Structural Analysis of Microphase Separated Interface in an ABC-Type

Apr 6, 2015 - Structural Analysis of Microphase Separated Interface in an ABC-Type Triblock Terpolymer by Combining Methods of Synchrotron-Radiation G...
0 downloads 11 Views 4MB Size
Download PDF
Article pubs.acs.org/Macromolecules

Structural Analysis of Microphase Separated Interface in an ABCType Triblock Terpolymer by Combining Methods of SynchrotronRadiation Grazing Incidence Small-Angle X‑ray Scattering and Electron Microtomography Ryohei Ishige,† Takeshi Higuchi,†,§ Xi Jiang,§ Kazuki Mita,∥ Hiroki Ogawa,⊥ Hideaki Yokoyama,# Atsushi Takahara,†,§,‡ and Hiroshi Jinnai*,†,‡,§ †

Institute for Materials Chemistry and Engineering (IMCE) and ‡International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan § Takahara Soft Interfaces Project, Exploratory Research for Advanced Technology (ERATO), Japan Science and Technology Agency (JST), 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan ∥ Sodegaura Center, Mitsui Chemicals, Inc., 580-32 Nagaura, Sodegaura, Chiba 299-0265, Japan ⊥ Japan Synchrotron Radiation Research Institute (JASRI/SPring-8), Sayo, Hyogo 679-5198, Japan # Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwano-ha, Kashiwa, Chiba 277-8561, Japan S Supporting Information *

ABSTRACT: Determination of the three-dimensional (3D) shape of microphase-separated block copolymers (BCPs) is essential to investigate the “packing frustration” of the constituent blocks, which dominates their self-assembled nanostructures. Electron tomography (ET) is often used to visualize the 3D shape of BCP interfaces in real space, with staining often employed to enhance contrast between domains of similar electron density. As the number of blocks in the BCP structure is increased and the accompanying microphaseseparated structure becomes more complicated, precise determination of interfacial structure from ET methods becomes progressively more difficult. Herein, the precise location of the interface was investigated for an intriguing complex double-helical structure formed by an ABC-type triblock terpolymer. The structure was characterized through the use of a novel structural analysis method combining the advantages of two dissimilar methods: intuitive real-space 3D observations provided by ET and quantitative, statistically accurate, nondestructive Fourier-space analysis provided by grazing-incidence smallangle X-ray scattering (GI-SAXS). The effect of staining on the helical structure is also discussed. interaction parameter, χ), as well as the packing (translational) entropy, govern the local three-dimensional (3D) shape of the interface under the constraint of distributing the chemical junction(s) along the interface.9,10 The local interfacial shape determines the global morphology of MPSs. Visualization and quantification of interfacial shape of MPSs is thereby an essential first step for fundamental understanding of the relationship between BCP molecular structure and the corresponding MPS. Jinnai et al. observed the 3D nanometer-scale interfacial structure for a bicontinuous gyroid structure using electron tomography (ET) and successfully measured the curvature

1. INTRODUCTION Recently, periodic nanostructures formed by the spontaneous microphase separation of block copolymers (BCPs) have been used as a promising key technology for nanoengineering applications, including templates for nanopatterning, electrolyte films, low-dielectric-constant (low-k) films, and nanoporous membranes.1−7 In these applications, the precise control of both microphase-separated structures (MPS) of BCPs and orientation is essential. Although complex nanostructures of BCPs were once thought to favor minimal contact between immiscible blocks, the actual shape of the interface deviates from such ideal topological surfaces because the microdomainforming blocks must uniformly fill space in the most entropically favored manner.8 In the strong segregation regime, the conformational entropy and repulsive interactions between the constituent blocks (as represented by the Flory−Huggins © 2015 American Chemical Society

Received: December 28, 2014 Revised: March 14, 2015 Published: April 6, 2015 2697

