Following the kinetic theory, gases consist of large quantities of moving molecules, constantly colliding with each other. These collisions depend on the amount of molecules per volume (pressure), as well as their kinetic energy (temperature), with the average distance between two molecular colisions being known as the mean free path. The theory breaks down, when the space surrounding the molecules is extremely limited, for example by solid walls. Is the distance between two solid walls smaller than the mean free path, molecule-molecule collosions become less likely and the gas-characteristics are dominated by molecule-wall collisions. The relation between the mean free path of a molecule and a representative physical length (e.g. wall distance) is known as the Knudsen number and the special movement of fluids at high Knudsen numbers (>1) is called Knudsen flow.
The Knudsen number is mainly driven by pressure and representative length scale. Therefore, systems with high Knudsen numbers can be found under conditions of diluted gases at very low pressures combined with macroscopic objects, as well as gases at near-ambient pressure limited by very small objects. For instance, a satellite in the exosphere or a measurement capsule in Bremens’s drop tower, are examples of large objects at very low pressure. In contrast, in (porous) gas separation membranes and chromatography columns high Knudsen numbers are present at near-ambient pressures.
Especially for gas separation and chromatography, functional porous coatings are often used to enhance or decrease the flow of desired gas species. Often though, a full understanding of the involved mechanisms resulting in the desired behavior is still missing, limiting applicability and effectivity of chemical surface functionalizations. In mesopores (2-50 nm) under ambient conditions, the Knudsen number is large and gases propagate according to Knudsen flow through porous structures. Fortunately, the Knudsen flow has a linear relation to pressure and the theoretical values are in very good agreement with experimental data. Therefore, systems characterized by Knudsen flow are perfect model structures to study the influence of chemical surface functionalizations on the gas flow.
To analyze the gas transport and the influence of functionalized surfaces, we prepare mesoporous (inorganic) membranes with monomodal pore size distributions, serving as model structures. The membrane surface is then functionalized using different functional groups, such as alkyl-chains of different length, phenol- or amino-groups. Afterwards, gas peremation measurements at different temperatures using different gas types are carried out to investigate the fundamental mechanisms between gas molecules and functional surface.