Contributions to frequency response models for mass transfer in adsorbents

Analytical models are presented for the interpretation of adsorption rate data measured using frequency response techniques. The first is a general model for a bidisperse particle including the contributions of micropore diffusion, macropore diffusion, a surface barrier resistance, and nonisothermal effects caused by the heat of adsorption. The remaining two models describe the degenerate case in which a surface barrier resistance is limiting. These two models pertain to the “shell and core” interpretation of the carbon molecular sieve (CMS) surface barrier with different levels of complexity. The more complex model treats the shell and core as two concentric spheres for which the adsorption rate is limited by micropore diffusion through the outer sphere, while the simpler model treats steady diffusion through a thin sheet, ignoring shell curvature and time dependence. These two models are used to explore the implications of having different isotherm characteristics in the shell compared to the core of a CMS microparticle. In the simple model, allowing for a different isotherm in the shell results in a loading dependence of the surface barrier transport coefficient that is different from what would be expected if the isotherms in the two regions were the same. In the more complex concentric sphere model, a different shell isotherm can result in rate behavior that no longer resembles that of an LDF-equivalent surface barrier.