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Abstract
In this paper, polyvinyl chloride (PVC) gels microlens arrays (MLAs) with controllable curvatures were prepared by evaporation of the solvent under DC electric fields. In order to obtain these arrays, the PVC gel solution was first injected into the cofferdam of a ring array patterned electrode substrate. Upon polarization under DC electric field, the electric charge injected from the cathode was carried by the plasticizers towards the anode to accumulate on its surface. After complete evaporation of the solvent, the PVC gels formed stable MLAs. The focal length of the formed MLAs obtained after evaporation of the 100 µL PVC gel solvent under 30 V DC field was 8.68 mm. The focal length of the as-obtained PVC gel-based MLAs can be well-controlled by merely tuning the strength of the electric field or by changing the volume of the PVC gel solution. Thus, it can be concluded that the proposed methodology looks very promising for future fabrication of MLAs with uniform size in larger areas.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microlens arrays (MLAs) have attracted increasing attention due to their broad applicability [1] in microelectromechanical systems, image processing, optical communication, semiconductor solar cells, light-emitting diodes, three-dimensional (3D) displays, and sensors. The control over the curvature of MLAs aspheric shape significantly reduces the spherical aberration. Various optical materials have so far been tested for the fabrication of MLAs. For instance, glass MLAs [2] have been studied for decades using several techniques, including ion exchange, photothermal expansion, reactive ion etching, direct laser writing, and femtosecond-laser-enhanced local wet etching. However, these manufacturing processes are more complex, time-consuming, less cost-effective, and not suitable for mass applications.
Liquid lenses [3] based on electrowetting actuation or dielectrophoresis force have shown excellent controllability over the curvature of the lens under applied electric fields, leading to enhanced optical performances. Nevertheless, the nature of droplet-wise manipulation, which often merges the neighboring droplets, leads to challenging formation of arrayed microlenses with high fill factors and stable curvatures over large areas. Liquid crystal (LC) lenses [4–7] exhibit low driving voltage and fast dynamic response, while most LC lenses rely on polarized light, resulting 50% of the light loss. Hence, various types of plastic MLAs have been recently fabricated due to their high optical performances, easy processing, lightweight, low cost, and excellent flexibility. These plastic MLAs could be fabricated by various techniques, such as micromolding [8], thermal reflow, [9,10] inkjet printing [11–13], and electrohydrodynamic patterning [14].
Polydimethylsiloxane (PDMS) [15–17] is an excellent optical material, often manipulated by micromolding method to replicate the configuration of the mould to form MLAs. However, the surface morphologies of PDMS based MLAs could easily be damaged during the peel-off process from the mould. Thermally reflowed photoresists (PRs) [9,18] allows the fabrication of large MLAs with excellent optical quality and response wavelengths ranging from deep UV to far IR. Nevertheless, the time and temperature requirements are relatively strict during PRs melting process.
On the other hand, pre-cured polymer inks [13] used in the fabrication of MLAs by direct application on the substrate surface by inkjet printing technique suffer from the limited viscosity range. Dielectric UV-curable prepolymers [14,19–22] with high dielectric constants used in electrohydrodynamic patterning techniques could be employed for the fabrication of MLAs with high cost-efficiency. This can be achieved through the use of electrically conductive microhole-arrayed templates [23] producing spatially modulated electric fields on initially flat liquid prepolymer films. Using this method, the curvature of the liquid prepolymer can be controlled by applying high voltages, while the removal of microhole templates from the adhesion areas of solidified polymers remains challenging.
Polyvinyl chloride (PVC) gels [24] are promising for fabrication of MLAs due to their high transparency, superior compactness, lightweight, and remarkable electromechanical deformation without noise [25–29]. Unlike most of LC lenses, the PVC gel lens was polarization independent. PVC gels are electroactive polymers that may deform under DC electric fields. The electric charge (or electrons) injected from the cathode will migrate towards the anode, where they accumulate to promote the electrostatic force between the gels and the anode to yield creep deformation [30–32]. This process often requires power consumption of the order of several tens of nanowatts per square millimetre thanks to the small leakage current of PVC gels. The deformation of PVC gels depends significantly on the boundary conditions of the gels and electrodes, as well as the strength of the applied DC electric field.
One method to fabricate PVC gel-based MLAs [33] is by using a conductive polymeric cavity to compress the PVC gels on the electrode substrate. After complete evaporation of the tetrahydrofuran (THF) solvent, PVC gel-based MLAs are formed in the cavity array. The application of a voltage across the conductive polymer (anode) and bottom electrode (cathode) would allow the injection of electrons into the PVC gels from the cathode, which then move the charged plasticizer towards the anode. The induced electrostatic force could allow the charged plasticizer to creep up on the polymeric wall and shift, thereby changing the shape of the droplet. However, the high driving voltage (250 V) is limiting the applicability of this approach.
