Flow‐dependent rejection of polystyrene from microporous membranes

Abstract

Abstract 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 \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma \tau < < 1 $\end{document} , where \documentclass{article}\pagestyle{empty}\begin{document}$ \dot \gamma $\end{document} is the mean rate of strain of solvent at the pore entrance. However, when the polymer chains exceeded the pore in size, σ depended on flow rate and decreased from almost unity, at small q , toward zero at high q . The relationship between σ and q was nearly independent of polymer and pore size, consistent with a theory based on scaling concepts of how polymer chains deform at the entrance of a pore, but the reduction in σ as q increased was very gradual and did not exhibit the sharp transition predicted by the theory. We were able to empirically correlate all the data for σ when r s > r o by a single similarity variable \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} \mathord{\left/ {\vphantom {{({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})} {(\dot \gamma \tau)^n}}} \right. \kern-\nulldelimiterspace} {(\dot \gamma \tau)^n}} \sim ({{r_s} \mathord{\left/ {\vphantom {{r_s} {r_0}}} \right. \kern-\nulldelimiterspace} {r_0}})^{1 - 3n} q^{- n} $\end{document} ; a least‐squares fit gave n = 0.33, showing that σ is insensitive to polymer size for large chains.