Interconversion of Triply Periodic Constant Mean Curvature Surface

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Interconversion of Triply Periodic Constant Mean Curvature Surface Structures: From Double Diamond to Single Gyroid Xin Cao, Dongpo Xu, Yuan Yao, Lu Han, Osamu Terasaki, and Shunai Che Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b00308 • Publication Date (Web): 09 May 2016 Downloaded from http://pubs.acs.org on May 11, 2016

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Chemistry of Materials

Interconversion of Triply Periodic Constant Mean Curvature Surface Structures: From Double Diamond to Single Gyroid Xin Cao,† Dongpo Xu,† Yuan Yao,† Lu Han,†,* Osamu Terasaki‡,§ and Shunai Che†,* †

‡

School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

Department of Materials & Environmental Chemistry, EXSELENT Stockholm University, Stockholm, Sweden §

Graduate School of EEWS, KAIST Daejeon, Republic of Korea

ABSTRACT The triply periodic constant mean curvature surface structures have been discovered in a variety of biological and self-assembly systems. Among them, the single gyroid is of significant interest because of its unique geometry, inherent chirality and corresponding spectacular optical properties. In spite of theoretical and experimental efforts on this structure, limited progress has so far been made regarding the formation of the single-network structures and the structural relationships with the thermodynamically stable double-networks. Herein, we report the electron microscopic observation and analysis on the interconversion between the single gyroid and double diamond structure in an amphiphilic ABC triblock terpolymer templated macroporous silica synthesis system with a mixture solvent of tetrahydrofuran and water. The two structures were interconnected by a “side-by-side” epitaxial relationship with rescaling of the unit cell. The single-network structure was formed by a new type of alternating gyroid under the restricted epitaxial intergrowth, in which the hydrophilic block with the silica source and the solvent tetrahydrofuran formed the two chemically distinct, interpenetrating gyroid networks of opposite chirality in a matrix of the hydrophobic block.

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1. Introduction Biological organisms have evolved the extraordinary abilities to fabricate exquisitely complex structures and morphologies that are amazingly optimized to meet the physical or chemical demands of different life events.65,66 Among these delicate biological structures, the triply periodic constant mean curvature (CMC) surface structures have sparked immense interest for numerous applications owing to their complex and highly symmetrical structures with optimised material properties.2-4 These structures and their analogies have been widely discovered in many natural and artificial systems including zeolite crystals,5 lyotropic and thermotropic liquid crystals4,6-8 and their inorganic replicas9,10, block copolymer systems11-17, biological membranes18,19, and ultrastructured biomineralized skeletons and scaffolds.20-22 The triply periodic CMC surfaces can be viewed as deformations of the triply periodic minimal surfaces (TPMS). A minimal surface is a surface with zero mean curvature H; a surface with H constant is a CMC surface; For a fixed lattice and space group, there is a family of the corresponding CMC surfaces.23 The best-known examples include three basic categories: the Schoen gyroid surface, the Schwarz diamond surface and the Schwarz primitive surface.2,3 In these structures, a single balanced continuous matrix with the CMC interfaces on both sides separate two intertwined labyrinths, which are well known as bicontinuous phases or interpenetrating networks. These structures can thus be called double gyroid (DG), double diamond (DD) and double primitive (DP). The DG is one of the most appealing bicontinuous structure,24,25 which composed of two minority chiral gyroid skeletal networks (networks of rods representing the centre of the labyrinths) with each node interconnected with three arms.26,27 The two networks have opposite chirality and are related by an inversion operation. The overall structure is achiral and belongs to the central symmetric space group Ia-3d (230). The DD structure separates two intertwined diamond networks, and each node of the network is tetrahedrally interconnected, the space group symmetry of which is Pn-3m (224). The DP structure has an interface between two interlocked simple cubic lattices, and the nodes are sixcoordinate interconnected; the space group is Im-3m (229). The DG along with other bicontinuous 2


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phases have been widely discovered and extensively studied in the lyotropic liquid crystal (LC) phases4,6-8 and block copolymer systems11-17, which have also been utilized to fabricate a variety of inorganic meso- and macroporous materials through their structural transcriptions9,10. The single gyroid (SG) and single diamond (SD) structures found in biological systems20-22 are very rare compared to the thermodynamically stable DG and DD phases. The SG structure exhibits unique photonic properties and shows a complete photonics bandage with the minimum dielectric contrast of 5.2 at 17% volume fraction.28-30 The polarization-dependent optical properties and negative refractions of SG have also been shown to be a versatile source of biomorphic scaffold designs owing to its exceptional symmetry and inherent chirality.31,32 The SG composes only one network with the CMC surface, and the space group is chiral I4132 (214), which is a subgroup of Ia3d. It is also known as the topological structure srs-net.33 It has been reported that the butterfly photonic nanostructures were formed initially as the DG precursors, which subsequently transformed into SG through the deposition of chitin in the extracellular space and the degeneration of the rest of the cell.22 The single network structures have been artificially achieved by physical holographic lithography34 and replication of butterfly wing scales with SG structure35. Besides, Ryoo et al. reported the SG Pt-network formed by using DG mesoporous material as template, which the mesoporous channels were impregnated with aqueous Pt precursor and reduced by H2 gas and washed by HF.36,37 In another report, SD Pt-network was formed by the electrochemical templating through a thin layer of a self-assembled DD phase of a lipid. The Pt only occupied the single network of DD to form the SD lattice.38 The single network of both system are obtained by the partial occupancy of the initial formed double network template. Nevertheless, the direct self-assembly of the metastable single network structure in soft matter system is extremely difficult. In particular, a so-called alternating gyroid39-43 structure is fabricated using ABC triblock terpolymers. For example, poly(isoprene-b-styrene-b-ethylene oxide) has been widely used, in which the DG is originally formed where the A and C blocks have similar volume fractions and are chemically distinct; one block is then subsequently selectively etched to yield a

