We demonstrate a new method to fabricate a large-area polymer gravel array. The formation of the polymer gravel array on the substrates of the liquid crystal (LC) cell during polymerization is attributed to the surface tension interaction among the LC, prepolymer, and substrate surface. The gravel can be oriented along the rubbing direction of the substrate. Moreover, the diameter and pitch of the oriented gravel array can be controlled by means of UV curing intensity and supplied voltage under curing because of the competition between the dipole and quadrupole interactions of the colloidal prepolymer droplets. The estimated anchoring energy given by the oriented polymer gravel array can align LCs. The possible application of the formed periodical gravel array on optical devices is explained in this paper.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In the past decade, liquid crystal (LC)–polymer composites have attracted considerable attention and presented a technological basis for optical devices owing to their interesting dynamic properties [1, 2]. The LC–polymer composites appear in the form of networks or droplets depending on the used type, concentration, and polymerization condition of the polymers. The concentration of components acts as a decisive factor for the formed polymer matrix morphology. In the case of low polymer content (1–2 wt.%), the response time of the LC cell can be evidently improved, but a slight light scattering is generated in the visible range. When the polymer concentration is increased to 3–8 wt.%, the polymer-stabilized LC structure is formed in the homogeneously or homeotropically aligned cell. In these cases, the polymer network LC (PNLC) structure is created in the LC matrix [3, 4]. As the polymer concentration exceeds 30 wt.%, LC domains are dispersed in the continuous polymer matrix [5, 6]. The corresponding composites are designated as polymer-dispersed LCs (PDLCs). No surface alignment layers on the substrates of the PDLC cell are necessary, and the microscale LC droplets are immersed in the polymer matrix. In this case, visible light is strongly scattered, and this scattering is independent of the polarization of incident light. In the high polymer concentration regime (60–70 wt.%), nanoscale PDLC droplets can be achieved. Given that the droplet size was markedly smaller than the visible wavelength, PDLCs were free of light scattering, and their response time reached the levels of 30–200 μs. In general, the polymer structures in the LC–polymer composites depend on the phase separation of the LC–polymer mixture during photo-polymerization . The formation of polymer morphology is regulated by several processes, such as polymerization, phase separation, and phase ordering. These processes are interconnected, and their detailed exploration is difficult. The works related to self-organized LC-polymer photonics have been demonstrated [8–10]. Different scientific groups have concentrated on the different aspects of composite formation. In the LC–polymer composite, prepolymer NOA65 is a common polymer material that is mixed with nematic LCs. For the system with the mixture of LCs and NOA65, when the NOA65 concentration is high and UV irradiation is exposed on only one side of the cell, most prepolymers are polymerized on the substrate that faces the exposed UV light because of the anisotropic phase separation originating from the differences in light absorption and the diffusion rate between the prepolymer and LCs [11–13]. By contrast, the generated polymer textures are similar on both substrates at low doped prepolymer concentration because of the isotropic phase separation (or vertical phase separation) facilitated by the differences in the surface tensions of the employed components [14–17]. These two different phase separations occur without curing voltage. Recently, Kang, H. et al. studied the photo-induced vertical phase separation of prepolymer NOA65 in the LC system to improve the electro-optical performance of the LC cell [14–16]. We previously proposed a method to control the LC pretilt angle by filling the mixture of nematic LC and NOA65 in the homeotropically-aligned cells . The pretilt angle of LCs can be changed by changing the prepolymer concentration, and this changes the distribution density of generated polymer gravels on the substrate and, consequently, the polarity of the formed polymer gravel surface.