Another common way to fabricate PVC gel-based MLAs [34,35] is by spin-coating of PVC gel solution onto patterned electrode substrates followed by evaporation of the solvent (THF) to form flat membranes. Under external DC voltage, the electric charge (or electrons) will be injected from the cathode allowing the movement of the plasticizers in PVC gels towards the anode, where they accumulate on the PVC gels surface near the anode. However, the creep deformation of PVC gels changes the focus. By comparison, flat PVC gels membranes have no lens effect when in the absence of voltage. Therefore, PVC gels-based MLAs should form only under continuously applied voltages, and the lens effect will vanish once the voltage is removed. Therefore, PVC gel-based MLAs with initial focal-length and voltage-independent are highly desirable for proper future applications.
In this paper, PVC gel-based MLAs were fabricated by applying DC electric fields on ring array patterned electrodes to actuate the equilibrium state of PVC gel solutions and evaporate the THF solvent. Under DC polarization, the molecules of the plasticizer (dibutyl adipate - DBA) in PVC gel solutions moved toward the anode under the action of the electric force, leading to their accumulation in the anode vicinity. Maintaining the voltage for a sufficiently long period could ensure the establishment of equilibrium, thereby yielding PVC gel-based MLAs with controllable initial focal lengths.
2. Concepts and device fabrication
COMSOL Multiphysics software was used to investigate the distribution of the potential in the ring array patterned electrodes. The simulated results are collected in Fig. 1. In simulated finite element modelling, the distance between two adjacent rings was set to 30 µm, and the inner and outer radii of the ring were respectively 100 µm and 115 µm. The anode and cathode were connected to the inner circle electrode and outer area, respectively. The top view of the simulated results under 30 V DC applied voltage is illustrated in Fig. 1(a). The high to low potential was defined by colour code (red to blue). Under polarization, the potential can be resolved into three components along: X-direction, Y-direction, and Z-direction [Fig. 1(b)]. The electric fields in the inner circle were strong, implying that the plasticizers could move toward the center of the inner circular electrode. Along Z-direction, the electric field distribution was stronger near the inner circular electrode surface than in the surrounding area. The connection of two adjacent inner circular electrodes also generated an electric field, responsible for the destruction of formed shapes of PVC gel-based MLAs. The asymmetrical shapes became more serious in the case of MLAs with smaller diameter. This problem can be resolved by reducing the width of the connecting line or by designing the floating (nonconnected) electrodes.
Fig. 1. Simulation of the potential distribution of ring array patterned electrode substrates at V = 30V: (a) top view and (b) vertical view.
The fabrication procedure of PVC gel-based MLAs is described in Fig. 2. The PVC gels solution was prepared by dissolving PVC powder (Mn ∼ 99000, Sigma-Aldrich) and DBA (purity 96%, Sigma-Aldrich) in tetrahydrofuran (THF, purity 99.9%, Sigma-Aldrich) at a weight ratio of 1:9 [Fig. 2(a)]. The patterned electrode substrate was based on Indium-Tin Oxide (ITO) etched with a ring array pattern (white colour) to divide the electrode into two parts: electrode-1 (red colour) and electrode-2 (blue colour). The inner and outer radii of the ring were 100 µm and 115 µm, respectively. The distance between two adjacent rings was 30 µm. A hollow square made of silicone rubber served as a cofferdam on the substrate, and the active surface of the electrode was 2 × 2 cm2 [Fig. 2(b)]. The fabrication process consisted of first thoroughly stirring the PVC/DBA in THF solvent at room temperature followed by filling of the cofferdam [Fig. S1(b)] with a specific volume of the mixture [Fig. S1(a)] under DC voltage polarization. The solvent THF was then let to evaporate while maintaining a constant voltage at room temperature [Fig. 2(c)].
Fig. 2. Fabrication procedure of the proposed PVC gels based-MLAs: (a) preparation of PVC gels solution, (b) cofferdam on the ring array patterned electrode substrate, (c) evaporation of the solvent under DC voltage, and (d) formation of PVC gel based-MLAs.