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single gyroid template25,44-47. To explore the formation and the intrinsic characterizations of these relevant biological structures, considerable theoretical and experimental studies have been carried out to understand the structural relationship and interconversion among the TPMS and CMC surface structures in the LC systems. 7,48-51

However, the soft nature of the LC phases prevents detailed structural study, and only limited

experimental data on these systems has been obtained.52,53 The stable inorganic replicas as structural analogies of the CMC surfaces provide us with more possibilities for structural study, and direct observation of delicate structural relationships such as intergrowth and defects has been made practicable.54,55 However, the structural interconversion between bicontinuous double-network systems and the single-network structures has not been revealed. Considering the extensive appearance and the important properties of these CMC surface structures, this results in a real challenge to a fundamental understanding of their structures and the structural relationships. Herein, we report on the structural study and interconversion of the DD and the SG silica scaffolds. A triblock terpolymer poly(tert-butyl acrylate)-b-polystyrene-b-poly(ethylene oxide) (PEO117-b-PS77-b-PtBA179) has been used as the template, and tetraethyl orthosilicate (TEOS) has been used as a silica source under acidic conditions in a mixture of common solvent tetrahydrofuran (THF) and the selective solvent water.56 The structures of the silica scaffolds were characterized by small-angle X-ray scattering (SAXS), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) analysis. The epitaxial intergrowth of the structures and the mechanism of the structural formation were also investigated.

2. Experimental Section 2.1. Chemicals. Monomethoxy poly(ethylene oxide) (PEO5k with molecular weight of 5000 g/mol) was purchased from Aldrich. Tert-butyl acrylate (t-BA), 2-bromo-2-methypropionyl bromide (> 98%), N,N,N’,N’,N’’-pentamethyldiethylenetriamine (PMDETA) and N,N-dimethylformamide (DMF) (> 99%) were purchased from J&K. Cuprous bromide (CuBr), styrene, anhydrous ether (> 4


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99%), methyl alcohol (> 99%), tetrahydrofuran (THF) (> 99%), and tetraethyl orthosilicate (TEOS) were purchased from Sinopharm Chemical Reagent Corp. t-BA was purified by filtration through an Al2O3 column to remove the polymerization inhibitor. Millipore water was used in all experiments. 2.2. Synthesis of PEO-b-PS-Br. PEO-b-PS-Br diblock copolymers were synthesized using the well-established atom transfer radical polymerization (ATRP) technique of St at 110 °C using PEOBr as the macroinitiator and CuBr/PMDETA as the catalyst system. Typically, 10.0 g of PEO117-Br was dissolved in 50.0 g of St (0.288 mol) in a 250-mL Schlenk flask, then 1.18 mL PMDETA (5.64 mmol) and 0.27 g of CuBr (1.88 mmol) were added into the solution. The reaction system was fully degassed with more than three freeze–pump–thaw cycles and sealed under vacuum. The bottle was then placed in an oil bath of 110 °C to allow the polymerization to take place. The catalyst was removed by exposing filtration through an Al2O3 column using methylene chloride as eluent after the polymerization was terminated by exposing the reaction mixture to air. Five hundred millilitres of cold ether was poured into the clear filtrate to precipitate the PEO-b-PS-Br diblock copolymer, which was collected by filtration and dried under vacuum at room temperature. 2.3. Synthesis of PEO-b-PS-b-PtBA-Br. PEO-b-PS-b-PtBA-Br was synthesized by ATRP of tBA at 70 °C using PEO-b-PS-Br as the initiator, and CuBr/PMEDTA as the catalyst system. A 250 mL Schlenk flask containing 10.0 g of PEO117-b-PS77-b-Br (0.76 mmol), 0.47 mL of PMDETA (2.28 mmol) 25.0 mL of DMF and 50.0 mL of tBA waspurged thoroughly and then sealed with a rubber stopper. After the solution became clear with stirring, 0.109 g of CuBr (0.76 mmol) was added into the solutions. The bottle containing reactants was fully degassed with more than three freeze–pump– thaw cycles and sealed under vacuum. The flask was then placed in an oil bath of 70 °C to allow the polymerization to take place. The reaction time was controlled at 6 h. After the reaction, just like the synthesis of PEO-b-PS-Br, the mixtures were cooled to room temperature, the catalyst was removed, and the polymer was finally obtained by precipitation using cold methanol (500 mL). 2.4. Synthesis of silica scaffold. The solvent evaporation-induced self-assembly method was applied by using (PEO117-b-PS77-b-PtBA179) triblock copolymer as a template; 2.0 g of HCl (3M) was

