Novel Strategy for Fabricating Multilayer Porous Membranes with Varying Porosity

CO2-assisted polymer compression (CAPC) is a method for fabricating porous polymer materials in which the polymer is plasticized with CO2 and then pressed. In this work, a two-step molding method is adapted, and a porous membrane with multiple layers of varying porosity is fabricated by laminating sheets of a single starting material. A model is constructed in which the expansion owing to CO2 and compression reflected by the longitudinal elastic modulus are considered. The model is constructed based on a two-layer experiment and extended to three layers. From the model simulation, the conditions for fabricating a multilayer porous polymer membrane with three layers of varying porosity (0.6, 0.5, and 0.4) and identical thickness (0.6 mm) are calculated. Finally, a porous membrane with varying porosity is fabricated based on the simulated design.


■ INTRODUCTION
Polymers are indispensable materials in daily life because of their lightweight and durable nature. 1 Among polymer materials, porous materials have numerous applications, such as filters, catalysts, bioreactors, and thermal insulators. 2 For example, porous fibrous materials are used for face masks, 3 2.5 μm particulate matter filters, 4 water filters, 5 and filters for oil-inwater filtration. 6 In particular, nonwoven fabrics are often used in filters owing to their high productivity and low price. 7 These materials can also be functional; for example, porous membranes have been used as battery separators. 8 In the study of porous materials, obtaining a high-functionality material via precise manufacturing is the major theme.
The latest studies on the fabrication of porous polymer materials using CO 2 include injection molding with a mixture of CO 2 , 9 fabrication by impregnating CO 2 into a solid polymer, 10 and polymeric membranes by supercritical CO 2 -assisted phase inversion. 11 In a previous study, a simple method for producing porous polymer materials was presented, in which fibrous sheets, such as nonwoven fabrics, were pressed by CO 2 ; this process was termed as CO 2 -assisted polymer compression (CAPC). 12 The shape of the CAPC product is flexible and depends on the shape of the pressure vessel; moreover, the porosity and pore diameter can be controlled by the processing conditions. 13 The tunability of pore size of porous materials is crucial for practical use because pore geometry affects the diffusion in porous media. 14 The mechanical properties, such as the peel resistance and penetration resistance, of the CAPC products have been analyzed, and the peel resistance has been found to be well described by a cross-sectional analysis model that considers the aggregation of point adhesions in regions of overlapping fibers. 15 As an application for CAPC products, a tablet encapsulating a drug has been considered, and the drug release rate has been shown to be controllable. 16 Because CAPC is a batch process, productivity may be hindered. However, the productivity can be improved by utilizing an upscaling method in which multiple samples are simultaneously produced with a single press. 17 As described above, CAPC has the significant advantage of controllability based on process conditions. However, when sheets of the same material are stacked and pressed together, a uniform porous membrane is produced. From the viewpoint of high-performance filter applications, pore diameters with gradient are desirable. Therefore, this study aimed to produce a porous membrane with multiple layers of varying porosity by laminating sheets of the same material. This study aims to establish a design method for multilayer filters comprising three layers with the same thickness and different porosities.

