Polymer composites with high haze and high transmittance Articles/2015/Polymer... · Novel light...

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Polymer Chemistry COMMUNICATION Cite this: Polym. Chem., 2015, 6, 6632 Received 10th July 2015, Accepted 5th August 2015 DOI: 10.1039/c5py01072a www.rsc.org/polymers Polymer composites with high haze and high transmittanceYue Ru, a,b Xiaohong Zhang, a Li Wang, b Liming Dai,* c Wantai Yang* b and Jinliang Qiao* a,b Novel light scattering polymer composites with high transmittance and high haze have been developed by using cross-linked co- polymer (CM-SMC) microspheres as light scattering llers. By using these novel light scattering polymer composite materials, compared to the conventional materials, 20% of the illumination energy can be saved when used for LEDs. The rising global energy demand and the environmental impact of traditional energy resources pose serious challenges to human health, energy security, and environmental protection. 13 Surprisingly enough, around 25% of the worlds power energy consumption is used for lighting, in which a large amount of energy is converted into waste heat. One promising solution to save energy and reduce CO 2 emission is the use of light-emitting diodes (LEDs) for lighting and displays. 4,5 LEDs directly convert electricity into light emission by injecting electrons and holes from electrodes into a pn junction to combine with photons. 4 The colour of the light emitted can be tuned by changing the band gap energy of the materials forming the pn junction. 5 This lighting technology currently receives intensive research and development focus because of its high energy conversion eciency, ease with which full color tuning can be achieved, good environmental adoptability, long lifetime, and virtually no waste heat or pollution. As the press release for the Nobel Prize of Physics in 2014 says: Incandescent light bulbs lit the 20th century; the 21st century will be lit by LED lamps. 6 However, currently available LED lamps emit extremely high luminance with a point light source, which produces an uncomfortable glare to human eyes. Therefore, light-scattering materials are needed to convert the point light source to a surface light source for LED lighting and displays. 7,8 Traditionally, silicone resin, polymethyl methacrylate, polyacrylate, or certain inorganic par- ticles have been used as the scattering fillers. 911 Without exception the use of conventional light scattering fillers increases the haze of transparent polymers but also compro- mises transmittance, and hence significantly reduces the emitted light and energy saving for LED lighting and displays (Fig. S1). Therefore, it is highly desirable to identify alterna- tive light scattering materials that are readily available, cost eective, and can simultaneously enhance the haze and trans- mittance of transparent polymers for LED lighting and dis- plays. However, there is no such light-scattering filler reported in the literature. In this study, we developed a new class of cross-linked α-methyl styrene/maleic anhydride copolymer (CM-SMC) microspheres with a narrow particle size distri- bution (Fig. 1, Experimental section (see the ESI)) as the scat- tering fillers for modifying the transparent polycarbonate (PC). Despite the challenge to synthesize monodispersed polymer microspheres with a controllable particle size, 12 Yang and co- workers have reported an elegant self-stable precipitation polymerization method for preparing polymer microspheres of controllable sizes. 1315 Building on our previous work, 1316 we have successfully synthesized in this study, crosslinked micro- spheres of α-methyl styrene/maleic anhydride copolymers with various diameters of 400, 800 and 1200 nm (designated as: 400CM-SMC, 800CM-SMC, and 1200CM-SMC, respectively). Fig. 1B shows the SEM images for 400CM-SMC, 800CM-SMC and 1200CM-SMC while detailed descriptions of their syn- theses can be found in the Experimental section. For compari- son, non-crosslinked microspheres of the α-methyl styrene/ maleic anhydride copolymer (NCM-SMC) were also prepared according to the same procedure described above, but without the addition of DVB. Fig. 1C shows an SEM image for 800 nm non-crosslinked microspheres. To form the microspheres of a controlled size, we performed a stabilizer-free precipitation polymerization starting with a homogeneous reaction mixture at the initial stage of the polymerization process. As the co- polymerization of AMS and MAH took place in the solution for Electronic supplementary information (ESI) available. See DOI: 10.1039/ c5py01072a a SINOPEC Beijing Research Institute of Chemical Industry, Beijing 100013, China. E-mail: [email protected] b College of Materials Science and Engineering, Beijing University of Chemical and Technology, Beijing 100029, China. E-mail: [email protected] c Centers of Advanced Science and Engineering for Carbon, Department of Macromolecular Science and Engineering, School of Engineering, Case Western Reserve University, Cleveland, OH 44106, USA. E-mail: [email protected] 6632 | Polym. Chem. , 2015, 6, 66326636 This journal is © The Royal Society of Chemistry 2015 Published on 07 August 2015. Downloaded by CASE WESTERN RESERVE UNIVERSITY on 12/11/2015 23:46:59. View Article Online View Journal | View Issue

Transcript of Polymer composites with high haze and high transmittance Articles/2015/Polymer... · Novel light...

