Phase-Field Modeling of the Polymer Membrane Formation Process for Micro- and Ultra-Filtration

Porous polymer membrane filters are widely used in separation and filtration process. Micro- and ultra-filtration membranes are commonly used in biopharmaceutical applications such as filtering viruses and separating proteins from a carrier solution. The formation of these membrane filters via phase inversion is a complex and interconnected process where varying casting conditions can have a wide variety of effects on the final membrane morphol- ogy. Tailoring membrane filters for specific performance characteristics is a tedious and time consuming process. The time and length scales of membrane formation make it extremely difficult to experimentally observe membrane formation. Modeling the membrane formation process allows one to slow down time and closely observe the formation of complex pore net- works. This allows new understanding and visual representations of the effects of different casting conditions and the resulting pore networks that form. This dissertation presents two separate models for two different membrane formation processes - thermally induced phase separation (TIPS) and non-solvent induced phase sepa- ration (NIPS). The Phase-Field method is employed to model the mesoscopic morphological structures that emerge during membrane formation. The Cahn-Hilliard equation is used to capture the diffusive nature of membrane formation and the Flory-Huggins free energy of mixing describes the thermodynamic equilibriums of the polymer solutions. Large-scale two- and three-dimensional simulations are used for capturing the resulting pore morphology under various casting conditions. The model for TIPS evaluated different casting conditions for the membrane forming system PVDF/DPC (polyvinylidene fluoride/diphenyl carbonate). The effects of casting surface temperature, thermal conductivity, quench rate, and polymer concentration were in- vestigated. Isotropic thermal quenches were used to analyzed pore size and interconnectivity while varying the quench rate and polymer concentration. Anisotropic thermal quenches in which a constant temperature cooling surface is imposed at the top surface were used to an-alyze the pore size and formation of a dense pore region near the casting surface. Different polymer concentrations, casting surface temperatures, and polymer thermal conductivities were used to characterize their effects on pore morphology. The formation of a dense pore region occurs near the top surface and the thickness of this dense pore region is dependent on the previous mentioned casting conditions. The model for NIPS evaluated the effects of coagulation bath composition and polymer concentration on final membrane morphology for PES/NMP/Water (polyethersulfone/n- methyl-2-pyrrolidone/water). These simulations were then compared to handcast mem- branes of a similar membrane forming system for comparison the simulated structures. The NIPS model evaluated coagulation bath composition and polymer concentration and the resulting morphologies. Two and three dimensional simulations were used to look at cross section and top surface morphology respectively. The concentration of NMP in the co- agulation bath was varied to verify the predictive capabilities of the model. The resulting simulations of cross sections and top surfaces had good agreement with handcast membranes when NMP is added to the coagulation bath