Photonic Crystals Fabricated by Block Copolymerization-Induced

Article pubs.acs.org/Macromolecules

Photonic Crystals Fabricated by Block Copolymerization-Induced Microphase Separation Ryuhei Motokawa,*,† Tatsuo Taniguchi,*,‡ Takayuki Kumada,† You Iida,§ Shota Aoyagi,‡ Yusuke Sasaki,‡ Michinari Kohri,‡ and Keiki Kishikawa‡ †

Materials Sciences Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan Division of Applied Chemistry and Biotechnology, Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan § Department of Physics, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan ‡

S Supporting Information *

ABSTRACT: We present a method for fabricating photonic crystals (PCs) by polymerization-induced microphase separation of block copolymers (BCPs). Molecular weight of BCP for PCs is so large that it has been difficult for conventional solution casting and annealing methods to complete the microphase separation to form periodically ordered submicron structures. Our method overcomes the difficulty by inducing the microphase separation and transitions during the polymerization, when the molecular weight of the BCPs is small enough for the microphase separation and transitions. The microphase-separated structure is then enlarged while maintaining the selfsimilarity. We succeeded in fabricating PCs with reflection wavelength λm ≈ 1000 nm and a full width at half-maximum Δλ = 0.05λm by living-radical bulk block copolymerization of poly(methyl methacrylate)-block-polystyrene.

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INTRODUCTION Photonic crystals (PCs) are materials containing a periodic structure with a length scale of hundreds of nanometers.1−3 PCs reflect visible light selectively in accordance with Bragg’s law of diffraction. Thus, they exhibit structural color under natural light without chromophores. The unique optical properties of PCs have attracted considerable attention for visual recognition sensors including test agents,4 fadeless energy-saving displays,5 and other optoelectric and optoelectronic devices such as surface-emitting semiconductor lasers,6 telecommunication devices,7 and thermophotovoltaic solar energy converters.8 Currently, PCs are fabricated by using semiconductor nanofabrication technology, such as electron-beam lithography and etching methods,9−13 and lamination techniques, such as assembling periodically ordered submicrometer colloids.14−23 However, these approaches are not suitable for mass production.24 Block copolymers (BCPs) are an alternative candidate for the mass production of PCs24 because the A and B block chains in AB BCPs spontaneously undergo microphase separation into periodically ordered A- and B-rich microdomains in accordance with statistical thermodynamics25 (see Supporting Information). In addition, a large variety of microdomain structures, such as lamellae, gyroids, cylinders, and spheres, can be formed by optimizing the composition of BCPs.26 Therefore, BCPs are fascinating materials for creating multidimensional PCs. Complete structural relaxation during the microphase separation on a practical time scale is crucial for fabricating © 2016 American Chemical Society

PCs from BCPs. Generally, the molecular weight of BCPs used for PCs is so large (M > 500 000)24,27−29 that the structural relaxation is extremely slow due to extensive chain entanglement. Yoon et al. fabricated PCs with a reflection wavelength, λm, of 470 nm and a full width at half-maximum, Δλ/λm, of 0.5 by solution casting polyolefin BCPs.30 Hustad et al. annealed bulk BCPs composed of linear low-density and ultralow-density polyethylene block chains to obtain PCs with λm = 430 nm and Δλ/λm ≈ 0.4.31 Moreover, Urbas et al. obtained PCs with λm = 580 nm and Δλ/λm ≈ 0.3 by swelling poly(isoprene-blockstyrene) microdomains with styrene and isoprene homopolymers.27 However, according to the reptation model,32 the disentanglement time for linear polymer chains increases in proportion to the cube of the chain length of the polymers. Thus, it is difficult to form PCs with larger λm and smaller Δλ/λm. This problem has been overcome by altering the polymer architecture. Sveinbjörnsson et al. exploited the small chain entanglement of brush BCPs, on which polymers with a small chain length dispersion were densely grafted, to fabricate PCs with λm up to 1300 nm and Δλ/λm ≈ 0.3.33 Macfarlane et al. swelled the brush BCPs with homopolymers to obtain PCs with λm = 1400 nm and Δλ/λm ≈ 0.2.34 Kang et al. used BCP gels that were precisely prepared by introducing cross-linkages into one of the two block chains in the BCP lamellar microdomains to avoid losing the Received: June 3, 2016 Revised: July 20, 2016 Published: August 4, 2016 6041

