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Phase Behavior of Block Copolymers in Selective Supercritical Solvent Masateru M. M. Ito,† Kohzo Ito,† Mitsuhiro Shibayama,‡ Kenji Sugiyama,§ and Hideaki Yokoyama*,†,∥ †

Department of Advanced Materials Science, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan § Department of Chemical Science and Technology, Hosei University, 3-7-2 Kajino-cho, Koganei, Tokyo 184-8584, Japan ∥ Precursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology Agency, 3-5 Sanbancho, Chiyoda-ku, Tokyo 102-0075, Japan ‡

S Supporting Information *

ABSTRACT: The phase behavior of a block copolymer and supercritical fluid system was investigated. When a particular block was selectively swollen by the supercritical fluid, the apparent volume fraction of one domain was controlled by the pressure of the supercritical fluid. The morphological variation of polystyrene-b-poly[2-(perfluorooctylethyl) methacrylate]s (PS−PFMAs) with different ratios of PS to PFMA and the total degree of polymerization were analyzed. Time-resolved small-angle neutron scattering measurement revealed that lamellar and hexagonal phases coexist metastably, which may be induced by fluctuation of the supercritical fluid.

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INTRODUCTION When two blocks in a single block copolymer (BCP) chain are immiscible, the BCP melt may assembly itself into a wide variety of morphologies.1 BCPs often exhibit reversible thermotropic order−order transitions (OOT) between these morphologies, resulting from changes in the interblock interaction induced by variation of the temperature. The phase behavior and OOT of BCPs have been evaluated in a number of studies,2,3 and existing theories such as the Ginzburg−Landau theory and path integral method have been applied to BCPs for the past 30 years.4 From these experiments and theories on BCPs, the key parameters affecting the phase behavior of the BCP melt were found to be the fraction of component f, the degree of polymerization, N, and the Flory−Huggins parameters for interaction between two monomers, χab, χaa, and χbb, where “a” and “b” denote blocks a and b, respectively, in the BCP. It is well-known that the phase diagram of a BCP melt is determined by χN and f, where χ can be expressed as χ=

1 (χ + χbb ) − χab 2 aa

solutions can be classified into two categories depending on the relationship between the copolymer and solvent: the first is the neutral system, where χas = χbs, and the other is the selective system, where the solvent has higher affinity for one block, χas ≠ χbs. In the neutral system, the interaction between a and b segments is screened and the degree of segregation decreases. In the neutral system, the solvent is randomly partitioned in the BCP, including the domain interface. Decreasing φ effectively leads to a decrease in χab; therefore, the degree of segregation, χN, can be replaced approximately with the effective degree of segregation, χφN. Phase diagrams of χφN vs f successfully represent the corresponding experimental results.5 On the other hand, when the solvent is selective for one block (χas ≠ χbs), one of the blocks is preferentially swollen by the solvent. Selective solvents act as diluents for the BCP and may also enhance segregation of one block from the other, leading to chain-stretch normal to the domain interface.5,6 Therefore, decreasing φ changes the apparent volume fraction, fapp, and may trigger phase transition to a different morphology. The physics of a BCP with a selective solvent is similar to that of a surfactant/solvent system7 because both systems consist of amphiphilic molecules with selective absorption of solvents into one part of the molecules. Thus, the phase diagram of a surfactant is similar to that of a BCP with a selective solvent. Consequently, surfactant and BCP systems are universally

(1)

Because the relationship between χab and temperature, T, can be expressed as χab ∼ T−1, a change in the temperature induces thermotropic OOT due to a change of χab. In the case of BCP solutions, in addition to χ, N, and f, the other parameters affecting the phase behavior are the copolymer to solvent ratio (φ) and the two interaction parameters χas and χbs,5 where “s” denotes solvent. BCP © XXXX American Chemical Society

Received: February 2, 2015 Revised: April 12, 2015

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Macromolecules Table 1. Characteristics of PS−PFMA Block Copolymers PS sample code PS−PFMA PS−PFMA PS−PFMA PS−PFMA PS−PFMA

