Monte Carlo Simulations of Asymmetric Diblock Copolymer Thin Films Confined between Two Homogeneous Surfaces

Geometry-controlled interface localization-delocalization transition in block copolymers

Lamellar copolymers confined into a film of thickness D by two stripe-patterned surfaces, which are rotated against each other by a twist angle α, form lamellar domains that register and align with the respective chemical surface patterns. The two domains of thickness x and D-x are separated by an interface that resembles a twist grain boundary. At small twist angles α or strong selectivity of the surface patterns, this interface fluctuates around the middle of the film, x≈D/2, while the interface is localized at one of the surfaces, x≈0 or x≈D, in the opposite limit. These two morphologies are separated by an interface localization-delocalization transition (ILDT) that can be controlled by the twist angle α. For thin films, we find a second-order ILDT while the ILDT is first-order for large D values. A phenomenological interface Hamiltonian is used to relate the findings to the ILDT of symmetric mixtures, and the predictions are confirmed by molecular simulation.

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.

Soft confinement-induced morphologies of diblock copolymers

The self-assembly of diblock copolymers under soft confinement is studied systematically using a simulated annealing method applied to a lattice model of polymers. The soft confinement is realized by the formation of polymer droplets in a poor solvent environment. Multiple sequences of soft confinement-induced copolymer aggregates with different shapes and self-assembled internal morphologies are predicted as functions of solvent-polymer interaction and the monomer concentration. It is discovered that the self-assembled internal morphology of the aggregates is largely controlled by a competition between the bulk morphology of the copolymer and the solvent-polymer interaction, and the shape of the aggregates can be non-spherical when the internal morphology is anisotropic and the solvent-polymer interaction is weak. These results demonstrate that droplets of diblock copolymers formed in poor solvents can be used as a model system to study the self-assembly of copolymers under soft confinement.

Geometric frustration phases of diblock copolymers in nanoparticles

The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated.

Thermally reversible surface morphology transition in thin diblock copolymer films

Many phase transitions exhibit ordering transitions at the boundary of the material that are distinct from its interior where intermolecular interactions can be significantly different. The present work considers the existence of a surface thermodynamic order-order transition between two distinct morphologies in thin block copolymer (BCP) films that are of interest in nanomanufacturing applications. Specifically, we find a thermally reversible interfacial transition between sphere-like structures and cylinders in flow-coated films of poly(styrene-block-methyl methacrylate) (PS-b-PMMA), where the BCP forms a cylinder microphase in the bulk. We present direct evidence from atomic force microscopy (AFM) of ion-etched films and grazing-incidence small-angle X-ray scattering (GISAXS) on films without etching, which shows that the order-order transition is restricted to the outer layer of the film, while the film interior remains in the cylinder state. Moreover, we find this order-order transition to be insensitive to film thickness over the range investigated (40-170 nm). This morphological transition is of importance in characterizing the thermodynamics and dynamics of thin BCP films used as templates in nanomanufacturing applications.

Microdomain orientation dependence on thickness in thin films of cylinder-forming PS-b-PMMA

The self-assembly of block-copolymer thin films in periodic nanostructures has received considerable attention during the last decade due to their potential applications in nanofabrication and nanolithography. We followed the morphologies developed in thin films of a cylinder-forming diblock copolymer polystyrene-b-poly(methylmethacrylate) ((PS-b-PMMA), PS 46.1 kg mol( - 1), PMMA 21.0 kg mol( - 1), lattice spacing L(0) = 36 nm), as a function of the film thickness (t), analyzing the effect of thickness commensurability on domain orientation in respect to the substrate. The study was circumscribed to the unexplored range of thickness below L(0). Two thickness windows with perpendicular orientation of the PMMA domains were identified: a well-known window at t approximately L(0) and a new window at t approximately L(0)/2. A half-parallel cylinder morphology was observed for [Formula: see text] with a progressive change in morphology [Formula: see text] when thickness increases from L(0)/2 to L(0). This experimental evidence provides new insights on the mechanism of block copolymers self-organization and indicates the possibility to tune the thickness of the nanostructured polymeric film below L(0), allowing the fabrication of ultrathin soft masks for advanced lithographic processes.

