Cylinder Phase Research Articles

The Effect of Colloidal Nanoparticles on Phase Separation of Block and Heteroarm Star Copolymers Confined between Polymer Brushes.

The effect of colloidal nanoparticles on the phase changes of the amphiphilic AB linear diblock, A1A2B, and A2B heteroarm star copolymers confined between two polymer brush substrates was investigated by using a real-space self-consistent field theory. By changing the concentrations of nanoparticles and polymer brushes, the phase structure of the amphiphilic AB copolymer transforms from lamellar to core-shell hexagonal phase to cylinder phase. The pattern of A2B heteroarm star copolymer changes from core-shell hexagonal phases to lamellar phases and the layer decreases when increasing the density of the polymer brushes. The results showed that the phase behavior of the system is strongly influenced by the polymer brush architecture and the colloidal nanoparticle numbers. The colloidal nanoparticles and the soft confined surface of polymer brushes make amphiphilic AB copolymers easier to form ordered structures. The dispersion of the nanoparticles was also investigated in detail. The soft surfaces of polymer brushes and the conformation of the block copolymers work together to force the nanoparticles to disperse evenly. It will give helpful guidance for making some new functional materials by nano etching technology, nano photoresist, and nanoprinting.

Cross-domain Chirality Transfer in Self-Assembly of Chiral Block Copolymers.

Chirality transfer is essential to acquire helical hierarchical superstructures from the self-assembly of supramolecular materials. By taking advantage of chirality transfers at different length scales through intra-chain and inter-chain chiral interactions, helical phase (H*) can be formed from the self-assembly of chiral block copolymers (BCPs*). In this study, chiral triblock terpolymers, polystyrene-b-poly(ethylene oxide)-b-poly(L-lactide) (PS-PEO-PLLA), and polystyrene-b-poly(4-vinylpyridine)-b-poly(L-lactide) (PS-P4VP-PLLA) are synthesized for self-assembly. For PS-PEO-PLLA with an achiral PEO mid-block that is compatible with PLLA (chiral end-block), H* can be formed while the block length is below a critical value. By contrast, for the one with achiral P4VP mid-block that is incompatible with PLLA, the formation of H* phase would be suppressed regardless of the length of the mid-block, giving cylinder phase. Those results elucidate a new type of chirality transfer across the phase domain that is referred as cross-domain chirality transfer, providing complementary understanding of the chirality transfer at the interface of phase-separated domains.

Cross‐domain Chirality Transfer in Self‐Assembly of Chiral Block Copolymers

AbstractChirality transfer is essential to acquire helical hierarchical superstructures from the self‐assembly of supramolecular materials. By taking advantage of chirality transfers at different length scales through intra‐chain and inter‐chain chiral interactions, helical phase (H*) can be formed from the self‐assembly of chiral block copolymers (BCPs*). In this study, chiral triblock terpolymers, polystyrene‐b‐poly(ethylene oxide)‐b‐poly(L‐lactide) (PS‐PEO‐PLLA), and polystyrene‐b‐poly(4‐vinylpyridine)‐b‐poly(L‐lactide) (PS‐P4VP‐PLLA) are synthesized for self‐assembly. For PS‐PEO‐PLLA with an achiral PEO mid‐block that is compatible with PLLA (chiral end‐block), H* can be formed while the block length is below a critical value. By contrast, for the one with achiral P4VP mid‐block that is incompatible with PLLA, the formation of H* phase would be suppressed regardless of the length of the mid‐block, giving cylinder phase. Those results elucidate a new type of chirality transfer across the phase domain that is referred as cross‐domain chirality transfer, providing complementary understanding of the chirality transfer at the interface of phase‐separated domains.

Horizontal to perpendicular transition of lamellar and cylinder phases in block copolymer films induced by interface segregation of single-chain nanoparticles during solvent evaporation.

How to fabricate perpendicularly oriented domains (PODs) of lamellar and cylinder phases in block copolymer thin films remains a major challenge. In this work, via a coarse-grained molecular dynamics simulation study, we report a solvent evaporation strategy starting from a mixed solution of A-b-B-type diblock copolymers (DBCs) and single-chain nanoparticles (SCNPs) with the same composition, which is capable of spontaneously generating PODs in drying DBC films induced by the interface segregation of SCNPs. The latter occurs at both the free surface and substrate and, consequently, neutralizes the interface selectivity of distinct blocks in DBCs, leading to spontaneous formation of PODs at both interfaces. The interface segregation of SCNPs is related to the weak solvophilicity of the internal cross-linker units. A mean-field theory calculation demonstrates that the increase in the chemical potential of SCNPs in the bulk region drives their interface segregation along with solvent evaporation. We believe that such a strategy can be useful in regulating the PODs of DBC films in practical applications.

