Existing polymer membranes used in dialysis and ultrafiltration have been extensively studied. The pores in such membranes are formed by extrusion and solvent casting techniques. The geometry and surface chemistry of the pores arise from the chemistry of the polymers and the fluid dynamics of the casting process. In general, the hollow-fiber membranes are fairly thick or employ a multilayer scaffold for mechanical support, and have a distribution of pore sizes rather than a regular array of uniform pores. Pores in conventional polymeric membranes tend to be either roughly cylindrical, have a round orifice terminating a larger channel, or have a structure resembling an open-cell sponge. Extensive description of porous structures used in commercial ultrafiltration and microfiltration may be found in [9, 10]. It is not clear that any of these structures provide optimal geometries for membrane filtration for two reasons.
First, a wide dispersion in pore sizes within a membrane leads to imperfect retention of molecules larger than the mean pore size of the membrane. This is remedied in practice by engineering the mean pore size of the membrane to be sufficiently small that negligibly few pores are large enough to allow passage of a solute above the desired molecular weight cutoff of the membrane. This has the undesired effect of reducing the mean pore size in the membrane and thus reducing the hydraulic permeability of the membrane. Engineering narrower pore size distributions ameliorates this dilem ma, allowing sharper transitions from passage to retention and maximizing the mean pore size of the membrane .
Second, the round shape of conventional pores dictates a fourth-power dependence of hydraulic permeability on pore radius:
where Q denotes volumetric flow, P is hydrostatic pressure, r is the radius of the pore, ^ is viscosity, and L is the length of the pore, which may or may not be the same as the thickness of the membrane. A pore that is slit-shaped allows steric hindrance to solute passage dictated by the smallest critical dimension of the pore, while increasing hydraulic permeability by a factor of the long dimension of the pore:
where w is the long dimension of the slit, h is the thickness of the slit, and L is again the length of the pore. Consequently, it might be predicted that filtration structures with parallel slit-shaped pores might have superior performance when compared to structures with round pores. With that in mind, it is interesting but speculative to note that natural selection has produced filtration structures with elongated, slit-shaped geometries in the kidney, in the beaks of filter-feeding birds such as the flamingo, and in the baleen of filter-feeding whales. Arrays of slit-shaped pores with small dimensions to 5-7 nm have been manufactured and tested as immunoisolation membranes, filters, and substrates for tissue culture [6, 7, 12].
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