# Geometric Confinement of 3D Smectic Liquid Crystal Foams
## 3 Results  
Fabrication and creation of the foams: With the setup described above, we successfully fabricated the foam in the three containers with different geometries, with airflow rates changing from 2 mL/min to 62 mL/min. The experimental results show that the LC foams cannot be created in the pure smectic or nematic phases. The reason is that the 8 CB material is too viscous in the smectic phase. Therefore, the bubbles could not be fabricated due to the strong elasticity preventing them from forming. When the 8 CB is in the nematic phase, we can create bubbles. However, they are unstable. They collapse immediately due to the lack of the lamellar structure in the LC film. Our solution to generate stable foams was to create bubbles in a container with a temperature gradient; a nematic phase near the bottom, where air is injected; and a smectic phase near the interface, where the bubbles are packed. This helps to reduce the viscosity of the 8 CB, where bubbles are created, and stabilize them via the lamellar structure, where they are packed. For simple fluid foams, we found that the concentration difference of SDS does not lead to fundamental changes in the sample properties, except that the higher concentration enhances the creation of bubbles. For this reason, we focused on SDS samples with 1 wt% concentrations in this study. Rectangular confinement: The goal of fabricating foams in rectangular containers is to understand how geometric confinement will affect the properties of LC foams under different airflow rates. We started with an airflow rate of 2 mL/min, as shown in Figure 2a. In this case, the LC bubbles pack and line up nicely, similar to the bubbles generated from the SDS solution (Supplementary Figure S1a). In addition, they are stable for about two hours. Their overall size near the container wall is almost uniform, with an average area of \(\sim\)2.21 \(\pm\) 0.049 mm\({}^{2}\). However, their shapes change from circular near the LC reservoir (bottom of the foam) to polygonal (hexagon) near the smectic-air interface. This result indicates that the foam volume fraction, usually affected by the drainage due to gravity, plays a vital role in the formation and assembly of LC bubbles. Here we analyze the 2D projection of cells at the wall container to predict the behavior of cells in bulk because studying foams in 3D is complex experimentally. Figure 2: Fabrication of smectic foam under rectangular confinement. The rectangular containers were constructed from glass slides with a length of 25 mm and a width of 6 mm. Images of LC foams created at an airflow rate of (**a**) 2 mL/min, (**b**) 14 mL/min, (**c**) 26 mL/min, and (**d**) 38 mL/min. (**e**) Average areas of the foam cells near the container’s wall for LC (squares) and SDS (triangles) as a function of the airflow rate. Here, we assume that the volume of the 3D cells is proportional to their areas near the glass wall. When the airflow rate is increased to 14 mL/min, we found a slight increase in the size of cells (from 2.21 \(\pm\) 0.05 mm\({}^{2}\) to 2.247 \(\pm\) 0.13 mm\({}^{2}\)). However, there is no significant difference in their characteristics (see Figure 2b), except for slightly diminished stability to approximately one hour. The cells are still well organized with better-defined polygonal shapes near the smectic-air interface. If the airflow rate is increased to 26 mL/min, we start to see some polydispersity in cell size and irregularity in their organization, as shown in Figure 2c (average area of \(\sim\)2.73 \(\pm\) 0.37 mm\({}^{2}\)). At 38 mL/min, all bubbles become random, and no more regularity can be observed in the sample, as shown in Figure 2d. When we continued to increase the airflow rate beyond 38 mL/min, we found that the LC foams could no longer be fabricated because their cells could not hold and would collapse quickly. To study the difference between an ordered fluid and an isotropic material, SDS foams were fabricated in the same conditions and were compared to LC ones, as shown in Supplementary Figure S1.