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Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Martensitic Transformation of Close-Packed Polytypes of Block Copolymer Micelles Liwen Chen,† Han Seung Lee,‡ Mikhail Zhernenkov,§ and Sangwoo Lee*,† †

Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, United States Characterization Facility, University of Minnesota, Minneapolis, Minnesota 55455, United States § National Synchrotron Light Source-II, Brookhaven National Laboratory, Upton, New York 11973, United States ‡

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ABSTRACT: We report martensitic shear transformation of strongly segregated block copolymer micelles on face-centered cubic (FCC) lattices to hexagonally close-packed (HCP) structures elucidated by X-ray scattering characterizations. The initial FCC crystal structures of the block copolymer micelles were prepared by direct dissolution of poly(1,2-butadiene-b-ethylene oxide) (PB-PEO) diblock copolymer in the water at 25 °C, and the FCC crystal domains were shear-aligned during the sample preparation process for the X-ray scattering measurements. Heating the shear-aligned FCC crystals of the PB-PEO micelles above 80 °C initiated the transformation to HCP structures, which are also found stable at 25 °C when cooled from the transition temperature. Remarkably, we found that the HCP crystal domains are also aligned, and this suggests that the FCC-to-HCP phase transition has occurred by the martensitic shear transformation. Scattering pattern analysis reveals that the martensitic shear transformation proceeds by preferentially dislocating a specific set of two-dimensional hexagonal close-packed (2D-HCP) layers among four equivalent 2D-HCP layers of the initially shear-aligned FCC crystals. We believe that the selective martensitic shear transformation originates from the orthorhombic-like morphology of the FCC crystal domains formed by slip dislocations and stratifications of initial FCC crystal grains during the sample preparation process. In the shear-aligned FCC crystals with the orthorhombic-like crystal domains, the specific 2D-HCP layers chosen for the martensitic shear transformation have the least area of dislocations, i.e., the least kinetic energy barrier, for the FCC-to-HCP phase transition and appear to be preferentially utilized. These findings show that the size and morphology of crystal domains are critical to the formation, stability, and transformation of crystalline structures and consequently control the polymorphism of solid compounds.

1. INTRODUCTION Martensitic transformation is a diffusionless phase transition mechanism that transforms crystal structures to different structures by straining the lattice sites of the initial crystals in highly coordinated ways.1,2 Nearly all material classes in crystalline states have been observed utilizing martensitic transformation as a phase transformation mechanism in their solid-to-solid structure transitions. In metals, martensite transformed from hot austenite carbon steels by rapid cooling is a representative example.3 In organic materials, graphite is known to transform into a diamond by shock-induced martensitic transformation.4 Martensitic transformation is also known to occur in biological systems. The contraction of the tail-sheath of bacteriophages during the injection of their genome in host cells and the shape changes of bacterial flagella are representative examples in which martensitic transformations are employed in living organisms.5 In polymers, the mechanical strain martensitically transforms orthorhombic polyethylene crystals to monoclinic polymorph.6 Polymorphism is the phenomena of solid materials forming different crystal structures, i.e., polymorphs, without changing the chemical compositions of materials.7 Polymorphs of a chemical compound have different thermodynamic states, and the associated microstructures directly impact on the properties © XXXX American Chemical Society

of the solid compounds for target applications. Therefore, controlling the polymorphism of crystalline compounds is critical for practical applications of crystalline compounds and also scientific interests. However, the fundamental understanding of polymorphism and controlled transformations between polymorphs are far from complete.8−10 Polytypism is a type of polymorphism referring to the arrays of crystal structures made by stacking 2D-crystalline layers in different orders. The crystal structures formed by stacking 2D layers in different orders are referred to as polytypes. Closepacked structures are the polytypes made by stacking 2Dhexagonal close-packed (2D-HCP) layers of equal spheres or lattice sites. Close-packed structures are widely occurring in elements, hard-sphere colloids, and chain-tethered nanoparticles in crystalline states.11−16 In block copolymer melts, the phase domains of close-packed structures of spherical domains exist at the phase boundary of the disordered and longrange ordered domains.17−19 Close-packed structures are also widely observed from polymeric micellar systems.20−26 Received: May 3, 2019 Revised: July 12, 2019

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DOI: 10.1021/acs.macromol.9b00917 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

of the phase behaviors of the solid xenon and the aqueous block copolymer micelles. The solid xenon transforms from FCC to HCP by pressurization, which increases the number density of xenon atoms, and the block copolymer micelles under the nonnegligible Laplace pressure have the relatively higher osmotic pressure in the corona domains of the micelles, which increases the number density of micelles in the crystal domains and compacts the micelles. The correlation between the polytypes of close-packed block copolymer micelles and the micelle number density is also observed from other block copolymer micelle systems: the block copolymer micelle solutions forming HCP structures have relatively higher number densities of micelles than the micelle solutions forming FCC structures.25,38 Interestingly, the other noncubic RHCP structures of block copolymer micelles also appear related to the mechanical stress as shearing FCC structures of block copolymer micelles often produces the RHCP structures.39,40 The correlation between the polytypes of close-packed block copolymer micelles and micelle concentration leads us to search the noncubic close-packed polytypes of the PB-PEO block copolymer micelles. We investigated the long-range ordered structures in the high-concentration solutions in which the micelle number density is high and also the corona domains of micelles are under relatively high osmotic pressure, which are qualitatively similar to the high Laplace pressure condition of the small crystal domains that stabilizes the micellar noncubic closepacked structures. However, contrary to our anticipation, the long-range ordered structure of high-concentration micelle solutions prepared by the direct dissolution of a block copolymer surfactant was found to form only FCC polytypes.41 We speculated that the observed FCC structures are kinetically trapped states, investigated temperature-dependent phase transition behavior of the high-concentration micelle solution, and identified HCP structures developing from the initial FCC states near the melting temperature of the close-packed micellar crystals. Surprisingly, a careful examination of the X-ray scattering patterns reveals that the transformation from the initial FCC to HCP by heating proceeds by a martensitic shear transformation process that selectively dislocates a specific set of 2D-HCP layers of initially shear-aligned FCC crystals among other equally available sets of 2D-HCP layers in different orientations. We believe that the selective martensitic shear transformation that utilizes the specific set of 2D-HCP layers originates from anisotropic morphology of the FCC crystal domains formed during the sample preparation process that shears, plastically deforms, and breaks the initial FCC crystals into small domains. More specifically, shear stress applied during the sample preparation process appears to have induced local shear slips in the FCC crystals and broke the initial FCC crystals into small stratified crystal domains of orthorhombic-like morphology.42 In the FCC crystal domains with orthorhombic-like morphology, the specific 2D-HCP layers dislocated for the martensitic shear transformation have the smallest cross-sectional areas, i.e., the lowest kinetic energy barrier, for the diffusionless transformation. We believe that the orthorhombic-like morphology of the FCC crystal domains formed by shear leads to the selective martensitic shear transformation process that produces the aligned HCP crystal structures. The selective martensitic transformation process observed from the close-packed structures of model block copolymer micelles in this report reveals the critical role of the size and morphology of crystal domains in the phase transformations