DOI: 10.1021/ma502596a Macromolecules 2015, 48, 2697−2705

Article

Macromolecules

2. EXPERIMENTAL SECTION

distribution of the complex nanostructure based on the 3D images.11,12 Numerical simulations based on self-consistent field theory8 have indicated that in order for the minority blocks to uniformly fill space, the interface should self-adjust so that no blocks are excessively stretched from their most favorable conformation. The “packing frustration” of the blocks is reflected in the curvature distribution. Jinnai et al. confirmed the importance of packing frustration in the stabilization of such complex nanostructures.11 By combining computer simulations with experimentally obtained ET 3D images, Morita et al. were able to visualize the anisotropic chain conformation near a bent interface of the lamellar phase of poly(styrene-b-isoprene) (SI).13 They used the experimentally determined interface as a boundary condition so that the chemical junctions between PS and PI blocks existed only at the interface. In these studies, the measurements were heavily dependent on the position and 3D shape of the BCP interface, and thus the precise and high resolution imaging of the interface is crucial. In transmission electron microscope (TEM) observations for polymeric materials, selective staining of one of the phases is often required. Such contrast enhancement for TEM necessitates special care, particularly in the quantitative analysis of BCP interfaces, because the staining protocol can potentially alter the position of the MPS interface. In order to eliminate (or at least, reduce) such image artifacts, staining is often carried out under controlled condition in which some experimental variables, e.g., temperature, time, and pressure, are fixed. A further requirement for TEM investigation is that the position of the interface must be verified by volumetric analysis of each phase (after the 3D reconstruction and segmentation), so that the output volume fraction matches the known composition of copolymer.11 However, such quantitative 3D imaging of interface becomes increasingly difficult as the number of components increases. Here, we have investigated the MPS interface formed in an ABC-type triblock terpolymer, poly(styrene-b-butadiene-bmethyl methacrylate) (SBM), which forms a complex interfacial structure. Our previous study revealed that SBM forms a double-helical structure of the poly(butadiene) (PB) wrapped around cylindrical poly(styrene) (PS) domains, which are arranged in a hexagonal fashion in the poly(methyl methacrylate) (PMMA) matrix. Although the double-helical structure has been clearly identified from ET observations,14,15 the structure of the interface between the helical PB and cylindrical PS domains has not yet been clarified. It is still unclear whether the PB helix penetrates into the PS cylindrical domains. To determine the interface between the PS core-cylinder and PB helical domains, we present a combined method utilizing real space and Fourier space methods to achieve a complete and quantitative structural characterization of a complex nanometer-scale interface structures. In this method, ET was used to provide a detailed 3D structural model of the complicated structure, which was then used to analyze 2D scattering profiles obtained from grazing incidence small-angle X-ray scattering (GI-SAXS) measurements for the same unstained sample and stained sample. The advantage of this method is that the staining processes are essentially not required, and structural parameters, including the precise position of the interface, can be evaluated with much higher accuracy than either ET or GI-SAXS alone.

2.1. Preparation Procedure of Oriented SBM Thin Film. Poly(styrene-b-butadiene-b-methyl methacrylate) (SBM) triblock terpolymer used for the following measurements were purchased from Polymer Source Inc., Dorval, Quebec, Canada. The numberaverage molecular weight (and volume fraction) of the PS, PB, and poly(methyl methacrylate) (PMMA) blocks in the SBM were 30 000 g/mol (0.21), 12 000 g/mol (0.10), and 110 100 g/mol (0.69), respectively. The polydispersity index was 1.06. A film of the poly(styrene-b-butadiene-b-methyl methacrylate) (SBM) triblock terpolymer deposited on a disk-shaped Si wafer was prepared by spin-coating from the 1 wt % chloroform solution (CHCl3).15 The size of the wafer was 25.4 mm diameter and 3 mm thickness. The film on the Si wafer was annealed under saturated CHCl3 vapor for 2 days at ambient temperature and gradually dried. This annealing protocol was found to give an oriented film where PS cylindrical domains preferably align perpendicular to the film surface.2 The film on the substrate before staining with OsO4 was used directly for the first GI-SAXS measurements. After the measurement, the very film on the Si wafer was then stained with OsO4 vapor and used for the second GI-SAXS measurements. Finally, for ET observation, the film (after the SAXS measurements) was floated off the Si wafer and ultramicrotomed to a thickness of ∼150 nm in film surface direction using an Ultracut UCT microtome (Leica, Germany) with a diamond knife at room temperature. The cross-sectional image perpendicular to the film surface was observed by ET. The same film was used for both the GISAXS measurements and the ET observation. Additionally, TEM observations were also conducted for different films used for the above ET observation and GI-SAXS measurements. The films used for TEM observation were prepared in same procedure as that for ET observation. 2.2. ET Observation Method. ET 3D observations were conducted using a JEM-2200FS microscope (JEOL, Ltd., Japan) operated at 200 kV and equipped with a slow-scan USC 4000 CCD camera (Gatan, Inc., USA). To obtain a 3D ET image, a series of TEM images were acquired at tilt angles in the range of ±75° at an angular interval of 1°. The electron dose to acquire each TEM image was 15 000 electrons/nm2. The tilt series of the TEM images were then aligned by the fiducial marker method, using gold nanoparticles as the markers.16 The tilt series of TEM images after the alignment were reconstructed by filtered back-projection.17 The alignment and reconstruction processes were carried out by using a homemade software. 2.3. TEM Observation of SBM Film. SBM films stained with different agents were observed by TEM with the same equipment and the same condition as those of ET observation. The SBM thin film was then floated off the substrate, transferred onto a TEM grid with a supporting membrane (polyvinyl formal), and stained on the grid. Iodine(I), osmium tetroxide (OsO4), and ruthenium tetroxide (RuO4) were used for the stained agents and selectively stained PMMA, PB, and PS domains, respectively. It should be noted that these films were different from the film used for GI-SAXS measurements, and the observed plane of TEM image was parallel to the film surface. 2.4. GI-SAXS Measurement Configuration. SAXS measurements in grazing incidence (GI) condition were conducted twice at BL03XU beamline in the SPring-8 (Japan Synchrotron Radiation Research Institute, Hyogo, Japan) for the thin film deposited on a Si wafer before and after staining process with OsO4. The wavelength of the X-ray beam (λ) was 0.1000 nm, and the camera length was 2270 and 2225 mm for the first and second measurements, respectively. The camera length was calibrated using silver behenate standard. The 2dimensional (2D) scattering profiles were exposed to a 3000 × 3000 pixel imaging plate (IP) with pixel size of 100 × 100 μm2 (Fujifilm Co., Tokyo, Japan). The IP was equipped on an R-AXIS IV++ system (Rigaku Co., Tokyo, Japan). Although, the experimental configuration, i.e., incidence angle of X-ray, was corresponding to GI-SAXS condition, X-ray beam was found to penetrate the film even though the incidence angle was smaller than the critical angle of the film possibly due to a roughness and convex curvature of the film surface. 2698