DOI: 10.1021/acs.macromol.6b01190 Macromolecules 2016, 49, 6041−6049

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Figure 1. Fabrication of PCs by bulk block copolymerization-induced microphase separation and transitions. As the polymerization degree of B block chains in AB BCPs increases, microphase separation and transitions are spontaneously induced. The AB BCPs form PCs when the interdomain distance of the microdomains becomes comparable to visible wavelengths. The interdomain distance increases until monomer B is consumed.

periodicity during swelling, and they obtained a PC with λm = 1600 nm and Δλ/λm ≈ 0.1.35 Here, we propose a new method of block copolymerizationinduced microphase separation for fabricating PCs with linear BCPs. Figure 1 shows a schematic of the concept. AB BCPs are formed by extending B block chains from a radically activated terminus of the A block chains through living-radical polymerization in B monomer solution. The AB BCPs in solution (Figures 1a,b) form periodically ordered A- and B-rich microdomains (Figure 1c), when the degree of polymerization of the AB BCP exceeds the critical conditions for microphase separation.25 As the B block chains are extended further, the spacing between A-rich microdomains increases owing to the increase in the volume fraction of the B-rich microdomain, accompanying microphase transitions (Figures 1c−e). Accordingly, the interdomain distance keeps increasing to optical wavelengths (Figures 1e−g), while maintaining the periodicity. This technique overcomes the problem of the structural relaxation by inducing the microphase separation and transitions when the molecular weight of the BCPs is small enough for relaxation to occur quickly. In this study, we demonstrate the advantage of this method by fabricating PCs of poly(methyl methacrylate) (PMMA)-blockpolystyrene (PS). In-situ and time-resolved proton nuclear magnetic resonance (1H NMR), optical reflection spectrum, and small-angle neutron scattering (SANS) measurements were performed to elucidate the relationship among the polymerization, the polymerization-induced microphase separation and transitions, and the color development of the BCPs.

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kindly provided by Nippon Steel Chemical (Japan) and was distilled under reduced pressure. Styrene-d8 (Sigma-Aldrich, USA) was purified with an activated alumina column to remove the inhibitor and then bubbled with dry nitrogen for more than 15 min. Chloroform, methanol, and dimethyl sulfoxide-d6 (Wako Pure Chemical) were used as received. Polymerization and in-Situ Measurements. The PMMA-blockPS was synthesized by RAFT living-radical bulk polymerization of styrene monomers from one terminus of PMMA-RAFT.38,39 PMMARAFT dissolved in styrene at a ratio in weight of approximately 1:7 was loaded into the cells for each in-situ measurement and heated to start the polymerization at 130 °C, which is above the glass transition temperatures (Tgs) for both PMMA and PS, to allow the BPCs to move and undergo microphase separation and transitions (Figure 1). In the NMR measurements, an aliquot of the reaction solution, consisting of PMMA-RAFT (0.20 g) dissolved in a mixture of styrene-h8 (0.10 g) and styrene-d8 (1.34 g), was loaded into an NMR tube with an external diameter of 3 mm under nitrogen. The solution in the tube was inserted into a 5 mm diameter tube containing dimethyl sulfoxide-d6 for the deuterium frequency field lock, set to a 500 MHz NMR spectrometer (JNM-ECA-500, JEOL, Japan), and then heated. The time course of the intensities of the two α-proton peaks of styrene-h8 (4.95 and 5.43 ppm) were measured to obtain the styrene monomer conversion, CM. In the optical reflection spectrum measurements, PMMA-RAFT (0.025 g) in styrene-h8 (0.18 g) was loaded into a quartz cell with inside dimensions of 55 mm long, 10 mm wide, and 0.5 mm thick and then heated in a brass heating block with 5 mm diameter apertures (see Figure S1 in Supporting Information). The normal incidence optical reflection spectrum was measured by using a reflectance spectrometer (LVmicro/SUV-100s, Lambda Vision, Japan) in the wavelength region of 400−1000 nm. The reflection spectrum of the quartz cell was subtracted from each spectrum. In the SANS measurements, PMMA-RAFT (0.18 g) in styrene-d8 (1.36 g) was loaded into a quartz cell with inside dimensions of 45 mm long, 22 mm wide, and 2 mm thick and then heated in a vertically mounted brass heating block with 18 mm diameter apertures. The SANS measurements were performed with the SANS-J diffractometer at research reactor JRR-3 at Japan Atomic Energy Agency.40 Collimated incident neutrons with a center wavelength, λN, of 0.65 nm and a distribution, ΔλN/λN, of 0.13 were scattered in the reaction solution. The scattered neutrons were detected with a position-sensitive 3He detector at sample-to-detector distances of 10 and 2.2 m to obtain the SANS intensity distribution, I(q), as a function of the magnitude of the scattering vector, q, given by a scattering angle, 2θN, q = (4π/λN) sin θN. These two distances covered the q ranges of 0.03−0.25 and 0.14−0.8 nm−1, respectively. Additionally, I(q) in the q range of 0.005−0.05 nm−1

