Close-Packed Spherical Morphology in an ABA ... - ACS Publications

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Close-Packed Spherical Morphology in an ABA Triblock Copolymer Aligned with Large-Amplitude Oscillatory Shear Shu Wang,† Renxuan Xie,‡ Sameer Vajjala Kesava,‡ Enrique D. Gomez,‡ Eric W. Cochran,§ and Megan L. Robertson*,† †

Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas 77204-4004, United States Department of Chemical Engineering and the Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, United States § Department of Chemical and Biological Engineering, Iowa State University, Ames, Iowa 50011, United States ‡

S Supporting Information *

ABSTRACT: A microphase-separated poly(styrene-b-(lauryl-co-stearyl acrylate)-bstyrene) (SAS) triblock copolymer exhibiting a disordered spherical microstructure with randomly oriented grains was aligned through the application of large-amplitude oscillatory shear (LAOS) at a temperature below the order−disorder transition temperature of the triblock copolymer, yet above the glass transition temperature of the polystyrene spherical domains. The thermoplastic elastomeric behavior of the SAS triblock copolymer provided a convenient means to observe the aligned morphology. Following application of LAOS, the specimen was quenched to room temperature (below the glass transition temperature of polystyrene), and small-angle X-ray scattering data were obtained in the three principal shear directions: shear gradient, velocity, and vorticity directions. The analysis revealed that the SAS triblock copolymer formed coexisting face-centered cubic and hexagonally close-packed spherical microstructures. The presence of a close-packed microstructure is in stark contrast to an extensive body of literature on sphere-forming bulk block copolymers that favor body-centered cubic systems under quiescent conditions and under shear. The aligned microstructure observed in this bulk block copolymer was reminiscent of that observed in various spherical soft material systems such as colloidal spheres, sphere-forming block copolymer solutions, and star polymer solutions. The highly unanticipated observation of close-packed spherical microstructures in a neat block copolymer under shear is hypothesized to originate from the dispersity of the block copolymer.

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and transverse with respect to the shear flow direction.12 Factors governing the preferred alignment include the frequency, shear strain, and temperature.3,13−19 Additionally, entanglements20 and differences in the viscoelastic properties of the block copolymer components (i.e., mechanical contrast)21 govern the structural alignment. A number of mechanisms for alignment have been proposed and explored such as grain rotation, defect migration, and grain melting and formation.3 In the case of block copolymers forming hexagonal close-packed cylinders, the predominant orientations are cylinders oriented parallel or perpendicular to the shear direction.22−28 The transverse orientation has been observed when there are also liquid crystalline domains present that have a preference in the alignment.29,30 The shear alignment of sphere-forming block copolymers has been explored less extensively in the literature. Prior studies have investigated the alignment of body-centered cubic (BCC) systems in the bulk and thin films, in which the predominant orientation includes the {111} plane parallel to the shear direction.31−38 In thin films with BCC structure, the application

INTRODUCTION Block copolymers composed of two incompatible polymers spontaneously self-assemble into various equilibrium nanoscale phases, including lamellae, hexagonally close-packed cylinders, body-centered cubic spheres, and a bicontinuous gyroid morphology.1,2 These materials have many potential applications, such as thermoplastic elastomers, membranes for batteries, fuel cells and water purification, and solution-based assemblies for encapsulation of hydrophobic guest molecules and drug delivery.1,2 Block copolymer morphologies formed spontaneously in the melt are randomly oriented, lacking longrange order, and the materials are macroscopically isotropic. The application of external forces, such as shear,3 electric fields,4,5 magnetic fields,6 or preferential surfaces,7 can lead to alignment of the block copolymer into anisotropic structures and induce long-range ordering. Control of structural orientation is key to manipulating the properties of these materials for desired applications. The application of shear, whether steady shear or largeamplitude oscillatory shear (LAOS), is a common approach for the alignment of bulk block copolymers. Extensive studies have focused on alignment of lamellae-forming systems through steady shear or LAOS.3,8−16 Three possible alignment orientations have been identified as parallel, perpendicular, © XXXX American Chemical Society

Received: March 9, 2016 Revised: May 17, 2016

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DOI: 10.1021/acs.macromol.6b00505 Macromolecules XXXX, XXX, XXX−XXX

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higher dispersity block copolymers using self-consistent field theory.73 FCC spheres have been observed experimentally in a higher dispersity diblock copolymer following melt processing.74 Here, we report the alignment of a poly(styrene-b-(lauryl-costearyl acrylate)-b-styrene) (SAS) triblock copolymer through the application of LAOS. Prior to application of shear, the compression-molded block copolymer exhibited an isotropic and disordered spherical morphology lacking long-range order. The thermoplastic elastomeric nature of the SAS triblock copolymer provided a convenient route for examination of the morphology: LAOS was applied, and then the polymer was quenched to room temperature, at which small-angle X-ray scattering (SAXS) data were obtained in all three shear directions (shear gradient, velocity, and vorticity directions). Upon application of shear, the block copolymer transitioned to coexistence of aligned FCC and HCP spheres. In this article, alignment conditions and analysis of the resulting structures are discussed as well as the potential role of dispersity of the triblock copolymer.

