Numerical study of the effect of the relative mobilities of chemical components on the Non solvent induced phase separation process for membrane elaboration

TL;DR

This study examines how the relative mobilities of polymer, solvent, and non-solvent influence Non-Solvent Induced Phase Separation (NIPS) in ternary polymer–solvent–nonsolvent films using a Cahn-Hilliard framework. By performing 2D simulations with varying polymer mobility $M_p$ and initial compositions, the authors show mobility determines whether phase separation occurs and what morphology emerges, ranging from banded, SDSD-like patterns to maze-like structures; 3D simulations reveal widespread bicontinuous morphologies across a broad composition range and quantify connectivity via tortuosity and conductance. The results demonstrate that slower polymer mobility expands the domain of phase separation and can shift pattern formation toward complex, interconnected networks, with a quantifiable transition around certain initial compositions. Overall, the work provides mechanistic insight into how kinetic factors shape membrane microstructure during NIPS and offers quantitative descriptors (connectivity, tortuosity) to guide membrane design and optimization.

Abstract

The filtration membranes are often elaborated through a phase separation process where a polymer rich phase and a polymer poor phase spontaneously form through spinodal decomposition. One process that is still not well understood from a theoretical point of view is the Non-Solvent induced phase separation where a thermodynamically stable film of a a polymer mixture is put in contact with a bad solvent of the polymer. The invasion of the film by this non-solvent drives the film out of stability and leads to spinodal decomposition. During this phase separation polymer poor and polymer rich regions form. In this article we present a numerical study of the effect of kinetic coefficients: namely the relative mobilities of polymer and solvent/non-solvent on the observed patterns. Using 2D numerical simulations of the ternary Cahn-Hilliard model we show that for a given thermodynamic landscape, this parameter has dramatic effects: depending on its value phase separation can be observed or not. We also show that it can affect the nature of the observed pattern. In addition analysing 3D simulations we analyse the final pattern using a quantitative indicator of its connectivity and show that for a wide range of initial composition of the film the final pattern is bicontinuous. We also quantify the transport properties of both polymer rich and polymer poor domains.

Figures (15)

• Figure 1: A schematic showing the NIPS membrane manufacturing process
• Figure 2: 2D simulation geometry: Polymer film ($L_f$) and Non-solvent bath ($L_b$) with periodic boundaries
• Figure 3: Ternary Gibbs phase diagram computed using an in-house simulation code. The ligh gray region corresponds to the domain of compositions for which the system is linearly unstable. The medium gray region to the metastable domain. And the dark gray region corresponds to the homogeneous stable domain. C is the critical point, M, and N are two points that are at equilibrium with each other. The dashed line is the corresponding tie line. The solid line that is drawn at the bottom of the binodal domain corresponds to the points for which $\mu_{ns}=\mu_{ns}^{bath}$.
• Figure 4: Illustration of three behaviors observed in the NIPS process simulations, with all species having equal mobility ($M_p = M$): (a) Phase separation; (b) Delayed phase separation; (c) No phase separation. The initial composition ($\phi_p^0$, $\phi_n^0$) for each case is: (a) (0.3, 0.3); (b) (0.5, 0.1); (c) (0.4, 0.1). The evolution of the polymer volume fraction is shown at four distinct simulation times (each time is multiplied by $10^5$): (a) $[0.075, 0.22, 0.45, 1.5]$; (b) $[0.05, 1, 2.5, 5]$; (c) $[0.015, 0.75, 1.95, 3]$. The three initial compositions are indicated by points on the phase diagram shown below. At final time the composition of the different phases that can be seen above are independent of the initial film composition. They are represented by the P (polymer poor) and R (polymer rich) points on the phase diagram.
• Figure 5: Results from 2D simulations of the NIPS process with an initially perturbed film are shown in the phase diagram, where each point signifies the film's initial composition. The initial composition ($\phi_p^0$,$\phi_n^0$) for each case : a)(0.4,0.25); b)(0.6,0.1); c)(0.4,0.1). The evolution of the polymer volume fraction is depicted at four different simulation times $t$ multiplied by $10^5$. The dotted line is the $\phi_p = \text{const}$ line that passes through the intersection point between the $\mu_{ns} = \mu_{ns}^{\mathrm{bath}}$ curve and the spinodal line.