DOI: 10.1021/ma502596a Macromolecules 2015, 48, 2697−2705

Article

Macromolecules

Figure 1. TEM images of stained SBM films with different staining agents: (a) iodine, (b) OsO4, and (c) RuO4. The PMMA, PB, and PS domains were selectively stained in the images (a), (b), and (c), respectively. (d) Digitally sliced ET image of the cross section perpendicular to the surface of the SBM thin film stained with OsO4. (e) Magnified view of the stained dark region (PB domain) extracted from the 3D ET image.

ET was exactly the same film used for the GI-SAXS measurements below. The dark regions are the OsO4-stained PB domains. A magnified view of the dark region extracted from the 3D image is shown in Figure 1e. A double-helical structure of continuous tubes (continuous double helix) is observed, which is consistent with the microstructure previously reported by Jinnai et al.12 The sliced and 3D images show that the PB domains form a double helix of tubes with helical axes mostly perpendicular to the substrate surface. The helices were periodically arranged in the lateral direction. From the image, the helical pitch P, radius of the helix rh, and thickness of the PB domain (dark region) d, were estimated to be 28 ± 1, 14 ± 1, and 7.5 ± 1 nm, respectively. The PS blocks formed cylindrical domains inside the double helix. In addition, the right- and left-handed helices coexist in the image, and there seems to be no correlation of the phases between neighboring helices. 3.2. GI-SAXS Measurements. In general, GI-SAXS 2D profiles are interpreted as a superposition of two scattering 2D profiles: (1) scattering from the transmitted X-ray beam and (2) scattering from the reflected X-ray beam at the Si substrate interface.18,19 The origins of the reciprocal space in the two scattering profiles correspond to the transmitted and reflected X-ray beam positions, respectively (details are provided in Supporting Information). The profiles arising from the two different beams are essentially the same in the horizontal direction but can be distinguished by measuring the incident angle dependence in each profile; i.e., the profile from the transmitted beam does not change the position with αi, while that from reflected beam moves upward with increasing αi.

The details are discussed in section 3.2. Therefore, the measurements were not strictly conducted under ideal GI condition.

3. RESULTS AND DISCUSSION 3.1. TEM and ET Observations. TEM images of SBM films stained with different agents are shown in Figure 1. The observed planes were parallel to the film surface. The circular cross sections of the unstained (white) and stained (black) PS cylindrical domains are observed in the stained and unstained PMMA matrix in Figures 1a and 1c, respectively. These images indicate that the PS cylinders are aligned perpendicular to the film surface. Moreover, Figure 1c shows that PS cylindrical domain aligned in hexagonal fashion. In Figure 1b, PB domains are observed as black doughnut shape, indicating that the PB helical domains wraps around the PS cylindrical domain. The hexagonal alignment is not clearly seen in Figures 1a and 1b, and some possible causes can be considered: (1) the observed planes were not strictly perpendicular to the electron beam, and apparently the hexagonal arrangement seemed to be distorted even though it was not distorted; (2) the film and also the hexagonal arrangement were distorted in the floating process and/or the staining process after the floating process. However, the SBM film used for GI-SAXS measurements was stained with fixed on the Si wafer, and these problems were not essential for precise structural analysis by GI-SAXS. The most important conclusion is that these TEM images clearly demonstrate the segregation and location of three different blocks. Figure 1d presents a digitally sliced ET image showing the cross section of the SBM thin film perpendicular to the substrate surface. It should be noted that the film observed by 2699

DOI: 10.1021/ma502596a Macromolecules 2015, 48, 2697−2705

Article

Macromolecules

Figure 2. Thin-film SAXS profiles of (a) the unstained film and (b) the stained film. The incident angle αi for each image is inset in each image. Xray beam direction and the film thickness direction are defined as the y- and z-axes, respectively, as indicated in the images. (c) GI-SAXS configuration is schematically presented.

