Triboelectrification-Induced Self-Assembly of Macro-Sized Polymer

Jan 2, 2018 - Here we report an electrostatic-templated self-assembly (ETSA) method for arbitrarily patterning millimeter-sized polymer beads on a nan...
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Triboelectrification-Induced Self-Assembly of Macro-Sized Polymer Beads on Nanostructured Surface for Self-Powered Patterning Ying Wang, Xiao Yan Wei, Shuang Yang Kuang, Hua Yang Li, Yang Hui Chen, Fei Liang, Li Su, Zhong Lin Wang, and Guang Zhu ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b06758 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 3, 2018

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Triboelectrification-Induced Self-Assembly of Macro-Sized Polymer Beads on Nanostructured Surface for Self-Powered Patterning Ying Wang†,‡, Xiao Yan Wei†,‡, Shuang Yang Kuang†,‡, Hua Yang Li†,‡, Yang Hui Chen†,‡, Fei Liang†,‡, Li Su†,‡,Zhong Lin Wang†,‡,‖, Guang Zhu*,†,‡,§ †

CAS Center for Excellence in Nanoscience, Beijing Institute of Nanoenergy and Nanosystems,

Chinese Academy of Sciences, Beijing, 100083, China. ‡

School of Nanoscience and Technology, University of Chinese Academy of Sciences, Beijing

100048, P. R. China. §

Department of Mechanical, Materials and Manufacturing Engineering, The University of

Nottingham Ningbo China, Ningbo 315100, P. R. China. ‖

School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA

30332, USA * E-mail: [email protected]

KEYWORDS: self-assembly, patterning, triboelectrification, electrostatic force, macro-sized beads

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ABSTRACT: Here we report an electrostatic-templated self-assembly (ETSA) method for arbitrarily patterning millimeter-sized polymer beads on nanostructured surface without using an extra voltage source. A patterned electrode underneath an electrification layer generates “potential wells” of the corresponding pattern at pre-defined window sites, which capture and anchor the beads within the window sites by electrostatic force. Analytical calculation is combined with numerical modeling to derive the electrostatic force acting on the beads, which is in great agreement with experimentally measured values. The generated pattern is solely determined by the pre-defined underlying electrode, making it arbitrary switchable by using different electrode patterns. By transferring the assembled beads into an elastomer matrix, possible applications of the ETSA in fabricating optical displays and flexible display are demonstrated.

Self-assembly is a process in which individual components form an ordered structure in a self-organized way as enabled by non-covalent interactions, and it has broad and promising applications in optoelectronics,1,2 microfabrication,3 biomembranes4,5 and nanoelectronics.6 Basic principles, such as hydrogen bonding,7-9 Van der Waals force10 electrostatic force,11 surface tension,12 and ion absorption, 13 have been exploited for the purpose of self-assembly. Normally, self-assembly involves constituent objects that have feature sizes at the scale of micrometer or nanometer,14 where gravity and inertia are insignificant. However, for millimetersized objects, self-assembly becomes challenging as gravity becomes dominant.15 For example, charges patterned by techniques such as contact printing,16 ion-beam irradiation,17 and electrolyte adsorption18 relied on electrostatic force for the self-assembly of micro-sized objects. But for significantly larger objects such as millimeter-size polymer beads, externally applied voltage sources ranging from several to tens of kV were normally required.

19-22

In an attempt to

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eliminate the need of additional voltage sources, Grzybowski et al.23 used contact electrification among beads of dissimilar polymeric materials to achieve a highly ordered array without power input. However, the two types of beads had to be closely packed and arrayed in a specific arrangement, which made it difficult to form desired patterns in a variable and arbitrary way.23-25

In this work, we report an electrostatic-templated self-assembly (ETSA) method for arbitrarily patterning millimeter-sized polymer beads on a nanostructured planar substrate without using an extra voltage source. Essentially, triboelectric charges of opposite signs on the beads and on the substrate induce in-plane electrostatic forces that drive the self-assembly process. A grid electrode underneath an electrification layer defines the distribution of surface electric potential, generating deep “potential wells” at pre-defined window sites. As a polymer bead rolls over or by a window site, it is attracted and captured to the center of the window by electrostatic force. The “potential well” then becomes a trapping site that anchors the bead, preventing it from rolling away. As a result, patterns of either arrayed or arbitrary shape are achieved. Here, analytical calculation is combined with numerical modeling to derive the electrostatic force, which is in great agreement with experimentally measured values. The straightforward nature of this proposed ETSA is demonstrated by its convenient and selfpowered setup. Individual beads serve as independent pixels in the patterned image without requiring a specific arrangement. The pattern is solely governed by the pre-defined underlying electrode, making it arbitrarily switchable with different sets of electrode patterns. By transferring the assembled pattern into an elastomer matrix, possible applications of the ETSA in fabricating optical displays and flexible display are demonstrated. RESULTS AND DISCUSSION

