Hexagonal Cylinder Phase Research Articles

Small-Angle X-Ray Scattering Studies of Block Copolymer Nano-Objects: Formation of Ordered Phases in Concentrated Solution During Polymerization-Induced Self-Assembly.

We report that polymerization‐induced self‐assembly (PISA) can be used to prepare lyotropic phases comprising diblock copolymer nano‐objects in non‐polar media. RAFT dispersion polymerization of benzyl methacrylate (BzMA) at 90 °C using a trithiocarbonate‐capped hydrogenated polybutadiene (PhBD) steric stabilizer block in n‐dodecane produces either spheres or worms that exhibit long‐range order at 40 % w/w solids. NMR studies enable calculation of instantaneous copolymer compositions for each phase during the BzMA polymerization. As the PBzMA chains grow longer when targeting PhBD80–PBzMA40, time‐resolved small‐angle X‐ray scattering reveals intermediate body‐centered cubic (BCC) and hexagonally close‐packed (HCP) sphere phases prior to formation of a final hexagonal cylinder phase (HEX). The HEX phase is lost on serial dilution and the aligned cylinders eventually form disordered flexible worms. The HEX phase undergoes an order–disorder transition on heating to 150 °C and a pure HCP phase forms on cooling to 20 °C.

Small‐Angle X‐Ray Scattering Studies of Block Copolymer Nano‐Objects: Formation of Ordered Phases in Concentrated Solution During Polymerization‐Induced Self‐Assembly

AbstractWe report that polymerization‐induced self‐assembly (PISA) can be used to prepare lyotropic phases comprising diblock copolymer nano‐objects in non‐polar media. RAFT dispersion polymerization of benzyl methacrylate (BzMA) at 90 °C using a trithiocarbonate‐capped hydrogenated polybutadiene (PhBD) steric stabilizer block in n‐dodecane produces either spheres or worms that exhibit long‐range order at 40 % w/w solids. NMR studies enable calculation of instantaneous copolymer compositions for each phase during the BzMA polymerization. As the PBzMA chains grow longer when targeting PhBD80–PBzMA40, time‐resolved small‐angle X‐ray scattering reveals intermediate body‐centered cubic (BCC) and hexagonally close‐packed (HCP) sphere phases prior to formation of a final hexagonal cylinder phase (HEX). The HEX phase is lost on serial dilution and the aligned cylinders eventually form disordered flexible worms. The HEX phase undergoes an order–disorder transition on heating to 150 °C and a pure HCP phase forms on cooling to 20 °C.

Enhanced sampling of cylindrical microphase separation via a shell-averaged bond-orientational order parameter.

The formation of a hexagonal phase from disordered phase is one of the typical order-disorder transitions (ODTs) observed in asymmetric diblock copolymer systems. In order to drive this transition in a particle-based simulation, we introduce a shell-based bond-orientational order parameter that selectively responds to the mesoscopic order of the hexagonal cylinder phase. From metadynamics simulations in a bond-free particle model system, the characteristic pathway involved with the underlying free energy surface is deduced for the disordered-to-hexagonal transition. It is shown consecutively that the transition pathway and the metastable state are reproduced in dissipative particle dynamics simulations for the corresponding transition in a bulk asymmetric block copolymer melt system. These agreements suggest that efficient strategies for enhanced sampling with particle-based simulations of block copolymer systems can be devised using coarse-grained pictures of the mesoscopic order.

Transition Kinetics of Self-Assembled Supramolecular Dodecagonal Quasicrystal and Frank-Kasper σ Phases in ABn Dendron-Like Giant Molecules.