of shear produced hexagonal ordering (viewed in the shear gradient direction),32,34,36 and BCC spheres transitioned to hexagonally close-packed cylinders,33 described by a meltingrecrystallization model.34 A transition from hexagonal to BCC packing was observed in thin films as the number of sphere layers increased.39 The observance of close-packed spheres has been conspicuously absent in the majority of literature reports of sphereforming block copolymers, both under quiescent conditions and under shear. The theoretical block copolymer phase diagram describes a large range of compositions and temperatures over which BCC spheres are predicted to form.40 A narrow region of the theoretical phase diagram indicates the presence of a close-packed spherical morphology,40−42 yet very few literature studies report the presence of this phase. One notable study by Huang and co-workers described facecentered cubic (FCC) spheres in a bulk block copolymer under quiescent conditions.43 Additionally, Imaizumi and coworkers observed the FCC phase in a thermoplastic elastomeric triblock copolymer, which transitioned to BCC under extensional flow.44 One hypothesis to explain the lack of observation of close-packed spheres in the block copolymer literature is that the presence of thermal fluctuations may destroy long-range order in spherical systems, promoting the formation of spherical micelles.45,46 Indeed, a transition from BCC spheres to spherical micelles has been observed at elevated temperatures.47−50 If the disordered phase is instead considered as spherical micelles, it has been predicted that close-packed spheres are no longer stable.51 To our knowledge, no literature studies report the close-packed spherical phase in block copolymer melts under shear. The formation of close-packed spheres can be promoted by alleviating the packing frustrations of the block copolymer melt. This can be accomplished through various means: addition of solvent (formation of block copolymer micellar solutions), addition of homopolymer (formation of homopolymer/diblock copolymer blends), and increase in the dispersity of the block copolymer. We will briefly discuss these three scenarios. A wide body of literature exists for block copolymer micellar solutions, in which close-packed spheres are readily observed. The formation of close-packed vs BCC spheres is influenced by the relative sizes of the core and corona, solvent penetration of the core, and aggregation number.52−58 FCC spherical micellar solutions transition to hexagonal close-packed (HCP) spheres, or a mixture of FCC and HCP spheres, in the presence of shear.53,59−63 In close-packed spherical micelle systems, the close-packed planes (i.e., {0001} and {111} planes in the HCP and FCC sphere unit cells, respectively) generally align within the shear plane (vorticity−velocity plane) and are stacked along the shear gradient direction. As FCC and HCP spherical systems have very similar energies, both ABABAB (i.e., HCP) and ABCABC (i.e., FCC) packing sequences are often observed along the shear gradient direction.54,60,62,64,65 Closepacked spheres have also been observed in diblock copolymer/ homopolymer blends by Huang et al.66,67 The stabilization of close-packed spheres in these blends through alleviation of packing frustrations is predicted by theory.68−71 Self-consistent field theory indicates a broad region of the phase diagram over which FCC spheres are predicted, at appreciably high homopolymer content (around 40% and above).70,71 Finally, close-packed spheres are stabilized in neat block copolymers with polydisperse components.72 A much larger region of the phase diagram has been predicted for close-packed spheres in

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EXPERIMENTAL METHODS

Materials. All chemicals were purchased from Sigma-Aldrich unless otherwise noted. Synthesis and Characterization of SAS Triblock Copolymer. The synthesis and characterization of the poly(styrene-b-(lauryl-costearyl acrylate)-b-styrene) (SAS) triblock copolymer used in this study were previously reported in ref 75. Briefly, the SAS triblock copolymer was synthesized with reversible addition−fragmentation chain transfer (RAFT) polymerization. Proton nuclear magnetic resonance (1H NMR) experiments were performed on a JEOL ECA-500 instrument using deuterated chloroform (99.96 atom % D) as the solvent. The number-average molecular weight (Mn) and dispersity (Đ) were measured by a Viscotek gel permeation chromatography (GPC) instrument with Agilent ResiPore columns, using THF (OmniSolv, HPLC grade) as the mobile phase at 30 °C. The flow rate was 1 mL/min, and the injection volume was 100 μL. A triple detection system, including light scattering, a viscometer, and refractometer, was employed to characterize the molecular weight distribution. Data obtained from the refractometer are shown in Figure S1. The order−disorder transition temperature (TODT) of the SAS triblock copolymer was probed using a TA Instruments DHR-2 rheometer. The storage modulus at a frequency of 10 rad/s (using a strain in the linear viscoelastic region) was plotted versus temperature, and the sharp decrease in storage modulus indicated the TODT. The characteristics of the polymer are reported in Table 1. Alignment through Large-Amplitude Oscillatory Shear (LAOS). The SAS triblock copolymer was initially prepared by compression molding on a Carver hot press at an applied load of 4000 lbs at 240 °C for 5 min into a disc of 25 mm diameter and 1.1 mm thickness. The sample was loaded in a TA Instruments DHR-2

Table 1. Characteristics of the SAS Triblock Copolymer Mn of midblocka Mn of triblock copolymera Đa wt % of lauryl acrylate in midblockb vol % styrene in triblock copolymerb,c TODTd

58.2 kg/mol 78.4 kg/mol 1.65 76 23.9 233.7 °C

a

Determined from GPC (light scattering). bDetermined from 1H NMR. cRoom temperature densities were used to calculate the vol % of each component (1.04 and 0.94 g/mL for polystyrene and poly(lauryl-co-stearyl acrylate), respectively, reported in. refs 76 and 75. dOrder−disorder transition temperature, determined with rheology. B


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for the analysis of small-angle scattering data78,79 which was designed for the case of a polydisperse core with a Gaussian distribution of core radii and shell of fixed thickness. Transmission electron microscopy (TEM) was employed to directly observe the morphology of the SAS triblock copolymer under two conditions: (1) following compression molding (i.e., the unaligned sample) and (2) after alignment with LAOS at 180 °C and 1 rad/s (in both cases the sample was quenched to room temperature before TEM analysis). Sections of approximately 70 nm thicknesses were prepared for TEM experiments using a Leica EM UC6 microtome operating at −100 °C with a Leica EM FC6 cryo-attachment and a glass knife. Contrast between the polystyrene and polyacrylate domains was enhanced using 0.5 wt % (aq) RuO4 vapor staining (15 min staining time). Imaging was done at the Materials Characterization Lab of the Pennsylvania State University on a JEOL 2010 LaB6 transmission electron microscope. Zero-loss images were recorded using a Gatan energy filter with a slit size of 20 eV such that inelastic scattering is largely removed.

