1. INTRODUCTION

Recently, fabrication and manufacturing have become more personalized and distributed due to information technology (IT) and computer networks. Three-dimensional printers have been used in novel ways for specific manufacturing in IT fields. The issue of personalization and distribution is important for chemical analysis, but optical technology requires a highly accurate fabrication on glass or hard polymers. Recently, our research group proposed a soft-material-based optical system, and discussed the on-demand fabrication of optical surfaces based on imprinting. The unified and integrated optical systems were fabricated with 3D-printing technology and simple casting with prepared optical components as the molds [1]. For an aperture size of $\sim 1\mathrm{cm}$, the traditional method must still be used for the optical surface mold, for example, roughing, polishing, grinding, and washing. There are also polishing-free methods for spherical surfaces that use the surface tension. For example, there are some methods using photolithography, imprinting, or hydrophobicity and hydrophilicity [2–4]. Also, a method by hanging a droplet and another one by inkjet printing and heat assistance are unique techniques [5,6]. Although these methods are great techniques, respectively, there are some issues in that they cannot control a curvature of the surface or fabricate only a concave lens.

In this study, we propose an optical surface fabrication method for a more complicated monolithic optical system with an aperture size of 5–10 mm. The spherical surfaces were prepared using the large surface tension force of liquid metals, and its solidification is also discussed for polydimethylsiloxane (PDMS) molding and casting. Liquid–liquid phase casting is also demonstrated. After the PDMS had cured, the gallium was dissolved and suctioned out from a hole drilled through a part other than the optical surface. In addition, the mold in this study was an internal mold and is different from a general shell mold. We believe it is possible to produce on-demand optical elements (e.g., lenses and mirrors) with a miniaturized manufacturing machine, such as a printer, after systematizing because the manufacturing process is simple and takes up less space. In addition, our laboratory conducts research on single-material optical elements based on PDMS, and it is thought that not only lenses but also optical devices can be made by combining these materials [7].

2. STUDY ON LIQUID METAL AS MOLD FOR PDMS CASTING

First, we checked the physical properties of the liquid metal as shown in Table 1. The capillary lengths (CL) are the primary criteria to obtain a larger aperture size, because the maximal radius of the self-formed spherical surface is limited by the capillary length [10] as shown in Fig. 1. The surface tension force $\gamma$ of liquid metal must be large to obtain a large contact angle of its droplet form. The maximum aperture size can be predicted by using the capillary length $k$ that is estimated by $k^{-1}=\sqrt{\gamma /(pg)}$, where $p$ is a density and is listed in the right column. Gallium has the largest surface tension, the melting point near room temperature, longest capillary length of the metals listed, and is herm-free. In addition, gallium has a reflectively $>80\%$ in the visible and UV regions [11]. Since PDMS has a surface tension as low as 20 mN/m, and some product provides a curable catalyst under 29.7°C, a larger contact angle and imprinting without melting can be expected for gallium mold casting. In addition, solid PDMS can retain its form at the gallium melting point, and an even more complicated gallium mold can be extracted with melting. On the other hand, indium also can be another candidate according to the above requirements, but we focused on gallium as a first candidate in this study. We did so for the following reasons: (1) low temperature gap of melting (156°C) and of imprint (25–80°C) can reduce risk of the heat expansion problem; (2) for application in biology, a process temperature higher than 60°C is not appreciated; (3) there is report of risk of health about indium tin oxide [12]; and (4) a high process temperature needs more complicated equipment in future. Also, the others were excluded from the list because of the higher melting point or toxicity.

Table 1. Physical Properties of Liquid Metals

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Fig. 1. Surface shape of the droplet based on the relationship between the length of the capillary tube and the radius. (a) Spherical surface is formed under the condition of $\mathrm{CL}>\mathrm{R}$. (b) Flattened surface is formed when a droplet satisfies $\mathrm{CL}<\mathrm{R}$.

