Introduction

Block copolymers (BCP) can form diverse structures with a periodicity of several tens of nanometers, both in bulk and in thin films. Recently, BCP thin films have attracted great attention as materials applicable to several fields, for example, nanolithography,1, 2, 3 solar cells,4, 5, 6 size-selective separation7, 8 and adhesive materials.9, 10 In the bulk state, a microphase-separated structure is predicted by the Flory–Huggins interaction parameter, the degree of polymerization and the block volume fraction,11, 12, 13 while in thin film, the film thickness,14, 15 substrate–polymer interaction and polymer–air interaction16 must also be considered. Although the phase-separation behavior of BCP in thin films is more complicated, controlling the morphology, orientation and size of the structure is necessary for practical use. This need has motivated many studies with respect to orientation control methodologies, such as film thickness,14, 15, 17, 18 surface free energy,18, 19, 20, 21, 22, 23, 24 surface topology,19, 25, 26, 27 external applied fields28, 29, 30, 31, 32, 33, 34 and solvent vapor or thermal annealing.21, 35, 36, 37, 38, 39, 40, 41, 42 Because the functionality and physical properties are also strongly related to the structure and the mobility in the vicinity of the interface, a detailed description of the structure is required. Thus, a number of characterization methods, such as atomic force microscopy (AFM), electron microscopy, dynamic secondary ion mass spectrometry (DSIMS), X-ray photoelectron spectroscopy (XPS), grazing-incidence small-angle X-ray or neutron scattering (GISAXS, GISANS) and X-ray or neutron reflectivity (XRR, NR),17, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56 have been used to study the structure of BCP thin films.

Gu et al.57 performed an in situ GISAXS measurement of a BCP thin film during solvent vapor annealing to reveal the changes in the microphase-separated structure. According to their report, the swelling ratio, that is, the thickness of the swollen film divided by the original thickness, and the solvent removal rate affect not only the domain spacing but also the lateral ordering. Furthermore, the swelling ratio also influences the grain size. Hence, the swelling ratio and solvent removal rate have a key role in structure development during solvent vapor annealing. Albert et al.58 investigated the effects of surface free energy on the wetting behavior of BCP prepared on a Si substrate with a nearly linear gradient of surface free energy. They showed that the wetting behavior of poly(styrene-b-methyl methacrylate) on the chemically modified Si substrate strongly depends on the surface free energies. Although many studies related to BCP morphology, orientation, wetting behaviors and so on have been reported, the depth profile of the phase-separation behavior is still unknown. In the phase-separation behavior of BCP thin films, selective segregation at the polymer–substrate and air–polymer interfaces due to the difference of the surface (interfacial) free energy, microdomain orientation and relaxation of domain spacing over different time scales must be taken into account to investigate the structure development. Thus, further precise structural analysis must be conducted. In addition, the higher mobility of polymer chains in the vicinity of the air surface and interactions at the interfaces cause changes to the structure and orientation with increasing depth.49, 59, 60 To achieve depth-resolved structure analysis, several approaches have been employed. DSIMS can reveal BCP morphology and polymer chain diffusion with increasing depth.45, 46 Recently, time-of-flight (ToF) SIMS with an ion cluster beam was reported to be a particularly well-suited technique that enables the in-depth profiling of polymers.61 Müller-Buschbaum and co-workers have developed the GISANS measurement, which possesses depth sensitivity, for BCP thin films.50, 52, 62 Moreover, the GISANS measurement provides structure information near not only the air–polymer interface but also the polymer-substrate surface because a neutron beam can propagate into a silicon substrate. SAXS and GISAXS measurements have often been conducted using X-ray energies of 8–13 keV (hard X-ray). However, under this condition, the X-ray penetration depth rapidly reaches micrometer order, which is generally greater than the thickness of the probed films. Near the critical angle of total reflection αc at the surface, a depth-resolved GISAXS measurement with hard X-rays is impractical. Recently, Okuda et al.63 introduced a depth-sensitive GISAXS technique utilizing soft X-rays with an X-ray energy of 1.77 keV. They investigated the structural relaxation near the surface and the dynamic heterogeneity of polymer chains in thin films with this technique. We have also reported a depth-resolved structure analysis with GISAXS measurement using tender (soft) X-ray.64 It was revealed that a polystyrene-b-poly(2-vinylpyridine) thin film formed a hexagonally close-packed cylinder structure aligned parallel to the surface that deformed along the depth direction in the thin film (thickness 420 nm), while the deformation was relaxed in the vicinity of the surface.

