Sorption Measurements

Micro- and mesoporous materials have pores below 2 and 50 nm, respectively and can be analyzed by gas adsorption experiments, which is a suitable technique17 to determine porosity18 and surface area19,20.

Thus physisorption describes the interaction between the adsorptive (gas) and adsorbent (solid), which is of fundamental importance to get information about the adsorbents´ morphology. This process is reversible due to the weak Van-der-Waals interactions involved21. In contrast, chemisorption is often an irreversible process, because of the formation of a chemical bond between the adsorptive and the adsorbent.

Adsorption is an exothermic process and proceeds preferably at higher pressures and lower temperatures. Usually a gas such as nitrogen, krypton or argon is used as adsorptive. Kr is favorable for small amounts and/ or low surface areas and therefore is used for porous films. Argon is also widely used for microporous materials. These gases are more expensive than nitrogen, which is commonly used for mesoporous samples. Prior to every measurement, the adsorbent has to be properly outgassed under vacuum for several hours at temperatures above

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100 °C to obtain a complete desorption of residual molecular contaminations, e.g. water or solvents, from the surface. The measuring vessel, usually a glass flask with a small volume, is finally cooled with a constant volume of liquid nitrogen (-196 °C) during the measurement.

Depending on the adsorbents´ porosity, the absorber gas has different ways for the penetration into the adsorbent bulk. Thus gas interacts with the surface, and depending on the specimens’ porosity characteristic layer formation is observed. The International Union of Pure and Applied Chemistry (IUPAC) has classified six types of sorption isotherms (I – VI), represented in Figure 2.2.

Figure 2.2. Schematic description of the UIPAC isotherms (type I to VI).23

A type I isotherm is obtained by a reversible ad- and desorption process within a microporous material, which has typical pore widths of up to 2 nm. If the pore dimensions have a similar

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scale than the adsorbate, the formation of a monolayer correlates to a complete pore filling. For this reason a plateau is formed at higher relative pressures. The relative pressure represents the ratio between the applied pressure p and the saturation vapor pressure of the gas, p0.

If the material is dense or has macropores (> 50 nm) a type II isotherm is formed, which shows the development from a closed gaseous monolayer to multilayers. The type III isotherm is not so common, here the interactions between the individual absorber molecules are strong and layer formation on the surface is unfavorable.

Furthermore there are a series of mesoporous materials, which have a defined pore width in the range of 2 to 50 nm. Their sorption behavior is represented in the shape of type IV, where the isotherm is similar to type II at lower relative pressures. However, an additional appearance of a hysteresis loop between the branches is observed at higher relative pressures. The loop is attributed to the effect of capillary condensation within the mesopores, and desorption of the multilayers often occurs at lower relative pressures.

The type V isotherm represents a system with very low interactions between the adsorbate molecules and the existence of mesoporosity. Type VI shows a stepwise adsorption of multilayers on a dense surface, but also different pore widths can be present in this material. There exist different models for the description of sorption isotherms. The Langmuir model describes the monolayer formation of the adsorptive on a solid surface. The Brunauer- Emmett-Teller (BET) theory is based on the Langmuir model but assumes infinite multilayer formation; it is commonly used for a detailed evaluation of the isotherms. Thus the Langmuir model is used for describing the individual gas layers, and physical absorption of the gaseous adsorptive on a solid surface is also assumed. Additionally, there is no interaction between the

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adsorptive molecules within one layer. The following linear BET equation is used for isotherm modeling.

p0: saturation pressure of the adsorptive

na: amount of adsorbate at relative pressure p/p0 : monolayer capacity

C: BET constant with an exponential relation to the adsorption enthalpy

The total surface area As(BET) and specific surface area as(BET), or just SBET, can also be calculated with the BET theory.

am: molecular cross-sectional area; for N2 it is 0.162 nm2 at 77 K NA: Avogadro constant, 6.022*10-23 mol-1

m: mass of adsorbent

Another important information about the porous material is provided with the pore size distribution, which is accessible by applying the Barret-Joyner-Halender (BJH) method. For the description of the pore volume distribution with respect to the pore size, the Kelvin equation is used.

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rn, n = 1, 2: principal curvature radii of the liquid meniscus in the pores at the relative pressure σ1g

: surface tension of the condensate ν1

: molecular volume of the condensate

R: ideal gas constant, 8.324 Jmol-1K-1, produkt of NA and kB T: temperature in Kelvin

Additionally, Density Functional Theory (DFT) can be used to determine pore diameters. This specific calculation gives more correct values for microporous and mesoporous materials with small pore diameters, in comparison with the BJH method. Here, models are available that consider the pore geometry as well as the adsorbent. Depending on the material, pores can be more cylindrical, spherical or slit shaped. The models are applicable to the adsorption and the desorption branch of the isotherm.17,23 A new Quenched Solid Density Functional Theory (QSDFT) can be applied to carbon materials, and considers the specimens heterogeneity and roughness, which makes it difficult to compare results with literature values based on the previous methods.24,25

For macroporous solid materials other techniques for surface determination are suitable and based on liquid intrusion and extrusion, commonly performed with mercury.26

In this thesis a Quantachrome Instruments NOVA 4000e at 77 K was used in combination with nitrogen for all sorption measurements.

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