Reexamine the emergence and stability of the square cylinder phase in block copolymers.

Recently, a few AB-type multiblock copolymers have been successfully designed to form stable square cylinder phase based on self-consistent field theory (SCFT) calculations. The previous works only identify the stability region of the square phase but not analyzing its stability, which is closely related to the free-energy landscape. In this work, we have reexamined the stability of the square phase in $\mathrm{B_1 A_1 B_2 A_2 B_3}$ linear pentablock and $\mathrm{(B_1AB_2)_5}$ star triblock copolymers by drawing the free-energy landscape with respect to the two dimensions of a rectangular unit cell. Our results demonstrate that the square phase continuously transfers to the rectangular phase as the degree of packing frustration is gradually released. Moreover, the prolate contour lines of the free-energy landscape indicate the weak stability of the square phase in the $\mathrm{B_1 A_1 B_2 A_2 B_3}$ copolymer. In contrast, the stability of the square phase is notably improved in the $\mathrm{(B_1AB_2)_5}$ copolymer due to its enhanced concentration of bridging configurations. Our work sheds light on the understanding of the stability of the square cylinder phase in block copolymers. Accordingly, we propose some possible strategies for further designing new AB-type block copolymer systems to obtain more stable square phase.

Sequence-Isomerism-Controlled Macromolecular Self-Assembly in Dendritic Rod-Like Molecules.

Although in Nature sequence control is widely adopted to tune the structure and functions of biomacromolecules, it remains challenging and largely unexplored in synthetic macromolecular systems due to the difficulties in a precision synthesis, which impedes the understanding of the structure-property relationship in macromolecular sequence isomerism. Herein, we report the sequence-controlled macromolecular self-assembly enabled by a pair of rationally designed isomeric dendritic rod-like molecules. With an identical chemical formula and molecular topology, the molecular solid angle of the dendron isomers was determined by the sequence of the rod building blocks tethered with side chains of different lengths. As a result, entirely different supramolecular motifs of discs and spheres were generated, which were further packed into a hexagonally packed cylinder phase and a dodecagonal quasicrystalline sphere phase, respectively. Given the efficient synthesis and modular structural variations, it is believed that the sequence-isomerism-controlled self-assembly in dendritic rod-like molecules might provide a unique avenue toward rich nanostructures in synthetic macromolecules.

Tuning conformational asymmetry in particle-forming diblock copolymer alloys.

Self-consistent field theory is employed to compute the phase behavior of binary blends of conformationally asymmetric, micelle-forming diblock copolymers with miscible corona blocks and immiscible core blocks (a diblock copolymer "alloy"). The calculations focus on establishing conditions that promote the formation of Laves phases by tuning the relative softness of the cores of the two different Laves phase particles via independent control of their conformational asymmetries. Increasing the conformational asymmetry of the more spherical particles of the Laves structure has a stabilizing effect, consistent with the expectations of increased imprinting of the Wigner-Seitz cells on the core/corona interface as conformational asymmetry increases. The resulting phase diagram in the temperature-blend composition space features a more stable Laves phase field than that predicted for conformationally symmetric systems. The phase field closes at low temperatures in favor of macrophase separation between a hexagonally-packed cylinder (hex) phase and a body-centered cubic phase. Companion calculations, using an alloy whose components do not produce a hex phase in the neat melt state, suggest that the Laves phase field in such a blend will persist at strong segregation.

Curving and Twisting in Self-Assembly of Triblock Terpolymers Driven by a Chiral End Block

A series of triblock terpolymers composed of a chiral end block, poly(l-lactide) (PLLA) (designated as chiral triblock terpolymers), are designed and synthesized for self-assembly. The chiral PLLA block can contribute the chirality effect for the twisting of microphase-separated domains. By attaching an asymmetric amount of the chiral block to a symmetric diblock of polyisoprene-b-polystyrene (PI-PS), compositional asymmetry can be created for the curving of microphase-separated domains. Moreover, the difference in persistence lengths of PS and PLLA blocks can give conformational asymmetry to the curving. With the combined effects of twisting and curving, the curvature at the saddle surface of microphase-separated domains might become significant to give the formation of a network phase. Consequently, a transformation from two-domain lamellae to core–shell network phases, then to a core–shell cylinder phase, and finally to a three-domain lamellar phase with undulation due to the rod–rod interaction with the chirality effect from the semiflexible PLLA, can be found in the isopleths of the triblocks. Interestingly, a core–shell double diamond phase could be found near the center of the ternary phase diagram; we speculate that the alleviation of packing frustration in the core of the self-assembled microdomain is attributed to the character of semiflexible PLLA. Accordingly, the phase window of network formation can be enlarged by the combined effects of compositional asymmetry, conformational asymmetry, and chirality.

