Analysis of Mesoporosity

The signals in the isotherm that indicate mesoporosity are the type IV and V isotherm or feature 3 in the standard plot designation, that is a positive curvature at pressure well above the threshold in the standard or x plot. This would be a practical definition for purposes of analysis. The lUPAC definition is 

Nearly all of the analysis of mesoporosity starts with the Kelvin-Cohan [14] formulation. Foster [15] proposed the Kelvin equation for the effect of vapor pressure on capillary rise but did not anticipate its use for very small capillaries where the adsorbate thickness is a significant geometrical perturbation. Cohan formulation subtracts the adsorbate film thickness from the radius of the pore to yield the modified Kelvin equation 

Whether one is referring to a 2D or 3D case is not necessarily the same as the pore geometry and is embedded in whatever theory is being used. This could be a confusing point and herein it will be clearly stated as whether a 2D or 3D interface is being referred to. There could be intermediate cases between strictly a cyhndrical interface and a spherical interface and there could be, in principle at least, cases where m is 2. Obviously for flat surfaces m=0 and P=Ps- Therefore P/ wiU always be used for the flat surface vapor pressure. (The notation P has been used occasionally in the literature for the vapor pressure over a pure liquid with possibly a curved interface. Therefore it will be avoided here.) 

---