Experimental Formulation of Photonic Crystal Properties for

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

Experimental Formulation of Photonic Crystal Properties for Hierarchically Self-Assembled POSS−Bottlebrush Block Copolymers Chang-Geun Chae,†,‡ Yong-Guen Yu,†,‡ Ho-Bin Seo,†,‡ Myung-Jin Kim,†,‡ Robert H. Grubbs,‡,§ and Jae-Suk Lee*,†,‡ †

School of Materials Science and Engineering and ‡Grubbs Center for Polymers and Catalysis, Gwangju Institute of Science and Technology (GIST), 123 Cheomdangwagi-ro, Buk-gu, Gwangju 61005, Republic of Korea § Division of Chemistry and Chemical Engineering, California Institute of Technology (Caltech), Pasadena, California 91125, United States S Supporting Information *

ABSTRACT: Rodlike “POSS−bottlebrush block copolymers” (POSSBBCPs) containing crystalline polyhedral oligomeric silsesquioxane (POSS) pendants in A block and amorphous polymeric grafts in B block were utilized to create onedimensional (1D) photonic crystals (PCs). 3-(12-(cis-5Norbornene-exo-2,3-dicarboximido)dodecanoylamino)propylheptaisobutyl POSS (NB-A16-POSS, MA) and exo-5-norbornene-2-carbonyl-end poly(benzyl methacrylate) (NBPBzMA, MB) were employed in sequential ring-opening metathesis polymerization to afford poly[3-(12-(cis-5-norbornene-exo-2,3dicarboximido)dodecanoylamino)propylheptaisobutyl POSS]-block-poly(exo-5-norbornene-2-carbonylate-graf t-benzyl methacrylate)s, P(NB-A16-POSS)-b-P(NB-g-BzMA)s, with well-modulated block compositions (fA = 34, 50, and 67 wt %) and overall degrees of polymerization (DP = 323−939). The P(NB-A16-POSS)-b-P(NB-g-BzMA)s hierarchically self-assembled to form highly ordered 1D PC films with periodic lamellar arrays that can reflect visible light with particular wavelengths. Their reflectance bandwidths, reflectivities, and ranges of peak reflectance wavelnegth (λpeak) were largely dependent on the block composition. The 1D PC films based on lamellar P(NB-A16-POSS)-b-P(NB-g-BzMA)s demonstrated the capability of formaulation of λpeak as linear functions of initial polymerization parameter ([M]0/[I]0).

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INTRODUCTION

Recent advances have focused on the lamellar self-assembly of rodlike bottlebrush and dendronized BCPs with ultrahigh molecular weights (MWs) to fabricate 1D PCs.27−35 Main chains that are highly extended by the steric repulsion of the bulky side groups are beneficial to prevent chain entanglement, which is a major kinetic barrier to chain organization. The extended main chains also enable the expansion of lamellar periodicity according to a function of degree of polymerization (DP) with a scaling power α close to 1, L0 ≈ 2l0DPα, where l0 is the statistical segmental length of main chain, and the scaling coefficient, 2l0, originates from the bilayer arrangement of rodlike blocks with symmetry of two side chain lengths.36−39 The unique periodicity scaling is more advantageous than that of linear BCPs40 to expand the lamellar periodicity to the PC range. Sequential ring-opening metathesis polymerization (ROMP) of two macromonomers has been well established as a grafting-through method to synthesize bottlebrush and dendronized BCPs with ultrahigh MWs.27−35 In this method, the precise synthesis of macromonomers has been important for the controlled ROMP. Accordingly, living anionic polymerization has been increasingly desired to prepare well-defined