■ RESULTS AND DISCUSSION
A nonwoven fabric composed of poly(ethylene terephthalate) was used as a raw material sheet, and a three-layer porous membrane was established as a target, in which the layers obtained by stacking 10, 12, and 15 sheets have a constant thickness. Because the target thickness of each layer is the same, a layer of 10 sheets should have a density that is two-thirds that of a 15-sheet layer with higher porosity. In addition, the relationship between the porosity and pore diameter has been previously reported; 13 thus, in a multilayer porous membrane, both the porosity and pore diameter are expected to decrease as the number of layers increases from 10 to 15 sheets.
If 37 sheets (total of 10, 12, and 15 sheets) are placed in a pressure vessel and subjected to CAPC, a uniform porous membrane should be formed, without a three-layer structure. Therefore, a two-step molding process is proposed in this work. The first CAPC product, which has a low density, is manufactured in the first step, and the final CAPC product, which has a three-layer structure, is fabricated by pressing the initially stacked CAPC products in the second step ( Figure 1).
First, three CAPC products with a thickness of 0.7 mm were manufactured by compressing 10, 12, or 15 sheets. Based on the density (1.34 g mL −1 ) provided in the datasheet, the thickness L solid of a solid cylinder with 18 mm diameter is 0.238 mm at 0.081 g (10 sheets), 0.288 mm at 0.098 g (12 sheets), and 0.357 mm at 0.122 g (15 sheets). Regions with greater thicknesses were pores. Then, its porosity α can be derived from the calculated L solid and its real thickness L porous as follows Hence, the porosity of first CAPC products with 0.7 mm thickness is 0.66, 0.59, and 0.49 for 10, 12, and 15 sheets, respectively. Thereafter, the three samples were stacked, and the second CAPC process was performed to obtain a final CAPC product with a thickness of 1.8 mm. To clarify the layer boundaries, the surfaces of the middle and bottom samples were colored with a felt-tip pen before the second CAPC process. Figure 2 presents a microscopic image of the cross section of the fabricated product. The first layer, consisting of 10 sheets, corresponds to the top region of the red area, the second layer of 12 sheets is located in the top region of the blue area, and the third layer of 15 sheets accounts for the remaining regions. Obviously, the upper layer is compressed, indicating that a weaker layer with a lower density is more strongly compressed than the higher-density layer. Performing the second CAPC process at the same thickness did not yield the desired results. For a strict analysis of the thickness, the adhesion between the layers was suppressed with polyimide films interposed between the layers, and the thickness of each layer was measured with a micrometer caliper. The layer thicknesses were found to be 0.50, 0.59, and 0.71 mm with the porosity of 0.52, 0.51, and 0.50, respectively. Because a layer with larger porosity compresses more strongly, the porosity of each layer becomes close due to this compression. As a trial, three CAPC products with thicknesses of 0.70 (10 sheets; porosity: 0.66), 0.65 (12 sheets; porosity: 0.56), and 0.60 mm (15 sheets; porosity: 0.41) were prepared, and the second CAPC process was used. The thicknesses of the final products were 0.54, 0.60, and 0.66 mm with the porosity of 0.56, 0.52, and 0.46, respectively. It was extremely difficult to produce a multilayer product with the same layer thickness by trial and error, suggesting the need for a design method. In both cases, the bottom layer (15 sheets) after the CAPC process is thicker than the initial sample, indicating that expansion occurred during the CAPC treatment.
Before considering a three-layer compression, a two-layer compression was analyzed. First, the CAPC treatment was performed by stacking 64 sheets to produce 2, 3, 4, and 5 mm samples. Figure 3 shows a scanning electron microscopy image of the sample surfaces. The fiber surface was compressed by being pushed by the bottom of the piston, and the compression region became larger as the compression progressed to 5, 4, 3, and 2 mm. Note the part on the left side of the 2 mm image where the fibers overlap each other in a cross shape. The origin of CAPC adhesion is point adhesion, in which the overlapping portions of fibers are deformed to cause crimping. In a previous study in which the adhesive strength was evaluated by changing the compressibility, it has been reported that adhesive strength can be explained by the analysis of aggregation of point adhesive. 15 Even in the case of the 2 mm sample, the fiber remains on the surface, and it is expected that the fiber-to-fiber