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The configuration of a self-assembled setup, as depicted in Figure 1a, consists of multiple parts. On an underlying insulating polymethyl methacrylate (PMMA) substrate deposited a 200 nm thick copper electrode layer. The electrode has a planar grid pattern. The hollow square regions are referred to as window sites in the following discussion. The side length of a single window is 1.58 mm, and the interval between adjacent windows is also 1.58 mm. The grid electrode is grounded through a lead wire. A 50 µm thick Teflon film acts as the topmost electrification layer. Vertically aligned Teflon nanowires (NWs) were created by plasma etching (Figure 1b). The NWs have an average diameter and length of 180 nm and 1.2 µm, respectively, which play an important role in achieving high electrostatic force.26 Nylon beads that are 1.58 mm in diameter are used as the self-assembly constituent components. As shown in Figure 1a, the assembled beads sit within the window sites with one-to-one correspondence. A photograph of an assembled 9×9 array is shown in Figure 1c, and the inset shows a magnified view of a single bead located at the center of a window. To illustrate the self-assembly principle, a crosssectional view of the magnified unit is shown in Figure 1d. The negative charges on the electrification layer and the positive charges on the nylon bead are attributed to the triboelectrification-enabled charge transfer during a pre-charging treatment (See Experimental Section for details).27 The triboelectric charges can be preserved in a quasi-permanent way because of the insulating property of polymers.28 Driven by electrostatic induction, charge flow occurs between the grid electrode and the ground, making positive induced charges accumulate on the electrode, as shown in Figure 1d. It is known that triboelectric charges of opposite signs exert an attractive force between two charged objects.29 Considering that the positive induced charges on the electrode can largely screen the negative triboelectric charges on the electrification layer, the attractive electrostatic force can only exist between the bead and the

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window site where the triboelectric charges are unscreened. As both the bead and the window site have tetrahedral symmetry, an equilibrium state without a net electrostatic force in the lateral direction is achieved if the bead sits at the center of a window, which corresponds to the position “I” in Figure 1e. Here, we mainly focus on the electrostatic force (Fes) exerted on a bead. In a two-dimensional illustration of Figure 1e, the force is resolved into an x-component (Fes-x) and a z-component (Fes-z). Once the bead deviates from the center to the perimeter of the window (position “II” in Figure 1e), the Fes-x tends to draw the bead back to the equilibrium position. If bead is beyond the perimeter of the window, minimal Fes-x is obtained. Therefore, during the self-assembly process, a window becomes a trapping site that can capture a bead and anchor it at the center, whereas the rest of the surface (e.g. position “III” in Figure 1e) cannot hold the bead. In the following section, the above self-assembly process is quantitatively investigated using a two-step method that combines analytical calculation with numerical simulation. In the first step, a numerical simulation by COMSOL modeling was conducted to reveal the electrical potential distribution of the self-assembled system. A three-dimensional model of a 3×3 array was built. The detailed modeling parameters are discussed in the Methods. In particular, the surface charge density on the electrification layer and on the nylon beads is set to 100 µC/m2 and 0.2 µC/m2, respectively. They are obtained experimentally by using an electrostatic voltmeter (Model 279, Monroe Electronics) and a home-made Faraday cup, respectively. The obtained electric potential distribution of the assembly is shown in Figure 2. The breakdown views of the four parts are presented separately. The bottom of the assembled beads has a significantly lower electrical potential than the top part (Figure 2a) because it is in close proximity to the negatively charged electrification layer. The grounded electrode has an equipotential of 0 V (Figure 2c), which enables the patterned distribution of the electric potential

