Asymmetric block copolymers confined in a thin film

Microscopic derivation of the thin film equation using the Mori-Zwanzig formalism

The hydrodynamics of thin films is typically described using macroscopic models whose connection to the microscopic particle dynamics is a subject of ongoing research. Existing methods based on density functional theory provide a good description of static thin films but are not sufficient for understanding nonequilibrium dynamics. In this work, we present a microscopic derivation of the thin film equation using the Mori-Zwanzig projection operator formalism. This method allows to directly obtain the correct gradient dynamics structure along with microscopic expressions for mobility and free energy. Our results are verified against molecular dynamics simulations for both simple fluids and polymers.

Equilibrium phase behavior of gyroid-forming diblock polymer thin films

Thin-film confinement of self-assembling block polymers results in materials with myriad potential applications-including membranes and optical devices-and provides design parameters for altering phase behavior that are not available in the bulk, namely, film thickness and preferential wetting. However, most research has been limited to lamella- and cylinder-forming polymers; three-dimensional phases, such as double gyroid (DG), have been observed in thin films, but their phase behavior under confinement is not yet well understood. We use self-consistent field theory to predict the equilibrium morphology of bulk-gyroid-forming AB diblock polymers under thin-film confinement. Phase diagrams reveal that the (211) orientation of DG, often observed in experiments, is stable between nonpreferential boundaries at thicknesses as small as 1.2 times the bulk DG lattice parameter. The (001) orientation is stable between modestly B-preferential boundaries, where B is the majority block, while a different (211)-oriented termination plane is stabilized by strongly B-preferential boundaries, neither of which has been observed experimentally. We then describe two particularly important phenomena for explaining the phase behavior of DG thin films at low film thicknesses. The first is "constructive interference," which arises when distortions due to the top and bottom boundaries overlap and is significant for certain DG orientations. The second is a symmetry-dependent, in-plane unit-cell distortion that arises because the distorted morphology near the boundary has a different preferred unit-cell size and shape than the bulk. These results provide a thermodynamic portrait of the phase behavior of DG thin films.

Boundary Frustration in Double-Gyroid Thin Films

Self-consistent field theory for thin films of AB diblock polymers in the double-gyroid phase reveals that in the absence of preferential wetting of monomer species at the film boundaries, films with the (211) plane oriented parallel to the boundaries are more stable than other orientations, consistent with experimental results. This preferred orientation is explained in the context of boundary frustration. Specifically, the angle of intersection between the A/B interface and the film boundary, the wetting angle, is thermodynamically restricted to a narrow range of values. Most termination planes in the double gyroid cannot accommodate this narrow range of wetting angles without significant local distortion relative to the bulk morphology; the (211)-oriented termination plane with the "double-wave" pattern produces relatively minimal distortion, making it the least frustrated boundary. The principle of boundary frustration provides a framework to understand the relative stability of termination planes for complex ordered block polymer phases confined between flat, nonpreferential boundaries.

Epitaxial Growth of Surface Perforations on Parallel Cylinders in Terraced Films of Block Copolymer/Homopolymer Blends

Due to incommensurability between initial thickness and interdomain distance, thermal annealing inevitably produces relief surface terraces (islands and holes) of various morphologies in thin films of block copolymers. We have demonstrated three kinds of surface terraces in blend films: polygrain terraces with diffuse edges, polygrain terraces with step edges, and pseudo-monograin terraces with island coarsening. The three morphologies were obtained by three different thermal histories, respectively. The thermal histories were imposed on blend films, which were prepared by mixing a homopolystyrene (hPS, 6.1 kg/mol) with a weakly segregated, symmetry polystyrene-block poly(methyl methacrylate) (PS-b-PMMA, 42 kg/mol) followed by spin coating. At a given weight-fraction ratio of PS-b-PMMA/hPS = 75/25, the interior of the blend films forms parallel cylinders. Nevertheless, the surface of the blend films is always dominated by a skin layer of perforations, which epitaxially grow on top of parallel cylinders. By oxygen plasma etching at various time intervals to probe interior nanodomains, the epitaxial relationship between surface perforations and parallel cylinders has been identified by a scanning electron microscope.