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added into a 12.0 g THF solution of the template and then stirred for approximately 2 h. Finally, 0.7 g of TEOS was added into the solution. The mixed solution was stirred for another 2 h and then allowed to evaporate completely at 25 °C. All reactions were conducted at ambient temperature. The silica/template composite was washed with water three times and finally freeze-dried. The as-made sample was then calcined at 550 °C in air for 10 h to remove the template. 2.5. Characterizations. The nuclear magnetic resonance (NMR) spectra were measured on a Varian Mercury Plus 400 MHz NMR spectrometer using tetramethylsilane (TMS) as the internal reference. The polymers were dissolved in deuterated chloroform. The molecular weights and molecular weight distributions of the polymers were determined on an HLC-8320GPC (TOSOH Corp.) gel permeation chromatography (GPC) apparatus, and the measurements were taken using DMF as the eluent at a flow rate of 10–2000 µL/min. The SAXS experiments were recorded by synchrotron radiation at beamline BL16B1, provided by the Shanghai Synchrotron Radiation Facility (SSRF). The microscopic features of the samples were observed using SEM, which was performed on a JEOL JSM-7800 Prime. The samples were observed without any metal coating. A low accelerating voltage (1 kV with the deceleration method, point resolution of 0.7 nm) was employed. TEM observations were performed using a JEOL JEM-2100 microscope that was equipped with a LaB6 gun operated at 200 kV (Cs 1.0 mm, point resolution of 2.3 Å). Images were recorded using a TENGRA CCD camera (2304 × 2304 pixels with a 2:1 fibre-optical taper and an effective pixel size of 18 µm2).

3. Results and Discussions 3.1 Properties of the triblock terpolymer and the synthesis of the material. The liquidcrystal-templating route has attracted great attention for the synthesis of various inorganic mesostructured materials according to the packing behaviour of the amphiphilic surfactants and interaction between micelles and inorganic sources, including bilayer lamellar structure, cylindrical structure, CMC surface-type bicontinuous structures, and micellar cubic structure.9,10 These 6


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structures have been also found in the melt and the solution of the block polymer systems based on the microphase separation, which has a lot of similarities of the principles of amphiphilic small molecule self-assembly and have significantly expanded the complexity of the phase diagram. The use of ABC triblock terpolymers especially enables several CMC surface type structures.11-17 Thus, new types of mesostructured inorganic materials would be accessed via a microphase-templating route through thermodynamic and kinetic controlling. In both cases, the unit cell size and the interfacial curvature of the obtained structures are highly determined by the size and shape of the template molecules. However, we employed a different strategy for the material synthesis, which combines the microphase separation method and the inverted micelle liquid crystal templating route to form the inorganic network. The silica scaffold was synthesized through the cooperative self-assembly of an amphiphilic ABC triblock terpolymer PtBA-b-PS-b-PEO and silica source. The template molecule has a total molar mass of 36,100 g/mol, a polydispersity index of 1.386, and volume fractions of 63.6 %, 20.9 %, and 13.6 % for the PtBA, PS and PEO blocks (Supplementary Figure S1, S2 and Table S1), respectively. The Flory–Huggins interaction parameters57 for terpolymer are calculated as approximately χASN =10.6, χSON=51.7 and χAON=109.1 by χN = ∑ N × Vref (δ1 − δ2)2 / RT where Vref is the segment reference volume (100 cm3/mol), and δi is the Hildebrand solubility parameter for polymer i (δA=18.5 (J/cm3)1/2, δS=19.3 (J/cm3)1/2, and δO=21.2 (J/cm3)1/2) (Supplementary Table S2 and S3). The relationship χAON >> χSON >> χASN tends to form strong microphase separation between the PEO and PS/PtBA blocks while no obvious microphase separation between PS and PtBA blocks occurs, behaving like an AB block copolymer. The THF is the common solvent owing to the similar solubility parameters of THF (δ = 18.6 [J/cm3]1/2), whereas water is the selective solvent (δ = 23.4 [J/cm3]1/2)58. The hydrophobic blocks PtAB and PS are present in the THF-rich phase, whereas H2O is driven out of the hydrophobic segments of the polymer and the silicate species would be hydrolysed and condensed in the H2O-rich phase through the co-

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interaction of hydrogen bonding between ethylene oxide and silanol and the electrostatic interaction between EOm-y[(EO)·H3O+]y and [yCl−·Si−OH2+]59. The final silica scaffold was obtained through evaporation of both THF and H2O with the simultaneous hydrolysation and condensation of TEOS, and the template molecules were removed by calcination (Supplementary Figure S3). Thus, the scaffold with extraordinary large unit cell size can be achieved by relatively small molecular due to the solvent was incorporated into the microphase separation and the polymer molecules only stay on the hydrophilic/hydrophobic interface.

