Hysteresis in Adsorption and Desorption Isotherm How to evaluate the pore size distribution

It has been always a discussion whether to evaluate the pore size distribution by using the adsorption isotherm or desorption isotherm.

The hysteresis between the adsorption isotherm and desorption isotherm is thought to be caused by the gradual desorption mechanism (percolation theory) due to the different size pores being combined. This percolation theory suggests that the pore size distribution obtained from the desorption isotherm is problematic to be used. It is commonly said that the pore size distribution obtained from the adsorption isotherm has less problems and is closer to the true value.

Ad-desorption hysterisis

Additionally, there is a phenomenon that the desorption isotherm is closed to the adsorption isotherm side at the same equilibrium pressure even if the pore size is changed (without the special case of low pressure hysteresis). This phenomenon shows that the reason of desorption isotherm to be closed is not related to the pore size and is due to the adsorptive physical property at the adsorption temperature. This behavior is caused by the cavitations of adsorption phase in the pores. The pore size distribution analysis obtained from the desorption isotherm always has the peak of 3.4 nm pore due to the pressure of cavitations. This pore needs to be ignored when using the desorption of N2 isotherm at 77 K because this is not related to the pore condensation on the material.

Desorption of nitrogen with cavitations at 77.4 K

Pore size distribution of mesoporus silica The following figures are the pore size distribution graph and TEM  picture of porous silica material.

The pore size peak (29 nm) shown with the red circle is calculated from the adsorption isotherm and the pore size peak (18 nm) shown with the blue circle is calculated from the desorption isotherm. These two are about 10 nm different. Comparing these two with the observation of sliced material by TEM shows a good agreement with the pore size obtained from the adsorption isotherm. Also, on this material, there are non-homogeneous pores combined with complexity. Currently, the gas adsorption technique is useful for determining the pore size, but it is difficult to determine the pore shape.

Therefore, it is necessary to select the proper analysis theory by determining the pore shape from the literature or TEM/SEM observations.