Review of Kelvin's Equation and Its Modification in Characterization of Mesoporous Materials

Abstract

Physical and mathematical models as well as calculation methods of nitrogen bed on porous media have been introduced to evaluate the structural parameters of mesoporous materials. Kelvin's equation is a link between the relative adsorbate pressure, the mean pore radius, and pore capillarity on the basis of macroscopic capillary condensation. However, Kelvin's equation has been identified that it underestimates the calculated pore size of a material especially in the boundary of pore size which is between 2 and 4 nm. Various modifications on Kelvin's equation were mentioned in order to develop a new model to improve the accuracy of pore size calculation. The problems on conventional mathematical models were analyzed and discussed. A number of calculation methods on physisorption and pore size, especially fundamental theories of physisorption, basis of models and their deficiencies are reviewed. It can provide guidance on developing a modified Kelvin's equation for pore size calculation.

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“…A model-independent Barrett–Joyner–Halenda (BJH) fit to the desorption branch yielded a pore size of 25.0 Å and a pore volume of 0.21 cc/g, which matches extremely well with the modeled structure (Figure S1). − This high N 2 uptake confirms the porosity of the COF (Figure A). Drastic lowering of the N 2 uptake is witnessed upon loading the nanoparticles (Figure B).…”

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“…The majority of literature employs the BJH method [33] for determination of pore diameter and pore size distribution. It was observed that the BJH method and related approaches, based on the modified Kelvin equation, underestimate the pore size up to 25% for pores smaller than 10 nm [34]. In this case, the density functional approach was found to provide reliable values for pore diameter and pore size distribution.…”

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