A critical issue for the experiments was to identify the time required to reach the equilibrium state. To this end, ethyl acetate with a boiling point close to room temperature (26.5 °C) was used as a standard reference. Assuming the volatilization speed of ethyl acetate as 100, boiling point of THF as 66 °C and its relative volatilization rate as 501, the calculations suggested that a few hours should be long enough to ensure the establishment of an equilibrium state. After complete evaporation of THF (after 2 h), the electric field was disconnected, and cofferdam was peeled off, leading to the formation of PVC gel-based MLAs with an initial focal length [Fig. 2(d)].
At a fixed size of the cofferdam and active area of the ring array pattern, the volume of PVC gels solution in the cofferdam and strength of DC electric field would affect the curvature of PVC gel-based MLAs. To evaluate the influence of the electric field, five control groups were prepared and tested at the volume of PVC gels solution of 100 µL and different applied voltages (10 - 50 V). To evaluate the influence of PVC gels solution volume, five other control groups were prepared and tested at an applied voltage of 50 V and volumes of PVC gels solutions of (60 µL, 80 µL, 100 µL, 120 µL, and 140 µL). The PVC gel-based MLAs prepared by evaporation of THF at 100 µL PVC gels solution under 30 V DC voltage were selected as a case study.
The operating mechanism of PVC gel-based MLAs is shown in Fig. 3. A lens unit was selected for analysis. The inner circular electrode was connected to the anode, and the outer electrode was connected to the cathode. The THF solvent was evaporated under DC electric field. During the process, the electric charge (or electrons) was injected from the cathode and migrated towards the anode. Here they were accumulated to promote the electrostatic force between the gels and the anode, thereby leading to creep-deformation [Fig. 3(a)]. After the evaporation of THF solvent, stable PVC gel-based MLAs with fixed convex shape were obtained. After the removal of the electric field [Fig. 3(b)], the convex shape of the PVC gels-based MLAs kept its configuration. Besides, the as-obtained PVC gel-based-MLAs with convex shape exhibited lens characteristics with an initial focal length. The shape significantly depended on the boundary conditions of the electrodes and the strength of the applied DC fields. Also, the curvature can be controlled by tuning the electric field and volume of the PVC gels solution.
Fig. 3. Operating principles of the PVC gels microlens: (a) THF evaporation under DC electric field and (b) formation of PVC gels-based MLAs with a convex shape.
3. Results and discussion
Fourier transform infrared spectrometry (FT-IR, Nicolet IS10, Thermo Fisher) was used to analyze the surface components of PVC gels based-MLAs at different points of the electrode substrate. The FT-IR spectra of pure PVC and DBA material are compared in Fig. 4(a). The ester (C = O) stretching band was recorded between 1700 and 1750 cm−1, and characteristic peak of pure DBA was observed at 1743 cm−1. The contents of DBA at different positions could be compared by estimating the intensities and bandwidths of the ester band (C = O) [Fig. 4(b)]. Note that point A referred to the centre of the inner circle connected to the anode, point B represented the gap between the anode and cathode, and point C was located on the cathode surface. The intensity and bandwidth of the ester (C = O) stretching band decreased as DBA content declined. [36] The intensity of the 1700-1750 cm−1 band at point A (anode) looked stronger than at other locations. Thus, DBA content was higher on the anode due to the migration of DBA under the applied electric field. The 1700-1750 cm−1 band at point B shifted to lower wavenumbers and showed the lowest intensity, suggesting the presence of low DBA content on the gap surface. The intensity of the band at 1700-1750 cm−1 of point C also shifted to lower wavenumbers and looked lower than that at point A but higher than that at point B. This implied that the content of DBA at point C was smaller in comparison with the value observed point A, even though some DBA remained on the surface of the cathode. Thus, PVC gels formed a convex shape on each circular electrode.
Fig. 4. FT-IR spectra of (a) pure PVC and DBA, and (b) at different positions of PVC gels after evaporation of THF under 30 V voltage.
The spatial distributions of DBA in PVC gel-based MLAs prepared at voltages of 0 and 30 V were analyzed by FT-IR mapping. The maps were created based on the peak heights in each area. A small area of 150 × 150 µm2 covering a microlens unit was used for measurements. Figure 5(a) exhibits the intensity distribution at 1743 cm−1 (peak height) in the mapping area of PVC gel-based MLAs formed by THF evaporation without applied external electric fields. The DBA content appeared randomly distributed in the map, suggesting the random distribution of DBA molecules in PVC gels during THF evaporation at V = 0.
Fig. 5. Changes in FT-IR intensity of the 1743 cm−1 band calculated obtained by mapping in the 150 × 150 µm2 square of PVC gels during THF evaporation at (a) 0 and (b) 30 V. High to low intensities in the maps are described by colour code (red to blue).