Periodical dielectric structures, commonly known as photonic crystals (PCs), possess fascinating optical properties that allow the control of light propagation in materials. In PCs, the photonic band gap (PBG) phenomena, that is, where light within a certain frequency range is prohibited from propagating in PCs with the designated period, refractive index, and the order of periodicity. The PBG in dielectric lattices has been applied in mirrors, filter, and waveguides [19–21]. Various methods, such as soft lithography , nanoimprinting , and templates using either block copolymers or polystyrene nanospheres , have been reported in the fabrication of periodic structures. At present, high-brightness light-emitting diodes (LEDs) are widely used in solid-state lighting and backlights of LC displays. However, the total internal refraction (TIR) at the interface between the LED semiconductor and surrounding media confines a significant portion of the light generated by the active region of LEDs and therefore permits only a small percentage of light to be extracted from the LED chips. The etched periodic indium tin oxide (ITO) hole structures  and graded-refraction-index periodic protrusion patterns  have been demonstrated to enhance the light extraction efficiency (LEE) of LEDs. In the current study, we demonstrate the possibility of fabricating the large-area periodic structure with self-assembly polymer gravels on the substrates of the LC cell doped with the prepolymer NOA65. The proposed method is capable of achieving large-area PC or lens array with variable periods and amplitudes. Moreover, the modulation of polymer gravels in the orientation, diameter, and pitch are demonstrated. The contact angles of LC and prepolymer on the substrates are measured to explain the mechanisms of the formed polymer morphology. Scanning electron microscopy (SEM) is used to observe the polymer gravel array created on the substrate and quantify the diameter and pitch of the oriented gravel array. Moreover, the application of polymer gravel array on the enhancement of LEE of LEDs is exhibited by simulation. The experimental preparations, results, and discussions are demonstrated in the following content.
2. Experimental preparations
Empty cells with 3 µm thickness and different surface alignments were used in this experiment. The homogeneous empty cell was assembled with two ITO glass substrates coated with homogeneous polyimide (PI) AL-58 (from Daily Polymer, Taiwan) and the vertical empty cell was assembled with two ITO glass substrates coated with vertical PI AL-8088C (from Daily Polymer, Taiwan). By contrast, the rubbing-free cell was assembled with two bare ITO glass substrates without any surface treatment. The ITO glass substrate coated with homogeneous PI (vertical PI) was defined as H-PI (V-PI) substrate. In the homogeneous and vertical empty cells, the inner surfaces of both substrates were either antiparallel rubbed or free of rubbing treatment to observe the influence of the rubbing effect on the polymer gravel formation. The LC mixture was composed of nematic E7 (Δn = 0.22, Δε = + 14.50, K11 = 12.00 pN, K22 = 9.00 pN, K33 = 19.50 pN, and γ1 = 232.60 mPa•s at room temperature, obtained from Daily Polymer, Taiwan) and a small amount of the nonpolar prepolymer NOA65 (Norland Optical Adhesive, USA) . In the study, the concentration of the doped NOA65 was maintained at 2.5 wt.%. This mixture was then injected into the empty cells by capillary action. A UV light source was used to polymerize the filled cells. UV curing intensity was set to 3 or 30 mW/cm2, and the curing time was 50 min. To observe the polymer morphology on the substrate surface, the polymerized cells were individually peeled off after UV curing, and the substrates were dipped in cyclohexane solution for 3 days to wash off the residual LCs on the substrate surfaces. When the LCs on the substrates were washed off completely, the substrates were coated with a thin gold film measuring ~100 nm and observed with SEM. Furthermore, the LC (E7) and prepolymer (NOA65) were dropped onto the H-PI, V-PI, and ITO substrates. The optical images of LC or prepolymer on these substrates were captured with a CCD camera to estimate the contact angles of the prepolymer and LCs on these substrates. The angle between the substrate/liquid interface and the liquid/air interface was defined as the contact angle (θ).