Photonic crystals (PCs) are nanostructured materials composed of periodic arrays of two dielectric media. The alternating modulation of low and high reflective indices (nL/nH, nL < nH) generates particular photonic bandgaps as the frequency ranges of the photons whose propagation is prohibited.1,2 Since progressive investigations on the physics of photonic bandgaps began,3−5 the development of one-, two-, and three-dimensional (1D, 2D, and 3D) photonic-bandgap structures has granted PCs roles as dielectric mirrors capable of modulation of light flow.6−10 These efforts have given rise to utility of PCs in diverse optical devices, such as color displays, photovoltaics, and a variety of sensors.11−14 With the accelerating demand to downsize the periodicity (L0) of PC toward color-display materials with photonic bandgaps at visible wavelengths, two types of bottom-up approaches have been extensively developed. One is the selfassembly of colloidal spheres,15−20 and another is the selfassembly of block copolymers (BCP).21−35 The latter approach has recently attracted more interest due to the accessibility to a diversity of nanostructures (1D lamellae, 2D cylinders, and 3D gyroids and spheres), high reflectivities attributed to large numbers of periods, and the peak reflectance wavelength (λpeak) efficiently tunable by the modulation of L0. © XXXX American Chemical Society

Received: February 7, 2018 Revised: April 2, 2018

A

DOI: 10.1021/acs.macromol.8b00298 Macromolecules XXXX, XXX, XXX−XXX

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Scheme 1. Synthesis of P(NB-A16-POSS)-b-P(NB-g-BzMA)s through Sequential ROMPs of NB-A16-POSS (MA: MW = 1218 Da) and NBPBzMA (MB: MW: 5440 Da, Đ = 1.02) Initiated by G3 (I) in THF at 25 °C

Table 1. Sequential ROMPs of NB-A16-POSS (MA: MW = 1218 Da, [MA]0 = 0.4 M) and NBPBzMA (MB: Mn = 5440 Da, Đ = 1.02, [MB]0 = 0.1 M) Initiated by G3 (I) in THF at 25 °C convb (%) polymer code

MA:MB (wt:wt)

[MA]0/[I]0:[MB]0/[I]0

[M]0/[I]0a

34-1 34-2 34-3 34-4 50-1 50-2 50-3 50-4 67-1 67-2 67-3 67-4

33:67 33:67 33:67 33:67 50:50 50:50 50:50 50:50 67:33 67:33 67:33 67:33

300:134 400:180 500:224 600:269 500:112 600:135 700:157 800:179 700:79 800:90 900:101 1000:112

434 580 724 869 612 735 857 979 779 890 1001 1112

MA:MB

Mn,theoc (kDa)

Mnb (kDa)

Đb

DPA:DPBd

DPe

100:99 100:98 100:97 100:97 100:100 100:100 100:100 100:100 100:100 100:100 100:100 100:100

1087 1457 1791 2150 1218 1465 1707 1948 1282 1464 1645 1827

805 1123 1345 1643 1022 1193 1378 1536 1053 1201 1352 1522

1.20 1.30 1.29 1.27 1.06 1.15 1.16 1.17 1.17 1.20 1.21 1.24

225:98 313:136 375:163 459:199 420:94 490:110 566:127 631:141 579:64 661:73 744:82 837:92

323 449 538 658 514 600 693 772 643 734 826 929

[M]0/[I]0 = [MA]0/[I]0 + [MB]0/[I]0. bDetermined from SEC-MALLS. cMn,theo = [MA]0/[I]0 × conv/100% × MW of NB-A16-POSS + [MB]0/[I]0 × conv/100% × Mn of NBPBzMA. dDP of P(NB-A16-POSS) block:DP of P(NB-g-BzMA) block. eDP = DPA + DPB. a

crystalline POSS pendants in A block and amorphous polymeric grafts in B block to produce highly ordered 1D PCs. Through the scaling analysis, we demonstrate the linear relationship of initial polymerization parameter, DP, L0 and λpeak. Taking into consideration that realistic physics of rodlike BCPs has certain deviations from theory,36−39 the experimental study to establish the scaling formula is the most fundamental step to ensure the prediction of the light-reflection property of a PC from the initial polymerization parameter.

