Bicontinuous Double Diamond Research Articles

Bicontinuous Double-Diamond Structures Formed in Ternary Blends of AB Diblock Copolymers with Block Chains of Different Lengths

We report on the formation of a bicontinuous double diamond (DD) structure in ternary blends of poly(styrene-b-isoprene) (SI) diblock copolymers with chains of different lengths merely in a polyisoprene block. Certainly, the materials revealing the DD structure with mesoscopic length scale have strongly been expected due to high potential for applications; however, it is difficult to form owing to thermodynamically evident disadvantages such as wider surface area and larger domain thickness variation, particularly for monodisperse copolymers. The DD structure was successfully formed for ternary blends composed of three parent diblock copolymers; SI-L (M = 190k, φs = 0.46), SI-G (M = 151k, φs = 0.62), and SI-C (M = 124k, φs = 0.73), resulting in covering the overall composition range 0.57 ≤ φs ≤ 0.60, where φss denotes volume fractions of polystyrene blocks. Four-branched double network structure with space group symmetry of Pn3m was clearly proved by transmission electron microscopy (TEM) observation aid...

Order–Order Transition from Ordered Bicontinuous Double Diamond to Hexagonally Packed Cylinders in Stereoregular Diblock Copolymer/Homopolymer Blends

Our previous works have disclosed a thermodynamically stable ordered bicontinuous double diamond (OBDD) structure and the order–order transition (OOT) between OBDD and ordered bicontinuous double gyroid (OBDG) phases in a stereoregular diblock copolymer, syndiotactic polypropylene-block-polystyrene (sPP-b-PS). Here we investigate the effect of blending with a small amount of sPP homopolymer (h-sPP) on the stability of the OBDD phase, where h-sPP formed the dry-brush mixture with the minority sPP block chains in the network microdomains due to their comparable molecular weights. The OBDD structure developed in the blend was found to exist over a broader temperature window than that formed in the neat sPP-b-PS. Nevertheless, the OBDD–OBDG transition displayed by the neat diblock was no longer observed in the blends; instead, the OBDD phase transformed into the hexagonally packed cylinder (HEX) structure on heating, indicating that HEX superseded OBDG upon blending with h-sPP. According to the experimentally...

Double diamond phase in pear-shaped nanoparticle systems with hard sphere solvent

The mechanisms behind the formation of bicontinuous nanogeometries, in particular in vivo, remain intriguing. Of particular interest are the many systems where more than one type or symmetry occurs, such as the Schwarz’ diamond surface and Schoen’s gyroid surface; a current example are the butterfly nanostructures often based on the gyroid, and the beetle nanostructures often based on the diamond surface. Here, we present a computational study of self-assembly of the bicontinuous Pnm diamond phase in an equilibrium ensemble of pear-shaped particles when a small amount of a hard-sphere ‘solvent’ is added. Our results are based on previous work that showed the emergence of the gyroid Iad phase in a pure system of pear-shaped particles (Schönhöfer et al 2017 Interface Focus 7 20160161), in which the pear-shaped particles form an interdigitating bilayer reminiscent of a warped smectic structure. We here show that the addition of a small amount of hard spherical particles tends to drive the system towards the bicontinuous Pnm double diamond phase, based on Schwarz diamond minimal surface. This result is consistent with the higher degree of spatial heterogeneity of the diamond minimal surface as compared to the gyroid minimal surface, with the hard-sphere ‘solvent’ acting as an agent to relieve packing frustration. However, the mechanism by which this relief is achieved is contrary to the corresponding mechanism in copolymeric systems; the spherical solvent tends to aggregate within the matrix phase, near the minimal surface, rather than within the labyrinthine channels. While it may relate to the specific form of the potential used to approximate the particle shape, this mechanism hints at an alternative way for particle systems to both release packing frustration and satisfy geometrical restrictions in double diamond configurations. Interestingly, the lattice parameters of the gyroid and the diamond phase appear to be commensurate with those of the isometric Bonnet transform.

Stabilizing the Ordered Bicontinuous Double Diamond Structure of Diblock Copolymer by Configurational Regularity

We investigate the formation of the ordered bicontinuous structures in a stereoregular diblock copolymer, isotactic polypropylene-block-polystyrene (iPP-b-PS), in which the minority PP block possessed isotactic configuration. This diblock displayed the conventional ordered bicontinuous double gyroid (OBDG) morphology upon heating above the crystal melting point of the iPP block from the as-cast state. The OBDG phase remained stable in the heating process up to the order–disorder transition. In the subsequent cooling process from the nearly disordered state, the OBDG phase first developed, but when the temperature was sufficiently low, an order–order transition from OBDG to the ordered bicontinuous double diamond (OBDD) phase occurred, and OBDD eventually became the dominant structure. The results attested that OBDD and OBDG represented the thermodynamically stable structure at the lower and the higher temperature, respectively, and the OBDG morphology formed in the as-cast state was metastable. The presen...