Face-centered cubic (FCC) structures with the stacking order of the 2D-HCP layers of ...ABCABC... and the hexagonal closepacked (HCP) structure of the ...ABABAB... are two prevalent close-packed structures in nature (Figure 1).11 However, other

Figure 1. Unit cell and 2D-HCP layer stacking representations of closepacked structures of equal spheres. (a) FCC structure in the ...ABCABC... stacking order of the 2D-HCP layers of equal spheres. (b) HCP structure in the ...ABABAB... stacking order.

close-packed structures with different stacking orders also have been observed. Lithium metal at a cryogenic temperature (4.2 K) forms a close-packed structure that has a nine repeating 2DHCP layer sequence.27 Randomly stacked 2D-HCP layer (RHCP) structures are formed during the martensitic transformations of FCC crystals of xenon and cobalt to HCP.28,29 RHCP structures are also observed during the crystallization of hard-sphere colloids as transitional states that eventually transform to stable FCC as the colloidal crystal domains grow.12,30,31 Intriguingly, the crystal structures of ice at ambient pressure also develop transitional polytypes similar to the states of hard-sphere colloids. Ice formed from supercooled water or in mesopores develops the crystal structure of randomly stacked layers of hexagonally arranged water molecules that is a mixed state of metastable cubic ice (Ice Ic) and stable hexagonal ice (Ice Ih).32,33 Similar to the growing close-packed structures of hard-sphere colloids, the ice crystals with the random stacking configurations transform to the stable Ice Ih as the ice crystals grow.33 Recently, we reported the HCP and RHCP polytypes of strongly segregated poly(1,2-butadiene-b-ethylene oxide) (PBPEO) block copolymer micelles in aqueous solutions induced by temperature quenching of disordered PB-PEO micelles at elevated temperatures.23 We found that these noncubic closepacked structures transform to stable FCC structures as the crystal domains of block copolymer micelles grow. This finding also casts a question regarding the phase transition kinetics of the polytype-to-polytype or solid-to-solid phase transitions of the block copolymer micelles on the close-packed lattices. The observed transitions of the close-packed structures of block copolymer micelles likely occur by the diffusionless phase transition mechanism such as martensitic or shuffle transformations. However, direct observations of diffusionless transitions from model spherical particle systems for the fundamental understanding of the phase transformation mechanisms in the solid states are still rare.34−37 In our earlier report,23 we identified the metastable HCP and RHCP structures from aqueous block copolymer micelles under the crystal growth process and realized that the formation and stabilization of these noncubic metastable close-packed polytypes appear related to the sizes of crystal domains. We observed that small crystal domains stabilize the micellar noncubic HCP and RHCP structures, and the stability of these noncubic close-packed micelles was attributed to the nonnegligible Laplace pressure originating from the small size of the crystal domains. This reasoning is based on the assumed analogy B


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Macromolecules between crystalline states.12,23,32 This finding suggests important insights regarding the material-processing strategies to control the crystal structures and the morphology of crystal domains for target applications of crystal compounds such as pharmaceutically active ingredients.10,43−46

3. RESULTS 3.1. Molecular Characterization of Block Copolymer Surfactant. The number-averaged molecular weights of the PB-PEO diblock copolymer Mn = 6.8 kg/mol and the weight fraction of PEO block wPEO = 0.71 were determined by the 1H NMR characterizations. The polydispersity Đ = 1.10 was determined by the SEC characterization. The molecular structure and schematic representation of the PB-PEO diblock copolymer are presented in Figure 2a.

2. EXPERIMENTAL SECTION 2.1. Synthesis and Molecular Characterization of Polymeric Surfactant. Poly(1,2-butadiene-b-ethylene oxide) (PB-PEO) diblock copolymer surfactant was synthesized by the two-step anionic polymerization process.47 Butadiene (Sigma-Aldrich) and ethylene oxide (Sigma-Aldrich) were purified twice by vacuum distillation over n-butyllithium. Tetrahydrofuran (Sigma-Aldrich) was purified by purging dry argon and passing through activated basic alumina columns. Polymerization of 1,2-polybutadiene was initiated using secbutyllithium initiator (Sigma-Aldrich) in tetrahydrofuran at −78 °C. The temperature of the polymerization solution was slowly increased to −30 °C over 5 h to accelerate the polymerization reaction, and the polybutadiene chains were end-capped with the excess amount (∼10 molar equivalents to the living anions) of purified ethylene oxide. The end-capping reaction was conducted at 25 °C for a day, and the reaction was terminated with methanol. The ω-hydroxyl poly(1,2-butadiene) was dried, redissolved in tetrahydrofuran, and titrated with potassium naphthalenide to produce poly(1,2-butadiene) macroinitiators with oxyanions for the anionic ring-opening polymerization of ethylene oxide at 45 °C for 2 days. The polymerization of poly(ethylene oxide) block was terminated with methanol. The molecular weight and chemical composition of the synthesized PB-PEO diblock copolymer were determined by 1H NMR characterization (Agilent 500 MHz). The polydispersity of the PB-PEO diblock copolymer was determined by the size exclusion chromatography (Agilent) characterization using tetrahydrofuran as the eluent. Three consecutive mixed-C columns are employed as the stationary phase. 2.2. Preparation of Micelle Solutions. PB-PEO micelle solutions investigated in this study were prepared by the direct dissolution of the PB-PEO in deionized water. The solutions were stirred and visually inspected to confirm the homogeneity of the solutions. 2.3. Measurements of Small-Angle X-ray Scattering (SAXS) Patterns. SAXS characterizations were conducted at the 12-ID-SMI beamline at the National Synchrotron Light Source II (NSLS-II) in the Brookhaven National Laboratory, NY. The sample capillaries were characterized with polarized X-ray with the wavelength λ = 0.7749 Å, and 2D scattering patterns were obtained using the 1 M Pilatus detector located at 8.3 m from the samples. The full width at the half-maximum of the beam intensity of radiated X-ray was 200 μm in the horizontal and 20 μm in the vertical directions. We note that the horizontal dimension of the X-ray beam is important to understand the 2D-SAXS patterns of the long-range ordered structures of block copolymer micelles (see Section 3.4). The obtained 2D scattering patterns were azimuthally integrated to produce one-dimensional (1D) scattering intensity patterns versus the scattering vector q = 4π·sin(θ/2)/λ, where θ is the scattering angle. 2.4. Cryogenic Transmission Electron Microscopy (CryoTEM) Characterization. Real space images of the PB-PEO micelles in vitrified water were obtained using a Tecnai G2 F30 S-TWIN TEM (FEI) operating at 300 kV. A Vitrobot Mark IV (FEI) was employed to prepare cryo-TEM specimens. Cryo-TEM specimens were prepared by applying a small amount (∼2 μL) of the 1 wt % PB-PEO micelle solution diluted from the 23 wt % solution onto a lacey carbon grid (Cu, 300 mesh, Ted Pella) in a 100% relative humidity environment at 22 °C. The excess solution in the grid was blotted, and then the blotted grid was plunged into liquid ethane at −183 °C. The prepared cryoTEM specimen was transferred to a cryotransfer holder (Gatan) at −176 °C for imaging. The micrographs were recorded in the low-dose mode using an Ultrascan 4000 CCD camera (Gatan) with underfocus conditions (∼5 μm) to enhance the contrast of the core domains of the PB-PEO micelles.

