Double Gyroid Research Articles

Immiscible polydiene blocks in linear copolymer and terpolymer sequences

ABSTRACTSynthesis, molecular, and morphological characterization of two linear diblock copolymers consisting of two polydienes with specific geometric isomerisms and two triblock terpolymers with a combination of the same polydienes with polystyrene are investigated for both lower and very high molecular weights. This work is inspired from a previous research study which demonstrated that linear ABC terpolymers consisting of polystyrene, poly(butadiene), and poly(isoprene), with specific geometric isomerisms for the polydienes, lead to 3‐phase microphase separated systems. We report also the coexistence of the core‐shell double gyroid and the 3‐phase 4‐layer alternating lamellae morphologies with the majority fraction being the lamellar structure. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 1238–1246

Enzyme Kinetics in Liquid Crystalline Mesophases: Size Matters, But Also Topology.

Lyotropic liquid crystalline systems (LLCs) are excellent immobilizing carriers for enzymes, due to their biocompatibility and well-defined pore nanostructure. Here we show that the liquid crystalline mesophase topology can greatly influence the enzymatic activity in a typical peroxidase (Horseradish peroxidase, HRP) enzymatic reaction. Enzyme kinetics was investigated in different LLC mesophases based on monolinolein, with varying symmetries and dimensions such as the 1D cylindrical inverse hexagonal phase (HII), the 2D planar lamellar phase (Lα), and two 3D bicontinuous cubic phases of double diamond (Pn3m) and gyroid (Ia3d) space groups. As expected, the mesophase with largest water channel size shows highest activity, regardless of the topology. Interestingly, however, when mesophases with different topologies have the same water channel size, then the topology plays the dominant role, and the enzyme showed the highest activity in the 3D tetra-fold connected Pn3m, followed by the Ia3d with trifold connectivity, and finally the 1D HII phase. This study demonstrates that the enzymatic activity in LLC mesophases depends on both the water channel size and the topology of the mesophase.

Linker Length-Dependent Control of Gemini Surfactant Aqueous Lyotropic Gyroid Phase Stability.

Network-phase lyotropic liquid crystals (LLCs) derived from the water-directed self-assembly of small molecule amphiphiles comprise a useful class of soft nanomaterials, with wide-ranging applications in structural biology and membrane science. However, few known surfactants enable access to these mesophases over wide temperature and amphiphile concentration phase windows. Recent studies have demonstrated that gemini ("twin tail") dicarboxylate surfactants, in which alkyl carboxylates are covalently linked near the headgroups by a hydrophobic bridge, exhibit increased propensities to form double gyroid network phase LLCs. We demonstrate herein that the lyotropic self-assembly behaviors of gemini dicarboxylates sensitively depend on the linker length, whereby odd-carbon linkers stabilize the double gyroid network LLC over unprecedented amphiphile concentration windows up to ∼45 wt % wide between T ≈ 22-80 °C. These self-assembly phenomena, which arise from the linker length-dependent preferred molecular conformations of these amphiphiles, will broaden the technological applications of these nanostructured LLCs.

Real-space evidence of the equilibrium ordered bicontinuous double diamond structure of a diblock copolymer.

The ordered bicontinuous double diamond (OBDD) structure has long been believed to be an unstable ordered network nanostructure, which is relative to the ordered bicontinuous double gyroid (OBDG) structure for diblock copolymers. Using electron tomography, we present the first real-space observation of the thermodynamically stable OBDD structure in a diblock copolymer composed of a stereoregular block, syndiotactic polypropylene-block-polystyrene (sPP-b-PS), in which the sPP tetrapods are interconnected via a bicontinuous network with Pn3̄m symmetry. The OBDD structure underwent a thermally reversible order-order transition (OOT) to OBDG upon heating, and the transition was accompanied with a slight reduction of domain spacing, as demonstrated both experimentally and theoretically. The thermodynamic stability of the OBDD structure was attributed to the ability of the configurationally regular sPP block to form helical segments, even above its melting point, as the reduction of internal energy associated with the helix formation may effectively compensate the greater packing frustration in OBDD relative to that in the tripods of OBDG.

