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Determination of specific surface area and pore size distribution by isothermal adsorption and desorption of nitrogen - Master's thesis - Dissertation
The six types of adsorption isotherms are commonly referenced in many scientific textbooks. The first five fall under the BDDT classification, introduced by Brunauer, Deming, Deming, and Teller. These researchers categorized a wide range of isotherms into five distinct types. The sixth type, known as the Sing isotherm, is also widely recognized. Each type has its own characteristic shape and interpretation. In general, an adsorption isotherm can be visualized with relative pressure on the x-axis and nitrogen adsorption amount on the y-axis. The x-axis is typically divided into three regions: low pressure (0.0–0.1), medium pressure (0.3–0.8), and high pressure (0.90–1.0). The adsorption curve behaves differently in these regions:
At the low-pressure end, the material shows strong interaction with nitrogen, which is typical for Type I, II, and IV isotherms. If the material has many micropores, the adsorption curve starts immediately due to the strong adsorption potential within those pores. On the other hand, at the high-pressure end, the adsorption is weaker, which is characteristic of Types III, V, and VI.
In the medium pressure region, nitrogen condenses inside the pores of the material. This part is crucial for mesopore analysis, including pores formed by particle aggregation or ordered/gradient mesopores. The BJH method uses this data to calculate pore size distribution.
At high pressure, the adsorption curve can indicate the degree of particle aggregation. If the isotherm rises sharply at the end, it may suggest non-uniform particle size. The total pore volume is usually estimated from the nitrogen adsorption value at a relative pressure of around 0.99.
Several constants are important in interpreting adsorption data. For example, at liquid nitrogen temperature (77K), the cross-sectional area of a nitrogen molecule is about 0.162 nm², and the monolayer thickness is approximately 0.354 nm. At standard temperature and pressure (STP), one mL of nitrogen corresponds to a volume of 0.001547 mL when condensed. Using this, if the maximum nitrogen adsorption is 400 mL, the total pore volume would be roughly 0.61 mL. Additionally, each mL of nitrogen that forms a monolayer covers about 4.354 m². The BET method calculates specific surface area using the formula S = 4.354 × Vm, where Vm is derived from the slope and intercept of the BET plot.
As an example, the adsorption isotherm of SBA-15 molecular sieve is classified as Type IV with an H1 hysteresis loop according to IUPAC. In the low-pressure region, the adsorption increases gradually, indicating multilayer adsorption on the inner surfaces of mesopores. The BET calculation is most accurate when the relative pressure (p/p₀) is between 0.10 and 0.29. A sharp increase occurs at p/p₀ = 0.5–0.8, reflecting the pore size and uniformity. At higher pressures, a third rise might appear, suggesting larger pores or particle agglomerates.
The Kelvin equation forms the basis of the BJH model. It relates the curvature radius of the liquid surface in a pore to the pore diameter. The contact angle plays a role in determining the actual pore size. Hysteresis loops arise due to capillary condensation during adsorption and the slower desorption process. Different hysteresis loop types (H1, H2, H3, H4) correspond to different pore structures. For instance, H1 loops are often associated with uniform cylindrical pores, while H2 loops suggest "ink-bottle" shaped pores.
The BJH model is commonly used for mesoporous analysis but tends to underestimate pore sizes. More advanced methods like KJS (Kruk-Jaroniec-Sayari) offer better accuracy, especially for materials like MCM-41 and SBA-15. These models have been refined to cover a wider pore size range, up to 30 nm in some cases.
Other methods such as t-plot and αs are used to analyze the entire adsorption or desorption curve. The t-plot method considers the thickness of the adsorbed layer, while the αs method uses the adsorption amount at a specific relative pressure (usually 0.4) instead of the monolayer capacity. Both approaches are complementary and can be converted into one another.
Microporous analysis requires more precise equipment and longer measurement times. Due to the small size of micropores, some probe molecules may not penetrate, making it challenging to obtain accurate pore size distributions. Techniques like NLDFT (Non-Linear Density Functional Theory) provide better results but are less commonly used in publications. Overall, understanding adsorption isotherms is essential for characterizing porous materials and their applications in catalysis, separation, and energy storage.