Phase Diagram for Block Copolymer and Homopolymer Blends: The Phase Boundary of the Ordered Bicontinuous Double Diamond Network Structure

Phase Diagram for Block Copolymer and Homopolymer Blends: The Phase Boundary of the Ordered Bicontinuous Double Diamond Network Structure

Self-assembled Lyotropic Liquid Crystalline Phase Behavior of Monoolein-Capric Acid-Phospholipid Nanoparticulate Systems.

We report here the lyotropic liquid crystalline phase behavior of two lipid nanoparticulate systems containing mixtures of monoolein, capric acid, and saturated diacyl phosphatidylcholines dispersed by the Pluronic F127 block copolymer. Synchrotron small-angle X-ray scattering (SAXS) was used to screen the phase behavior of a library of lipid nanoparticles in a high-throughput manner. It was found that adding capric acid and phosphatidylcholines had opposing effects on the spontaneous membrane curvature of the monoolein lipid layer and hence the internal mesophase of the final nanoparticles. By varying the relative concentration of the three lipid components, we were able to establish a library of nanoparticles with a wide range of mesophases including at least the inverse bicontinuous primitive and double diamond cubic phases, the inverse hexagonal phase, the fluid lamellar phase, and possibly other phases. Furthermore, the in vitro cytotoxicity assay showed that the endogenous phospholipid-containing nanoparticles were less toxic to cultured cell lines compared to monoolein-based counterparts, improving the potential of the nonlamellar lipid nanoparticles for biomedical applications.

特異値分解法を用いた共連続ダブルダイアモンド-ダブルジャイロイド転移における小角X線散乱の解析 中間体構造は存在するのか？

Microdomain structures formed in the mixture of polystyrene-b-polyisoprene (SI) diblock copolymer, whose number-averaged molecular weight, Mn, and volume fraction, ƒPS are, respectively, 45,000 and 0.70, with a polyisoprene homopolymer (PI, Mn = 18,000) and dioctyl phthalate (DOP) were studied by the singular value decomposition (SVD) of small-angle X-ray scattering. The volume ratio of SI/PI/DOP was 43.7/16.3/40 vol.%. SAXS measurement was performed on the mixture every 20 ℃ from 130 to 30 ℃ in a cooling cycle and successively every 20 ℃ from 30 to 130 ℃ in a heating cycle. The scattering observed at the corresponding temperatures in both of the cycles were in good agreement. The scattering measured at 130 ℃ had multiple peaks; the relative peak position ratios to the primary peak was close to 1 : √8/6 : √14/6 : √16/6 : √20/6 : √22/6 that are typical to an ordered bicontinuous double gyroid (OBDG) structure, while the one at 30 ℃ had multiple peaks; the relative peak position ratios to the primary peak were 1 : √3/2 : √4/2 : √6/2 : √8/2 typical to an ordered bicontinuous double diamond (OBDD) structure. The scattering at the intermediate temperatures from 50 to 110 ℃ showed more complex multiple peaks. The SVD was conducted on the set of the SAXS profiles: The rank was 6 but the first two singular values were significantly larger than the rest of the four values. Thus, the low-rank approximation with the first two singular values was employed. All of the temperature dependent SAXS were successfully rebuilt with the first two basis functions obtained by SVD. The weighting functions used to reconstruct the profiles relate to the first two singular values; the second weighting function relating to the temperature change of the SAXS showed only one drastic change between 70 and 90 ℃. This means that no intermediate structure between OBDD and OBDG exists. The fraction of OBDD was also calculated by the temperature change in SAXS: 0.98, 0.85, 0.28 and 0.11 at 50, 70, 90 and 110 ℃, respectively.

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.

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

Correction for 'Real-space evidence of the equilibrium ordered bicontinuous double diamond structure of a diblock copolymer' by C. Y. Chu et al., Soft Matter, 2015, 11, 1871-1876.