28 23 20 13 9

PFMA

PFMA (wt %)

initial structure

DP

Mn

DP

Mn

Mn

Mw/Mn

28 23 20 13 9

lamellae hex PFMA cylinder hex PFMA cylinder PFMA sphere PFMA sphere

147 66.9 133 92.5 212

16500 7730 14900 10600 22300

12.2 4.3 7.0 2.9 4.4

6490 2270 3700 1560 2320

23000 10000 18600 12200 24600

1.06 1.02 1.07 1.03 1.02

(SANS) measurements and φ-dependence of χ by monitoring the order−disorder transition (ODT) using birefringence measurements. They dealt only with variation of the lamellar spacing and lamellae−disorder transition. The present authors also conducted a similar type of experiment by using polystyrene-b-poly[2-(perfluorooctylethyl) methacrylate]s (PS−PFMAs) and CO2.16 In that study, OOT was induced by variation of the pressure of the system. However, the OOT of BCPs in scCO2 is still not fully understood. In this paper, we explore the phase behavior of BCPs in scCO2. In situ SANS measurements of the order-toorder transition of PS−PFMAs in scCO2 are conducted by preparing several samples that differ in terms of the ratio of PS to PFMA and total degree of polymerization. Focus is placed on the difference between the thermotropic transition and the lyotropic transition. The lyotropic OOT mechanism is unique to the scCO2 system and represents a breakthrough for research on phase transitions in “amphiphilic systems”. In the case of the thermotropic OOT, the particle number is conserved, whereas in the lyotropic OOT, φ(P,T) is changed by tuning nCO2(P,T), where nCO2 denotes the particle number of CO2.

called “amphiphilic systems”. In amphiphilic systems, OOT can be induced by temperature variations as well as by changes in the effective volume fraction. The phase behavior in “amphiphilic systems” is related to the parameters f, χ, N, and φ. Of these parameters, χ is the only parameter that can be continuously varied by changing the temperature. In contrast, polymerization of a new molecule is required for changing N and f. Similarly, the concentration, φ, cannot be varied continuously while maintaining the ordered structure. Hence, experimental studies on the phase transition of amphiphiles have been limited to thermotropic transition. It is impossible to induce a lyotropic transition by continuous variation of the fraction of liquid solvent. Therefore, temperature has been the sole parameter for continuous manipulation of the OOT. Recently, we successfully injected a supercritical fluid (SCF) into a particular block of a BCP, thereby inducing selective swelling by pressure control.8−10 Because of the high diffusivity of the SCF, it is rapidly absorbed by the BCP, even in the ordered structure. For the BCP/SCF system, the BCP concentration, φ, is a function of temperature and pressure, φ = φ(P,T). Our previous study of polystyrene-b-poly[2(perfluorooctylethyl) methacrylate] (PS−PFMA) and supercritical carbon dioxide (scCO2) systems8 demonstrated that these are optimum systems for high selective swelling contrast. Because χ(PS-CO2) is much larger than χ(PFMA-CO2), PFMA becomes significantly swollen, whereas PS is only slightly plasticized by scCO2. The PS−PFMA and scCO2 systems offer another experimental advantage. Because PS is only slightly plasticized, PS can be rubbery at room temperature or above but is glassy at low temperature in CO2. The glass transition temperature of PS in scCO2 is higher than that of PFMA11−13 and hence dominates the dynamics of the BCP. Upon depressurization at intermediate temperatures between the glass transition temperatures of PS and PFMA, the frozen PS block prevents shrinkage of the swollen BCP. Upon depressurization, the PFMA domains release CO2 and shrink back to the original volume. Consequently, the BCP forms “pores” with a volume that approximates the volume of CO2 in the PFMA domain. This process can be used to produce porous structures reflecting the swollen BCP morphology in CO2. We reported various porous structures of PS−PFMA (such as spherical pores) that reflect the sphere domain and horizontally and vertically oriented sheet-like pores.10 Therefore, the swollen morphologies can be approximated from the resulting porous structures. CO2-induced OOT can be controlled by manipulating the properties of CO2 by variation of the temperature and pressure. Francis et al. used a high-pressure vessel with windows and reported in situ measurements of lamellae-forming poly(styrene-b-dimethylsiloxane) in scCO2.14,15 Their study demonstrated φ-dependence of the domain spacing of poly(styreneb-dimethylsiloxane) based on small-angle neutron scattering