EXPERIMENTAL SECTION

Materials. Methyl methacrylate (MMA) was purchased from a commercial source (Tokyo Kasei, Japan), dried overnight over calcium chloride, and distilled under reduced pressure. The initiator, 2,2azobis(isobutyronitrile) (AIBN) (Wako Pure Chemical, Japan), was purified by recrystallization from methanol. Cumyl dithiobenzoate (CDB) was synthesized according to the literature.36 Benzene (Wako Pure Chemical) was purified by distillation prior to use as a solvent. PMMA with one dithiobenzoate terminus (PMMA-RAFT) was obtained by reversible addition−fragmentation chain transfer (RAFT) polymerization37 of the MMA with AIBN and CDB in benzene by using the method described in the Supporting Information. Styrene-h8 was 6042


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Macromolecules was measured by using a set of neutron lenses and a position-sensitive photomultiplier.40 In gel permeation chromatography (GPC), aliquots of the reaction solution for the reflection spectrum measurements were measured with a GPC system (Eco-SEC 8320, TOSOH, Japan) after polymerization time, tp, of 0, 60, 150, and 360 min. All reaction solutions dissolved in chloroform eluent were passed through two TSK gel Super Multipore HZ-H columns, a TSK gel Super Multipore HZ-M column, and a TSK gel Super Multipore HZ-N column (TOSOH) at a flow rate of 0.2 mL/ min and 40 °C and then monitored with a refractive index detector. PMMA (Cat. No. F8604075, Showa Denko, Japan) and PS (Cat. No. 0021914, TOSOH) standards in chloroform were used to determine the molecular weight of the PMMA-RAFT at tp = 0 min and the reaction products of the PMMA-block-PS at tp = 60, 150, and 360 min, respectively.

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RESULTS AND DISCUSSION Polymer Synthesis and Characterization. Figure 2a shows GPC charts of the reaction products. The GPC chart at tp = 0 min is from PMMA-RAFT and at tp ≥ 60 min are from polymerized PMMA-block-PS. As the polymerization proceeded, the peak gradually broadened and moved toward a shorter retention time. Figure 2b shows the time course of the weightaveraged molecular weight, Mw, and its distribution, Mw/Mn, determined from the GPC charts. Mw increased from 169 000, which was the value of PMMA-RAFT, Mw,PMMA, at tp = 0 min to an asymptotic value of 869 000 at tp = 360 min. This result indicates the molecular weight ratio of the PS to PMMA block chains, Mw,PS/Mw,PMMA, was 4.1 in the final BCP products. The distribution Mw/Mn increases from 1.12 in PMMA-RAFT at tp = 0 min to 1.5 in BCPs at tp ≥ 60 min. Figure 2c shows CM of the styrene monomer in the reaction solution obtained by 1H NMR measurements. CM increased with tp and asymptotically reached 0.9. Comparing the Mw,PS/Mw,PMMA and CM values with the feed weight ratio, more than 20% of the styrene homopolymer was found to be generated as a by-product. This fraction is rather a lot as compared with that produced during the bulk RAFT polymerization of PMMA-block-PS (Mw ∼ 60 000) of less than 5%.38 Moreover, Mw/Mn = 1.5 of our BCP is remarkably larger than the typical value of living RAFT polymerization of Mw/Mn = 1.04−1.20.37,41 We consider that such remarkably large fraction of the by-product and Mw/Mn arose from the disadvantageous condition for precision polymerization as follows: the number density of RAFT agent at the chain end of PMMA-block-PS in our reaction solution was made much smaller than that in ref 38 in order to synthesize BCPs with very large molecular weight for PCs, and our polymerization temperature of 130 °C was set higher than the typical temperature of 100−110 °C37,41 for bulk RAFT polymerization of styrene. In addition, we speculate that the spatially inhomogeneous distribution of the styrene monomer and the radically activated chain end of the microphase-separated BCPs in the reaction solution would also enlarge Mw/Mn.42,43 Optical Reflection Spectrum Measurements. Figure 3 shows photographs of the reaction solution during the in-situ optical reflection spectrum measurements. The reaction solution was colorless at tp ≤ 30 min but turned bright blue around tp = 60 min. Subsequently, the solution turned bright green and then reddish (see Figure S2 in Supporting Information). Figure 4 shows the reflection spectrum during the polymerization. In agreement with the visual observations in Figure 3, a sharp peak appeared abruptly at λm = 450 nm around tp = 45 min, and λm increased continuously with tp to 1000 nm, whereas Δλ/λm