GI-SAXS images with incident angle αi = 0.08 and 0.16° for the unstained film and those with αi = 0.08, 0.10, 0.12, 0.14, and 0.16° are shown in Figures 2a and 2b, and the GI-SAXS configuration (the transmitted and reflected X-ray beam positions) is schematically illustrated in Figure 2c. The vertical and horizontal directions in the images are defined as the z- and x-axis, respectively. The stained thin film shows clearer (higher contrast) profiles and scattering positions in the profiles are more easily estimated than those in the unstained profiles. These results indicate that stained PB domains with OsO4 had much higher electron density than unstained PS and PMMA domains to give stronger electron-density contrast. In other words, the shape and arrangement of the stained PB domains dominate the scattering profile of the stained film. Incident angle dependence of the profiles is discussed based on the profiles of the stained film. In the profiles of the stained film, the sharp diffractions appear near z = z0 and z1 and broad scatterings appear near z = z2 and z3 (indicated by dashed lines in Figure 2b). The position z = z0 corresponds to the original direct beam position estimated from the Debye−Scherrer ring of silver behenate standard in transmitted configuration (without the substrate). In Figures 3a and 3b, line intensity profiles for these 2D profiles are plotted along the z-axis at x = x1 and x2 which are indicated by dotted vertical lines in Figure 2b (the profiles are mutually shifted in vertical direction for easy viewing). The height positions of the diffractions near z0 and z1 (hereafter z0_d and z1_d) and those of the scatterings near z2 and z3 (hereafter z2_s and z3_s) are indicated by dotted lines in Figures 3a and 3b. z1_d and z3_s clearly show incident angle dependence while z0_d and z2_s do not. The height positions of z1_d and z3_s are plotted with αi in Figure 3c. The solid lines in Figure 3c show the calculated position from the preset incident angle, αi. Therefore, the diffractions at z = z0_d and the scatterings at z = z2_s correspond to those from the transmitted X-ray beam, while the diffractions at z = z1_d and the scatterings at z = z3_s correspond to those from the reflected X-ray beam.

The above results, particularly incident angle dependence of z1_d, indicate that the X-ray beam penetrates throughout the film, even for the incident angles smaller than the critical angle, αc, of the films (the αc of the unstained film is larger than 0.11°, and that of the stained film should be larger than the unstained film). Thus, it is implied that there are surface roughness and convex curvature of the surface of the film. In this paper, however, the intensity profiles along the z-axis (vertical direction) are not used to estimate the structural parameters, and the surface roughness and surface curvature are not essential problem. The highest-contrast 2D GI-SAXS profiles were obtained with αi = 0.16° and αi = 0.10° for the unstained and stained films, respectively (Figures 4a and 4b). These profiles were used in the following structural analysis. It also should be noted that the same SBM sample was used for ET observation and GI-SAXS measurements to enable unambiguous construction of appropriate structural model. The angles α and 2θxy in the GI-SAXS 2D profiles are the vertical and horizontal components of the output angle, respectively. These angles were defined based on incident angle dependence of the patterns, as presented in Figure 3c. In both cases, the X-ray beam penetrated through the entire film (even though the αi was smaller than the critical angle of the film, as mentioned above). The unstained film shows a series of sharp diffractions near α = ±0.1°, while the stained film shows diffractions near α = −0.1° and 0.15°. Broad diffuse scatterings split into the left and right sides of the meridian were presented for the unstained and stained films near α = 0.2° and α = 0.3°, respectively. Consequently, the GI-SAXS profiles consist of two SAXS 2D profiles with different origins, which show diffraction spots on the equator and diffuse scattering off the equator. Herein, (ξ, η, ζ) are defined as Cartesian coordinate in reciprocal space, respectively, where the incident X-ray beam is in the yz-plane and tilted from the y-axis with αi, the film surface normal is parallel to the z-axis, and the origin is defined as the position of the transmitted or reflected X-ray beam, as 2700

DOI: 10.1021/ma502596a Macromolecules 2015, 48, 2697−2705

Article

Macromolecules

Figure 4. 2D GI-SAXS profiles for (a) the unstained thin film with αi = 0.16° and (b) stained thin film with αi = 0.10°. Inserted dashed lines represent the (i) 0th layer line for the reflected beam and (ii) Nth layer line for the transmitted beam. The height of the Nth layer line from the direct beam position corresponds to (P/N)−1. Cartesian coordinates (ξ, η, ζ) of the reciprocal spaces for the transmitted Xray are inserted of the profiles. hk indices of the 2D hexagonal lattice are inset in the unstained profile.

value of (P/N)−1. The line intensity profiles in the horizontal direction were analyzed at ζ = (P/N)−1, so-called layer line, where diffraction or scattering peaks appeared. 3.3. Theoretical Model for Intensity Calculation Based on ET Observation. A model for the SAXS analysis based on the ET real-space observations is shown in Figure 5, where PB domains form double helix around PS cylindrical domain. (Details of the derivation processes for the following equations are provided in the Supporting Information.) First, the SAXS intensity I(q) was calculated in the Born approximation, and then the effect of reflectivity at the surface and substrate interfaces was considered. The SAXS intensity I(q) derived from a paracrystal model consists of two terms: the lattice factor, L(q), and form factor, f(q), for particles in the lattice as given by20,21

Figure 3. Line intensity profiles on (a) x = x1 and (b) x = x2 on the 2D GI-SAXS profiles. The positions of z0, z1_d, z2, and z3_s are indicated by dotted lines (i), (ii), (iii), and (iv). (c) The position z1_d and z3_s, where diffractions and scatterings appear, respectively, are plotted with αi.