rheometer between two preheated parallel plates with a diameter of 25 mm, and the plates were brought to a gap of 1 mm. The sample was aligned at a chosen oscillatory frequency (1, 10, or 100 rad/s) and temperature (130, 180, or 210 °C) for 3 h in a nitrogen atmosphere. The shear strain was kept constant at 100% unless otherwise noted. The sample was quenched to room temperature immediately following alignment. Morphology Characterization and Analysis. Small-angle X-ray scattering (SAXS) measurements were performed using a Rigaku SMAX 3000 SAXS instrument at the University of Houston, equipped with CMF optic incident beam (λ = 0.154 nm), 3 pinhole collimation, and a 2-dimensional multiwire area detector with 1024 × 1024 pixels. The sample-to-detector distance was 3 m. The two-dimensional scattering patterns were azimuthally integrated to a one-dimensional profile of intensity versus scattering vector, q = 4π sin(θ/2)/λ [θ is the scattering angle; λ is the wavelength]. Following compression molding, the SAS triblock copolymer was quenched to room temperature, and SAXS data were obtained at room temperature (i.e., the unaligned sample). The SAS triblock copolymer was then aligned at a specified temperature with LAOS (LAOS procedure described above) and quenched to room temperature, and SAXS data were obtained at room temperature in the shear gradient, velocity, and vorticity directions (Figure 1). In order to obtain the SAXS data on the aligned sample, a

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RESULTS AND DISCUSSION Morphology of the SAS Triblock Copolymer Prior to Application of Shear. The room temperature morphology of the SAS triblock copolymer following compression molding and subsequent quenching to room temperature was characterized through SAXS and TEM, as shown in Figure 2. The 2D SAXS data exhibited isotropic rings, indicating random orientation of grains following compression molding (Figure 2a). Azimuthal integration of the 2D isotropic rings produced the 1D data (Figure 2a), in which the primary scattering peak maximum was observed at q = 0.026 Å−1, and three higher order scattering peak maxima were observed at 0.051, 0.064, and 0.086 Å−1, respectively. The presence of higher order peaks indicates microphase separation of the SAS triblock copolymer. The 1D data are consistent with that observed previously in block copolymers,80−84 spherical block copolymer gels,85−87 and spherical micellar solutions88−90 and are well-described by a modified Percus−Yevick hard-sphere model.77 The modified hard-sphere model assumes a dense core of the polystyrene domains with radius rc, surrounded by a shell with thickness of rs, leading to an effective hard-sphere radius, RHS (= rc + rs). The scattering intensity (I) as a function of scattering vector (q) can be approximated by

Figure 1. Schematic of beam directions utilized in SAXS experiments (shear gradient, velocity, and vorticity directions). strip was removed from the rheology disk, starting at the disk center and moving out to the disk edge, with a width of 1 mm (and thickness of 1 mm). This strip was mounted in the SAXS sample holder, and data were obtained in the shear gradient direction. The strip was then rotated 90°, and data were obtained in the velocity direction. Finally, cubes were removed with 1 mm edge length at specified positions along the strip (corresponding to each desired local strain at which the measurements were taken), and each cube was loaded in the SAXS sample holder to obtain data in the vorticity direction. 2D SAXS data were analyzed using an internally developed program to identify the structure and orientation of the grains. Generation of the crystographically permitted Bragg peak positions was managed through custom macros written in Visual Basic for Applications in Microsoft Excel (freely available by request). Given proposed space group symmetry and lattice constants, the routines compute the reciprocal space coordinates for a list of wavevectors satisfying the Laue condition qhkl such that |qhkl| < qmax and that Miller indices are chosen such that they are not systematically extinguished by the symmetry rules. The subset of wavevectors qhkl such that qsaxs·qhkl = 0 define a plane in reciprocal space corresponding to the allowed peak positions in a scattering experiment for a direct beam parallel to qsaxs. The allowed peak positions are then projected onto the plane and compared directly with the measured 2D spot patterns for consistency. It is important to note that while the presence of a peak disallowed by a model invalidates the model, the absence of an allowed peak allows no such conclusions to be drawn. 2D SAXS data obtained in the three shear directions (shear gradient, velocity, and vorticity directions; refer to Figure 1) were considered in combination with one another to assign the appropriate morphology obtained under each LAOS condition (temperature and oscillatory frequency). 1D SAXS data obtained on a sample following compression molding (without application of shear) were analyzed using a modified Percus−Yevick hard-sphere model77 using the function PolyCore_HS in an Igor Macro developed by the NIST Center for Neutron Research

I(q) = KNP(q)S(q)

(1)

where K is a constant depending on the type of radiation and sample properties, N is the number of scattering units, P(q) is the form factor corresponding to the spherical core, and S(q) is the structure factor, which accounts for the interactions between the hard spheres with effective hard-sphere radius, RHS, and effective volume fraction of the hard spheres, η.80 Mischenko et al.86 and Kleppinger et al.87 considered a Gaussian distribution in the core sphere radius and an outer shell with zero contrast with the surrounding matrix. Other studies incorporated a polydisperse core size and a diffuse boundary between the core and matrix.80,84,90 The data in Figure 2a were analyzed using the function PolyCore_HS in an Igor Macro developed by the NIST Center for Neutron Research for the analysis of small-angle scattering data78,79 that was designed for the case of a polydisperse core with a Gaussian distribution of core radii and shell of fixed thickness. The parameters obtained from the curve fitting were η = 0.519, rc = 9.85 nm, polydispersity of core size (p) = 0.117 (p = σ/rc, σ2 is the variance of the Gaussian distribution), and rs = 3.31 nm. Other block copolymer morphologies were also C