In this report, we use GISAXS measurements to investigate the phase-separation behavior of poly(methyl methacrylate-b-n-butyl acrylate) (PMMA-PnBA) forming a lamellar structure aligned parallel to the substrate after appropriate thermal annealing. Both components of PMMA-PnBA possess polarity, and the phase-separated PMMA-PnBA is a thermoplastic elastomer. Thus, PMMA-PnBA is applicable as a pressure sensitive adhesive (PSA) material. Understanding phase-separation behavior in films (thin films) is essentially important to advance the functionality of PMMA-PnBA as a PSA material. Herein, we investigated the structure development through parameters such as the degree of lamellar orientation and the relaxation of the lamellar domain spacing using GISAXS. The time scale of each process was also evaluated. As a result, the time scale of the orientation was found to be shorter than that of the relaxation. Moreover, we also performed GISAXS measurement with tender X-rays for depth-resolved structure analysis. This technique revealed that the domain spacing of the lamellar structure was slightly larger in the vicinity of the air surface and was closer to the value of the bulk state inside the film. This result indicates that the relaxation of the domain spacing is faster near the air surface, arising from the higher mobility of the polymer chains.

Materials and methods

Materials

Methyl methacrylate (MMA), tert-butyl acrylate (tBA) and N,N,N′,N″,N″-pentamethyldiethylenetriamine (PMDETA) were purchased from Sigma-Aldrich Co., Ltd (St Louis, MO, USA), p-Toluenesulfonyl chloride (TsCl), CuBr, anisole, 1-butanol, p-toluenesulfonic acid monohydrate (PTSA), toluene, n-hexane, methanol and tetrahydrofuran (THF) were obtained from Nacalai Tesque (Japan). MMA and tBA were purified by distillation over aluminum oxide granules before polymerization, and other reagents were used as received.

Synthesis of PMMA-b-PnBA

To obtain PMMA-PnBA (Mn=32000, Mw/Mn=1.17, fPMMA=0.44), poly(methyl methacrylate-b-tert-butyl acrylate) (PMMA-PtBA) was synthesized via atom transfer radical polymerization (ATRP), followed by transesterification. ATRP is known as a powerful tool to synthesize various block copolymers, as comprehensively reviewed elsewhere.65 Herein, a typical ATRP procedure was used as reported previously.36, 66 MMA, TsCl, CuBr, OMDETA and anisole were added to a round-bottomed flask. The flask was degassed with several freeze–pump–thaw cycles, sealed in vacuum and immersed in an oil bath at 90 °C for 3 h to promote the polymerization reaction. After the reaction time, the flask was exposed to air, and the solution was stirred with active aluminum powder for several hours to remove the catalysts. Subsequently, PMMA macroinitiator was precipitated in a large amount of n-hexane, followed by filtration and drying in a vacuum oven. Chain extensions were performed using a similar procedure. PMMA macroinitiator, tBA, CuBr, PMDETA and anisole were added to a round-bottom flask. After several freeze–pump–thaw cycles, the flask was sealed and immersed in an oil bath at 100 °C to start polymerization. After 24 h, the PMMA-PtBA block copolymer was precipitated in a large volume of a methanol/water (9/1 vol) mixture, followed by drying in a vacuum oven.

Transesterification was conducted to obtain PMMA-PnBA. The synthesized PS-PtBA, PTSA (0.1 equivalent of tBA unit), 1-butanol (10 equivalent of tBA unit) and toluene (to fully dissolve the block copolymer) were added to a round-bottom flask. The flask was immersed in an oil bath at 120 °C to promote the transesterification of tBA to nBA. After 48 h, PMMA-PnBA was precipitated in a large amount of methanol, followed by drying in a vacuum oven (the exchange rate was > 99% as revealed by NMR).