shown in Figure 4. The x-component of the reciprocal vector, ξ, is equal to sin θxy/λ regardless of the transmitted or reflected profiles, whereas the z-component, ζ, differs for the two profiles. The position of the origin for the transmitted profiles, i.e., transmitted beam position, was α = −0.16° and −0.10° for the unstained and stained films, respectively (Figure 4, yellow dotted lines). The ratio of ξ at the diffraction positions (indicated by white dashed lines as the zeroth layer in Figure 4) was 1:31/2: 2:71/2: ..., which indicates 2D hexagonal order parallel to the surface. The hk indices of 2D hexagonal lattice are inset in the unstained film profile (Figure 4a). Offequatorial diffuse scattering, which will be not present for a simple 2D hexagonal lattice of cylinders aligned perpendicular to the surface, were assigned to form factors of the helical structure. In Figure 4, the height position is referred to as the Nth layer line, where the integer N corresponds to the number of strands of helix, as explained in section 3.3. The height of the Nth layer line from the direct beam position corresponds to the

I(q) ∝ ⟨f (q)2 ⟩ − ⟨f (q)⟩2 + ⟨f (q)⟩2 L(q)

(1)

In eq 1, q is a scattering vector with components (qx, qy, qz) and |q| = 2π(ξ2 + η2 + ζ2)1/2. The brackets in eq 1 represent statistically averaged quantities. If there is no correlation between the phase of the neighboring helices, the lattice factor L(q) becomes 1, except for Z = 0; i.e., a 2D hexagonal lattice with lattice vectors a1 and a2 is sufficient to calculate I(q) and I(q) ∝ ⟨f(q)2⟩ except for Z = 0. The lattice factor L(q) for a 2D hexagonal lattices with infinite domain size (lattice vectors, a1 and a2, and the angle between the vectors, γ = 120°) aligned in 2701

DOI: 10.1021/ma502596a Macromolecules 2015, 48, 2697−2705

Article

Macromolecules I(q) = I(R ) ∝ ⟨f (R )2 ⟩ − ⟨f (R )⟩2 + ⟨f (R )⟩2

∫0

2π

L(qx , φ) dφ

(3)

In the CCV model mentioned above, the thickness of helix is neglected and assumed to be a wire, while the experimentally observed double helix of PB domains are not wires of negligible width, but tubes with finite thickness d, which is an independent parameter. The parameter, d, is able to be taken into account by introducing distribution functions D(rh), where the full width at half-maximum (fwhm) is equal to d, and using D(rh) to calculate ⟨f(q)2⟩ and ⟨f(q)⟩2. The statistically averaged quantities for f(q) in eq 2 are given by ⟨f (R )⟩ =

∫0

∞

D(rh)f (R ) drh ,

⟨f (R )2 ⟩ =

∫0

∞

D(rh)(f (R ))2 drh

(4) Figure 5. (a) Schematic model of the PB double helix around the PS cylinder. (b) Double helix around the cylinder forms a hexagonal lattice with lattice parameter a. The helical pitch P, radius of the helix, rh, diameter of the PB wire, d, and radius of the cylinder, rc, are indicated in (a). The hexagonal lattices freely rotate around the z-axis, resulting in ring-shaped diffraction on the ξ−η plane in reciprocal space, as shown in (c).

In eq 4, the distribution of rc is neglected. The calculated intensity in eq 3 is a line profile at the mN-th layer line (Z = mN/P). Comparing the observed line intensity, Iobs(q), with that calculated using eq 3, the characteristic parameters, including the radius of the helix, rh, tube thickness of the helix, d, radius of the PS cylinder, rc, lattice parameter, a, and degree of disorder, g, can be evaluated. These parameters are indicated in Figure 5. The helical pitch is estimated from the height of the first off-equatorial (Nth layer) line (Z = N/P, shown in Figure 4). 3.4. GI-SAXS Intensity Analysis Based on Model Calculation. The GI-SAXS line intensity profiles in the horizontal direction were analyzed in the Born approximation, because, although the scattering amplitude for GI-SAXS contains the reflectivity terms R(α), as in eq S1 of the Supporting Information, they do not affect the horizontal line intensity profile. Additionally, although αi was less than the critical angle of the SBM film for the stained and unstained films, the X-rays penetrated into the film. This result indicates that the surface roughness was large and refraction of the scattering X-rays at the surface could be neglected. The intensity, I(R), corresponds to the integrated intensity, Iobs(ξ)Δχ(ξ2 + (mN/P)2)1/2, in the horizontal direction because there was a slight misorientation around the surface normal direction (the relationship between I(R) and Iobs(ξ) is provided in the Supporting Information). Herein, Iobs(ξ) will be defined as the observed intensity profile, which was sector-averaged around the horizontal direction (the central angle of the sector Δχ was 2.5°), and ξ = R on the observed plane (ξ−ζ plane at η = 0). Following from the above discussions, a series of diffractions at α ≈ 0.1° and α ≈ 0.15° for the unstained and stained films, respectively, were identified as the zeroth layer line (Z = 0) diffractions from the reflected X-ray beam. Similarly, the broad scattering at α ≈ 0.2° for the unstained film and at α ≈ 0.3° for the stained film were identified as the Nth layer line (Z = N/P) scattering from the transmitted X-ray beam. These Nth layer lines are indicated by the dashed lines in Figure 4. Consequently, observed intensity, Iobs(ξ) was compared with I(R) calculated according to eq 3, using a commercial formula-manipulation software, Mathcad 14 (PTC Software, Needham, MA). The observed integrated intensity, Iobs(ξ)(ξ2 + (mN/P)2)1/2, and calculated intensity I(R) on these layer lines for the unstained and stained films are shown in Figure 6. The hk indices for the hexagonal lattice are indicated in the zeroth layer line diffraction profiles. To calculate I(R), two types of distribution functions were used for D(rh): a boxcar function,