3.2 Overall structure. Figure 1a shows the SAXS pattern of the calcined material. The structure was later determined to be the shifted double diamond (SDD) structure with space group tetragonal I41/amd (#141). The unit cell parameters are aSDD = 140 nm and cSDD = 198 nm ≈ √2aSDD. As indicated by the black tick marks, a few reflections can be indexed. Due to the shifted structure and the unique relationship of the unit cell parameters, many reflections are overlapped, e.g. the 112/200 reflections, 220/004 reflections, etc. Nevertheless, the existence of SG structured domains was confirmed via SEM and TEM observations. The low-magnification SEM image of the sample is shown in Figure 1b, revealing the overall information of the sample. The SDD structure is the main phase, which consists of domain structures with different crystal orientations. However, small regions corresponding to the SG structure are often observed that are hundreds of nanometres to several microns in size, which are indicated by white regions in Figure 1b. The unit cell parameter of SG is determined to be aSG = 70 nm (vide post), which is particularly the half of the unit cell parameter aSDD (140 nm) of SDD structure. The Bragg positions of the 110 and 112 reflections of the SG are indicated by red tick marks in Figure 1a, for which the 110 reflection of SG overlaps with the 220/004 reflections of the SDD.

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Figure 1. SAXS pattern and low-magnification SEM image of the product. (a) SAXS pattern of the calcined material with positions of the expected reflections from SDD (lattice const aSDD = 140 nm and cSDD = 198 nm) in black and SG (lattice const aSG = 70 nm) in red. (b) SEM image of the calcined product, in which SG can be often found as shown by white enclosures within the SDD domains at sizes of several hundred nanometres to microns.

3.3 Characterizations of the SDD structure. The enlarged SEM images of the SDD domain are shown in Figure 2a and 2b. Two sets of continuous hollow silica networks can be identified (indicated by red and blue arrows), and the two networks are interwoven. Each network contains tetrahedral arrangements at their nodes, and each node is interconnected by four arms and thus is an interpenetrated diamond network structure. The unit cell parameter calculated from the SEM image is aSDD = ~140 nm as shown in Figure 2a.

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Figure 2. SEM and TEM images of the SDD structure. (a, b) SEM image of the SDD domain taken from near the [010] and [111] directions, respectively. A set of red and blue arrows indicates two sets of hollow diamond networks adhering to each other at their node sites. (c–g) TEM images and the corresponding FDs of the SDD domain taken from the [010], [001], [101], [201] and [111] directions, respectively. (h) The structural model of one unit cell using nodal surface approximation.

The TEM images of the calcined SDD structure taken from the [010], [101], [201], [111] and [001] directions are shown in Figure 2c–g. A highly ordered structure with complex and regular TEM contrast has been observed, showing hollow networks with a thin silica wall. The corresponding Fourier diffractograms (FDs) shown in the insets indicate the reflection conditions [hkl: h + k + l = 2n, hk0: h, k = 2n; 0kl: k + l = 2n; hhl: 2h + l = 4n, l = 2n; 00l: l = 4n; 0k0: k = 2n; hh0: h = 2n], suggesting the unique space group tetragonal I41/amd (#141). The shift value of the original two cubic networks along the unique c-axis is ~0.25c judging from the TEM observations. This structure is very similar to that in our previous report, for which it has been found that the SDD networks shifted along one of the cubic axes and adhered to each other crystallographically.56 The SD structure has the space group of cubic Fd-3m (#227), while the normal DD structure has the space group of cubic Pn-3m (#224), which is a subgroup of Fd-3m. However, if the two networks of the DD shifted along different directions, the symmetry elements will be broken. By shifting along 10


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one of the cubic axis, the original four equivalent -3 axis are destroyed while one of the four fold axis is preserved. The structure became tetragonal with space group I41/amd (#141), which is also a subgroups of Fd-3m. In this case, the unit cell is rotated 45 degrees along the c axis and the unit cell parameter is changed to aSDD = √2/2 cSDD = √2/2 aDD. This geometry relationship is also consistent with the normal DD structure embedded in the subgroup symmetry I41/amd.60

3.4 Characterizsations of the SG structure. The SG domains have been found as the minor phase, which are distributed randomly in the bulk crystal. Figure 3a–c shows the SEM images of the SG structure, which contains only one set of networks, and each node is interconnected with three arms—i.e. a threefold connection. The unit cell parameter calculated from the SEM image is aSG = ~70 nm, which is half of the unit cell parameter aSDD of the SDD structure (aSG = 1/2 aSDD = √2/2 cSDD). The DG contains two sub-networks, which have opposite chirality and are related by an inversion operation and the overall structure is achiral. For SG, it only contains one set of network as one of two enantiomers. The left-handed (LH) enantiomer of the SG has LH screw axis along the direction centered within the void domain and right-handed (RH) screw axis within the solid domain. It also presents the RH screw axis along the direction centered within the void domain and the RH screw axis within the solid domain.29,61 The RH enantiomer of SG is related by a mirror symmetry. The screw axes can be observed by SEM observations so that the handedness of the network can be identified. From the SEM image, the [100] axis possesses local LH helical elements centered in the void domain as highlighted by the pink arrow, suggesting the RH enantiomer configuration (Figure 3a). The [110] direction possess same handedness (Figure 3b). However, the SEM image of [111] direction (Figure 3c) shows the network with the LH SG enantiomer structure. By check different particles by SEM observations, the SG networks with both LH and RH enantiomer were observed. However, it is very difficult to perform a statistical analysis to judge the overall chirality from limited number of specimen. As our synthesis system contains no chiral chemical components and hence the symmetry between right handed and left handed should be preserved.