Order–Order Transition between Equilibrium Ordered Bicontinuous Nanostructures of Double Diamond and Double Gyroid in Stereoregular Block Copolymer

While ordered bicontinuous double diamond (OBDD) in block copolymers has always been considered as an unstable structure relative to ordered bicontinuous double gyroid (OBDG), here we report the existence of a thermodynamically stable OBDD structure in a diblock copolymer composed of a stereoregular block. A slightly asymmetric syndiotactic polypropylene-block-polystyrene (sPP-b-PS) as cast from xylene was found to display the OBDD morphology. When the OBDD-forming diblock was heated, this structure transformed to the OBDG phase at ca. 155 °C. Interestingly, OBDD was recovered upon cooling even in the temperature range above melting point of sPP, indicating that OBDD was a thermodynamically stable structure for sPP-b-PS melt, which was in contradiction to the conventional view. We propose that the larger free energy cost encountered in OBDD due to the larger packing frustration may be compensated sufficiently by the release of free energy due to local packing of the conformationally ordered segments of sPP blocks, which stabilizes the OBDD structure at the lower temperatures.

Spontaneous Formation and Characterization of Silica Mesoporous Crystal Spheres with Reverse Multiply Twinned Polyhedral Hollows

A crystal is an object with translational symmetry. Basic research into and production of new materials necessitates the preparation of crystals of a particular morphology and with well-defined crystal defects. In this work, we found novel silica mesoporous crystal spheres with polyhedral hollows (icosahedral, such as those observed for proteins of virus capsids, decahedral, Wulff polyhedral, etc.) formed by the reverse multiply twinned bicontinuous double diamond mesostructure. Vesicles with a low-curvature lamellar structure were first formed by the self-assembly of amphiphilic carboxylic acid molecules in the presence of a nonionic surfactant and then underwent a structural transformation process that gave a reverse multiply twinned mesoporous shell while maintaining the hollow shape. These polyhedral hollow crystals showed an enhanced contrast of backscattering signatures relative to the incident acoustic signals and thus could be used as a potential contrast agent in medical ultrasonography with drug loadings in the mesopores.

SAXS investigation of a cubic to a sponge (L3) phase transition in self-assembled lipid nanocarriers

The encapsulation and release of peptides, proteins, nucleic acids, and drugs in nanostructured lipid carriers depend on the type of the self-assembled liquid-crystalline organization and the structural dimensions of the aqueous and membraneous compartments, which can be tuned by the multicomponent composition of the systems. In this work, small-angle X-ray scattering (SAXS) investigation is performed on the 'melting' transition of the bicontinuous double diamond cubic phase, formed by pure glycerol monooleate (MO), upon progressive inclusion of varying fractions of pharmaceutical-grade glycerol monooleate (GO) in the hydrated system. The self-assembled MO/GO mixtures are found to form diamond (Pn3m) inverted cubic, inverted hexagonal (H(II)), and sponge (L(3)) phases at ambient temperature in excess of aqueous medium without heat treatment. Mixing of the inverted-cubic-phase-forming MO and the sponge-phase-forming GO components, in equivalent proportions (50/50 w/w), yields an inverted hexagonal (H(II)) phase nanostructured carrier. Scattering models are applied for fitting of the experimental SAXS patterns and identification of the structural changes in the aqueous and lipid bilayer subcompartments. The possibility of transforming, at ambient temperature (20 °C), the bicontinuous cubic nanostructures into inverted hexagonal (H(II)) or sponge (L(3)) mesophases may facilitate novel biomedical applications of the investigated liquid crystalline self-assemblies.

Monodisperse nonionic phytanyl ethylene oxide surfactants: high throughput lyotropic liquid crystalline phase determination and the formation of liposomes, hexosomes and cubosomes

