Gas adsorption is a powerful technique for characterizing porous materials in detail. It provides valuable information about surface area and pore size distribution. However, this process requires a thorough understanding of how the material interacts with the adsorbing fluid, including the changes in phase and the impact on the adsorption isotherm—key factors for accurate surface and pore analysis.
The behavior of pore filling depends on the pore size. In micropores (pore width < 2 nm), the filling process occurs continuously. For mesopores (2–50 nm), the process involves gas condensation inside the pores, leading to a first-order gas-liquid phase transition. These differences mean that different models are needed to analyze microporous and mesoporous structures.
Previously, we discussed the capillary condensation theory (BJH) for mesoporous materials and microporous models like HK and SF. These macroscopic thermodynamic methods have limitations, as they cannot unify the analysis of both micropores and mesopores. The BJH method, based on the Kelvin equation, applies well to mesopores but fails for micropores or narrow mesopores. On the other hand, methods like the DR and radius-based approaches focus only on micropores and are not suitable for mesoporous analysis. When a material contains both types of pores, two separate techniques are typically required to extract pore size distribution from the adsorption/desorption isotherms.
Recent studies have shown that the thermodynamic properties of fluids confined in pores differ significantly from those of bulk fluids. This has led to the development of more advanced methods, such as density functional theory (DFT) and molecular simulations (like Monte Carlo and molecular dynamics). These approaches provide a more realistic representation of adsorption at the molecular level, capturing details like density oscillations near solid surfaces or fluid behavior in slit-shaped, cylindrical, or spherical pores.
Compared to traditional macroscopic methods, DFT and MC simulations offer a microscopic view of the adsorption process, allowing for a more accurate description of the fluid's thermodynamic properties within the pores. These methods calculate the equilibrium density distribution of the fluid and consider both fluid-fluid and fluid-solid interactions. Parameters for these interactions are determined by matching macroscopic properties, such as the behavior of nitrogen or argon at low temperatures, and by fitting experimental data from smooth surfaces.
While standard DFT can struggle with accurately modeling the density fluctuations at the solid-fluid interface, especially in narrow pores, non-localized DFT (NLDFT) and Monte Carlo simulations provide more precise results. Figure 1 illustrates the density profile in wedge-shaped mesopores, where coexisting gas and liquid phases are observed. The adsorption layer near the pore walls shows multilayer adsorption, with density decreasing as distance from the wall increases. In larger mesopores, the core region exhibits a uniform density distribution, resembling an unconstrained fluid.
DFT calculates the equilibrium density profile by minimizing the free energy function. This approach considers the potential energy and interactions between fluid molecules and pore walls. One challenge is accurately describing the fluid-fluid interactions, which has led to the development of localized and non-localized DFT methods over the past decade. These advancements continue to improve our ability to model and understand the complex behavior of fluids in porous systems.
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