Modelless pore-size analysis

The ideas of Wheeler that condensation and evaporation occur within a center core during adsorption and desorption and that an adsorbed film is present on the pore wall has led to the proposal of various methods for pore size analysis. In addition to the methods of Pierce and the BJH technique, other schemes have been proposed, including those by Shull, Oulton, Roberts, Innes, and Cranston and Inkley. These ideas are all based upon some assumption regarding the pore shape. 

Brunauer et alP have developed a means of determining the pore volume distribution wherein the pore shape has a negligible influence. 

Equation (8.4) establishes the relationship between the moles of adsorbate condensed into pores and the corresponding decrease in the pore area. Rewriting equation (8.4) and eliminating the negative sign, since during condensation pore surface is disappearing, one obtains 

Kiselev, using the above equation by graphical integration of the isotherm between the limits of saturation and hysteresis loop closure, was able to calculate surface areas for wide-pore samples in good agreement with BET measured areas. For micropores, the absence of hysteresis at the low-pressure end of the isotherm indicates that only adsorption and not condensation occurs, thereby rendering Kiselev s method inapplicable. 

Brunauer s modelless method uses pore volume and pore area not as functions of the Kelvin radius but rather as functions of hydraulic radii that he defines as  

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