Figure 2. PB-PEO diblock copolymer, Cryo-TEM micrograph of the PB-PEO micelles, and schematic representation of the micelles. (a) Schematic representation of the PB-PEO diblock copolymer chain. (b) Representative cryo-TEM micrograph obtained from the 1 wt % PBPEO solution prepared by diluting the 23 wt % PB-PEO and water solution. The dark domains are the PB core domains. The faint halolike features around the core domains are the Fresnel fringes caused by underfocusing (∼5 μm) of the micelles to enhance the micrograph contrast. The PEO corona domains are not visible. (c) Schematic representation of a spherical micelle with unsolvated core and solvated corona domains.

3.2. Cryo-TEM Characterization. We prepared 23 wt % PB-PEO solutions by the direct dissolution of the dry PB-PEO diblock copolymer in the water at 25 °C. The dry PB-PEO diblock copolymer has a lamellar morphology (Figure S2), and the direct dissolution of the PB-PEO in water transforms the lamellar domains into spherical micelles by the selective hydration of the PEO block.48 The morphology and dimension of the PB-PEO micelles in water were characterized by the cryo-TEM imaging of the 1 wt % PB-PEO micelle solution, which is prepared by the dilution of the 23 wt % PB-PEO solution (Figures 2b and S3). The spherical geometry of micelles is confirmed (Figure 2c), and the size of the micelles is nearly monodisperse. Strongly hydrophobic PB block forms the core domains of the micelles, which are nearly free of water, and the hydrophilic PEO block forms the water-swollen corona domains. We note that the 1 wt % PB-PEO micelle solution characterized with cryo-TEM characterization was prepared by diluting the 23 wt % PB-PEO solution to confirm that the aggregation number, i.e., the size of PB core domains, of the PB-PEO micelles in the 23 wt % solution is nearly identical to the aggregation number of the micelles prepared at different concentrations. This is important to confirm that the change of the polymer concentration does not significantly change the aggregation number of micelles, and, consequently, the concentration of the polymer in the solution is directly correlated with the number density of micelles in the solutions. We also note that the aggregation number of each PB-PEO micelle does not change in the dilution process of the 23 wt % C


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Figure 4a shows the representative 1D-SAXS patterns obtained from the 23 wt % PB-PEO soft solid solution by

solution because the PB-PEO micelles in water cannot exchange PB-PEO polymer chains due to the strong hydrophobicity of the PB block that practically eliminates free PB-PEO chains in the selective water solvent, i.e., the critical micelle concentration is practically zero.49 The PB core radius of the micelles based on the cryo-TEM micrographs Rc,TEM = 8.0 ± 0.4 nm, and the micelle radius Rm,TEM = 20 ± 0.4 nm based on the lattice size of the two-dimensional hexagonal close-packed (2D-HCP) layer of micelles in vitrified water films in the lacey carbon TEM grids (Figures 2b and S3). These micelle dimensions are comparable to those of the PB-PEO micelles in the 1 wt % solutions prepared by the direct dissolution of the unsolvated PB-PEO diblock copolymer, which were reported in our earlier study, Rc,1wt% = 7.7 nm and Rm,1wt% ≈ 21 nm.23 This result shows that the aggregation number of the PB-PEO micelles does not significantly vary with the initial dissolution concentration of the unsolvated PB-PEO diblock copolymer. 3.3. One-Dimensional SAXS Pattern Analysis: Transition from FCC to HCP by Heating. The 23 wt % PB-PEO solutions were annealed for at least a week before the solutions were transferred into thin-walled quartz capillaries (Charles Supper) with a nominal diameter of 1.5 mm for SAXS characterizations. Because the 23 wt % PB-PEO and water solutions are soft solids, we transferred the PB-PEO solid solutions to capillaries using syringes attached with a 3 inch-long and 18-gauge (inner diameter 0.84 mm) needle (Figure 3). The quartz capillaries are flame-sealed to prevent any loss of water during the characterization. The transfer rate was approximately 0.01 mL/s. This sample injection process shear-aligned FCC crystals of which morphology is realized important to understand the phase transformation kinetics of the initial FCC crystals to HCP structures (see Sections 3.4 and 3.5).

Figure 4. Time-resolved 1D-SAXS patterns obtained by heating the 23 wt % PB-PEO micelle solutions prepared by the direct dissolution of the PB-PEO diblock copolymer in water. The arrows in the right show the order of measurements. (a) SAXS patterns obtained by the stepwise heating of the initial micellar FCC crystals at 25 °C to the temperatures marked in the right of the scattering patterns. (b) Time-resolved SAXS patterns by heating shear-aligned FCC crystals at 25−84 °C. The dashed line in red is after the 1D-SAXS pattern of disordered micelles at 90 °C in the panel (a). The top 1D-SAXS pattern is obtained from the sample cooled to 25 °C after annealing at 84 °C over 11 min.

heating from 25 °C. The 1D-SAXS patterns at the first and second minima at ∼0.018 and 0.05 Å−1 originate from the form factor of micelles as evidenced by the form factor of micelles obtained from the 1 wt % solution prepared by the dilution of the 23 wt % solution (Figure S4). The positions of the Bragg peaks of the 1D-SAXS pattern obtained at 25 °C (marked with the black arrows in Figure 4a) match with the diffraction pattern of the FCC crystal with the lattice parameter a = 48.8 nm (the Miller indices of the FCC structure are listed in Table S1). The effective hard-sphere radius of the PB-PEO micelles on the FCC lattices Rm,FCC = 17.3 nm, which is ∼14% smaller than the micelle size of the PB-PEO micelles based on the cryo-TEM characterization, Rm,TEM = 20 ± 0.4 nm. Since the aggregation number of micelles in the 23 wt % solid solution must be the same as the aggregation number of the micelles in 1 wt % solutions, the smaller micelle radius in the 23 wt % solid solution

Figure 3. Sample transfer process of the 23 wt % PB-PEO solid solutions into a thin-walled quartz capillary using a syringe attached with a needle. The elucidated pluglike flow of the PB-PEO soft solid is schematically presented in the right panel (see the text).50 D