macromonomers because of its excellent MW control and capability of 100% end-functionalization with polymerizable groups.41−43 Despite the merits of bottlebrush and dendronized BCPs, extremely high DP has often caused low morphological quality (lack of layer ordering, broadness of interfacial width, and trapping of defects), leading to low peak reflectivity and broadness of bandwidth in the 1D PCs.27−30 The negative effects of high DP on the self-assembly is generally due to microphase separation impeded by slower chain diffusion.44−46 However, the incomplete microphase separation can be complemented by an additional organization process such as crystallization and molecular clustering.47−50 Polyhedral oligomeric silsesquioxane (POSS, (RSiO1.5)8) which contains a crystalline nanocage51−53 is desirable bulky pendant group to induce the hierarchical self-assembly of BCPs as well as the rodlike main chain conformation. 54−56 The ROMP of norbornene-substituted POSS monomers is considered the most rational approach to prepare to POSS-containing BCPs with ultrahigh MWs due to its high reactivity and excellent living nature.57 In this work, we explore the hierarchical self-assembly of rodlike “POSS−bottlebrush BCPs” (POSSBBCPs) containing

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RESULTS AND DISCUSSION Synthesis of POSSBBCPs through Sequential ROMPs. Two types of bulky monomers were employed in the sequential ROMP to synthesize rodlike POSSBBCPs. The monomer A (M A ) is 3-(12-(cis-5-norbornene-exo-2,3-dicarboximido)dodecanoylamino)propylheptaisobutyl POSS (NB-A16-POSS: MW = 1218 Da, where A16 indicates 16-atom-chain spacer), and the monomer B (MB) is exo-5-norbornene-2-carbonyl-end poly(benzyl methacrylate) (NBPBzMA: number-average MW (Mn) = 5440 Da, dispersity (Đ) = 1.02). While NB-A16-POSS was prepared by particular organic reactions, NBPBzMA was prepared by living anionic polymerization of benzyl methacrylate and subsequent end-caption using exo-5-norbornene-2B

DOI: 10.1021/acs.macromol.8b00298 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules carbonyl chloride. The heptaisobutyl POSS unit was decoupled from the norbornenyl group by long 16-atom-chain spacer to facilitate the crystallization of POSS pendants in the polymer. The block copolymerization of these two monomers generates poly[3-(12-(cis-5-norbornene-exo-2,3-dicarboximido)dodecanoylamino)propylheptaisobutyl POSS]-block-poly(exo5-norbornene-2-carbonylate-graf t-benzyl methacrylate), P(NBA16-POSS)-b-P(NB-g-BzMA). This POSSBBCP features a large asymmetry of two side-chain lengths. Prior to the block copolymerization, the homopolymerization behavior for NB-A16-POSS was initially examined to confirm its MW precision. The ROMPs of NB-A16-POSS ([MA]0 = 0.4 M) were carried out by a Grubbs third-generation catalyst, Ph−CHRu(Cl)2(H2IMes)(pyridine)2 (G3, I), in tetrahydrofuran (THF) at 25 °C to produce P(NB-A16-POSS) s. The molar feed ratio of monomer to initiator ([MA]0/[I]0) varied to 50, 100, 250, 500, and 1000. Size exclusion chromatography−multiangle laser light scattering (SECMALSS) measurement was conducted to characterize Mn and Đ values of the polymers at final monomer conversion (∼100%). All cases for ROMPs of NB-A16-POSS reached 100% monomer conversion. The resulting P(NB-A16-POSS)s had Mn values of 67, 124, 310, 626, and 1236 kDa in accordance with theoretical values (Mn,theo = 61, 122, 305, 609, and 1218 kDa, respectively) while having low Đ values within 1.02−1.20. This result indicated that the ROMP of NB-A16POSS is living in the [MA]0/[I]0 range of 50−1000. To prepare P(NB-A16-POSS)-b-P(NB-g-BzMA)s with a variety of block compositions and MWs, sequential ROMPs of NB-A16-POSS ([MA] = 0.4 M) and NBPBzMA ([MB] = 0.1 M) were carried out using G3 (I) in THF at 25 °C varying the weight ratio between two monomers (MA:MB = 33:67, 50:50, and 67:33 wt:wt) as well as the overall molar ratio of two monomers to initiator ([M]0/[I]0 = [MA]0/[I]0 + [MB]0/[I]0) (Scheme 1). Mn and Đ values of products at final conversions were determined by SEC-MALLS. The block copolymerization results are summarized in Table 1. The sequential ROMPs quantitatively yielded 12 P(NB-A16-POSS)-b-P(NB-g-BzMA) s, 34-1-4, 50-1-4 and 67-1-4, where the values of 34, 50, and 67 correspond to the three weight percentages of P(NB-A16POSS) block, fA = 34, 50, and 67 wt %, respectively. P(NB-A16-POSS)-b-P(NB-g-BzMA)s possessed a wide range of MWs (Mn = 805−1833 kDa) and reasonably narrow dispersities (Đ = 1.06−1.30). SEC differential refractive index (dRI) traces of the POSSBBCPs showed shift to higher MWs by the increase of [M]0/[I]0 (Figure 1). The SEC-dRI traces also showed existence of low- or high-MW byproducts. LowMW byproducts were contained in most of the polymers, and the proportions were larger particularly in fA = 34 wt %. On the other hand, the proportions of high-MW byproducts increased with the increase of fA. The low-MW byproducts were considered a result of intramolecular chain transfer, whereas the high-MW byproducts were considered one of intermolecular chain transfer of chains that were aggregated by larger amounts of crystalline parts. Most of the POSSBBCPs had MWs lower than theoretical ones despite the quantitative conversions. This indicated that intramolecular chain transfer was more active than intermolecular one. Overall DP values (= DPA + DPB) of P(NB-A16-POSS)-bP(NB-g-BzMA)s were plotted against [M]0/[I]0 values (Figure 2). Although most of the DP values were lower than [M]0/[I]0, these values were well in proportion to the [M]0/[I]0. As a result, three linear equations of [M]0/[I]0 with slopes of 0.755,