The phase behaviour (both neat and lyotropic) and toxicity of eight new ethylene oxide amphiphiles (EO = 1 to 8) with a single phytanyl chain (3,7,11,15 tetramethylhexadecyl) is reported. There is a discontinuity at EO > 4 where the neat and lyotropic behaviour exhibit a tipping point which is qualitatively rationalised in terms of the molecular geometry of the surfactant. Below four EO units the behaviour of the neat surfactants show only a glass transition, Tg ∼ −90 °C. Above four EO units crystallisation (Tcrys) and crystal-isotropic liquid (Tm) transitions are also observed. These increase monotonically with the hydrophilicity of the surfactant; consistent with the greater cohesiveness of the molecules due to van der Waals interactions. The increase in hydrophilicity corresponds to a decrease in curvature of the surfactant layer towards water. However, the exaggerated splay of the phytanyl chain is effective in promoting various self-assembled structures with inverse cubic and hexagonal phases preferred below ambient temperatures for EO < 4, and these are stable to dilution. Variation of the EO head group length promotes an interesting diversity of cubic phases, with an inverse micellar cubic phase (Fd3m) present for EO = 2 and the bicontinuous gyroid cubic (Ia3d) and double diamond cubic (Pn3m) phases present at higher ethoxylation. DIT-NIR microspectroscopy provided a high throughput, low volume, fast equilibrating method for obtaining the approximate partial temperature-composition phase diagrams of the binary systems with water. The toxicity of colloidal dispersions of these amphiphiles was assayed against normal breast epithelial (HMEpiC) and breast cancer (MCF7) cell lines. The IC50 of the EO amphiphiles was similar in both cell lines with moderate toxicity ranging from ∼80–110 μM in an in vitro cell viability assay.

Dissipative Particle Dynamics Study of Order−Order Phase Transition of BCC, HPC, OBDD, and LAM Structures of the Poly(styrene)−Poly(isoprene) Diblock Copolymer

A Gaussian chain model of poly (styrene)−poly (isoprene) (PS−PI) block copolymer with a dissipative particle dynamics (DPD) simulation was employed to study the formation of specific characteristic structures such as body-centered-cubic (BCC), hexagonal packed cylinders (HPC), ordered bicontinuous double diamond (OBDD), and lamellar (LAM) via order−disorder transition (ODT). The BCC, HPC, OBDD and LAM microphases were then subjected to thermal cycles of heating and cooling. The order−order phase transition (OOT) from HPC to BCC was monitored and two new transitions, OBDD to LAM and LAM to hexagonal perforated layers (HPL), were detected during the thermal process. Two metastable states (cylinders and HPL) were observed in the OOT process from the OBDD to LAM microphases. It is shown that all order−order transitions between the different kinds of structures are thermoreversible. The results were compared with the predictions of recent theories and with available experimental outcomes and thus provide a tes...

Self-Organization Process of Ordered Structures in Linear and Star Poly(styrene)−Poly(isoprene) Block Copolymers: Gaussian Models and Mesoscopic Parameters of Polymeric Systems

Mesoscopic simulations of linear and 3-arm star poly(styrene)-poly(isoprene) block copolymers was performed using a representation of the polymeric molecular structures by means of Gaussian models. The systems were represented by a group of spherical beads connected by harmonic springs; each bead corresponds to a segment of the block chain. The quantitative estimation for the bead-bead interaction of each system was calculated using a Flory-Huggins modified thermodynamical model. The Gaussian models together with dissipative particle dynamics (DPD) were employed to explore the self-organization process of ordered structures in these polymeric systems. These mesoscopic simulations for linear and 3-arm star block copolymers predict microphase separation, order-disorder transition, and self-assembly of the ordered structures with specific morphologies such as body-centered-cubic (BCC), hexagonal packed cylinders (HPC), hexagonal perforated layers (HPL), alternating lamellar (LAM), and ordered bicontinuous double diamond (OBDD) phases. The agreement between our simulations and experimental results validate the Gaussian chain models and mesoscopic parameters used for these polymers and allow describing complex macromolecular structures of soft condensed matter with large molecular weight at the statistical segment level.

Polyisoprene-Polystyrene Diblock Copolymer Phase Diagram near the Order-Disorder Transition

The phase behavior of ten polyisoprene-polystyrene (PI-PS) diblock copolymers, spanning the composition range from 0.24 to 0.82 polyisoprene volume fraction (f PI ), has been studied near the order-disorder transition (ODT). Dynamic mechanical spectroscopy, transmission electron microscopy, and neutron and X-ray scattering have been used to characterize phase transition temperatures and ordered state symmetries. Five distinct microstructures were observed for this chemical system : spheres, hexagonally packed cylinders (HEX), lamellae (LAM), hexagonally perforated layers (HPL), and a bicontinuous cubic phase having an Ia3d space group symmetry. The bicontinuous Ia3d phase only occurs in the vicinity of the ODT between the HEX and LAM states at compositions of 0.65 ≤ f pI ≤ 0.68 and 0.36 ≤ f pI ≤ 0.39 (prior report). Farther from the ODT, within these composition ranges, the HPL phase occurs. We did not find the ordered bicontinuous double diamond (OBDD) morphology at any composition or temperature studied, and the overall phase diagram is qualitatively different from those reported previously for PI-PS block copolymers.