the xy-plane is equal to multiple product of L1(q) L2(q), as elaborated by Hashimoto et al. (the equations are presented in Supporting Information).22 The L(q) contains two important parameters a and g and depends on azimuthal angle φ: a and g are averaged value of the lattice constant, ⟨|a1|⟩ = ⟨|a2|⟩, and the degree of disorder of the lattice constant, respectively, and φ is defined as angle between the a2 and η-axis. The form factor, f(q), consists of two terms: one is the form factor of PB helical domain, and another is that of PS cylindrical domain. The former is calculated based on the Cochran− Crick−Vand (CCV) model23 for a continuous helix, which assumes a wire helix with delta-function type electron density distribution, δ(r − rh) δ(φ − 2πz/P) (r = (x2 + y2)1/2). In present case, PB domain is assumed to form N-strand helix (N is an integer). The latter, form factor of a cylinder with infinite length, was already drivatived.22 In both cases, f(q) was calculated in a cylindrical coordinate to simplify the calculation and f(q) is given by eq 2. ⎧ J1(2πrcR ) ⎪ for Z = 0 ⎪ vPB J0 (2πRrh) + vPS 2πrcR f (q) = f (R ) = ⎨ ⎪ imNψ ⎪e 0v for Z ≠ 0 PB JmN (2πRrh) ⎩ (2)

Herein, R, Z, and ψ are defined as the radius, height, and azimuthal angle, respectively, in the reciprocal space cylindrical coordinate system, (ξ = R cos ψ, η = R sin ψ, ζ = Z). rh and rc are the radius of the helix of PB and that of the cylinder of PS, respectively. vPB and vPS are the volume of PB and PS domains. ψ0 is azimuthal angle in the cylindrical coordinate in reciprocal space and corresponds to phase term in the form factor of a single strand helix in the N-strand helix. Jn(x) is n-th order Bessel function, and m is an integer. For the observed film, the directions of lattice vectors, a1 and a2, of the 2D hexagonal lattice were considered to be randomly rotated around the zaxis in the xy-plane, and I(q) is independent of φ in L(q). Thus, I(q) is azimuthally averaged with respect to φ and only depend on the radius, R, as presented in eq 3: 2702

DOI: 10.1021/ma502596a Macromolecules 2015, 48, 2697−2705

Article

Macromolecules

DB(rh), with width d, and a Gaussian function, DG(rh), with d as the full width at half-maximum (see the Supporting Information for additional details). If the first off-equatorial scattering (m = 1) is proportional to J2(2πRrh), then the helix is identified as a double helix (N = 2). For the unstained films, DB(rh) provided a closer intensity to observed one, while DG(rh) provided a closer one for the stained film measurements. In particular, calculated intensity largely deviates from the observed intensity in the second layer line profiles of the unstained (stained) film when DG(rh) (DB(rh)) is used. The intensity profiles on the equatorial layer line (lower, zeroth layer) and off-equatorial layer line (upper, Nth layer) in Figure 6 are in good agreement with the calculated profiles when N, the order of the Bessel function in eq 2, was 2. It should be emphasized that same structural parameters were used for the two model calculation protocols based on DB(rh) and DG(rh). Additionally, smearing by X-ray beam size and finite domain size were not involved in the intensity calculation because computational effort for inevitable multiple integrations was significantly large and the exact shape and size of the X-ray beam at detector position could not be measured at the beamline. Thus, calculated I(R) did not exactly reflect the shapes of the minima and maxima of observed intensity. Nevertheless, the structural parameters can be precisely estimated from the model calculation because the structural parameters dominate the intensity ratio at peak positions and the smearing does not essentially affect the ratio, e.g., rh and d dominate the peak position and the peak intensity distribution on second layer line and g and rc (and also rh) drastically affects the peak-intensity ratio of 11, 20, 21, and 30 diffractions which appear around 2πRa = 12−22. The SAXS results indicate that the double-helical structure (N = 2) observed via ET existed not only on the local scale but also throughout the f ilm on the macroscopic scale. Thus, it can be concluded that helices with different numbers of strands, e.g., triple helices, do not exist in the film, as no scattering was observed in the third layer line. Furthermore, no clear diffraction (lattice factor) appeared except for Z = 0, and the scattering intensity at the second layer line was very consistent with the form factor of the helix in eq 2. These results indicate that the phases of the helices were random in the film. In other words, the helices are freely rotated or were randomly translated along the helical axis (long axis of the PS domain).24 If the helical senses of the PB domain in a grain are the same and helical axes are parallel, rotation and translation motions would be relatively difficult to achieve because the PMMA chains attached at the neighboring PB helical domains would interfere with one another and be strongly deformed. On the other hand, if helical senses are opposite in a grain, the PMMA chains at the interface of the helix may potentially be accommodated in the grooves of the neighboring helical PB domain. As reported previously, helices with opposite senses can be more easily accommodated than those with the same sense,12 although it is impossible for all the neighboring helices to take the opposite sense in the hexagonal lattice. The results with respect to the phases of the helices obtained from the SAXS analysis of the present SBM system were in good agreement with the local structure determined from the ET observation, in which helices with opposite senses were randomly accommodated in a hexagonal lattice. The structural parameters used for the intensity calculation and estimated from the ET images are listed in Table 1. The electron densities for the components of the unstained SBM,