Figure 1. SEC-dRI traces of P(NB-A16-POSS)-b-P(NB-g-BzMA)s. Samples: (a) 34-1-4 (fA = 34 wt %), (b) 50-1-4 ( fA = 50 wt %), and (c) 67-1-4 ( fA = 67 wt %).

Figure 2. Plots of DP versus [M]0/[I]0 for P(NB-A16-POSS)-bP(NB-g-BzMA)s (34-1-4, 50-1-4, and 67-1-4: fA = 34, 50, and 67 wt %, respectively).

0.807, and 0.829 were established to formulate DP values of 341-4, 50-1-4, and 67-1-4, respectively. Thermal Properties of P(NB-A16-POSS)-b-P(NB-gBzMA)s. Thermal properties of NB-A16-POSS, P(NB-A16POSS), P(NB-g-BzMA), and P(NB-A16-POSS)-b-P(NB-gBzMA)s (34-4, 50-4, and 67-4: fA = 34, 50, and 67 wt %, respectively) were examined through differential scanning calorimetry (DSC) measurement on the second heating at a rate of 2 °C/min under a nitrogen atmosphere (Figure 3). NBA16-POSS exhibited an endothermic transition at 123 °C, which is the melting temperature (Tm) of crystalline POSS clusters. As the monomer was converted to ultrahigh MW and semicrystalline P(NB-A16-POSS), the Tm value shifted to 137 °C and the peak area was reduced due to low mobility of rigid main chains. The lack of glass transition temperature (Tg) for P(NB-A16-POSS) indicated that the coordinated molecular motion of polynorbornene main chains was highly suppressed by the crystalline POSS clusters. On the other hand, brush P(NB-g-BzMA) exhibited an apparent endothermic shift of heat flow at 67 °C, which is the Tg of amorphous PBzMA grafts. 34-4, 50-4, and 67-4 had thermal properties of both semicrystalline POSS clusters and amorphous PBzMA grafts. C

DOI: 10.1021/acs.macromol.8b00298 Macromolecules XXXX, XXX, XXX−XXX

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Figure 4. (a) Procedure to fabricate PC films using P(NB-A16POSS)-b-P(NB-g-BzMA)s (34-1-4, 50-1-4 and 67-1-4: fA = 34, 50, and 67 wt %, respectively): self-assembly through solvent evaporation from THF solutions at RT and post thermal annealing at 160 °C for 30 s. (b) Color photographs of thermally annealed PC films.