Page 1: Polymer composites with high haze and high transmittance Articles/2015/Polymer... · Novel light scattering polymer composites with high transmittance and high haze have been developed

PolymerChemistry

COMMUNICATION

Cite this: Polym. Chem., 2015, 6,6632

Received 10th July 2015,Accepted 5th August 2015

DOI: 10.1039/c5py01072a

www.rsc.org/polymers

Polymer composites with high haze and hightransmittance†

Yue Ru,a,b Xiaohong Zhang,a Li Wang,b Liming Dai,*c Wantai Yang*b andJinliang Qiao*a,b

Novel light scattering polymer composites with high transmittance

and high haze have been developed by using cross-linked co-

polymer (CM-SMC) microspheres as light scattering fillers. By

using these novel light scattering polymer composite materials,

compared to the conventional materials, 20% of the illumination

energy can be saved when used for LEDs.

The rising global energy demand and the environmentalimpact of traditional energy resources pose serious challengesto human health, energy security, and environmentalprotection.1–3 Surprisingly enough, around 25% of the world’spower energy consumption is used for lighting, in which alarge amount of energy is converted into waste heat. Onepromising solution to save energy and reduce CO2 emission isthe use of light-emitting diodes (LEDs) for lighting anddisplays.4,5 LEDs directly convert electricity into light emissionby injecting electrons and holes from electrodes into a p–njunction to combine with photons.4 The colour of the lightemitted can be tuned by changing the band gap energy of thematerials forming the p–n junction.5 This lighting technologycurrently receives intensive research and development focusbecause of its high energy conversion efficiency, ease withwhich full color tuning can be achieved, good environmentaladoptability, long lifetime, and virtually no waste heat orpollution. As the press release for the Nobel Prize of Physics in2014 says: “Incandescent light bulbs lit the 20th century; the21st century will be lit by LED lamps”.6 However, currentlyavailable LED lamps emit extremely high luminance with apoint light source, which produces an uncomfortable glare tohuman eyes. Therefore, light-scattering materials are needed

to convert the point light source to a surface light source forLED lighting and displays.7,8 Traditionally, silicone resin,polymethyl methacrylate, polyacrylate, or certain inorganic par-ticles have been used as the scattering fillers.9–11 Withoutexception the use of conventional light scattering fillersincreases the haze of transparent polymers but also compro-mises transmittance, and hence significantly reduces theemitted light and energy saving for LED lighting and displays(Fig. S1†). Therefore, it is highly desirable to identify alterna-tive light scattering materials that are readily available, costeffective, and can simultaneously enhance the haze and trans-mittance of transparent polymers for LED lighting and dis-plays. However, there is no such light-scattering filler reportedin the literature. In this study, we developed a new class ofcross-linked α-methyl styrene/maleic anhydride copolymer(CM-SMC) microspheres with a narrow particle size distri-bution (Fig. 1, Experimental section (see the ESI†)) as the scat-tering fillers for modifying the transparent polycarbonate (PC).Despite the challenge to synthesize monodispersed polymermicrospheres with a controllable particle size,12 Yang and co-workers have reported an elegant self-stable precipitationpolymerization method for preparing polymer microspheres ofcontrollable sizes.13–15 Building on our previous work,13–16 wehave successfully synthesized in this study, crosslinked micro-spheres of α-methyl styrene/maleic anhydride copolymers withvarious diameters of 400, 800 and 1200 nm (designated as:400CM-SMC, 800CM-SMC, and 1200CM-SMC, respectively).Fig. 1B shows the SEM images for 400CM-SMC, 800CM-SMCand 1200CM-SMC while detailed descriptions of their syn-theses can be found in the Experimental section. For compari-son, non-crosslinked microspheres of the α-methyl styrene/maleic anhydride copolymer (NCM-SMC) were also preparedaccording to the same procedure described above, but withoutthe addition of DVB. Fig. 1C shows an SEM image for 800 nmnon-crosslinked microspheres. To form the microspheres of acontrolled size, we performed a stabilizer-free precipitationpolymerization starting with a homogeneous reaction mixtureat the initial stage of the polymerization process. As the co-polymerization of AMS and MAH took place in the solution for

†Electronic supplementary information (ESI) available. See DOI: 10.1039/c5py01072a

aSINOPEC Beijing Research Institute of Chemical Industry, Beijing 100013, China.

