Effects of molecular shape on osmotic reflection coefficients

Abstract

The effects of molecular shape on the osmotic reflection coefficient ( σ 0) for rigid macromolecules in porous membranes were analyzed using a hydrodynamic model. In this type of model, employed first by Anderson and Malone [1], steric exclusion of the solute from the periphery of the pore induces a concentration-dependent drop in pressure near the pore wall, which in turn causes the osmotic flow. Results were obtained for prolate spheroids (axial ratio, γ > 1) and oblate spheroids ( γ < 1) in cylindrical and slit pores. Two methods, one of which is novel, were used to compute the transverse pressure variation. Although conceptually different, they yielded very similar results; the merits of each are discussed. For a given value of a/ R, where a is the prolate minor semi-axis or oblate major semi-axis and R is the pore radius, σ 0 increased monotonically with increasing γ. When expressed as a function of a SE/ R, where a SE is the Stokes–Einstein radius, the effects of molecular shape were less pronounced, but still significant. The trends for slits were qualitatively similar to those for cylindrical pores. When σ 0 was plotted as a function of the equilibrium partition coefficient, the results for all axial ratios fell on a single curve for a given pore shape, although the curve for cylindrical pores differed from that for slits. For spheres ( γ = 1) in either pore shape, σ 0 was found to be only slightly smaller than the reflection coefficient for filtration ( σ f). That suggests that σ 0 can be used to estimate σ f for spheroids, where results are currently lacking.