To determine the molecular weights and polydispersity indices of the synthesized polymers, size exclusion chromatography (SEC) was performed under the following conditions: in THF (1 ml per min) at 313 K on four polystyrene gel columns (Tosoh TSK, Tokyo, Japan), gel GMH (base size 7 mm) and G400H, G200H and G100H (5 mm), which were connected to a Tosoh CCPE pump (Tosoh) and ERC-7522 RI reactive index detector (ERMA Inc, Tokyo, Japan). The SEC columns were calibrated against standard PMMA (Tosoh) samples.

Proton nuclear magnetic resonance (1H NMR) spectra were recorded with a Bruker 200M NMR instrument with tetramethylsilane (TMS) as the internal standard, using CDCl3 as the solvent at room temperature.

SEC and NMR charts of block copolymer are provided in the Supplementary Figures S1 and S2.

Preparation of thin films

For thin films, 5 wt% polymer solutions were prepared with THF, followed by spin casting on a silicon substrate at 3000 r.p.m. for 30 s. The thin films were dried at room temperature. Subsequently, thermal annealing was performed at 160 °C. The thickness of the thin films was measured to be ~280±30 nm using an Optical Nanogauge C10178-01 optical interferometer (Hamamatsu Photonics, Co., Ltd, Japan).

Grazing-incidence small-angle X-ray scattering

To study the microphase-separated structures in thin films, GISAXS measurements utilizing hard X-ray and tender (soft) X-ray were performed. Hard X-ray GISAXS measurements were conducted at beamlines BL6A and BL10C of the KEK Photon Factory in Tsukuba, Japan, and BL03XU at SPring-8 in Hyogo, Japan,67, 68 with wavelengths of 0.15 (BL6A), 0.1488 (BL10C) and 0.1 nm (BL03XU). At beamlines BL6A and BL10C, PILATUS 1M (Dectris) and PILATUS 2M (Dectris) detectors were used, which were set at positions 2~3 m from the sample position. In BL03XU, a charge-coupled device with an image intensifier (II-CCD, Hamamatsu Photonics Co., Ltd) was used as the detector; it was positioned 2 m away from the sample position. Tender X-ray GISAXS measurements were performed at BL15A2 in the KEK Photon Factory. Tender and soft X-ray GISAXS have recently been used as powerful tools for surface-sensitive and depth-resolved structure analysis of thin films.63, 64, 69, 70 BL15A2 offers X-rays in a wide energy range, from 2.1 to 15 keV (with an energy resolution of 2 × 10−4). Herein, the X-ray energy was set at 2.40 keV (corresponding to a wavelength of 5.16 Å), and the sample to detector distance was ~830 mm. To record the GISAXS images, PILATUS 2 M, which is designed to operate under vacuum, was used. All detectors were calibrated with lead stearate prepared in-house (d=5.01 nm) and chicken tendon collagen (d=65.3 nm). The magnitude of the scattering vector is given by q=4πsin θ/λ, where λ is the X-ray wavelength and 2θ is the scattering angle. The scattering vector qz denotes the component perpendicular to the film surface. The qx and qy are the scattering vector components in the sample surface, perpendicular to and parallel to the X-ray beam, respectively. For each set I(y,z), the detector pixels are converted into an exit angle αf perpendicular to the surface and an angle ψ parallel to the surface by simple geometrical considerations, resulting in a set I(ψ,αf). Using

and

where αi is the incident angle that is hereafter defined for convenience as the angle between the incident X-ray and the surface. This data set was further converted into I(qy, qz).

We confirmed that both PMMA-PnBA thick (1 mm) and thin films (spin cast) formed lamellar morphology with given sufficient annealing temperature and time as indicated in Supplementary Figures S3 (SAXS) and S4 (GISAXS), respectively.

