Cylinder Phase Research Articles

Polygonal Cylinder Phases of 3-Alkyl-2,5-diphenylthiophene-Based Bolaamphiphiles: Changing Symmetry by Retaining Net Topology

Novel bolaamphilic triblock molecules consisting of a bent 2,5-diphenylthiophene unit, two terminal glycerol units, and a lateral n-alkyl chain have been synthesized via Ni- and Pd-catalyzed coupling reactions as key steps. The thermotropic liquid crystalline behavior of these compounds was investigated by polarized light optical microscopy, DSC, and X-ray scattering and the influence of the length of the lateral alkyl chains on the mesomorphic properties was studied. With elongation of the lateral alkyl chains, three different columnar phases (Colsqu/p4mm, Colsqu/p4gm and Colhex/p6mm), representing polygonal cylinder structures were found, where the cells have a square, pentagonal, and hexagonal cross-section, respectively. In the observed phase sequence, the change of the net topology is the same as seen for related linear biphenyl derived bolaamphiphiles, but the symmetry is increased, i.e, rectangular phases are replaced by square lattices.

Specific Features of Defect Structure and Dynamics in the Cylinder Phase of Block Copolymers

We present a systematic study of defects in thin films of cylinder-forming block copolymers upon long-term thermal or solvent annealing. In particular, we consider in detail the peculiarities of both classical and specific topological defects, and conclude that there is a strong "defect structure-chain mobility" relationship in block copolymers. In the systems studied, representative defect configurations provide connectivity of the minority phase in the form of dislocations with a closed cylinder end or classical disclinations with incorporated alternative, nonbulk structures with planar symmetry. In solvent-annealed films with enhanced chain mobility, the neck defects (bridges between parallel cylinders) were observed. This type of nonsingular defect has not been identified in block copolymer systems before. We argue that topological arguments and 2D defect representation, sufficient for lamellar systems, are not sufficient to determine the stability and mobility of defects in the cylindrical phase. In-situ scanning force microscopy measurements are compared with the simulations based on the dynamic self-consistent mean field theory. The close match between experimental measurements and simulation results suggests that the lateral defect motion is diffusion-driven. In addition, 3D simulations demonstrated that the bottom (wetting) layer is only weakly involved into the structure ordering at the free surface. Finally, the morphological evolution is considered with the focus on the motion and interaction of the representative defect configurations.

Phase Behavior of Symmetric Sulfonated Block Copolymers

Phase behavior of poly(styrenesulfonate-methylbutylene) (PSS-PMB) block copolymers was studied by varying molecular weight, sulfonation level, and temperature. Molecular weights of the copolymers range from 2.9 to 117 kg/mol. Ordered lamellar, gyroid, hexagonally perforated lamellae, and hexagonally packed cylinder phases were observed in spite of the fact that the copolymers are nearly symmetric with PSS volume fractions between 0.45 and 0.50. The wide variety of morphologies seen in our copolymers is inconsistent with current theories on block copolymer phase behavior such as self-consistent field theory. Low molecular weight PSS-PMB copolymers (<6.2 kg/mol) show order−order and order–disorder phase transitions as a function of temperature. In contrast, the phase behavior of high molecular weight PSS-PMB copolymers (>7.7 kg/mol) is independent of temperature. Due to the large value of Flory–Huggins interaction parameter, χ, between the sulfonated and non-sulfonated blocks, PSS-PMB copolymers with PSS and PMB molecular weights of 1.8 and 1.4 kg/mol, respectively, show the presence of an ordered gyroid phase with a 2.5 nm diameter PSS network. A variety of methods are used to estimate χ between PSS and PMB chains as a function of sulfonation level. Some aspects of the observed phase behavior of PSS-PMB copolymers can be rationalized using χ.

Phase diagram of diblock copolymer confined in a cylindrical nanopore with polymer-grafted surface

Using self-consistent field calculation, the new equilibrium morphology of a diblock copolymer melt confined in a brush_covered cylindrical nanopore can be found. The morphology is formed as a function of brush density and A-monomer fraction f. When f=0.7, due to the wetting effect produced by polymer brush the outside concentric lamellar ring will come up again with increasing φAB. We carefully examined the intermediate phases and discovered a rich variety of new two_dimensional structures that have no analogue in the unconfined system, which include nonhexagonally coordinated cylinder phases and structures intermediate between lamellae and cylinders, like CRCR, when f=0.35. Then we map the stability regions and phase boundaries for all the structures we found.

