Tunable Photonic Crystals: Control of the Domain Spacings in

Oct 7, 2014 - The domain spacing was varied in this manner over a wide range. ... Kyunginn Kim , Sungmin Park , Yeongsik Kim , Joona Bang , Cheolmin ...
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Tunable Photonic Crystals: Control of the Domain Spacings in Lamellar-Forming Diblock Copolymers by Swelling with Immiscible Selective Solvents and a Neutral Solvent Akifumi Matsushita and Shigeru Okamoto* Department of Materials Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan ABSTRACT: The phase-separated morphology of three different molecular weights of polystyrene-block-polyisoprene (PS-b-PI) swollen with mixed solvents was studied by small-angle X-ray scattering (SAXS) and UV−vis spectroscopy. The solvent mixtures consisted of dimethyl phthalate (DMP) and ntetradecane (C14), selective solvents for PS and PI, respectively, and a neutral solvent, di-n-octyl phthalate (DOP). DMP and C14 are immiscible and hence selectively sequestered in the corresponding phases. SAXS measurements confirmed that a lamellar morphology was observed in most cases and that the domain spacing depended on the polymer molar mass, the concentration in solution, and the composition of the mixed solvent. The incompatibility of the PS and PI phases was increased by addition of DMP and C14 and decreased by addition of the neutral solvent DOP. The domain spacing was varied in this manner over a wide range. The diblock copolymer PS-b-PI with the largest molecular weight showed reflection peaks at wavelengths from 345 to 793 nm. The results are supported by calculations of the structure of the block copolymers in the presence of the solvents on the basis of the self-consistent field theory.

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INTRODUCTION Block copolymers (BCPs) are fascinating materials because of their propensity to self-assemble into periodic structures on the order of tens of nanometers. These structures have been investigated for a large number of potential applications such as solar cells, lithography, membrane filters, and photonic crystals.1−3 The morphology and the dimensions of the assembly are determined by the volume fractions of the blocks, the segregation power of the interactions (measured by the Flory−Huggins interaction parameter (χ)), the molecular weight, the composition, and the architecture of the constituent chains. While BCPs may be prepared having complex architectures, the simplest arrangement is for two linear polymer chains to be covalently attached at an end of each block. Despite such a simple architecture, the phase behavior of such diblock copolymers is rich, with structures such as lamellae, cylinders, spheres, gyroid structures, etc., being accessible. The phase diagram of diblock copolymers is theoretically and experimentally well-known.4,5 The work described in this paper is aimed at controlling the dimensions or repeat distances in lamella-forming diblock copolymers, for potential application of these materials as photonic crystals. Photonic crystals which manipulate visible light (ca. 380−780 nm) have been extensively studied for application as photofilters, superprisms, and optical resonators, but most of them do not meet the level of practical demand.6−11 In particular, BCPs are expected to play an important role in this development as they form nanostructures by a process of self-assembly. In addition, they are prepared © XXXX American Chemical Society

from inexpensive materials compared to other approaches to photonic crystals. For example, in 2004 Valkama and coworkers prepared films of diblock copolymers for which a bandgap could be switched over a narrow temperature range. The materials they utilized were complexes of polystyreneblock-poly(4-vinylpyridinium methanesulfonate) and 3-n-pentadecylphenol. The sulfonate group of the vinylpyridinium block is a hydrogen-bond acceptor, and the 3-n-pentadecylphenol (PDP) is a hydrogen-bond donor at low temperatures (below ∼125 °C). As the system is heated above this temperature, the hydrogen bonding is disrupted and the PDP becomes a nonselective solvent for the two blocks, thus changing the periodicity of the structure.9 In 2006, Yoon et al. achieved laser emission from a device consisting of self-assembled distributed Bragg reflectors based on polystyrene-block-polyisoprene diblock copolymers, sandwiching the gain medium composed of chromophore 1,4-di(2-methylstyryl)benzene dissolved in poly(methyl methacrylate).10 More recently, Yamanaka and coworkers demonstrated a narrow (∼8 nm) bandgap filter based on diblock copolymers of polystyrene-block-poly(tert-butyl methacrylate) stabilized by photocuring of a photopolymerizable acrylate monomer. The band rejection wavelength was tuned over the range of 350−1000 nm by blending diblock copolymers with two different molecular weights.11 Received: July 30, 2014 Revised: September 22, 2014

