Determination of Surface Area

Physisorption measurements, i.e. low-temperature gas adsorptions, are used in order to determine the pore size and surface area. The host material and adsorbate should not be affected by adhesive interactions and the pore volume needs to be entirely emptied before physisorption takes place, which is achieved by the sample activation at reduced pressure and elevated temperatures. Once the material is activated, a suitable probe gas is applied to infiltrate the pores. The amount of absorbed gas is monitored as a function of pressure changes in the measuring cell, the relative pressure 𝑝/𝑝₀. By means of the empirical method, differently shaped adsorption curves are detected, which are contingent on size and geometry of the pores.

If the total volume of the measuring cell is saturated by the probe gas, the gradual decrease of pressure gives the desorption isotherm. In case adsorption and desorption curves do not concur, a so-called hysteresis is observed.^[11,13]

The obtained adsorption-desorption isotherms were classified into six types and their corresponding hysteresis types by IUPAC (Figure 3).^[11] The reversible type I isotherm typically occurring for microporous solids shows a pronounced increase at low pressures (< 0.1 𝑝/𝑝₀) and merges into a near-flat plateau over the given pressure range. Due to the relatively small external surfaces of microporous materials, the uptake of gas is limited to accessible pore volume rather than by the internal surface.^[11] Meaning that after a monolayer of absorbate is generated, no multilayer formation can take place due to the restricted micropore volume.

Type II isotherms are characteristic for non-porous or macroporous adsorbents. The referred point ‘B’ marks the initiation of an almost linear curve section at which the formation of a monolayer is accomplished, and multilayers of adsorbed gas start growing.

Figure 3: Classes of isotherm and hysteresis types determined by IUPAC.^[11,13]

Type III isotherms, which are convex to the x-axis are less common and the absence of point ‘B’ indicates that monolayer formation is excluded, but the clusters of guest species occur due to weak adsorbent-absorbate interactions. Mesoporous materials are typically represented by type IV isotherms, which distinguish from reversible isotherms due to their hysteresis loop.

The occurrence of a hysteresis is based on capillary condensation of probe gas in the mesopores.

As describe for type II isotherms, point ‘B’ determines the stage on which monolayer coverage is completed and multilayer formation is initiated. At high relative pressures the uptake of gas is limited and consequently a plateau in the curve shape is observed. Similar to type III, type V isotherms show a flat increase at low relative pressures that could be attributed to comparatively weak adsorbent-absorbate interactions. Moreover, this type is irreversible and shows a hysteresis loop. For reversible isotherm type VI, several steps in the curve shape are notable, which suggests the unrestricted growth of layer by layer. Each step presents the generation of a new monolayer. This phenomenon occurs on uniform non-porous surfaces.^[11,13]

Besides different classes of isotherms, four hysteresis types were identified by IUPAC.^[11] The hysteresis loops are located in the multilayer range of physisorption isotherms, which are linked to capillary condensation. Hysteresis types H1 and H4 (Figure 3, right panel) outline two extreme cases whereas type H2 and H3 feature the intermediate between H1 and H4. The nearly vertical desorption branch of H1 is provoked by desorption at a defined value of 𝑝/𝑝₀,that can be ascribed to materials possessing a narrow pore size distribution. In contrast, type H2 is associated to samples with less uniform pore geometries and sizes, hence a more

complex pore architecture. A H3-like hysteresis is characteristic for non-rigid aggregates and plate-shaped particles. The adsorption branch of type H4 combines type I and II isotherms and thus a high uptake at low relative pressures, which is attributed to micropores. Hysteresis type H4 is often affiliated with narrow slit-shaped pores. Especially for materials containing micropores, low pressure hysteresis (marked as dashed lines in Figure 3) occur due to the ‘soft’, non-rigid structures which are swelling during the uptake of probe gas. If swelling of pores impedes the closure of desorption and adsorption branch, the physisorption of gas is irreversible and may only be removed at elevated temperatures.^[11,13]

The results obtained by physisorption measurements are evaluated via a method developed by Brunauer, Emmett and Teller (BET method) to calculate the specific surface area of a given material.^[24] The BET method is an extended concept of Langmuir’s adsorption theory, in whose model it is assumed that only a monolayer of gas molecules is absorbed on a homogeneous, perfectly flat and energetically equivalent surface.^[25] Further assumptions were added by BET theory, most important the extension to multilayer formation making the validation of the method more realistic. Additionally, it is supposed that the probe gas is adsorbed as infinite layers on the material surface, there are no specific interactions between layers and each layer is treated as a monolayer suggested by Langmuir’s theory, like the ‘ideal localized monolayer’.^[24,26] Considering the previous assumptions, it results in the equation

𝑝

where 𝑛^𝑎 describes the molecular amount of adsorbed gas and 𝑛_𝑚^𝑎 the molecular amount of adsorbate forming the first monolayer, 𝑝 is the pressure and 𝑝₀ stands for the saturation pressure. The linear formulation of the equation is presented below the BET equation in which 𝑆 gives the slope and 𝐼 the y-intercept.

The BET constant 𝐶 is defined as follows 𝐶 = exp (𝐸₁− 𝐸_𝐿

𝑅𝑇 ) (3)

in which 𝐸₁ and 𝐸_𝐿 represent the enthalpy of adsorption for a single layer and second or higher adsorbed layers, respectively. BET constant 𝐶 is exponentially growing with the energy of monolayer adsorption meaning strong adsorbent-adsorbate interactions are taking place if parameter 𝐶 reaches high values. 𝐶 and the monolayer capacity 𝑛_𝑚^𝑎 can be calculated by means of the linear BET equation using following equation:

𝐶 = 1 + (𝑆

𝐼) 𝑎𝑛𝑑 𝑛_𝑚^𝑎 = 1 𝑆 + 𝐼

(4)

The total surface area 𝑆𝐴_{𝑡𝑜𝑡𝑎𝑙} is determined by 𝑛_𝑚^𝑎, which gives the value of how much moles of gas are adsorbed on a completely covered surface, the Avogadro’s constant 𝑁_𝐴 and the area occupied by one adsorbate molecule 𝑎_𝑚. To compare materials, total surface area The linearity of the BET graph is just given in case specific points of the isotherm are chosen. In most instances relative pressures 𝑝/𝑝₀ ranging from 0.05 to 0.30 result in a linear graph which is valid for isotherm type II and IV.^[11,13] In the presence of micropores further criteria need to be taken into consideration to achieve a consistent evaluation. Rouquerol et al.

suggest that the selected pressure range should continuously increase with 𝑛^𝑎(𝑝₀− 𝑝) as a function of 𝑝/𝑝₀ as well as a positive value for the y-intercept meaning a parameter 𝐶 becomes greater than zero.^[27]