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EXPERIMENTAL SECTION

Materials. Polystyrene-b-poly[2-(perfluorooctylethyl) methacrylate]s (PS−PFMAs) were synthesized by sequential living anionic polymerization of corresponding monomers. The details of the polymer synthesis are described elsewhere.17 The molecular weights of the PS blocks were determined by size exclusion chromatography with a small portion of PS solution sampled during the polymerization, and the molecular weights of the PFMA blocks were determined by 1H NMR signal ratio of the CH2CF2/C6H5 assigned to PFMA/PS blocks. The molecular weights are listed in Table 1. Respective PS−PFMAs were dissolved in α,α,α-trifluorotoluene (Aldrich), and each solution was cast into tablets for the high-pressure neutron scattering experiment or was spin-coated on silicon wafers (Shinetsu Co.) for thickness measurements. Small-Angle Neutron Scattering (SANS). In situ SANS measurements were conducted using SANS-U (SANS beamline at the University of Tokyo, To̅kai, Japan). The neutron wavelength was 7.0 Å. Scattering images were recorded on a 2-D detector. The sampleto-detector distances were 1, 4, and 8 m, covering the q range from 0.005 to 0.35 Å−1. The samples were placed into a high-pressure vessel (TERAMECS) with pressure and temperature control. This high-pressure vessel was designed for in situ SANS measurements in scCO2; the vessel has twin sapphire windows for the path of the neutron beam in the stainless body. The cell was connected to a pressure control system that consists of a pump (Nihon Seimitsu Kagaku) and pressure regulator (SCF-Bpg, JUSCO). The pressure was incremented at a rate of 10 MPa/min or faster and reduced at a rate of 2 MPa/s or slower. Here, the temperature was fixed at 60 °C above the critical temperature of CO2, and the pressure was varied stepwise from atmospheric pressure (ca. 0.1 MPa) to 30 MPa. SANS data were acquired at 1−4 min time intervals. B

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Macromolecules Film Preparation and Porous Process. PS−PFMA films on silicon wafers were prepared by spin-coating. The films were 130−150 nm thick, as measured using an ellipsometer (M200 spectrometer, JASCO). Specimens were placed in a high-pressure vessel (Taiastu) controlled by a liquid chromatography pump (PU-2086 plus, JASCO) and pressure regulator (SCF-Bpg, JASCO). After reaching the supercritical state, the pressure and temperature were maintained for 30 min. The vessel was then placed in a cooling bath to reduce the temperature to −5 °C while maintaining the pressure using the pump and pressure regulator. The vessel was depressurized to atmospheric pressure at a rate of 0.5 MPa/min in a cooling bath. Scanning Electron Microscope (SEM) Analysis. To eliminate the surface covering layer of the PFMA blocks, a reactive ion etcher (RIE, Compact Etcher FA-1 from SAMCO or Basic Plasma Kit BP-1 from SAMCO) was used. The RIE with CF4 plasma was operated at a CF4 pressure of 10 Pa and power density of 10 W/cm2, where the PS− PFMA thin films were etched at a rate of 1 nm/s. For the field emission scanning electron microscope (FE-SEM) measurements, it was not necessary to coat the PS−PFMA films with conducting materials because the films were very thin and had sufficient conductivity to the substrate. The acceleration voltage of the FESEM was 15.0 kV. In Situ Thickness Measurement. Measurement of PS−PFMA swelling was performed by reflection measurement of the PS−PFMA films on silicon wafers in a high-pressure vessel (Taiastu) filled with scCO2. The PS−PFMA films were prepared by spin-coating, and the thickness of the films was adjusted to 150−200 nm. The cell is equipped with a sapphire window, which provides a path for a probe light. The probe light from the light source (MC-2530, Otsuka Electronics) has a wavelength range of 230−800 nm. The reflectivity was measured by using a spectrometer (MCPD-3700, Otsuka Electronics) and was fit to the n-Cauchy model. In this analysis, the reflections on the window and substrate were taken into account. The error in the thickness determined through the high-pressure window was within 5%.