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above the TODT for 5 min, and then quenched to room temperature (which is below the Tg of the polystyrene end-blocks). Following prior literature,82 the quenching process likely did not provide enough time above the Tg of the endblocks for the equilibrium ordered structure to evolve. (We did attempt to equilibrate the sample above the polystyrene Tg, and we did not observe a change in morphology following annealing at 130 °C for up to 46 h, shown in Figure S2.) The SAS triblock copolymer exhibited a high storage modulus at low temperatures (below TODT) when the disordered spherical morphology was observed, attributed to the elastomeric behavior of the polymer and bridging of the distinct glassy spherical domains by rubbery midblocks in the triblock copolymer (thermoplastic elastomer) architecture. A drastic change in the storage modulus was observed at the TODT.75 Prior studies on body-centered cubic spherical diblock copolymers observed a transition from the body-centered cubic phase to disordered spherical micelles, in which the disordered spherical micelles existed at temperatures above the TODT (in place of the disordered phase) and exhibited a low modulus.51,90 In our study, the abrupt decrease in modulus at elevated temperatures suggests a significant change in the morphology at the TODT, either homogenization of the sample (loss of spherical domains) and/or loss of the bridging chains which impart the elastomeric behavior in a triblock copolymer thermoplastic elastomer. Influence of Shear Strain, Temperature, and Oscillatory Frequency on Alignment in the Shear Gradient Direction of the SAS Triblock Copolymer under LAOS. The morphology in the shear gradient direction (defined in Figure 1) was examined in order to identify sufficient LAOS conditions for the alignment of the SAS triblock copolymer. An alignment temperature of 210 °C was first employed, which is slightly below the order−disorder temperature of this polymer (233.7 °C). Oscillatory frequencies of 1, 10, and 100 rad/s were employed, and the morphology was examined at three positions within the sample. The local strain applied to the sample at the three positions was calculated as

Figure 2. (a) 1D SAXS data and (b) TEM image obtained at room temperature following compression molding (prior to application of LAOS). In (a), the Percus−Yevick equation for hard spheres (solid curve) is fit to the data (open circles). Isotropic 2D SAXS data are shown in the inset to (a). Intensity as a function of azimuthal angle of the primary diffraction ring in the 2D SAXS data is shown in Figure S3.

γ=

r × 100% R

(2)

where r is the distance from the disc center, R is the radius of the sample disc (12.5 mm), and 100% is the shear rate applied at the edge of the sample disc. In the chosen experimental conditions, the morphology was observed at 0, 50 and 90% (local) strain. Regardless of the oscillatory frequency used, or position within the disc that was examined, the obtained 2D SAXS data showed isotropic concentric circles, consistent with random orientation of grains and absence of alignment (Figure S4). Thus, 210 °C was not a suitable temperature for the alignment of this triblock copolymer. Next, we chose an alignment temperature of 180 °C, which is further away from the order−disorder transition temperature of this polymer. 2D SAXS data obtained in the shear gradient direction, following LAOS at 180 °C, are shown in Figure S5 (again employing three oscillatory frequencies of 1, 10, and 100 rad/s and observing the morphology at local strains of 0, 50, and 90%). As expected, the morphology observed in the center of the disc (corresponding to a local strain of 0%) remained unaligned (Figure S5); however, the 2D SAXS data observed at 50 and 90% showed diffraction patterns consistent with the alignment of grains (Figure S5). Aligned morphologies were

considered, though the experimental higher order peak locations were not in good agreement with theoretical predictions (summarized in Figure S2). Though the broad primary and higher order peaks observed in Figure 2a are in good agreement with the fit from the Percus−Yevick model for disordered hard spheres, the morphology may also be influenced by the presence of homopolymer or diblock copolymer in the SAS triblock copolymer sample (the molecular weight distribution of the SAS triblock copolymer is provided in Figure S1 and was discussed in ref 75). The observation of broad primary and higher order peaks may also be indicative of coexisting microstructures. In summary, the Percus−Yevick model for disordered hard spheres provided the best fit to the data of all morphologies considered. TEM micrographs were consistent with a disordered spherical morphology as well (Figure 2b). The order−disorder transition temperature (TODT) of the SAS triblock copolymer was previously characterized through rheology (233.7 °C).75 We attribute the presence of disordered spheres at low temperatures to the sample preparation process, in which the triblock copolymer was compression molded just D


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Figure 3. 2D SAXS data obtained (at room temperature) in the shear gradient, velocity, and vorticity directions, after LAOS at (a) 180 °C and (b) 130 °C (strain at disc edge = 100%, frequency = 1 rad/s). Data were obtained at five different positions within the sample disc, corresponding to different local strain values (γ, calculated with eq 2).

aligned structures are present (Figure 3). This is quantified through determination of the intensity as a function of azimuthal angle, calculated along the constant q-value at the location of the principal scattering ring in Figure 3. In Figure 4a, the intensity as a function of azimuthal angle exhibits scattering peaks at 60° intervals, as expected for hexagonal packing. The degree of alignment obtained at each shear strain and alignment temperature was quantified through an orientation function, defined as

observed regardless of the choice of oscillatory frequency used in application of LAOS (1, 10, and 100 rad/s). On the basis of these results, we chose to conduct a thorough analysis of the aligned morphology employing the following LAOS conditions: oscillatory frequency of 1 rad/s, maximum strain (applied at the edge of the disc) of 100%, and two alignment temperatures of 180 and 130 °C. Aligned Morphologies Observed in Shear Gradient, Vorticity, and Velocity Directions Following LAOS at 180 and 130 °C. 2D SAXS diffraction patterns obtained following alignment with LAOS at 180 and 130 °C are shown in Figure 3. Five locations within the sample disc were examined, corresponding to the following local strains: 16, 32, 48, 64, and 80% (calculated using eq 2). Regardless of the temperature used in the alignment, a local strain of 16% was not sufficient to produce a well-aligned structure (Figure 3). At higher local strains (greater than 32%), the sample became well-aligned, showing anisotropic diffraction patterns in all three shear directions (shear gradient, velocity, and vorticity directions). The innermost ring of spots observed in the shear gradient direction is indicative of hexagonal packing, observed at both alignment temperatures and at all shear strains for which

ψ = ⟨cos(6δθ )I ⟩

(3)

where δθ is the angle of the bond vector and the factor 6 is considered for the 6-fold symmetry of the lattice.34,91 For each data set, the orientation function was calculated using the lowest q-value at which non-negligible scattering was observed (i.e., innermost ring of spots). The orientation function is shown in Figure 4b as a function of the local strain at which the 2D SAXS data were obtained (based on the position within the sample disc, calculated using eq 2). The orientation function quantifies the lack of alignment in the sample at a local strain of 16%. For both alignment temperatures, the orientation function E


