Porosity of materials with mesopores (pore diameters between 2-50 nm) is most commonly determined by gas physisorption. Pore size distribution, pore volume, and area can be derived from the adsorption data using an appropriate mathematical model. Although the technique can be used to evaluate samples of up to 300 nm, porosity characterization using this method is best for pores between 2-100 nm and in cases where Types II or IV isotherms are obtained. The technique is referenced by several standard organizations such as ISO, USP, and ASTM.
The fundamental principles and procedures of mesopore measurement are similar to BET surface area analysis using the static volumetric method. First, any excess adsorbed gases are removed from the sample surface using vacuum or inert gas flow, typically at elevated temperature. Then the adsorbate gas, most commonly nitrogen, is allowed to adsorb onto and desorb from the surface at liquid nitrogen temperature at varying relative pressures. The use of other gases such as argon at liquid argon temperature has also been proven beneficial, especially if investigation into the micropore range (pore diameter of < 2 nm) is of interest.
During analysis, the adsorbate gas first forms a monolayer on the surface at low relative pressures, then continues to form multilayers at increasing relative pressures. The BET surface area is typically evaluated at the juncture of the adsorption isotherm between the monolayer and multilayer formation, while porosity is typically evaluated above the juncture. If the monolayer and multilayer adsorption are indistinguishable on the isotherm, then the surface area and mesopore analysis results are not reliable. As the pressure continues to increase towards saturation, larger pores are filled and the adsorbate gas condenses inside the pores during the adsorption branch of the isotherm. The total pore volume is evaluated near the saturation point, typically from the desorption branch of the isotherm which is recorded by decreasing the relative pressures over the sample. During this process, the adsorbate evaporates from the pores.
Any differences between the capillary condensation and evaporation processes can give rise to a hysteresis loop in the isotherm. The shape of the isotherm and/or the hysteresis loop can provide valuable information on the shape and interconnectivity of the pores. The pore size distribution can be calculated from either the adsorption or desorption branch of the isotherm depending on the model used to evaluate the data and the shape of the hysteresis. Generally, the more data points collected over the relative pressure of interest, the higher the resolution of the pore size distribution.
The Barrett-Joyner-Halenda (BJH) theory is commonly used to evaluate the physisorption isotherm data. The BJH theory is derived from the Kelvin equation and assumes that all pores are rigid and of regular shapes, and contain no micropores nor macropores beyond the scope of the isotherm. Some Density Functional Theory (DFT) models are now available for certain material types, particularly where micropores are also of interest.
PTL provides expertise in porosity analysis and interpretation of the results. Additionally, results from porosity measurements by gas physisorption and mercury intrusion porosimetry can be blended to provide comprehensive pore size distributions from microporosity to macroporosity, upon request.