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Figure 3. SEM and TEM images of the SG structure. (a–c) SEM image of the SG domain from near the [100], [110] and [111] directions, respectively. The stick model is overlaid on the figures. (d–f) TEM images with the corresponding FDs of the SG domain taken from the [100], [110] and [111] directions, respectively. Projected potential maps obtained by crystallographic image processing assuming indicated plane groups by CRISP were also inserted in the HRTEM images. The origin of each projection (shown in yellow) was moved to the common origin (shown in blue) of the unit cell.

The TEM images and the corresponding FDs of the calcined material taken from the [100], [110] and [111] directions are shown in Figure 3d–f. The reflection conditions obtained from the FDs are summarized as {hkl: h+k+l = 2n; 0kl: k+l = 2n; hhl: l = 2n; 00l: l = 4n}, which suggest the unique space group cubic I4132 (#214). The unit cell calculated from the TEM image is ~70 nm. The threedimensional (3D) electrostatic potential map of the SG is obtained by electron crystallography reconstruction to elucidate the structural details. The amplitudes and phases (with amplitudes >0.5% of the largest amplitude for each direction) were extracted from the Fourier transforms of the TEM images along the three main directions using the crystallographic image-processing software CRISP62. From the averaged TEM images, plane groups of p4mm, p2mm and p3m1 were assigned to 12


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the [100], [110] and [111] directions, respectively. The structure factors of reflections from different projections were merged into a 3D dataset by adjusting the common origin and normalized by scaling the amplitudes with the common reflections. The contrast transfer function was corrected by a Wiener filter to avoid a zero division.63 52 unique reflections were calculated to generate the 3D electrostatic potential map φ(x, y, z) by employing the software application VESTA (Supplementary Table S4). 64 A threshold for the isosurface was determined from the TEM images because the boundary of the silica wall could be directly observed. Figure 4a presents the reconstructed 3D map of one unit cell, clearly showing the triply linked networks grown along the gyroid CMC surface, whereas the centre of the network is hollow. The nodes are arranged at the Wyckoff position 8a site (1/8, 1/8, 1/8) with site symmetry of .32, which has the RH enantiomer arrangement. The different screw axes are highlighted in Figure 4. The LH helices centered within the void domain (red arrows) and the RH helices centered within the solid domain (blue arrows) are possessed along the [100] direction (Figure 4b), whereas the [111] direction (Figure 4c) possesses opposite RH and LH local helical elements. Notably, the TEM images are projections for which the handedness of the SG cannot be identified. The structure with opposite handedness (LH enantiomer) and the nodes arranged at the Wyckoff position 8b site (7/8, 7/8, 7/8) can be obtained simply by reversing the phases for all reflections (Figure 4d). Moreover, the CMC surface was calculated using the software application Surface Evolver.65 With the space occupancy inside the silica/space interface of ~30% (volume fraction of the silica and the inner hollow channel), the surface agreed well with the experimental results (Figure 4e and 4f).

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Figure 4. Representations of the 3D reconstruction and the structural model of the SG. (a) 3D structure (1 unit cell) reconstructed from the HRTEM images along three directions, whose nodes occupy the Wyckoff position 8a site (RH enantiomer). (b, c) 3D porous system with the stick model superimposed in the hollow channels, illustrating the connectivity and the topology of the porous structure. (d) 3D structure of the enantiomer whose nodes are arranged at the Wyckoff position 8b site (LH enantiomer). (e–f) Evolved G surface with a volume fraction of 30%.

3.5 Structural relationships between DD and SG. It can be imagined that the structural relationship between SG and SDD is the key to understanding the structural behaviour of the system. In a few cases, the epitaxial relationship between SG and SDD has been discovered in SEM observations (Figure 5a–-5e). The [010]SDD direction of SDD is parallel to the [100]SG direction of SG. The node of SDD was pulled apart into two small arms to connect to SG (black arrows, Figure 5b–-5e). Notably, either the SDD or SG domain around the boundary shows structural fluctuations and becomes disordered (Figure 5b–5d). However, both the ordered SG and DD domains can be found only when SG is connected to the original cubic DD structure with space group Pn-3m (Figure 14


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5e). From TEM observations, the connection of the structures can also be revealed in which the node of the hollow DD structure splits into small arms to connect to the SG domain (Figure 5f).

Figure 5. The structural relationship between DD and SG and the schematic drawing of the SG formation. (a– e) SEM images of the intergrown structure of DD and SG, in which SG can be often found within the DD domains. (f) TEM images of the intergrown structure (g, h) The schematic drawing of the structural relationships between the original DD and SG.

