Highlighting Thermodynamic Coupling Effects in the Immersion Precipitation Process for Formation of Polymeric Membranes

Abstract

In the immersion precipitation process for membrane formation, a polymer casting film is placed in contact with a nonsolvent in a coagulation bath; an essential feature of the membrane formation process is the foray into the metastable region of the ternary phase diagram for the nonsolvent/solvent/polymer system. The primary objective of this article is to trace the origins of such forays. The Maxwell–Stefan diffusion formulation is combined with the Flory–Huggins description of phase equilibrium thermodynamics to set up a model for describing the transient equilibration trajectory that is followed in the polymer casting film. Four different systems are analyzed: water/acetone/CA, water/DMF/PVDF, water/NMP/PSF, and water/NMP/PEI (CA = cellulose acetate; PVDF = poly­(vinylidene fluoride); PSF = polysulfone; PEI = polyetherimide, DMF = dimethyl formamide; NMP = N-methyl-2-pyrrolidone). The analysis shows that diffusional forays are mainly engendered due to thermodynamic coupling effects; such effects are quantified by the set of thermodynamic factors , where a i , the activity of species i, is dependent on the volume fractions, ϕ i and ϕ j , of both nonsolvent (i) and solvent (j). In regions close to phase transitions, the off-diagonal elements Γ ij (i ≠ j) are often negative and may attain large magnitudes in relation to the diagonal elements Γ ii . Strong thermodynamic coupling effects cause the transient equilibration trajectories to be strongly curvilinear, causing ingress into the metastable region. If thermodynamic coupling effects are ignored, no such ingress occurs. It is also shown that analogous diffusional forays may lead to emulsion formation in partially miscible liquid mixtures.