Thin films of block copolymer

HipGISAXS: a high-performance computing code for simulating grazing-incidence X-ray scattering data

This article describes the development of a flexible grazing-incidence small-angle X-ray scattering (GISAXS) simulation code in the framework of the distorted wave Born approximation that effectively utilizes the parallel processing power provided by graphics processors and multicore processors. The code, entitledHigh-Performance GISAXS, computes the GISAXS image for any given superposition of user-defined custom shapes or morphologies in a material and for various grazing-incidence angles and sample orientations. These capabilities permit treatment of a wide range of possible sample structures, including multilayered polymer films and nanoparticles on top of or embedded in a substrate or polymer film layers. In cases where the material displays regions of significant refractive index contrast, an algorithm has been implemented to perform a slicing of the sample and compute the averaged refractive index profile to be used as the reference geometry of the unperturbed system. A number of case studies are presented, which demonstrate good agreement with the experimental data for a variety of polymer and hybrid polymer/nanoparticle composite materials. The parallelized simulation code is well suited for addressing the analysis efforts required by the increasing amounts of GISAXS data being produced by high-speed detectors and ultrafast light sources.

Stability and orientation of lamellae in diblock copolymer films

The dynamics of microphase separation and the orientation of lamellae in diblock copolymers are investigated in terms of a mean-field model. The formation of lamellar structures and their stable states are explored and it is shown that lamellae are stable not only for the period of the structure corresponding to the minimum of the free energy. The range of wavelengths of stable lamellae is determined by an efficient functional approach introduced with this work. The effects of the interaction of diblock copolymers with two confining substrates on the lamellae orientation are studied by an extensive analysis of the total free energy. By changing the wetting property at one boundary, a transition from a preferentially perpendicular to a parallel lamellar orientation with respect to the confining plates is found, which is rather independent of the distance between the boundaries. Simulations of the dynamics of microphase separation reveal that the time scale of the lamellar orientational order dynamics, which is quantitatively characterized in terms of an orientational order parameter and the structure factor, depends significantly on the properties of the confining boundaries as well as on the quench depth.

Morphology Induced Spinodal Decomposition at the Surface of Symmetric Diblock Copolymer Films

Atomic force microscopy is used to study the ordering dynamics of symmetric diblock copolymer films. The films order to form a lamellar structure which results in a frustration when the film thickness is incommensurate with the lamellae. By probing the morphology of incommensurate films in the early ordering stages, we discover an intermediate phase of lamellae arranged perpendicular to the film surface. This morphology is accompanied by a continuous growth in amplitude of the film surface topography with a characteristic wavelength, indicative of a spinodal process. Using self-consistent field theory, we show that the observation of perpendicular lamellae suggests an intermediate state with parallel lamellae at the substrate and perpendicular lamellae at the free surface. The calculations confirm that the intermediate state is unstable to thickness fluctuations, thereby driving the spinodal growth of surface structures.

Film thickness dependent ordering dynamics of lamellar forming diblock copolymer thin films

Ellipsometry is used in a novel way to study the ordering dynamics of symmetric poly(styrene-methyl methacrylate) diblock copolymer thin films. Ordered thin films form lamellae parallel to the substrate which can form islands or holes at the free surface to ensure commensurability of the layers. The sensitivity of ellipsometry provides the unique ability to probe morphological changes during the ordering process before the ultimate formation of islands or holes at the free surface. We observe three distinct stages in the ordering process: i) an ordering into an intermediate state, ii) an incubation time where the film structure remains constant and iii) the nucleation of islands or holes to achieve equilibrium lamellar morphology. The time-resolved measurement of an incubation period and initial ordering stage provides a means for studying the effect of thickness on the ordering kinetics. The dependence of incubation time on the commensurability of the initial film height is explained using strong segregation theory.

Directed Self-Assembly of Lamellar Copolymers: Effects of Interfacial Interactions on Domain Shape

The depth-dependent structure of a poly(styrene-b-methylmethacrylate) (PS-PMMA) line grating (46 nm pitch) was calculated from quantitative analysis of small-angle X-ray scattering profiles. These data demonstrate that domain shapes are significantly deformed near the substrate interface, where the local PS domain shape resembles an hourglass. The bulk equilibrium dimension is recovered near the center of a 64 nm thick film. Simulations based on self-consistent field theory suggest that deformations near the substrate are caused by extensive penetration of the copolymer domains into the underlying substrate coating (a PS-brush). These findings suggest that new coatings for block copolymer directed self-assembly should consider copolymer penetration lengths in addition to tailoring surface energetics. Furthermore, given the resolution and ensemble-averaging features of synchrotron X-ray scattering, we argue that it has the potential to emerge as a "gold-standard" or "benchmark" dimensional metrology and library validation tool for high density, sub-10 nm features.