Figure 2. (a) GPC chromatograms of the reaction solution during the polymerization: tp = 0 min (black), 60 min (red), 150 min (green), and 360 min (blue). (b) Mw (circles) and Mw/Mn (squares) determined by the GPC measurements as a function of tp. The open symbols at tp = 0 min are the values of PMMA-RAFT, and filled ones at tp ≥ 60 min are of PMMA-block-PS. (c) CM (triangles) determined by the 1H NMR measurements.

decreased from 0.1 at tp = 45 min to 0.05 at tp ≥ 75 min. The reflectivity outside the peak was less than one-tenth of that at the peak. As shown in the inset, a subpeak was also observed at λm/2. This result suggests that the color of the reaction solution arose from structural coloration whose peaks in the normal incidence reflection spectrum appear at

λ = 2nD/j

(1) 44

according to Bragg’s law. Here, n is the refractive index, D is the largest interplanar spacing for crystallographic planes that lead to the constructive interference, and the integers j of 1 and 2 correspond to the main peak and subpeak at λ = λm and λm/2, respectively. SANS Measurements. Figure 5 shows the SANS profiles during the polymerization. The profile at tp = 0 min was attributed to the PMMA-RAFT dissolved in styrene-d 8 monomer. A single broad peak (thick arrow) appeared at tp = 30 min and grew up abruptly to form a sharp peak at tp = 60 min. As tp increased to tp = 240 min, the peak position, qm, gradually shifted toward a lower q and then remained the same at tp from 240 to 300 min. The second peak (dashed arrow) was also observed at tp = 60 and 70 min. The scattering intensity at q ≤ 0.01 nm−1 varied in accordance with power law scattering, I(q) ∼ 6043


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Figure 5. Double-logarithmic plots of the SANS profiles of the reaction solution during the polymerization. The solid and dashed arrows indicate the first and second peaks, respectively. The gray solid curves are the best-fit theoretical profiles using the RPA and paracrystalline models. RPA, L, C, and S stand for the models used for the fit. The instrumental resolution resulting from ΔλN/λN, spatial resolution of the position-sensitive detectors, and instrumental geometry was convoluted. The slope of the black solid line shows I(q) ∼ q−4 (Porod law). Figure 3. Photographs of the reaction solution during the optical reflection spectrum measurements.

random phase approximation (RPA) theory for disordered homopolymers in concentrated solution45 I(q) = v(ρPMMA − ρDS )2 ⎡ ⎤−1 1 1 ×⎢ + − 2χ ⎥ ⎢⎣ ϕPMMA NPMMAgD(x) ⎥⎦ 1 − ϕPMMA (2)

with gD(x) =

2 [x − 1 + exp(−x)] x2

(3)

and q2b2NPMMA (4) 6 Here, ρPMMA and ρDS are the scattering length densities of PMMA and styrene-d8, respectively. v is a reference volume defined using the volume of MMA, vMMA, and styrene-d8, vDSt, as (vMMAvDSt)1/2 = 0.165 nm3. ϕPMMA is the volume fraction of PMMA (0.10). NPMMA is the degree of polymerization of PMMA-RAFT, determined as 1680 from the GPC measurement. χ is the segmental interaction parameter between PMMA segment and styrene-d8 (0.028).46 b is the segment length of PMMA (0.68 nm).47 The solid curve on the SANS profile at tp = 0 min in Figure 5 is obtained by substituting these values into eqs 2−4. The simulated curve reproduces the SANS profile, indicating that PMMA-RAFT disperses homogeneously in styrene-d8. I(q) at tp = 30 min was simulated by using the RPA theory for a ternary mixture48−50 including BCP, styrene-d8, and the byproduct of the deuterated styrene homopolymer (HP) x=

