Fundamental Understanding of the Effect of Air-Gap Distance on the Fabrication of Hollow Fiber Membranes

The objectives of this work are, fundamentally, to understand hollow fiber membrane formation from an engineering aspect, to develop the governing equations to describe the velocity profile of nascent hollow fiber during formation in the air gap region, and to predict fiber dimension as a function of air-gap distance. We have derived the basic equations to relate the velocity profile of a nascent hollow fiber in the air-gap region as a function of gravity, mass transfer, surface tension, drag forces, spinning stress, and rheological parameters of spinning solutions. Two simplified equations were also derived to predict the inner and outer diameters of hollow fibers. To prove our hypotheses, hollow fiber membranes were spun from 20 : 80 polybezimidazole/polyetherimide dopes with 25.6 wt % solid in N,N-dimethylacetamide using water as the external and internal coagulants. We found that inner and outer diameters of as-spun fibers are in agreement with our prediction. The effects of air-gap distance or spin-line stress on nascent fiber morphology, gas performance, and mechanical and thermal properties can be qualitatively explained by our mathematical equations. In short, the spin-line stresses have positive or negative effects on membrane formation and separation performance. A high elongational stress may pull molecular chains or phase-separated domains apart in the early stage of phase separation and create porosity, whereas a medium stress may induce molecular orientation and reduce membrane porosity or free volume. Scanning electron microscopic photographs, coefficient of thermal expansion, and gas selectivity data confirm these conclusions. T_g of dry-jet wet-spun fibers is lower than that of wet-spun fibers, and T_g, decreases with an increase in air-gap distance possibly because of the reduction in free volume induced by gravity and elongational stress.