E-mail: [email protected] of Materials Science and Engineering, Beijing University of Chemical and

Technology, Beijing 100029, China. E-mail: [email protected] of Advanced Science and Engineering for Carbon, Department of

Macromolecular Science and Engineering, School of Engineering, Case Western

Reserve University, Cleveland, OH 44106, USA. E-mail: [email protected]

6632 | Polym. Chem., 2015, 6, 6632–6636 This journal is © The Royal Society of Chemistry 2015

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a certain period of time to form polymer chains of a criticallength, they precipitated out from the solution as tiny nucleiand grew into particles of a desirable size via the deposition ofpolymer chains formed in the solution phase to the particlesurface. The size of the CM-SMC microspheres thus formedcould be tuned by adjusting monomer concentration andpolymerization time, which was found to increase with theincreasing monomer concentration and polymerization time.In a typical experiment, maleic anhydride (MAH, 83.40 g) andα-methyl styrene (AMS, 100.35 g) monomers, divinylbenzene(DVB, 25.50 g) crosslinking reagent, and AIBN (0.4935 g)initiator were dissolved in 589.50 g of N2-purged (for 20 min)in solvent acetate in a 1000 mL flask placed in an oil bath at70 °C. After polymerization for 6 h without agitation, cross-linked microspheres were obtained by centrifugation, followedby thoroughly washing with methanol to remove the monomerand initiator residues prior to vacuum drying (20 Torr) at 50 °Covernight.

Fig. 1D and E show the haze and transmittance of PCbefore and after blending with 0.05 wt% CM-SMC micro-spheres of different sizes. Surprisingly, it was found that thehaze and transmittance of PC increased simultaneously byblending with the CM-SMC microspheres, which is in starkcontrast to Fig. S1† that shows about 50% loss in transmit-tance (equivalent to ca. 50% energy loss; Fig. S1(B)†) by usingthe conventional DC light-scattering filler. The haze of PCincreased monotonously with increasing the microsphere size(Fig. 1D) while the transmittance of PC showed a size-depen-dent enhancement (Fig. 1E); significantly increased transmit-

tance over the entire visible wavelengths upon the addition of400CM-SMC or 800CM-SMC microspheres, but a marginallyincreased transmittance for 1200CM-SMC. As can be seen inFig. 1D and E, the PC composite with 800CM-SMC showed thehighest transmittance and a reasonably high haze among allthe samples investigated in this study, though its haze reachedonly to a moderate level (ca. 40%) and could be increased upto 96% by incorporating a small amount of conventional lightscattering fillers (e.g., ca. 0.3 wt% DC) with high transmittanceand additional cost advantages (Table S3†). Thus, we will focuson the PC composite with 800CM-SMC for the subsequentstudy to gain a better fundamental understanding of the filler-induced simultaneous increase in haze and transmittance, aphenomenon which has not been observed in any compositesand is not allowed by existing theories.

In addition to the influence of the CM-SMC microspheresize described above, we further investigated the possibleeffect of the 800CM-SMC content on haze and transmittanceof the PC composites. As can be seen in Table 1, both trans-mittance and haze for all of the PC composites with differentamounts of 800CM-SMC fillers covered by this study arehigher than those of the pure PC starting material. Theobserved increase in haze, more than 40% with increasing theCM-SMC content up to 2.00% can be attributed to the scatter-ing induced by the addition of CM-SMC microspheres, as isthe case for the conventional scattering fillers.17 As mentionedearlier, however, it is completely out of our expectation to seethe transmittance increased from 85.43% for the pure PC upto 90.16% for the PC composite containing 1.00 wt%800CM-SMC fillers (Table 1). Hence, the origins of theabnormal transmittance increase are of great interest forfurther study.