Figure 3. DSC thermograms of P(NB-A16-POSS), P(NB-g-BzMA), and P(NB-A16-POSS)-b-P(NB-g-BzMA)s (34-4, 50-4, and 67-4: fA = 34, 50, and 67 wt %, respectively) recorded on the second heating cycle at a heating rate of 2 °C/min under a nitrogen atmosphere.

Their Tg and Tm values were almost comparable to those of two homopolymers. Self-Assembly of POSSBBCPs To Form 1D PCs. To fabricate the PC films using P(NB-A16-POSS)-b-P(NB-gBzMA)s, the self-assembly of those polymers was performed on glass or silicon substrates through solvent evaporation from THF solutions at room temperature (RT). Then, the resultant films were annealed at 160 °C for 30 s (Figure 4a). Most of the films displayed distinct structural colors even before thermally annealed. However, the colors were not consistent at every experiment. When the post thermal annealing was applied to the films for complete main chain extension, the red-shift of original structural colors occurred immediately at 160 °C and was finished within 30 s. As a result, most of films possessed distinct photonic bandgaps in the range of visible wavelengths (Figure 4b). The order−disorder transition temperature (TODT) of each P(NB-A16-POSS)-b-P(NB-g-BzMA) was roughly predicted as the onset temperature at which the structural color of each PC film disappears. The TODT values for P(NB-A16-POSS)-bP(NB-g-BzMA)s were observed to be approximately 190 °C for 34-1-4, 200 °C for 50-1-4, and 210 °C for 67-1-4. These temperatures were above the Tm value of crystalline POSS clusters in P(NB-A16-POSS) blocks. Wide-angle X-ray scattering (WAXS) measurement proved that at the annealing temperature of 160 °C hierarchical self-assembly of P(NB-A16POSS)-b-P(NB-g-BzMA)s was maintained by amorphous POSS clusters (Figure 5). In detail, WAXS profiles of nonannealed PC films based on 34-4, 50-4, and 67-4 displayed three diffraction peaks at 2θ = 8.35°, 11.2°, and 18.9° corresponding to the rhombohedral arrangement of POSS pendants (Figure 5a).51−56 The microphase separation of the POSSBBCPs began at high concentrations above their saturation points in solutions and

increasingly entered the order state with further solvent evaporation. The crystallization of POSS pendants would occur immediately after the order transition, reinforcing the strong segregation until the solvent was completely removed. By annealing at 160 °C, the crystalline formation of POSS pendants collapsed, but amorphous clustering was alternatively maintained, which was confirmed by the disappearance of diffraction peaks at 2θ = 11.2° in WAXS profiles (Figure 5b). This result suggests that the post thermal annealing at a temperature between Tm and TODT facilitates the segmental motion of side chains in POSSBBCPs to extend the main chains while preserving the ordered formation of nanostructures. Meanwhile, a 1D PC film based on 34-4 displayed WAXS profiles with the relatively weak diffraction intensities compared to two PC films based on 50-4 and 67-4 (Figure 5). This was probably because the clustering of minor POSS pendants was interrupted by major PBzMA grafts. Accordingly, it was anticipated that the low fA might be unfavorable for the microphase separation and periodic array of microdomains. To identify morphologies of thermally annealed P(NB-A16POSS)-b-P(NB-g-BzMA)s, cross sections of the 1D PC films were prepared by fast fracture, stained with ruthenium tetroxide (RuO4), and imaged by scanning electron microscopy (SEM) (Figure 6a). All PC films displayed lamellar nanostructures corresponding to 1D PCs. The L0 values were within ranges of 138−290, 162−238, and 140−198 nm for fA = 34, 50, and 67 wt %, respectively, and those were well modulated by DP. The 1D PC films based on 50-1-4 and 67-1-4 (fA = 50 and 67 wt %, respectively) exhibited high morphological order compared to the PC films based on 34-1-4 ( fA = 34 wt %). Moreover, the order remained consistent in the full ranges of DP values. These results indicated that the organization of POSS pendants D