Molecular-weight effects of a homopolymer on the AB- and ABC-stacks of perforations in block copolymer/homopolymer films

We have demonstrated the molecular-weight effects of adding homopolystyrene (hPS) on the evolution of perforated layers and double gyroids in polystyrene-block-poly(methyl methacrylate)-based films during isothermal annealing. Two homopolystyrenes of 2.8 and 17 kg mol-1 were used. To prepare blend films, PS-b-PMMA and hPSx (x: 2.8 or 17) were mixed at a weight-fraction ratio of 75/25 in toluene and then spin-coated at SiOx/Si. Spin coating inevitably produced films with thick edges at the periphery of the substrate. The structural evolution of the spun films was in situ characterized by grazing incidence small-angle X-ray scattering (GISAXS). The annealed films were then characterized using a scanning electron microscope (SEM). We found that thin middle regions behaved differently from thick beads for the films. The middle of the blend films mainly formed perforated layers with different spatial orders and orientations, depending on the molecular weight of added hPS chains. Hexagonally perforated layers quickly formed at 205 °C for PS-b-PMMA/hPS2.8 films. However, when hPS17 was used instead of hPS2.8, perforated layers formed with defects in PS-b-PMMA/hPS17 films annealed at 205 °C. Annealing at 240 °C improved the spatial order and orientation of perforated layers for a PS-b-PMMA/hPS17 film. Nevertheless, annealing at 240 °C inversely depressed the in-plane spatial order of perforated layers for a PS-b-PMMA/hPS2.8 film. The depression in the in-plane spatial order is ascribed to a dilution effect of added short chains. Compared to the middle regions, the thick beads went through several metastable phases, such as perpendicularly oriented perforated layers and double gyroids.

Effect of Film Thickness on the Self-Assembly of CBABC Symmetric Pentablock Terpolymer Melts under 1D Confinement: A Dissipative Particle Dynamic Study

The study investigates the impact of film thickness on the phase behavior of pentablock terpolymers, denoted as C3B3A6B3C3, when subjected to wall confinement by utilizing the dissipative particle dynamics method. Phase diagrams were constructed to elucidate how factors such as block-block interaction strength, film thickness, and wall properties affect the self-assembly structures. In cases where the wall exhibits no preference for any of the blocks, lamellae phases with orientations perpendicular to the wall are observed. The order-disorder transition (ODT) temperature is found to be influenced by the interaction between the polymer and the wall in thin confinement scenarios. When the wall displays a preference for specific blocks, the orientation of lamellae structures undergoes variations. Lamellae tend to align parallel to the wall when the wall favors A or C blocks, and they orient perpendicularly when B blocks are favored. Furthermore, the mechanical properties of the lamellae structures are related to the conformations of the polymer chains. Structures where chains predominantly adopt a loop conformation exhibit enhanced elastic properties. The ratio of looping to bridging conformations can be adjusted by altering the film thickness and wall selectivity.

Phase behavior in thin films of weakly segregated block copolymer/homopolymer blends

We have demonstrated the phase behavior of substrate-supported films of a symmetric weakly segregated polystyrene-block-poly (methyl methacrylate), P(S-b-MMA), block copolymer and its blends with homopolymer polystyrene (PS) at different compositions. Upon increasing the content of added PS in the blends, lamellae (L), perforated layers (PL), double gyroid (DG) and cylinders (C) are obtained in sequence for films. Among these nanodomains, PL and DG only exist in a narrow ϕ_PS region (ϕ_PS denotes the volume fraction of PS). At ϕ_PS = 64%, tuning film thickness and annealing temperature can produce parallel PL or DG with {121}_DG lattice planes being parallel to the substrate surface. The effects of annealing temperature and film thickness on the formation of PL and DG are examined. In thin films with n ≈ 3 (n denotes the ratio of initial film thickness to inter-domain spacing), the PL phase solely exists regardless of temperature. However, for thick films with n ≈ 6 and 10, thermal annealing at the most accessible temperature produces films containing both PL and DG of various fractions, but a low temperature tends to favor a greater fraction of PL. The PL phase becomes the only discernible phase if thick films are shortly annealed at 230 °C.

