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Gas Sorption, Physisorption, B.E.T Methods

Physical adsorption (physisorption) is used to measure surface area and pore size. As more gas molecules are introduced into the system, the adsorbate molecules tend to form a thin layer that covers the entire adsorbent surface. Based on the well-known Brunauer, Emmett and Teller (B.E.T.) theory, one can estimate the number of molecules required to cover the adsorbent surface with a monolayer of adsorbed molecules, Nm. Multiplying Nm by the cross-sectional area of an adsorbate molecule yields the sample's surface area.

 

Continued addition of gas molecules beyond monolayer formation leads to the gradual stacking of multiple layers (or multilayers) on top of each other. The formation of multilayers occurs in parallel to capillary condensation. The latter process is described by the proportionality between residual (or equilibrium) gas pressure and the size of capillaries capable of condensing gas within them. Computational methods such as the clasical one by Barrett, Joyner and Halenda (BJH), or preferably state-of-the-art calculations like Density Function Theory (DFT) allow the determination of pore sizes from equilibrium gas pressures.   One can therefore generate experimental curves (or isotherms) linking adsorbed gas volumes with relative saturation pressures at equilibrium, and convert them to cumulative or differential pore size distributions.   

 

As the equilibrium adsorbate pressures approach saturation, the pores become completely filled with adsorbate. Knowing the density of the adsorbate, one can calculate the volume it occupies and, consequently, the total pore volume of the sample. If at this stage one reverses the adsorption process by withdrawing known amount of gas from the system in steps, one can also generate desorption isotherms. Adsorption and desorption isotherms rarely overlay each other. The resulting hysteresis leads to isotherm shapes that can be mechanistically related to those expected form particular pore shapes.