Figure 4. Optical reflection spectra of the reaction solution during the polymerization. The inset shows the spectra magnified in the wavelength region of 400−600 nm at tp ≥ 195 min.

q−α, where the exponent, α, was approximately 2 at tp = 60 min and decreased with increasing tp. However, α remained around 4 at q > 0.1 nm−1 between tp = 60 and 300 min. Similarly to the mechanism of structural coloration, the sharp peaks in the SANS profiles arise from Bragg diffraction peaks of periodically ordered microdomains. We will elucidate the BCP microdomain structure by analyzing the SANS profiles at each tp and then discuss the structural coloration. Analysis of SANS Profiles with RPA Theory. The SANS intensity distribution at tp = 0 min was simulated by using 6044


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oriented microdomain in each grain over the polar (θ), azimuthal (ϕ), and rotational (ψ) angles

I(q) = v(ρPMMA − ρDS )2 ⎡S ⎤ (q) + SDPS ‐ DPS(q) + 2SPMMA ‐ DPS(q) × ⎢ PMMA ‐ PMMA − 2χ ⎥ 2 ⎣ SPMMA ‐ PMMA(q)SDPS ‐ DPS(q) − SPMMA ‐ DPS(q) ⎦

−1

I(q) =

(5)

with the Fourier transforms of the density−density correlation functions for PMMA and the deuterated polystyrene block chain (DPS) SPMMA ‐ PMMA(q) = ϕBCPNBCPgB(1 − f , NBCP)

+ ⟨fK (q)⟩2 ZK (q)}

gB(f , Ni) =

1 ϕ NBCP[gB(1, NBCP) − gB(f , NBCP) 2 BCP (8)

2 [fy − 1 + exp( −fy)] y2

fL̃ (q) =

(9)

fC̃ (q) =

and 2 2

y=

q b Ni 6

(i ∈ BCP, HP)

fS̃ (q) =

(10)

where ϕBCP and ϕHP are the volume fractions, NBCP and NHP are the degrees of polymerization of BCP and HP, respectively, and f = 1 − NPMMA/NBCP. The segment length of b of 0.68 nm was communized among PMMA, DPS, and styrene-d8,47,51,52 and the same ρDS value was used for DPS and styrene-d8 for simplicity. The SANS profile was reproduced by substituting the fitting parameters in Table 1 into eqs 5−10, where NBCP, NHP, and ϕBCP were referred to these estimated from Mw and CM around tp = 30 min and ϕHP to a previously reported value.38 The χ value of 0.008 was much smaller than the literature values of 0.028− 0.055.47,53−55 However, considering the sensitive trend of χ on degree of polymerization,56,57 which decreases from 0.055 to 0.028 as NBCP increases from 130 to 330,47,53−55 the χ value in our BCP with NBCP = 4000 is in line with the literature values. This result indicates that the BCPs were still dissolved in the styrene-d8 solvent homogeneously. Styrene-d8 is a good solvent for both PMMA and PS block chains.

NHP

ϕBCP

ϕHP

χ

4000

3000

0.21

0.04

0.008

I (̃ q) sin θ dθ dϕ dψ

(11)

(K ∈ L, C, S)

(12)

sin(qRL /2) qRL /2

(13)

2J1(qR C/2) qR C/2

(14)

3[sin(qR S/2) − qR S cos(qR S/2)] (qR S/2)3

(15)

with the thickness of the discoid, RL, the diameter of the cylindrical, RC, and the diameter of spherical, RS, microdomains. Angular brackets ⟨...⟩ denote an average with respect to the length scale and orientation of microdomains. ⟨f K(q)⟩ and ⟨f K2(q)⟩ are related to ⟨fK̃ (q)⟩ and ⟨fK̃ 2(q)⟩ ⟨fK (q)⟩2 = AK ⟨fK̃ (q)⟩2 q−LK

(16)