It can be concluded that the SG domains are formed together with DD by an epitaxial relationship in the synthesis. The unit cell of SDD is rotated 45° along the common z-axis to the original cubic DD structure. The [110]DD of the original cubic DD become the [010]SDD of SDD structure. The unit 15



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cell parameter relationship is aSG = 1/2 aSDD = √2/2 cSDD . Therefore, the relationship between aSG and the original DD structure should be DD//SG with aSG = √2/2 aDD. Due to the shift of DD networks with the solvent evaporation process, in which the mutual support is lost and the original cubic symmetry cannot be maintained. This structural change leads to the disordered region and the structural fluctuations in either the DD or SG domain near the boundary. Considering the SEM observations and the aSG = √2/2 aDD relationship, a model is made in which the SG can be connected to a cubic DD lattice sharing the common DD/SG direction by connecting every other node, and the nodes of the DD can be pulled apart to become the threefold junction of SG; thus, the surface can be evolved to interconnect even without an intermediate phase (Figure 5g and 5h). For the minimal surface structures, the diamond, gyroid and primitive are topologically equivalent and can be interconverted with each other by a theoretical process called Bonnet transformation.

3

This process preserves all lengths, angles and areas of the surface without tearing or stretching. It also maintains the Gaussian curvature unchanged everywhere. However, the Bonnet transformation is unreasonable in real experiments because the surfaces must interpenetrate through each other, which is thermodynamically unfavoured. To maintain the Gaussian curvature unchanged and keep the areas of equivalent parts of the each structure equal, the calculated ratio of aDG : aDD = 1.57 is required, which is obtained theoretically by the DG ➛DD transformation reported by Hyde et al.66,67 Sadoc and Charvolin7 proposed the transition mechanism of these structures based on “merging” or “pulling apart” the nodes. The six-coordinate node of the primitive surface can be formed by merging the two adjacent four-coordinate nodes of the diamond; similarly, the diamond can be transferred to the gyroid surface by pulling apart each four-coordinate node into two nodes with three arms. Benedicto and O’Brien48 reported a mechanism in which the different surfaces can be evolved continuously with a homotopic transformation through intermediate surfaces that need not be minimal or isometric; however, the transformation results in a high-energy intermediate state and is difficult to observe. Fogden and Hyde49 demonstrated a global pathway for the structural transition, in which a rhombohedral distortion and a tetragonal pathway have been reported for the deformation between

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DD and DG with a continuous minimal surface preserving both topology and zero mean curvature throughout. The energetic costs of the increase in Gaussian curvature heterogeneity in the intermediate surfaces are relatively slight. In a later report by Schröder-Turk et al., for these deformations, the curvature and packing homogeneity of the tetragonal pathway were significantly superior to that of the rhombohedral route60. In addition, Templer and Seddon et al. reported a pressure-jump structural transition, which the ratio of the lattice parameters of the aDG : aDD was found in the range of 1.615 to 1.571, similar to the Bonnet ratio. The transition contains no detectable intermediate phase and the pressure-jump amplitude, temperature, and water content are the key factors for the transformation kinetics.68 In a report by Squire et al.51, a pictorial representation of both diamond-to-gyroid and diamondto-primitive transition was presented based on these earlier models. Each transition includes three processes. (i) The rearrangement within the unit cell by either pulling apart or merging nodes of the network. (ii) A change in the shape of the unit cell by tetragonal or rhombohedral distortion, jn which a cubic-to-tetragonal transition occurs in the DD-to-DG transition. (iii) A further rescaling to fit the overall size of the unit cell corresponding to the change in the bilayer area or volume fraction must be considered. These three processes may act in coordination and probably affect the structural transition coinstantaneously. In their DD-to-DG phase transformation, the area of the minimal surface in a repeat cell is allowed to change and the transformations follow the relationship of the lattice parameter ratios is aDG : aDD = √2, which is different from the value of 1.57 that retain the Gaussian curvature. Besides, the transformation process especially occurs with the rearrangement of the minority networks by pulling apart each four-arm node in different axes, which imparts opposite chirality of the minority networks and causes two identical diamond networks to become enantiomeric. This epitaxial relationship is confirmed experimentally in the DD-to-DG transition of a lipid.69 Very recently, Oka reported a similar transformation pathway, which the DD//SG relationship is retained while one direction in the four-branched arms of the DD was preserved in the three-branched arms of the DG structure.70