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on the electrification layer (Figure 2c). The electric potential within the window sites is substantially lower than that outside, making them become “potential wells” that tend to capture the positively charged beads. The two-dimensional electrical potential distribution across the “potential wells” is plotted in Figure S1 (Supporting Information). Shown in Figure 2, the maximum electric potential difference exceeds 1.2 kV, which is comparable to the externally applied voltage in previous reports for assembling millimeter-sized beads. 22 In the second step, the electrostatic force acting on the nylon bead is calculated by Maxwell’s stress tensor 30 as below:

Fes = −

1 ( E ⋅ D ) n + (n ⋅ E ) D 2

(1)

where E, D, and n are the electric field, the electric displacement vector, and the outwardpointing normal vector, respectively. The distribution of the E and D can be derived based on the electric potential in Figure 2, as presented in Figure S2 (Supporting Information). Here, we resolve the electrostatic force Fes into the lateral x-component (Fes-x) and the vertical zcomponent (Fes-z). To illustrate the position-dependence of the electrostatic force acting on the bead, a row of three windows is selected from the 3×3 array (dashed area in Figure 2b). The topdown view of the three windows is plotted in Figure 3a and 3d. “Line 1” and “Line 2” in Figure 3, Figure 3a and 3d represent the positions across the center of the window region and the electrode region, respectively. The “a” in Figure 3a and 3d represents the side width of a window (a = 1.58 mm). By submitting Equation (1) into the numerical model, the Fes-x and Fes-z acting on a bead can be obtained (see Experimental Section for details).

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In the first case, if the center of the bead locates along the “Line 1”, the corresponding lateral Fes-x is revealed in Figure 3b. It can be observed that the Fes-x becomes minimal when the bead sits at the center of a window. Once it deviates from the center, the magnitude of the Fes-x substantially increases until the bead reaches the window’s perimeter where the maximum Fes-x is calculated to be 8.65 µN. Further deviation beyond the perimeter causes a considerable decrease of the force magnitude. The sign of the Fes-x represents the lateral force direction, with the positive sign pointing to the right while the negative sign pointing to the left. Typical positions and their corresponding Fes-x are illustrated in Figure 3g, which are in consistence with the qualitative description of Figure 1e above. Considering the square symmetry of the window, it can be then obtained that the lateral Fes-x attempts to attract and then to anchor the bead at the window center once the bead is within the shadowed square region plotted in Figure 3a. Through the similar calculation process, the vertical electrostatic force at different positions along the “Line 1” is shown in Figure 3c. The maximum Fes-z of -22.5 µN occurs when the bead locates exactly at the window center. The Fes-z is found to have a constant negative sign, indicating that this force always points downward. It needs to be figured that the vertical Fes-z does not play a decisive role in determining the bead position. In the second case, if the nylon bead is placed along the “Line 2”, how the Fes acts on the bead is similar to the first case above. It is obtained that both the Fes-x and the Fes-z significantly drops in magnitude by over 95% when compared the first case (Figure 3b and 3c). The lateral Fes-x is only as small as 0.25 µN. This observation proves that negligible lateral electrostatic force is applied onto the bead if it stays away from the window, making self-assembly unlikely to occur. Therefore, the comparison of the two cases above quantitatively explains the origin of the self-assembly. As a measure to experimentally determine the electrostatic force, a tilting angle

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test is conducted. As the substrate is tilted to 70° (Figure 3h), an anchored bead is found to stay at the perimeter of a window, shown in the zoom-in view of Figure 3h (Movie S1 for details, Supporting Information). It is mainly because of the lateral Fes-x that holds the bead from rolling down the tilted surface. At this state, three types of forces act on the bead, i.e. electrostatic force, static friction force, and gravity force, as plotted in Note S1 (Supporting Information). The static friction force of 3.41 µN can be quantitatively obtained via another tilting angle test in which the triboelectric charges are eliminated beforehand (Movie S2 for details, Supporting Information). The experimentally obtained Fes-x is found to be greater than 5.48 µN when Fes-z is 10.53 µN as predicted by numerical simulation (Note S1 for details, Supporting Information), which is in excellent agreement with the theoretical value in Figure 3c. Given that the maximum Fes-x is over 2-fold larger than the static friction force, the charged bead can be easily anchored within the window, which further justifies the proposed self-assembly process above. In the following section, a series of factors that influence self-assembly are investigated, including the electrification layer thickness, the window size and the window shape. Here, the electric potential distribution across a row of three windows (top section in Figure 4a) on the electrification layer is investigated. We specifically focus on the maximum electrical potential difference (△U in Figure 4a) as a major parameter to characterize the self-assembly because the