Epitaxial Phase Transition between Double Gyroid and Cylinder Phase in Diblock Copolymer Thin Film

The epitaxial relationship in the thermal phase transition between double gyroid (DG) and hexagonally packed cylinder (HEX) phases in polystyrene-block-polyisoprene thin films on Si wafer was investigated using transmission electron microtomography and grazing incidence small-angle X-ray scattering. Two different types of epitaxial transitions were observed, and they appeared to be selectively favored depending on the transition direction. One type of epitaxial relationship prevails in the phase transition from DG to HEX upon heating in which {121}DG, {111}DG, and {220}DG are converted to {100}HEX, {110}HEX, and {001}HEX, respectively. The interphase planes are {220}DG and {001}HEX, and the cylinders meet the {220}DG plane perpendicularly (head-on, Type A) at the grain boundary between DG and HEX. Although there are small dimensional mismatch and distortion in the location of the cylinders in this epitaxial relationship, all cylinders are formed along the topologically equivalent DG skeletal path. On the other hand, in the transition from HEX to DG upon cooling, another epitaxial relationship as well as the head-on type epitaxy was observed, in which {100}HEX, {110}HEX, and {001}HEX are converted to {121}DG, {220}DG, and {111}DG, respectively. The interphase planes are {220}DG and {110}HEX, and the cylinders meet the {220}DG plane in parallel (side-on, Type B) at the grain boundary between HEX and DG. The domain spacing and the symmetry of the two phases are matched near perfectly, but cylinders are converted to two different DG skeletal paths. The Type B epitaxy is hardly observed in the transition from DG to HEX.

A Facile Method To Fabricate Double Gyroid as a Polymer Template for Nanohybrids

Here, we suggest a facile method to acquire double gyroid (DG) phase from the self-assembly of chiral block copolymers (BCPs*), polystyrene-b-poly(l-lactide) (PS–PLLA). A wide region for the formation of DG can be found in the phase diagram of the BCPs*, suggesting that helical phase (H*) from the self-assembly of BCPs* can serve as a stepping stone for the formation of the DG due to an easy path for order–order transition from two-dimensional to three-dimensional (network) structure. Moreover, the order–order transition from metastable H* to stable DG can be expedited by blending the PS–PLLA with compatible entity. Unlike the conventional way for blending BCP with homopolymer, PS–PLLA blends are prepared by using styrene oligomer (S) to fine-tune the morphologies of the blends at which the molecular weight ratio of the S and compatible PS block (r) is less than 0.1. Owing to the use of the low-molecular-weight oligomer, the increase of BCP chain mobility in the blends significantly reduces the transformation time for the order–order transition from H* to DG. Consequently, by taking advantage of degradable character of the PLLA, nanoporous gyroid SiO2 can be fabricated using hydrolyzed PS–PLLA blends as a template for sol–gel reaction followed by removal of the PS matrix.

The Tricontinuous 3ths(5) Phase: A New Morphology in Copolymer Melts

Self-assembly remains the most efficient route to the formation of ordered nanostructures, including the double gyroid network phase in diblock copolymers based on two intergrown network domains. Here we use self-consistent field theory to show that a tricontinuous structure with monoclinic symmetry, called 3ths(5), based on the intergrowth of three distorted ths nets, is an equilibrium phase of triblock star-copolymer melts when an extended molecular core is introduced. The introduction of the core enhances the role of chain stretching by enforcing larger structural length scales, thus destabilizing the hexagonal columnar phase in favor of morphologies with less packing frustration. This study further demonstrates that the introduction of molecular cores is a general concept for tuning the relative importance of entropic and enthalpic free energy contributions, hence providing a tool to stabilize an extended repertoire of self-assembled nanostructured materials.

Nanoporous Sheets and Cylinders via Bulk Templating of Triblock Terpolymer/Homopolymer Blends

The selective cross-linking of individual domains in block copolymer bulk morphologies represents an elegant strategy to generate nanostructured materials of tunable size and geometry. We demonstrate the preparation of highly periodic nanoporous sheets and core–shell cylinders from a stimuli-responsive triblock terpolymer, polybutadiene-block-poly(tert-butyl methacrylate)-block-poly(2-(dimethylamino)ethyl methacrylate) (PB-b-PtBMA-b-PDMAEMA). By blending the terpolymer with different types and amounts of homopolymers, a variety of bulk morphologies is accessible, including rarely found examples such as tetragonally perforated lamellae and double gyroid networks. Selective cross-linking of the PB domains of the generated morphologies followed by sonication-assisted dispersion allows the preparation of well-defined nanostructures in nonselective solvents. Because of the PDMAEMA corona, the cross-linked structures are soluble in aqueous media. The high regularity of the pore diameter in combination with a tu...

