# Geometric Confinement of 3D Smectic Liquid Crystal Foams
## 2 Materials and Methods  
To study the effect of geometric confinements and airflow rates on the fabrication of 3D smectic foams and the assembly of their cells, we utilized cylindrical, square, and rectangular containers, as shown in Figure 1. We used glass containers to help visualize the foam's inner structure. The procedure and preparation methods for the foam fabrication under these different confinements were similar. We utilized the 8 CB LC (4'-octyl-4-biphenylcarbonitrile!, purchased from Kingston Chemicals Limited), which exhibits a crystal phase below 22 \({}^{\circ}\)C, a smectic phase between 22 \({}^{\circ}\)C and 34 \({}^{\circ}\)C, a nematic phase between 34 \({}^{\circ}\)C and 42 \({}^{\circ}\)C, and an isotropic phase starting at 42 \({}^{\circ}\)C, because this material presents a smectic A phase at room temperature. A syringe pump (from KD Scientific) was used with a 30 mL syringe connected to a 19 g \(\times\) 3\" needle (from Cadence Science, Inc., Cranston, RI, USA) via polyethylene tubing (from BD Intramedic, I.D. 1.14 mm, O.D. 1.57 mm) for a consistent airflow with rates varying between 2 mL/min and 62 mL/min. The rectangular container was constructed from glass slides with a length of 25 mm and a width of 6 mm (base area of \(\sim\)150 mm\({}^{2}\)). The square container was a square glass vial with a side length of 15.78 mm (base area of \(\sim\)250 mm\({}^{2}\)). The cylindrical container was a glass vial with a base area of \(\sim\)230 mm\({}^{2}\). A similar initial amount of smectic LC was placed inside these three containers. To fabricate the foam, a hot plate (from Fisher Scientific, Waltham, MA, USA) was used at 40 \({}^{\circ}\)C to keep the LC near the isotropic-nematic phase transition temperature and reduce the high viscosity of the 8 CB at room temperature. Since the containers are also in contact with air, a temperature gradient is then created in the LC. This gradient also induces a viscosity gradient in the LC, with lower values near the bottom (hot surface) and higher ones near the smectic-air interface (cold air). These gradients were found to be very helpful for fabricating and stabilizing the LC bubbles. The air was injected into the samples by using a needle placed in their centers, near the bottom. We adjusted the airflow rate from 2 mL/min up to 62 mL/min to study the effect of airflow rate on the properties of the foam. When the bubble was formed at the bottom of the container, where the LC was in the nematic phase, it moved up to the interface in contact with air and cooled down to the smectic phase. After the foam grew to an optimal height, the hot plate and the syringe pump were turned off, allowing the entire sample to cool down to the smectic phase at a temperature around 22 \(\pm\) 2 \({}^{\circ}\)C. Our analysis started after we ensured that the sample was stable and its temperature was homogenous. For SDS foams, we prepared three solutions with three different concentrations (0.1 wt%, 0.5 wt%, and 1 wt% of SDS in water) to create regular soap foams under the same geometric confinements and airflow rates. A digital camera (Nikon D5600) was used to capture the structure of the foam in the LC and SDS. To better understand the difference between the isotropic liquid and anisotropic smectic foams, as well as how the geometric confinement and the airflow rates affect their properties, we used the technique of image processing (Image) software version 1.53 t) to measure some essential parameters of the foams, such as the cell area near the glass walls, thicknesses, and 3D symmetry. Pictures taken from the digital camera were transformed into 8-bit black-and-white images, and the appropriate threshold values were set for the best analysis of the results. All cells in each image were analyzed individually, and their properties were extracted. To minimize error analysis, the foams that were in contact  
Figure 1: Experimental setup used to fabricate LC foams under different geometric confinements: (**a**) rectangular, (**b**) cubic, and (**c**) cylindrical.