A

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(C14) swells the polyisoprene block only. The third solvent di-n-octyl phthalate (DOP) is nonselective, i.e., perfectly neutral for PS-b-PI and equally swells both blocks. Interestingly, DOP is also a mutual solvent for both of DMP and C14. It is worth noting that DMP and C14 are immiscible with each other. Thus, by varying the volume fractions of diblock copolymer and added solvents, the size of the lamellar domains could be varied across a wide range. The approach is similar to the work of Hanley et al.,18 who showed that addition of a highly selective solvent to an AB diblock copolymer (polystyrene-block-polyisoprene) enhances the effective Flory−Huggins χ parameter (χeff) between the two phases described by all the possible combinations of the constituents and widens the domain spacings. Addition of large amounts of solvents selective to either the blocks induces morphological transitions to a spherical morphology by selective dissolution or in fact induces macrophase separation. Here we used carefully selected mixtures of A-selective and B-selective solvents to balance the volume fractions and hence maintain the desired lamellar morphology. This enables us to examine the influence of the solvents on the domain spacing without the complication of changes in the morphology of the material. In addition, a neutral solvent was added so as to increase the compatibility of the A and B domains as a further control of the domain spacings. Using this combined approach, we could successfully vary the lamellar domain spacing over a wide range. The relationship between the domain spacings and the composition of polymer and solvents was described with high accuracy by simulations based on the self-consistent field theory. This approach allowed us to calculate the spatial distribution of the solvents across the periodic polymer structure.

The photonic properties of BCPs originate from their periodic structure. The wavelength (λpeak) is proportional to the material periodicity (D) as expressed by kλpeak = 2nD sin θ

(1)

where k is order of diffraction and n is the average refractive index of the reflecting elements. Most polymers have a refractive index at the sodium D-line of around 1.5. Thus, BCPs which form periodic structures of dimensions D equal to 120 nm or larger display photonic properties in the visible light range. As described above, it is highly desirable to be able to modify the domain spacings in periodic lamella-forming BCPs in a photonic device so as to be able to vary the wavelength of reflected light. This can of course be achieved by varying the molecular weight of the blocks while maintaining a ratio of volume fractions close to unity. However, this requires repeated and laborious synthesis; as described below, the requirements of narrow molar mass dispersity and high molar mass of each block mean that such synthesis is especially demanding. For a given BCP composition, the domain spacing can be varied across a limited range by changing the temperature of the device. The domain spacing at equilibrium is generally proportional to the cubic root of inverse temperature.12,13 In practice, however, the range of achievable domain spacings is very limited because of the proximity of the glass transition temperatures of the blocks and the confounding effect of thermal degradation of the polymer. A number of reports have appeared of approaches to varying the wavelength of reflected light in the visible light region. For example, Parnell et al. demonstrated that two symmetric high molecular weight diblock copolymers of polystyrene-blockpolyisoprene, of differing molecular weights, can be blended together without macrophase separation to form a single period lamellar structure. The domain spacing of the lamellae depended on the composition of the blend and was readily tunable so that the wavelength maximum of the reflection peak ranged from 400 to 850 nm.14 In another approach, Urbas et al. reported blending of constitutive homopolymers with diblock copolymers of polystyrene-block-polyisoprene to form lamellar structures. The structures so formed give rise to reflection peaks in the range of 330−620 nm depending on the blend composition.15 Small molecular additives can also be used to alter the total volumes of the lamellae. In an interesting example, Kang and co-workers showed that films of polystyrene-block-poly(2-vinylpyridine) could be swollen to varying extents by exposure to a reservoir of a salt solution and that the osmotic swelling of the poly(2-vinylpyridine) varied with changes in the salt concentration. In this manner lamellar structures could be maintained, and the wavelength of the reflection peak could be varied from 350 to 1600 nm.16 In a similar study, Zhang et al. studied films of polystyrene-block-(2vinylpyridine), which forms lamellar structures exposed to water/ethanol mixtures. They found that the domain spacing depending on the potential of an applied voltage; for an applied voltage between −2.1 and +2.5 V reversible changes in the wavelength of the reflection peak from 470 to 630 nm were observed.17 In this report, we examine the behavior of symmetric polystyrene-block-polyisoprene (PS-b-PI) diblock copolymers on exposure to solvents with selectivity to one or both of the blocks. The solvent dimethyl phthalate (DMP) swells selectively the polystyrene domains, while n-tetradecane