Penetration depth of X-ray

The X-ray penetration depth Λ is defined as the depth at which the X-ray intensity is attenuated by 1/e. The value of Λ depends on the X-ray energy (in other words, the wavelength λ), the critical angle of total reflection αc and the angle of incidence αi. Under this definition, Λ is given by71

where β is the imaginary part of the complex refractive index. The critical angle αi; δ, which specifies the deviation from the real part of the refractive index; and β are given by

where re is the classical electron radius (2.82 × 10−5 Å), NA is Avogadro’s number, ρM is the mass density, wZ is the fraction of element Z, AZ is the relative atomic mass, f0Z is the non-resonant term of the atomic scattering factor corresponding to the atomic number, and fZ′(E) and fZ″(E) are the real and imaginary parts of the anomalous dispersion for the incident X-ray energy E. For example, here we used 4.2503 × 10−5 for δ and 9.4521 × 10−7 for β of PnBA at 2.40 keV. Furthermore, using Equation (5), the critical angle of total reflection was calculated to be 0.528°. Figure 1 shows the calculated penetration depth of PMMA-PnBA. It is difficult to precisely control the penetration depth Λ at the nanometer scale for a GISAXS experiment conducted using hard X-rays (1.00–1.50 Å) because the value of Λ rises abruptly at αc. However, it can be seen that as the X-ray energy decreases (wavelength increases), Λ changes more gradually near the critical angle and shows decreased depth values at angles greater than the critical angle. Therefore, better control of Λ is expected for depth-resolved GISAXS measurements using tender X-rays (2.40 keV) because the critical angle and attenuation coefficient values are much larger than those for the hard X-rays.

Figure 1
figure 1

Penetration depth calculated for the present PMMA-PnBA film for different X-ray wavelengths (different energies). Symbols indicate the penetration depth at the critical angle of total reflection. A full color version of this figure is available at Polymer Journal online.

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Results and discussion

Orientation and relaxation of lamellar structures

Two-dimensional (2D) GISAXS (hard X-ray) patterns with varying annealing times are summarized in Figure 2. The 2D GISAXS pattern of the as-spun sample (Figure 2a) is shaped like an ellipse, which may arise from poorly ordered or kinetically frozen morphology. Partially intense scattering was observed at qz values of 0.25–0.28 nm−1, where it was intensified by the so-called Yoneda peak, which does not correspond to a specific orientation. This result suggests that PMMA-PnBA (as cast film) does not orient without thermal annealing. However, after thermal annealing for even 1 min, the scattering intensity around qy=0, that is, the sides of the beam stop, became strong. In addition, two clear ring-shaped scattering patterns similar to the Debye–Scherrer rings were observed. Each scattering pattern can be assigned to scattering contributions arising from transmitted X-rays (denoted as T) or reflected X-rays (denoted as R). This phenomenon is typical of GISAXS measurements.72, 73 The scattering intensity around qy=0 becomes stronger with increasing annealing time. This change in GISAXS patterns indicates the growth of the parallel orientation of the lamellar microphase-separated structure. To evaluate the degree of orientation quantitatively, the azimuthal angle dependence of the scattering intensity is normally analyzed in the case of normal-transmission SAXS. In the GISAXS geometry, it is quite difficult to analyze the degree of orientation in this way. It may be preferable to consider the scattering intensity ratio of Iparallel (parallel lamellae) to Iin-plane (perpendicular lamellae) to estimate the degree of orientation. The scattering intensity in-plane at qy=0.29 is essentially produced by the overlapping scattering contributions of transmitted and reflected X-rays, and it also includes the Yoneda band. It is quite difficult to deconvolve the overlapping intensity into individual components. In addition, these scattering contributions to the in-plane intensity change as the incident angle αi varies. Under the present experimental conditions, the GISAXS patterns of thin films with different annealing times were obtained independently, and each pattern was measured with different incident angles. In this situation, the change of the in-plane intensity depends not only on the orientation but also the degree of overlapping of the scatterings discussed above. Quantitative analysis of the degree of orientation still comes with difficulty because of these reasons. Thus, to discuss the orientation behavior qualitatively, the apparent scattering intensity of the parallel orientation (Iparallel=Ipara0+Ipara,BG) was compared with the scattering intensity of a random orientation (Irandom=Iran0+Iran,BG), as shown in Figure 3b. The value of Iparallel was read from nearest position to the beam stop (near a qy value of 0). The value of Irandom was obtained from the position where qy=0.2 nm−1 and a qz position on the Debye–Scherrer-like ring (assuming a random orientation). Here, Ipara0 and Iran0 are true values of parallel and random components, respectively. Both experimentally obtained intensities (Iparallel and Irandom) include what are essentially background scatterings, Ipara,BG and Iran,BG, respectively. The value of Iparallel/Irandom was used as a measure of the orientation behavior, although it is quite difficult to analyze the degree of the orientation from the value of Iparallel/Irandom in GISAXS quantitatively because of the different X-ray transmission and reflectivity values, which depend on the film thickness, surface roughness and incident angles (also background), and Irandom is still somewhat variable under the present experimental condition. Figure 3a presents plots of the values of Iparallel/Irandom as a function of annealing time. Orientation is nearly complete after annealing at 160 °C for 60 min.