△ U is in positive correlation with the magnitude of the electrostatic force. First, the electrification layer thickness largely determines the electric potential distribution. The resulting distribution as a function of the thickness is plotted in Figure 4a. The electric potential within the windows is substantially lower than that in the surrounding regions, forming a deep “potential well” as discussed above. The △U is then referred to the difference between the baseline and the lowest point. As the electrification layer thickness increases from 0.02 to 0.3 mm, the ∆U

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decreases from 1.37 to 0.84 kV, representing a drop of 38.6% as exhibited in Figure 4b. Moreover, the increase of the thickness is also accompanied with the shift of the overall electric potential distribution to a lower value (Figure 4a). As the electrification layer becomes thicker, the top surface becomes further away from the grounded electrode. As a result, the negative triboelectric charges play an increasingly more decisive role in determining the surface electric potential. Because the ability of capturing the nylon bead is closely related to the ∆U, thin electrification layer is beneficial for the self-assembly. Second, the window size is also found to be a governing factor. Here, the density of the windows keeps constant, whereas the window size varies as indicated in Figure 4c. As the window becomes larger, the “potential well” becomes substantially deeper. Shown in Figure 4d, the ∆U experiences a 2.7-fold enhancement as the window size increases from 1.00 to 2.30 mm. Although higher ∆U does benefit the selfassembly, excessively large size will result in the assembly of multiple beads within in a single window. That’s why the window size in this work is purposely chosen to match that of the bead. Third, the window shape also plays an important role. If the window has a round shape, as shown in Figure 4e, the obtained electric potential distribution also exhibits “potential wells” within the window. Compared to the square window with identical feature size, the circular window generates smaller ∆U of 1.39 kV. This is attributed to the fact that the square is larger in area than the circle provided with the same feature size. This is the reason why square windows are adopted in this work. The ETSA reported in this work can potentially be used in the fabrication of patterns for a variety of applications. Here, the fabrication of a flexible display panel is demonstrated. The fabrication procedures are plotted in Figure 5 (Figure 5a to 5e). A luminous paint is first spraypainted on the nylon beads. After being assembled into a pre-defined pattern, the nylon beads are

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then half anchored into a layer of partially cured polydimethylsiloxane (PDMS) with the assistance of a pressing force. After the PDMS matrix is completely cured, it is peeled from the substrate. As a result, the pattern of the assembled beads is then transferred into the flexible PDMS matrix. For the ETSA reported here, the individual windows are independent without having to comply with any specific arrangement rule. Then, an arbitrary pattern can be defined at will during the fabrication of the electrode layer. This is the most prominent advantage of our ETSA compared to other zero-power methods.

3, 23

For example, as shown in Figure 5f, a four-

letter pattern “BINN” is assembled in which the beads and the windows have one-to-one correspondence. The transferred pattern on the PDMS matrix is shown in Figure 5g. In darkness, the pattern emits luminescence as a display panel (Figure 5h) because of the pre-coated luminous paint on the beads. Based on the principle demonstrated here, our proposed ETSA can be potentially used in the self-assembly of other structures in addition to polymer beads, which may result in other functional applications in fabricating low-cost, large-area electronic devices. It is worth noting that the nylon beads can be replaced by other materials that are easily positively charged, such as metals, polyurethane, silicon dioxide etc. CONCLUSIONS In summary, we report a method of electrostatic templated self-assembly (ETSA) for arbitrarily patterning millimeter-sized polymer beads without relying on an external power source. By introducing a grounded grid electrode underneath an electrification layer, the triboelectric charges on the electrification layer are fully screened by opposite charges induced on the patterned electrode. Comparing with the usual ETSA method, this ETSA method realized arbitrary patterning of millimeter-sized polymer beads in a self-powered way. From point of zero-power, driving voltage up to several kV induced by triboelectrification can be reached to