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Figure 5. Summary of the SAXS patterns of the shear-aligned FCC crystal structures of the PB-PEO micelles. (a, b) 2D-SAXS patterns of the 23 wt % PB-PEO solutions prepared by the direct dissolution of the PB-PEO surfactant in water at 25 °C. In the panel (a), the triangles denote the locations of the intensity maxima of Bragg peaks. The brown arrows note expected locations of the (020), (2̅00), (200), and (02̅0) spots at the rotation angle γ = 54.7°, and the experimentally observed locations of the (020), (2̅00), (200), and (02̅0) spots are marked with the brown triangles with white stars (*). The yellow arrows note the locations of the missing (220) and (2̅2̅0) Bragg spots at γ = 54.7°. These missing (020), (2̅00), (200), (02̅0), (220), and (2̅2̅0) Bragg spots are also noted with the crosses in the panel (b). (c) Configuration of the circularly shear-aligned FCC crystals elucidated from the 2D-SAXS pattern. The angles between the incident X-ray and the [111] direction of FCC crystals, γ, are noted. (d) 2D-HCP stacking representations of the shear-aligned FCC crystals with the notations of flow and capillary directions. The top panel is the projected FCC unit cell in the radial cross section of the capillary, and the lower panel is in the axial cross section.

immediately started, and the scattering pattern saturated at 84 °C at 11 min. The Bragg peaks of the new structure match with the diffraction pattern of the HCP lattices with the lattice parameter a = 35.0 nm and c = 56.8 nm (the Bravais−Miller indices of the Bragg peaks of the HCP structure are listed in Table S2). The ratio of the lattice parameters c/a = 1.623, nearly identical to the ratio of the hard-sphere regular HCP structures 1.633 = 8/3 . The effective hard-sphere radius RHCP = 17.5 nm at 84 °C, which is ∼1.7% larger than the hard-sphere radius of micelles on the FCC lattices at 25 °C. Cooling the micellar HCP solution to 25 °C maintained the set of the Bragg peaks of the HCP structure and even promoted the growth of HCP crystal domains, as indicated by the stronger Bragg peaks and the disappearance of the background intensity from the micelles in disordered states (The top pattern in Figure 4b. The dashed line in Figure 4b is after the scattering pattern of disordered micelles at 90 °C in Figure 4a.) 3.4. Two-Dimensional SAXS Pattern Analysis of the Initial FCC Structures: Shear-Aligned FCC Crystals by Pluglike Flows. The 1D-SAXS patterns reveal the thermally activated phase transition from the FCC to HCP structures. We conducted a morphology analysis of the initial FCC and final

is due to the lower degree of hydration of the PEO corona domains compared to the degree of hydration of the corona domains of the PB-PEO micelles in the 1 wt % solution. To investigate the temperature-dependent long-range ordered structures of the PB-PEO micelles in the 23 wt % solution, the capillary containing the FCC crystals at 25 °C was heated, and the long-range ordered structures of micelles are investigated with SAXS measurements. The initial FCC diffraction pattern persists nearly up to 80 °C though the baseline intensity of the liquid-like packing of block copolymer micelles grows due to the dissolution of the parts of the FCC crystal domains. The pattern begins to develop a new set of diffraction peaks at 83 °C (marked with the red arrows in Figure 4a). Further increase of the temperature of the capillary to 85 °C promoted the growth of the new Bragg peaks, and heating above 87 °C made nearly all of the Bragg peaks disappear that signals the melting of the long-range ordered micellar structures. The phase transition from the initial FCC to the new structure was reproducible from a new capillary containing the 23 wt % PB-PEO solution. The new sample was directly heated to 84 °C from 25 °C, and time-resolved scattering patterns were obtained (Figure 4b). The phase transition of the heated FCC crystals E


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Figure 6. Two-dimensional (2D) SAXS patterns of shear-aligned FCC crystals. (a) Top view of the reciprocal space of a single crystal FCC structure. Reproduced from Abramova et al.52 (b) Bragg spot positions in the 2D-SAXS patterns at different rotation angles of a single crystal FCC. The Bragg spots in red in the 2D-SAXS patterns represent the pattern by the configuration of the crystal structure at the specified rotation angle γ.

in Figure 5d: the [11̅0] direction of the shear-aligned FCC crystals is the velocity direction of the flow (v⃗). The (111) 2DHCP layers of the shear-aligned FCC crystals are aligned normal to the capillary radial direction [111], which is also the velocity gradient direction (v⃗). We simulated 2D-SAXS patterns of the shear-aligned FCC crystals at different rotation angles, γ, between the direction of incident X-ray and the [111] direction of shear-aligned FCC crystals (Figure 5c) and compared the simulated 2D-SAXS patterns with the observed 2D-SAXS pattern of shear-aligned FCC crystals of the PB-PEO micelles. Figure 6a shows the top view of the reciprocal space of a single crystal FCC structure at γ = 0° after Abramova et al.,52 and Figure 6b presents the simulated 2D-SAXS patterns at different rotation angles for the {111}, {200}, and {220} Bragg spots shown in Figure 5b. The comparison of the simulated and experimental Bragg spots at different rotation angles is consistent except the Bragg spots at the rotation angle γ = 54.7°. The first noticeable discrepancy is the azimuthal locations of the experimental (020), (2̅00), (200), and (02̅0) Bragg spots marked with brown triangles with white stars (*) to the locations of the simulated Bragg spots marked with the brown arrows in Figure 5a. This deviation of the azimuthal locations indicates that these Bragg spots are the secondary Bragg traces from small and weakly aligned FCC crystals of which (020), (2̅00), (200), and (02̅0) diffraction spots are not in the Ewald plane.53 Small and weakly aligned morphologies of these FCC crystals produce broad diffraction spots in the reciprocal space, and the edges of the broad Bragg spots even touch the Ewald plane recorded in the 2D-SAXS detector despite the center of Bragg spots not being in the Ewald plane. A schematic configuration of a secondary Bragg spot is

HCP crystal domains with the 2D-SAXS patterns of these closepacked structures and found that the FCC-to-HCP phase transformation must have occurred by a martensitic shear transformation process. Figure 5a,b shows the 2D-SAXS pattern of the 23 wt % PBPEO soft solid solution at 25 °C containing the initial FCC crystals formed by the direct dissolution of the PB-PEO diblock copolymer and transferred by the syringe injection method. The 2D-SAXS pattern reveals azimuthally undulating Bragg scattering features, which indicate that the FCC crystals are shear-aligned in the capillary due to the shear applied during the sample injection process as shown in Figure 3. To confirm the shear-induced alignment, we also conducted SAXS characterization of a minimally sheared PB-PEO micelle solid solution and observed a polycrystalline 2D-SAXS pattern of FCC (Figure S5). The polycrystalline texture shows that the micellar FCC crystals are initially formed by the nucleation and growth mechanism during the direct dissolution process of the PB-PEO diblock copolymer in water, and the shear applied during the capillary sample preparation produces the shear-aligned FCC morphology. To elucidate the configuration of the shear-aligned FCC crystals, which is later found important to understand the configuration of thermally induced HCP crystals in the capillary, we analyzed the 2D-SAXS pattern in Figure 5a,b. Since the needle employed to transfer the 23 wt % PB-PEO solid solution is cylindrical, we assumed pluglike flows of yielding solids in the needle and shear-aligned FCC crystals are circularly arranged around the center axis of the capillary, as schematically presented in Figure 5c.42,51 The spatial relationships of the direction of flow and the crystal directions are shown F