Influence of Osmotic Pressure on Nanostructures in Thin Films of a Weakly-Segregated Block Copolymer and Its Blends with a Homopolymer

We studied the influence of osmotic pressure on nanostructures in thin films of a symmetric weakly-segregated polystyrene-block-poly (methyl methacrylate), P(S-b-MMA), block copolymer and its mixtures with a polystyrene (PS) homopolymer of various compositions. Thin films were deposited on substrates through surface neutralization. The surface neutralization results from the PS mats, which were oxidized and cross-linked by UV-light exposure. Thus, thermal annealing produced perpendicularly oriented lamellae and perforated layers, depending on the content of added PS chains. Nevertheless, a mixed orientation was obtained from cylinders in thin films, where a high content of PS was blended with the P(S-b-MMA). A combination of UV-light exposure and acetic acid rinsing was used to remove the PMMA block. Interestingly, the treatment of PMMA removal inevitably produced osmotic pressure and consequently resulted in surface wrinkling of perpendicular lamellae. As a result, a hierarchical structure with two periodicities was obtained for wrinkled films with perpendicular lamellae. The formation of surface wrinkling is due to the interplay between UV-light exposure and acetic acid rinsing. UV-light exposure resulted in different mechanical properties between the skin and the inner region of a film. Acetic acid rinsing produced osmotic pressure. It was found that surface wrinkling could be suppressed by reducing film thickness, increasing PS content and using high-molecular-weight P(S-b-MMA) BCPs.

A simulation study of the self-assembly of ABC star terpolymers confined between two parallel surfaces

The phase behavior of ABC star terpolymers confined between two identical parallel surfaces is systematically studied using a simulated annealing method. Several phase diagrams are constructed for systems with different bulk phases or with different interfacial interaction strength ratios in the space of surface distance (D) and surface preference for different arms, or in the space of D and the arm-length ratio x. Phases, including tiling patterns [6.6.6], [8.8.4], [8.6.6; 8.6.4], [8.6.6; 8.6.4; 10.6.6; 10.6.4] and hierarchical lamellar structures of lamella + cylinders and lamella + rods, are identified both in the bulk and in the films. Our results suggest that the self-assembled structure of a phase is largely controlled by x, while an increase of the interfacial interaction strength ratio shifts the x-window for each phase to the smaller x side. The orientation of a confined phase depends on the "effective surface preference" which is a combined effect of the interfacial interaction strength ratio, the surface preference, and the entropic preference. In the case of neutral or weak "effective surface preference", phases with a perpendicular orientation are usually observed, while in the case of strong "effective surface preference" phases with a perpendicular orientation or also with outermost wetting-layers can be frequently observed under some circumstances.

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

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.

Hybrid patterns from directed self-assembly of diblock copolymers by chemical patterns

The surface affinity is a critical factor for controlling the formation of monolayer nanostructures in block copolymer thin films. In general, strong surface affinity tends to induce the formation of domains with low spontaneous curvature. Abiding by this principle, we propose a facile chemoepitaxial scheme for producing large-scale ordered hybrid patterns by the directed self-assembly of diblock copolymers. The guiding chemical pattern is designed as periodic stripes with alternately changing surface affinities. As a consequence, two different geometries of domains are formed on the stripes with different affinities. The self-assembly process of block copolymers guided by the stripe patterns is investigated using cell dynamics simulations based on time-dependent Ginzburg-Landau theory, and the kinetic stability diagram is estimated. Hybrid patterns are successfully achieved with both cylinder-forming and sphere-forming diblock copolymers. In the cylinder-forming system, the major hybrid pattern exhibiting a considerable stability window is composed of parallel cylinders and perforated lamellae, while it is composed of monolayer spheres and parallel cylinders in the other system. Encouragingly, the chemoepitaxial method is valid till the period of the guiding pattern is a large multiple of the domain spacing. The chemoepitaxial scheme demonstrated in this work serves as a nice supplement to the graphoepitaxial one proposed in our previous work.