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EXPERIMENT

Dimethyl phthalate (DMP), di-n-octyl phthalate (DOP), dichloromethane, styrene, isoprene, toluene, sodium, methanol, and dichloromethane were purchased from Nacalai Tesque Inc., while ntetradecane (C14), sec-butyllithium in cyclohexane/n-hexane, and tert-butylmagnesium chloride in tetrahydrofuran were obtained from the Kanto Chemical Co., Inc. Symmetrical diblock copolymers of PS-b-PI were synthesized by living anionic polymerization under high vacuum. The solvent toluene was stirred with sodium metal for 15 h and distilled to a glass reactor. Styrene and isoprene were distilled over tert-butylmagnesium chloride and sec-butyllithium, respectively. The sec-butyllithium was injected into the reactor after isoprene was added. After 14 h of polymerization, styrene was added, and the reaction continued for another 24 h followed by termination of the polymerization by addition of methanol. The molecular weights of the diblock copolymers were evaluated by gel permeation chromatography using a TOSHO GPC system equipped with TSK gel columns (GMH, G4000H, G2000H, and G1000H) and an RI detector (ERMA Inc., ERC-7522) in tetrahydrofuran solvent and using PS samples as the molecular weight standards. The composition of the polymer was determined by 1H NMR in CDCl3 on a Bruker 200 MHz spectrometer (Bruker AVANCE 200). The PI blocks have 90.6 ± 2% 1,4-isoprene units as determined by NMR. The volume fraction of PS in the diblock copolymers was calculated from the known densities of the respective blocks (1.05 g/cm3 for PS, 0.92 g/cm3 for PI19). The properties of the three PS-b-PI BCPs prepared are summarized in Table 1. The BCPs are denoted as SI-X, where X is the total molar mass of the polymer in kDa. To assist the systems to come to equilibrium, all solutions of diblock copolymer and the three solvents were prepared using dichloromethane as a cosolvent. The cosolvent was removed by drying in air at 60 °C until a constant weight was achieved. The volume ratios of B

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Table 1. Characteristics of the Polymers Used in This Study

a

polymer code

Mw × 10−3

Mw/Mn

ϕPSa

SI-60 SI-117 SI-655

60.1 117 655

1.03 1.05 1.09

0.54 0.48 0.38

ϕPS is the volume fraction of polystyrene.

DMP to C14 for solutions of SI-60, SI-117, and SI-655 were fixed at 47:53, 51:49, and 39:61, respectively. Note that the volume ratios for SI-60 and SI-117 were determined as the ratios between the volume of the PS/DMP mixture to that of the PI/C14 mixture is close to unity, while the volume ratio for SI-655 was determined as the morphology remains constant (lamellae) with varying the DOP concentration: the volume of PS/DMP was reduced as mentioned below. Reflectivity spectra measurements were conducted at room temperature (23 °C) on a UV−vis spectrophotometer (Ocean Optics DH-2000-BAL and Maya-2000 PRO as a light source and a detector, respectively) across a wavelength range from 200 to 1100 nm. The incidence light was perpendicular to the detector. Small-angle X-ray scattering (SAXS) measurements were performed on Beamline 40B2 at SPring8, Japan. The X-ray wavelength was 0.15 nm. The camera length between the detector and the sample was 4000 mm. The scattering vector is defined as q = 4π sin θ/λ, where 2θ and λ are the scattering angle and the wavelength, respectively. An imaging plate (R-AXIS VII, Rigaku) was used as the detector. The beam size at the sample position was 0.5 × 0.4 mm2. Additional SAXS measurements were carried out on a Nanoviewer (Rigaku) instrument. The X-ray beam of the Cu Kα line (λ = 0.154 nm) was incident to the sample. An imaging plate (R-AXIS IV++, Rigaku) was used as the detector. A cell of thickness of 0.98 mm with Kapton film windows was used for these SAXS measurements. The scattering intensity was corrected for absorption due to samples, air scattering from an empty cell (also with two pieces of thin Kapton films), and dark current, i.e., electric noise due of the detector. On this instrument SAXS measurements were mainly conducted at room temperature (26 °C). For measurements above room temperature, the temperature was controlled with a TMS 94 controller (Linkam Scientific Instruments Ltd.). The temperature was controlled to within ±0.1 °C. The computer simulation program Simulation Utilities for Soft and Hard Interfaces (SUSHI), based on the self-consistent field (SCF) theory in the Open Computational Tool for Advanced Materials Technology (OCTA) system, was used to calculate the equilibrium concentration distributions of polymers and the various solvents.20,21

Figure 1. SAXS profiles of SI-60 at 30 vol % of polymer concentration with 100, 70, 30, and 0% of DOP in the solvent mixture. Using the nomenclature SI-60(30-x), the x refers to the volume percentage of DOP in the solvent mixture.

