The controlled adsorption of gases is one the most-established methods for the characterization of porous materials. Physisorption measurements can provide information about the surface area and the pore volume of a material. In a physi-sorption experiment, an absorptive such as nitrogen experiences attractive van-der-Waals forces to a potentially porous solid (for example a MOF), which serves as an adsorbent, and an adsorbate is formed on the solid surface. This reversible process mainly involves London and Van-der-Waals forces. The adsorption en-thalpies lie in the range of 4 kJ/mol to 40 kJ/mol.[222]
The progression of adsorption processes at constant temperatures can be rep-resented by sorption isotherms in which the adsorbed volume is plotted against the relative pressurep/p0wherepis the vapor pressure andp0is the saturation pressure of the absorptive. The progression of the isotherms in adsorption and desorption processes are characteristic of the type of porosity observed in the material. Isotherms are grouped in six different types according to the IUPAC.
These isotherms are denoted with Roman numerals and are depicted in Fig-ure 2.3.[223]
I II III
IV V VI
Figure 2.3 – Six different sorption isotherms according to IUPAC recom-mendations in which the adsorbed volume is plotted against the relative pressurep/p0; arrows indicate the pressure points where the adsorption in a monolayer is completed.[223]
IV and constitute the most relevant isotherms with regard to MOFs. Micropo-rous solids exhibit a type I adsorption isotherms. In these materials, the adsorp-tion potential is strong due to the narrow pores. This leads to an overlap of adsorption potentials of the walls and the adsorption enthalpy is increased sig-nificantly. Therefore, type I adsorption is dominated by the primary filling of micropores by fluid-wall interactions. This behavior is commonly observed for MOFs, which often exhibit, but are not limited to, pores with a diameter of less than 2 nm.
Materials that have pores in the range of 2 nm to 50 nm show type IV ad-sorption isotherms. This is the case, for example, for the MOFs with ultra-high surfaces areas described in Section 1.4 (see page 33). Here, a hysteresis may be observed in the isotherm as a result of differences between the adsorption and desorption process: Due to the formation of metastable films during adsorption, capillary-condensation occurs in partially filled pores and leads to a delay of the vapor-liquid transition. Such metastabilities do not occur during desorption, be-cause the liquid-vapor interface is already present.[222]
The type II adsorption isotherm is typically observed for non- or macropo-rous solids. The progress of this isotherm exhibits a shoulder which indicates the beginning of multilayer generation. The type III adsorption is considered a special case of the type II adsorption in which an increase in the interaction between the molecules of the adsorbate is observed. Another special case is the type V adsorption that can be derived from a type IV isotherm in which the interaction between adsorbent and adsorbtive is weak. A step-wise adsorption leads to the type VI isotherm, in which each step corresponds to a complete monolayer adsorption.
As can be seen from the type IV and type V isotherms, a hysteresis may oc-cur between the adsorption and the desorption process. This behavior is usually observed for mesoporous materials.[222]After the formation of a multilayer with a critical thickness, the prevalent role of fluid-fluid interaction leads to capillary condensation. Hystereses have been grouped by the IUPAC into four different types and are shown in Figure 2.4. The shape of a hysteresis loop generally cor-relates with the pore geometry in a material. For cylindrical pores with a narrow pore size distribution, hysteresis H1 is commonly observed. More complex pore structures that involve network effects, such as pore blocking or percolation, are typically associated with hysteresis H2. Hysteresis H3 and H4 are commonly ob-served if slit-shaped pores are present, whereas for H3 theses pores are formed by an interparticular arrangement.
H3 H4
Figure 2.4– Four different types of hysteresis according to IUPAC recom-mendations in which the a dashed line indicates a possible hysteresis at low pressures.[223]
2.3.1 Determination of the Specific Surface Area
The mathematic description of adsorption processes allows the calculation of the specific surface area of an adsorbent. These calculations are based on empir-ical models, such as the Brunauer-Emmet-Teller (BET) theory.[224]This approach is an extension to the Langmuir theory and takes the formation of multilayers into account. It is commonly used to describe the adsorption of gases by micro-and mesoporous materials. It is expressed by the following equation.
p/p0
n(1−p/p0) = 1
nmC+ C−1
nmC ·p/p0 (2.3)
wherenmis the monolayer capacity,nis the amount of adsorbate, andCis an empirical constant.[222]Knowledge of the monolayer capacity allows the calcu-lation of the specific surface area ifnmis divided by the molecular cross-sectional area of the adsorbate. To solve equation 2.3, a physisorption isotherm is trans-formed into a BET graph in which the left term of equation 2.3 is plotted against p/p0. The slope and the y-intercept of this linear graph are used to calculate the Cconstant. This permits the determination ofnmfrom which the specific surface area can be calculated by
SBET=nm·NA·σ (2.4)
whereNAis the Avogadro number andσis the cross-sectional area of a molecule of the adsorbate within a monolayer. For nitrogen, it is assumed thatσ=0.162 nm2. The BET equation is generally applicable in the relative pressure range ofp/p0
the BET method is not applicable for microporous adsorbents. However, the determination of the surface area by nitrogen physisorption is generally ac-cepted in the literature as an adequate expression for the surface area if certain quality criteria are applied.[227,228]
1. The empirical constantCmust be positive.
2. The term n·(p/p0) must increase monotonically in the chosen range of p/p0.
3. The endpoint of monolayer formation(p/p0)nm = √1
C+1must lie within the chosen range ofp/p0.
BET plots of adsorptions isotherms of nitrogen physisorption may exhibit linearity in more than one range ofp/p0. The application of these quality criteria provides reproducibility by excluding certain pressure ranges.