Self-assembly of AB diblock copolymers under confinement into topographically patterned surfaces

Motivated by recent experiments of copolymer patterning by nanoimprinting, we investigate microphase separation and morphology for symmetric AB diblock copolymers with lamellar structure in bulk, confined between a flat bottom surface and a square-wave top surface by using the self-consistent field theory (SCFT). The efficient and high-order accurate pseudospectral method is adopted to numerically solve the SCFT equations in irregularly shaped domains with the help of the "masking" technique by embedding the confined domains of arbitrary shape within a larger rectangular computational cell. Our simulations reveal that the inverted T-style and trapezoid structures occurring in the relatively strong and weak surface fields, respectively, are following our topographically patterned surface. For neutral walls, when the thickness of the lower section is commensurate with the lamellae period of bulk block copolymers, the topographically patterned surface in this work leads to parallel lamellae, and completely parallel lamellae are favored when both the width and height of the upper section are equal to the lamellae bulk period. Furthermore, the prevalent structures are the parallel lamellae in the upper section combined with the perpendicular lamellae in the lower section. When the walls repel one of the block species, parallel lamellae occur in a wide range of film thicknesses compared to the case of neutral walls. To our knowledge, some new structures, however, such as square and partial square structures and reversed-T and trapezoid structures, have not been reported before under parallel surface confinement. In general, the required structures can be obtained by choosing the proper degree of spatial confinement, characterized by variations of the ratio of film thicknesses to bulk repeat period, and the block-substrate interactions. Moreover, we show that the confinement width of the lower section (or the period of the square wave) plays a critical role in microstructure formation. These findings provide a guide to designing novel microstructures involving symmetric diblock copolymers via topographically patterned surfaces and surface fields, relevant to nanoimprinting.

Directed Block Copolymer Assembly versus Electron Beam Lithography for Bit-Patterned Media with Areal Density of 1 Terabit/inch(2) and Beyond

The directed self-assembly of block copolymer (BCP) offers a new route to perfect nanolithographic patterning at sub-50 nm length scale with molecular scale precision. We have explored the feasibility of using the BCP approach versus the conventional electron beam (e-beam) lithography to create highly dense dot patterns for bit-patterned media (BPM) applications. Cylinder-forming poly(styrene-b-methyl methacrylate) (PS-b-PMMA) directly self-assembled on a chemically prepatterned substrate. The nearly perfect hexagonal arrays of perpendicularly oriented cylindrical pores at a density of approximately 1 Terabit per square inch (Tb/in.(2)) are achieved over an arbitrarily large area. Considerable gains in the BCP process are observed relative to the conventional e-beam lithography in terms of the dot size variation, the placement accuracy, the pattern uniformity, and the exposure latitude. The maximum dimensional latitude in the cylinder-forming BCP patterns and the maximum skew angle that the BCP can tolerate have been investigated for the first time. The dimensional latitude restricts the formation of more than one lattice configuration in certain ranges. More defects in BCP patterns are observed when using low molecular weight BCP materials or on non-hexagonal prepatterns due to the dimensional latitude restriction. Finally, the limitations and challenges in the BCP approach that are associated with BPM applications will be briefly discussed.

Surface morphology diagram for cylinder-forming block copolymer thin films

We investigate the effect of the ordering temperature (T) and film thickness (h(f)) on the surface morphology of flow-coated block copolymer (BCP) films of asymmetric poly(styrene-block-methyl methacrylate). Morphology transitions observed on the ordered film surface by atomic force microscopy (AFM) are associated with a perpendicular to a parallel cylinder BCP microphase orientation transition with respect to the substrate with increasing h(f). "Hybrid" surface patterns for intermediate h(f) between these limiting morphologies are correspondingly interpreted by a coexistence of these two BCP microphase orientations so that two "transitional" h(f) exist for each T. This explanation of our surface patterns is supported by both neutron reflectivity and rotational SANS measurements. The transitional h(f) values as a function of T define upper and lower surface morphology transition lines, h(fu) (T) and h(fl) (T), respectively, and a surface morphology diagram that should be useful in materials fabrication. Surprisingly, the BCP film surface morphology depends on the method of film formation (flow-coated versus spun-cast films) so that nonequilibrium effects are evidently operative. This morphological variability is attributed primarily to the trapping of residual solvent (toluene) within the film (quantified by neutron reflectivity) due to film vitrification while drying. This effect has significant implications for controlling film structure in nanomanufacturing applications based on BCP templates.

Morphological transition behavior of ABC star copolymers by varying the interaction parameters

We employ dissipative particle dynamics (DPD) to examine the effects of composition and interaction parameter on the resulting phase behavior of ABC star copolymers. Here, we assume that the interaction parameters among the three components are equal. When the three components have comparable volume fractions, our DPD results illustrate that the unique formation of various types of three-phase separated polygonal cylinders is mainly dominated by the composition but not influenced by the interaction parameter. In contrast, when two of the three components are minor, the resulting morphology type is greatly influenced by the interaction parameter. Generally speaking, with an increase in the interaction parameter, the two minority components first act like one component and the system forms a one-length-scale ordered microstructure. Then a further segregation between the two minority components within the large-length-scale phase can be induced as the interaction parameter keeps increasing. In general, our DPD results, a systematic study of the morphological transition behavior obtained by varying the interaction parameter and composition, bridge the gap between the previous theoretical results in the strong and weak segregation regimes via Monte Carlo and two-dimensional self-consistent mean-field methods, respectively.