Figure 2
figure 2

GISAXS patterns (hard X-ray, 1.488 Å) of PMMA-PnBA thin films as cast (a) and annealed at 160 °C for different annealing times, (b) 1, (c) 3, (d) 5 and (e) 10 min. R and T represent the scattering from the reflected and transmitted X-ray beam, respectively.

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Figure 3
figure 3

(a) Time evolution of the lamellar orientation (blue solid symbols) and the relaxation of the lamellar domain spacing (red filled symbols). The solid lines are drawn as a guide for the eyes. The dotted line indicates the D|| value of the bulk. The open circle shows the D|| value near the surface. The scattering intensity used for estimation of the apparent degree of orientation is shown in b. The intensity of the parallel and random components at fixed positions on the Debye–Scherrer-like ring arising from transmitted X-ray (bottom dashed curves, upper one is coming from reflected X-ray) was used. A full color version of this figure is available at Polymer Journal online.

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The GISAXS measurement provided structure information about the domain spacing of the lamellar morphology. The parallel lamellar structure preferentially forms as described above. The domain spacing (D||) of the lamellar structures with alignment parallel to the surface was estimated. To determine the accurate domain spacing, the distorted wave Born approximation (DWBA) was applied to the analysis of the GISAXS patterns. The scattering contributions from the transmitted X-rays (Transmission) and reflected X-rays (Reflection) are notable in the GISAXS measurement. The peak positions of each scattering component along the qz direction can be estimated using DWBA as follows;72, 73, 74

where m represents the peak order, which is unity for this case. The upper (−) and lower (+) branches in the equation indicate the peak positions of the transmitted and reflected beams, respectively. Figure 4 shows the experimentally obtained Bragg spots as a function of the angle of incidence for PMMA-PnBA annealed for 240 min. When D was set to 21.5 nm, the calculation using Equation (8) gave the best fit for all Bragg spots, as shown by the dashed line in Figure 4. The values of D|| estimated in this way for all annealed samples were also plotted as a function of annealing time in Figure 3a. The value of D|| approached the domain spacing of the bulk sample (Dbulk, measured independently to be 21.6 nm, Supplementary Figure S3) with increasing annealing time. The domain spacing of the parallel-oriented structure was slightly smaller than that of the bulk, even after thermal annealing for 4 h. The polymer chains were fixed on the substrate, and the film thickness decreased during the rapid evaporation of the solvent. Consequently, the lamellar structure was deformed along the depth direction. However, thermal annealing induced the relaxation of the domain spacing. It seemed to take more than ~2 h to complete the relaxation of D|| to the bulk value.