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RESULTS AND DISCUSSION Phase Behavior of PS−PFMA with CO2. This section discusses the phase behavior of PS−PFMA with CO2. PFMAs are CO2-philic and swell to a greater extent in scCO2 than PS. Therefore, the swelling of PS−PFMA with CO2 is primarily due to swelling of PFMA. With increasing CO2 pressure, the original PS−PFMA morphology becomes unstable and pressure-induced OOT then occurs. In this study, the temperature of this OOT is higher than Tg of PS and PMMA in scCO2;11−13 therefore, the mobilities of PS and PFMA are high enough to cause OOT. Also, the fact that all pressure-induced OOTs were reversible is a good indication of high mobility of the block copolymers. The high diffusivity of scCO2 allows CO2 to flow into and out of the PFMA domains of the BCPs through the PS domains. The pressure dependence of the scattering profiles in the depressurizing process is presented below; the profiles are essentially the same as those in the pressurizing process. The SANS profiles of PS−PFMA 28 (see Table 1 for characteristics) in CO2 at 60 °C, over the pressure range of 30− 0.1 MPa, are shown in Figure 1a. The SANS profiles acquired during depressurization from 30 to 0.1 MPa are presented in Figure 1. Note that 0.1 MPa is atmospheric pressure filled with CO2. At 0.1 MPa, the SANS profile shows peaks with a relative peak ratio of 1:2:3. Thus, this profile corresponds to the lamellar structure. Certainly, 28 wt % is in the region of Hex in weak segregating BCPs. However, as discussed in subsection Pressure Dependence of the Domain Spacing the χ parameter between PS and PFMA is extremely large, and hence PS− PFMA 28 may form Lam. As the pressure of CO2 increases, the

Figure 1. (a) SANS intensity of PS−PFMA 28 as a function of wave vector, Q, at various pressures. (b) SANS intensity of PS−PFMA 28 as a function of wave vector, Q, at 30 MPa, and fit with a cylindrical form factor.

CO2 molecules penetrate into the PS−PFMA BCP, resulting in preferential swelling of the PFMA block. Integer multiples of the peak ratios are maintained up to 20 MPa, indicating that a swollen lamellar structure is formed by PS−PFMA with scCO2. At pressures higher than 25 MPa, the Bragg peaks decay, and at 30 MPa, the structure factor eventually disappears. The SAXS profile of PS−PFMA 28 at 30 MPa (Figure 1b) was fit to a cylindrical form factor (solid curve). The scattering profile shows the rod-like power law behavior (slope −1) in the lower q region, and the slope is −2 in the higher q region. If the lamellae are transformed into hexagonal or bicontinuous structures, the fundamental component of the resulting structures has a cylindrical shape, explaining the good fit of the scattering profile to the cylindrical form factor. From this fitting, the radius was evaluated to be 7.54 ± 0.01 nm. Because PFMA is preferentially swollen with CO2 under these conditions, the cylindrical micelles should have a PS core and PFMA shell. The PS core cylindrical micelles may form part of the branches of random networks as reported recently.18,16 It should be noted that the transition to the cylindrical random networks is reversible and BCP returned to the lamellar form with a decrease in the pressure to 0.1 MPa. Figure 2 shows the SANS patterns of PS−PFMA 20 in scCO2 at 60 °C over the pressure range of 30−0.1 MPa. The inset shows the higher resolution SANS patterns of the same C

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Figure 3. Peak positions (q values) versus pressure. The codes a, b, and c denote hexagonal PFMA-core cylinders, lamellae, and hexagonal PS-core cylinders, respectively. The numbers 1, 2, and 3 following the codes are first-, second-, and third-order Bragg peaks of each phase, respectively.

Figure 2. SANS profiles of PS−PFMA 20 at various pressures. Sample−detector distance was set to 4 m. The codes a, b, and c denote hexagonal PFMA-core cylinders, lamellae, and hexagonal PS-core cylinders, respectively. The numbers 1, 2, and 3 following the codes are first-, second-, and third-order Bragg peaks of each phase, respectively. The high-resolution profiles with 8 m sample−detector distance are shown in the inset.