Hybrid line-dot nanopatterns from directed self-assembly of diblock copolymers by trenches

We demonstrate that the directed self-assembly of AB diblock copolymers by periodic trenches can be used to fabricate large-scale ordered hybrid line-dot nanopatterns in addition to a defect-free dot nanopattern. The formation of line or dot nanopatterns in thin films with proper surface affinities is controlled by the film thickness, which is modulated by a topographic pattern consisting of steps and trenches. Two kinds of line-dot nanopatterns are achieved with cylinder-forming and sphere-forming copolymers, respectively. One kind of hybrid nanopatterns is composed of perpendicularly standing cylinders (dots) on the steps and parallel monolayer cylinders (lines) within the trenches, while the dots of the other kind are replaced by monolayer spheres on the steps. The thermodynamic stability region of target hybrid nanopatterns is identified by constructing two-dimensional phase diagrams with respect to two control parameters of step height and film thickness using self-consistent field theory. Furthermore, a process window of the line-dot nanopatterns is estimated using cell dynamics simulations based on time-dependent Ginzburg-Landau theory, confirming their feasibility in kinetics.

Nonequilibrium phase transitions of sheared colloidal microphases: Results from dynamical density functional theory

By means of classical density functional theory and its dynamical extension, we consider a colloidal fluid with spherically symmetric competing interactions, which are well known to exhibit a rich bulk phase behavior. This includes complex three-dimensional periodically ordered cluster phases such as lamellae, two-dimensional hexagonally packed cylinders, gyroid structures, or spherical micelles. While the bulk phase behavior has been studied extensively in earlier work, in this paper we focus on such structures confined between planar repulsive walls under shear flow. For sufficiently high shear rates, we observe that microphase separation can become fully suppressed. For lower shear rates, however, we find that, e.g., the gyroid structure undergoes a kinetic phase transition to a hexagonally packed cylindrical phase, which is found experimentally and theoretically in amphiphilic block copolymer systems. As such, besides the known similarities between the latter and colloidal systems regarding the equilibrium phase behavior, our work reveals further intriguing nonequilibrium relations between copolymer melts and colloidal fluids with competing interactions.

Designing an ordered template of cylindrical arrays based on a simple flat plate confinement of block copolymers: a coarse-grained molecular dynamics study

In this paper we study the morphology formed by asymmetric di-block copolymers (di-BCPs) under various confinements using a large-scale coarse-grained molecular dynamics (CGMD) framework. We start with a simple flat plate confinement with the bottom and the top substrate attractive to the minor phase. Studies at a lower confinement length of 17σ have shown that there exists a critical chain length above which a transition from a three-domain morphology to a two-domain morphology is observed. Increasing the confinement length to 42σ, where the chains experience considerably lower confinement effects, also revealed the existence of a critical chain length - a transition from a multi-domain morphology (>3) to a three-domain morphology. The results obtained from the flat plate study with two confinement dimensions were used to design a topography of silica pillars with and without a bottom substrate to form ordered cylindrical BCP arrays. The least and highest radial separation lengths between adjacent pillars are kept at 17σ and 42σ, respectively. A direct correlation was observed in the number of continuous micro-domains of the maximum and minimum confinement dimensions with the 17σ and 42σ flat plate trials. With the optimum chain length employed, the surfaces with affinity to the minor phase can direct the BCP self-assembly to form ordered arrays of minor phase cylinders. The current study thus elucidates a useful tool to predict the morphology formed in an intricate nano-lithographic template by using simple length scale arguments derived from a flat plate confinement study.

The One-Pot Directed Assembly of Cylinder-Forming Block Copolymer on Adjacent Chemical Patterns for Bimodal Patterning

The direct self-assembly of cylinder-forming poly(styrene-block-methyl-methacrylate) (PS-b-PMMA) block copolymer is successfully assembled into two orientations, according to the underlying guiding pattern in different areas. Lying-down and perpendicular cylinders are formed, respectively, depending on the design of chemical pattern: sparse line/space pattern or hexagonal dot array. The first chemical pattern composed of prepatterned cross-linked polystyrene (XPS) line/space structure has a period (L_S ) equal to twice the intercylinder period of the block copolymer (L₀ ). The PS-b-PMMA thin film on the prepared chemical template after thermal annealing forms a lying-down cylinder morphology when the width of the PS strips is less than the width of PS block in the PS-b-PMMA block copolymer. The morphology is only applicable at the discrete thickness of the PS-b-PMMA film. In addition to forming the lying-down cylinders directly on the XPS guiding pattern, the cylinder-forming block copolymer can also be assembled in a perpendicular way on the second guiding pattern (the hexagonal dot array). The block copolymer films are registered into two orientations in a single directed self-assembly process. The features of the assembled patterns are successfully transferred down to the silicon oxide substrate.

