(695g) Solubility Selectivity and the Upper Bound
The ability to tune the transport properties of polymeric materials through changes in primary and secondary chain architecture appears to be limited by the existence of an "upper bound". First reported in the literature by Robeson (Journal of Membrane Science, 62, 165-185, 1991 and updated in Journal of Membrane Science, 320 390-400, 2008), both polymer permeability and selectivity cannot be increased beyond a certain limit ? molecular changes that increase permeability ultimately lead to a decrease in selectivity and vice versa.
A theoretical explanation for this upper bound was proposed by Freeman (Macromolecules, 32, 375-380, 1999). Assuming diffusion is an activated process and using correlations suggested in the literature for the activation energy and front factor as well as a correlation for solubility, the observed upper bounds are predicted well by adjusting a single parameter related to the dependence of activation energy on molecular size.
While the theoretical expression provides very good estimates of the location of the upper bound, the correlations used in the derivation do not allow a critical evaluation of the influence of intrinsic material properties on transport. For example, the diffusion coefficient correlation lumps the effect of polymer-solvent interaction energy into a single parameter while the solubility correlation omits any influence of molecular size or polymer-penetrant interaction. Moreover, the relationship suggests all materials should lie near the upper bound.
To address these issues, the non-equilibrium lattice fluid theory is used to develop a relationship between solubility selectivity and solubility. This relationship is combined with the diffusivity selectivity relationship of Freeman to evaluate the selectivity-permeability tradeoff. For a given gas pair, the results are expressed solely in terms of the material properties of the polymer. By varying polymer properties, the predicted selectivity-permeability combinations are shown to lie along or below an upper bound established by materials with the largest known cohesive energy densities. Other molecular theories of solubility give similar results.