A series of noncrystalline ABn dendron-like giant molecules DPOSS-MPOSSn (n = 2-6, DPOSS: hydrophilic polyhedral oligomeric silsesquioxane (POSS) cage; MPOSS: hydrophobic POSS cage) were synthesized. These samples present a thermodynamically stable phase formation sequence from the hexagonal cylinder phase (plane group of P6mm), to the Frank-Kasper (F-K) A15 phase (space group of Pm3̅n), and further to the F-K σ phase (space group of P42/mnm), with increasing the number of MPOSS in a single molecule (n, from 2 to 6). Moreover, for DPOSS-MPOSS5 and DPOSS-MPOSS6, an intriguing dodecagonal quasicrystal (DQC) structure has been identified and revealed as a kinetic favorable metastable phase at lower temperatures, while the thermodynamically stable phase is the σ phase. The detailed investigation of the transition kinetics between the DQC and σ phase in these samples makes it possible to identify how the self-assembly directs the phase transition in terms of molecular and supramolecular aspects.

Effect of Geometrical Asymmetry on the Phase Behavior of Rod-Coil Diblock Copolymers.

The effect of geometrical asymmetry β (described by the length-diameter ratio of rods) on the rod-coil diblock copolymer phase behavior is studied by implementation of self-consistent field theory (SCFT) in three-dimensional (3D) position space while considering the rod orientation on the spherical surface. The phase diagrams at different geometrical asymmetry show that the aspect ratio of rods β influences not only the order-disorder transition (ODT) but also the order-order transition (OOT). By exploring the phase diagram with interactions between rods and coils plotted against β, the β effect on the phase diagram is similar to the copolymer composition f. This suggests that non-lamellae structures can be obtained by tuning β, besides f. When the rods are slim compared with the isotropic shape of the coil segment (β is relatively large), the phase behavior is quite different from that of coil-coil diblock copolymers. In this case, only hexagonal cylinders with the coil at the convex side of the interface and lamella phases are stable even in the absence of orientational interaction between rods. The phase diagram is no longer symmetrical about the symmetric copolymer composition and cylinder phases occupy the large area of the phase diagram. The ODT is much lower than that of the coil-coil diblock copolymer system and the triple point at which disordered, cylinder and lamella phases coexist in equilibrium is located at rod composition fR = 0.66. In contrast, when the rods are short and stumpy (β is smaller), the stretching entropy cost of coils can be alleviated and the phase behavior is similar to coil-coil diblocks. Therefore, the hexagonal cylinder phase formed by coils is also found beside the former two structures. Moreover, the ODT may even become a little higher than that of the coil-coil diblock copolymers due to the large interfacial area per chain provided by the stumpy rods, thus compensating the stretching entropy loss of the coils.

Reinvestigation of the Block Copolymer Modulated Lamellar Structure

We report extended crystallographic studies on shear-aligned block copolymer systems within the metastable modulated lamellae (ML) state. With studies limited to the “classical” orientations parallel and perpendicular to shear plane, the apparent modulated state would likely have been assigned simple lamellar. Surprisingly, upon rotating the sample to intermediate angles additional scattering reflections appear, which reveal the apparent ML phase much beyond what was expected. The modulated structure is a slightly distorted fcc structure. With the sample sheared at relatively low temperature, presumably below the stable gyroid phase, we find a very well resolved ML texture corresponding to a simple twin structure of the distorted fcc structure. When shear-aligned within the hexagonal cylinder phase, and quenced to the gyroid phase or slightly below, we find ML alignment into a two-dimensional powder texture.

Siloxanes and carbosilanes as new building blocks for T-shaped bolaamphiphilic LC molecules

T-shaped bolaamphiphiles composed of a 4,4′-disubstituted biphenyl core and terminal diol groups with laterally attached oligo(siloxane) and carbosilane units were synthesized and investigated with respect to their self-assembly into liquid crystalline superstructures (thermotropic mesophases). Two different types of bolaamphiphiles were investigated: one has two identical glycerol groups at both ends of the biphenyl core, which are connected by ether linkages and in the other type one of the ether linkages is replaced by an amide group. The position of the lateral groups on the biphenyl core was also varied. In addition to these silylated compounds two different types of n-alkyl substituted compounds were investigated and compared with the silylated bolaamphiphiles. A hexagonal cylinder phase and three distinct types of lamellar phases were observed and a phase sequence Colhex–LamSm–LamN–LamIso was found by increasing the size of the lateral substituent. The silyl units organize into distinct compartments either within columns or between layers. The increased flexibility of the silyl units compared to linear alkyl chains and perfluorinated chains leads to materials with phase transitions in convenient temperature ranges. For one of the carbosilanes an unusually broad region of the LamN phase was achieved. It turned out that an additional amide group leads to a significant mesophase destabilization which is attributed to a competition between intramolecular and intermolecular hydrogen bonding. The position of the lateral chain is also important, as it influences hydrogen bonding as well as the conformation of the biphenyl unit.