ACS Omega
http://pubs.acs.org/journal/acsodf Article overlapping portions will be combined by the second CAPC treatment. It is necessary for the polymer to be sufficiently plasticized to deform so that the fibers would crimp together. Fibers do not bond in the absence of CO 2 . CO 2 dissolves in the amorphous part of the polymer. 18 Differential scanning calorimetry measurement results of the raw fiber, first CAPC product, and second CAPC product are shown in Figure 4. The peak of crystallization is observed at approximately 120°C, which indicates that an amorphous portion exists. The peak slightly decreases each time the CAPC treatment is performed. This probably occurs because of CO 2 -induced crystallization. 19 A polyimide film was inserted between the CAPC samples with different thicknesses, and a second CAPC treatment was performed to assess the compression of each sample. The measurement was performed twice with the thinner sample at top and twice with the thinner sample at the bottom; the average values of the four experiments were used. The results are shown in Figure 5. In this figure, thick samples are indicated by positive numbers and thin samples are indicated by negative numbers. The sum of the thicknesses of the two samples is the total thickness (x-axis). The empty symbols indicate the initial sample thickness, while the filled symbols show the sample thickness after the CAPC process. For example, note the black circle. The initial sample values are shown by hollow symbols (thicker sample: 5 mm, thinner sample: 4 mm) for a total of 9 mm along the x-axis. The stacked two samples were compressed to 8, 7, 6, 5.5, and 4 mm in the pressure vessel, and the thickness of each layer is indicated by the filled symbols. Similarly, the red squares show the results for the 5 and 3 mm samples compressed to 7, 6, 5.5, and 4 mm. Because the samples have the same weight, the thicker sample has a lower density. In Figure 5, the low-density sample results are given in the top panel, which demonstrates that the low-density samples are more compressed.
Next, the expansion of the samples was analyzed. Figure 6 shows the initial sample density and the expansion ratio for the CAPC samples composed of 64 sheets with a thickness of 1.6− 5.5 mm upon exposure to CO 2 . It was found that the CAPC sample expanded upon exposure to CO 2 .
Based on the above results, a model is proposed, as shown in Figure 7. When CO 2 is introduced during the initial stage of the CAPC procedure, the samples expand. Then, the expanded samples are compressed by the piston, and a compressed sample is formed. The initial expansion data in Figure 6 are measured after the sample is exposed to the atmosphere; thus, the data may be slightly different from the expansion data measured in the presence of CO 2 . However, this difference may not be significant. The red line in Figure 6 presents fitting results obtained using the cubic equation with the least-squares method and the initial expansion. The initial expansion was assumed to follow a cubic equation. The sample compression should be related to the longitudinal elastic modulus of each layer, which must be a function of the density ρ of the porous material. According to Hooke's law, the stress σ is described as based on the longitudinal elastic modulus E(ρ) and strain ε. 20 The strain ε is obtained by dividing the compression length ΔL by the total length L. Let us consider how the total compression is distributed among each layer. When the cylinder is compressed from both ends, the stress of each layer in the cylinder is equal; thus, we have the following relationship Using the following definition and relationship the compression length of each layer was derived as follows ΔL must be small because compression influences the sample density and E (ρ). Therefore, in the simulation, the compression was performed in steps of 1 μm. For example, to achieve a compression of 2 mm, a compression of 1 μm was repeated 2000 times. To understand this further, consider a case where the thicknesses of the upper and lower samples are 3 and 2 mm, respectively. The initial expansion occurs according to the density of each sample, and if the upper and lower samples expand 1.15 and 1.16 times, the thicknesses of the upper and lower samples become 3.45 and 2.32 mm, respectively, after the introduction of CO 2 . In the case of compression to a total of 4 mm, the total thickness of 5.77 mm will be reduced to 1.77 mm. According to eqs 7 and 8, the compression process is conducted in 1770 steps with 1 μm compression in each step. The longitudinal elastic modulus E (ρ) was determined by approximation to the fifth order, as follows. First, the initial samples are subjected to an initial expansion, which is described by a cubic equation. Then, the compression of each layer is calculated from the layer thickness and the longitudinal elastic modulus described by the quintic equation as a function of the layer density. Compression steps of 1 μm are repeated until the entire thickness reaches the target thickness. This step was performed by fitting the coefficient of the cubic initial expansion equation and the coefficient of the quintic longitudinal elastic modulus equation to match the experimental results in Figure 5. Fitting was conducted using the least-square method. Because it is difficult to determine derivatives under repetitive compression, the fitting was performed by the Downhill Simplex method, 21,22 which does not require derivatives. First, the initial expansion is fixed, as shown in Figure 6, and the fifth-order coefficient of the elastic modulus, which depends on the density, is determined by the fitting. Subsequently, the third-order coefficient of the initial expansion and the fifth-order coefficient of the longitudinal elastic modulus are determined, where the first fitting result is set as the initial value to perform the fitting. Figure 8 presents plots of a cubic equation for the initial expansion and a quintic equation for the longitudinal elastic modulus, as determined by the fitting. Because only relative values are important for the longitudinal elastic modulus, a value was normalized by the value at a density of 1 g mL −1 . The initial expansion is not significantly different from that shown in Figure  6, and the fitting form appears to be accurate, with the longitudinal elastic modulus strongly increasing with increasing density.
The compression-after-expansion model was expanded from two-layer compression to three-layer compression. Using the expanded model, a compression of 0.7 (10 sheets), 0.7 (12 sheets), and 0.7 mm (15 sheets) was calculated as 0.51, 0.60, and 0.69 mm, respectively. The experimental data show good agreement with the model results. In addition, a compression of 0.7 (10 sheets), 0.65 (12 sheets), and 0.6 (15 sheets) was calculated as 0.55, 0.61, and 0.64 mm, respectively. These values are close to the experimental results, thus validating the model. After the simulation model was established, the initial sample thicknesses were varied to identify a combination in which each layer is 0.6 mm thick. Unlike the experimental results, the simulated results were obtained immediately, and although the input values were changed manually, with repeated calculations, the desired combination was found in a short period of time. When the CAPC treatment was simulated for samples with thicknesses of 0.738 (10 sheets; porosity: 0.68), 0.574 (12 sheets; porosity: 0.50), and 0.538 mm (15 sheets; porosity: 0.34), each layer was found to have a thickness of 0.60 mm. Based on this result, samples of 0.74, 0.57, and 0.54 mm were applied, which are close to the calculation results, and the samples of 0.61, 0.60, and 0.59 mm were produced with the porosity of 0.61, 0.52, and 0.39, respectively, thus validating the model. The results are summarized in Table 1. Figure 9 shows a cross section of the obtained sample. Each layer has equal thickness, indicating that the desired multilayer porous material was fabricated.