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From these reports, it can be deduced that: (i) The transformation of the unshifted original DD and DG should take place with an epitaxial relationship in which the DD axis is parallel to the DG “side by side” and the unit cell parameter distortion by aDG : aDD = √2 ~ 1.57. (ii) The surfaces of the DD and SG should be directly connected. The nodes of one structure need to evolve by either pulling apart or merging to fuse with the other structure and no transition phase should be observed. (iii) As the two structures are different in occupying the space, the epitaxial structural transformation between them must maintain either the topology or the contents of the microphases throughout. This illustrates that the transformation maintains the topology should result in a change of the content of the microphase separation—i.e., either the water or the THF content. Meanwhile, if the content of the microphones are fixed in the structural transition, it should lead to a topology change or a change in the lattice parameter. As seen from our experimental results presented here, (i) two structures have been formed in this system, and the epitaxial relationship follows the same rule, in which DD axis is parallel to the SG with a “side-by-side” epitaxial relationship, which is agree with the previous studies. However, the DG is replaced by SG and the unit cell parameter of SG is rescaled by aSG : aDD = √2/2, which is half scale relationship of the normal DD-to-DG transitions. (ii) The connectivity of the structures is consistent with the previous report that the surfaces of the DD and SG are directly connected, including the rearrangement within the unit cell by either pulling apart or merging nodes of the network. Although, disordered intermediate regions and structural fluctuations have been observed, which are formed by rearrangement and rescaling of the structures according to the shift of DD networks with the evaporation of the solvent before the completion of the silica condensation. It can still be confirmed that the direction connection of the SG and DD structure with proper connectivity are retained. This process is also consistent with the structural transition process suggested by Fogden and Hyde.49 In such a process, the elastic energy of the surface is minimized, and thus it is assumed to be energetically favourable. (iii) From the 3D reconstructed structure, the water core inside the SG channel is significantly reduced and the THF content is also changed, which

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show that this is not a content-conserving process. This transformation also involves the change that double network changed to single network, which is very uncommon. In addition, it is important to note that the structural transition reported here is not a curvature driven process because the Gaussian curvature change in the DD and SG is so obvious.

3.6 Speculation of the formation of SG structure. From the foregoing observations, the DD and SG are related by a “side-by-side” epitaxial relationship, in which the axis of DD is parallel to the axis of SG with rescaling of the unit cell by √2/2, which is half scale of the conventional DD-to-DG transition. The unique phase behaviour of the SG scaffold can be a subject of speculation based on the microphase segregation behaviour of the system. The proper hydrophilic PEO volume fraction of 13.6% is in the range of 4–14% vol%71, providing a wide window for the triply periodic network structures in the phase map. In a mixture of a amount of THF and a small amount of water, the microphase separation occurs in which PtBA and PS are present in the THF-rich phase, and PEO is located in the H2O-rich phase (Figure 6a). The DD structure has been formed as the main phase by the co-assembly and the microphase separation of the ASO, solvents and the silica source, in which the multilayer core-shell bicontinuous structure of H2Orich / PEO(TEOS) / PS~PtBA / THF-rich / PtBA~PS / PEO(TEOS) / H2O-rich is formed with two equivalent labyrinths with a double-diamond pattern of the cubic structure with space group Pn-3m (Figure 6b). The inorganic scaffold with an SDD feature is then formed owing to the loss of the mutual support with the solvent evaporation (Figure 6c). It is worthy to note that the ordered DD is not a stable phase in the phase diagram of the purely copolymeric system alone. It is not an equilibrium structure and was only discovered in very narrow composition windows, the free energy of which was always higher than other types of structures.43 However, in our system, the microphase separation behaviour have been greatly changed due to the incorporation of the solvent and inorganic source. The inorganic source disperses in the PEO part and the volume fraction of the hydrophilic part is increased. Besides, the synthesis is under the evaporation condition, suggesting the final

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structure are both thermodynamically and kinetically controlled. Thus, the DD structure is stabilized and the phase diagram is enriched. In the liquid crystal structure of the lipid bilayer or the microphase separation of the block polymers, all molecules should have equivalent packing conditions. Besides, the two structures should have very similar bending energy and the phase transition enthalpies between the two phases should be as close as possible. However, the formation of the SG structure in our system is very unusual. The SG phase appeared in a very small region in the DD phase near the lamellar structure, which the phase diagram of the whole synthesis system will be reported separately. As the unit cell size and the interfacial curvature of the obtained structures are highly determined by the size and shape of the template molecules, our results are a substantial challenge to the established notion to formation of these relevant structures. The polymeric chain-length polydispersity may plays an important role because of the triblock terpolymer we employed has a wide polydispersity of 1.386. We also considered if the SG was formed by very few unreacted diblock copolymer PS-PEO while the DD was formed by the triblock terpolymer PtBA-PS-PEO. Besides, the intergrown structure can be also formed by some of the chemical components which are not homogeneously distributed and/or separate throughout the self-assembly. We have carefully considered these possible factors that may affect the final structure. It is worthy to note that all the DD domains and all the SG domains have consistent unit cell parameters, respectively, suggesting the template molecules should have the uniform distribution and the same geometrical relationship within the domains of either DD or SG structures. Considering the epitaxial relationship between the two structures, it must have some relationship between the two kinds of microphase domains. Besides, the SG domains were only observed in a small region, while all the triblock terpolymer we have synthesized have wide polydispersity, indicating the SG structure is not formed by the inhomogeneous distribution of the template molecules. We also tried to mechanically mix the diblock copolymer PS-PEO with triblock terpolymer PtBA-PS-PEO with different ratio under the similar synthesis conditions to see if the SG is formed by PS-PEO, however,