3. Experimental results and discussions
In this experiment, vertical phase separation happened in the NOA65-doped LC cell with the doped NOA65 concentration at 2.5 wt.% [14–16, 18]. Figure 1 shows the schematic of vertical phase separation and photo-induced polymerization in the NOA65-doped LC cell. Initially, the colloidal particles were randomly dispersed in the LC matrix, as shown in Fig. 1(a). With molecular diffusion, the neighboring colloidal particles started to coalesce with each other and formed large droplets. The droplets spontaneously assembled into chains with the hyperbolic hedgehog point defect via the dipolar attractive force  explained as follows. When two particles with radius a and positioned at r (0, 0) and r (r, θ) are interacting via dipole–dipole forces, the dipolar attractive force (F) can be expressed in terms of the dipole moment pz as shown Eq. (1) :Fig. 1(b). The colloidal droplets accumulated and coalesced on the substrates and eventually polymerized as polymer gravels under UV irradiation, as shown in Fig. 1(c).
Figure 2 shows SEM photographs of the polymerized morphologies formed on the ITO, H-PI, and V-PI substrates in the rubbing-free cells. Only SEM photographs on the top substrates in the cells are shown in the figure because of the similar polymerized morphologies on both substrates of the cell in this experiment via vertical phase separation. The polymerized morphology was significantly affected by the surface interaction among the LC, prepolymer, and substrate surface [29, 30]. Figure 3 shows the optical images of the LC (E7) and prepolymer (NOA65) dropped on the ITO, H-PI, and V-PI substrates. The estimated contact angles are listed in Tab. 1. Notably, the LC was almost wetted on the ITO substrate, whereas NOA65 was almost dewetted on the ITO substrate. Therefore, the ITO substrate was almost occupied by the LCs and the prepolymers were propelled toward the middle of the LC cell during vertical phase separation in the NOA65-doped LC cell. When the cell was peeled off and the LCs were removed from the substrate after UV polymerization, a smooth surface profile was obtained on the ITO substrate, as shown in Fig. 2(a). With the H-PI substrate, the contact angle of NOA65 on the substrate was less than that of E7 on the substrate. The interaction between the H-PI substrate and prepolymer was stronger than that between the H-PI substrate and LC. The strong interaction in the vertical direction (substrate surface normal) induced plenty of prepolymers to occupy and coalesce on the H-PI substrate. Consequently, gravels with large diameters were obtained on the H-PI substrate, as seen in Fig. 2(b). By contrast, the gravels with small diameters were formed on the V-PI substrate because of the weak interaction between the V-PI substrate and prepolymer, as seen in Fig. 2(c). The estimated diameters of the spherical gravel on the H- and V-PI substrates were ~1 and 0.3 μm, respectively. As seen in Fig. 2 (b), the nonuniform amplitude of gravels on the H-PI substrate might be caused by nonuniform UV exposure and rough H-PI layer surface, and which could be improved by using a collimated UV light source and coated with a smooth alignment layer. The resultant SEM photographs revealed that the diameter of polymer gravel created on the substrate depends on the surface tension difference among the substrate surface, prepolymer, and LC. Furthermore, the difference between roughness on the H- and V- PI surfaces may also influence the formation of gravels.
Polymer gravels created on the substrate surfaces without rubbing treatment showed disordered orientated, whereas those created on the rubbed substrate surfaces were orientated orderly along the rubbing direction, as seen in Figs. 4(a) and 4(b). Polymer gravels formed on the H-PI substrates with twisted nematic (TN) cell were also obtained, as shown in Figs. 4(c) and 4(d). Notably, the orientations of gravels on the top and bottom substrates were orthogonal with each other and along the rubbing directions of the substrate surfaces. The result revealed that the formed polymer gravel array was induced by interaction near the substrate surfaces despite the twisted structure in the LC bulk. Furthermore, the average amplitudes of gravel and the pitches of gravel array formed in the homogeneous and TN cells were similar, as seen in Fig. 4(b) and the inset of Fig. 4(d). That indicated the amplitude of gravel and the pitch of gravel array were independent of the alignment structure of cell. However, the non-uniform pitch and amplitude of gravels in the periodic structures (Fig. 4) have to be further improved using a collimated UV light source or using substrates with uniform surface treatments. In the experiment, the amplitudes of gravels created on the V-PI substrate were more uniform than those created on the H-PI substrate. Therefore, only SEM photographs on the V-PI substrates are demonstrated hereafter.
