NLDFT (Non Localized Density Functional Theory) and GCMC (Grand Canonical Monte Carlo method) from the computer simulation have been developed in recent years as the evaluation method of pore size distribution of porous materials. NLDFT/GCMC method well describe the adsorption of adsorptive to the porous materials and are useful for micropore and mesopore analysis. NLDFT/GCMC method can analyze from micropore to mesopore size distribution as a unified theory, which is one of big advantages compared to other pore size analysis theories. Also, the accuracy of micropore size analysis is improved by these theories.

The feature of NLDFT/GCMC method is that they can describe the gradual density change of adsorbate near the pore wall which the classical theory (Kelvin equation) only assumed the density to be the same as the liquid state.

Density profile curve in slit shape pore

As the graph shows, the adsorbate density is high near the solid surface and is changed with some frequency due to the interaction between the surface atoms and adsorbate. The 1^{st} and 2^{nd} adsorption layers are established due to the increasing pressure, and by the time 4^{th} layer is established, there is very weak interaction from the pore wall atoms. The 4^{th} layer is analyzed to be in the bulk liquid density due to the adsorbate molecule interaction.

In NLDFT/GCMC method, it requires to select the pore structure (Slit/Cylindrical), and the adsorptive and adsorbent parameters (N_{2}/Ar/CO_{2}, Carbon/Oxygen). The theoretical adsorption isotherm is created by using these chosen parameters.

Simulated isotherm (Cylindrical pore model)

As shown in the graph, the condensation pressure is increased with the pore size. In the simulation, Type I isotherm is shown in the microporous range and Type IV isotherm is shown in the mesoporous range. The change of isotherm according to the pore size is well reproduced. The interesting point is that the simulated isotherm is created when the pore size is smaller than the gas molecule size, and the relative pressure to condense is higher than the one of the larger pore size. This means that if the gas molecular size is close to the pore size, the gas molecules can only adsorb into the pore at higher pressure. Another interesting point is that the simulation shows that above a few nm pore size, the monolayer adsorption is established first, and then, the condensation in the pore occurs. These phenomena are not expressed in the classical theories such as Kelvin equation and other potential theories. This is the reason why NLDFT/GCMC method is believed to be the better theory for expressing the adsorption state on materials.

The pore size distribution for slit shape pore is calculated from integrating the assumed pore size distribution f(H) and theoretical isotherm ρ(P, H) which is called Integrated Adsorption Equation (IAE).

The software calculates the pore size distribution curve by fitting the IAE isotherms to the experimental ones and by minimizing the deviation.

One important thing about NLDFT/GCMC theory is that other classical pore size analysis theories calculate the pore size distribution directory from the experimental isotherm, and from this calculation, the analysis result is always the same. On the other hand, NLDFT/GCMC theory assumes the pore size distribution and obtains the IAE isotherm first, and then, fit the IAE isotherm to the experimental isotherm. Therefore, it is possible that the analysis result is changed due to the software fitting algorism. Because of this behavior, it is recommended to check the validity of analysis result by comparing the fitting result of IAE isotherms and experimental ones, and also, by using other experimental information (TEM, XRD, and others). To be more specific, if there is no information about the pore structure of the material, use the classical method. If the pore structure of the material is known, and also, it fits to the assumption of NLDFT/GCMC theory well, it is better to use NLDFT/GCMC theory. The graphs show the Ar isotherm (87K) of ZSM-5 and MCM-41 mixture (3 to 1 ratio) and the pore size distribution obtained from NLDFT.

Adsorption isotherm and pore size distribution from NLDFT theory of ZSM-5 and MCM-41 mixture

- Technical Information
- Seminar on Adsorption
- Adsorption
- What is adsorption?
- Adsorption Isotherm
- Method of Adsorption Amount Measurement
- Measurement of Free Space
- Ultimate Pressure in Gas Adsorption Measurement
- Specific Surface Area
- Specific Surface Area and Particle Size
- BET Theory
- Method of Specific Surface Area Measurement for Microporous Materials (Type I Isotherm)
- Method of Small Surface Area Measurement by Kr Adsorption
- Pore Size Dictribution
- Definition of Pore Size
- Method of Pore Size Distribution Measurement
- Adsorption Isotherm and Pore Size
- Micropore Analysis
- Mesopore and Macropore Analysis
- NLDFT/GCMC Method
- Hysteresis in Adsorption and Desorption Isotherm
- Expression of Pore Size Distribution
- Literature

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