The BET equation, the inflection points of N2 adsorption isotherms and the estimation of specific surface area of porous solids

摘要

The N2-adsorption isotherms of porous solids are received in the form V=f[PIP_o). If such data are depicted in the form V(1-P/P_o)=f[P/P_o) or V(1 - P/P_o)/(P/P_o) =f[V(1 -P/P_o)), they show an identical inversion point (I-point, Inversion or Inflection point), which corresponds exactly to the monolayer volume V_m. As a result the value of specific surface area S is determined with unique precision via the trivial relationship S (m~2 g~(-1)) = 4.356V_m (cm~3 g~(-1)) without any use of the classic BET treatment. The derivates dV/d[(P/ P_n)] vs. (P/P_o) and d(V[1 - (P/P_o)])/d[(P/P_o)] vs. (P/P_o) exhibit maxima exactly at the same pressure (P/P_o), while the second order derivative d~2V/d[(P/P_o)]~2 vs. (P/P_o) exhibits a minimum exactly at the same pressure (P/P_o) with the I-point. As a consequence the specific surface area of solids can be determined just from experimental raw {P/P_o), V data without any use, neither of linear BET treatment nor the Inversion or Inflection type graphs. For some MCM-41 type mesoporous materials, the I-plots show not one but two Inversion points/I-points. The first inversion/inflection point at lower (P/P_o} values, "I_(LP)-point, corresponds to the completion of the adsorption procedure on the bare surface and the formation of monolayer and is useful for the determination of specific surface area S. The second inversion/inflection point at higher (P/ P_o) values, "I_(HP)-point", corresponds to the completion of the pore filling via condensation and may be useful for the determination of mesopore volume.