■ CONCLUSIONS
Using the CAPC treatment in two steps, multilayered porous structures with varying porosity were successfully fabricated. To design the desired multilayered porous membrane, a compression-after-expansion model was constructed in which compression was performed after an initial expansion by CO 2 , while considering the longitudinal elastic modulus. The simulation and experimental results show good agreement. Although this study was conducted for three layers, this model can be easily extended to four or more layers and is extremely effective for designing multilayer filters using CAPC.

■ EXPERIMENTAL SECTION
The fiber sheets used in this study were composed of a poly(ethylene terephthalate) nonwoven fabric (fiber diameter: 8 μm, basis weight: 30 g m −2 ) manufactured by Nippon Nozzle Co. Poly(ethylene terephthalate) pellets (model number: TK3) were supplied by Bell Polyester Products, Inc. The nonwoven fabric was punched into 18.0 mm circles. The sample weights were 0.081 g for 10 sheets, 0.098 g for 12 sheets, 0.122 g for 15 sheets, and 0.521 g for 64 sheets.
The CAPC process is illustrated in Figure 1, based on a press machine (JP-1504, Janome Sewing Machine, Co.). A piston with an outer diameter of 19.5 mm and an O-ring was attached on the side of the piston, and a sample was placed in a pressure vessel with an inner diameter of 20.0 mm. The experiments were performed at room temperature. The processing procedure is as follows. In the initial state, the valves are V1: closed, V2: open, ACS Omega http://pubs.acs.org/journal/acsodf Article and V3: closed. After a sample is placed in the pressure vessel, the piston is moved to a lower position to introduce CO 2 . After V2 is closed, V1 is opened to introduce CO 2 through the piston shaft from the CO 2 cylinder. Then, V1 is closed and V2 is opened to release CO 2 . Through this procedure, the air inside the pressure vessel is replaced with CO 2 . Thereafter, V2 is closed, V1 is opened, and gaseous CO 2 is introduced at vapor pressure (6 MPa). After V1 is closed, the piston is lowered to the press position and pressed for 10 s. During the initial CAPC process, the sample is removed after V2 is opened, with a rapid release of CO 2 to the atmosphere. When multiple samples are combined in the CAPC process (second CAPC in Figure 1), V3 is opened with a slow release of CO 2 through the V4 metering valve (Swagelok Inc., SS-SS1) for 30 s; then, V2 is opened. The press position approximately matches the product thickness. When separators are inserted, the press position is adjusted to a higher position based on the total thickness of separators. In this study, it is important to know the thickness of each layer. Therefore, when samples were prepared for optical microscopy, before the second CAPC treatment, the sample surfaces were colored with red and blue felt-tip pens, indicating the layer boundaries. To measure the thickness of each layer, a polyimide film with a thickness of 125 μm was interposed between the samples, and the sample was pressed under conditions in which the layers did not adhere to each other. Because polyimide is a polymer that cannot be plasticized by CO 2 , the polyimide film can be used as a separator in the CAPC method (S in Figure 1). The thickness of each layer was measured by determining the center of the sample using a micrometer caliper. The average of six experiments is shown for the three-layer sample in the main text, and the average of four experiments is shown for the two-layer experiment.
To measure the initial expansion, after the CO 2 was introduced, the piston was moved 1 mm higher than the sample thickness; then, V2 was opened and immediately exhausted. This experiment was performed five times.
An RH-2000 (Hirox Co., Ltd.) optical microscope was used for cross-sectional imaging, and a TM-1000 scanning electron microscope (Hitachi High-Technologies) was used to observe the sample surfaces. Differential scanning calorimetry measurements were performed using Thermo Plus Evo DSC 8230 (Rigaku Co.) to explore the crystallinity. All experiments, model development, and analyses were conducted by T.A.

Notes
The author declares no competing financial interest. The error of thickness is standard deviation of six experiments. Figure 9. Optical microscopy image of the cross section of a multilayer porous material with the same thickness for each layer, as designed by the compression-after-expansion model.