and hexagonal PS-core cylinders, respectively. The peak ratio of b1 and b2 at 7.5−10 MPa and at 22.5−30 MPa is 1:2, which indicates that the lamellar structure persists up to 30 MPa. The q values of the peak positions around 10−20 MPa are not plotted in Figure 3 because the peaks of the lamellar and PFMA hexagonal phases were too close to be separated. The phase behavior of PS−PFMA 13 and PS−PFMA 9 in scCO2 was investigated using SANS. The SANS scattering profiles of PS−PFMA 13 during the depressurization process are plotted in Figure 4. The CO2 temperature was 60 °C, and the pressure was varied in the range of 30 to 0.1 MPa. In contrast, with the two PS−PFMAs discussed above, the profiles of PS−PFMA 13 are characterized by single peaks and do not show any qualitative change. Because the volume fraction of PFMA in PS−PFMA 13 is 13 wt %, it is likely that PS−PFMA 13 forms spherical domains in the neat bulk phase. The profiles

sample acquired at a longer sample−detector distance than that of the main figure. The SAXS profiles changed remarkably with pressure, indicating multiple order−order transitions. At 0.1 MPa, PS−PFMA 20 forms a hexagonally packed cylindrical phase, which was confirmed by the a1 to a2 peak ratio of 1:√3. This cylinder consists of a PFMA core and PS matrix (PFMA hexagonal). At 10 MPa, the primary peak in Figure 2 is broader than that at 0.1 MPa, and the profile in the inset clearly shows that this broadened peak consists of two peaks. The ratio between the peak-top q values of a1 and a2 is 1:√3, indicating that the PFMA hexagonal phase is maintained. A new first peak (b1) appears at 10 MPa that coexists with the PFMA hexagonal phase. Similar coexistence is also observed in the pressure range of 10−15 MPa, and finally lamellae with a characteristic peak ratio of 1:2:3 are formed in the pressure range of 17.5−20 MPa. Therefore, lamellae and hexagonally packed cylinders coexist in the pressure range of 10−15 MPa, similar to the case reported for the phase diagrams of the BCP/solvent mixture.5 At higher pressure (22.5 MPa), another coexistent phase of lamellae and hexagonally packed cylinders is observed; this phase is similar to that found in the pressure range of 10−15 MPa, where PFMA core hexagonal cylinders and lamellae coexist; however, in the higher pressure range, the hexagonally packed cylindrical phase is composed of “inverted” PS core micelles. The coexistence of inverted hexagonal cylinders and lamellae has also been observed for BCPs with conventional solvents.5 Figure 3 shows a plot of the q value of the peak positions vs pressure for two pressurization and depressurization cycles in the pressure range of 0.1−30 MPa. No hysteresis was observed over the two pressurization and depressurization cycles. The peak positions change with pressure, but the relative positions in each group (a, b, and c) remain constant. Therefore, a, b, and c are classified into three different structures. In this notation, a, b, and c denote the hexagonal PFMA-core cylinders, lamellae,

Figure 4. SANS profiles of PS−PFMA 13 at various pressures. D

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Macromolecules in Figure 4 acquired at 0.1 MPa (before the process) indicate spherical domains without long-range order, and the single peaks correspond to the correlation length between neighboring spherical domains. With increasing CO2 pressure, no qualitative change of the SANS profiles was observed, which indicates that the spherical phase is maintained over the pressure range of 0.1−30 MPa without any evidence of OOT. In addition, at certain pressures in the higher q value region (0.06−0.10 Å−1), fringes of the spherical form factor are apparent. No evidence of OOT from the spherical phase is observed in the SANS analysis of PS−PFMA 9. The fact that the sphere domain of PS−PFMA 13 is maintained at 23−30 MPa is clearly confirmed by SEM observation. Figure 5 shows

Figure 6. Pseudo phase diagram of mixture of PS−PFMA and CO2 as a function of pressure. The labels refer to hexagonal (Hex), nonlattice cylinder (Cyl), and coexistence of lamellar and hexagonal (Hex + Lam) phases.

the coexistence of lamellar and hexagonal phases is further discussed in the next subsection. Coexistence of Lamellar and Hexagonal Phases in Supercritical System. The classic BCP/solvent mixture is closed system where the polymer/solvent ratio is fixed and the number of molecules in the mixture is conserved. In contrast, the BCP/SCF system is open system. BCP swollen with scCO2 is equilibrated with the scCO2 reservoir, and the polymer/ scCO2 ratio changes as a function of the pressure of CO2. Even in the open system, PS−PFMA block copolymers only swell up to equilibrium swelling ratio and do not reach infinite swelling or dissolution. As noted in the previous section, in the typical equilibrium phase, the lamellar and hexagonal species are in coexistence, as is widely observed for the BCP/solvent mixture. However, in the BCP and scCO2 system, this may not be the case. If the hexagonal and lamellar phases coexist in a closed system, the chemical potentials, μ, between the two phases [hexagonal (H) and lamellar (L)] must be balanced for the polymer (p) as well as CO2:

Figure 5. SEM image of PS−PFMA 13 film after the supercritical CO2 process at 27.5 MPa (top view); the surface covering layer (ca. 10 nm) was eliminated with an ion etcher. The scale bar indicates 100 nm.

the SEM image of PS−PFMA 13 prepared by the porous process, which is described in the Experimental Section. This image demonstrates that the PS−PFMAs form spherical closed cells. This spherical closed cell structure consists of an empty core surrounded by the PFMA shell in a PS matrix. A detailed discussion of porous structure formation by swelling and deswelling with CO2 can be found elsewhere, e.g., Yokoyama et al.8 Based on the SANS measurements, the “apparent” phase diagram was constructed as presented in Figure 6. The phase diagram indicates that PS−PFMA 20, which exists in the hexagonal phase at 0.1 MPa, shows multiple OOTs. PS−PFMA 28, which forms lamella at 0.1 MPa, shows a phase transition to the inverted phase. On the other hand, PS−PFMA 13 and PS− PFMA 9, which exist in the sphere domain at 0.1 MPa, do not show any transition. It is noteworthy that this “apparent” phase diagram may contain some nonequilibrium structures, as discussed in following part of this section. It is predicted that in lyotropic systems coexistence may occur between adjacent phases in the phase diagram.19 Previous study of BCP and a liquid mixture showed that the lamellar and hexagonal phases coexist in a wide region of the phase diagram.5,20,21 In particular, the coexistence of lamellar and hexagonal phases is apparent instead of the gyroid phase, and such coexistence is supported by the phase rule. Herein, the coexistence of lamellar and hexagonal phases in CO2 seems to be in equilibrium, similar to the ordinary lyotropic system. However, the relative ratio between the two phases shows some hysteresis and time evolution, which suggests that the coexistence is not the equilibrium state. For further clarification,

μpH = μpL H L μCO = μCO 2

2

(2)

where H and L denote the hexagonal and lamellar phases, respectively. This system can be characterized by four variables: pressure (P), temperature (T), and concentration (φ) of each phase, where the latter can be expressed as

φH =

φL =

H NCO 2

NpH

(3)

L NCO 2

NpL

(4)

where N is the particle number. Because these four variables are restricted by two equations for the chemical potentials, in this system, the number of thermodynamic degrees of freedom ( f) E

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Macromolecules is 2 according to Gibbs’ phase rule, f = 2 + C − P, where C and P represent the numbers of components and phases, respectively. When f = 2 in the two coexistence region, P and T can be determined independently; the coexistence of L and H phases is allowed. In contrast, the system of BCP swollen with scCO 2 controlled by pressure is an open system, where the chemical potential of CO2 in the reservoir is also balanced with CO2 in the polymer mixture: μpH = μpL H L R μCO = μCO = μCO 2

2

2

(5)

where R denotes “reservoir”; the phase consists of pure scCO2. It is not necessary to define φR because CO2 is the sole species in the reservoir. In this open system, the four variables are restricted by three equations; therefore, there is one degree of freedom (f = 1). When there is only one degree of freedom, T and P cannot be independently varied; therefore, equilibrium coexistence of the lamellar and hexagonal phases is possible only at the boundary between the two phases in the P−T phase diagram, and no two phase coexisting region should be observed. The evidence of nonequilibrium coexistence is presented in the Supporting Information. The nature of the SCF may account for this phase behavior. In general, the time scale of scCO2 fluctuation should be much shorter than the relaxation time of BCP. In addition, the fluctuation scale of CO2 is small in this temperature and pressure range. However, fluctuation of the SCF might couple with the two neighboring phases with a small free energy difference. For example, higher and lower scCO2 densities may induce formation of lamellar and hexagonal phases, respectively. It is possible that density fluctuation of CO2 may cause switching between both phases and induce two phase coexistence on the grain scale. Pressure Dependence of the Domain Spacing. Figure 7a shows the domain spacing, d, for each BCP extracted from the first-order peak position of the SANS profile [peak positions, q, were converted to domain spacing, d, using the relation: d = 2π/q]. The domain spacing of sphere-forming PS−PFMA increases monotonically with increasing pressure. In contrast, the domain spacing of the lamellar species is almost independent of pressure. The lamellar pitch of PS−PFMA 20 also remains constant with variation of the pressure. As shown in Figure 7b, in the pressure range of 10−30 MPa, d of the lamellar domain of PS−PFMA 20 is almost constant, whereas the domain spacing of the inverted hexagonal phase increases significantly with pressure. This result indicates that the domain spacing of the lamellae does not increase with pressure, whereas the domain spacing of the other structures increases with pressure. The increased domain spacing appears to be related to swelling of entire sample, but the questions of what happened in the lamellae and did the lamellae swell at all remain to be answered. To answer this question, a macroscopic swelling experiment was conducted. Swelling of BCPs in CO2 can be quantified by thickness measurements using the reflectivity of visible light on the BCP films on silicon wafers.22 The thickness of the PS− PFMA 13 (spherical), PS−PFMA 23 (hexagonal), and PS− PFMA 28 (lamellar) films was measured in CO2, and the swelling ratios were determined as shown in Figure 8. The film