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The surface roughness of gallium crystals implies their potential use as a lens mold and is shown in the magnified image of Fig. 1 using an atomic force microscope (AFM) (VN-8000, KEYENCE). The roughness of the fabricated gallium crystal under a nitrogen atmosphere at 28°C had a root-mean-square (rms) value of 5.9 nm. This value is satisfactory as a lens specification. This is an important point because it is possible to lower the requirement for the thermal process when commercializing the mold system according to the method in this paper. Although there are some liquid metals, such as gallium or bismuth alloys, these are mixed crystals with dull surfaces, and are therefore not suitable for mirrors. Another advantage is that this value is related to the maximum diameter of the lens. The value is $\sim 7\mathrm{mm}$ from the equation of capillary length. We used the density of liquid gallium at the melting point (0°C,1 atm.), and the value of the gallium surface tension reported by Hardy [13]. Moreover, gallium atoms exist as monatomic molecules in liquid gallium, and therefore the transfer capability is high. We investigate the capability in the next section.

3. INVESTIGATION OF GALLIUM ON PDMS IMPRINTING

As a preliminary experiment, the resolution and phase separation properties were investigated in a PDMS/gallium imprinting. We investigated the transfer capability and phase separation on the boundary surface between PDMS and gallium. (a)–(c) of Fig. 2 show imprinting processes in this experiment. First, liquid PDMS (SIM360, Shinetsu Chemical) was cured on a commercial grating (lattice constant, 1200; grid width, 820 nm; Thorlabs), and the pattern was transferred to PDMS. The curing condition is room temperature and 3 h. Subsequently, a liquid gallium of 100 μL was placed on the PDMS grating fabricated with pipet and the pattern copied at room temperature. The curing time was 8 h. Next, the sample was placed at $-20°\mathrm{C}$ for 15 min. Then, if the gallium solidified successfully, the gallium was lifted off the PDMS at room temperature. However, the success rate of the solidification was too low to discuss reproducibility. The surface of the gallium and the PDMS grating from the successful sample were observed by scanning electron microscopy with energy dispersive x-ray spectrometry (JCM-6000Plus with energy dispersive x ray (EDX), JEOL).

 

Fig. 2. Experimental setup and magnified images of the imprinted grating structure. (a)–(c) PDMS or liquid gallium was casted on the commercial grating or the PDMS grating, respectively. Image (d) shows the central part of the gallium grating. Image (f) shows the PDMS surface near the edge after gallium lifting off. Part 013 is located at the surface, the region below is on the edge. (e) and (g) is an enlarged view at 004 and 013. Table 2 is the energy dispersive x-ray spectrometry (EDS) spectra at the locations 004 and 013. All images and data were obtained using a JCM-6000Plus (JEOL).

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Table 2. Element Content Ratio in 013 and 004

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Figure 2 shows the SEM image of the transferred grating surfaces on (d) gallium and (f) PDMS by imprinting from the commercial grating surface. Table 2 shows the EDX spectra of the squares 004 in Fig. 2(e) and 013 in Fig. 2(g) in Figs. 2(d) and 2(f), respectively. The lifting off of the gallium from the PDMS was very smooth, and no damage due to adhesiveness was observed. Figure 2(d) shows the grating structure with a pitch of 0.82 μm and was transferred with a resolution of $\sim 0.2\mathrm{\mu m}$. As shown in Table 2, no residual silicon was observed at location 004. Even though the gallium had a solidification expansion of 4%, the surface grating structure was as shown in Fig. 2(d). At the contact interface of the liquid gallium and PDMS, the gallium solidification expanded in the thickness direction. Figure 2(f) shows the edge of the PDMS grating after imprinting to gallium, and square 013 is in the surface region. No residual gallium was observed at location 013 from Table 2.