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sample below the glass transition temperature of the polystyrene end-blocks). We verified that the quenched microstructure did not change over time (through occasional monitoring of the SAXS data obtained from the sheared and quenched specimens, for a time period as long as 5 months). All SAXS data presented in this article were obtained within 3 days of the shear alignment procedure. Analysis of 2D SAXS Data Obtained at Alignment Temperatures of 180 and 130 °C. Data sets that showed aligned morphologies were further analyzed to identify the sample morphology (Figures 5−7). The 2D SAXS data were compared with model predictions for various block copolymer morphologies, i.e., lamellae, HCP cylinders, BCC spheres, close-packed (FCC and HCP) spheres, and bicontinuous gyroid phases. Though data were obtained at different local strains (16−80%) and alignment (LAOS) temperatures (130 and 180 °C), in all cases the data are consistent with the presence of coexisting FCC and HCP spherical microstructures (Figures 5−7). Though the shear strain influenced the degree of alignment (quantified in Figure 4), the nature of the microstructure did not depend on the strain (within the range of strain values over which aligned structures were observed). Here we discuss in detail the assignment of the structure and orientation at an alignment temperature of 180 °C: data sets obtained at 32−80% strain were analyzed (Figure 5 and Figures S6−S8) (data taken at 16% local strain were not analyzed due to poor alignment, as evidenced by the orientation function in Figure 4). We will first discuss the data obtained in the shear gradient direction (a representative data set is shown in Figure 5a at a local strain of 48%). Clear hexagonal symmetry extending up to 4−5 orders is observed. In the principal scattering ring, six spots are observed, occurring at 60° intervals (Figure 5a and Figure S9). This scattering pattern alone is not definitive of the structure, as planes with hexagonal symmetry are found in many types of unit cells such as HCP cylinders and closepacked (FCC or HCP) spheres. We assign these patterns to planes viewed in the [111] direction of the FCC spherical microstructure and [0001] direction of the HCP spherical microstructure, both of which show good overlap with the SAXS diffraction patterns (Figure 5a). This assignment is consistent with a wide body of literature on colloidal and block copolymer solution spherical morphologies, in which the predominant orientation includes close-packed planes (i.e., FCC {111} and HCP {0001}) viewed in the e− ⃗ v ⃗ plane (thus, in the shear gradient direction).53,54,58,59,64,65,92−94 This will be further clarified through discussion of our data obtained in the velocity and vorticity directions. In the vorticity direction (Figure 5b), the principal scattering ring also exhibits six spots, but in this case two of the spots show significantly higher intensities than the others. (The relationship between the intensity and the azimuthal angle of the primary scattering ring in the vorticity direction is shown in Figure S10.) We assign the [11̅0] direction of the FCC spherical microstructure, which correlates well with the relative placement of the spots in the diffraction pattern but does not explain the variations in the spot intensity observed. Coexistence with an HCP spherical microstructure in which the vorticity direction is parallel to the [011̅0] direction provides a suitable explanation for the distribution of intensities observed within the principal scattering ring (Figure 5b and Figure S10). In the velocity direction (Figure 5c), the principal scattering ring exhibits two diffraction spots which are brighter

Figure 4. (a) Intensity as a function of azimuthal angle and (b) orientation function (ψ, defined in eq 3) determined from the 2D SAXS data obtained in the shear gradient direction, after LAOS at 130 and 180 °C. Both figures were generated using the innermost ring of spots (at constant q) observed in the shear gradient direction in Figure 3. In (a), data are shown at local strains of 32 and 64% for alignment temperatures of 130 and 180 °C, respectively. In (b), the orientation function of the unaligned sample (Figure 2a) was determined to be 0.004.

increased with increasing local strain until a maximum in the orientation function was observed; at higher local strain values the orientation function then decreased. In the following sections, the analysis of the 2D SAXS data and assignment of morphologies will be discussed. We note that our study is unique in the respect that data were obtained in all three shear directions (shear gradient, velocity, and vorticity directions) on the same specimen. The assignment of the microstructure and alignment relative to the applied shear accounted for the diffraction patterns observed in all three directions simultaneously. The microstructure shown here is that obtained following quenching of the sample to room temperature after LAOS was complete. Though some structural changes may have occurred during the quenching process, the room temperature structure was preserved through the thermoplastic elastomeric nature of the sample (i.e., the presence of glassy polystyrene domains resulted in physical cross-linking of the F


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Figure 5. Comparison of 2D SAXS data obtained after LAOS at 180 °C (local strain = 48%, frequency = 1 rad/s) and patterns predicted for coexisting FCC spheres (red △) and HCP spheres (blue □). In the prediction of FCC spheres, the unit cell is aligned such that the shear gradient, vorticity, and velocity directions are parallel to the [111], [11̅0], and [112]̅ directions along the unit cell, respectively. In the prediction of HCP spheres, the unit cell is aligned such that the shear gradient, vorticity, and velocity directions are parallel to the [0001], [011̅0], and [21̅ 10] directions along the unit cell, respectively. Indexing of the predicted diffraction pattern is shown in Figure S14. The unit cell dimension used in the theoretical prediction was a = 42 nm for FCC and a/c = 0.612, c = 47.2 nm for HCP. Data obtained at other local strains are shown in Figures S6−S8.

presence of overlapping spots resulting from the [112̅] and

than the rest (the relationship between the intensity and the azimuthal angle of the primary scattering ring in the velocity direction is shown in Figure S11) and are explained through the