Kinetics of Phase Transition from Lamellar to Hexagonally Packed Cylinders for a Triblock Copolymer in a Selective Solvent

We examined the kinetics of the transformation from the lamellar (LAM) to the hexagonally packed cylinder (HEX) phase for the triblock copolymer, polystyrene-b-poly (ethylene-co-butylene)-b-polystyrene (SEBS) in dibutyl phthalate (DBP), a selective solvent for polystyrene (PS), using time-resolved small-angle X-ray scattering (SAXS). We observe the HEX phase with the EB block in the cores at a lower temperature than that observed for the LAM phase due to the solvent selectivity of DBP for the PS block. Analysis of the SAXS data for a deep temperature quench well below the LAM−HEX transition shows that the transformation occurs in a one-step process. We calculate the scattering using a geometric model of rippled layers with adjacent layers totally out of phase during the transformation. The agreement of the calculations with the data further supports the continuous transformation mechanism from the LAM to HEX for a deep quench. In contrast, for a shallow quench close to the order−order transition, we find agreement with a two-step nucleation and growth mechanism.

The Triangular Cylinder Phase: A New Mode of Self-Assembly in Liquid-Crystalline Soft Matter

The Triangular Cylinder Phase: A New Mode of Self-Assembly in Liquid-Crystalline Soft Matter

Anomalous Small-Angle X-ray Scattering Characterization of Bulk Block Copolymer/Nanoparticle Composites

We demonstrate the versatility of anomalous small-angle X-ray scattering (ASAXS) to investigate the morphology of bulk multicomponent composites comprising poly(stryrene-b-2-vinylpyridine) (PS−PVP) and Au nanoparticles. Contrast variation near the L3 absorption edge of Au enables the separation of the partial scattering functions of the polymer and nanoparticle phases. Theoretical and experimental methodologies developed for our ASAXS analysis of the composites will be useful for the investigation of other such multicomponent systems with heavy elements. This study shows that at 8.8% Au loading the Au nanoparticles remain well dispersed in the lamellar polymer matrix, while at 27.0% Au loading the polymer morphology transforms to a hexagonal packed cylinder phase due to the change in the curvature caused by the higher concentration of the dispersed nanoparticles in the PS domain. In the case of 27.0% Au nanocomposite we also observe strong concentration fluctuations of nanoparticles in the polymer phase, ...

Lattice Model Simulation of Penetrant Diffusion along Hexagonally Packed Rods in a Barrier Matrix As Determined by Pulse-Field-Gradient Nuclear Magnetic Resonance

The structural influence on translational diffusion of 2,2,4-trimethylpentane (TMP) through SEBS triblock polymer (poly(styrene)-block -poly(ethene-co-but-1 -ene)-block -poly(styrene)) was studied using pulse field gradient (PFG) NMR coupled with lattice model simulation. Two types of PFG experiments were performed: one observing the time-dependent apparent diffusion constant and another observing the diffusion-induced NMR signal attenuation. TMP is selectively sorbed into the rubbery ethylene/butylenes (EB) phase while the glassy poly(styrene) (PS) phase acts as a barrier to TMP diffusion. The observed apparent diffusion constant drops drastically at the grain boundary, in which the orientation of the minor EB cylinder phase changes from grain to grain. In the lattice model simulation, in order to match the large drop of diffusion constant, the diameter of the EB cylinder at the interface had to be reduced by a factor of about 0.7. This extra restriction in the size of the conductive phase indicates the important role of the grain boundary on diffusion in membrane applications of block copolymers. The simulation also shows that the grain boundary influence on diffusion becomes significant when the solubility and diffusivity of the penetrant are greatly different between the rubber and glass phases. In addition, we extended the lattice model to simulate the diffusion-induced PFG NMR signal attenuation. From the simulation and theoretical fitting, it is obvious that the EB phase at grain boundary is not connected well, which is in agreement with our observation of a drastic apparent diffusion constant drop at the grain boundaries in the PFG experiment.

Poly(ethylene oxide) Crystal Orientation Changes in an Inverse Hexagonal Cylindrical Phase Morphology Constructed by a Poly(ethylene oxide)-block-polystyrene Diblock Copolymer

A poly(ethylene oxide)-block-polystyrene (PEO-b-PS) diblock copolymer with number-average molecular weights of 7.7k g/mol for the PS block and 21.4k g/mol for the PEO block was used to study the PEO crystal orientation changes at different crystallization temperatures (Tx) via small- and wide-angle X-ray scattering techniques. For this diblock copolymer, an inverse hexagonal cylinder (IHC) phase morphology was identified with PS cylinders hexagonally packed within the PEO matrix. In this IHC morphology, the PEO blocks were tethered on the convex interfaces of the PS domains, and the crystallization of PEO blocks was outside of the cylinders. The crystal orientation of the PEO blocks (the c-axis of the PEO crystals) after crystallization among the PS cylinders was, for the first time, found to change with respect to the long cylinder axis, â, depending solely on Tx. At very low Tx's, when the samples were quenched into liquid nitrogen, the crystals possessed a random orientation. When −30 °C ≤ Tx ≤ 5 °C, P...