Various Low-Symmetry Phases in High-χ and Conformationally Asymmetric PDMS-b-PTFEA Copolymers

Since the discovery of the Frank–Kasper (FK) phase a decade ago, single-component block copolymer systems have offered unique opportunities to explore the structural and phase-transition properties of topologically close-packed FK phases composed of point-particle motifs. Here, we present the formation of complex low-symmetry phases and their thermodynamic stability using high-χ and high-ε linear diblock copolymers, where χ and ε are the Flory–Huggins interaction parameter and conformational asymmetry between the two blocks, respectively. A series of polydimethylsiloxane-b-poly(2,2,2-trifluoroethyl acrylate) (PDMS-b-PTFEA) copolymers are prepared by tuning the volume fraction (fPTFEA) of a minor PTFEA block. The packing structures of PDMS-b-PTFEAs are mapped in the space of temperature versus fPTFEA using X-ray scattering measurements. In addition to the packing structures reported earlier, we identify another A15 phase at higher fPTFEA close to a hexagonally packed cylinder (HEX) phase and establish the phase sequence of HEX–A15−σ–C14–BCC with decreasing fPTFEA. Theoretical calculation of relative free-energy densities confirms the experimental phase sequence of the composition-dependent sphere-packing structures. Interestingly, the domain sizes of three-dimensional (3D) sphere-packing structures are nearly temperature-invariant compared to that of a two-dimensional HEX structure, and we attribute this dimensional stability to the strong enthalpic effects in the formation of 3D packing structures and the geometrical characteristics of spherical domains. Our results demonstrate that the interaction parameter χ, together with the known role of conformational asymmetry ε, serves as the primary thermodynamic parameter for selecting and stabilizing various low-symmetry packing structures in sphere-forming linear diblock copolymer systems.

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.

The Phase Aggregation Behavior of the Blend Materials Block Copolymer Polystyrene‐b‐Polycarbonate (PS‐b‐PC) and Homopolymer Polystyrene (PS)

AbstractIn this paper, the cylindrical structures phase aggregation behavior of the blend materials is explored experimentally. The phase aggregation behavior is a phenomenon in which the cylinder phase aggregates nearby, which occurs after phase separation. With mixing the polystyrene‐b‐polycarbonate with polystyrene, a cylindrical state is first obtained, and then such state is changed to a larger cylinder state. It is found that such state aggregation behavior is the function of annealing time and temperature, while the maximum temperature is less than the molten temperature. First, a cylindrical state with 11–14 nm diameter is obtained, with a 3 nm standard deviation. Then the neighboring cylinders move to aggregate together and the cylinder diameter is enlarged quickly to ≈30 nm and above, with a higher standard deviation. It is also found that the aggregation behavior is consistent over a wide temperature range from 150 to 200 °C. For the blend material used, when cylinder is formed, the free energy of the system is not stable. Then, keeping the annealing temperature constant and the annealing time increasing, the neighboring cylinders aggregate and form large‐diameter cylinders. This dynamic behavior opens a new window of self‐assembly applications by obtaining different structures through process control.

Orientation of Microphase in Polystyrene-b-polyisoprene Thin Film under Solvent Vapor Annealing

We investigated the microphase in thin films of polystyrene-b-polyisoprene showing cylinder morphology to elucidate the orientation mechanism of the cylinder phase during solvent vapor annealing (S...

Light control elements as convex cylindrical lens and concave cylindrical mirror based on 2D high-index contrast gratings

Convex cylindrical lens and concave cylindrical mirror using 2D non-periodic high-index contrast gratings (HCGs) by introducing a parabolic cylinder phase front are proposed and numerically investigated, simulation results indicate that the transmitted or reflected light beam of the structures can be modulated by the grating blocks and will converge into a line of light or a linear spot on the image plane while maintaining high transmissivity or reflectivity with low polarization dependence. An HCG convex cylindrical lens sample with a focal length of 250 μm and a grating area of 400 μm × 400 μm are fabricated on an SOI wafer, which exhibits a liner focusing ability on the image side under normal incidence at the wavelength of 1.55 μm.