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Figure 7. SAXS patterns of aligned HCP crystals obtained from the 23 wt % PB-PEO micelle solution at 84 °C. (a) 2D-SAXS pattern with an expanded view (right side). Intense Bragg spots of (101̅0), (0002), and (101̅1) rings (first three inner rings) are marked with colored triangles. (b) Simulated 2DSAXS pattern of aligned HCP crystals by the martensitic shear transformation selectively dislocating (11̅1̅) 2D-HCP layers of shear-aligned FCC crystals. See the text. (c) Azimuthal intensity profiles of the first three inner rings. (d) Time-resolved 2D-SAXS patterns showing the development of the aligned morphology of HCP crystals.

presented in Figure S6. The (220) and (2̅2̅0) Bragg spots at the rotation angle γ = 54.7° are farther than the locations of the (020), (2̅00), (200), and (02̅0) Bragg spots from the Ewald plane, as shown in Figure 6a and accordingly not observed in the experimental 2D-SAXS pattern as marked with the yellow arrows in Figure 5a. The missing (220) and (2̅2̅0) Bragg spots also corroborate that the incident X-ray does not directly see the FCC crystals at the rotation angle γ = 54.7°. The missing Bragg spots at γ = 54.7° suggest that the configuration of the shear-aligned FCC crystals in the capillary is formed by a pluglike flow that has high-velocity gradient near the wall and low in the center domain (Figure 3). The horizontal full width at half-maximum intensity of the radiated X-ray is 200 μm, and thus the incident X-ray interacts only with the narrow center domain of the capillary of the 1.5 mm nominal diameter, as schematically represented in Figure 5c. If shear-aligned FCC crystals at all rotation angles exist in the center domain of the capillary, the 2D-SAXS pattern must contain the Bragg spots of the FCC crystals at γ = 54.7° in the 2D-SAXS pattern. Therefore, the missing Bragg spots at γ = 54.7° suggest that the shearaligned FCC crystals are mostly formed near the capillary wall away from the center axis of the capillary, and the incident X-ray interacted only with the shear-aligned FCC crystals at low rotation angles |γ| < 54.7°. For the diffraction patterns at high rotation angles |γ| > 54.7°, i.e., γ = −70.5° and γ = 90°, these are identical to the patterns at the smaller rotation angles γ = 0° and γ = 19.5° (Figure 6b). Also, the non-negligible powder scattering signatures in Figure 5a indicate that the center domain of the capillary contains unaligned polycrystalline FCC crystals due to the low-velocity gradient of a pluglike flow at the center of the flow that preserves the polycrystalline morphology. In sum, the configuration of the FCC crystals in the capillary elucidated by the analysis of the 2D-SAXS pattern shows that the pressure-driven injection process of the 23 wt % PB-PEO soft

solid solution into the capillary induced a plug-flow velocity profile in the needle, and the shear-aligned FCC crystals are transferred in capillaries. The low-velocity gradient in the center domain of the flow preserves the polycrystalline FCC morphology, and the large-velocity gradient near the needle wall produces shear-aligned FCC crystals. We also note that the inferred plug-flow velocity profile from the configuration of the shear-aligned FCC crystals is consistent with pluglike flow velocity profiles of other stress-yielding solids.50,54 3.5. Two-Dimensional SAXS Pattern Analysis of Aligned HCP Crystals: Evidence of the Martensitic Shear Transformation. Remarkably, we found that the 2DSAXS pattern of the HCP crystals of PB-PEO micelles induced from the shear-aligned FCC crystals at the elevated temperature (>80 °C) also displays azimuthally undulating Bragg spots, which suggests that parts of the HCP crystals are also aligned (Figure 7a,b). The signatures of undulating Bragg spot features of the aligned HCP crystals are more clearly revealed in the azimuthal intensity plot in Figure 7c. The time-resolved 2DSAXS patterns (Figure 7d) obtained during the phase transition also show that the azimuthally undulating 2D-SAXS pattern develops from the beginning of the phase transition, which suggests that the initial shear-aligned FCC crystals direct the formation of the aligned HCP crystal morphology by a particular transition pathway. We note that the Bragg peak features of the time-resolved 2D-SAXS patterns in Figure 7d become narrower and seemingly isotropic, e.g., {101̅1} ring, over time as more FCC crystals transform to HCP structures. The narrowing Bragg peaks during the transition indicate that the size of HCP crystal domains becomes larger.55 The isotropic Bragg peak features mostly emerging from 7 min (Figure 7d) show that the formation of nonaligned HCP crystal domains occurs at the late stage of the phase transformation after the aligned crystal domains are first formed. However, the strongly undulating G


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Macromolecules azimuthal intensity profiles in Figure 7c, for example, two strong Bragg spots of (0002) peaks, clearly show that a significant amount of HCP crystals is aligned. The formation of long-range ordered structures from isotropic disordered states of particles by the nucleation and growth mechanism produces powder or polycrystalline structures, and thus the formation of aligned HCP crystals cannot be explained with the nucleation and growth mechanism. We also considered the epitaxial growth of aligned HCP crystals from the shear-aligned FCC crystal domains. However, if a certain crystallographic plane of FCC crystals can serve as a substrate for the epitaxial growth process of HCP crystals, at least a few symmetrically identical crystallographic planes of the FCC crystals in different directions must be able to equally serve as substrate surfaces for the same epitaxial growth because FCC is a high-symmetry crystal structure (the symmetry group number of FCC is 229).56 Accordingly, if the epitaxial growth is the mechanism of the phase transition from FCC to HCP, polycrystalline HCP structures must be observed, but the observed HCP crystals are coherently aligned in a specific direction (see below). This discrepancy leads us to conclude that the phase transition from the initial shear-aligned FCC to aligned HCP must have occurred by a diffusionless transition mechanism utilizing the structural and morphological correlations between the initial FCC and final HCP crystal domains. The diffusionless martensitic transition of FCC-to-HCP structures proceeds by sliding every other 2D-HCP layers of initial FCC crystals in the directions of the Shockley partial dislocations, as schematically shown in Figure 8. Since FCC crystals have four equivalent 2D-HCP layers for the Shockley partial dislocations, (111), (11̅1̅), (11̅1), and (111̅), as shown in Figure 9, we simulated the 2D-SAXS patterns of HCP crystals by the martensitic shear transformations that slip one of the (111),

Figure 9. Unit cell representation of FCC with 2D-HCP planes available for the martensitic shear transformation to HCP structures.