Figure 7. Lattice constant of PS−PFMAs with CO2 versus pressure. (a) Lattice constants of lamella-forming sample and sphere-forming sample. Circles indicate PS−PFMA 28 (lamella), and inverted triangles indicate PS−PFMA 13 (sphere). (b) Lattice constant of PS−PFMA 20. Squares denote PFMA-core cylinder, circles denote lamella, and triangles denote PS-core cylinder.

thickness generally increased with increasing pressure, irrespective of the morphology. In general, the domain spacing, d, is scaled by the polymer concentration, φ:5,14

Figure 8. Thickness of PS−PFMA films swollen by CO2 versus pressure. F

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d ∼ φα

(6)

The value of φ was calculated from the swelling ratio (see Figure 8) and compared with d determined via SANS (see Figure 7). Figure 9 presents the plots of the domain spacing as

Figure 10. Conceptualization of directional PFMA swelling. Because of the large interaction (χ) between PS and PFMA and the low degree of polymerization of PFMA, PFMA would be fully stretched normal to the domain interface under no solvent/lower pressure conditions. When the mixture of PS−PFMA and CO2 is pressurized and the PFMA domain is swollen by CO2, PS−PFMA can only swell in the parallel direction.

system, adding solvent into the minor domains decreases the spontaneous curvature. There are two factors that reduce the curvature of domains: one is increasing radius, and the other is morphological transition, such as a sphere-to-cylinder transition. Because the size of the BCP domains is restricted by the length of the BCP chains, in bulk BCP, the former factor increases the elastic energy of the BCP chains to induce morphological transition. For example, the mean curvature decreases from 1/R in the spheres to 1/(2R) in cylinders having the same radius, R (see Figure 11a).

Figure 9. Polymer concentration dependence of the lattice constant.

a function of the corresponding concentration, φ. The exponents (α) determined from the data in Figure 9 are −0.05, −1.6, and −4.1 for the lamellae, cylinders, and spheres, respectively.23 If a solvent interacts neutrally with both blocks, the dilution effect dominates and α must be positive.5 If the solvent preferentially swells one block, the stronger the solvent selectivity, the smaller α becomes and eventually reaches a negative value. Because CO2 is strongly selective toward the PFMA blocks, a large negative value of α is expected. The cylindrical and spherical species large negative α values and satisfy the strong selectivity condition; however, for the lamellae, α is close to 0, suggesting only weak selectivity. The value of α does not simply depend on the selectivity of CO2 but clearly depends on the morphology of the BCPs. Therefore, swelling is restricted by the morphology and the chain conformation. The fluoroalkyl side groups of PFMA repel PS, with a relatively large Flory−Huggins parameter, χ, between PFMA and PS. In addition, the degree of polymerization of PFMA is relatively low (only 3−16 units; Table 1) due to the large perfluorooctylethyl methacrylate monomer unit. Thus, the repulsion between PS and PFMA easily outweighs the entropy loss of the main chain conformation. Thus, it is plausible that the PFMA chains are stretched in the neat bulk state (see Figure 10). In this situation, even if PFMA is selectively swollen by a large amount of CO2, PS−PFMA cannot swell any further in the direction normal to the interface between PS and PFMA. Consequently, CO2 induces swelling in the direction parallel to the interface and relaxes the stretched BCP chains. Such swelling in the direction parallel to the interface results in minimal change of the lamella domain spacing and an α value close to zero. On the other hand, swelling parallel to the interface in the cylindrical and spherical species inevitably increases the radius and hence the domain spacing. Therefore, α has a negative value. Phase Behavior of Sphere Domain. In general, the spontaneous curvature of the domains decreases with increasing volume of the minor domains. In the BCP/selective solvent