On the other hand, DBA contents on the anode surface during THF evaporation at V = 30 V were higher than those recorded in other locations [Fig. 5(b)]. The variation in colour from red to blue reflected the change in light intensity of DBA in the map from high to low. Thus, the blue colour in the ring-shaped gap would indicate the lowest DBA content in this area. By comparison, DBA content was higher on the cathode surface than in the gap surface due to the remaining of some PVC gels. Therefore, the distribution of DBA strongly depended on the boundary conditions of the electrode. The DC electric field induced the migration of DBA towards the anode and its accumulation in its vicinity. After complete evaporation of THF, PVC gel-based MLAs with stable convex shape were obtained.
A micrograph of optical microscopy (OM) of the ring array patterned electrode is illustrated in Fig. 6(a). To assess the uniformity of the focal length and visualize the formed PVC ges-based MLAs, the MLAs were placed at the stage of OM. The number “4” in group 1 of a negative USAF 1951 resolution test target was selected as an object and placed at the bottom. The object distance was 7 cm, which was far greater than the focal length of PVC gel-based MLAs. After light illumination, a clear image of the sample 4 array was captured by the OM [Fig. 6(b)]. The miniaturized images of sample 4 were evenly spaced with similar size and sharpness, validating the uniformity of focal length in the electric field induced PVC ges-based MLAs. Because of the dispersive nature of the PVC gels, chromatic aberration (CA) was inevitable due to the wavelength-dependent focal length of the viewing optics. The CA can be reduced by preprocessing images according to the chromatic dispersion of viewing optics or utilized two or more lens materials with different refractive index dispersions/Abbe numbers in the system to unite the focal length at two or more wavelengths [37].
Fig. 6. (a) OM image of the ring array patterned electrode and (b) number “4” observed by OM through the PVC gels MLAs.
Figure 7 shows a schematic diagram of the experimental setup used to verify the focusing performance of PVC gels MLAs. In the experiment, a He-Ne laser beam (λ ∼ 633 nm) was first expanded by a beam expander, and after passing through the PVC gels MLAs, the converging light was recorded by a Charge Coupled Device (CCD) beam profile (BC106 N-VIS, 350-1100 nm, Thorlabs) and analyzed by the computer. Also, the light intensity of the laser beam was attenuated by an attenuator.
The two-dimensional (2D) and three-dimensional (3D) light intensity distributions of PVC gel-based LMAs are shown in Figs. 8(a) and 8(b), respectively. The 6 × 8 MLAs were observed by CCD beam profile. To this end, the laser beam was focused at a spot array when passing through the MLAs [Fig. 8(a)]. The light looked like a sharp needle peak array [Fig. 8(b)], indicating the placement of a CMOS sensor of CCD camera at the focal plane of the PVC gels-based MLAs. The average intensities of light along the X-axis and Y-axis are displayed in Figs. 8(c) and 8(d). Along the X-coordinate, eight sharp peaks were observed, and six sharp peaks were noticed along the Y-coordinate. The average intensity of the peaks was estimated to ∼ 3500 arbitrary units. Since the laser beam possessed a Gaussian shape, the light intensity at the centre area was relatively stronger than at the margin.
Fig. 8. (a) 2D image of the light focusing spot, (b) 3D profile of light at the focusing plane, and light intensity of PVC gel-based MLAs along (c) X-coordinate and (d) Y-coordinate.
A White Light Interferometer (WLI, Bruker Contour GT-K) was utilized to observe the surface profile of a single PVC gel-based microlens. The 3D surface and cross-section profiles of a convex-shaped PVC gel microlens obtained by evaporation of THF at V = 30 V are depicted in Figs. 9(a) and 9(b), respectively. The curve was dealed with Gaussian fitting. The sag height was measured as 0.32 µm. After determination of the height of PVC gels microlens, the focal length was calculated according to Eq. (1):
where f is the focal length, r represents the radius of the microlens, h is the sag height of the microlens, and n denotes the refractive index of PVC gels materials. Here, r is 50 µm and n is 1.45.Fig. 9. (a) 3D surface profile and (b) cross-section profile of a PVC gels microlens prepared by evaporation of THF at V = 30 V.
