Flow‐dependent rejection of polystyrene from microporous membranes

Dilute solutions of polystyrene (molecular weight 1 × 10 5 −2 × 10 7 ) in a mixed solvent of 90% carbon tetrachloride‐10% methanol were filtered through track‐etched porous mica membranes. The reflection coefficient σ, defined as the fraction of polymer held back by the membrane, was measured as a function of polymer size r s , pore radius r o , and solvent flow rate q through each pore. Polymer size was characterized by the Stokes‐Einstein radius, as determined from diffusion coefficients measured by quasielastic light scattering, and chain relaxation times τ were estimated from measured intrinsic viscosities. In the case of chains whose unperturbed radius was smaller than the pore, σ depended on the ratio r s / r o in the manner predicted by a hard‐sphere theory, as long as {article}{empty}{document}γ τ < < 1{document} , where {article}{empty}{document}γ{document} is the mean rate of strain of solvent at the pore entrance. However, when the polymer chains exceeded the pore in size, σ depended on flow rate and decreased from almost unity, at small q , toward zero at high q . The relationship between σ and q was nearly independent of polymer and pore size, consistent with a theory based on scaling concepts of how polymer chains deform at the entrance of a pore, but the reduction in σ as q increased was very gradual and did not exhibit the sharp transition predicted by the theory. We were able to empirically correlate all the data for σ when r s > r o by a single similarity variable {article}{empty}{document}$ θ = {{({{r_s} {/ { {{r_s} {r_0}}} . -} {r_0}})} {/ { {{({{r_s} {/ { {{r_s} {r_0}}} . -} {r_0}})} {( γ τ)^n}}} . -} {( γ τ)^n}} ~ ({{r_s} {/ { {{r_s} {r_0}}} . -} {r_0}})1 - 3n q- n ${document} ; a least‐squares fit gave n = 0.33, showing that σ is insensitive to polymer size for large chains.