The t-plot method is a well-known technique which allows determining the micro- and/or mesoporous volumes and the specific surface area of a sample by comparison with a reference adsorption isotherm of a nonporous material having the same surface chemistry. In this paper, the validity of the t-plot method is discussed in the case of hierarchical porous materials exhibiting both micro- and mesoporosities. Different hierarchical zeolites with MCM-41 type ordered mesoporosity are prepared using pseudomorphic transformation. For comparison, we also consider simple mechanical mixtures of microporous and mesoporous materials. We first show an intrinsic failure of the t-plot method; this method does not describe the fact that, for a given surface chemistry and pressure, the thickness of the film adsorbed in micropores or small mesopores (< 10σ, σ being the diameter of the adsorbate) increases with decreasing the pore size (curvature effect). We further show that such an effect, which arises from the fact that the surface area and, hence, the free energy of the curved gas/liquid interface decreases with increasing the film thickness, is captured using the simple thermodynamical model by Derjaguin. The effect of such a drawback on the ability of the t-plot method to estimate the micro- and mesoporous volumes of hierarchical samples is then discussed, and an abacus is given to correct the underestimated microporous volume by the t-plot method.

Adsorption and transport in hierarchical materials are investigated by means of adsorption and nuclear magnetic resonance experiments. Using micro/mesoporous zeolites with well-defined mesoporosity, we show that adsorption at a given pressure can be described as a simple linear combination of the adsorbed amounts taken at the same pressure for the pure microporous (zeolite FAU-Y) and mesoporous (Al-MCM-41) solids. Such a quantitative decomposition allows us to demonstrate the ability of diffusion measurements by Pulsed Field Gradient Nuclear Magnetic Resonance (PFG NMR) to probe interconnectivity in hierarchical solids. On the one hand, transport in the mechanical mixtures can be described as the superimposition of diffusion in pure microporous and mesoporous solids. On the other hand, PFG NMR for the hierarchical sample provides an effective diffusivity that is intermediate between those for the pure zeolite and mesoporous silica. Furthermore, this effective diffusivity is slower than the linear combination of the two diffusivities weighted by the number of molecules present in each phase (used in the independent domain and fast-exchange theories) clearly showing interconnectivities and transfer limitations between the microporous and mesoporous domains. We also discuss the ability of combining theories such as the fast exchange model and the effective medium theory to quantitatively predict diffusion in such microporous/mesoporous materials.