Simulation of Membrane Fabrication via Solvent Evaporation and Nonsolvent-Induced Phase Separation

Abstract

Block copolymer membranes offer a bottom-up approach to form isoporous membranes that are useful for ultrafiltration of functional macromolecules, colloids, and water purification. The fabrication of isoporous block copolymer membranes from a mixed film of an asymmetric block copolymer and two solvents involves two stages: First, the volatile solvent evaporates, creating a polymer skin, in which the block copolymer self-assembles into a top layer, comprised of perpendicularly oriented cylinders, via evaporation-induced self-assembly (EISA). This top layer imparts selectivity onto the membrane. Subsequently, the film is brought into contact with a nonsolvent, and the exchange between the remaining nonvolatile solvent and nonsolvent through the self-assembled top layer results in nonsolvent-induced phase separation (NIPS). Thereby, a macroporous support for the functional top layer that imparts mechanical stability onto the system without significantly affecting permeability is fabricated. We use a single, particle-based simulation technique to investigate the sequence of both processes, EISA and NIPS. The simulations identify a process window, which allows for the successful in silico fabrication of integral-asymmetric, isoporous diblock copolymer membranes, and provide direct insights into the spatiotemporal structure formation and arrest. The role of the different thermodynamic (e.g., solvent selectivity for the block copolymer components) and kinetic (e.g., plasticizing effect of the solvent) characteristics is discussed.

Keywords: copolymer membranes; evaporation-induced self-assembly; micro- and macrophase separation; nonsolvent-induced phase separation; simulation and modeling.

Figure 1

Sketch of the simulation setup for the SNIPS process: For the simulation of the first step of SNIPS, EISA (left), we convert volatile solvent molecules that diffuse beyond the top of the film into gas molecules. This leads to the formation of a self-assembled top layer with perpendicular cylinders, as the solvent density at the top of the film decreases and the polymer density increases, in turn. In the second step, NIPS (right), we bring the top of the film into contact with a nonsolvent bath. The nonsolvent molecules exchange with both remaining solvents in the film. This leads to the creation of a macroporous structure beneath the self-assembled top layer by macrophase separation between the nonsolvent and polymer.

Figure 2

Dependence of the mobility modifier, eq 6, for A and B segments as a function of the local densities of the same block and the volatile solvent, S. The density of the other segment species is set to 0.

Figure 3

Snapshots of the majority-block density, ϕ_B, during SNIPS at different times. The EISA process continues until t = 58.1τ_R. Thereafter, the NIPS process commences.

Figure 4

Top: 1D density profiles of polymer, P = A + B, volatile solvent, S, nonvolatile solvent, C, and gas G, at the top of the system as a function of the perpendicular position, z. Bottom: two-dimensional (2D) cross section of the density difference, ϕ_A – ϕ_B, in the corresponding region. The snapshots show the systems at times t/τ_R = [1.5, 7.3, 13.1] from left to right. Three-dimensional (3D) snapshots of the majority-block density at the corresponding times are shown in Figure 3.

Figure 5

(a) Micro- and macrophase-separation-front positions as a function of time. The switch from EISA to NIPS occurs at t* = 58.1τ_R. For t < t*, macrophase separation refers to the coexistence between polymer film and gas (vapor); i.e., the corresponding front is the film surface. In the course of NIPS, t >t*, macrophase separation refers to the coexistence between nonsolvent and polymer-rich domains. During NIPS the film surface only very slightly retracts. (b) Average mobility of the matrix block, B, in a cross-sectional slice at the position of the maximum of the 1D density profile argmax_z[ϕ_B(t, z) ]. For the calculation of the average mobility we consider only regions in the cross section where ϕ_B > 0.4.

Figure 6

First and third row: 1D density profiles of polymer, P = A + B, solvents S and C, and nonsolvent, N, as a function of the perpendicular position, z. Second and fourth row: 2D cross section of the difference, ϕ_A – ϕ_B, between minority-block and majority-block density corresponding to the 1D graphs above. The images from top left to bottom right show the systems at times t/τ_R = 58.1, 62.5, 66.9, 71.2, 75.6, and 114.8. The NIPS process commences at t = 58.1τ_R. 3D snapshots of the majority-block density at the corresponding times are shown in Figure 3.