DOI: 10.1021/acs.macromol.8b00298 Macromolecules XXXX, XXX, XXX−XXX

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The L0 values for the thermally annealed P(NB-A16-POSS)b-P(NB-g-BzMA) lamellae were fitted with DP (Figure 6b). The resulting fits revealed that the L0 scaled almost linearly with DP within the given ranges, indicating that P(NB-A16POSS)-b-P(NB-g-BzMA) main chains well adopted the rodlike conformation. Noticeably, the scaling slope of L0 gradually declined with the increase of fA. As a result, the highest L0 also decreased with the increase of fA. It is important to note that the rod-like P(NB-A16-POSS)-b-(NB-g-BzMA) has a large asymmetry of two side chain lengths. Side chains of the P(NBA16-POSS) block are much shorter than those of the P(NB-gBzMA) block. Therefore, the most possible reason is the interdigitated and bilayer arrangements of P(NB-A16-POSS) and P(NB-g-BzMA) blocks, respectively (Figure 6c). In the case, the L0 value of P(NB-A16-POSS)-b-(NB-g-BzMA) lamellae can be determined by the following relationship: L0 = dA + dB = l0,A DPA α ,A + 2l0,B DPB α ,B

(1)

where dA and dB are the widths (d) of P(NB-A16-POSS) and P(NB-g-BzMA) domains, respectively, l0,A and l0,B are the statistical segment lengths (l0) of P(NB-A16-POSS) and P(NB-g-BzMA) blocks, respectively, and α,A and α,B are the scaling powers of P(NB-A16-POSS) and P(NB-g-BzMA) domains, respectively. As l0,A is expected to be lower than 2l0,B, the increase of fA reduces the overall scaling coefficient for L0. To prove the combination of interdigitated and bilayer arrangements, the width scaling of P(NB-A16-POSS) and P(NB-g-BzMA) domains was investigated. The cross sections of 1D PC films based on thermally annealed 50-1-4 ( fA = 50 wt %) were prepared by focused ion beam (FIB) and imaged by transmission electron microscopy (TEM) to measure the dA and dB. P(NB-A16-POSS) domains with high electron density scatter more amounts of incident electrons. Therefore, P(NBA16-POSS) domains appear dark in TEM micrographs. Ratios of dA to dB values for the thermally annealed 50-1-4 lamellae were determined to be 1.75−1.79 (Figure 4a). Accordingly, volume fractions of two layers in each period

Figure 5. WAXS profiles of 1D PC films based on P(NB-A16-POSS)b-P(NB-g-BzMA)s (34-4, 50-4, and 67-4: fA = 34, 50, and 67 wt %, respectively) (a) before and (b) after annealing at 160 °C.

played a leading role in the robustness of microphase separation.

Figure 6. (a) SEM micrographs of cross sections of 1D PC films based on P(NB-A16-POSS)-b-P(NB-g-BzMA)s (34-4, 50-4, and 67-4: fA = 34, 50, and 67 wt %, respectively) annealed at 160 °C. The cross sections were stained with RuO4. Scale bars represent 500 nm. (b) Plots of L0 versus DP for the lamellae. (c) Illustration displaying the chain arrangement of P(NB-A16-POSS)-b-P(NB-g-BzMA) in the lamellar self-assembly. E