The physical mechanism responsible for the formation of the polymer gravel array orientated along the rubbing direction is explained with the model that dispersing colloidal particles in nematic LCs [27, 31–33]. If k is the average elastic constant, the elastic cost of the distortions around a single particle should be of the order of ka; the characteristic energy designating a deviation from this preferential anchoring is given by Wa2, where W and a are the surface energy term and particle size, respectively. Initially, the contribution of the characteristic energy of the small colloidal particle was weaker than the bulk elastic energy (ka). Consequently, the colloidal particles did not induce strong distortions on the LC molecules (Fig. 5(a)), and the orientation of LC molecules near the colloidal particles was similar to that in the LC matrix (parallel with the rubbing direction of the substrate). During the vertical phase separation, the colloidal particles coalesced and formed large droplets by molecular diffusion. The surface anchoring energy of the droplets became dominant and the LC molecules became vertically aligned on the surface of the droplets. Consequently, the alignment of LC molecules near the droplets was distorted and differed from those of LC molecules in the LC matrix (Fig. 5(b)). The LC alignment around the droplets can be satisfied by the formation of a companion hyperbolic defect, which is similar to the electric dipole under electric fields. With electrostatic analog, the droplet–defect pairs were expected to behave similarly to electrostatic dipoles at a long range, and the long chains of the droplet–defect pairs pointed in the same direction (Fig. 5(c)). Notably, the long chains of droplet–defect pairs were orientated along the rubbing direction of the substrate because the companion hyperbolic defects should be parallel to the LC alignment direction in the LC matrix. The topological defect between neighbored droplets induced short-range repulsion that prevented the droplets from further coalescing. The long chains of droplet–defect pairs were sequentially pulled toward both substrates by vertical phase separation and eventually polymerized on the substrates with UV irradiation. As a result, the formed polymer gravel array was oriented along the rubbing direction on the substrate surface of the rubbed LC cell.
As illustrated in , the polymer morphology is correlated with the curing voltage and curing intensity. Figure 6(a) shows the formed polymer gravel array on the V-PI substrate when the rubbed cell was cured at 3 mW/cm2 without the supplement of curing voltage. Once the cell was cured with the supplement of curing voltage, the diameter of gravels created on the substrate became relatively large, as seen in Fig. 6(b). The mechanism can be explained as follows. As shown in Figs. 7(a) and 7(b), during vertical phase separation, the elastic dipole could be transformed into the quadrupolar Saturn ring configuration in the presence of an external small electric field along the normal surface (the electric field direction). The elastic repulsion between quadrupoles prevented the colloidal droplets from continuing to coalesce along the normal substrate surface and thus formed small colloidal droplets (Fig. 6(a)). However, the external electric field along the surface normal simultaneously polarized the colloidal droplets and induced electrostatic dipole–dipole interactions between quadrupoles. As shown in Figs. 7(c) and 7(d), at a high applied voltage, the induced electrostatic interaction (dipole–dipole interaction) was stronger than the elastic repulsion (quadrupole interaction) between the neighboring colloidal droplets along the normal substrate surface, the colloidal droplets came into contact and further coalesced along the normal substrate surface , large droplets formed, and the polymer gravels with relatively large diameters were obtained on the substrate when the cell was cured with the supplement of high curing voltage. Furthermore, the progress of colloidal particle coalescence resulted in increased gravel array pitch. Figure 6(c) shows the formed gravels on the V-PI substrate when the rubbed cell was cured at a curing intensity of 30 mW/cm2 without curing voltage supplementation. Curing intensity increased the polymerization rate  and impeded the diffusion and coalescence of droplets during vertical phase separation. Therefore, the diameters of the created gravels were relatively small. These findings indicated that the supplement of curing voltage and the increase in curing intensity increased and decreased the diameter and pitch of the generated gravels, respectively. In this experiment, the cell gap and NOA65 concentration have not been optimized yet. Thick cell gap decreases the uniformity of amplitude of gravels, because of the nonuniform cell gap resulted from the handmade cell. Moreover, thick cell gap also destroys the formation of gravel due to the gradient of UV intensity. A higher NOA65 concentration leads to a denser gravel distribution formed on the substrate.