Influence of Electric Field on the Phase Transitions of the Hexagonal Cylinder Phase of Diblock Copolymers

We have used the cell dynamic simulations (CDS) method to study the evolution of asymmetric and symmetric diblock copolymers under electric fields. For symmetric diblock copolymers, long-range-ordered lamellar phases form readily under electric fields. For asymmetric diblock copolymers, sphere-to-cylinder phase transitions occur rapidly when strong electric fields are applied, but it takes longer for the system to form hexagonal cylinder structures. The results of these simulations suggest that the sphere phase is stable under weak electric fields, but a threshold electric intensity exists for the sphere-to-cylinder phase transition. In addition, we also studied the kinetic pathways of the transition of the lamellar phase to the hexagonal cylinder phase of the asymmetric diblock copolymers under electric fields. Hexagonal cylinder structures form when the lamellar phase is subjected to a sudden temperature jump. The scattering functions suggest that the hexagonal cylinder structures are very regular and possess very few flaws.

Comparison of poly(ethylene oxide) crystal orientations and crystallization behaviors in nano-confined cylinders constructed by a poly(ethylene oxide)-b-polystyrene diblock copolymer and a blend of poly(ethylene oxide)-b-polystyrene and polystyrene

A poly(ethylene oxide)-b-polystyrene (PEO-b-PS) diblock copolymer with a number average molecular weight of PEO blocks, MnPEO=8.8kg/mol, and a number average molecular weight of PS blocks, MnPS=24.5kg/mol, (volume fraction of the PEO blocks, fPEO, was 0.26) exhibited a hexagonal cylinder (HC) phase structure. Small angle X-ray scattering results showed that the PEO cylinder diameter was 13.3nm, and the hexagonal lattice was a=25.1nm. The cylinder diameter of this HC phase structure was virtually the same as that in the blend system constructed by a PEO-b-PS diblock copolymer (MnPEO=8.7kg/mol and MnPS=9.2kg/mol) and a PS homo-polymer (MnPS=4.6kg/mol) in which the fPEO was 0.32. The cylinder diameter in this blend sample was 13.7nm and the hexagonal lattice was a=23.1nm. Comparing crystal orientation and crystallization behaviors of this PEO-b-PS copolymer with the blend, it was found that the crystal orientation change with respect to crystallization temperature was almost identical. This is attributed to the fact that in both cases the PEO block tethering densities and confinement sizes are very similar. This indicates that when the MnPS of PS homo-polymer is lower than the PS blocks, the PS homo-polymer is located inside of the PS matrix rather than at the interface between the PEO and PS in the HC phase structure. On the other hand, a substantial difference of crystallization behaviors was observed between these two samples. The PEO-b-PS copolymer exhibited much more retarded crystallization kinetics than that of the blend. Based on the small angle X-ray scattering results, it was found that in the blend sample, the HC phase structure was not as regularly ordered as that in the PEO-b-PS copolymer, and thus, the HC phase structure contained more defects in the blend. This led to a suggestion that the primary nucleation process in the confined crystallization is a defect-controlled process. The mean crystallite sizes were estimated by the Scherer equation, and the PEO crystal sizes are on the scale of the confined size.