The curvature of PVC gels microlens could be fine-tuned by changing the strength of the DC electric field during the evaporation of THF. The active area of the electrode and volume of PVC gels solution were fixed. The sag heights of PVC gels microlens could be increased by applying more DC voltage. The original curves were shown in Fig. S6(a), and the obtained curves were dealed with Gaussian fitting. Figure 10(a) shows cross-section profiles of PVC gel microlenses prepared by evaporation of THF from 100 µL PVC gels solution at different voltages. The sag heights of PVC gel microlenses prepared at V = 10, 20, 30, 40 and 50 V were measured as 0.2 µm, 0.27 µm, 0.32 µm, 0.41 µm and 0.44 µm, respectively. The calculated focal lengths at different voltages using Eq. (1) are compiled in Fig. 10. The focal lengths of PVC gel microlenses prepared at V = 10 V, 20 V, 30 V, 40 V and 50 V were recorded as 13.89 mm, 10.29 mm, 8.68 mm, 6.78 mm and 6.31 mm, respectively. Therefore, the application of more voltage shortened the focal lengths of formed PVC gels lenses. 2D images of the light focusing spot and 3D profiles of light at the focusing plane of PVC gels MLAs observed by the experimental setup (Fig. 7) are provided in Fig. S2. Optical images of an array of the number “4” observed through PVC gel MLAs are given in Fig. S3.
Fig. 10. (a) Cross-section profiles and (b) focal lengths of PVC gels microlenses prepared by evaporation of THF at different voltages.
Another critical factor influencing the curvature of PVC gel microlenses can be adjusted by the thickness of PVC gels solution. The fixing of cofferdam size will fix the active area on the ring patterned electrode and thickness were determined by the injection volume of PVC gels solution. Under DC polarization, the cross-section profiles of PVC gels microlens were only be affected by the injection volume of PVC gels solution. Figure 11(a) shows a cross-section profile of PVC gels microlens prepared by evaporation of THF at V = 50 V for two hours, measured by WLI. The original curves were shown in Fig. S6(b), and the obtained curves were dealed with Gaussian fitting. The sag heights of PVC gel microlenses obtained at injection volumes of 60 µL, 80 µL, 100 µL, 120 µL and 140 µL were estimated to 0.19 µm, 0.37 µm, 0.43 µm, 0.39 µm and 0.34 µm, respectively. At injection volumes exceeding 120 µL, the electric field was not high enough to drive the PVC gels far away from the electrode surface. The calculated focal lengths obtained by Eq. (1) are presented in Fig. 11(b). The focal lengths of PVC gel microlenses prepared at V = 50 V with an injection volume of 60 µL, 80 µL, 100 µL, 120 µL and 140 µL were calculated as 14.62 mm, 7.51 mm, 6.31 mm, 7.12 mm, 8.17 mm, respectively. It could be observed that at the injection volume of 100 µL, the focal length was the shortest. In sum, shorter focal lengths with higher injection volumes would require increased preparation voltages. 2D images of the light focusing spot and 3D profiles of the light at the focusing plane of PVC gels MLAs observed by the experimental setup (Fig. 7) are shown in Fig. S4. The optical images of an array of the number “4” observed through PVC gels MLAs are provided in Fig. S5.
Fig. 11. (a) Cross-section surface profiles of PVC gel microlenses obtained at different injection volumes of PVC gels solution during evaporation of THF solvent at V = 50 V. (b) Variation in focal length as a function of the injected volume.
4. Conclusions
PVC gel-based MLAs were successfully prepared by evaporation of THF solvent under DC polarization. Under the action of the electric field, the electric charge (or electrons) injected from the cathode led to the movement of DBA molecules towards the anode and accumulate near its surface. The solvent facilitated the transport of DBA molecules under low electric field strengths. After complete evaporation of the solvent, stable PVC gel-based MLAs with convex shapes and initial focal lengths were obtained. At fixed injection volume of PVC gels solution, the curvature of MLAs obtained with patterned electrode substrates at fixed sizes of cofferdam can be tuned by changing the preparation voltage. The evaporation of THF of 100 µL PVC gels solution under different voltages with a DC electrode field was demonstrated, the focal lengths of the MLAs were 13.89 mm, 10.29 mm, 8.68 mm, 6.78 mm and 6.31 mm, respectively. At fixed preparation voltage, the curvature of MLAs can be adjusted by changing the injection volume of PVC gels solution. Under 50 V DC electric field, the evaporation of THF from PVC gel solutions with volumes of 60 µL, 80 µL, 100 µL, 120 µL and 140 µL led to the formation of PVC gel-based MLAs with focal lengths of 14.62 mm, 7.51 mm, 6.31 mm, 7.12 mm and 8.17 mm, respectively. In sum, large-area PVC gel-based MLAs with controllable curvatures can be prepared by evaporation of THF under DC electric fields, which might be useful for future fabrication of MLAs with uniform size in larger areas.
Funding
The Natural Science Foundation of China (NSFC) (61805066); China Postdoctoral Science Foundation (2019M652168).
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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