(11̅1̅), (11̅1), and (111̅) 2D-HCP layers in the shear-aligned FCC crystals (Figures 10 and S7−S9) to elucidate the configuration of the aligned HCP crystals represented by the 2D-SAXS patterns in Figure 7. Comparison of the experimental 2D-SAXS pattern in Figure 7a with the simulated 2D-SAXS patterns (Figures 10 and S7− S9) shows that the observed 2D-SAXS pattern of the HCP crystals represents aligned HCP crystals by the martensitic shear transformation dislocating mostly the (11̅1̅) 2D-HCP layers of the shear-aligned FCC crystals (Figure 10). However, the simulated 2D-SAXS pattern in Figure 10 is only for the HCP crystals at the rotation angles γ between −90 and 90° (the front half of the sample capillary seeing the incoming X-ray). If the aligned HCP crystals are centrosymmetric at the capillary axis, as shown in Figure 5c, the Bragg spots of the 2D-SAXS pattern of aligned HCP crystals must be vertically symmetric, as shown in Figure 11. We investigated several capillaries containing thermally induced HCP crystals and found that the 2D-SAXS patterns of aligned HCP crystals are always vertically asymmetric at least in the Bragg peak intensity (Figure S10). This result suggests that the HCP crystals in the capillary are formed asymmetrically in the radial cross section. We also conducted the SAXS measurements of a capillary containing aligned HCP crystals by rotating the capillary to the incident Xray and observed the locations of (0002) peaks vertically flip by the rotation (Figure S11). This result also corroborates the asymmetric configuration of aligned HCP crystals in the capillary.

4. DISCUSSION The scattering pattern analysis of the close-packed PB-PEO micelles in the 23 wt % solutions described above is summarized as follows: • Direct dissolution of the lamellar PB-PEO diblock copolymer in the water at 23 wt % at 25 °C formed polycrystalline FCC crystals of the PB-PEO micelles. • The polycrystalline FCC crystals are shear-aligned by a pluglike flow during the injection process of the FCC crystals into sample capillaries for the X-ray characterization. The pluglike flow was inferred from the configuration of the shear-aligned FCC crystals revealed by the 2D-SAXS pattern. • Heating the shear-aligned FCC crystals above 80 °C produced aligned HCP structures. Cooling the induced HCP structures to 25 °C did not change the HCP

Figure 8. Martensitic shear transformation of FCC-to-HCP structures. (a) Unit cell representation of FCC and HCP structures with 2D-HCP layer representations. The (111) 2D-HCP layers of FCC structures (the planes in light red) are shown with the directions of Shockley partial dislocations, [2̅11], [12̅1], and [112̅]. The 2D-HCP layers of the HCP structure are the (0002) planes. (b) Side view of the martensitic shear transformation. Every other 2D-HCP layer dislocates for the shear transformation. The solid and open circles in the panel b represent the lattice sites above and below the page, respectively. Reproduced from Nishiyama.3 H


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Figure 10. Simulated 2D-SAXS patterns of HCP crystals formed by dislocating the (11̅1̅) 2D-HCP layers of shear-aligned FCC crystals. The Bragg spots in red represent the patterns by the crystal structure at the rotation angle γ of the initial FCC crystal to the incident X-ray. X-ray travels into the printed page at the right angle.

solutions are more stable than the initially formed FCC crystals, which are kinetically trapped metastable structures (see below). The observed phase transition from the kinetically trapped FCC to the stable HCP structures could initiate and proceed only when the FCC structures are heated above ∼80 °C. This thermal activation of the phase transformation process suggests that a certain kinetic energy barrier exists in the phase transition. The classical nucleation theory states that the required supercooling or superheating to initiate phase transitions is to increase the bulk free-energy difference between the metastable and stable phases to compensate for the energy penalty from the surface energy of the new-phase domain.57 Since our 2D-SAXS pattern analysis reveals that the phase transition from the FCC to HCP crystals of the PB-PEO micelles proceeds by the

structures and even promoted the growth of the HCP crystals. • Analysis of the 2D-SAXS patterns of the initial shearaligned FCC and the final HCP crystals, which are also aligned, suggests that the phase transition has occurred by the martensitic shear transformation that preferentially dislocates either (11̅1) or (11̅1̅) 2D-HCP layers of the shear-aligned FCC crystals among four equivalent 2DHCP layers in the FCC crystals. • The 2D-SAXS patterns of the aligned HCP crystals suggest that the aligned HCP crystals are formed asymmetrically in the radial cross section of the capillary. These observations show that the martensitically induced HCP structures of the PB-PEO micelles in the 23 wt % aqueous I


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Figure 11. Two-dimensional SAXS patterns of aligned HCP crystal domains formed by sliding the (11̅1̅) or (11̅1) 2D-HCP layers of circularly shear-aligned FCC crystals and also have radially symmetric configurations. The (0002) Bragg spots are marked in red.

Figure 12. Schematic representation of the dislocation and compression of a sphere in the Shockley dislocation process. At the maximum compression stage, which is marked with the sphere in purple, spheres are compressed by 1 − 11/12 ≈ 4.3% in the radial direction. (a) Top view of the sliding process. (b) Cross-sectional view along the dashed line in the panel (a).

martensitic shear transformation, the kinetic energy barrier of the FCC-to-HCP transitions must include new factors other than the surface energy barrier. We attribute the kinetic energy barrier of the martensitic shear transformation of the FCC to the HCP crystals to two factors. The first factor is the viscosity or yield stress of the disordered (fluid, jammed, or glassy) micelle domains coexisting with the FCC crystal domains. The martensitic shear transformation proceeds by straining FCC crystal domains (Figure 8), and, therefore, the transformation process must simultaneously overcome the kinetic energy barrier from the dislocation of the surrounding disordered or ordered micelles. The Bragg peak patterns of the 23 wt % PB-PEO micelle solution under the phase transition at 84 °C shown in Figure 4b have broad baselines (the intensity profile in a dashed line of the bottom pattern in Figure 4b), which suggest that the PB-PEO micelle solution at 84 °C is in the two-phase state of close-packed and disordered micelles. In our earlier report,23 we observed that the radius of the PB-PEO micelles decreases with temperature because the PEO chains have low critical solution temperatures, i.e., the compatibility of PEO chains with water decreases with temperature, and the volume fraction of the PB-PEO micelles in the solution decreases with temperature.58 Since the viscosity of the colloid solution decreases as the volume fraction of colloidal particles decreases,59 the viscosity of the disordered micelle domain coexisting with the FCC crystal domains decreases with increasing temperature, and the kinetic energy barrier required for dislocating disordered micelle domains also decreases. This is possibly one of the reasons that the martensitic shear transformation of the FCC to HCP of the PB-PEO micelles in the 23 wt % solutions initiates only above ∼80 °C. The second kinetic energy barrier of the martensitic shear transformation of the PB-PEO micelles is the micelle compression required for the dislocation of 2D-HCP layers. Figure 12 describes a Shockley dislocation of a single sphere in the martensitic shear transformation.60 For the case of that the dislocation proceeds at a constant interlayer distance between the dislocating 2D-HCP layers, the radius of micelles in these dislocating 2D-HCP layers are compressed up to 4.3% in the dislocation process. In the observed martensitic shear transformation of the FCC to the HCP crystals, the most intriguing and puzzling behavior is the formation of the aligned HCP crystals by the preferential dislocations of either (11̅1) or (11̅1̅) 2D-HCP layers of the shear-aligned FCC crystals. We believe this selective phase transformation pathway originates from the morphology of the shear-aligned FCC crystal domains resulted by the plastic