respectively. As mentioned above the volume ratio of DMP to C14 was kept constant at 47:53 for the solutions of SI-60. In Figure 1 the scattering intensities of each profile are shifted for clearer presentation. The solutions with lower volumes of DOP show a primary peak at a smaller q region. The solutions SI60(30-0) and SI-60(30-30) show multiple sharp scattering peaks, SI-60(30-70) shows only the sharp primary peak, while SI-60(30-100) shows a broad peak. The positions of the peaks for SI-60(30-0) and SI-60(30-30) are consistent with the formation of lamellae in the solution. The sharp scattering peak from SI-60(30-70) indicates that a well-ordered microphase-separated structure has been formed however the precise morphology of this solution cannot be discerned from the SAXS profile. By comparison with the scattering profiles from solutions of SI-60 at higher polymer concentration (40% polymer, results not shown) with 30% DOP in the solvent mixture, we conclude that a lamellar morphology is also present in this sample. The scattering maxima in the SAXS profile for the sample SI-60(30-100) is obviously much broader than those in the other three. 2-D SAXS pattern from SI-60(30-100) showed anisotropic slight-arc scattering with low intensity and a broad peak width, which indicates that this solution is in the poorly phase-separated state of slight orientation with short-range order. Hence, we simply designate this as the “lattice-disordered” state. The solutions SI60(20-60) and SI-60(20-70) are also considered to be in the lattice-disordered state because their 2-D SAXS indicated slight orientation and also the domain spacings had the solvent composition dependence, i.e., segregation power dependence; however, SI-60(20-100), showing no anisotropy in SAXS, is in

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RESULTS AND DISCUSSION In this study the behavior of three different diblock copolymers exposed to selective and neutral solvents is examined in detail. The phase structure is determined using small-angle X-ray scattering (SAXS) while the optical reflection is measured by UV−vis spectroscopy. A series of solutions of PS-b-PI were prepared in the presence of the ternary solvent mixture DOP/DMP/C14. A constant volume fraction of polymer was maintained on each series of experiments while the composition of the solvents was varied. However, the volume ratios of DMP to C14 were fixed for solutions of SI-60, SI-117, and SI-655 at 47:53, 51:49, and 39:61, respectively. In each series the volume fraction of the neutral solvent DOP was varied with respect to the cosolvent volume fractions. Figure 1 shows the SAXS profiles of solutions of SI-60 prepared at a constant polymer concentration of 30 vol % with different volume percentages of the neutral solvent DOP. The percentage of DOP in the solvent mixtures (DOP/DMP/C14) for the four samples designated SI-60(30-0), SI-60(30-30), SI60(30-70), and SI-60(30-100) are 0, 30, 70, and 100 vol %, C

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disordered state (i.e., the constituent block chains are molecularly mixed). The four scattering profiles in Figure 1 indicate that with a decrease in the volume fraction of the neutral solvent, DOP, or rather an increase in the volume fraction of the selective solvents, there were three distinctive changes in the SAXS: the scattering peaks shifted toward the lower q region, the total scattering intensity (i.e., the intensity integrated over all the accessible q range) increased, and the higher-order scattering maxima appeared. The shift is attributed to the expansion of the domain spacings arising from the increase in the effective segregation power, χeff. The increase in the total scattering intensity arises from two sources. First, a larger χeff value also enhances the concentration fluctuation, i.e., the scattering contrast is larger. Second the presence of the selective solvents in the respective blocks increases the difference in electric density between the domains and hence the contrast. Generally, scattering intensity is proportional to squared difference in the electron density. The electron densities of PS, PI, DMP, and C14 are 339.9, 309.0, 376.3, and 265.3 electrons/nm3, respectively. Thus, enrichment of the PS phase with DMP and the PI phase with C14 will increase the difference in electron density. The ratios of the total scattering intensities were in good agreement with those of the electron-density difference squared. The increase in the segregation power followed by the enhancement of the fluctuation at higher concentration of the selective solvents leads to more highly ordered microdomain structures, which causes the higher-order scattering maxima to appear and increase in intensity. Here, it is also worthy to note that the scattering peak of SI-60(30-70) is already well sharp. All the scattering maxima seen in the profiles at the DOP concentration smaller than or equal to 30% are very sharp, while the intensity of the peaks decreases without broadening as the DOP amount increases. This can be attributed to a possible excess scattering due to the fluctuation of the solvents. Actually, the scattering intensity decays asymptotically as q−2 in the high-q region. In other words, DMP and C14 are separately sequestered into the PS and PI phases while DOP added is well mixed with the already existing DMP or C14 and causes Ornstein−Zernike type fluctuation. It is also noticeable that the peaks are not the usual Bragg ones, and their widths at the bottoms are obviously wider. This will be because of another structure factor arising from undulation of the interface at the phase boundary that was described by Gunther et al.22 for smectic A liquid crystal as a Landau−Peierls system. They showed such long-wavelength fluctuation wash out long-range order of the order parameter whose decay is of the power-law type. However, analyses of these effects are beyond the scope of this work and will be discussed elsewhere. In Figure 1 it can also be seen that in the profiles of SI60(30-0) and SI-60(30-30) the even-numbered peaks are greatly attenuated or missing. This extinction is attributed to the match with the valleys of the particle scattering because the PS and PI domains have almost identical volume fractions. Though the profiles are not shown, some solutions, close to the lamella−cylinder transition that is described below, show scattering profiles with even-numbered peaks having relatively large intensities compared with these two profiles, indicating in those systems the volume fractions are far from equal. In Figure 2 domain spacings of the solutions of SI-60 at polymer concentrations of 20, 30, 40, and 50 vol % are plotted as a function of DOP fraction in the solvent mixture. The domain spacings were calculated from the position of the