As shown in Fig. 2A, the use of conventional light-scatteringfillers (e.g., DC) could significantly increase the reflectanceof PC. In contrast, the addition of 800CM-SMC into the PCreduced its reflectance. The reflectance of the PC compositewas continuously reduced with increasing the CM-SMCcontent, especially over the wavelength from 400 to 500 nm(Fig. 2A). Given that the addition of a low content of CM-SMC(≤2.00 wt%) would not cause an obvious change in the opticalabsorption of PC (cf. Fig. 3C), the observed reflectance dropcould be responsible for the transmittance increase in the PCand CM-SMC composites as the total intensity of the transmit-ting beam and reflecting beam should be a constant if the

Fig. 1 (A) Molecular structure of NCM-SMC. (B) SEM images ofCM-SMC microspheres with different sizes. (C) SEM images of 800 nmnon-crosslinked microspheres; (D) haze of pure PC and PC compositeswith 0.05 wt% CM-SMC microspheres of different sizes. (E) Transmit-tance of pure PC and PC composites with 0.05 wt% CM-SMC micro-spheres of different sizes.

Table 1 Transmittance and haze of PC and PC composites withdifferent contents of 800CM-SMC

Samples CM-SMC (wt%) T (%) H (%)

Pure PC 0.00 85.43 0.63PC + 0.05 wt% CM-SMC 0.05 88.35 3.22PC + 0.50 wt% CM-SMC 0.50 89.85 14.37PC + 1.00 wt% CM-SMC 1.00 90.16 18.61PC + 1.50 wt% CM-SMC 1.50 89.54 29.38PC + 2.00 wt% CM-SMC 2.00 86.03 42.58

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optical absorption and the incident light intensity are kept un-changed. Clearly, therefore, one of the important questionsthat need to be addressed is why the addition of 800CM-SMCreduced the reflectance of PC, as opposed to the conventionalfiller (Fig. 2A). A literature survey shows that the most effectiveway to reduce the reflectance is to form the “moth eye” struc-ture on a polymer surface.18–21 In 1962, Bernhard and Miller22

discovered that there are many sub-micron structures on themoth eyes to reduce the reflectance for hiding from predators.These sub-micron structures are composed of protuberanceswith about 200 nm in height (h), and the pitch of the protuber-ances is about 300 nm. Later, it was found that the pitch mustbe narrower than the wavelength (λ) of light for reducing thereflectance, which then depends also on the ratio of h and λ

with the minimum reflectance at h/λ ≈ 0.4. Based on theseconsiderations, Mundo and co-workers have recently deve-loped a transparent polymer surface with the bio-inspired “motheye” sub-microstructures to significantly reduce its surfacereflectance from 11% to 0.5%.23 These studies prompted us to

examine the presence of possible “moth eye” sub-microstruc-tures on the surface of our PC and CM-SMC composites.

Fig. 2B–D show the SEM and AFM images of the surface ofa PC composite with 1.00 wt% 800CM-SMC microspheres. Itcan be seen that microspheres are distributed over the compo-site surface to form a concave–convex structure at the micronscale. The AFM section analysis reveals that the width of thebottom of the groove is approximately 400 nm (Fig. 2D), whichis smaller than the wavelength of visible light to satisfy thebasic conditions for generating the “moth eye” effect. Fig. 2Dalso shows that the height of the protuberance (h) is about170 nm, and hence the most obvious drop of reflectanceshould be at 425 nm where h/λ ≈ 0.4.22 Indeed, our experi-mental results given in Fig. 2A show the most obvious reflec-tance drop at about 425 nm. Therefore, the observedreflectance reduction for our PC and CM-SMC composites isindeed due to the “moth eye” effect.22–24 For the PC andCM-SMC composites, therefore, the reflectance reductionseems to be responsible for the observed transmittanceincrease, along with the increase in haze. However, Fig. 3Ashows that the transmittance increase does not match thereduction in reflectance, particularly over 400–450 nm. Morespecifically, the transmittance increase is far less than thereflectance reduction at wavelengths of 400–450 nm while thetransmittance increase is more than the reflectance reductionover 500–800 nm. Clearly, therefore, an unknown yet decisivefactor, in addition to the reflectance reduction associated withthe “moth eye” effect, is also responsible for the observedtransmittance increase.