Figure 6. GI-SAXS intensity profiles of the (a) unstained and (b) stained films. The upper and lower profiles correspond to the 2nd and 0th layer lines, respectively. The open circles, solid blue line, and solid green lines represent the observed intensity, calculated intensity with DB(rh), and calculated intensity with DG(rh), respectively. The horizontal axis corresponds to the radius (R) of the cylindrical coordinate and normalized with lattice constant, a. The R is equal to ξ in the observed plane. The vertical line corresponds to I(R) in eq 3 and integrated observed line intensity, Iobs(ξ) (ξ2 + (mN/P)2)1/2. The hk indices are included in the 0th layer line diffraction profile in (a). 2703

DOI: 10.1021/ma502596a Macromolecules 2015, 48, 2697−2705

Article

Macromolecules

do not penetrate the cylindrical PS domains. Such a complex interface structure is difficult to analyze using SAXS or ET alone. Furthermore, a comparison of the structural parameters obtained for the stained and unstained SBM double-helical structures showed that staining of the helical domains in the ET experiments slightly altered the nanometer-scale structure of the SBM in a quantitative manner. It is advantageous that such detailed interfacial structural information can be obtained using this combinatorial structural analysis method without the need for difficult, multiple-staining techniques that are otherwise required for microscopy analyses. The ability to determine quantitative structural parameters with high precision and to obtain detailed interfacial structure information should be useful for visualizing the polymer chain conformations that dominate the morphology of the microphase-separated structures for BCPs. Moreover, if helices with different strand numbers coexist in a sample, as reported previously14 for double helices that partially transformed into triple helices upon the addition of a PS homopolymer to an SBM triblock terpolymer, an SAXS profile intensity analysis combined with ET observation should enable estimation of the precise fractions of triple and double helices, which is difficult to achieve from the ET image alone due to the limited observation volume.

Table 1. Structural Parameters Used for Model Calculation of I(R) and Observed in ET Image unstained SAXS stained SAXS ET sliced image

a/nma

gb

rh/nmc

d/nmd

69.7

0.037

17.0

7.2

67.0

0.050

16.5 14 ± 1

7.9 7.5 ± 1

rc/nme

P/nmf

13.5

31 ± 1 30 ± 1 28 ± 1

a

Lattice parameter for the hexagonal lattice. bDegree of disorder in the hexagonal lattice. cRadius of the double helix. dTube thickness of the PB phase. eRadius of the cylinder. fHelical pitch.

ρPS, ρPB, and ρPMMA, were 353, 294, and 383 electrons/nm3, respectively, were estimated from the weight densities of the PS, PB, and PMMA homopolymers (1.07, 0.88, and 1.18 g/ cm3, respectively). As it was not possible to estimate the precise density of each domain for the stained film, ρ′PS (prime symbol represents the density of the stained sample), it was assumed to have the same value as that of PMMA in the calculation. In other words, the difference in the electron densities of the PS and PMMA domains in the stained sample was not directly included in the estimate, and the PB domain was assumed to exist in a nearly homogeneous matrix (ρ′PMMA ≈ ρ′PS ≪ ρ′PB and PB domains dominate f(R), as discussed in section 3.2). Thus, rc was indirectly estimated from rh and d (if the situation was the same as that for the unstained film, rc ≈ rh − d/2 = 12.5 nm). There was almost no variation in P, while g and d increased and a and rh decreased after staining. This result indicates that after the staining process the selectively stained PB domains are slightly swollen, resulting in an increase in the second-kind lattice disorder. In the unstained film, the value (rh − rc) was equal to d/2. The model calculation results therefore provide detailed information on the structure of the interface between the PS and PB domains and demonstrate that the tube in the PB domain does not penetrate into the PS domain in unstained sample. Rather, it only contacts the cylindrical surface, as evidenced by the sharp interface that is well described by the step function DB(rh). Such an interface structure is difficult to observe using only ET because a double staining process with RuO4 (for the PS domain) and OsO4 (for the PB domain) is required, and it is very difficult to prevent understaining or overstaining of the domains in practice. On the other hand, in the stained film, the interface was better expressed with the Gaussian function DG(rh), indicating that for the stained film the interface is roughened because of locally heterogeneous staining of the PB domain.

■

ASSOCIATED CONTENT

S Supporting Information *

Details of DWBA approximation for GI-SAXS intensity; derivation process for L(q) and f(q); relationship between calculated intensity, I(R), and observed line intensity profile, Iobs(η), distribution functions DB(rh) and DG(rh). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (H.J.). Present Addresses

R.I.: Department of Chemistry and Materials Science, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 1528552, Japan. T.H.: Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai, Miyagi, 980-8577, Japan. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS H.J. gratefully acknowledges the financial support received through a Grant-in-Aid (number 24310092) from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan. Synchrotron small-angle X-ray scattering measurements for the thin film on an Si wafer (GI-SAXS) were conducted on the BL03XU beamline at SPring-8.