(Polystyrene- g-polyisoprene)- b-polystyrene comb-coil block copolymer in selective solvent

Comb-coil block copolymers consisting of two components polystyrene (PS) and polyisoprene (PI) were synthesized through combining TEMPO living free radical polymerization (LFRP) and anionic polymerization using “grafting-onto” strategy. Two typical samples with the same backbone but grafted with different numbers and lengths of branches, forming lamellar and cylinder phases, respectively, were investigated. As the selective solvent was added into these block polymers, the micro-structures transformed from disordered or weakly ordered structure into well-organized lamellar structure in the intermediate polymer concentration. The power law behavior of the lamellae space with respect to polymer concentration indicates that the two samples form the well-organized structure through different paths. The sample with longer branch length thus less branch points forms lamellae phase with smaller lamellae space. This difference at lamellae spacing is attributed to the two different ways that the chain assembles.

Domain nucleation dictates overall nanostructure in composites of block copolymers and model nanorods

The detailed nanostructure of composites formed from block copolymers and nanoparticles is known to depend sensitively on the preferred morphology of the block copolymer, on the shapes of the particles, and on interactions between the two components. But it can also depend on the kinetics of self-assembly in the polymer, and there are circumstances under which the kinetics of morphologically selective domain nucleation and growth determine the overall nanostructure of the composite. To study the mechanism of morphological seeding in block-copolymer nanocomposites, we have combined cylinder phases of polystyrene- block-polyisoprene diblock (as a solution in dibutylphthalate) and poly(styrene- block-isoprene- block-styrene) triblock (as a blend with homopolystyrene) copolymers with gold nanorods of different diameters and surface treatments. Polarized optical microscopy and transmission electron microscopy on these composites demonstrate that the nanorods selectively nucleate coaxial domains of copolymer cylinders (i.e., domains of cylinders aligned along the same axis as the nanorod). These single nucleation events occur regardless of nanorod diameter and surface character, and determine the order of most of the surrounding polymer. Mesoscale modeling of the nucleation process, performed with nanorods of different diameters and with different polymer–surface interactions, illustrates the mechanism by which copolymer-dispersed nanorods with different sizes and surface chemistry can template the organization of cylindrical copolymer domains.

Development of Strategies to Improvement Ordering and Perpendicular Alignment of Cylinder Phase Block Copolymers Used as Templates for Bit Patterned Media

AbstractBit patterned media, including media fabricated with a gradient in composition, is being developed as a potential path to higher information storage density. The noise level in such media is significantly impacted by the precision of the ordering of the individual bits and by the narrowness of their size distribution. Block copolymers that phase separate on the appropriate length scale are one method of pattern generation that is receiving considerable attention. For cylinder forming block copolymer phases the ordering and degree of perpendicular alignment is largely determined by the matching of the substrate surface to the block copolymer. If the chemical properties of the substrate surface match the average for the block copolymer, then thin films of the block copolymer align perpendicularly on annealing. Although there are a number of examples where the substrate surface fortuitously matches the block copolymer, in general an orienting layer is necessary to provide the appropriate match. The most popular approach has been to synthesize a random copolymer with the same average composition as the block copolymer. In order to produce suitably thin orienting layers it has been necessary to chemically tether the random copolymer to the substrate. Previously used chemistry has not been suitable for noble metal substrates such as platinum. We have been developing an alternate approach using thiol functional groups which we anticipate will be more suitable for Pt capped substrates.

Water Entry and Exit of a Horizontal Circular Cylinder

In this paper we describe the fully nonlinear free-surface deformations of initially calm water caused by the water entry and water exit of a horizontal circular cylinder with both forced and free vertical motions. Two-dimensional flow conditions are assumed in the study. This has relevance for marine operations as well as for the ability to predict large amplitude motions of floating sea structures. A new numerical method called the CIP (Constrained Interpolation Profile) method is used to solve the problem. In this paper, the circular cylinder and free surface interaction is treated as a multiphase problem, which has liquid (water), gas (air), and solid (circular cylinder) phases. The flow is represented by one set of governing equations, which are solved numerically on a nonuniform, staggered Cartesian grid by a finite difference method. The free surface as well as the body boundary is immersed in the computational domain. The numerical results of the water entry and exit force, the free surface deformation and the vertical motion of the cylinder are compared with experimental results, and favorable agreement is obtained.