Orientational phase transitions in the hexagonal cylinder phase and kinetic pathways of lamellar phase to hexagonal phase transition of asymmetric diblock copolymers under steady shear flow

For asymmetric diblock copolymers under steady shear flow, the orientational phase transitions in the hexagonal cylinder phase and the kinetics of lamellar to hexagonal phase transition were studied based on the time-dependent Ginzburg–Landau approach. As to orientational phase transitions in the hexagonal cylinder phase, the simulation results show that the parallel orientation is stable at low shear rate and the perpendicular orientation is stable at high shear rate. In addition, different kinetic pathways of lamellar phase to hexagonal phase transition are observed after a sudden temperature jump from one phase to other. When the temperature jump is deep into the hexagonal phase from the shear-orientated lamellar phase under steady shear flow, the lamellae are transformed into hexagonally ordered cylinders directly via the short so-called modulated instability of the lamellar layers. However, if the temperature jump is only slight into the hexagonal phase with or without steady shear flow, lamellae are transformed into hexagonally ordered cylinders going through a distinct modulated and perforated lamellar phase stage. Moreover, without steady shear flow the perforated lamellar phase stage can survive for longer time, indicating that the steady shear flow cannot lead to stabilization of perforated lamellar phase. The simulation results also indicate that the perforated lamellar phase has abab…stacking.

The phase diagram of molten randomly grafted copolymers

We study the microphase segregation of molten randomly grafted copolymers (RGCs) using a Landau field theory. Under one wave number approximation, we find three equilibrium ordered microphases: lamellar phase (LAM), hexagonal cylinder phase (HEX), and bcc sphere phase (BCC). The stability of these phases strongly depends on the architectural parameters describing the RGC chains (e.g., the backbone length, the branch length, and the number of branches). Our calculation reveals that RGCs with high average composition of backbone monomers or with low branching density tend to form LAM microstructures. For a small average composition of backbone monomers, HEX and BCC microphases appear in turn with increasing branching density. Independent of the architectural parameters and composition, the disorder to order transition for molten RGCs is always from the disordered phase to the LAM microphase. The physical reasons underlying this behavior and experimentally testable predictions are discussed.

Kinetics of phase transitions in weakly segregated block copolymers: Pseudostable and transient states

We study the kinetics of order-disorder and order-order transitions in weakly segregated diblock copolymers using a time-dependent Ginzburg-Landau (TDGL) approach. In particular, we investigate the microstructural change as well as the order-parameter evolution after a sudden temperature jump from one phase to another. Direct numerical simulation of the TDGL equations shows that depending on the extent of the temperature jump, these transitions often occur in several stages and can involve nontrivial intermediate states. For example, we find that transition from the lamellar phase to the hexagonal cylinder phase goes through a perforated lamellar state within a certain temperature range. The numerical results are elucidated by a multimode analysis under the single-wave-number approximation. The analysis reveals that the geometric characteristics of the free energy surface, particularly saddle points and ridgelike features, are responsible for the nontrivial intermediate states on the kinetic pathways. On the basis of this analysis, a generalized kinetic ``phase diagram'' is constructed, which is able to account for all the different scenarios observed in the numerical simulation. Our results are discussed in connection with available experimental observations. In particular, we suggest the possibility that the perforated-modulated lamellar structures obtained by Bates and co-workers [I. W. Hamley, K. A. Koppi, J. H. Rosedale, F. S. Bates, K. Almdal, and K. Mortensen, Macromolecules 26, 5959 (1993); S. Forster, A. K. Khandpur, J. Zhao, F. S. Bates, I. W. Hamley, A. J. Ryan, and W. Bras, Macromolecules 27, 6922 (1994)] may be kinetic, intermediate states rather than new equilibrium phases.

Epitaxial relationship for hexagonal-to-cubic phase transition in a block copolymer mixture.

Small-angle neutron scattering experiments have revealed an epitaxial relationship between the hexagonal cylinder phase, and a bicontinuous cubic phase with $\mathrm{Ia}\overline{3}d$ space group symmetry, in a poly(styrene)-poly(2-vinylpyridine) diblock copolymer mixture. Proximity to the order-disorder transition and an inelastic low frequency rheological response suggest that the cubic phase is stabilized by fluctuations. These results identify block copolymers as model compounds for investigating the thermodynamics and dynamics of complex "soft" condensed matter.