The gas adsorption method is an excellent method for obtaining comprehensive characterization of porous materials. It can reflect information such as specific surface and pore size distribution. However, this requires a detailed understanding of the adsorption process, including the adsorption and phase change of the porous material to the fluid and its effect on the adsorption isotherm, which is the basis of surface analysis and pore analysis.
The hole width, hole shape and effective adsorption energy are related to the hole filling process. In the case of so-called micropores (according to IUPAC classification, pore width <2 nm), pore filling is a continuous process; while in the case of mesopores (mesopores, pore width is between 2nm-50nm), pore filling is gas in Within the condensation process, it manifests as a first-order gas-liquid phase transfer.
Earlier, we have introduced the capillary condensation theory of mesopore analysis (BJH) and the model of micropore analysis (HK and SF). These are macroscopic thermodynamic analysis methods, and it is impossible to unify micropores and mesopores with the same method. The so-called classic macroscopic thermodynamic concept is based on the assumption of a certain hole filling mechanism. Methods based on the Kelvin equation (such as the BJH method) are related to capillary condensation in pores, so they can be applied to mesopore distribution analysis, but they are not suitable for the description of micropore filling, even for narrow mesopores. Incorrect. Other classical theories, such as the Dupining-Landkovic (DR) method, and radius inspection methods (such as HK and SF methods) are only dedicated to describing micropore filling and cannot be applied to mesopore analysis. If the material contains both micropores and mesopores, we must at least have two different methods to obtain the pore size distribution map from the adsorption / desorption isotherm. In addition, the accuracy of the macroscopic thermodynamic method is limited because it assumes that the fluid in the pore is a free fluid with similar thermophysical properties. Recent theoretical and experimental work has shown that the thermodynamic properties of confined fluids are quite different from those of free fluids, and at least displacements at critical points, freezing points and triple points will occur. Therefore, more advanced aperture analysis methods such as density function theory were proposed. Non-localized density function theory (NLDFT) and computer simulation methods (such as molecular dynamics and Monte Carlo simulation) have developed into effective methods for describing the adsorption and phase behavior of non-uniform fluids restricted by porous materials. These methods can accurately describe the structure of some simple restricted fluids, such as the oscillation density distribution near the solid surface, or describe the structure of fluids that are restricted to some simple geometric shapes such as slit holes, cylindrical and spherical. Specific surface and pore size analysis.
Compared with those macro research methods, density function theory (DFT) and molecular simulation methods (MC, Monte Carlo simulation methods) are molecular dynamics methods. They not only provide a microscopic model of adsorption but also more realistically reflect the thermodynamic properties of the fluid in the pores. Those theories based on statistical mechanisms reflect the macroscopic nature of molecular behavior. Therefore, in order to achieve a more objective description of the adsorption phenomenon and a more comprehensive and accurate pore size analysis, a bridge must be established between the molecular level and the macroscopic exploration, and the DFT and MC simulation methods of non-uniform fluids are exactly at this point. These methods consider and calculate the equilibrium density distribution of the fluid adsorbed on the surface and the fluid in the pores, from which the adsorption / desorption isotherm, adsorption heat, neutron scattering mode and transfer characteristics of the model system can be derived. The density distribution is obtained by calculating the fluid-fluid and fluid-solid interactions between molecules through MC simulation and DFT theory. The parameters of fluid-fluid interaction are determined by regenerating their macroscopic overall properties (such as the properties of nitrogen and argon at low temperatures). The parameters of the solid-fluid interaction are obtained by calculating the fitting isotherms of standard nitrogen and argon fitting on a smooth surface.
The DFT method cannot produce a strong fluid density distribution vibration characteristic at the solid-fluid interface, which leads to an inaccurate description of the adsorption / desorption isotherms, especially the inaccurate pore size analysis of narrow micropores. Conversely, non-localized DFT (NLDFT) and Monte Carlo computer simulation techniques provide more accurate fluid structures in narrow pores. Figure 1 shows the density distribution of such characteristic oscillations. The density distribution diagram indicates that the gaseous state and liquid state of the fluid coexist in a wedge-shaped mesopore (fracture hole). The density of coexisting gas (spherical) and liquid (square) is a function of the distance of the pore wall. The adsorption layer close to the pore wall is reflected as multi-layer adsorption, and the density decreases as the distance from the pore wall increases. The density distribution diagram in Figure 1 clearly indicates that pore condensation is inherently present in the core area of ​​the pores, which results in seemingly unconstrained core liquid in larger mesopores (here, the pore width is 20 molecular diameters), just like It is the same in the core area of ​​the hole; and in the middle is the trend of density distribution with essentially no fluctuation.
The DFT method calculates the equilibrium density distribution map for all positions in the hole, which is obtained by minimizing the free energy function. The pore system that is in equilibrium with the mobile phase (that is, the state in which the adsorption experiment is performed) has a huge potential energy or free energy, which constitutes a condition for attraction or repulsion of fluid-fluid interaction and fluid-pore wall interaction. The difficulty of this method is to establish a correct description of the fluid-fluid interaction. Because of this, people have adopted different methods of DFT research in the past decade. The so-called localized DFT (LDFT) and non-localized DFT method.
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