4. CONCLUSION We have developed a novel method for the structural analysis of a highly oriented, complex double-helical structure formed in a poly(styrene-b-butadiene-b-methyl methacrylate) (SBM) block copolymer thin film by combining real-space electron tomography (ET) observations with GI-SAXS reciprocal space measurements for the same sample. This method enables determination of the precise interface location of the nanostructure of the unstained sample. The use of SAXS intensity analysis based on the structural model constructed from the intuitive ET observations enabled precise evaluation of several structural parameters for the nanometer-scale doublehelical structure of the SBM, including a, g, rh, rc, d, and P, without the potentially confounding influence of the staining process. The results demonstrate that the helical PB domains

■

REFERENCES

(1) Guarini, K. W.; Black, C. T.; Zhang, Y.; Kim, H.; Sikorski, E. M.; Babich, I. V. J. Vac. Sci. Technol., B 2002, 20, 2788−2792. (2) Hamley, I. W. Nanotechnology 2003, 14, R39−R54. (3) Stoykovich, M. P.; Muller, M.; Kim, S. O.; Solak, H. H.; Edwards, E. W.; Pablo, J. J.; Nealey, P. F. Science 2005, 308, 1442−1446. (4) Widawski, G.; Rawiso, M.; Francois, B. Nature 1994, 369, 387− 389.

2704

DOI: 10.1021/ma502596a Macromolecules 2015, 48, 2697−2705

Article

Macromolecules (5) Freer, E. M.; Krupp, L. E.; Hinsberg, W. D.; Rice, P. M.; Hedrick, J. L.; Cha, J. N.; Miller, R. D.; Kim, H. C. Nano Lett. 2005, 5, 2014− 2018. (6) Peinemann, K. V.; Abetz, V.; Simon, P. F. W. Nat. Mater. 2007, 6, 992−996. (7) Ro, H. W.; Peng, H.; Niihara, K. I.; Lee, H. J.; Lin, E. K.; Karim, A.; Gidley, D. W.; Jinnai, H.; Yoon, D. Y.; Soles, C. L. Adv. Mater. 2008, 20, 1934−1939. (8) Matsen, M. W.; Bates, F. S. Macromolecules 1996, 29, 7641−7644. (9) Kleman, M.; Lavrentovich, O. D. In Soft Matter Physics: An Introduction; Springer-Verlag: New York, 2002; p 1. (10) Bates, F. S.; Fredrickson, G. H. Annu. Rev. Phys. Chem. 1990, 41, 525−557. (11) Jinnai, H.; Nishikawa, Y.; Spontak, R. J.; Smith, S. D.; Agard, D. A.; Hashimoto, T. Phys. Rev. Lett. 2000, 84 (3), 518−521. (12) Jinnai, H.; Kaneko, T.; Matsunaga, K.; Abetz, C.; Abetz, V. Soft Matter 2009, 5, 2042−2046. (13) Morita, H.; Kawakatsu, T.; Doi, M.; Nishi, T.; Jinnai, H. Macromolecules 2008, 41, 4845−4849. (14) Higuchi, T.; Sugimori, H.; Jiang, X.; Hong, S. O.; Matsunaga, K.; Kaneko, T.; Abetz, V.; Takahara, A.; Jinnai, H. Macromolecules 2013, 46, 6991−6997. (15) Hong, S. O.; Higuchi, T.; Sugimori, H.; Kaneko, T.; Abetz, V.; Takahara1, A.; Jinnai, H. Polym. J. 2012, 44, 567−572. (16) Luther, P. K.; Lawrence, M. C.; Crowther, R. A. Ultramicroscopy 1988, 24, 7−18. (17) Crowther, R. A.; DeRosier, D. J.; Klug, A. Proc. R. Soc. London 1970, A 317, 319−340. (18) Omote, K.; Ito, Y.; Kawamura, S. Appl. Phys. Lett. 2003, 82, 544−546. (19) Lee, B.; Park, I.; Yoon, J.; Park, S.; Kim, J.; Kim, K. W.; Chang, T.; Ree, M. Macromolecules 2005, 38, 4311−4323. (20) Guinier, A. In X-Ray Diffraction In Crystals, Imperfect Crystals, and Amorphous Bodies; W.H. Freeman and Company: San Francisco, 1963; pp 295−317. (21) Hosemann, R.; Baguchi, S. N. In Direct Analysis of Diffraction by Matter; North-Holland: Amsterdam, 1962; pp 302−353. (22) Hashimoto, T.; Kawamura, T.; Harada, M.; Tanaka, T. Macromolecules 1994, 27, 3063−3072. (23) Cochran, W.; Crick, F. C. H.; Vand, V. Acta Crystallogr. 1952, 5, 581−586. (24) Klug, A.; Franklin, R. E. Discuss. Faraday Soc. 1958, 25, 104− 110.

2705

DOI: 10.1021/ma502596a Macromolecules 2015, 48, 2697−2705