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actuate the self-assembly process. By designing the pattern of grid electrode, arbitrary patterning of macro-sized polymer beads can be realized with simple fabricating technique and small amount of materials. On the basis of triboelectrification, this ETSA method can also transfer pattern into a flexible polymer elastomer matrix hinges on its capability for repeatable fabrication of arbitrary array. In view of the self-powered feature, brief fabrication process, and reusable templates, the ETSA method in this work is a feasible approach in self-assembly of macro-sized beads and may be developed for functional particles at all scales in the future. EXPERIMENTAL SECTION ETSA device fabrication. An acrylic substrate with dimensions of 32 mm × 32 mm × 2 mm was cut by laser cutting. On the substrate, a patterned copper electrode with an average thickness of 200 nm was prepared by DC magnetron sputtering. One end of a wire was then attached to the electrode with the assistance of silver paint. Subsequently, the acrylic substrate deposited with the copper electrode was covered by a Teflon adhesive film of 50 µm in thickness. Create vertically aligned polymer nanowires on the Teflon surface using plasma dry etching. Ar, O2 and CF4 gasses were introduced into the ICP chamber at flow rates of 15.0, 10.0 and 30.0 sccm (standard cubic centimeter per minute), respectively. The operation temperature was 55.0 ℃ with a pressure of 15 mTorr. One power source of 400 W was used to generate highdensity plasma while another one of 100 W was used to accelerate plasma ions toward the Teflon surface. The etching time was 240 s. The millimeter-sized (diameter=1.58 mm) nylon-6,6 (nylon) beads were purchased from McMaster-Carr, USA. Self-assembly procedures. The self-assembly procedures are as follows. First, a surface charging treatment was conducted. The electrification layer was repeatedly rubbed with an

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aluminum foil in a reciprocating way for 50 cycles, while tens of nylon beads were shaken in a Teflon-based container. Subsequently, the beads were spread gently onto the electrification layer while the substrate was vibrating laterally in a reciprocating way with a frequency of 5 Hz and an amplitude of 8 mm. Once all the windows were occupied by the beads, the substrate was slightly tilted at an angle of 8° so that excessive beads at undesired positions rolled off the substrate. COMSOL model settings. A 3D model of a 3×3 array was used to reveal the potential distribution. The dimensions of the acrylic substrate were 11.06 mm × 11.06 mm × 2 mm. The thickness of the electrification layer was set to be 0.05 mm. Nine nylon beads (1.58 mm in diameter) with a surface charge density of +0.2 µC/m2 were placed on the windowed sites with one-on-one correspondence. The Teflon electrification layer has a surface charge density of -100 µC/m2. The entire setup was surrounded by a grounded sphere of 200 mm in diameter. The dielectric permittivity used in the simulation were ε = 1.0 for air and copper, ε = 3.6 for acrylic (PMMA), ε = 2.4 for Teflon (PTFE) and ε = 4.0 for nylon. Preparation of flexible display panel. Nylon beads were spray-painted with alkaline earth aluminates luminous paint(Sr4Al14O25: Eu, Dy)with long-duration after-glow. First, we rubbed the Teflon layer together with an aluminum foil while and shook the nylon beads in a 10 mL Teflon cup. After each window was filled with a nylon bead, we slightly tilted the setup to remove extra beads (Figure 5b). Uncured PDMS (curing agent of 20 wt %) was slowly poured into an acrylic box (5 cm × 10 cm), which was then put into an oven at 80 °C for 7 min to partially cure the PDMS. Subsequently, a layer of the partially cured PDMS was placed on top of the assembled nylon beads while a downward force of 0.2 N was applied vertically. The entire setup was then dried in an oven at 80 ℃ for 1 h until the PDMS matrix was completely cured. Finally, we peeled off the cured PDMS into which the patterned beads were transferred.

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ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Figure S1-S2, Note S1 and Movie S1-S2 AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This research was supported by the National Key R & D Project from Ministry of Science and Technology, China (Grant No. 2016YFA0202701), National Science Foundation of China (Grant No. 51572030), and Beijing Natural Science Foundation (Grant No. 2162047). REFERENCES 1. Reese, C. E.; Baltusavich, M. E.; Keim, J. P.; Asher, S. A. Development of an Intelligent Polymerized Crystalline Colloidal Array Colorimetric Reagent. Anal. Chem. 2001, 73, 50385042. 2. Saeedi, E.; Kim, S.; Parviz, B. A. Self-assembled crystalline semiconductor optoelectronics on glass and plastic. J. Micromech. Microeng. 2008, 18, 075019. 3. Tien, J.; Terfort, A.; Whitesides, G. M. Microfabrication through Electrostatic Self-Assembly. Langmuir 1997, 13, 5349-5355.