Asymmetric Giant “Bolaform-like” Surfactants: Precise Synthesis, Phase Diagram, and Crystallization-Induced Phase Separation

A series of unique heterofunctionalized asymmetric giant “bolaform-like” surfactants composed of a polystyrene (PS) chain end-capped with two distinctly functionalized polyhedral oligomeric silsesquioxane (POSS) cages [one with seven isobutyl groups (BPOSS) and the other with 14 hydroxyl groups (DPOSS)] were designed and synthesized, and their self-assembly behaviors were investigated. Combining the atomic transfer radical polymerization using a BPOSS-containing initiator and the sequential “click” approach, BPOSS-PSn-DPOSS samples with different PS molecular weights were obtained. Investigation on their self-assembly behaviors revealed that they could form a variety of different ordered structures, such as lamellae, double gyroids, hexagonally packed cylinders, and body-center-cubic spheres, with feature sizes around or below 10 nm. Functional groups on the POSS cages govern the interaction parameters of different POSS cages with the PS interconnect and thus their compatibility. Hydrophilic DPOSS cages are phase-separated from the PS domains, while BPOSS cages are favorably associated within the PS domains. However, in the lamellae phase where the geometry of confinement seems compatible with the close-packing of BPOSS, the BPOSS cages tend to crystallize due to the existence of the flat interfaces, leading to further phase separation of the BPOSS cages from the PS interconnects. These results provide insights into the design of novel self-assembling materials based on POSS–polymer conjugates toward desired physical properties.

Experimental confirmation of transformation pathways between inverse double diamond and gyroid cubic phases.

A macroscopically oriented double diamond inverse bicontinuous cubic phase (QII(D)) of the lipid glycerol monooleate is reversibly converted into a gyroid phase (QII(G)). The initial QII(D) phase is prepared in the form of a film coating the inside of a capillary, deposited under flow, which produces a sample uniaxially oriented with a ⟨110⟩ axis parallel to the symmetry axis of the sample. A transformation is induced by replacing the water within the capillary tube with a solution of poly(ethylene glycol), which draws water out of the QII(D) sample by osmotic stress. This converts the QII(D) phase into a QII(G) phase with two coexisting orientations, with the ⟨100⟩ and ⟨111⟩ axes parallel to the symmetry axis, as demonstrated by small-angle X-ray scattering. The process can then be reversed, to recover the initial orientation of QII(D) phase. The epitaxial relation between the two oriented mesophases is consistent with topology-preserving geometric pathways that have previously been hypothesized for the transformation. Furthermore, this has implications for the production of macroscopically oriented QII(G) phases, in particular with applications as nanomaterial templates.

Tuning enantioselectivity in asymmetric hydrogenation of acetophenone and its derivatives via confinement effect over free-standing mesoporous palladium network catalysts

The confinement effect on enantioselective hydrogenation of acetophenone and its derivatives over free-standing mesoporous Pd network catalysts was systematically studied. It was found for the first time that the enantiomeric excess (ee) could be effectively tuned by altering the confinement effect optimized by precise control of the topology, pore size, and lattice structure of mesoporous Pd catalysts. The double gyroid structure with proper pore size and desired lattice structure formed by KBH4 reduction provided suitable microenvironment to generate optimized confinement effect. The optimized catalyst exhibited ee of 40–73% at 273K under atmospheric pressure of H2. DFT study revealed that the major enantiomeric product could be predicted by comparing relative energies of prochiral-R and -S complexes formed by acetophenone derivatives with S-proline. The energetically favored complex led to the formation of the corresponding enantiomer in excess upon hydrogenation, and ee was found to be linearly correlated with the energy difference between prochiral-R and -S complexes.

