Effects of Multisolute Steric Interactions on Membrane Partition Coefficients

Abstract

A key parameter in membrane and chromatographic separations is the partition coefficient, the equilibrium ratio of the solute concentration in a porous or fibrous material to that in bulk solution. The theoretical effects of solute size on partition coefficients in straight pores or randomly oriented fiber matrices have been investigated previously for very dilute solutions, where solute–solute interactions are negligible, and also for more concentrated solutions consisting of spherical solutes of uniform size. For concentrated solutions it has been found that steric and other repulsive interactions among solutes increase the partition coefficient above the dilute limit. To extend the results for porous or fibrous media to include concentrated mixtures of solutes with different sizes or shapes, we used an excluded volume approach. In this formulation, which describes steric interactions only, partition coefficients were computed by summing all volumes excluded to a solute molecule by virtue of its finite size, the finite size of other solutes, and the presence of fixed obstacles (pore walls or fibers). For a mixture of two spherical solutes, the addition of any second solute at finite concentration increased the partition coefficient of the first solute. That increase was sensitive to the size of the second solute; for a given volume fraction of the second solute, the smaller its radius, the larger the effect. When the total volume fraction of solutes was fixed, an increase in the amount of a second, smaller solute increased the partition coefficient of the first solute, whereas an increase in the amount of a second, larger solute had the opposite effect. Results were obtained also for oblate or prolate spheroidal solutes and for fibrous media containing fibers of different radii. For constant total fiber volume fraction, an increase in the amount of a second, smaller fiber decreased the partition coefficient of a spherical solute, whereas an increase in the amount of a second, larger fiber had the opposite effect. Overall, the theory suggests that the introduction of heterogeneities, whether as mixtures of solute sizes or mixtures of fiber sizes, may cause partition coefficients to differ markedly from those of uniform systems.