Tubular Nanostructures from Degradable Core–Shell Cylinder Microstructures in Chiral Diblock Copolymers

A core–shell cylinder phase is obtained from the self assembly of chiral diblock copolymers, polystyrene-b-poly(L-lactide) (PS–PLLA) with PLLA-rich fractions. After the self-assembly of the polymer chains, scrolling of the helical microdomains results in core–shell cylinder microstructures (see figure). The microstructures are then hydrolyzed to give polymeric nanotubes with potential applications in drug delivery and as nanoreactors.

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.

Undulated cylinders of charged diblock copolymers

We study the cylinder to sphere morphological transition of diblock copolymers in aqueous solution with a hydrophobic block and a charged block. We find a metastable undulated cylinder configuration for a range of charge and salt concentrations which, nevertheless, occurs above the threshold where spheres are thermodynamically favorable. By modeling the shape of the cylinder ends, we find that the free-energy barrier for the transition from cylinders to spheres is quite large and that this barrier falls significantly in the limit of high polymer charge and low solution salinity. This suggests that observed undulated cylinder phases are kinetically trapped structures.

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.

Inverted to Normal Phase Transition in Solution-Cast Polystyrene−Poly(methyl methacrylate) Block Copolymer Thin Films

We have investigated the inverted phase formation and the transition from inverted to normal phase for a cylinder-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymer in solution-cast films with thickness about 300 nm during the process of the solution concentrating by slow solvent evaporation. The cast solvent is 1,1,2,2-tetrachloroethane (Tetra-CE), a good solvent for both blocks but having preferential affinity for the minority PMMA block. During such solution concentrating process, the phase behavior was examined by freeze-drying the samples at different evaporation time, corresponding to at different block copolymer concentrations, φ. As φ increases from ∼0.1% (v/v), the phase structure evolved from the disordered sphere phase (DS), consisting of random arranged spheres with the majority PS block as a core and the minority PMMA block as a corona, to ordered inverted phases including inverted spheres (IS), inverted cylinders (IC), and inverted hexagonally perforated lamellae (IHPL) with the minority PMMA block comprising the continuum phase, and then to the lamellar (LAM) phase with alternate layers of the two blocks, and finally to the normal cylinder (NC) phase with the majority PS block comprising the continuum phase. The solvent nature and the copolymer solution concentration are shown to be mainly responsible for the inverted phase formation and the phase transition process.

Phase Diagram for a Diblock Copolymer Melt under Cylindrical Confinement

We extensively study the phase diagram of a diblock copolymer melt confined in a cylindrical nanopore using real-space self-consistent mean-field theory. We discover a rich variety of new two-dimensional equilibrium structures that have no analog in the unconfined system. These include non-hexagonally coordinated cylinder phases and structures intermediate between lamellae and cylinders. We map the stability regions and phase boundaries for all the structures we find. As the pore radius is decreased, the pore accommodates fewer cylindrical domains and structural transitions occur as cylinders are eliminated. Our results are consistent with experiments, but we also predict phases yet to be observed.

Grain shapes and growth kinetics during self‐assembly of block copolymers

AbstractWith block copolymer equilibrium phase behavior becoming increasingly better understood, a more detailed description of ordering kinetics is feasible. This article highlights recent experimental observations that provide new insight into ordering kinetics and grain structures when a block copolymer liquid is first cooled below the order–disorder transition. Measurements have been made on several concentrated poly(styrene‐b‐isoprene) solutions, with concentrations and temperatures adjusted to access the cylinder, lamellar, and gyroid phases. A diverse set of grain types were observed using polarized optical microscopy (POM). Cylinder grains were either oblate ellipsoids or spherulites, whereas the lamellar phase formed prolate ellipsoidal grains, twinned ellipsoidal grains, twofold twinned grains, and spherulites. The orientation of the cylinders and lamellae within the grains were unambiguously identified. The shapes of the ellipsoidal and twinned grains were dictated by the relative interfacial tensions of the available growth surfaces with respect to the disordered state. Grain growth front velocities were also quantified before grain impingement, and consistent values were obtained among different grains for a given sample and quench temperature. The experimental growth velocities were compared to an expression derived by Goveas and Milner. There was good agreement in terms of the temperature dependence, and the absolute magnitude was predicted with some success. The rates of nucleation and overall conversion to the ordered phase were also determined. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 481–491, 2006