Based on the Berreman groove theory , the created polymer gravel array can align the LCs along the groove direction in the cell. Table 2 shows that the estimated anchoring energies generated by the oriented gravels in the vertical cells all exceeded those generated by laser-etched gratings , thereby minimizing the elastic strain energy and forcing the LCs to align along the grating groove.
Besides the capability to align LC molecules in the LC cell, the formed periodical polymer gravel array can be adopted in the emissive device to increase the LEE of LEDs or as a diffuser in the backlight system . Figure 8 numerically verifies the possibility to increase LEE of a multi-quantum well-LED (MQW-LED) using the fabricated polymer gravel array. Two-dimensional simulation was performed with the commercially available finite element method software COMSOL to provide a conceptual understanding of the light extraction mechanism of the formed polymer gravel array. The structure of the MQW-LED is similar to that shown in , that is, consisting of a 120 nm p-GaN, 50 nm InGaN/GaN MQW active region, and 630 nm n-GaN, and 400 nm underlying Si substrate. The width of the MQW-LED was 12 µm, the diameter of the polymer gravel was 0.2 μm, and the pitch of the gravel array was 0.56 µm. A spherical light source polarized in the z-direction was emitted in the middle of MQW layer, as shown in Fig. 8(a). The wavelength of the emitted light was 526 nm. In the simulation condition, the refractive index of polymer gravel array was considered, but the absorption of polymer gravel array was neglected. As shown in Fig. 8 (b), TIR on the air-GaN surface confined the emitted light in the MQW-LED, and the formed polymer gravel on the surface of LED destroyed the TIR condition and therefore enhanced the LEE of the MQW-LED, as shown in Fig. 8(c). The intensities of emitted light into the air layer were evaluated in this calculation. With the polymer gravel array deposited on the top of p-GaN layer, the intensity of emitted light into the air layer increased by 1.4 times. Notably, the light extraction intensity of LEDs was dependent on the gravel diameter and pitch of gravel array deposited on the top of p-GaN layer. The gravel diameter and pitch of gravel array can be tunable by changing the curing voltage, curing intensity, and NOA65 concentration. The experiments on enhancing LEE of LEDs with polymer gravel array are underway.
In this paper, we have demonstrated an easy and low-cost method to fabricate a large-area polymer gravel array. The area of the fabricated gravel array is only limited by the exposure area of the UV light. The diameter of the gravels formed on the H-PI substrate is larger than that of the gravels formed on the V-PI substrate, due to strong surface interaction between the H-PI substrate and prepolymer. In the cell subjected to rubbing treatment, the gravel array created on the substrates is orientated along the rubbing direction of substrate surface because of the self-assembly chains of the droplet–defect pairs. The diameter and pitch of the oriented gravels becomes large with application of the curing voltage and becomes small when the cell is cured with high curing intensity. High anchoring energy is induced by the oriented gravels on the V-PI substrate. The proposed method can fabricate the large-area periodical array that can be used in the lighting system, backlight system, and PC devices. The applications of the modulated polymer gravel arrays are underway.
Ministry of Science and Technology, Taiwan (Most 101-2112-M-018-002-MY3, Most 103-2622-E-018-007-CC3, Most 104-2811-M-018-001, Most 105-2811-M-018-003, and Most 106-2811-M-018-004).
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