[2̅110] directions in the FCC and HCP units cells, respectively G


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Macromolecules (Figure 5c and Figure S11). Next, we will discuss the reasoning behind these assignments. Prior literature on colloidal and block copolymer solution spherical morphologies suggests the preferred orientation in the velocity direction is along a close-packed direction found on a close-packed plane.65,92−95 In the case of the HCP microstructure, the [2̅110] direction, which we have assigned to the velocity direction, is indeed a close-packed direction on the close-packed {0001} plane, in good agreement with the literature. The assignment of [011̅0] to the vorticity direction follows, as this direction is perpendicular to both the [0001] (shear gradient) and [2̅110] (velocity) directions. If we were to apply the same logic and literature precedence to the FCC microstructure, we would conclude that the vorticity and velocity directions should be parallel to the [112̅] and [11̅0] directions, respectively, as the [11̅0] direction is a close-packed direction on the close-packed {111} plane, and the [112̅] direction is perpendicular to both the [111] and [11̅0] directions. A comparison of these orientations with the data is shown in Figure S12: it is apparent that the combined predictions of the HCP [011̅0] direction and FCC [112̅] directions are coincident with one another and fail to predict the data observed in the vorticity direction. Most notably, the combination of these two directions does not predict four of the six diffraction spots within the principal scattering ring. We then considered the possibility of an orientation in which the shear gradient direction is unchanged (i.e., viewing the closepacked plane on the FCC and HCP unit cells), yet the HCP unit cell is rotated 90° such that the vorticity direction is parallel to the close-packed direction. In this case, there is very poor agreement with the data in both the vorticity and velocity directions (shown in Figure S13). However, if it is the FCC unit cell which is rotated by 90° (vorticity direction parallel to close-packed direction), then there is excellent agreement between the predicted diffraction pattern and data in the vorticity direction and relatively good agreement in the velocity direction; we have concluded this orientation provides the best agreement with the data (Figure 5). In summary, the structure obtained following alignment at 180 °C, determined through consideration of data obtained in all three shear directions, includes coexistence of FCC and HCP spherical morphologies. In the FCC spherical microstructure, the [111] direction was parallel to the shear gradient direction, the [112̅] direction was parallel to the velocity direction, and the [11̅0] direction was parallel to the vorticity direction. In the HCP spherical microstructure, the [0001] direction was parallel to the shear gradient direction, the [21̅ 10] direction was parallel to the velocity direction, and the [011̅0] direction was parallel to the vorticity direction. Indexing of the predicted diffraction patterns shown in Figure 5 is presented in Figure S14. A schematic depicting the FCC and HCP unit cells with their respective alignment with the shear gradient, velocity and vorticity directions is shown in Figure 6. At an alignment temperature of 130 °C, data sets obtained at 32−64% strain were analyzed (Figure 7 and Figures S15−S17), and all showed the coexistence of FCC and HCP spherical morphologies. Data obtained at 16 and 80% local strain were not analyzed due to poor alignment, as evidenced by the orientation function in Figure 4. Representative data sets obtained in the shear gradient, vorticity, and velocity directions at a local strain of 48% are shown in Figure 7 along with predictions based on the respective orientations of the HCP and FCC unit cells. Intensity as a function of azimuthal angle of

Figure 6. Schematic of the relative alignment of the FCC and HCP units cells with the principal shear directions (shear gradient, vorticity, and velocity directions), resulting from the analysis of data at alignment temperatures of 180 and 130 °C (Figures 5 and 7).

the primary scattering ring for each shear direction is shown in Figures S18−S20. The observed diffraction patterns are similar to that discussed for the data obtained at an alignment temperature of 180 °C (compare Figures 5 and 7), and therefore the orientations of the HCP and FCC units cells which best describe the data are the same as that discussed above (shown in Figure 6). Indexing of the predicted diffraction patterns shown in Figure 7 is presented in Figure S21. There are a few notable differences between the data obtained at alignment temperatures of 180 and 130 °C. While the alignment temperature of 130 °C produced a higher degree of order in the shear gradient direction (as evidenced by the orientation function in Figure 4b), the degree of order was noticeably worse in the vorticity and velocity directions (Figure 7 and Figures S15−S17), complicating the comparison of the predicted diffraction patterns and data. One simple explanation for this is based on how we obtained the SAXS data. A thin strip of the rheometer disk was removed in order to take data in the shear gradient direction, and the strip was then rotated 90° to take data in the velocity direction. Finally, cubes were cut from the strip (at specified locations) to take data in the vorticity direction. To the best of our ability, these measurements were taken at orthogonal angles to one another at the local strain values specified in the article. However, it is certainly possible that (1) we did not take data at these exact shear directions that we specified (there could have been a slight mismatch in the angle) or (2) the degree of order might have differed depending on the exact portion of the sample the SAXS beam went through (i.e., at a given local strain, there is some uncertainty in the exact local strain value at which we took the data, depending on how the sample was removed from the rheometer disk and then analyzed). Though we generally held the unit cell dimensions constant across the three shear directions (shear gradient, vorticity, and velocity) in the theoretical predictions, allowing the unit cell dimensions to differ among the shear directions did not significantly improve the quality of fit (Figure S22). It is well established in the literature that soft spherical systems accommodate many types of defects.96 The data presented in this article do not reflect perfect ordering of the samples, and there may be multiple grains present (i.e., faint isotropic rings are observed underlying the spot patterns discussed here). At the alignment temperature of 130 °C, features are observed in the vorticity direction (Figure 7b and Figure S16) characteristic of twinned structures.58,64,65,92,96,97 H


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Figure 7. Comparison of 2D SAXS data obtained after LAOS at 130 °C (local strain = 48%, frequency = 1 rad/s) and patterns predicted for coexisting FCC spheres (red △) and HCP spheres (blue □). In the prediction of FCC spheres, the unit cell is aligned such that the shear gradient, vorticity, and velocity directions are parallel to the [111], [11̅0], and [112]̅ directions along the unit cell, respectively. In the prediction of HCP spheres, the unit cell is aligned such that the shear gradient, vorticity, and velocity directions are parallel to the [0001], [0110̅ ], and [21̅ 10] directions along the unit cell, respectively. Indexing of the predicted diffraction pattern is shown in Figure S21. The unit cell dimension used in the theoretical prediction was a = 45 nm for FCC and a/c = 0.62, c = 51 nm for HCP. Data obtained at other local strains are shown in Figures S15−S17.