Figure 2. Domain spacings of SI-60 solutions at polymer concentrations of 20, 30, 40, and 50 vol % plotted against fraction of DOP in the solvent mixture. Also plotted as a dotted horizontal line is the estimated domain spacing of SI-60 at 26 °C.

primary SAXS maximum as 2π/qmax, where qmax is the magnitude of the scattering vector at the first peak position. The solution with polymer concentration of 20 vol % without DOP was macroscopically phase separated. Note that the solvents DMP and C14 are immiscible with each other; however, on addition of PS-b-PI and DOP, the solvents are able to mix. Thus, in the absence of certain amounts of PS-b-PI and DOP, the solution macroscopically phase separates. In the majority of the solutions, either lamella or latticedisordered morphology was formed. At the four concentrations of polymer examined the solutions show increasing domain spacings as the fraction of DOP in the solution decreases, and this effect is more pronounced at lower DOP contents. The added DOP is miscible with DMP and C14 and shields the segregation power between the two highly selective solvents. This means that the value of χeff significantly dropped when small amounts of DOP is added to the systems at the DOP fraction less than ca. 0.3 while at higher DOP contents the effect of the addition is less pronounced. The curves in Figure 2 show a crossover point at DOP fractions around 0.36. At the higher DOP fractions the domain spacings became larger as the polymer concentration was increased while the converse is true at the lower DOP fractions. It is known that dilution of diblock copolymers by a neutral solvent will lead to a decrease in the value of χeff.13,18 Thus, the use of a solvent mixture with a high fraction of the neutral solvent DOP will lead to a decrease in the domain spacing. On the contrary the strong segregation power between the blocks rich in the selective solvents DMP and C14 will lead to an increase in χeff. Thus, addition of the selective solvents (lower DOP fraction) will lead to an increase in domain spacings, as observed in Figure 2. The fact that there is the above-mentioned crossover point in Figure 2 also means that the diblock copolymer SI-60 has the same domain spacing of 39.0 nm at any polymer concentration in this solvent mixture. It follows that the domain spacing of SI60 in the absence of solvent, i.e., polymer concentration of 100%, should have the same value. However, SI-60 cannot D

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reach the equilibrium state at room temperature without addition of solvent because polystyrene has a glass transition temperature at ca. 100 °C. By an independent measure, the domain spacing at room temperature can be obtained from extrapolation of the temperature dependence of domain spacing.12,13 In Figure 3, the logarithm of the domain spacings (log D) of SI-60 is plotted against logarithmic inverse absolute temper-

Figure 4. Domain spacings of SI-117 solutions at polymer concentrations of 20, 30, 40, and 50 vol % plotted against fraction of DOP in the solvent mixture and the estimated domain spacing of SI-117 at 26 °C.

3:√4:√7:√12:√13, which are characteristic of hexagonal cylindrical morphology. The existence of cylindrical morphology for the solutions at 20 vol % polymer concentration and DOP fraction of 0.4 and 0.5, and lamellar morphology for compositions on either side of this, suggests that at these fractions of DOP the volume fraction of either polystyrene domain or polyisoprene domain must be substantially increased. It is assumed that difference in the affinities of DOP to DMP and C14 affects the volume fractions of the domains as examined below. The miscibility of DMP and C14 at the temperature of the SAXS measurements (26 °C) was examined initially. An equalvolume mixture of these two solvents formed two layers indicating high immiscibility. The volumes of the layers were close to the initial volumes of the liquids prior to mixing, and samples were withdrawn from each phase to allow analysis of the composition by 1H NMR (see Table 2).