deformation of the FCC crystals under shear, which is related to the second kinetic energy barrier discussed above. In the sample preparation process, the polycrystalline FCC crystals of PB-PEO micelles in the 23 wt % solution are shearaligned by pluglike flows, as evidenced by the misaligned and missing Bragg spots at γ = 54.7° in Figure 5a,b. The FCC crystals under the high-velocity gradient domains of a pluglike flow near the capillary wall (Figure 3) must have been plastically deformed and break into smaller FCC crystal domains because unless the FCC crystals break, the solid solution cannot flow.60 Since the plastic deformation of close-packed crystal structures occurs by slipping (111) layers of shear-aligned FCC crystals, the broken FCC crystals by the plastic deformation also must have relatively shorter dimensions in the [111] directions compared to the other orthogonal dimensions of the broken FCC crystal domains. This reasoning suggests that the shear-aligned crystals of FCC crystals have orthorhombic-like crystal domains that have smaller dimensions in the velocity gradient direction (v⃗) than the crystal dimensions in other directions, the velocity (v⃗) and capillary tangent directions. Figure 13a,b presents such postulated orthorhombic-like morphology of an FCC crystal domain formed by the plastic deformation process. In the martensitic shear transformation of the FCC crystals of PB-PEO micelles, the dislocation process of the {111} 2D-HCP layers must overcome the kinetic energy barrier from the micelle compression (Figure 12), and this kinetic energy barrier is proportional to the area of dislocating 2D-HCP layers of the FCC crystals, i.e., the number of micelles to be dislocated. In the assumed orthorhombic-like domains of the shear-aligned FCC crystals shown in Figure 13, the (11̅1) and (11̅1̅) 2D-HCP layers have the smallest cross-sectional areas compared to those of the other (111) and (111̅) layers. This explains the observed preferential dislocations of the (11̅1) or (11̅1̅) 2D-HCP layers for the martensitic shear transformation forming the aligned HCP structures: dislocation of the (11̅1) or (11̅1̅) 2D-HCP layers has the smallest kinetic energy barrier for the martensitic shear transformations. A brief discussion on the relative crosssectional areas of the FCC {111} layers is provided in the Supporting Information. We note that although we realized the importance of the morphology of the crystal domains for the kinetic pathways of the martensitic shear transformation from the elucidated spatial relationships between the initial FCC and final HCP crystal domains, the shear alignment of the FCC crystal domains is not necessary for the martensitic shear transformation since we believe that the size of crystal domains J


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Figure 13. Schematic representation of an orthorhombic-like shear-aligned FCC crystal domain. The dimension of the crystal domain in the velocity gradient direction is shorter than the dimensions in the velocity and capillary tangent directions. (a) Quasi-orthorhombic FCC crystal domain with a unit cell representation and an octahedron showing the spatial relationships between 2D-HCP layers of the FCC crystal. (b) Quasi-orthorhombic FCC crystal domain with 2D-HCP {111} layers for the martensitic shear transformation of FCC-to-HCP structure. The cross-sectional areas of (11̅1̅) and (11̅1) planes are the same.

Another question regarding the aligned HCP crystals is why the martensitic shear transformation selectively utilizes either the (11̅1) or (11̅1̅) 2D-HCP layers of FCC crystals, not both layers as evidenced by the asymmetric 2D-SAXS patterns in Figures 7, S10, and S11 despite the chances of dislocating these 2D-HCP layers being statistically equal. For example, the aligned HCP crystals in Figure 7 are formed by dislocating mostly (11̅1) 2D-HCP layers of shear-aligned FCC crystals. This selective transformation process shows that the initially selected set of 2D-HCP layers for the martensitic shear transformation of the FCC-to-HCP crystal persists during the transformation process, which is also corroborated by the timeresolved 2D-SAXS patterns in Figure 7d. It also suggests that the hydrodynamic interaction between transforming crystal domains is important in the kinetics of martensitic shear transformation:35 the martensitic shear transformation likely initiates from small FCC crystal domains, and the transformation propagates through hydrodynamic interactions between crystal domains in a coordinated way. Perhaps, the asymmetric configurations of the aligned HCP crystals in the capillary observed in Figures 7, S10, and S11 may be the result of the hydrodynamic interactions between transforming crystals. If the shear-aligned FCC crystals in the vertically divided half of a sample capillary transform to HCP crystals by dislocating the (11̅1) 2D-HCP layers, the crystallographic planes of the 2DHCP layers transforming the FCC crystals in the other half of the capillary have the center of inversion symmetry to the (11̅1) 2D-HCP layers of the FCC crystals in the first half, which are the (11̅1̅) layers (Figure 13b). Because the directions of the Shockley partial dislocations of these (11̅1̅) and (11̅1) 2D-HCP layers are not commensurate, the dislocating directions of these 2D-HCP layers in both halves of the capillary are not coherent, and this may result in the poorly aligned domains leaving the asymmetrically formed HCP crystals in the radial cross sections of the capillary. These incommensurate 2D-HCP planes may also be the reason of the appearance of the pronounced nonaligned HCP crystal domains at the late stages of the martensitic shear transformation observed from the time-

and the viscosity of the surrounding medium are the key limiting factors for the martensitic shear transformation. The recognition of the importance of the size of the dislocating domains in the martensitic shear transformation also explains the long-lasting metastability of the initial FCC crystals in the 23 wt % PB-PEO micelle solution. In the initial dispersion process of dry PB-PEO diblock copolymer in water, the FCC crystals grow by the nucleation and growth mechanism as the number density of PB-PEO spherical micelles increases as the PB-PEO diblock copolymer is selectively solvated and dispersed into spherical micelles (Figure S2). At a relatively low concentration of the PB-PEO micelles (12.7 wt %), the FCC crystal is found stable in our earlier report,23 and as the concentration of the PB-PEO micelles increases, the HCP crystal structure becomes more stable than the other closepacked structures, as found in this report. However, although the HCP structures are more stable in the high-concentration micelle solutions, once the FCC crystals grow by the nucleation and growth mechanism and become too large, the kinetic energy barrier of the martensitic transformation to the stable HCP structures becomes insurmountable, and, consequently, the initially formed FCC crystals become kinetically stable. The martensitic phase transformation at the elevated temperatures shows that the phase transition to the HCP structures can occur when the domain size of FCC crystals becomes sufficiently small and also likely the surrounding environment of transforming crystal domains becomes displaceable for the thermallyactivated straining motions of the martensitically transforming crystal domains. We note that the observed stability of the HCP crystals in the high concentration of the PB-PEO micelle solutions is qualitatively supported by the simulation results of hard spheres by Pronk and Frenkel:61 they found that moderately deformed HCP crystals of hard spheres are more stable than the FCC crystals under the same degree of deformation, and this result is qualitatively consistent with the observed stability of the HCP structures of the block copolymer micelles under high osmotic pressure conditions, which impose mechanical stress on the micelles. K


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receives partial support from the NSF through the MRSEC program.

resolved 2D-SAXS pattern measurements in Figure 7d,a at 7 and 11 min, respectively.