To further investigate the underlying principle for theobserved transmittance increase, we performed a test to seeif CM-SMC microspheres are fluorescent. Fig. 3B is thefluorescence spectra (λex = 410 nm) of the crosslinked800CM-SMC and its non-crosslinked counterpart (i.e.,800NCM-SMC), showing fluorescence emissions with twopeaks centered at 520 and 620 nm for both the samples withthe crosslinked one being the stronger fluorescent chromo-phore. Due to the fluorescent nature of the CM-SMC, the netlight loss over 400–450 nm shown in Fig. 3A is, most likely,

Fig. 2 (A) Reflectance of PC and PC composites with different contentsof DC and 800CM-SMC. Surface microstructures of PC composites with1.00 wt% 800CM-SMC: (B) SEM image, (C) AFM image, and (D) surfacesection analysis of (C) by the nanoscope analysis software.

Fig. 3 (A) The sum values of increased transmittance and decreased reflectance, ΔT = TComposite − TPure PC, ΔR = RComposite − RPure PC, whereTComposite and TPure PC are the transmittance of PC composites and pure PC, respectively; RComposite and RPure PC are the transmittance of PC compo-sites and pure PC, respectively. (B) The fluorescence spectra of 800CM-SMC and 800NCM-SMC at λex = 410 nm. (C) The optical absorbance of purePC and PC composites.

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because the PC and 800CM-SMC composites absorbed morelight at low wavelengths, as confirmed by Fig. 3C, and emittedmore light at high wavelengths over 500 nm than the pure PC.Therefore, it is the combination of the reflectance reductioninduced by the “moth eye” effect and the fluorescent nature ofthe CM-SMC microspheres that makes the PC and CM-CMScomposites to show a higher transmittance than that of purePC to visible light (cf. Fig. 1E).

Finally, how can the CM-SMC and NCM-SMC microspheresbe fluorescent? In fact, Yan and co-workers have previouslyfound that fluorescent multiblock polymers could be syn-thesized from nonfluorescent monomers through the π–πinteraction between the phenyl units and the neighbouringcarbonyl units.25 In view of the similarity in the molecularstructures of our NCM-SMC (Fig. 1A) and polymers studied byYan et al. (Fig. S2†), we believe that the observed photo-luminescence could also arise from the π–π interactionbetween the phenyl units and the neighbouring carbonyl unitsin both the CM-SMC and NCM-SMC microspheres. The for-mation of cross-linked microspheres could bring the phenylmoieties in the α-methyl styrene units more closely towardsthe carbonyl groups in the maleic anhydride units within theCM-SMC copolymer to enhance the π–π interaction,25–27 andhence the enhanced fluorescence emission for the CM-SMCwith respect to its NCM-SMC counterpart (Fig. 3B).

In summary, we have developed the first polymer compo-sites with a higher haze and a higher transmittance than thoseof the pure polymer matrix by blending crosslinked micro-spheres of the α-methyl styrene/maleic anhydride copolymer(CM-SMC) with the pure transparent polycarbonate (PC).Unlike conventional light-scattering fillers (e.g., silicone resin,polymethyl methacrylate, polyacrylate, or certain inorganic par-ticles) that could increase the haze at the cost of transmit-tance, the CM-SMC microspheres can increase the haze andtransmittance simultaneously. The increase in transmittanceby the addition of CM-SMC microspheres into PC was demon-strated to result from the reflectance reduction induced by the“moth eye” effect, in conjunction with the fluorescent natureof the CM-CMS microspheres this leads to absorption of thereduced reflecting light at low wavelengths and emits morelight at high wavelengths over 500 nm than the pure PC. There-fore, the newly-developed CM-SMC microspheres could beideal light-scattering fillers for polymer composites to achieveboth high haze and high transmittance for LED lighting anddisplays, which could significantly save energy and cost (Fig. S3and 4 and Table S1–3†). The methodology developed in thisstudy can also be applied to the development of many otherhigh-performance polymer composites for various optoelectronicapplications, ranging from solar cells to optical sensors, forfurther enhancing the environmental and energy impact.

Notes and references

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3 F. A. Rohrman, B. J. steigerwald and J. H. Ludwig,Industrial emissions of carbon dioxide in the united states:A Project, Science, 1967, 156, 931–932.