Furthermore, azimuthal smearing in the vorticity direction may indicate rotational grain reorientation, in which slower dynamics are observed at 130 °C, compared to 180 °C

(compare Figures 5b and 7b). Additionally, in the velocity direction, anomalous spots present which are not captured by the predicted diffraction patterns (Figure 7c and Figure S17), I


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specimen and it is possible we are not looking directly at the e− ⃗ v ⃗ plane (shear gradient direction), though we have not identified hypothetical directions for the FCC and HCP units cells that are consistent with the FFT shown in Figure S23. Nonetheless, the presence of ordered spheres is confirmed through this direct view of the microstructure. The primary peak locations observed in the 1D SAXS data and FFT of the TEM micrograph obtained from the aligned sample are comparable to one another (Figure S24). Literature Precedence for Close-Packed Spheres in Soft Material Systems. Sphere-forming block copolymers predominantly form BCC structures, both under quiescent conditions40 and under shear.31−38 The narrow phase window of close-packed spheres in block copolymers predicted by theory40−42 has only been observed in a few quiescent bulk block copolymer systems.43,44 Theoretical studies indicate thermal fluctuations destabilize the close-packed sphere morphology,45,46,51 promoting the formation of spherical micelles.47−50 Alleviation of the packing frustrations of a block copolymer melt may stabilize the close-packed sphere phase: close-packed spheres have been observed in block copolymer micelle solutions53,57,58,61,64,65,92 and homopolymer/ diblock copolymer blends.66,67 An additional method of alleviating packing frustrations is to increase the dispersity of the polymer, which increases the size of the close-packed sphere region of the block copolymer phase diagram predicted by theory.73 Experimental observation of FCC spheres has been reported in a higher dispersity diblock copolymer following melt processing.74 The triblock copolymer employed in our study was synthesized through RAFT polymerization and had a trimodal molecular weight distribution (Figure S1). As discussed previously,75 the lower molecular weight mode to the right of the primary peak is attributed to the presence of poly(lauryl-costearyl acrylate) precursor that was not chain extended, and the higher molecular weight mode to the left of the primary peak is attributed to the presence of chain branching. We note that the poly(lauryl-co-stearyl acrylate) precursor content is likely too low to explain the formation of close-packed spheres based on the presence of homopolymer contamination alone (in refs 70 and 71, close-packed spheres were predicted when the homopolymer content was around 40% or higher in diblock copolymer/homopolymer blends). However, the increased dispersity of the triblock copolymer in our study (1.65) is comparable to that employed in ref 73, for which the closepacked sphere phase window was predicted to be significantly larger than that of a monodisperse block copolymer. Furthermore, the morphology observed prior to alignment in the SAS triblock copolymer studied here (Figure 2) is very similar to that reported previously for an unaligned poly(styrene-b-butadiene-b-styrene) triblock copolymer containing a higher dispersity butadiene block.99 We therefore attribute the existence of close-packed spheres in our study to the higher dispersity of the block copolymer. Many soft material systems form close-packed spheres, and these prior studies provide context for the data analysis we have presented in this article. For instance, FCC and HCP spherical microstructures are prevalent in colloidal crystals,93,100 star polymers,101 and block copolymer solutions,.53,57,58,61,64,65,92 In general, in spherical systems, the interaction potential governs the relative stabilities of close-packed (FCC or HCP) and BCC structures. Spherical block copolymer solutions in which the corona thickness is small relative to the micelle core size adopt

indicate the possibility of a coexisting microstructure or orientation that has not been quantified by our analysis. As these features are not evident in the shear gradient and vorticity directions, we did not attempt to identify the origins of this discrepancy. Once again these differences may be due to the exact angles and locations within the specimen that the SAXS data were obtained in the three shear directions. These features were not observed at an alignment temperature of 180 °C (Figure 5 and Figures S6−S8). Confirmation of Ordered Spherical Morphology with TEM. The presence of an ordered spherical morphology was confirmed through electron microscopy. The specimen that was aligned at 180 °C and 1 rad/s was quenched to room temperature and subsequently prepared through cryo-microtoming and ruthenium oxide staining for TEM analysis. The microtomed section was removed from the sample in an orientation approximately perpendicular to the shear gradient direction. A representative image is shown in Figure 8. An

Figure 8. TEM image obtained following alignment with LAOS at 180 °C and 1 rad/s.

ordered array of spheres is clearly observed in Figure 8 (the dark domains are polystyrene and the light domains are polyacrylate), in stark contrast to the disordered spherical morphology observed for the unaligned specimen in Figure 2. Though hexagonal packing is expected based on the 2D SAXS diffraction pattern (Figure 5), it is not observed in Figure 8. The fast Fourier transform (FFT) of the micrograph (Figure S23) is clearly distinct from the SAXS data shown in Figure 5a. There are a number of possible explanations for this discrepancy. First, the microtoming process to create the section for TEM analysis can distort the structure.98 Next, the microtome temperature (−100 °C) was below the melting point of the polyacrylate matrix of the triblock copolymer (10.3 °C, reported in ref 75), and the observed structure may have been distorted by crystallization of the matrix. Third, it is possible that the staining conditions do not reveal the full extent of the structure. Finally, it is difficult to precisely control the angle at which the microtomed section is removed from the J


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the SAS triblock copolymer provided a convenient means to observe the aligned morphology. Following the application of LAOS, the specimen was quenched to room temperature (below the glass transition temperature of polystyrene), and small-angle X-ray scattering (SAXS) data were obtained in the three principal shear directions: shear gradient, velocity, and vorticity directions. When LAOS was applied at 210 °C (around 30 °C below the order−disorder transition temperature of the polymer), 2D SAXS data showed the presence of isotropic rings, consistent with the lack of orientation of the domains. When LAOS was applied at lower temperatures (180 and 130 °C), however, clearly anisotropic scattering patterns were observed, consistent with alignment of the grains in the presence of shear. The scattering data in all three directions (shear gradient, velocity, and vorticity directions) were analyzed and compared to theoretical predictions. The analysis revealed that the SAS triblock copolymer formed coexisting facecentered cubic (FCC) and hexagonally close-packed (HCP) spherical microstructures, in stark contrast to an extensive body of literature on sphere-forming bulk block copolymers that favor body-centered cubic systems under quiescent conditions and under shear. The microstructure observed in this bulk block copolymer was reminiscent of that observed in various spherical soft material systems such as colloidal spheres, sphereforming block copolymer solutions, and star polymer solutions. The observation of close-packed spherical microstructures in this neat triblock copolymer is hypothesized to originate from the dispersity of the block copolymer.