Diblock and triblock copolymer thin films on a substrate with controlled selectivity

Using self-consistent field theory (SCFT), morphology development in symmetric linear ABC triblock copolymer films on neutral and selective substrates has been studied, and it is compared with the triblock copolymer morphologies in bulk. In particular, the effects of the substrate preferable to B (interior) block on nanopattern formation of the copolymer films are of our central interest. Here, we report various nanopatterns with tunable square morphologies. The domain patterns are much more diverse than those parallel to the substrate with substrate selectivity for end-block or those vertical to the substrate without substrate selectivity. Furthermore, in order to figure out an economical and efficient way to fabricate useful passive pattern transfer layers, which have potential applications in microelectronic processes and ultrahigh density storage media, we propose a two-step strategy and scrutinize the conditions for generating square symmetries using cylinder-forming or lamella-forming AB diblock copolymers deposited on substrates created from ABC triblock copolymer films. It is found that a thinner film with weak incompatibility can produce square patterns.

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.

Block copolymer films with free interfaces: ordering by nanopatterned substrates

We study block copolymers (BCPs) on patterned substrates, where the top polymer film surface is not constrained but is free and can adapt its shape self-consistently. In particular, we investigate the combined effect of free interface undulations with wetting of the BCP film as induced by nanopatterned substrates. Under wetting conditions and for a finite volume of BCP material, we find equilibrium droplets composed of coexisting perpendicular and parallel lamellar domains. The self-assembly of BCPs on topographic patterned substrates is also investigated and it is found that the free interface induces mixed morphologies of parallel and perpendicular domains coupled with a nonflat free interface. Our study has some interesting consequences for experimental setups of graphoepitaxy and nanoimprint lithography.

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.

Confinement of elastomeric block copolymers via forced assembly coextrusion

Forced assembly processing provides a unique opportunity to examine the effects of confinement on block copolymers (BCPs) via conventional melt processing techniques. The microlayering process was utilized to produce novel materials with enhanced mechanical properties through selective manipulation of layer thickness. Multilayer films consisting of an elastomeric, symmetric block copolymer confined between rigid polystyrene (PS) layers were produced with layer thicknesses ranging from 100 to 600 nm. Deformation studies of the confined BCP showed an increase in ductility as the layer thickness decreased to 190 nm due to a shift in the mode of deformation from crazing to shear yielding. Postextrusion annealing was performed on the multilayer films to investigate the impact of a highly ordered morphology on the mechanical properties. The annealed multilayer films exhibited increased toughness with decreasing layer thickness and resulted in homogeneous deformation compared to the as-extruded films. Multilayer coextrusion proved to be an advantageous method for producing continuous films with tunable mechanical response.

Surface energies and self-assembly of block copolymers on grafted surfaces

We present a theoretical analysis of the self-assembly of diblock copolymers on surfaces grafted with random copolymers. Our results demonstrate that the surface energies of homopolymeric components on grafted surfaces differ from the corresponding values for self-assembled morphologies. Moreover, grafted random copolymers are shown to adapt their conformations in response to the morphology of the overlaying block copolymer film to create chemical inhomogeneities which modulate the interfacial interactions. Consequently, the surface energy differences between the different components on the grafted substrate do not serve as a useful measure to predict the stability of self-assembly of the diblock copolymer film.

Liquid-crystalline ordering helps block copolymer self-assembly

Interaction between liquid-crystalline elastic deformation and microphase separation in liquid-crystalline block copolymers enables them to supramolecularly assemble into ordered nanostructures with high regularity. With the help of liquid-crystalline alignment, parallel and perpendicular patterning of nanostructures is fabricated with excellent reproducibility and mass production, which provides nanotemplates and nanofabrication processes for preparing varieties of nanomaterials. Furthermore, nanoscale microphase separation improves the optical performance of block-copolymer fi lms by eliminating the scattering of visible light, leading to advanced applications in optical devices and actuators. Recent progress in liquid-crystalline block copolymers, including their phase diagram, structure-property relationship, nanostructure control and nanotemplate applications, is reviewed.