4. DEVELOPMENT OF THE FABRICATION PROCESS

Liquid gallium had the longest capillary length, and an aperture size of up to 7 mm was expected for the spherical surface formation. Several imprinting schemes were expected, as follows:

For each scheme, microscopic and macroscopic properties must be evaluated by using microscopy and a spherical surface check, respectively. In addition, concave and convex properties must be checked, individually.

At first, we evaluated microscopic properties by using simple droplet fabrication with scheme (a) in subsection 4.A, and stable solidification will be investigated. Secondarily, we developed newly a push–pull method to improve the macroscopic properties in subsection 4.B. Next, in subsection 4.C the convex meniscus of gallium was investigated in the solidification, and microscopic and macroscopic evaluation was described. Finally, the concave properties were evaluated in subsection 4.D. Scheme (a) was insufficient to obtain the result of the optical surface; schemes (b) and (c) were adopted to obtain better results.

A. Fundamental Gallium Solidification Control for Optical Surface and Microscopic Investigation

Solidification of gallium in PDMS was investigated. Severe supercooling as low as $-20°\mathrm{C}$ was observed, affecting the spontaneous solidification stability using the cooling method. Furthermore, the surface oxidation of liquid gallium might partially prevent the solidification. After the optimization, we adopted the following methods to solidify the cooled gallium: 1) melt solid gallium at $<50°\mathrm{C}$ or, 2) contact solid gallium crystal ($\alpha$-gallium) to liquid gallium at 25°C. In addition, all processes were performed with nitrogen purging to reduce oxidization. Because of the larger heat of melting (5.59 kJ/mol) and smaller heat capacity, gallium requires contact with a heat sink for solidification. Sufficient heat solidification starts from the contact point. Solidification can be triggered by residual microcrystals using a lower melting temperature. Since the ratio of the heat of melting to the heat capacity of gallium is as large as $\sim 200\mathrm{K}$, the rapid solidification of supercooled liquid gallium may be self-stopped by heat emission. However, it was found that contacting a heat sink, such as an aluminum plate, can suppress the self-stopping.

Figure 3(c) shows the gallium droplet solidified by the solid gallium contact. This sample was fabricated with a procedure like Figs. 3(a) and 3(b). Since the supercooled gallium liquid had a viscosity as high as 1.7 mPa, the surface tension force was not able to remove the distortion from the spherical surface of the gallium droplet. This was especially true for the case of the uncured PDMS. Even in atmosphere, the gallium oxide skin might affect the spherical surface. Figure 3(d) shows an optical microscope image of the convex surface solidified in the atmosphere, and Fig. 3(f) shows a three-dimensional image of a part of Fig. 3(d) by AFM data. The square part in Fig. 3(d) is considered a structure derived from an oxide crystal, and many crevasses were observed due to the solidification expansion. With nitrogen purging, the convex surface was improved as shown in Fig. 3(e). Also, Fig. 3(g) shows a three-dimensional image of a part of Fig. 3(e) by AFM data. A rms surface roughness of 5.9 nm was obtained from the AFM (VN-8000, KEYENCE) observation. The microscopic smoothing was seemingly sufficient for a small-scale optical component, but the macroscopic profile still needs improvement.

 

Fig. 3. Droplet surface of solid gallium. (a) and (b) fabrication steps of a sample. (c) Top view of a solidified gallium droplet with gallium crystal contacting. The length of the scale bar is 1 mm. (d) Optical microscope image of droplet surface solidified in atmosphere. (e) A similar surface solidified in nitrogen. A roughness of 5.9 nm in rms was estimated by AFM (VN-8000, KEYENCE). (f) AFM data of a part in (d). (g) AFM data of a part in (d). (f) and (g) the length of $x$ and $y$ is 50 μm, and the length of $z$ shows from (f) 0 to $8.\times {10}^{-6}$ or (g) $3.\times {10}^{-6}$. The unit of $z$ is m.