Shifting Networks to Achieve Subgroup Symmetry Properties

A simple method for the preparation of nanomaterials with new functionality by physical displacement of a network phase is suggested, giving a change in space group symmetry and hence properties. A double gyroid structure made by the self-assembly of block copolymers is used as a model system for the demonstration of shifting networks to achieve single gyroid-like scattering properties. Free-standing single gyroid-like network materials can be fabricated to give nanophotonic properties, similar to the photonic properties of a butterfly wing structure.

Effects of molecular geometry on the self-assembly of giant polymer–dendron conjugates in condensed state

A series of giant polymer-dendron conjugates with a dendron head and a linear polymer tail were synthesized via"click" chemistry between azide-functionalized polystyrene (PS(N), N: degree-of-polymerization) and t-butyl protected, alkyne-functionalized second generation dendron (tD), followed by a deprotection process to generate a dendron termini possessing nine carboxylic acid groups. The molecular structures were confirmed by nuclear magnetic resonance, size-exclusion chromatographic analyses, and matrix-assisted laser desorption ionization time-of-flight mass spectra. These well-defined conjugates can serve as a model system to study the effects of the molecular geometries on the self-assembly behaviour, as compared with their linear analogues. Four phase morphologies found in flexible linear diblock copolymer systems, including lamellae, bicontinuous double gyroids, hexagonal packed cylinders, and body-centred cubic packed spheres, were observed in this series of conjugates based on the results of small angle X-ray scattering and transmission electron microscopy. All of the domain sizes in these phase separated structures were around or less than 10 nm. A 'half' phase diagram was constructed based on the experimental results. The geometrical effect was found not only to enhance the immiscibility between the PS(N) tail and dendron head, but also systematically shift all of the phase boundaries towards higher volume fractions of the PS(N) tails, resulting in an asymmetrical phase diagram. This study may provide a pathway to the construction of ordered patterns of sub-10 nm feature size using polymer-dendron conjugates.

Double and Single Network Phases in Polystyrene-block-poly(l-lactide) Diblock Copolymers

Here, the phase behaviors of polystyrene-block-poly(l-lactide) (PS–PLLA) diblock copolymers are studied, and network phases can be found. In addition to conventional double gyroid phase with double networks, a single network phase (an Fddd phase with orthorhombic network) can be found, as evidenced by small-angle X-ray scattering and transmission electron microscopy (TEM). The single network texture with trivalent connectors of the Fddd can be directly visualized by using 3D TEM (i.e., electron tomography), and the observation under polarized light microscopy shows its birefringence character. The formation of stable Fddd is attributed to intrinsic inhomogeneity in the chain conformations of the chiral block (i.e., PLLA). Subsequently, nanoporous PS with continuous nanochannel networks can be obtained by hydrolysis of the PLLA block in the PS–PLLA and then used as a template for sol–gel reaction of tetraethyl orthosilicate. Consequently, nanoporous SiO2 with free-standing, well-defined network texture can be fabricated after removal of the PS template to give an open-cell porous ceramic material with high specific surface area (as high as 1170 m2/g) due to its nanostructured texture and high porosity.

Direct Visualization of Order-Order Transitions in Silicon-Containing Block Copolymers by Electron Tomography.

Here, we aim to comprehend the mechanism of the order-order transition (OOT) from nonequilibrium, metastable phase to equilibrium phase. Polystyrene-block-polydimethylsiloxane (PS-PDMS) block copolymer (BCP) bulks with metastable cylinder (C) and double gyroid (G) phases can be obtained from lamellae (L) forming PS-PDMS by simply tuning the selectivity of casting solvent. The recovery of the intrinsic L phase can be achieved by thermal annealing through OOT. Time-resolved small-angle X-ray scattering (SAXS) experiments are carried out to reveal the variation of the structural evolution in reciprocal space during annealing. The structural evolution in real space is directly visualized by using electron tomography (i.e., 3D transmission electron microscopy (TEM)). As a result, combining the time-resolved scattering experiments and the morphological observations from electron tomography offers new insights into the phase behaviors of the OOT of BCPs.