4 S. Nakamura, The roles of structure imperfections inInGaN-Based blue Light-Emitting Diodes and LaserDiodes, Science, 1998, 281, 956–961.

5 H. Morkoc and S. N. Mohammad, High-luminosity blueand blue-green Gallium Nitride Light-Emitting Diodes,Science, 1995, 267, 51–55.

6 http://www.nobelprize.org/nobel_prizes/physics/laureates/2014/press.html.

7 H. Daicho and T. Iwasaki, A novel phosphor for glareless white light-emitting diodes, Nat. Commun., 2012, 3,1132.

8 I. Charles and A. Z. Zovko, EL lamp with light scatteringparticles in cascading layer, US2003218420A1, 2003.

9 E. Juergen, S. Craig and J. Willen, Light diffuser compo-sition, EP0634445A, 1994.

10 W. James and W. Jiun-Chen, Particulate polymercomposition-a method of making particulate polymercompositions and light-scattering thermoplastic polymercompositions containing the particulate polymers,EP0269324, 1987.

11 M. S. Perry, Extruded sheet with controlled surface glossand process for the manufacture thereof, WO01162843,2001.

12 Y. Wu, Y. Li, L. Qin, F. Yang and D. Wu, Monodispersed ornarrow-dispersed melamine–formaldehyde resin polymercolloidal spheres: preparation, size-control, modification,bioconjugation and particle formation mechanism,J. Mater. Chem. B, 2013, 1, 204–212.

13 C. Xing and W. Yang, A novel facile method for the prepa-ration of uniform, reactive maleic anhydride/vinyl acetatecopolymer micro-and nanospheres, Macromol. RapidCommun., 2004, 25, 1568.

14 C. Xing and W. Yang, Stabilizer-Free DispersionCopolymerization of Maleic Anhydride and VinylAcetate. I. Effects of Principal Factors on Microspheres,J. Polym. Sci., Polym. Chem. Ed., 2005, 43, 3760–3770.

15 C. Xing, Y. Yu and W. Yang, Stabilizer-Free DispersionCopolymerization of Maleic Anhydride and Vinyl Acetate.II. Polymerization Features, Macromol. Chem. Phys., 2006,207, 621–626.

16 C. Chen, J. He and J. Deng, Preparation of cross-linked poly(α-mehtyl styrene-co-maleic anhydride) through self-stableprecipitation polymerization, J. Beijing Univ. Chem.Technol., 2014, 41, 70–75.

17 M. Marek and J. Steidl, Light diffusing polycarbonate-polycycloolefin blends, Journal of Materials, Science, 2006,41(10), 3117–3121.

18 K. Nagato, H. Moritani and T. Hamaguchi, Fabrication ofantireflection-structured surface using vertical nanowires

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as an initial structure, J. Vac. Sci. Technol., B, 2010, 28,39–42.

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20 K. Tsui, Q. Lin, H. Chou, Q. Zhang, H. Fu, P. Qi and Z. Fan,Low-Cost, Flexible, nd Self-Cleaning 3D Nanocone Anti-Reflection films for High-Efficiency Photovoltaics, Adv.Mater., 2014, 26, 2805–2811.

21 H. Hattori, Anti-reflection surface with particle coating de-posited by electrostatic attraction, Adv. Mater., 2001, 13, 51–54.

22 C. G. Bernhard and W. H. Miller, A corneal nipple patternin insect compound eyes, Acta Physiol. Scand., 1962, 56,385–386.

23 R. D. Mundo, M. Troia, F. Palumbo, M. Trotta andR. Agostino, Nano-texturing of Transparent Polymers

with Plasma Etching: Tailoring Topography for a LowReflectivity, Plasma Process, Polym., 2012, 9, 947–954.

24 P. B. Clapham and M. C. hutley, Reduction of Lensreflection by “moth eye” principle, Nature, 1973, 244, 281–282.

25 J. J. Yan, Z. k. Wang, X. S. Lin, C. H. Hong, H. J. Liang,C. Y. Pan and Y. Z. You, Polymerizing non-fluorescentmonomers without incur-porating any fluorescent agentproduces strong fluorescent polymers, Adv. Mater., 2012,24, 5617–5624.

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27 R. Hu, N. L. C. Leung and B. Z. Tang, AIE macromolecules:syntheses, structures and functionalities, Chem. Soc. Rev.,2014, 43(13), 4494–4562.

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