2 ⟨fK 2 (q)⟩ = AK ⟨fK̃ (q)⟩q−LK

(17)

where AK is equal to 1/4π, 1/2π, and 1, and the Lorentz factor, LK, is 2, 1, and 0 for L, C, and S, respectively.63,64 ZK(q) is the orientational average of Z̃ K(q)59 ZK (q) =

1 8π 2

2π

2π

∫0 ∫0 ∫0

π

ZK̃ (q) sin θ dθ dϕ dψ (18)

Here, Z̃ L(q) is given by

Table 1. Summary of Characteristic Parameters Determined by RPA Theory for a Ternary System at tp = 30 min NBCP

π

with the number density, nd, and volume of the microdomains, V. Subscript K indicates lamellar (L), hexagonally packed cylindrical (HPC; C), and body-centered cubic (BCC) spherical (S) microdomains. f K(q) is orientational average of fK̃ (q), which is given by59,61,62

(7)

− gB(1 − f , NBCP)]

2π

I(q) = ndV 2(ρPMMA − ρDPS )2 {⟨fK 2 (q)⟩ − ⟨fK (q)⟩2

SDPS ‐ DPS(q) = ϕBCPNBCPgB(f , NBCP) + ϕHPNHPgB(1, NHP)

SPMMA ‐ DPS(q) =

2π

∫0 ∫0 ∫0

which is given by the form factor amplitude, f K(q), and the paracrystal lattice factor, ZK(q)60

(6)

+ (1 − ϕBCP − ϕHP)

1 8π 2

Z̃ L(q) =

61

1 − |PL(q)|2 1 − 2|PL(q)| cos(Dq) + |PL(q)|2

(19)

with ⎡ (gDq)2 ⎤ ⎥ PL(q) = exp( −Dq) exp⎢ − 2 ⎦ ⎣

Analysis of SANS Profiles with Paracrystal Theory. The RPA theory cannot reproduce the SANS profiles with the sharp peaks at tp ≥ 45 min. Therefore, we analyzed the profiles on the basis of paracrystal theory58,59 on the assumption that the periodically ordered microphase-separated structure is formed in grain with random orientations (see Figure S3 in Supporting Information). In this model, I(q) is given by the orientational average of the intensity distribution, I(̃ q), from a perfectly

(20)

58

g is Hosemann’s g-factor, i.e., standard deviation of D divided by D. Z̃ C(q) is given by62 ̃ (q)ZC,2 ̃ (q) ZC̃ (q) = ZC,1

(21)

with

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Table 2. Summary of Structural Parameters of Lamellar, Cylindrical, and Spherical Microdomains and Their Packing States Determined by Paracrystal Theory from the SANS Profiles at tp ≥ 60 min tp (min)

morphology

D (nm)

g

60 70 80 120 240 300

lamellar cylindrical cylindrical spherical spherical spherical

120 140 160 250 350 350

0.12 0.11 0.12 0.13 0.13 0.13

̃ (q) = ZC,1

aC (nm)

aS (nm)

(

σC (nm)

52 54

5 6

π 6

)⎤⎦ + exp(−g 2aC2q2PC)

1 − exp( −g 2aC 2q2PC) 1 1 − 2 exp⎡⎣ − 2 (−g 2aC 2q2PC)⎤⎦ cos(aCq sin ψ ) + exp( −g 2aC 2q2PC)

RS (nm)

σS (nm)

62 61 61

15 15 15

(22)

(23)

were convoluted in the simulation. Note that D is uniquely determined irrespective of the morphology used in the fitting, and related to qm as follows: (24)

qm ≈ 2π/D

where aC is the distance between neighboring cylindrical microdomains. D = √3aC/2 is the distance between (100) planes of the HPC. We use the BCC model for Z̃ S(q) because BCC spherical microdomains are generally formed in the microphase transition from HPC microdomains.65,66 Z̃ S(q) is given by67−69 ⎡

RC (nm)

350 490 490

⎛ π⎞ PC = cos2⎜ψ − ⎟ + sin 2 ψ ⎝ 6⎠

⎤ ⎥ 1 − 2|PS(q)|cos(ad⃗ ·q ⃗) + |PS(q)| ⎦ d=1 ⎣ 3

6

160 190

and

∏⎢

σL (nm)