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B. Meniscus Control for Variable Lens Curvature on Liquid Gallium

Since the free-forming convex produced an insufficient result by using only the gallium surface tension force, a new formation procedure was developed in this study. We used a large contact angle hysteresis (CAH) and contact line pinning (CLP) of liquid gallium on a nonideal surface of PDMS. In the preliminary experiment, the advancing and receding contact angles were measured as ${\theta }_{\mathrm{A}}=150°$ and ${\theta }_{\mathrm{R}}=30°$, respectively. For example, for mercury on glass, ${\theta }_{\mathrm{R}}=106°$ and ${\theta }_{\mathrm{A}}=140°$ [14]. Figure 4 shows the developed push–pull method, which forcibly forms the gallium surface meniscus. First, a tube (height of 10 mm, internal diameter of 5 mm) of PDMS (SIM360, Shinetsu Chemical) was fabricated with a rough internal surface ($<1\mathrm{\mu m}$ rms value). One end was capped by an aluminum plate and the cylinder placed vertically. The liquid gallium (200 μL) in a syringe was injected via a side hole (diameter of 1 mm) at the bottom as shown in Fig. 4(a). Since the applied pressure strongly lifted up the top surface of the injected gallium, the contact line on the surface edge also lifted up slowly with an advance contact angle ${\theta }_{\mathrm{A}}$ [Figs. 4(b) and 4(c)]. Therefore, a sufficient injection amount was needed to balance the contact line, and the top surface formed a convex meniscus. Subsequently, the gallium was suctioned out from 0–40 μL with the syringe as shown in Fig. 4(d). Owing to the strong CLP and large CAH of this system, the curvature of the top meniscus was continuously reduced without lifting down, and the meniscus eventually turned concave. When the contact angle on the edge decreased below the receding contact angle ${\theta }_{\mathrm{R}}$, the gallium surface started lifting down according to the extracted volume $V_{\mathrm{EXT}}$ of the syringe as shown in Fig. 4(e). Only the spherical volume decreased, and the convex shape changed to a concave shape. The experiment was conducted at 25°C and the aluminum plate was heated at 50°C to ensure gallium did not become solid during the fabrication process. The aluminum plate ($20\times 20\times 1.5{\mathrm{mm}}^3$) worked as a heat sink for cooling down the gallium pool on its bottom [Fig. 4(f)]. This ensured that the starting point of the solidification was stable at the bottom and prevented random solidification.

 

Fig. 4. Experimental setup of push–pull injection. (a) PDMS chamber (height, 10 mm; diameter, 5 mm) was set on an aluminum plate, which was heated at 50°C. (b) and (c) The gallium was injected into the chamber through the path (diameter: 1 mm). The aluminum plate was heated, preventing solidification during injection. (d) The gallium was suctioned out from 0–40 μL after injecting. The contact end point was fixed using the pinning effect and only the spherical volume was changed. (e) Meniscus receding by suction of over 40 μL. (f) Solidification at 25°C.

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C. Evaluation of Convex Meniscus

It is commonly known that liquid gallium has a solidification expansion of 3.2% in volume [15]. This expansion may have affected the formed meniscus profile described above. Figures 5(a), 5(b), 5(c), and 5(d) show side-view images of the convex meniscus of the gallium solidified under nitrogen by varying the extraction volume $V_{\mathrm{EXT}}$ (0 μL, 5 μL, 10 μL, and 15 μL, respectively). After the meniscus was formed, the temperature of the aluminum plate was decreased to 25°C, and the solidification started from the bottom and then finally the top surface solidified. The solidification took $\sim 15\min$. The PDMS tube absorbed the radial expansion of the solidified gallium, and no distortion was observed from the top convex meniscus as shown in Fig. 5(e). All cross-section profiles showed good agreement with the circular curves. The standard deviations were in the range of 0.012–0.017% of the fitted spherical radius $R_{\mathrm{Ga}}$. The minimum $R_{\mathrm{Ga}}$ was 2.66 mm at $V_{\mathrm{EXT}}=0$, and increased to 3.43 mm at $V_{\mathrm{EXT}}=15\mathrm{\mu L}$, where the aperture size $d$ was 5 mm. The surface microscopic morphology was similar to Fig. 3(e) because of the solidification just under the surface of the gallium/nitrogen interface.