Figure 3. Temperature dependence of the domain spacing of SI-60. The dotted line is the extrapolation of the domain spacings between 181.4 and 111.5 °C.

ature. Across this temperature range (181−111 °C) log D is proportional to log 1/T, with a strong linear dependence. The domain spacing at 26 °C was estimated by least-squares analysis of the data at high temperature to be 39.8 ± 0.2 nm, as indicated by the dotted line in Figure 3. The values obtained from the two sets of observations are in very good agreement; the small difference in the values must arise from errors in the extrapolation procedure. The domain spacings of solutions of SI-117 as a function of fraction of the neutral solvent DOP were examined in the same manner (Figure 4). Conclusions similar to the results for SI-60 solutions can be drawn. However, the plots for solutions of SI117 and SI-60 differ in three important aspects. First, solutions of SI-117 show much larger domain spacings,23 as expected for a higher molecular weight polymer. This is because the molecular weight of SI-117 is nearly the twice that of the small diblock copolymer SI-60; the effective block−block segregation power, which is expressed by the product χeffN, is nearly twice for SI-117. Here, N is the number-average degree of polymerization. Second, the larger effective segregation power also causes SI-117 to form more ordered solutions across the range of solvent compositions and polymer concentrations. In the case of SI-117, only one lattice-disordered solution was observed; however, for SI-60 there were one disordered solution and three lattice-disordered solutions within the range of concentrations examined. Third, at two compositions of solutions of SI-117 a hexagonal cylindrical morphology was observed. The solutions at polymer concentrations of 20 vol % and DOP fractions of 0.4 and 0.5 showed hexagonally packed cylinders. This is evident by the SAXS scattering peaks being relatively spaced at the relative positions of 1:√

Table 2. Volume Fractions of Solvents in the DMP and C14 Liquid Phases in the Mixture of the Three Solvents prepared volume ratios (DOP/DMP/C14) 0/1/1 1/1/1

phase

measured compositions (DOP/DMP/C14)

volume fraction of DMP-rich phase

DMP-rich C14-rich DMP-rich C14-rich

0/0.997/0.003 0/0.005/0.995 0.365/0.500/0.135 0.294/0.127/0.579

0.50 0.58

Next, DOP was added to the phase-separated solution of DMP and C14. For DOP fraction of 0.4 and 0.5, a single phase was observed. Therefore, we could not measure the compositions of DMP and C14 phases. For DOP fractions of 0.34 ± 0.005 or below, however, separated phases were seen, and samples could be withdrawn for analysis of composition. Therefore, we examined the composition of the phases on mixing of equal volumes of the three solvents, i.e., at ratios of E

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for PS-b-PI. Thus, the system passes through cylindrical morphology as shown by the dashed line. Actually, cylindrical morphology was observed at the DOP volume fraction of 0.4− 0.5 as mentioned above. Note that the DOP fraction in the DMP phase is still smaller than that of DMP at DOP/DMP/ C14 = 1/1/1 in Table 2. Note also that cylindrical structures were not observed for the SI-60 system and the system remained within the lamellar phase boundary. This may be because SI-60 has a slightly smaller amount of DMP, in which PS is less swollen. In Figure 6, the domain spacings of the SI-117 and SI-60 solutions at the polymer concentrations of 20−50 vol % are

1/1/1 DOP/DMP/C14, just below the boundary to a single phase. The results are given in Table 2. On addition of DOP the volume of the DMP-rich layer increases and is 1.4 times that of the C14-rich layer. This observation and the compositions of the phases provided in Table 2 suggest that DOP has a higher affinity to DMP than to C14. This result strongly suggests that expansion of the polystyrene domains causes the observation of cylindrical domains for solutions on SI-117 in a small solvent composition window. A transition between lamellar and cylindrical morphologies through gyroid morphology for PS-b-PI is generally observed at PI fraction around 0.35−0.405,18 Actually, our fitting results for the SAXS profiles suggest the fractions of the PI phases are minimum at the DOP fraction of 0.4 and 0.5 where cylindrical morphology was formed with the PI fraction of 0.36 and 0.37, respectively. This result indicate that phase separation between the two selective solvents was induced in the homogeneous solvent mixture at the DOP fraction above 34 vol % by the presence of the SI-117, where PS and PI attracted DMP and C14, respectively, and DOP accumulated largely in the PS phase. Therefore, the effective volume fraction of the PS phase is increased up to the DOP fraction of 40−50 vol % and passes into the cylindrical morphology. The effect of addition of the solvents to PS-b-PI can be represented by the trajectories in the phase diagram in Figure 5.

