytical framework, establishing itself as a benchmark in adsorption theory. It enables accurate PSD calculations and provides robust theoretical support for interpreting adsorption isotherms. Additionally, a simplified D-BJH method allows for direct point-by-point PSD calculation, reducing computational complexity and eliminating cumulative errors inherent in traditional methods like BJH, DH, CI, and VBS. The D-BJH model demonstrates that PSD is directly related to the differential function of the isotherm and pore size concerning relative pressure. Comparative analyses with BJH, DH, and NLDFT models show that D-BJH effectively explains fundamental adsorption mechanisms, such as the "spurious peak" observed in desorption branches. This work expands the applicability of the BJH model, proving that both the D-BJH model and its simplified method are accurate and comprehensive for characterizing the pore structures of microporous and mesoporous materials.