 

Fig. 5. Side-view images of the convex meniscus of gallium (solidified). The sucked-out volume is, respectively, (a) 0 μL, (b) 5 μL, (c) 10 μL, and (d) 15 μL. The scale bars show 2 mm. (e) The fitted curves of the profiles of the images showing the relationship between the curvature and emissions of the convex gallium. The right graphs were obtained from the processed images of the left photographs.

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D. Evaluation of Concave Meniscus

The concave meniscus lost its surface quality in the solidification due to the expansion. This is considered that the volume expansion of gallium worked shrinking the concave surface area. Figure 6(a) shows the effect of the gallium’s volume expansion for convex or concave surfaces. In the solidification method, solidifying starts from the bottom to the surface. Therefore, the surface receives the effect of all increased volume. In the case of convex, the volume expansion works to expand the surface area. On the other hand, the concave surface area decreases by expanding each microgallium on the surface. Further, the solidifying speed of microgallium particles or masses in a same mold is different. Therefore, the part solidified later collides with the previously solidified part, and microcracks are formed. To avoid the microcracks by the volume expansion, taking into account the results of Fig. 2, 30 μL of uncured PDMS was dropped onto the center of the concave meniscus after the formation, and a solidification order of two patterns was tried. One pattern is that the liquid gallium mold was solidified at first by decreasing the temperature to 25°C for 30 min (liquid PDMS on liquid gallium). The other pattern is that the PDMS was cured at a temperature of 50°C for 3 h at first. Then, the liquid gallium mold was also solidified by decreasing the temperature to 25°C for 30 min (or solid PDMS on liquid gallium). Figure 6 shows the optical microscope images of (b) the surface of gallium solidified with the nitrogen interface, (c) PDMS solidified with liquid gallium meniscus, (d) gallium solidified in liquid PDMS, and (f) gallium solidified with interface of (c).

 

Fig. 6. (a) Effect to the convex and concave surface by volume expansion. (b)–(e) The macroscopic images of the concave meniscus obtained using the push–pull method for (b) gallium solidified in nitrogen, (c) PDMS cured with liquid phase gallium, (d) gallium solidified in uncured PDMS, (e) gallium solidified in solid PDMS, and (f) three-dimensional image of a part in (c) by AFM. The surface roughness was under 1 nm in rms. The length of $x$ and $y$ is 50 μm, and the length of $z$ shows from 0 to $10.\times {10}^{-6}$. The unit of $z$ is m.

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Generally, the solidification of supercooled liquid gallium by cooling leads to an $\alpha$-crystal with an expansion of 3.2% in volume. In Fig. 6(b), a large crack, 10 μm in width, on the meniscus that faced the nitrogen was observed, contrary to the results of the surface of the convex meniscus in Fig. 3(c). This appears to be due to the gallium expansion and crystallization stating from the far side from the meniscus. The crystallization from the meniscus was not enough to remove the microcracks in the case of the liquid gallium and nitrogen interface. Therefore, liquid PDMS was put on the concave meniscus, and the liquid gallium and uncured PDMS interface were investigated. First, only the PDMS was cured and is shown in Fig. 6(c). Figure 6(f) shows the AFM image of a part of Fig. 6(c). The surface roughness of Fig. 6(c) was under 1 nm in rms. This liquid–liquid phase molding showed an acceptable quality that was similar to the surface of Fig. 3(c). However, the solidification of gallium after forming the meniscus with uncured PDMS still obtained microcracks as shown in Fig. 6(d). This implied that microcracks can occur if the stress caused by the expansion affects the form of the molding boundary, even though the liquid PDMS interfaced with the liquid gallium on the boundary. Therefore, the solidification of liquid gallium was investigated using a molding boundary with solidified PDMS, and Fig. 6(e) shows the microscopic image of the gallium surface. Though the molding boundary condition was similar to that of Fig. 2(d), it still contained microcracks of 1–5 μm width. This difference seemed to be dependent on whether the gallium bulk had a free surface other than the surface of the molding boundary, and therefore the microcracks were decreased by improving the push–pull chamber for smaller amounts of gallium and stress release. Based on these results, an optical surface of solidifying PDMS on liquid gallium is evaluated macroscopically in next section.