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21. Winkleman, A.; McCarty, L. S.; Zhu, T.; Weibel, D. B.; Suo, Z.; Whitesides, G. M. Templated self-assembly over patterned electrodes by an applied electric field: geometric constraints and diversity of materials. J. Microelectromech. Syst. 2008, 17, 900-910. 22. Wesson, P. J.; Grzybowski, B. A. Electrostatically Templated Self-Assembly of Polymeric Particles: The Role of Friction and Shape Complementarity. Adv. Funct. Mater. 2011, 21, 4763-4768. 23. Grzybowski, B. A.; Winkleman, A.; Wiles, J. A.; Brumer, Y.; Whitesides, G. M. Electrostatic self-assembly of macroscopic crystals using contact electrification. Nat Mater 2003, 2, 241245. 24. Cademartiri, R.; Stan, C. A.; Tran, V. M.; Wu, E.; Friar, L.; Vulis, D. L.; Clark, W.; Tricard, S.; Whitesides, G. M. A simple two-dimensional model system to study electrostatic-selfassembly. Soft Matter 2012, 8, 9771-9791. 25. Soh, S.; Liu, H.; Cademartiri, R.; Yoon, H. J.; Whitesides, G. M. Charging of Multiple Interacting Particles by Contact Electrification. J. Am. Chem. Soc. 2014, 136, 13348-13354. 26. Fang, H.; Wu, W.; Song, J.; Wang, Z, L. Controlled growth of aligned polymer nanowires. J. Phys. Chem. C 2009, 113, 16571-16574. 27. http://www.trifield.com/content/tribo-electric-series/ (accessed on Oct 10, 2017). 28. Wang, Z. L. Triboelectric Nanogenerators as New Energy Technology for Self-Powered Systems and as Active Mechanical and Chemical Sensors. ACS Nano 2013, 7, 9533-9557. 29. Horn, R. G.; Smith, D. T.; Grabbe, A. Contact electrification induced by monolayer modification of a surface and relation to acid-base interactions. Nature 1993, 366, 442-443. 30. Jackson, J. D. Classical Eletrodynamics; Wiley, New York, 1999; pp 260-290, 609.

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Figure 1. Schematic illustrations of the ETSA setup and the self-assembled beads. (a) Structure of the ETSA setup. (b) SEM image of polymer NWs created by plasma dry etching. (c) Photograph of the assembled nylon beads, inset: Enlarged view of a single nylon bead at the center of a window. (d) Diagram of charge distribution in a cross-sectional view. (e) Diagram of electrostatic force acting on the beads at different positions.

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Figure 2. Three-dimensional distribution of electric potential of different parts of the ETSA setup calculated by COMSOL. (a) Assembled nylon beads. (b) Electrification layer. (c) Copper electrode layer. (d) PMMA substrate.

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Figure 3. Calculated electrostatic force acting on a nylon bead. (a) Top-down view of a threewindow region in which Line 1 represents the positions across the window center. (b) Fes-x acting on a bead as it locates along Line 1. (c) Fes-z acting on a bead as it locates along Line 1. (d) Topdown view of the three-window region in which Line 2 represents the positions away from the windows. (e) Fes-x acting on a bead as it locates along Line 2. (f) Fes-z acting on a bead as it locates along Line 2. (g) Fes-x and corresponding positions of the bead. (h) Photograph of a bead anchored within in a window site as the substrate is tilted at an angle of 70°.

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Figure 4. Influencing factors of the electric potential distribution. (a) One-dimensional distribution of electric potential as the electrification layer thickness varies. (b) Dependence of the ∆U on the electrification layer thickness. (c) One-dimensional distribution of electric potential as window size varies. (d) Dependence of the ∆U on the window size. (e) Threedimensional distribution of electric potential provided with round-shaped windows. (f) Electric potential distribution of the circle window in comparison with the square window.

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Figure 5. Flexible display panel fabrication. (a) to (e) Fabrication procedures to transfer the painted beads in an assembled pattern into a polymer matrix. (f) Self-assembly result of nylon beads into a pre-defined pattern. (g) Flexible display panel with the patterned beads embedded into the polymer matrix. (h) Luminescence of the display panel in darkness.

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