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nm).58 On the other hand, the scaling coefficient for dB was 0.945 nm, which is 2 times larger than that for dA. This result proves that the P(NB-A16-POSS) and P(NB-g-BzMA) blocks formed the interdigitated monolayers and bilayers, respectively, in the lamellar nanostructures. Therefore, the l0,A and l0,B values could be determined to be 0.461 and 0.473 nm, respectively. The scaling rules for 50-1-4 were not correct for 34-1-4 and 67-1-4 which have broader dispersities. This is probably because larger amounts of low- or high-MW byproducts can more influence the width of each domain. For the provided P(NB-A16-POSS)-b-P(NB-g-BzMA)s, the 2D hexagonal columnar packing of interdigitated P(NB-A16POSS) blocks might be frustrated by much longer side chain length of P(NB-g-BzMA) blocks. This is reflected by the dominant volume percentage of P(NB-A16-POSS) layer ( fA = 64 vol %) in 50-1-4 lamellae with a symmetric weight fraction. This issue is expected to be solved by the effort to shorten the chain length of macromonomer in the stage of living anionic polymerization. This contribution will enhance the effect of POSS pendants on the morphological order. Light Refection Properties of 1D PCs and Formulation of Peak Reflectance Wavelength (λpeak) Scaling. The lightreflection properties of 1D PC films based on thermally annealed P(NB-A16-POSS)-b-(NB-g-BzMA)s were confirmed by reflectance spectra upon normal incidence of light. Peak reflectivity of 1D PC on the normal incidence is theoretically determined by refractive index ratio (nL/nH, nL < nH) and number of period (N): ⎡ ⎢1 − peak reflectivity = ⎢ ⎢1 + ⎢⎣

Figure 7. (a) TEM micrographs of cross sections of 1D PC films based on 50-1-4 (fA = 50 wt %) annealed at 160 °C. The crosssectional TEM samples were prepared by FIB. Scale bars represent 500 nm. Dark and bright regions represent P(NB-A16-POSS) and P(NBg-BzMA) domains, respectively. The L0 values are expressed as dA + dB. (b) Plots of dA or B versus DPA or B for the 50-1-4 lamellae.

2N

( ) ( ) nL nH nL nH

2N

⎤2 ⎥ ⎥ ⎥ ⎥⎦

(2)

According to this equation, the peak reflectivity is enhanced by increasing the number of period or the refractive index ratio. Most of the 1D PC films showed reflectance peaks without broad scattering backgrounds, indicating that P(NB-A16POSS)-b-P(NB-g-BzMA)s self-assembled to form lamellae without any unwanted irregular precipitation (Figure 8). The peak reflectivity tended to decline with the increase of λpeak. This result is natural because the increase of L0 reduced the number of period on a similar film thickness. The ranges of λpeak values for 34-1-4, 50-1-4, and 67-1-4 were observed to be 391−841, 451−670, and 395−562 nm, respectively. The dependence of light-reflection performances of P(NBA16-POSS)-b-(NB-g-BzMA)-based PC films on the block composition was confirmed by the bandwidths and the peak

(volA:volB) were calculated to be 64:36. Both domain widths was fitted to distinguished power-law functions with respect to DP (Figure 4b). In the case, both P(NB-A16-POSS) and P(NB-g-BzMA) domains exhibited large scaling powers close to 1 (0.900 and 0.911, respectively), proving that P(NB-A16POSS) and P(NB-g-BzMA) main chains adopted the rodlike conformation. Meanwhile, the scaling coefficients of P(NBA16-POSS) and P(NB-g-BzMA) domains were largely different. The scaling coefficient for dA was 0.461 nm, which is close to the statistical segment length of polynorbornene (0.46−0.51

Figure 8. Light-reflectance spectra upon normal incidence of light for 1D PC films based on P(NB-A16-POSS)-b-P(NB-g-BzMA)s annealed at 160 °C. P(NB-A16-POSS)-b-P(NB-g-BzMA): (a) 34-1-4 ( fA = 34 wt %), (b) 50-1-4 ( fA = 50 wt %), and (c) 67-1-4 ( fA = 67 wt %). F

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Figure 9. Light-reflection properties on normal incidence of light for 1D PC films based on P(NB-A16-POSS)-b-P(NB-g-BzMA)s (34-4, 50-4, and 67-4: fA = 34, 50, and 67 wt %, respectively) annealed at 160 °C: (a) plots of gap−midgap ratio versus λpeak, (b) plots of peak reflectivity versus λpeak, (c) plots of λpeak versus L0, and (d) plots of λpeak versus [M]0/[I]0.