5. CONCAVE MENISCUS MACROSCOPIC EVALUATION

The obtained concave meniscus was evaluated by taking a negative pattern of PDMS. Figure 7(a) shows the curvature $R_{\mathrm{Ga}}^{-1}$ of the meniscus, with positive and negative values referring to convex and concave, respectively, as a function of the extraction volume $V_{\text{Ext}}$. The theoretical curve of the curvature and the volume of the spherical cap $V$ can be given by

 

Fig. 7. (a) Curvature versus extracted volume of gallium’s spherical surfaces. (b) and (c) Example images of grid lines with the largest curvature lens. These were photographed by attaching the lens to grid lines or a camera’s lens, respectively. The green points show the constant pitch, and the red ones are the detected cross points from the image. A negative lens fabricated by transferring concave gallium with a $\text{diameter}=5\mathrm{mm}$, radius of $\text{curvature}=4.2\mathrm{mm}$, $\text{thickness}=3\mathrm{mm}$, focal $\text{length}=6.6\mathrm{mm}$, F $\text{value}=2.1$, and $\mathrm{NA}=0.498$. The scale bar is 1 mm in (b) or 2.5 mm in (c).

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Figure 7(b) is an example image of the largest curvature lens ($f=6.6$, $\text{aperture}=5\mathrm{mm}$, center $\text{thickness}=3\mathrm{mm}$, F $\text{value}=2.1$, and $\mathrm{NA}=0.5$). The NA was calculated with PDMS’s refractive index (1.41), focal length (6.6 mm), and aperture (5 mm). The image was obtained by placing the lens directly on a grid of paper (0.5 and 0.1 mm pitch) and taken with a microscopic camera (44302-A Deluxe Handheld Digital Microscope, Celestron). Owing to the large spherical aberration for large NA, barrel distortion was observed. The green points are the constant pitch, and the red points are the detected cross points from the image. The image distortion outside the aperture was due to the PDMS envelope of the PDMS lens. Near the center, 27 green points $\sim 0.1\mathrm{mm}$ from the red points with small irregular distortion were observed at the bottom right. Since the center of the image seemed acceptable, a mobile phone camera with the lens attached was used to take the magnified image as shown in Fig. 7(c). A slight pincushion distortion was observed, but the images of the macrogrid (LCD image) had good focus. Owing to the lens deformation, a slight aberration was observed on the bottom left part of the image, but over the whole area, the image focus was confirmed. To realize a more high-performance lens by this method, consider that the inner surface roughness of PDMS tube in push–pull method is under a few nm. This makes the wetting position remain at the same height, and the liquid surface will be able to keep the macroscopic shape without distortion. Therefore, the aberration of the lens can be decreased. This is also expected by mechanical control of all fabrication steps, due to precise control of the fabrication process, such as gallium’s volume control.

6. CONCLUSION

In this paper, we found out the wide controllability of the contact angle of gallium on PDMS and described a new fabrication method of optical surfaces by liquid metal molding and casting. The variable range of the contact angle was $\sim 30°$ to 150° due to the hysteresis because of a large interface energy between them. It also provides that liquid gallium and PDMS are separated by an interface, without mixing and reacting, so fabrication by molding is feasible. Furthermore, a smooth surface (microscopic) and controllable curvature (macroscopic) were evaluated and obtained, simultaneously. In the future, polishing-free and on-demand fabrication of optical elements is conceivable as an application of this work.