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no ordered structure was formed by the mixed polymer solution. Nevertheless, during the synthesis, we kept stirring the reaction solution for very long time before the addition of the inorganic precursors, so that all molecules should have uniform distributions all over the reaction solution. However, with the solvent evaporation, the nonuniform distribution of the template molecule and the synthesis gel with silica source may vary to create some inhomogeneous domains. From the connectivity of the structures observed by SEM images, both structures have been formed in the very early stage in the microphase separation process. Thus, the SG scaffold structure was formed with the DD when a certain concentration of the reactants is reached with the solvent evaporation. Therefore, we suppose the formation of the two structures can be referred to an epitaxial restricted intergrowth with the kinetic control with the evaporation process, which the microphase separation process during the synthesis plays an important role. The formation of the SG can be interpreted by a new type of the alternating gyroid structure by the microphase separation process. It has been reported that the use of compositions with similar A and C block fractions of ABC triblock terpolymer are crucial for the formation of an alternating gyroid.17 DG networks may be considered to be formed by the two end blocks separated by a continuous matrix of the middle block. However, in our case, the H2O-rich core with PEO block and the THF-rich phase form the two chemically distinct, interpenetrating gyroid networks of opposite chirality in a matrix of the PS~PtBA block. On the one hand, owing to the PS block and PtBA block having low χASN =10.6 around the weak segregation limit; the segregation of the PtBA and PS blocks is not favoured and tends to form one continuous microphase.72 On the other hand, the space occupancy of the silica interface is determined by electron crystallography to be 30%, suggesting that the H2O-rich core with the PEO block should have a 30% volume fraction. While the volume fractions are 63.6 %, 20.9 %, and 13.6 % for the PtBA, PS and PEO blocks, respectively. Assuming that the PtBA also fills 30% of the volume, the PS block is too small to participate in the remaining 40% of the space. Thus, it can be concluded that the two interwoven minority networks are occupied by the H2O-rich core with the PEO block and the THF-rich phase, respectively (Figure 6d). Thus, the

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microphase separation of H2O-rich / PEO(TEOS) / PS~PtBA / THF-rich occurs. This conclusion is different from that of the normal alternating gyroid reported elsewhere, in which the sub volumes must be occupied by A and C blocks of the ABC triblock terpolymer. Finally, the TEOS is hydrolysed and condensed in the PEO region, and the other network is removed by calcination (Figure 6e). In this synthesis system, the DD is the main structure, the SG structure exists as the minor phase in the DD domains and both structures are interconnected. From our previous discussions, both structures have been formed simultaneously with the epitaxial relationship at the early stage of the reaction. It must be considered that the structural relationships between DD and SG are the key factor for the SG formation. The synthesis of the material is carried out by the evaporation induced selfassemble, which is under a continuous metastable state. Under some synthesis conditions, inhomogeneous distribution of the solvent contents in some regions maybe formed due to the evaporation of the solvent and the condensation of the inorganic source, forming the two structures with different size. The structural scale and the formation of the SG are limited by the restriction of the epitaxial growth of DD and that the unit cell parameter distortion of aDG = aDD√2/2. In this case, only the single-network structure was able to be formed owing to the occupancy of space by the template molecules and the solvent. Considering the structural relationship, the structure is limited by the restriction of the epitaxial growth. The formation of the two structures with the certain size difference may be both energetically favoured under this synthesis condition and the two structures may interconvert into each other under certain circumstances. The microphase separation behaviour of SG is distinguished from the conventional bicontinuous phases, and the final product consists of a continuous single gyroid network.

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Figure 6. Schematic drawing of the multilayer core−shell microphase separation and the formation of the SG structure by the epitaxial-relationship-restricted intergrowth by microphase separation. The numbers “1” and “2” denote the two interwoven minority networks.

4. Conclusions The interconversion of the DD to SG structures has been observed in a self-assembly system of triblock terpolymer and an inorganic source. A detailed structural study of the DD, SG and epitaxial intergrowth of the structures has been carried out. It has been found that the microphase separation and the structural relationship between the DD and the SG structure are the key for the formation of the SG phase. The two structures often appear together in this synthesis system, which may suggest that the formation of the DD structure and the SG are both energetically favoured under this synthesis condition and that the synthesis condition of DD and SG are very close and may convert into each other under certain circumstances. This is different from the conventional thought in which the SG must be evolved from the DG structures. The finding reported here brings a new understanding to the 23



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structure and the structural relationship of these bio-relevant structures, and it will be interesting to further investigate these aspects.

ASSOCIATED CONTENT Supporting Information Characterizations of the triblock terpolymer, calculation of the χN values and the structure factors of the 3D reconstruction are presented in the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (S. C.), [email protected] (L. H.) Author Contributions The manuscript was written through contributions of all authors.

ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation (21471099, 21571128) the National Basic Research Program (2013CB934101), and National Excellent Doctoral Dissertation of PR China (201454). The authors thank the Shanghai Synchrotron Radiation Facility (SSRF) for providing the BL16B1 beamline for collecting synchrotron SAXS data.

ABBREVIATIONS SEM, scanning electron microscopy; TEM, transmission electron microscopy; SG, single gyroid; DG, double gyroid; DD, double diamond; SDD, shifted double diamond; FD, Fourier diffractogram.

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Interconversion of Triply Periodic Constant Mean Curvature Surface

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