The limitations of using Flory-Huggins equation for the states of solutions during asymmetric hollow-fiber formation

The Flory-Huggins equation of solutions, derived in 1942, has been extensively used to study the phase-inversion process during the formation of asymmetric flat membranes. In this report, we point out the limitations of using Flory-Huggins theory to describe the Gibbs free energy for the states of solutions during hollow-fiber formation. It is concluded that the Flory-Huggins equation of solution may not be fully capable of describing the Gibbs free energy for the state of as-spun hollow-fiber solutions (nascent fibers) spun non-isothermally with tension. At least two additional terms have to be included in this equation if the fiber is spun isothermally; one is a work done by the external stresses on the as-spun nascent fiber and the other is an extra entropy change, Delta S-extra/RT, induced by these stresses. Experimental results have confirmed our analysis. SEM observation of as-spun 6FDA-polyimide fibers indicates that external stresses (work) probably have three effects on the states of solution: (1) creating extra-phase instability; (2) facilitating phase separation; and (3) inducing orientation. The first two will either shorten the time for a solution moving from the binodal to the spinodal boundary or reduce the distance of precipitation path between binodal and spinodal boundaries, while the last one results in an oriented fiber structure. Experimental results also suggest that the effectiveness of external stresses (work) on the phase stability of a spinning solution depends on the chemistry of coagulants.