Macroscopically Oriented Porous Materials with Periodic Ordered Structures: From Zeolites and Metal-Organic Frameworks to Liquid-Crystal-Templated Mesoporous Materials

Porous materials with molecular-sized periodic structures, as exemplified by zeolites, metal-organic frameworks, or mesoporous silica, have attracted increasing attention due to their range of applications in storage, sensing, separation, and transformation of small molecules. Although the components of such porous materials have a tendency to pack in unidirectionally oriented periodic structures, such ideal types of packing cannot continue indefinitely, generally ceasing when they reach a micrometer scale. Consequently, most porous materials are composed of multiple randomly oriented domains, and overall behave as isotropic materials from a macroscopic viewpoint. However, if their channels could be unidirectionally oriented over a macroscopic scale, the resultant porous materials might serve as powerful tools for manipulating molecules. Guest molecules captured in macroscopically oriented channels would have their positions and directions well-defined, so that molecular events in the channels would proceed in a highly controlled manner. To realize such an ideal situation, numerous efforts have been made to develop various porous materials with macroscopically oriented channels. An overview of recent studies on the synthesis, properties, and applications of macroscopically oriented porous materials is presented.

Electric-field-induced lamellar to hexagonally perforated lamellar transition in diblock copolymer thin films: kinetic pathways

Symmetric block-copolymers, hitherto, are well known to evolve into parallel, perpendicular and mixed lamellar morphologies under the concomitant influence of an electric field and substrate affinity. In the present work, we show that an additional imposed confinement can effectuate a novel parallel lamellar to hexagonally perforated lamellar (HPL) transition in monolayer and bilayer films. Three dimensional numerical studies are performed using the Ohta-Kawasaki functional, complemented with an exact solution of Maxwell's equation. HPL is shown to stabilize at large substrate affinity in a narrow region of the phase diagram between parallel and perpendicular lamellar transitions in ultra-thin films. Additionally, we also identify perforated lamellae as intermediate structures during parallel-to-perpendicular lamellar transition. A systematic analysis using Minkowski functionals yields deeper insights into the associated kinetic pathways.

Influence of substrate interaction and confinement on electric-field-induced transition in symmetric block-copolymer thin films

In the present work, we study morphologies arising due to competing substrate interaction, electric field, and confinement effects on a symmetric diblock copolymer. We employ a coarse-grained nonlocal Cahn-Hilliard phenomenological model taking into account the appropriate contributions of substrate interaction and electrostatic field. The proposed model couples the Ohta-Kawasaki functional with Maxwell equation of electrostatics, thus alleviating the need for any approximate solution used in previous studies. We calculate the phase diagram in electric-field-substrate strength space for different film thicknesses. In addition to identifying the presence of parallel, perpendicular, and mixed lamellae phases similar to analytical calculations, we also find a region in the phase diagram where hybrid morphologies (combination of two phases) coexist. These hybrid morphologies arise either solely due to substrate affinity and confinement or are induced due to the applied electric field. The dependence of the critical fields for transition between the various phases on substrate strength, film thickness, and dielectric contrast is discussed. Some preliminary 3D results are also presented to corroborate the presence of hybrid morphologies.

Directed self-assembly of solvent-vapor-induced non-bulk block copolymer morphologies on nanopatterned substrates

We report a study on directed self-assembly (DSA) with solvent annealing to induce the formation of non-bulk block copolymer microdomains on chemical patterns. Ultrathin films of symmetric polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) display morphologies of PMMA dots, stripes, and PS hexagons with increasing exposure time to acetone vapor, a PMMA-selective solvent. All three nanostructures form long-range-ordered and registered arrays on striped chemical patterns with periods (LS) commensurate to the solvated PS-b-PMMA microdomain period (L0,s). Solvent annealing is shown to facilitate DSA on non-regular chemical patterns, on which the local periods are incommensurate to L0,s. DSA with feature density multiplication, via solvent annealing, is also demonstrated.