38

1 − exp( −g 2aC 2q2PC) 1 1 − 2 exp⎡⎣ − 2 ( −g 2aC 2q2PC)⎤⎦ cos⎡⎣aCq cos ψ −

̃ (q) = ZC,2

Z̃S(q) =

RL (nm)

Although the BCC microdomain structure was tentatively used for the fitting at tp ≥ 120 min, almost the same fitting curve is obtained even with other crystalline structures formed by spherical microdomain. SANS profiles at tp ≥ 60 min were reproduced by the models, except at q < 0.02 nm−1 and tp ≥ 120 min. The decrease in exponent α of the profiles at q < 0.02 nm−1 with increasing tp was attributed to the sequential microphase transition of the PMMA microdomains from lamellar, cylindrical, to spherical structures whose scattering profiles show the power law with α of 2, 1, and 0 for qRK ≪ 1, respectively. In contrast, the power law scattering with α ≈ 4 at q > 0.2 nm−1 followed Porod law,59,63,70,71 which is common to these morphologies for qRK ≫ 1. The second peak position of q = 2qm and √3qm at tp = 60 and 70 min are characteristic of the scattering profiles of the lamellar and cylindrical microdomains, respectively.25 The change of the morphology with tp (microphase transition) is supported by the theory of microdomain structure of BCPs,25 where microphase transitions from lamellar to cylindrical and spherical microdomains occur sequentially, as the B block chains become longer than the A block chains in the AB BCPs. Although Mw was much smaller than that of ours, atomic force microscopy and smallangle X-ray scattering measurements have confirmed the formation of ordered spherical microdomain structure of PMMA-block-PS with Mw,PS/Mw,PMMA ≈ 4 that was close to ours at tp ≥ 120 min.72 The deviation of the SANS profiles from the spherical model at q < 0.02 nm−1 and tp = 120 min could have resulted from cylindrical microdomains remaining in the spherical ones. Consistent with the theory of the microdomain structure of BCPs,25 RL, RC, and RS of the PMMA microdomains were several times larger than the radius of gyration of PMMA of approximately 11 nm. The relation RL < RC < RS was attributed to the decrease in the radius of curvature of the PMMA microdomain interface from lamellar, to cylindrical, to spherical

1 − |PS(q)|2

2

(25)

with 1 PS(q) = exp − g 2[(a1⃗ ·q ⃗)2 + (a 2⃗ ·q ⃗)2 + (a3⃗ ·q ⃗)2 ] 2

{

} (26)

a1⃗ , a2⃗ , and a⃗3 are the crystalline lattice unit cell vectors of the principal axes of the BCC lattice, defined as a1⃗ ·q ⃗ =

1 aSq(sin θ cos ϕ + sin θ sin ϕ + cos θ) 2

(27)

a 2⃗ ·q ⃗ =

1 aSq( −sin θ cos ϕ − sin θ sin ϕ + cos θ) 2

(28)

a3⃗ ·q ⃗ =

1 aSq( −sin θ cos ϕ + sin θ sin ϕ − cos θ) 2

(29)

(30)

where aS is the unit lattice constant. D = aS/√2 is the distance between (110) planes of the BCC lattice. In this model, ZK(q) does not include the term that contributes to the scattering from the grains, namely, zero-order scattering,58 and HP is dissolved in the PS matrix of the microdomains for simplicity. The solid curves on the SANS profiles at tp ≥ 60 min in Figure 5 show the simulated profiles with the morphology and parameters in Table 2. σL, σC, and σS, which are the standard deviation of the Gaussian distribution function of RL, RC, and RS, 6046


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interference, the intensity profile, Iref(λ), of the reflection spectrum is given by75

microdomains. At tp = 60 min, the volume fraction of lamellar PMMA microdomains, which is given by RL/D, was close to Mw,PMMA/(Mw,PMMA + Mw,PS) ≈ 1/3 determined from the GPC result at the timing. However, the fraction of the spherical microdomains (RS/D)3 at tp ≥ 120 min is much smaller than Mw,PMMA/(Mw,PMMA + Mw,PS) ≈ 1/5. In AB BCPs with a large mismatch in length, chemical potential drives the BCP chain away from the microdomain interface and swells the domain preferred by the longer blocks.31 This result suggests that a large amount of the BCP chains would be swollen in the PS matrix rather than chemical junction point of BCPs are fixed at the interface between PMMA and PS phases. Structural Coloration Caused by Microphase Separation. Figure 6 compares D determined by the analysis of the