Figure 6. Logarithmic domain spacings of solutions of SI-60 and SI117 at polymer concentrations of 20, 30, 40, and 50 vol % plotted against the fraction of DOP in the solvent mixture. The domain spacings for SI-60 are vertically shifted by a factor of 1.91.

plotted on a logarithmic scale as a function of DOP ratio to solvent mixture. The domain spacings of SI-60 solutions have been scaled by a factor of 1.91. The scaled domain spacings for the two solutions overlap within the error of 2.5%, apart from the solutions identified as lattice-disordered. This indicates that the behavior of the domain spacing as a function of the solvent composition is identical despite the difference in the molecular weight. A number of solutions of the higher molar mass polymer SI655 were also prepared; however, the high viscosity of the solutions prevented accessing the higher polymer concentrations achieved for the lower molar mass polymers. The volume fraction of DMP was reduced and the volume ratio of DMP to C14 was 39:61 to maintain the lamellar morphology by avoiding the transition to cylinders. This is because the solutions of SI-117 (DMP:C14 = 51:49) showed cylindrical morphology in the small solvent composition window as mentioned above. For the SI-655 solutions prepared the domain spacings were large enough so that visible light was reflected by the periodic structures. The reflectance spectra are shown in Figure 7; sharp reflectance peaks are observed at wavelengths from 345 to 793 nm, depending on the polymer

Figure 5. Phase diagram and trajectories describing effect of addition of DOP, DMP, and C14 to SI-117.

To explain, addition of equal volume of the selective solvents C14 or DMP will increase the segregation power (bold vertical arrow), while addition of pure DOP reduce the segregation power. However, the addition of DOP to DMP/C14 mixed solvent results in a change in the respective volume fractions and specifically an increase in the volume fraction of the DMP phase compared with the C14 phase. The volume fraction of PS phase increases with increasing the fraction of DOP as long as the volume fraction of DOP in the PS/DMP/DOP phase is smaller than that of DMP. The volume asymmetry in the PS/ DMP/DOP and PI/C14/DOP phases is highest when the volumes of DOP and DMP in the PS/DMP/DOP phase are close to each other. Then the asymmetry becomes less pronounced when the fraction of DOP in the PS/DMP/ DOP phase decreases with the decrease of DMP after the DOP fraction exceeds the DMP fraction. Eventually, the volume ratio of the PS phase to the PI phase is unity in the case of the fraction of DOP = 1 because DOP is perfectly neutral solvent F

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component pair are listed in Table 3. The systems are assumed to be in equilibrium. Finally, to improve the speed of calculation, the degree of polymerization for each block was reduced to 40. Table 3. Polymer−Polymer, Polymer−Solvent or Solvent− Solvent Interaction Parameters, χ, Used in the Calculations Performed Using the SUSHI Program styrene isoprene DOP DMP

Figure 7. Reflectance spectra for solutions of SI-655 (a) and polymer concentrations and solvent compositions (b).

isoprene

DOP

DMP

C14

0.52

0.01 0.01

0 1.08 0.02

1.08 0 0.02 3.1

The results of the simulations shown in Figure 8 are in close agreement with the experimental results for the system SI-60/

concentration and solvent composition. The DOP and polymer concentrations were strategically selected using the relationship shown in Figure 6: First, we measured the domain spacings without the selective solvents (the DOP fraction = 1) at various polymer concentrations; second, the obtained domain spacings are plotted in Figure 6 (though not shown here); the domain spacings at various DOP fraction were estimated from the plots for the SI-60 and SI-117 solutions. Though the change in domain spacing is larger at the lower polymer concentration, the lowest concentration for the phase separation at the fraction of DOP = 1 was 13.1 vol %: the solution was in the disordered state at concentrations lower than the value. Thus, we decreased the polymer concentration as the segregation power was increased with decreasing the fraction of DOP. Note that the decrease in the polymer concentration also resulted in the decrease of solution viscosity that help the solutions achieve highly ordered structures at equilibrated state easily. The reflectance peaks at longer wavelengths are relatively broader compared with peaks at shorter wavelengths. However, the peak widths scaled by the individual wavelengths of the peaks are almost identical though they are scattered with the error of ±43%, and there was no significant relationship between the widths and the peak wavelengths. This result indicates that the structures formed in these solutions are all well ordered to the similar extent despite the compositions. Note also that for the three samples with reflectance at the highest wavelengths there is a second-order peak above 300 nm; for clarity, only the first-order peaks are plotted in Figure 7. The wavelength of a reflectance peak is determined with a domain spacing and average refractive index of a domain and a medium as expressed by eq 1. The variation in the refractive index across all solutions examined here is within 0.7% of 1.484. Therefore, the changes in the wavelength of the reflectance peaks arise mainly from changes in the domain spacings. The distribution of each component and the effect of solvent composition on the domain spacing were calculated using the software program SUSHI. SUSHI stands for Simulation Utilities for Soft and Hard Interfaces, a program based on the self-consistent field (SCF) theory, and is part of the Open Computational Tool for Advanced Materials Technology (OCTA) integrated simulation system. In these simulations we assume a model of a symmetric diblock copolymer in the presence of two selective solvents and a neutral solvent. For simplicity, the same value of χ is used for the polymer/solvent pairs, styrene/C14 and isoprene/DMP. We assume that there is no preferential affinity of DOP to either domain for simplicity. The values of the interaction parameters, χ, for each