Structure and Dynamics of Asymmetric Poly(styrene-b-1,4-isoprene) Diblock Copolymer under 1D and 2D Nanoconfinement

The impact of 1- and 2-dimensional (2D) confinement on the structure and dynamics of poly(styrene-b-1,4-isoprene) P(S-b-I) diblock copolymer is investigated by a combination of Scanning Electron Microscopy (SEM), Atomic Force Microscopy (AFM), Grazing-Incidence Small-Angle X-ray Scattering (GISAXS), and Broadband Dielectric Spectroscopy (BDS). 1D confinement is achieved by spin coating the P(S-b-I) to form nanometric thin films on silicon substrates, while in the 2D confinement, the copolymer is infiltrated into cylindrical anodized aluminum oxide (AAO) nanopores. After dissolving the AAO matrix having mean pore diameter of 150 nm, the SEM images of the exposed P(S-b-I) show straight nanorods. For the thin films, GISAXS and AFM reveal hexagonally packed cylinders of PS in a PI matrix. Three dielectrically active relaxation modes assigned to the two segmental modes of the styrene and isoprene blocks and the normal mode of the latter are studied selectively by BDS. The dynamic glass transition, related to the segmental modes of the styrene and isoprene blocks, is independent of the dimensionality and the finite sizes (down to 18 nm) of confinement, but the normal mode is influenced by both factors with 2D geometrical constraints exerting greater impact. This reflects the considerable difference in the length scales on which the two kinds of fluctuations take place.

Elucidating Water Transport Mechanisms in Nafion Thin Films

Ion-exchange membranes are critical components of hydrogen fuel cells, where these ionomers can be confined to nanoscale thicknesses, altering the physical properties of these films from that of bulk membranes. Therefore, it is important to develop methods capable of measuring and elucidating the transport mechanisms under thin film confinement compared to bulk Nafion. In this study, water sorption and diffusion in a Nafion thin film were measured using time-resolved in situ polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS). Interfacial mass transport limitations were confirmed to be minimal, while restricted water diffusion was observed, where the effective diffusion coefficient of water in the thin Nafion film was many orders of magnitude lower (between 4 and 5 orders of magnitude) than those reported for bulk membranes and was dependent on the initial hydration state of the Nafion. Furthermore, the response of the hydrophobic domains (Teflon backbone) to the swelling of the hydrophilic domains (ionic clusters) was shown to be orders of magnitude slower than that of bulk Nafion.

Complex microstructures of ABC triblock copolymer thin films directed by polymer brushes based on self-consistent field theory

The morphology and the phase diagram of ABC triblock copolymer thin film directed by polymer brushes are investigated by the self-consistent field theory in three dimensions. The polymer brushes coated on the substrate can be used as a good soft template to tailor the morphology of the block copolymer thin films compared with those on the hard substrates. The polymer brush is identical with the middle block B. By continuously changing the composition of the block copolymer, the phase diagrams are constructed for three cases with the fixed film thickness and the brush density: identical interaction parameters, frustrated and non-frustrated cases. Some ordered complex morphologies are observed: parallel lamellar phase with hexagonally packed pores at surfaces (LAM3 (ll) -HFs), perpendicular lamellar phase with cylinders at the interface (LAM(⊥)-CI), and perpendicular hexagonally packed cylinders phase with rings at the interface (C2 (⊥)-RI). A desired direction (perpendicular or parallel to the coated surfaces) of lamellar phases or cylindrical phases can be obtained by varying the composition and the interactions between different blocks. The phase diagram of ABC triblock copolymer thin film wetted between the polymer brush-coated surfaces is very useful in designing the directed pattern of ABC triblock copolymer thin film.

Simulations on a swollen gyroid nanostructure in thin films relevant to systems of ionic block copolymers

Self-assembly of symmetric A/S-B copolymer melt to gyroid nanostructure, partitioning space into interpenetrating nano-labyrinths (channels), in thin films, is investigated using a minimal lattice model with short-range interactions. This model is relevant to poly(styrenesulfonate)-b -polymethylbutylene melt consisting of three types of segments, A, B and S, corresponding to styrene, methylbutylene and styrenesulfonate, respectively. A single sequence of A, B, and S is used in simulations and the fraction of S segments is fixed at p = 0.647 which corresponds to experimental data. The film thickness, L(z), is restricted to nine values (L(z) = 17 , 22, 26, 30, 34, 42, 51, 60, and 68 in units of the underlying lattice constant). The gyroid nanostructure is found to be stable if the film thickness is equal to or greater than the bulk period of the nanophase. The observed gyroid is referred to as swollen since the volume fraction of two continuous networks made of the B segments is anomalous with respect to that of conventional diblock copolymers. In contrast to bulk state, we do not directly observe the order-disorder transition to the gyroid nanophase for thin films. In this case, however, simulations indicate a direct order-disorder transition to a lamellar phase and the order-disorder transition temperature is higher than that in the bulk state, varying strongly with the film thickness.

