Correlating N₂ and CH₄ adsorption on microporous carbon using a new analytical model

A new pore size distribution (PSD) model is developed to readily describe PSDs of microporous materials with an analytical expression. Results from this model can be used to calculate the corresponding adsorption isotherm to compare the calculated isotherm to the experimental isotherm. This aspect of the model provides another check on the validity of the model's results. The model is developed on the basis of a 3-D adsorption isotherm equation that is derived from statistical mechanical principles. Least-squares error minimization is used to solve the PSD without any preassumed distribution function. In comparison with several well-accepted analytical methods from the literature, this 3-D model offers a relatively realistic PSD description for select reference materials, including activated-carbon fibers. N₂ and CH₄ adsorption is correlated using the 3-D model for commercial carbons BPL and AX-21. Predicted CH₄ adsorption isotherms at 296 K based on N₂ adsorption at 77 K are in reasonable agreement with experimental CH₄ isotherms. Use of the model is also described for characterizing PSDs of tire-derived activated carbons and coal-derived activated carbons for air-quality control applications.