Predictions of Gas Separation

As explained earlier, the permeability for surface diffusion is dominated by the surface concentration and therefore the model predicts a peak at which the heat of adsorption is maximized. The permeability for Knudsen diffusion increases as a cubic function of pore size (see Equations 5.16 and 5.17) since the diffusivity depends linearly on the pore size d and the concentration depends on the volume of the pore (assuming cylindrical pores). 

The parallel transport model assumes that surface diffusion and Knudsen diffusion are occurring simultaneously such that the total permeability is given by Equation (5.18). This model is explained in further detail earlier in this chapter and has been used by various groups [27,49,50]. Parallel transport is initially dominated by surface diffusion within the smaller pores where the surface concentration is high while the mode of Knudsen diffusion dominates within the larger pores. 

CH4 because of its lighter mass resulting in a higher molecular velocity and does not change with pore size. Parallel transport follows the same trend as surface diffusion in small pores and tends toward Knudsen behaviour as the pore sizes increase. Finally, the resistance in series transport model predicts a decrease in selectivity as the permeability of CH4 increases more rapidly than for CO2 with increasing pore size. 

Tailoring the pore size distribution within materials has been suggested as a means of fine tuning the transport properties in membranes [61,62]. To facilitate the development 

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