Figure 8. Domain spacing versus solvent composition at the polymer concentrations of 20, 30, 40, and 50 vol % as determined using the simulation program SUSHI.

DOP/DMP/C14, with small differences in the shape of the curves. Domain spacings for the lattice-disordered solutions could not be calculated using the program, and so these points are missing from the plot. However, the overall agreement between experimentally obtained and simulated structures is excellent. The distribution of each component across the domain structures was also calculated for a polymer concentration of 30 vol % at two different DOP fractions of 0.1 and 0.7 in the solvent mixture (Figure 9a,b). In both cases the selective solvents are largely located in the respective preferential domains. At the lower fraction of DOP in the solvent mixture (10 vol %, Figure 9a) the selective solvents DMP and C14 are more strongly distributed within the respective blocks. The simulations suggest that the addition of the mutual solvent, DOP, increases the miscibility of the other components and leads to a more equal distribution of the components across the phase structures. Therefore, the domain spacings are determined by the extent of dilution of the effective segregation power among the polymers and the selective solvents by the G

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selective for polystyrene and polyisoprene, respectively, while DOP is a neutral solvent for the two blocks. SAXS measurements of the solutions revealed strong variation in the lamellar domain spacings as a function of both polymer concentration and composition of the solvent mixture. The addition of the neutral solvent DOP lead to a decrease in the domain spacings as a result of the reduction in the effective block−block interaction parameter χeff. A comparison of the behavior of the diblock copolymers having two different molar masses (SI-60 and SI-117) confirmed that scaling of the domain spacing as a function of solvent composition are independent of the molecular weight. A number of solutions were prepared with a larger molecular weight diblock copolymer (SI-655), and as expected these formed photonic structures that displayed reflectance spectra with wavelength maxima ranging from 345 to 793 nm, i.e., across the whole of the visible light region. The software program SUSHI based on the self-consistent field theory was used to calculate the domain spacings in a model system and the distribution of the various components in the system across the periodic structures. The use of mixtures of selective and neutral solvents as solvents for diblock copolymers is shown here to be a powerful approach to achieving structures with photonic properties.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (S.O.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.M. greatly thanks Prof. Andrew Whittaker for his constructive suggestions and editorial help. The synchrotron radiation experiments were performed at the BL40B2 of SPring8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2011B1502, 2012B1476, 2013B1236). This work was supported by JSPS KAKENHI Grant No. 21550208.

Figure 9. Spatial distribution of each component in the diblock copolymer−solvent systems, as calculated using the program SUSHI. The simulations considered a polymer concentration of 30 vol % and DOP fractions in the solvent mixtures of 10 vol % (a) and 70 vol % (b).

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neutral and mutual solvent and by the selectivity of the solvents DMP and C14. Note also that the simulations predict bimodal maxima in the concentrations of PS and PI in their respective domains near the either interface with the partner blocks. As a result that the very strong selectivity of the solvents DMP and C14 for the blocks sequesters the selective solvents themselves to the center of the domains, the small decrease in concentration of the blocks at the center of the respective domains is considered to be caused to satisfy the incompressibility. Furthermore, the simulations predict slightly higher concentrations of DOP at the interface so as to shield the unfavorable contact between the two components at the interface. Finally, the simulations predict nonzero concentrations of the highly selective solvents in the counter domains driven to avoid the entropic loss accompanying perfect segregation into the preferential domains.

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CONCLUSIONS Solutions of polystyrene-block-polyisoprene (PS-b-PI) of three different molecular weights were prepared in mixed solvents of DOP, DMP, and C14. Immiscible DMP and C14 are highly H

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