Figure 4
figure 4

The incident angle dependence of the scattering positions along the qz direction of PMMA-PnBA thin film annealed for 240 min with X-ray energy of 8.265 keV (corresponding to the wavelength of 1.5 Å). Red and blue symbols represent the spots arising from transmitted and reflected X-ray, respectively. Dashed lines are the simulated qz using Equation (8) with a D|| of 21.5 nm and an αc of 0.153°. A full color version of this figure is available at Polymer Journal online.

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As is well known, the preferential wetting of surface and substrate interfaces has an important role in the orientation of thin films.16, 21 In this case, the surface energies of PMMA, PnBA and Si substrate are 41.1, 33.7 and 77.4±0.5 mJ m−2, respectively.20 According to the surface free energies, it is predicted that PMMA segregates to the surface at the silicon substrate, while PnBA segregates to the air surface. As a result of preferential wetting, a parallel orientation of the lamellar morphology is induced at both the air and polymer/substrate interfaces and propagates through the entire film.75 In fact, XPS measurements revealed that the molar fraction of PnBA at the surface was 80 mol% (repeat unit) in the cast film, and the PnBA component fully covered the surface even after annealing for only 60 s.

According to the results discussed here, the segregation of each component, orientation of the lamellae and relaxation of the domain spacing occurred on different time scales. It can be concluded that the PnBA first segregated at the air surface within 1 min of annealing (PMMA may have segregated at the interface). Second, the microphase-separated structure aligned parallel to the surface, followed by relaxation of the domain spacing. Because the estimation of the intensity ratio Iparallel/Irandom in a highly qualitative way includes a large uncertainty, we would like to provide as quantitative an interpretation of the observed behaviors as possible in the future.

Structure at near surface revealed by tender X-ray GISAXS measurement

It has been reported that polymer thin films have different mobilities that depend on the local region, that is, near the surface, in the interior, or near the polymer/substrate interface. It is quite intriguing to investigate whether depth dependence exists in the structure variation or, in other words, whether there is difference between the structure (orientation, morphology, d spacing and so on) in the vicinity of the surface and inside the film. Okuda et al.63 and our group64 have reported that tender X-ray GISAXS has the capability to perform depth-resolved analysis of the structure of thin films. In this study, tender X-ray GISAXS measurements of PMMA-PnBA thin films thermally annealed for 2 h were performed at various incident angles. As shown in Figures 5a and b, in the case where αi was below αc, the scattering (marked arrows) of the lamellar structure oriented parallel to the substrate was considerably diffused and broadened, while in the case where αi was greater than αc, the scattering became clear and sharp. The one-dimensional scattering profiles vertically cut at qy as close to the beam stop as possible are summarized in Figure 5c. As discussed above, the scattering peaks are assigned to transmission (denoted as T) and reflection (denoted as R). The peak position shifts and full width at half maximum (FWHM) magnitudes varied with the change of the incident angle. The shifts of the peak position can be explained using the DWBA (Equation (8)), as shown previously in Figure 4, while the change of the FWHM can be discussed in terms of the change of penetration depth of X-rays.63, 64

Figure 5
figure 5

Tender X-ray (2.40 keV) GISAXS patterns of PMMA-PnBA thin film annealed at 160 °C for 2 h measured at angles of incidence (a) 0.525° and (b) 0.625°. (c) One-dimensional profiles vertically cut at qy in the vicinity of the beam stop obtained at various incident angles αi. Each profile is shifted vertically to avoid overlapping. A full color version of this figure is available at Polymer Journal online.

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The FWHM depends on the grain size of a crystal as expressed with the Laue function, L(q)

where N is the number of the reflection plane. Here, the attenuation decay of the X-rays must be considered, that is, the X-ray wave decays exponentially. The Laue function can be re-expressed as

Because the scattering intensity is proportional to the square of the Laue function, the FWHM can be calculated simply.

The FWHMs along the qz direction obtained from the scattering peak of D|| (Transmission) are plotted as a function of the incident X-ray in Figure 6. As shown in Figure 6, the FWHM decreased remarkably in the vicinity of the critical angle of total reflection. Furthermore, the FWHM calculated using Equation (10) is also plotted in Figure 6. The calculated value also decreases drastically near the critical angle, indicating an identical trend to that observed in the experimental values. The experimental values are in accord with the calculated values for increasing penetration depth Λ given by Equation (4), indicating that the penetration depth can be controlled in agreement with the theory. Therefore, we conclude that the depth-resolved analysis was performed completely for the various incident angles considered in this measurement.