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5. CONCLUSIONS In this report, we found that the metastable FCC crystals of PBPEO micelles in the 23 wt % solution martensitically transform to stable HCP structures at elevated temperatures by selectively dislocating either (11̅1) or (11̅1̅) 2D-HCP layers. We attributed the origin of the selective dislocation of the initial shear-aligned FCC to aligned HCP crystals to the orthorhombic-like morphology of shear-aligned FCC crystal domains. The (11̅1) or (11̅1̅) 2D-HCP layers of the initial shear-aligned FCC crystal domains have the least areas of slip dislocation, i.e., least kinetic energy barriers for the martensitic shear transformation. In our earlier report,23 the close-packed crystal structure induced by rapidly cooling disordered PB-PEO micelles is found to progressively transform from metastable HCP and RHCP to stable FCC structure as the crystal domains grow.23 The observed metastable HCP and RHCP structures are explained with the small size of crystal domains imposing a non-negligible Laplace pressure, which stabilizes the noncubic micellar crystals. Such a crystal-size-dependent polymorphism has been observed from other compounds such as ice, glycine, and hard-sphere colloids.30−32,44,62−64 In this report, the size-dependent polymorphism of crystalline compounds is further detailed: not only the size but also the morphology of crystal domains is important for the formation, stabilization, and phase transformation of polymorphs of crystalline materials, as demonstrated by the selective martensitic shear transformation of the close-packed polytypes of the model block copolymer micelles.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.9b00917.

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REFERENCES

(1) Delaey, L. Diffusionless Transformations. In Materials Science and Technology; Kostorz, G., Ed.; Wiley-VCH, 2001; pp 583−654. (2) Bhattacharya, K.; Conti, S.; Zanzotto, G.; Zimmer, J. Crystal symmetry and the reversibility of martensitic transformations. Nature 2004, 428, 55−59. (3) Nishiyama, Z. Martensitic Transformation; Academic Press: New York, 1978. (4) Erskine, D. J.; Nellis, W. J. Shock-induced martensitic phase transformation of oriented graphite to diamond. Nature 1991, 349, 317. (5) Olson, G.; Hartman, H. Martensite and Life: Displacive Transformations as Biological Processes. J. Phys. Colloques 1982, 43, 855−865. (6) Bowden, P. B.; Young, R. J. Deformation mechanisms in crystalline polymers. J. Mater. Sci. 1974, 9, 2034−2051. (7) Bernstein, J. Polymorphism in Molecular Crystals; Clarendon Press: Oxford, 2002. (8) Brittain, H. G. Polymorphism in Pharmaceutical Solids; Informa: New York, NY, 2016. (9) Akune, Y.; Gontani, H.; Hirosawa, R.; Koseki, A.; Matsumoto, S. The effects of molecular flexibility and substituents on conformational polymorphism in a series of 2,5-diamino-3,6-dicyanopyrazine dyes with highly flexible groups. CrystEngComm 2015, 17, 5789−5800. (10) Morissette, S. L.; Soukasene, S.; Levinson, D.; Cima, M. J.; Almarsson, Ö . Elucidation of crystal form diversity of the HIV protease inhibitor ritonavir by high-throughput crystallization. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 2180−2184. (11) Young, D. A. Phase Diagrams of the Elements; University of California Press: Berkeley, 1991. (12) Martelozzo, V. C.; Schofield, A. B.; Poon, W. C. K.; Pusey, P. N. Structural aging of crystals of hard-sphere colloids. Phys. Rev. E 2002, 66, No. 021408. (13) Petukhov, A. V.; Dolbnya, I. P.; Aarts, D. G. A. L.; Vroege, G. J.; Lekkerkerker, H. N. W. Bragg Rods and Multiple X-Ray Scattering in Random-Stacking Colloidal Crystals. Phys. Rev. Lett. 2003, 90, No. 028304. (14) Zeng, X.; Liu, Y.; Impéror-Clerc, M. Hexagonal Close Packing of Nonionic Surfactant Micelles in Water. J. Phys. Chem. B 2007, 111, 5174−5179. (15) Macfarlane, R. J.; Lee, B.; Jones, M. R.; Harris, N.; Schatz, G. C.; Mirkin, C. A. Nanoparticle Superlattice Engineering with DNA. Science 2011, 334, 204−208. (16) Liu, C. K.; Warr, G. G. Hexagonal closest-packed spheres liquid crystalline phases stabilised by strongly hydrated counterions. Soft Matter 2014, 10, 83−87. (17) Huang, Y.-Y.; Hsu, J.-Y.; Chen, H.-L.; Hashimoto, T. Existence of fcc-Packed Spherical Micelles in Diblock Copolymer Melt. Macromolecules 2007, 40, 406−409. (18) Matsen, M. W. Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing. Eur. Phys. J. E 2009, 30, 361−369. (19) Liu, M.; Li, W.; Qiu, F.; Shi, A.-C. Stability of the Frank-Kasper σPhase in BABC Linear Tetrablock Terpolymers. Soft Matter 2016, 12, 6412−6421. (20) McConnell, G. A.; Gast, A. P.; Huang, J. S.; Smith, S. D. Disorderorder transitions in soft sphere polymer micelles. Phys. Rev. Lett. 1993, 71, 2102. (21) Lodge, T. P.; Bang, J.; Park, M. J.; Char, K. Origin of the Thermoreversible fcc-bcc Transition in Block Copolymer Solutions. Phys. Rev. Lett. 2004, 92, No. 145501. (22) Soni, S. S.; Brotons, G.; Bellour, M.; Narayanan, T.; Gibaud, A. Quantitative SAXS analysis of the P123/water/ethanol ternary phase diagram. J. Phys. Chem. B 2006, 110, 15157−15165. (23) Chen, L.; Lee, H. S.; Lee, S. Close-Packed Block Copolymer Micelles Induced by Temperature Quenching. Proc. Natl. Acad. Sci. U.S.A. 2018, 115, 7218−7223.

Structure analysis and characterization; Miller and Bravais−Miller indices of FCC and HCP structures; and comparison of the cross-sectional areas of the 2D-HCP layers in shear-aligned and orthorhombic FCC crystal domains (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Mikhail Zhernenkov: 0000-0003-3604-0672 Sangwoo Lee: 0000-0003-4215-0317 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Patrick Underhill and Benjamin Ocko for helpful comments. This research used resources of the 11-BMCMS and 12-ID-SMI beamlines of the National Synchrotron Light Source II, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under Contract No. DESC0012704. Parts of this work were carried out in the Characterization Facility, University of Minnesota, which L


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