We present a mean-field
density functional theory (MFDFT) study
of adsorption and desorption for nitrogen at 77 K in three-dimensional
(3D) geometrical models of ordered and random mesoporous silicas obtained
by electron tomography. Parameters of the lattice MFDFT model, such
as reduced temperature, the ratio between the energies of fluid–solid
and fluid–fluid interactions, and the lattice unit size, were
investigated to achieve best qualitative agreement with experimental
isotherms in the hysteresis region. Equilibrium and metastable equilibrium
states were analyzed for 500 pressure values in the range of 0 < p/p
0 ≤ 1 for both adsorption
and desorption, which allowed us to resolve subtle features of the
isotherms. Calculated and experimental isotherms show good agreement
in the hysteresis region, identifying type IV(a) isotherms with a
H1 hysteresis loop for ordered silicas (SBA-15, KIT-6) and H2(a) hysteresis
loop for random silica. Hysteresis loops are particularly narrow and
hysteresis branches parallel and almost vertical for the ordered silicas.
This indicates homogeneous microstructures of uniform, cylindrical
pores and confirms that the SBA-15 silica has a highly interconnected
3D mesopore network, as targeted with its preparation, mimicking the
pristine 3D mesopore structure of KIT-6 silica. For the random silica,
characterized by a heterogeneous microstructure with many narrow and
highly constricted pores, the available phase distributions allowed
us to distinguish between pore blocking and cavitation along the desorption
branch and to monitor the dependence of cavitation bubble size on
relative pressure using image analysis. Complementary calculated desorption
scanning isotherms reflect pore evaporation in the ordered silicas
as expected from an independent pore model, whereas the representative
behavior of dependent pores in the random silica involves pore blocking/percolation.