Figure 11. Schematic illustrations of the chain conformation and morphology in swollen spherical domains: (a) ordinary transition from sphere to cylinder due to CO2 swelling; (b) proposed mechanism by which fully stretched chain of PFMA is strongly segregated from PS swollen parallel to the interface only. Core−shell separation in sphere domains may occur.

If the radius of the sphere increases to accommodate the increasing effective volume of the minority domains with CO2, the chains would be stretched in the direction perpendicular to the interface. Therefore, the elastic energy of the BCP chains hinders any significant increase of the sphere radius. The other option for accommodating CO2 in the spherical domains is through core−shell separation, in which BCP swells parallel to the interface and leaves empty cores filled with CO2, as in Figure 11b. In a closed system such as the BCP and ordinary liquid mixture, core−shell separation in the sphere domain is hindered by loss of the translational entropy of the solvent. However, in the current open system comprising CO2 and PFMA, the CO2 in the core is chemical potentially balanced G

DOI: 10.1021/acs.macromol.5b00162 Macromolecules XXXX, XXX, XXX−XXX

Macromolecules

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ACKNOWLEDGMENTS This work was performed using SANS-U of the Institute for Solid State Physics, the University of Tokyo (Proposal No. 8904B and 9608) This research has been financially supported by PRESTO-JST.

with the reservoir of CO2. Therefore, core−shell separation with the CO2 core may not significantly increase the free energy of the system. This hypothesis is compatible with the observation that the lattice constant increases significantly while maintaining the spherical domains without any transition to the cylindrical phase. As was observed for the lamellar morphology swollen with CO2, the bilayers of lamellae swell only in the direction parallel to the lamellae (see previous subsection); therefore, such swelling also enhances introduction of the CO2 core into the spherical morphology. In addition to the slower kinetics of the morphological transition of BCP from spherical-to-cylindrical domains, relatively fast swelling with SCF may be operative.

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CONCLUSIONS The phase behavior of mixtures of polystyrene-b-poly[2(perfluorooctylethyl) methacrylate]s (PS−PFMAs) and scCO2 was evaluated on the basis of in situ SANS measurements. Phase transitions from hexagonal (PFMA-core) cylinders → coexistence of lamellar and hexagonal (PFMAcore) phases → lamellae → coexistence of lamellar and hexagonal (PS-core) cylindrical phases were induced by variation of the pressure from 0.1 to 30 MPa. The coexistence of lamella and hexagonal phases is not an equilibrium condition as supported by the phase rule. Such metastable phase coexistence might be induced by density fluctuation of scCO2. The quantitative relationship between the domain spacing and macroscopic swelling ratio in scCO2 was analyzed. Swelling of PS−PFMA with CO2 increases the domain spacings of the cylindrical and spherical domains. In contrast, the domain spacing of the lamellar phase remains constant upon swelling with CO2. It is postulated that the PFMA chains are fully stretched due to strong segregation of PS and PFMA, and further swelling of the BCP chains perpendicular to the interface is hindered. Under such circumstances, the lamellae only swell parallel to the interface with almost constant domain spacing. On the other hand, the spherical and cylindrical domains cannot simply swell in the direction parallel to the interface. Such parallel swelling also increases the radius. For the cylindrical domains, a relatively smooth transition to lamellae occurs to accommodate CO2 in the PFMA domains. However, the spherical domains show no sign of morphological transition despite an increase in the domain spacing and sphere diameter. This discrepancy could be explained by the core− shell separation of CO2 in the spherical PFMA domains. Further investigation is necessary to probe the core−shell separation. ASSOCIATED CONTENT

S Supporting Information *

Evidence of nonequilibrium coexistence; Figures S1 and S2. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.5b00162.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (H.Y.). Notes

The authors declare no competing financial interest. H

DOI: 10.1021/acs.macromol.5b00162 Macromolecules XXXX, XXX, XXX−XXX