Validity of the <i>t‑plot</i> Method
to Assess Microporosity in Hierarchical Micro/Mesoporous Materials
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Abstract
The <i>t-plot</i> 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 <i>t-plot</i> 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 <i>t-plot</i> 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 <i>t-plot</i> 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 <i>t-plot</i> method