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Determination of specific surface area and pore size distribution by isothermal adsorption and desorption of nitrogen - Master's thesis - Dissertation
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The six types of adsorption isotherms are commonly referenced in many textbooks. The first five are classified under the BDDT (Brunauer-Deming-Deming-Teller) system. These classifications were developed by four researchers who grouped 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 set of characteristics and is used to interpret different pore structures.
In general, the x-axis represents the relative pressure, while the y-axis shows the amount of nitrogen adsorbed. The relative pressure 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). At the low-pressure end, the adsorption curve reflects strong interactions between the material and nitrogen, often seen in Type I, II, and IV isotherms. When there are more micropores, the adsorption starts early due to the strong adsorption potential within these pores.
At the high-pressure end, the adsorption indicates weak interactions between the material and nitrogen, which is typical for Type III and V isotherms. In the medium-pressure region, nitrogen condenses within the pores, and this data is crucial for mesopore analysis. The BJH method is based on this section, helping to determine pore size distribution, including both interparticle and ordered or gradient mesopores.
At high relative pressures, the adsorption behavior can indicate the degree of particle aggregation. If the isotherm shows a sudden increase at the end, it may suggest non-uniform particle sizes. The total pore volume is often estimated using the nitrogen adsorption value at around p/pâ‚€ = 0.99.
Several constants are important in gas adsorption analysis. For instance, at liquid nitrogen temperature (77K), the cross-sectional area of a nitrogen molecule is approximately 0.162 nm². A monolayer thickness is considered to be 0.354 nm. Under standard temperature and pressure (STP), 1 mL of nitrogen corresponds to about 0.001547 mL when condensed. Using this, the total pore volume can be calculated from the maximum adsorption capacity.
The BET method is widely used to calculate specific surface area. It involves plotting the adsorption data and determining the monolayer volume (Vm). The formula S = 4.354 × Vm gives the specific surface area in m²/g. For example, if the adsorption capacity is 400 mL, the total pore volume would be approximately 0.61 mL.
The Kelvin equation plays a key role in the BJH model. It relates the pore diameter to the curvature of the liquid surface during capillary condensation. The contact angle affects the calculation, and different materials have varying contact angles. Understanding this helps in interpreting hysteresis loops.
Hysteresis loops occur due to differences in adsorption and desorption processes. During adsorption, nitrogen condenses in the pores, but during desorption, it escapes from the pore mouths, leading to a loop. There are several types of hysteresis loops, such as H1, H2, H3, and H4, each corresponding to different pore structures.
Type H1 is associated with uniform cylindrical pores, while H2 suggests ink-bottle shaped pores. H3 and H4 are slit-shaped pores formed by particle stacking or layered structures. The absence of a hysteresis loop in some cases, like MCM-41, indicates small pore sizes where adsorption and desorption curves overlap.
For mesoporous materials, the BJH model is commonly used, though it tends to underestimate pore sizes. The KJS method offers higher accuracy, especially for materials like MCM-41 and SBA-15, with a broader applicability range.
Other methods like 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 a reference point at p/p₀ = 0.4. Both methods provide complementary insights.
Microporous analysis requires more precise equipment and longer testing times. Due to the similarity between probe molecules and pore sizes, some molecules may not penetrate, making the analysis more complex. Techniques like NLDFT offer better results but are less commonly used in practice.
Overall, gas adsorption techniques remain essential for characterizing porous materials, providing valuable information about surface area, pore size, and structure.