Figure 7

Top: Average lateral cylinder size at position, z, at the start of the NIPS process, t = 58.1τ_R, and at t = 59.6τ_R. Bottom: 1D density profiles of ϕ_B and ϕ_N at the corresponding times. The self-assembled top layer ends at z ≈ 11R_e for t = 58.1τ_R and at z ≈ 11.5R_e for t = 59.6τ_R.

Figure 8

3D view of the total polymer density, ϕ_A + ϕ_B, in the upper part of the membrane after NIPS for the reference system at time t = 114.8τ_R. The left image shows a 3D snapshot of the structure, where the arrow and the plane at the bottom indicate the perspective from which the snapshot on the right was taken.

Figure 9

Lateral domain size of the macroporous structure after 58.1τ_R EISA followed by 58.1τ_R NIPS: The top-left image shows a cross section of the polymer density, ϕ_P = ϕ_A + ϕ_B in the yz plane. The three horizontal lines indicate the z positions of the polymer-density xy cross sections depicted in the three right panels. Bottom row: The leftmost image shows the radially projected collective structure factor, S(q_∥,z), calculated in xy cross sections at the positions z/R = 6, 15, and 35. The dotted lines depict the corresponding smoothed S_G(q_∥) . The images next to it present the collective, 2D structure factor in the corresponding planes. The parameters are identical to those of the reference system, but the xy cross section is quadrupled, i.e., L_x × L_y × L_z = 27.6 × 32 × 50R_e³.

Figure 10

Domain size, d(z), according to eq 9, as a function of depth, z, as well as d_G, obtained from the smoothed structure factor. Linear fits in the region 10R_e ≤ z ≤35R_e are indicated by lines. The three dots indicate the z-position, at which the cross sections are shown in Figure 9.

Figure 11

Top row: 1D density profiles of polymer, P = A + B, solvents, S and C, and nonsolvent, N, as a function of the perpendicular position, z, after 58.1τ_R NIPS. From left to right, the interaction between nonsolvent, N, and matrix block, B, increases, χ_BNN = 100, 200, and 500, where the latter, rightmost system corresponds to the reference system. Bottom row: 2D cross section of the difference, ϕ_A – ϕ_B, between minority-block and majority-block density corresponding to the 1D profiles above.

Figure 12

Top row: 1D density profiles of polymer, P = A + B, solvents S and C, and nonsolvent, N, as a function of the perpendicular position, z, after 58.1τ_R NIPS. From left to right, the interaction between the nonsolvent and the cylinder-forming block increases, χ_ANN = 0, 10, and 25. χ_ANN = 10 corresponds to the reference system. Bottom row: 2D cross section of the difference, ϕ_A – ϕ_B, between the minority-block and majority-block density corresponding to the 1D profiles above.

Figure 13

First and third row: 1D density profiles of polymer, P = A + B, solvents S and C, and nonsolvent N, as a function of the perpendicular position, z, at the end of EISA (first row) and after subsequent 23.3τ_R NIPS (third row). The initial amount of polymer, ϕ_P0, increases from left to right, ϕ_P0 = 0.344, 0.387, and 0.424, where the middle value corresponds to the reference system. Second and fourth row: 2D cross section of the difference, ϕ_A – ϕ_B, between the majority-block and minority-block density corresponding to the 1D graphs above.

Figure 14

First and third row: 1D density profiles of polymer, P = A + B, solvents S and C, and nonsolvent, N, as a function of the perpendicular position, z, measured from the top of the film. The panels in the top row depict the beginning of the NIPS process after 58.1τ_R EISA (left) or 189τ_R EISA (right). The third row depicts profiles after 58.1τ_R NIPS. Second and fourth row: 2D cross section of the difference, ϕ_A – ϕ_B, between the minority-block and majority-block density corresponding to the 1D graphs above.