Ordered Bicontinuous Double Diamond Research Articles

Effect of Block Copolymer Composition and Homopolymer Molecular Weight on Ordered Bicontinuous Double-Diamond Structures in Binary Blends of Polystyrene–Polyisoprene Block Copolymer and Polyisoprene Homopolymer

We investigated the effect of block copolymer composition and homopolymer molecular weight on the stability of ordered bicontinuous double-diamond (OBDD) phases in polystyrene-rich polystyrene–polyisoprene block copolymer (PS–PI) and polyisoprene (PI) blend using small-angle X-ray scattering. PS–PI with PI volume fractions (fPI) of 31–40 vol % and a degree of polymerization of ca. 320 were prepared. Stable OBDD regions could be observed at fPI = 31–35 vol %, but no OBDD could be observed at fPI = 40 vol %. Moreover, OBDD morphology was formed only when the chain length of the homopolymer was greater than that of the same constituent chain in the copolymer (dry-brush conditions). Furthermore, OBDD formation required a homopolymer content of at least 11 wt % in the blend. These results indicate that the added homopolymer localized in the middle of the microdomains and relieved packing frustration inside the four-fold nodes of OBDD, resulting in a stable OBDD structure.

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the OBDD phase transformed into the hexagonally packed cylinder (HEX) structure on heating, indicating that HEX superseded OBDG upon blending with h-sPP.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...

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

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.

3D-TEM study on the novel bicontinuous microdomain structure.

An ordered bicontinuous double-diamond (OBDD) morphology was found in polystyrene-block-(poly-4-vinylphenyldimethylvinylsilane-graft-polyisoprene), PS-b-(PVS-g-PI), block-graft copolymer. We obtained a 3D image of the microdomain structure formed in PS-b-(PVS-g-PI) using 3D-TEM. The 3D image shows that the polystyrene (PS) phase consists of two independent and interwoven networks. The structures of the two networks are identical and include tetrapod units that form planar six-membered rings. The features of the networks agree with those in the OBDD morphology, indicating that PS-b-(PVS-g-PI) exhibits ordered three-dimensional OBDD networks with the PS phase in the polyisoprene (PI) matrix phase. The grafted PI chains induce the frustration of the PS chains; thus, the effects of the specific interface are more dominant than those of packing frustration in the formation of the morphology, and the OBDD phase is stabilized.

Ordered-bicontinuous-double-diamond structure in block copolymer/homopolymer blends

The morphologies of the microdomain structures in polystyrene-polyisoprene (PS-PI) diblock copolymer and polyisoprene (PI) homopolymer blends were investigated by small-angle X-ray scattering. The PS-PI investigated in the present study has number-average molecular weight and volume fraction of PI , and PI has . The weight fraction of added homopolymer was 0.17. We demonstrated that the existence of ordered-bicontinuous-double-diamond (OBDD) structure was explicitly identified in the PS-PI/PI blend by the scattering method. It was confirmed that OBDD microdomain changed to gyroid (Gyr) when the sample was heated, and the order-order transition between OBDD and Gyr thermo-reversibly occurred. The kinetics of the transformation between OBDD and Gyr was also investigated. In this study, the intermediate structure during the transition between OBDD and Gyr was not observed. A comparison between the rates of transformation revealed that the rate of the OBDD to Gyr transformation is faster than that of the Gyr to OBDD.

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.

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.

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.

Analytical Weak-Segregation Theory of Bicontinuous Phases in Diblock Copolymers

We compute phase diagrams for diblock copolymers in the mean-field weak- segregation regime as a function of the fraction f of A-monomers and the repulsive interaction XN. We include the ordered bicontinuous double-diamond (OBDD) phase (space group Pn3m) and the gyroid phase (space group Ia3d) as well as lamellae, hexagonal cylinders, and BCC spheres. We find a stable region of gyroid phase between cylinders and larnellae just above the mean-field critical point, in agreement with numerical mean-field calculations. The stability of gyroid depends on the presence of the next higher (220) reflections in addition to the (211) fundamental. The gyroid free energy is favored by terms of the form ~(~~~j ~bj220j and ~b(~i~j~bj220j; the analogous terms are not permitted for OBDD.

