Polymer Brushes Make Nanopore Filter Membranes Size Selective to Dissolved Polymers

Ceramic (aluminum oxide) nanoporous filter membranes, resistant to both aqueous and organic solvents, have numerous applications in the filtration of mobile phases. These include removal of particles from solvents, removal of virus particles from blood, and capture of microorganisms from fluid phases. As shown in Figure 1, the filter membranes contain densely packed parallel pores arranged in a honeycomb pattern and passing completely through the thickness of the membrane. The monodisperse diameters of the pores confer a precise size cutoff to themembrane, allowing particles smaller than the cutoff size to pass through, while retaining all larger particles. Dissolved linear polymers undisturbedby shear flow sweepout spherical volumes analogous to those of solid, spherical particles. However, when subjected to shear flow, these polymers can undergo a coil-to-stretch transition and pass through the nanopores of a filter membrane, even when their radii of gyration are larger than the radii of the pores. In this Note, we report that polymer brushes grafted to the walls and reaching the centerlines of the pores in a nanopore filter membrane render the membrane size-selective to linear polymers. We attribute this to the recently demonstrated behavior of the polymer brush as a size selective penetration barrier, as described briefly below. A polymer brush is a layer of polymer chains, all the same length and all attached, or grafted, by one end to a surface and bathed in good solvent. The essence of a polymer brush is that the surface attachment density is sufficiently high for the chains to stretch away from the surface in response to the osmotic pressure generated within the brush. A grafted layer is deemed a brush if the distance between grafting points is less than the value computed for radius of gyration, Rg, of the brush chains if they were well separated from each other and not stretched away from the grafting surface. This Rg is exactly that computed for the grafted chain if it were free in good solvent and will be referred to hereafter as the “Rg of the brush chains”. Recent work in our laboratory has shown that a moderately stretched polymer brush attached to a flat surface can act as a selective penetration barrier to free polymers in dilute solution, preventing free polymers above a certain size from penetrating the brush to reach the underlying surface. Specifically, when the Rg of the free chains in solution is smaller than the Rg of the brush chains, the free chains penetrate the brush completely; free polymers having Rg values larger than the Rg of the brush chains do not. This behavior was found to be quite general, i.e., for brushes and free species of various chemical structures. The success of relative Rg as a criterion for penetration may seem surprising at first. However, a rationale based on entropy is provided by a theoretical study showing that brush chains can splay around a small incoming particle and then fill in behind the particle as it moves toward the grafting surface, gaining back the entropy lost during splaying. The ability of the brush chains to splay and fill in was a function of the length of the grafted chain with respect to the particle radius, and if the particle is too large, it merely compresses the brush chains and cannot enter. Another theoretical work suggested that the increase in energy of the distorted brush chain becomes too high to permit penetration by the free species when the lateral displacement of the brush chain is on the order of its own computed radius of gyration. For the present work, we made the hypothesis that polymer brushes grafted to the walls and reaching to the centerlines of the pores, as depicted in Figure 2, would make a nanopore filter membrane size selective to polymers in dilute solution. Ceramic nanopore filter membranes (Anodisc, Whatman, Ltd.) 60 μm thick with 20 nm pore diameters were used. We used previously developed procedures to derivatize the walls of the nanopores Figure 1. Top and cross-sectional views of an alumina nanopore filter membrane (reproduced from Web site of SPI Supplies) showing monodisperse and parallel nature of pores.