Figure 6
figure 6

FWHM values of Bragg peak of D|| obtained experimentally (filled circles) and calculated (diamond and dashed line) using Equation (10). A full color version of this figure is available at Polymer Journal online.

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In the case of GISAXS measurements utilizing soft X-rays, the effect of large Ewald sphere curvature on the GISAXS pattern cannot be neglected. Hence the curvature may affect the peak position and scattering intensity (distorted scattering pattern).76 If the curvature strongly affects the scattering peak positions, Equation (8) must be modified. Structure analysis of the same specimen (thermally annealed for 2 h) using Equation (8) was performed to confirm whether Equation (8) works out without any modification. Analysis of the incidence dependence of the scattering positions observed in Figure 5c using Equation (8) gave the same structural parameter, D||=21.4 (inside the film), that was obtained in the case of an X-ray energy of 2.40 keV (Supplementary Figure S5). Thus, it was concluded that Equation (8) worked well even in the tender X-ray regime within the observed q-range in this article.

Near the critical angle, surface-sensitive measurements are possible, as calculated by Equation (4) (Figure 1). When αi is below αc, X-ray waves reach the film surface but cannot propagate into the film. Only the evanescent wave can penetrate from the surface into the film. In this situation, the experimentally observed scattering spot αz along the qz direction is given by the sum of the incident angle αi and the scattering angle αs derived from the period of the observed structure. Thus, αs can be expressed as

Using Equation (11), the true qz value of the lamellar structure oriented parallel to the surface can be estimated using the experimentally observed peaks, that is, D|| can be estimated. In the case where αi was 0.525° (corresponding to a Λ of 32.4 nm), D|| was estimated to be 21.6 nm, which is equal to the 21.6 nm value of the bulk sample. The value of D|| near the surface is larger than the 21.4 nm value obtained from the DWBA simulation (inside the film). This result indicates that the domain spacing in the vicinity of the film surface preceded was relaxed to that of the interior. As reported previously, polymer chains near the surface possess higher mobility (lower glass transition temperature or viscosity).77, 78, 79 Moreover, the lamellar structure begins to orient from both the air/polymer and polymer/substrate interfaces, induced by segregation of one component of the BCP. Therefore, it can be concluded that the faster relaxation of the d spacing (D||) of the lamellar structure near the surface, causing the D value of the bulk to be reached, was caused by the faster segregation of the PnBA component at the surface and the higher mobility of the polymer chains in the vicinity of the surface.

Conclusion

We investigated the orientation behavior and the domain spacing relaxation of the phase-separated structure of PMMA-PnBA thin films using GISAXS. The PMMA-PnBA formed a lamellar structure, and the lamellar structure was aligned parallel to the substrate after thermal annealing. XPS measurements indicated that the segregation of the PnBA (PMMA) component occurred rapidly, within 1 min after annealing at 160 °C. The parallel orientation of the lamellar structure was observed successfully, and the domain spacing D|| was analyzed by the DWBA calculation. GISAXS measurements revealed that the apparent degree of orientation and the value of D|| increased with annealing time, while the domain spacing relaxation took a longer time than the orientation of the lamellae of the BCP. Moreover, we conducted low-energy GISAXS (tender X-ray) to enable the in-depth profiling of the microphase-separated structure. It was found that D|| in the vicinity of the surface was larger than inside the film, which indicates that the domain spacing near the surface relaxed faster than the inside, a phenomenon that arises from the higher mobility of the polymer chains. If the orientation behavior and precise time-dependent d spacing are analyzed more quantitatively, the local time scale of those attributes, which are dependent on the region, for example, near the surface or near the substrate (exhibiting spatial inhomogeneity) in the film will be discussed more precisely in future works.