Harmonic corrections to the mean-field phase diagram for block copolymers

Allowance is made for harmonic corrections within mean-field theory for weakly segregated block copolymers. The theory of Marques and Cates [C. M. Marques and M. E. Cates, Europhys. Lett. 13, 267 (1990)] for the stability of phases near the ordering transition is applied to diblock copolymer melts. A wave-vector dependence of the coefficients in the Landau mean-field free energy is included. We find that the face centered cubic (fcc) and square phases predicted by Marques and Cates to be stable near the ordering transition depending on the structure factor for the system are not stable for diblock copolymers. In addition, hexagonal close packed (hcp) and ordered bicontinuous double diamond (OBDD) structures are found to be unstable with respect to the classical lamellar, cylinder, and body centered cubic phases. The hexagonal intermediate phases and complex bicontinuous structures recently observed near the order–disorder transition are not accounted for in this theory.

Recent morphological surprises in diblock copolymer systems

Diblock copolymers form ordered interfacial surfaces that range from lamellae, to cylinders, to the ordered bicontinuous double diamond (OBDD) structure, and spheres on a cubic lattice as the size of one component is increased. Flexible control of these materials presents an opportunity for structural materials, adhesives and selective separations. Mixtures of diblock copolymers with homopolymers exhibit similar structures due to changes in the interfacial curvature that accompany "swelling" the like-component of the diblock with homopolymer. Ordering behavior in systems of this type depends on the elastic properties and molecular weights (MW's) of the polymers, annealing temperature and annealing time. We have examined the changes in morphology of a styrene-butadiene (SB) diblock copolymer mixed with homopolymer polystyrene (hS). Sample made by casting from toluene solution, annealing at 130°C for 2-10 days, staining B-rich regions with OsO4, and microtoming thin-sections at -90°C. The SB MW was 49 800 g/mol with an S-block MW of 25 500 g/mol, and 24 400 g/mol for the B-block. Two hS components were used, having MW's of 26 000 g/mol (h26) and 19 300 g/mol (h19). We refer to the samples by the hS molecular weight and total polystyrene volume fraction, e.g. h26/0.67.

Morphologies in Blends of Diblock Copolymer and Homopolymer: Morphology Diagrams and the Intermaterial Dividing Surface

AbstractBinary blends of diblock copolymer (AB) and homopolymer (hA) self assemble upon solvent evaporation into a great variety of microphase separated morphologies. The ordered lamellar, bicontinuous double diamond, cylindrical and spherical morphologies were observed by TEM and SAXS in our studies, as well as a range of micellar morphologies.The mean curvature (H) and the area per copolymer junction (σj), which characterize the intermaterial dividing surface, increased with increasing homopolymer concentration in the blend and/or with decreasing homopolymer molecular weight. These trends were generally obeyed both between and within ordered morphology types. The increase in H and σjwas related to an increased degree of mixing between the homopolymer and the block of the copolymer.Two types of isothermal morphology diagrams were constructed to consolidate the extensive morphological data and to illustrate the general morphological transitions in AB/hA blends. The constant molecular weight morphology diagrams illustrated the interdependence of the copolymer composition and the homopolymer concentration. The constant copolymer composition diagrams emphasized the importance of the relative homopolymer molecular weight and the overall blend composition.

A variety of morphologies in diblock copolymer/homopolymer blends

A wide range of morphologies and thereby physical properties can be achieved in block copolymer/homopolymer blends by varying the copolymer composition, copolymer concentration and molecular weights. Recently we investigated micelle shape transitions in diblock copolymer with homopolymer blends at low copolymer concentration. In this paper we study the microstructure over a wider concentration range for a polystyrene-polybutadiene (PS/PB) diblock copolymer of molecular weight 20.5 × 103/20.5 × 103 blended with 17.2 × 103 molecular weight homopolystyrene (hPS).Figure 1 shows schematically a possible spectrum of microdomain structures dependent on the copolymer concentration of a lamellar PS/PB and hPS. Below the critical micelle concentration (CMC) the block copolymer is molecularly dispersed in the homopolymer exhibiting a homogeneous phase. As diblock concentration increases the minority (i.e. PB) forms spherical and/or cylindrical micelles randomly dispersed in the hPS. Further increases in diblock concentration induces long range ordering of various microdomains. In addition three biphasic regions are proposed in which two phases coexist: isotropic cylinders with ordered cylinders, ordered cylinders with ordered bicontinuous double diamond (OBDD), and OBDD with swollen lamellae.