Iref (λ) ∝

sin 2(2πnND/λ) sin 2(2πnD/λ)

(31)

The reflection spectrum with Δλ/λm = 0.05 at tp ≥ 75 min in Figure 4 is reproduced by eq 31 with N = 16, indicating that the structural colors were produced by the constructive interference of the reflected light from at least 16 layers of the microdomain interfaces which correspond to the depth of 5 μm or more. On the other hand, the SANS profiles were reproduced by the model that did not take the zero-order scattering into account, and the optical reflectivity outside the peaks (white-light reflection) was much weaken than that at the main peak. These results indicate that the scatterings from the grain boundaries are much weaker than the Bragg scattering from the periodically ordered microdomains. As shown in Figure S4 in Supporting Information, positions and widths of the main and subpeaks and the small reflectivity outside the peaks were kept unchanged by cooling to room temperature with exposure to air. This result indicates that the microdomain structure was maintained even after the cooling. Neither the change of exterior view nor deformation was observed. Since Tg of both PMMA and PS are much higher than room temperature, the structure should be fixed in the rigid and stable grassy BCPs.

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CONCLUSION We overcame the problem of strong chain entanglement in large molecular weight BCPs for fabricating PCs by the polymerization-induced microphase separation method. We demonstrated the advantages of this method by fabricating PCs with λm ≈ 1000 nm and Δλ/λ m = 0.05 by living-radical bulk polymerization of PMMA-block-PS. In-situ and time-resolved 1 H NMR, optical reflection spectrum, and SANS measurements confirmed the followings: (i) the microphase separation of BCPs and structural coloration occurred early in the polymerization when the molecular weight of BCPs was small enough for structural relaxation, and (ii) the structural color changed continuously as the interdomain distance increased until the polymerization was completed. As described above, this method is superior to conventional solution casting and annealing methods in the point of fabricating PCs of BCPs with higher λm and smaller Δλ/λm unless specially designed polymers are used. Therefore, we believe that our method makes substantial progress in mass production of PCs. In addition, the method opens the possibility that multidimensional PCs with a large variety of the microdomain structures could be developed. We are planning to fabricate such PCs having specific optical characteristics by optimizing the feed composition and conditions in polymerization in the future.

Figure 6. Interdomain distance D determined from the SANS profiles (open squares) and that obtained by substituting λm in the optical reflection spectra into eq 1 (filled circles).

SANS profiles with that by substituting λm of the optical reflection spectrum into eq 1. Here, n = 1.54 was used as a weightaverage of the refractive index of PMMA (1.46)73 and PS (1.55)74 at 130 °C according to the feed composition of PMMA and styrene-d8 in the reaction solution. The D values determined from the SANS and optical reflection spectrum measurements at tp = 300 min agreed within 8%. This agreement is a strong evidence of structural coloration. The abrupt color development in Figure 3 and the appearance of a reflection peak around tp = 45 min in Figure 4 show that the structural color developed as a result of the polymerization-induced microphase separation. The change of color and the increase of λm with tp were caused by the increase in D until the polymerization reaction was complete around tp = 250 min. The difference in the rate of increase of the D value could be attributed to the difference in the polymerization rate, which was caused by small difference in temperature within the setting error in different dimensions of the quartz cells and heating blocks in the SANS and optical reflection spectrum measurements. A shoulder in the optical reflection spectrum was observed at the higher wavelength side of the peak at 75 min ≤ tp ≤ 135 min, but it became smaller at higher tp. The shoulder may have been caused by the coexistence of different morphologies. Δλ/λm is related to the number of the crystallographic layers that the optical right reflects. When normally reflected light from periodically ordered N-fold flat layers undergoes coherent

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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.6b01190. Synthesis of PMMA-RAFT, detailed descriptions of polymerization-induced microphase separation of BCPs and Lorentz factor in analysis of SANS profiles, and supplementary figures (Figures S1−S4) (PDF) 6047


Article

Macromolecules

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (R.M.). *E-mail: [email protected] (T.T.). Present Address

Y.I.: Base Technology Center, Toagosei Co., Ltd., 8 Showa-cho, Minato-ku, Nagoya 455-0026, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge Dr. Daisuke Yamaguchi of JAEA for enlightening discussions.

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