Microphase Separation of Ionic Liquid-Containing Diblock Copolymers: Effects of Dielectric Inhomogeneity and Asymmetry in the Molecular Volumes and Interactions between the Cation and Anion

We study the phase behavior of a block copolymer and ionic liquid mixture using the Landau theory of Leibler and field-theoretic techniques in polymer physics. Our weak-segregation theory of microphase separation accounts for electrostatic screening, the excluded volume effect, and the dielectric contrast between the species. The results of the phase diagrams for ionic liquid-containing poly(styrene-block-2-vinylpyridine) and poly(ethylene oxide-block-styrene) qualitatively agree with the observed transitions between the ordered microstructures corresponding to lamellae, hexagonally packed cylinders, and body-centered cubic lattices. We show that moderate changes in the model parameters for molecular volumes and nonbonded interactions can qualitatively alter the trend of the phase boundaries. Specifically, our theory highlights the following features: (a) The effect of the dielectric contrast between the constituent blocks may cause a driving force for microphase separation, whereas the effect of electrostatic screening is likely minimal. (b) Reentrance into a lamellar phase, hexagonally packed cylinder phase, or disordered phase may occur when the volume fraction of an ionic liquid is increased. (c) Asymmetry in the molecular volumes and interactions between the cation and anion in an ionic liquid may cause substantial changes in the phase boundaries. The present results also suggest that despite its simplicity, the Born solvation energy of the ions can be used to consider the dissolution of an ionic liquid in block copolymers when the dielectric contrast is large.

Positional Order in the Columnar Phase of Lyotropic Chromonic Liquid Crystals Mediated by Ionic Additives.

Positional order in the lyotropic chromonic liquid crystals (LCLCs) is investigated in the supramolecular assembly of benzene 1,3,5-tricarboxamide (BTA) derivatives with the glucono-delta-lactone (GdL) acid additive by high-resolution synchrotron radiation small-angle X-ray scattering. The formation of positionally ordered hexagonal phase is found to profoundly depend on the concentrations of BTA derivatives, cBTA, and GdL additives, caddtive, giving rise to unusual behavior distinctive from conventional lyotropic liquid crystals (LCs) with covalent bonds and fixed length. The hexagonal phase is observed to coexist with another phase in certain range of caddtive/cBTA. Intriguingly, the lattice spacing R of the hexagonal phase remains almost constant by varying caddtive but changes with cBTA. The above observations are attributed to unique sensitivities of the LCLC properties, such as the contour length and flexibility of individual cylinder assemblies and phase coexistence, to additives in the solutions. Our study reveals the complexity in positional ordering in the LCLCs which not only relates to the underlying principles of hierarchical reversible self-assembly but also attracts fundamental interests in LCs.

Surface-induced phase transitions in thin films of dendrimer block copolymers

Abstract The phase morphologies and phase transitions of dendrimer block copolymer thin films confined between two homogeneous, planar hard substrates had been investigated by a three-dimensional real space self-consistent field theory (SCFT). From the perspectives of property and strength of the preferential substrate, when the film system confined within neutral substrates, the thinner film was easier to take the undulated and perpendicular cylinder phases. For the attractive preference of the substrate on block segment A, the polymer films tended to take the surface-wetting structures that was composed by block segment A. On the contrary, for the repulsive preference of the substrate on block segment A, a phase transition of cylinder-lamellae could be observed increasing with the relative surface strength of the preferential substrate.

Aqueous Lyotropic Mesophase Behavior of Gemini Dicarboxylate Surfactants Swollen with n-Decane.

We report detailed small-angle X-ray scattering (SAXS) studies of the impact of variable n-decane loadings on the lyotropic liquid crystalline (LLC) phase behaviors of homologous bis(tetramethylammonium) gemini didecanoate surfactants TMA-7x, which derive from dimerizing decanoic acid through its α-carbon with hydrocarbyl linkers -(CH2)x- where x = 3, 4, 5, and 6. TMA-7x amphiphiles with x = 3 or 5 exhibit a strong propensity to form normal double gyroid (G) LLC network mesophases over wide surfactant hydration ranges, as compared to homologues with x = 4 or 6. On swelling aqueous TMA-7x LLC mesophases with up to 35 wt % n-decane, we demonstrate that odd-carbon linked surfactants (x = 3 or 5) form G and normal double diamond (D) phases over wide water concentration windows with T = 22-100 °C. Complementary studies of decane-swollen TMA-7x (x = 4 or 6) aqueous LLCs instead demonstrate significantly diminished network phase stability, in favor of hexagonally-packed cylinder phases and a zoo of complex quasispherical micelle packings, which include micellar C14 and C15 Laves phases (P63/mmc and Fd3(-)m symmetries, respectively) and high-symmetry hexagonally close packed (HCP) and body-centered cubic (BCC) arrangements. These rich phase behaviors are rationalized in terms of linker length parity-dependent surfactant conformations and the delicate free energy balance that guides the packing of these geometrically anisotropic amphiphiles by minimizing unfavorable water-hydrophobic contacts, maximizing ionic surfactant-headgroup counterion solvation with minimal local variations, and maximizing electrostatic cohesion within these supramolecular assemblies.

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.