67%, respectively. Given the resulting light-reflection properties including bandwidths, peak reflectivities, and λpeak ranges, it is possible to suggest that fA = 50 wt % allows the P(NB-A16POSS)-b-P(NB-g-BzMA)-based 1D PCs to fulfill the most excellent light reflection at the full range of visible wavelengths.

reflectivities of reflectance spectra (Figure 9a,b). The bandwidth for the reflectance peak was determined by a gap−midgap ratio as a full width of wavelength at halfmaximum divided by λpeak (Δλfwhm/λpeak × 100%). At fA = 50 and 67 wt %, the gap−midgap ratios of reflectance peaks reached low values (15.3−9.2%) (Figure 9a), and the peak reflectivities reached the high values (55−12%) (Figure 9b). On similar periodicities and numbers of periods, lower bandwidth and higher peak reflectivity indicate better layer ordering and narrower interfacial width. Both might be achieved through the microphase separation reinforced by the organization of POSS pendants. A λpeak for a 1D PC upon the normal incidence of light is generally approximated to 2neffL0 according to the Bragg−Snell law, where neff is the effective refractive index determined from the combination of the two refractive indices.35 The λpeak values for 1D PCs films based on thermally annealed P(NB-A16POSS)-b-P(NB-g-BzMA)s were well proportional to a wide range of L0 values exhibiting 2neff values ranging within 2.86− 2.82 (Figure 9c). The scaling analysis verified that [M]0/[I]0, DP, L0, and λpeak were closely correlated by a successive proportionality, λpeak ∝ L0 ∝ DP ∝ [M]0/[I]0. Accordingly, the λpeak could be directly formulated to a linear function of [M]0/[I]0, λpeak = β[M]0/[I]0, where β is the scaling coefficient dependent on the block composition (Figure 9d). The β values were determined to be 0.936, 0.709, and 0.507 nm for fA = 34, 50, and 67 wt %, respectively. The range of available λpeak became narrower with the increase of fA due to the interdigitated arrangement of the P(NB-A16-POSS) blocks. As a result, the highest λpeak was determined to be 841, 670, and 504 nm for fA = 34, 50, and

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CONCLUSIONS

We synthesized a series of rodlike POSSBBCPs containing crystalline POSS pendants and amorphous polymeric grafts through sequential ROMPs. The self-assembly of the POSSBBCPs produced 1D PCs composed of periodic lamellar arrays, in which POSS- and brush-based blocks adopted interdigitated and bilayer arrangements, respectively, due to large asymmetry of two side chain lengths. The organization of abundant POSS pendants assisted the strong microphase separation and high morphological order of lamellae in a wide range of chain lengths, thereby improving the lightreflection performance. The successive proportional correlation for the four scaling parameters, λpeak ∝ L0 ∝ DP ∝ [M]0/[I]0, was well achieved by the synergetic effect of (1) living nature of ROMP, (2) rodlike main chain conformation of the POSSBBCPs and (3) hierarchical self-assembly induced by the organization of POSS pendants. Therefore, linear functions of [M]0/[I]0 to formulate the λpeak of 1D PC were well established by the POSSBBCPs. This work presents an important insight that the self-assembly of POSSBBCPs can enable the access to PC-based color display devices with desired optical properties through the accurate prediction using the experimental scaling formula. G

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00298. Experimental details, NMR spectra of compounds, solubility parameters and refractive indices of octaisobutyl POSS and PBzMA, and thermogravimetric analysis (TGA) thermograms of NB-A16-POSS, P(NB-A16POSS), P(NB-g-BzMA), and P(NB-A16-POSS)-bP(NB-g-BzMA)s (34-4, 50-4, and 67-4) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel (+82)-62-715-2306 (J.-S.L.). ORCID

Chang-Geun Chae: 0000-0001-8805-6743 Robert H. Grubbs: 0000-0002-0057-7817 Jae-Suk Lee: 0000-0002-6611-2801 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Science, ICT and Future Planning (NRF-2015R1A2A1A01002493). This work was also supported by GIST Research Institute (GRI) grant funded by the GIST in 2018. We thank Ji-Hyun Lee, Dr. Wonjin Moon, and Dr. Youn-Joong Kim in Korea Basic Science Institute (KBSI) for supporting the preparation of FIB samples.

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