Simulation-aided design and synthesis of hierarchically porous membranes

Free-standing silica membranes with hierarchical porosity (ca. 300 nm macropores surrounded by 6-8 nm mesopores) and controllable mesopore architecture were prepared by a dual-templating method, with the structural design aided by mesoscale simulation. To create a two-dimensional, hexagonal macropore array, polymeric colloidal hemisphere arrays were synthesized by a two-step annealing process starting with non-close-packed polystyrene sphere arrays on silicon coated with a sacrificial alumina layer. A silica precursor containing a poly(ethylene) oxide-poly(propylene oxide)-poly(ethylene) oxide (PEO-PPO-PEO) triblock-copolymer surfactant as template for mesopore creation was spin-coated onto the support and aged and then converted into the free-standing membranes by dissolving both templates and the alumina layer. To test the hypothesis that the mesopore architecture may be influenced by confinement of the surfactant-containing precursor solution in the colloidal array and by its interactions with the polymeric colloids, the system was studied theoretically by dissipative particle dynamics (DPD) simulations and experimentally by examining the pore structures of silica membranes via electron microscopy. The DPD simulations demonstrated that, while only tilted columnar structure can be formed through tuning the interaction with the substrate, perfect alignment of 2D hexagonal micelles perpendicular to the plane of the membrane is achievable by confinement between parallel walls that interact preferentially with the hydrophilic components (PEO blocks, silicate, and solvent). The simulations predicted that this alignment could be maintained across a span of up to 10 columns of micelles, the same length scale defined by the colloidal array. In the actual membranes, we manipulated the mesopore alignment by tuning the solvent polarity relative to the polar surface characteristics of the colloidal hemispheres. With methanol as a solvent, columnar mesopores parallel to the substrate were observed; with a methanol-water mixed solvent, individual spherical mesopores were present; and with water as the only solvent, twisted columnar structures were seen.

Phase segregation of a symmetric diblock copolymer in constrained space with a square-pillar array

In this study, we apply a self-consistent field theory of polymers to study the structures of a symmetric diblock copolymer in parallel substrates filled with square-pillar arrays in which the substrates and pillars exhibit a weak preference for one block of the copolymer. Three classes of structures, i.e., lamellae, perpendicular cylinders, and bicontinuous structures, are achieved by varying the polymer film thickness, the pillar pitch (the distance between two centers of the nearest neighboring pillars), the gap and rotation of the pillars. Because of the confinement along horizontal directions imposed by the pillar array, eight novel types of perpendicular lamellar structures and eight novel types of cylindrical structures with various shapes and distributions occur. In the hybridization states of the parallel and perpendicular lamellar structures, several novel bicontinuous structures such as the double-cylinder network, pseudo-lamellae, and perforated lamellar structure are also found. By comparing the free energies of the various possible structures, the antisymmetric parallel lamellae are observed to be stable with the larger pillar gap at a certain film thickness. The structural transformations between the alternating cylindrical structures (alternating cross-shaped, square-shaped, and octagonal perpendicular cylinders) and parallel lamellae with increasing film thickness or pillar gap are well explained by the modified strong separation theory. Our results indicate that array confinement can be an effective method to prepare novel polymeric nanopattern structures.

Confined Self-Assembly of Asymmetric Diblock Copolymers within Silica Nanobowl Arrays

The confined self-assembly of asymmetric diblock copolymer polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) within an array of silica nanobowls prepared using a colloidal spheres templating technique is investigated. By manipulation of the nanobowl size, block copolymer (BCP) thickness, and interfacial interaction, a rich variety of ordered BCP nanostructures not accessible in the bulk system or under other confinements are obtained, resulting in hierarchically ordered nanostructures.