Reversible sphere-to-lamellar wetting transition at the interface of a diblock copolymer system

We use ellipsometry to investigate a transition in the morphology of a sphere-forming diblock copolymer thin-film system. At an interface the diblock morphology may differ from the bulk when the interfacial tension favours wetting of the minority domain, thereby inducing a sphere-to-lamella transition. In a small, favourable window in energetics, one may observe this transition simply by adjusting the temperature. Ellipsometry is ideally suited to the study of the transition because the additional interface created by the wetting layer affects the polarisation of light reflected from the sample. Here we study thin films of poly(butadiene-ethylene oxide) (PB-PEO), which order to form PEO minority spheres in a PB matrix. As temperature is varied, the reversible transition from a partially wetting layer of PEO spheres to a full wetting layer at the substrate is investigated.

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.

Dynamic assembly of block-copolymers

Block copolymers (BCs) are well-known building blocks for the creation of a large variety of nanostructured materials or objects through a dynamic assembly stage which can be either autonomous or guided by an external force. Today's nanotechnologies require sharp control of the overall architecture from the nanoscale to the macroscale. BCs enable this dynamic assembly through all the scales, from few aggregated polymer chains to large bulk polymer materials. Since the discovery of controlled methods to polymerize monomers with different functionalities, a broad diversity of BCs exists, giving rise to many different nanoobjects and nanostructured materials. This chapter will explore the potentialities of block copolymer chains to be assembled through dynamic interactions either in solution or in bulk.

Self-assembled microstructures of confined rod-coil diblock copolymers by self-consistent field theory

We employ the self-consistent field theory (SCFT) incorporating Maier-Saupe orientational interactions between rods to investigate the self-assembly of rod-coil diblock copolymers (RC DBC) in bulk and especially confined into two flat surfaces in 2D space. A unit vector defined on a spherical surface for describing the orientation of rigid blocks in 3D Euclidean space is discretized with an icosahedron triangular mesh to numerically integrate over rod orientation, which is confirmed to have numerical accuracy and stability higher than that of the normal Gaussian quadrature. For the hockey puck-shaped phases in bulk, geometrical confinement, i.e., the film thickness, plays an important role in the self-assembled structures' transitions for the neutral walls. However, for the lamellar phase (monolayer smectic-C) in bulk, the perpendicular lamellae are always stable, less dependent on the film thicknesses because they can relax to the bulk spacing with less-paid coil-stretching in thin films. In particular, a very thin rod layer near the surfaces is formed even in a very thin film. When the walls prefer rods, parallel lamellae are obtained, strongly dependent on the competition between the degree of the surface fields and film geometrical confinement, and the effect of surface field on lamellar structure as a function of film thickness is investigated. Our simulation results provide a guide to understanding the self-assembly of the rod-coil films with desirable application prospects in the fabrication of organic light emitting devices.

Self-assembly of lamellar- and cylinder-forming diblock copolymers in planar slits: insight from dissipative particle dynamics simulations

We present a dissipative particle dynamics simulation study on nanostructure formation of symmetric and asymmetric diblock copolymers confined between planar surfaces. We consider symmetric and slightly asymmetric diblock copolymers that form lamellar nanostructures in the bulk, and highly asymmetric diblock copolymers that form cylindrical nanostructures in the bulk. The formation of the diblock copolymer nanostructures confined between the planar surfaces is investigated and characterized by varying the separation width and the strength of the interaction between the surfaces and the diblock copolymers. Both the slit width and the surface interaction strongly influence the phase diagram, especially for the asymmetric systems. For the symmetric and slightly asymmetric diblock copolymer systems, the confinement primarily affects the orientation of the lamellar domains and only marginally influences the domain morphologies. These systems form parallel lamellar phases with different number of lamellae, and perpendicular and mixed lamellar phases. In a narrow portion of the phase diagram, these systems exhibit a parallel perforated lamellar phase, where further insight into the appearance of this phase is provided through free-energy calculations. The confined highly asymmetric diblock copolymer system shows, in addition to nanostructures with parallel and perpendicular cylinders, noncylindrical structures such as parallel lamellae and parallel perforated lamellae. The formation of the various confined nanostructures is further analyzed by calculating structural characteristics such as the mean square end-to-end distance of the diblock copolymers and the nematic order parameter.