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.

Molecular-weight factors affecting formation of the OBDD morphology in block copolymer blends.

Block copolymers undergo self-organization when the blocks are sufficiently incompatible, and generate a variety of periodic morphologies in the limit of strong segregation. An equilibrium morphology only recently added to the diblock copolymer phase diagram is the ordered bicontinuous double-diamond (OBDD) morphology, which possess a Pn3m space group. It has been observed over a very narrow composition range (ca. 4 vol%), thereby making it difficult to obtain in pure copolymers. This obstacle can, however, be surmounted by blending a copolymer with one of the parent homopolymers. In the present study, several symmetric poly(styrene-b-isoprene) diblock copolymers varying in molecular weight (M) have been blended with homopolystyrene to produce the OBDD morphology. Transmission electron microscopy is employed here to identify the morphologies in cryosections of each blend and reveals that, at intermediate molecular weights, the OBDD morphology is indeed observed. At low M, near the order-disorder transition, however, a lamellar catenoid or disordered morphology is preferred. At the other extreme, high-M blends are frustrated by molecular entanglements and adopt a cylindrical morphology.

Strong-segregation theory of bicontinuous phases in block copolymers.

We compute phase diagrams for diblock copolymers in the strong-segregation regime as a function of volume fraction \ensuremath{\varphi}. We include the ordered bicontinuous double-diamond (OBDD) phase, which is found to be stable between cylinders and lamellae, consistent with experiment, for \ensuremath{\varphi} (or 1-\ensuremath{\varphi}) between 0.19 and 0.27. Our phase diagram relies on taking into account the hexagonal shape of the unit cell for the cylindrical phase, and the unique geometry of the OBDD phase.

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.

Molecular-weight factors affecting formation of the OBBD morphology in block copolymer blends

Microphase-separated diblock copolymers have been known since 1970 to exhibit three principal morphologies. These morphologies depend on the composition of the copolymer and include dispersed spheres of the minor component on either a BCC or FCC lattice, dispersed cylinders of the minor component on a hexagonal lattice, or alternating lamellae. Recent microstructural studies of starblock and diblock copolymers have shown that an ordered bicontinuous morphology is observed between the lamellar and cylindrical regimes. This microstructure is currently referred to as the ordered bicontinuous double-diamond (OBDD) morphology and is an example of the Pn3m space group. In poly(styrene-b-isoprene) (SI) diblock copolymers, it exists at approximately 62-66 vol% polystyrene (PS). Efforts aimed at producing this morphology by blending a copolymer with various PS homopolymers have also been successful, when the blend composition is 65-67 vol% PS and the molecular weight of the hompolymer (Mhps) is less than that of the styrene block in the copolymer (Ms). In this work, we have used transmission electron microscopy to elucidate some additional factors responsible for development of the OBDD and other bicontinuous morphologies.

A MENAGERIE OF INTERFACE STRUCTURES IN COPOLYMER SYSTEMS

Diblock copolymer macromolecules may be viewed as giant amphiphiles. Such molecules readily self-assemble into a wide variety of structures which exhibit intermaterial dividing surfaces of approximately constant mean curvature. Order-disorder transitions in bulk materials result in ordered microdomain structures of BCC spheres, hexagonally packed cylinders and stacked lamella. An additional structure, the ordered bicontinuous double-diamond (OBDD) is also shown to occur as a cubic phase between the cylindrical and lamellar morphologies. The interface structure of the OBDD resembles a recently discovered family of constant mean curvature surfaces which include the Schwarz D minimal surface. Another interface structure which approximates Scherk's First Surface is a 90 twist boundary between grains of lamella. Blending of diblock copolymer with homopolymer provides a versatile binary system which displays a critical micelle concentration, spherical and cylindrical micelles, lamellar vesicles as well as ordering transitions depending on composition. The penetration of homopolymer into one side of the near-interface region accounts for the observed variations in interface curvature in blends from that of the pure diblock. Confining geometries, such as external surfaces, thin films and microdroplets can influence interface structures. Chaotic bicontinuous as well as parallel surface structures such as concentric spherical shells are shown to occur in microdroplets of a diblock copolymer which forms lamellar microdomains in the bulk.

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.