Abstract
A novel method to evaluate the fractal dimensions of solid adsorbents is developed in order to eliminate some of the drawbacks of the conventional methods. The Freundlich isotherm, which may be expressed as n = A p1/b, is taken as a starting point for the calculations and the point-slopes of the ln n vs ln p plot representing the 1/b values are employed to trace the isotherms at any stage of adsorption. The determination of the most favorable 1/b values allows the estimation of the fractal dimensions to be made. This method enables the evaluation of the fractal dimensions of adsorbents by employing a single adsorption isotherm and data available for a reference adsorbent. The fractal dimensions of the zeolites 13X, 5A, and silicalite are first determined by employing the Pfeifer−Avnir method and the results obtained are compared with those obtained from the proposed point−slope method. An optimization is made to determine the most favorable 1/b values to be employed in the calculations that will result in the least amount of error when the adsorbates methane, ethane, and propane are utilized. As a result, it is observed that the point−slope method may provide a good estimation of the fractal dimensions of the zeolites investigated in this study, namely 13X, 5A, and silicalite, especially when the adsorbates methane and ethane are utilized.
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