Well‐Defined Multibranched Gold with Surface Plasmon Resonance in Near‐Infrared Region from Seeding Growth Approach Using Gyroid Block Copolymer Template

Well-defined multibranched gold (Au) in polymers, both as bulk or continuous thin films, can be fabricated by using a nanoporous polymer with gyroid nanochannels as a template. The nanoporous polymer template is obtained from the self-assembly of a degradable block copolymer, polystyrene-b-poly (L-lactide) (PS-PLLA), followed by the hydrolysis of PLLA blocks. Templated seeding growth approach can be conducted to create precisely controlled nanostructured Au giving remarkable surface plasmon resonance (SPR) in (branched Au with uniform distribution in PS matrix) near-infrared (NIR) region. Controlled growth conditions allow the fabrication of three-dimensionally ordered nanoporous Au particles that possess NIR SPR. Double gyroid Au with dual networks in the PS matrix is obtained after completing the seeding growth at which the NIR SPR diminishes resulting from the reduction in the density of nanostructured edge.

The geometry of the double gyroid wire network: quantum and classical

Quantum wire networks have recently become of great interest. Here we deal with a novel nano material structure of a Double Gyroid wire network. We use methods of commutative and non-commutative geometry to describe this wire network. Its non--commutative geometry is closely related to non-commutative 3-tori as we discuss in detail.

Effect of nanoparticle polydispersity on the self-assembly of polymer tethered nanospheres

Recent simulations predict that aggregating nanospheres functionalized with polymer "tethers" can self-assemble to form a cylinder, perforated lamellae, lamellae, and even the double gyroid phase, which are phases also seen in block copolymer and surfactant systems. Nanoparticle size polydispersity is likely to be a characteristic of these systems. If too high, polydispersity may destabilize a phase. Using multiple thermodynamic paths to explore the phase diagram as a function of temperature and polydispersity, we explore the effect of nanosphere size polydispersity on the phase diagram. We show that in the portions of the phase diagram characterized by an icosahedral local nanoparticle packing motif, a low amount of polydispersity lowers the energy and a large amount of polydispersity raises the energy of the system by disrupting the icosahedral packing. In general, regions of the phase diagram characterized by liquid-like icosahedral packing have high terminal polydispersities from 15% to more than 30%. In the regions of the phase diagram characterized by crystalline local packing, polydispersity raises the energy of the system and induces a phase transition from crystalline to liquid-like ordering within the nanosphere rich regions of the microphase. We find the bilayer crystalline lamellae phase has a terminal polydispersity of 6%, but may still be partially crystalline up to 12%.

Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the Gyroid

Motivated by the Double Gyroid nanowire network we develop methods to detect Dirac points and classify level crossings, aka. singularities in the spectrum of a family of Hamiltonians.The approach we use is singularity theory. Using this language, we obtain a characterization of Dirac points and also show that the branching behavior of the level crossings is given by an unfolding of An type singularities. Which type of singularity occurs can be read off a characteristic region inside the miniversal unfolding of an Ak singularity.We then apply these methods in the setting of families of graph Hamiltonians, such as those for wire networks. In the particular case of the Double Gyroid we analytically classify its singularities and show that it has Dirac points. This indicates that nanowire systems of this type should have very special physical properties.

Design of Porous Three-Dimensional PDLLA/nano-hap Composite Scaffolds Using Stereolithography

The stereolithography process is based on the photopolymerization through a dynamic mask generator of successive layers of photocurable resin, allowing the manufactory of accurate micro objects with high aspect ratio and curved surfaces. In the present work the stereolithography technique is applied to produce nanocomposite bioactive scaffolds from Computer Assisted Design (CAD) files. Porous scaffolds are designed with computer software and built with a composite poly(D,L-lactide)/nano hydroxyapatite based resin. Triply-periodic minimal surfaces are shown to be a more versatile source of biomorphic scaffold designs and scaffolds with Double Gyroid architecture are realized and characterized from morphological, mechanical and biological point of view. The structures show excellent reproduction of the design and good mechanical properties. Human marrow mesenchimal cells (hMSC) are seeded onto porous PDLLA composites for 3 weeks and cultured in osteogenic medium. Presence of nano-hap seems to increase the mechanical properties without affecting the morphology of the structures. The composite Double Gyroid scaffolds exhibit good biocompatibility and confirm that nano-hap enhances the scaffold bioactive and osteoconductive potential. The presented technology and materials enable an accurate preparation of tissue engineering composite scaffolds with a large freedom of design, and really complex internal architectures. Results indicate that the scaffolds fulfill the basic requirements of bone tissue engineering scaffold, and have the potential to be applied in orthopedic surgery.