close-packed FCC structures; however, as the corona thickness is increased, a transition to the more open BCC structure is observed.52−56 Variations in solvent penetration of the micelle core, resulting in changes to the micellar radius and aggregation number, also lead to a transition from FCC to BCC spheres.57,58 In colloidal systems, long-range repulsive interactions produce BCC structures, whereas short-range repulsive interactions produce FCC systems.55 The BCC microstructure is favored in charged colloids at low ionic strength, while FCC is observed at high ionic strength.102,103 Acid aggregates in ionomers with precise sequencing have also been observed to form both FCC and BCC structures.104,105 In star polymer solutions, a decrease in packing density or arm number promotes transition from BCC to FCC spherical microstructures.101 Interestingly, in soft materials which form FCC spheres, the application of shear predominantly produces a transition to the HCP spherical microstructure.59−63,100 The coexistence of FCC and HCP spheres has also been observed in colloidal systems and block copolymer solutions.54,60,62−65,94,106−108 The free energies of FCC and HCP microstructures are close to one another, and random stacking of close-packed planes (along the shear gradient direction) is often observed (i.e., random occurrence of ABCABC, ACBACB, and ABABAB stacking sequences), in which closepacked planes not directly next to one another are uncorrelated. Under flow, close-packed layers may slide past one another, contributing to the random packing along the shear gradient direction.54,60,62−65,94,106−108 Prior studies have predominantly reported orientations of HCP and FCC unit cells in soft spherical systems in which close-packed planes (i.e., FCC {111} and HCP {0001}) are viewed in the e− ⃗ v⃗ plane (thus, in the shear gradient direction),53,54,58,59,64,65,92−94 and a close-packed direction on a close-packed plane is parallel to the velocity direction.65,92−95 Nonetheless, coexisting HCP and FCC spherical systems have been reported in which the FCC unit cell is tilted such that the close-packed planes are not aligned in the shear gradient direction,57,62,63 and similarly FCC systems have been reported in which close-packed planes are aligned perpendicular to the shear gradient direction.60,64 The alignments of the HCP and FCC spheres in our study follow the literature conventions described above: (1) closepacked planes are stacked along the shear gradient direction, (2) in the HCP structure, the velocity direction is parallel to the close-packed direction, and (3) the FCC structure is rotated 90° such that the close-packed direction is parallel to the vorticity direction (as described previously, prior studies have reported tilted or rotated FCC structures). This work demonstrates the highly unanticipated result of a close-packed spherical morphology (coexistence of FCC and HCP spheres) in a neat triblock copolymer under largeamplitude oscillatory shear. The formation of the close-packed spherical morphology is hypothesized to originate from the high dispersity of the block copolymer.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b00505. GPC data for the SAS triblock copolymer (Figure S1); comparison of 1D SAXS data (from the unaligned sample) and predictions for common block copolymer morphologies (Figure S2); intensity as a function of azimuthal angle of SAXS data from the unaligned sample (Figure S3); 2D SAXS data obtained in the shear gradient direction, after LAOS at 210 °C (Figure S4); 2D SAXS data obtained in the shear gradient direction, after LAOS at 180 °C (Figure S5); comparison of 2D SAXS data obtained after LAOS at 180 °C and theoretical predictions for HCP/FCC spheres (Figures S6−S8); intensity as a function of azimuthal angle of the primary scattering ring (following LAOS at 180 °C) (Figures S9− S11); comparison of FCC/HCP orientations that are inconsistent with the data (Figures S12 and S13); indexing of the diffraction spot predictions for FCC and HCP (following LAOS at 180 °C) (Figure S14); comparison of 2D SAXS data obtained after LAOS at 130 °C and theoretical predictions for HCP/FCC spheres (Figures S15−S17); intensity as a function of azimuthal angle of the primary scattering ring (following LAOS at 130 °C) (Figures S18−S20); indexing of the diffraction spot predictions for FCC and HCP (following LAOS at 130 °C) (Figure S21); comparison of 2D SAXS data obtained after LAOS at 130 °C and theoretical predictions for HCP/FCC spheres in which the unit cell dimensions were not held constant across the three shear directions (Figure S22); fast Fourier transforms (FFTs)

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CONCLUSIONS A microphase-separated poly(styrene-b-(lauryl-co-stearyl acrylate)-b-styrene) (SAS) triblock copolymer exhibiting a disordered spherical microstructure with randomly oriented grains was aligned through the application of large-amplitude oscillatory shear (LAOS) at a temperature below the order− disorder transition temperature of the triblock copolymer, yet above the glass transition temperature of the polystyrene spherical domains. The thermoplastic elastomeric behavior of K


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of TEM micrographs obtained from the SAS triblock copolymer before and after alignment (Figure S23); 1D SAXS data and 1D profile from the FFT of the TEM micrograph obtained from the aligned SAS triblock copolymer (Figure 24) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Ph 713-743-2748. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The UH Department of Chemical and Biomolecular Engineering Rigaku SAXS instrument is funded by the National Science Foundation under Grant DMR-1040446. We thank the NIST Center for Neutron Research for access to Igor routines used in 1D SAXS data analysis. We appreciate the assistance of Wenyue Ding in obtaining SAXS data following annealing of the unaligned sample. The authors appreciate the assistance of Dr. Charles Anderson for access and training in the University of Houston Department of Chemistry Nuclear Magnetic Resonance Facility. We thank Ramanan Krishnamoorti, Julia Kornfield, and Karen Winey for helpful discussions. S.W. and M.L.R. acknowledge financial support by the National Science Foundation through Grant DMR-1351788. R.X., S.V.K., and E.D.G. acknowledge financial support by the National Science Foundation through Grant DMR-1056199. E.W.C. acknowledges support by the U.S. Department of Agriculture (Grant 2014-38202-22318).

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