Step Edges in Thin Films of Lamellar-Forming Diblock Copolymer

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.

Hiking down the Free Energy Landscape Using Sequential Solvent and Thermal Processing for Versatile Ordering of Block Copolymer Films

The kinetics and morphology of the ordering of block copolymer (BCP) films are highly dependent on the processing pathway, as the enthalpic and entropic forces driving the ordering processes can be quite different depending on process history. We may gain some understanding and control of this variability of BCP morphology with processing history through a consideration of the free energy landscape of the BCP material and a consideration of how the processing procedure moves the system through this energy landscape in a way that avoids having the system becoming trapped into well-defined metastable minima having a higher free energy than the target low free energy ordered structure. It is well known that standard thermal annealing (TA) of BCPs leads to structures corresponding to a well-defined stable free energy minimum; however, the BCP must be annealed for a very long time before the target low free energy structures can be achieved. Herein, we show that the same target low-energy structure can be achieved relatively quickly by subjecting as-cast films to an initial solvent annealing [direct immersion annealing (DIA) or solvent vapor annealing (SVA)] procedure, followed by a short period of TA. This process relies on lowering the activation energy barrier by reducing the glass-transition temperature through DIA (or SVA), followed by a multi-interface chain rearrangement through sequential TA. This energy landscape approach to ordering should be applicable to the process design for ordering many other complex materials.

Chemical Composition and Strain at Interfaces between Different Morphologies in Block Copolymer Thin Films

Transitional composition between two thin-film morphologies of the block copolymer, polystyrene-block-poly(tert-butyl acrylate) (PS-b-PtBuA), was investigated using near-field infrared spectroscopy and atomic force microscopy mechanical measurements. These techniques allowed block identification with nanoscale spatial resolution and elucidated the material's sub-surface composition. PS was found to form coronae around the PtBuA block in spherical valleys on flat areas of the film, and coronae of PtBuA surrounding the PS lamellae were observed at the edge of the polymer film, where parallel lamellae are formed. Furthermore, we found that the peak position and width varied by location, which may be a result of block composition, chain tension, or substrate interaction.

Boundary-directed epitaxy of block copolymers

Directed self-assembly of block copolymers (BCPs) enables nanofabrication at sub-10 nm dimensions, beyond the resolution of conventional lithography. However, directing the position, orientation, and long-range lateral order of BCP domains to produce technologically-useful patterns is a challenge. Here, we present a promising approach to direct assembly using spatial boundaries between planar, low-resolution regions on a surface with different composition. Pairs of boundaries are formed at the edges of isolated stripes on a background substrate. Vertical lamellae nucleate at and are pinned by chemical contrast at each stripe/substrate boundary, align parallel to boundaries, selectively propagate from boundaries into stripe interiors (whereas horizontal lamellae form on the background), and register to wide stripes to multiply the feature density. Ordered BCP line arrays with half-pitch of 6.4 nm are demonstrated on stripes >80 nm wide. Boundary-directed epitaxy provides an attractive path towards assembling, creating, and lithographically defining materials on sub-10 nm scales.

Field-Theoretic Simulations of the Distribution of Nanorods in Diblock Copolymer Thin Films

Using block copolymer microphases to guide the self-assembly of nanorods in thin films can give rise to polymeric materials with unique optical, thermal, and mechanical properties beyond those found in neat block copolymers. Often the design and manufacture of these materials require exquisite control of the nanorod distribution, which is experimentally challenging due to the large parameter space spanned by this class of materials. Simulation approaches, on the other hand, can access the thermodynamics that contribute to the nanorod distribution and hence offer valuable guidance toward the design and manufacture of the materials. In this work, we employ complex Langevin field-theoretic simulations to examine the thermodynamic forces that govern the assembly of nanorods in thin films of block copolymers with a particular focus on vertically oriented cylindrical and lamellar domains. Our simulations show that the nanorod geometry, the substrate selectivity for the distinct blocks of the copolymer, and the film thickness all play important roles in engineering both the nanorod orientation and spatial distribution in diblock copolymer thin films. In addition, we employ thermodynamic integration to examine how the nanorods alter the stability of vertical and horizontal domains in thin films, where we find that the tendency of the nanorods to stabilize a vertical orientation depends on both the film thickness and the nanorod concentration.

Finite volume method for self-consistent field theory of polymers: Material conservation and application

For the purpose of checking material conservation of various numerical algorithms used in the self-consistent-field theory (SCFT) of polymeric systems, we develop an algebraic method using matrix and bra-ket notation, which traces the Hermiticity of the product of the volume and evolution matrices. Algebraic tests for material conservation reveal that the popular pseudospectral method in the Cartesian grid conserves material perfectly, while the finite-volume method (FVM) is the proper tool when real-space SCFT with the Crank-Nicolson method is adopted in orthogonal coordinate systems. We also find that alternating direction implicit methods combined with the FVM exhibit small mass errors in the SCFT calculation. By introducing fractional cells in the FVM formulation, accurate SCFT calculations are performed for systems with irregular geometries and the results are consistent with previous experimental and theoretical works.

Solvent vapor annealing in block copolymer nanocomposite films: a dynamic mean field approach

Polymer nanocomposites are an important class of materials due to the nanoparticles' ability to impart functionality not commonly found in a polymer matrix, such as electrical conductivity or tunable optical properties. While the equilibrium properties of polymer nanocomposites can be treated using numerous theoretical and simulation approaches, in experiments the effects of processing and kinetic traps are significant and thus critical for understanding the structure and the functionality of polymer nanocomposites. However, simulation methods that can efficiently predict kinetically trapped and metastable structures of polymer nanocomposites are currently not common. This is particularly important in inhomogeneous polymers such as block copolymers, where techniques such as solvent vapor annealing are commonly employed to improve the long-range order. In this work, we introduce a dynamic mean field theory that is capable of predicting the result of processing the structure of polymer nanocomposites, and we demonstrate that our method accurately predicts the equilibrium properties of a model system more efficiently than a particle-based model. We subsequently use our method to predict the structure of block copolymer thin films with grafted nanoparticles after solvent annealing, where we find that the final distribution of the grafted nanoparticles can be controlled by varying the solvent evaporation rate. The extent to which the solvent evaporation rate can affect the final nanoparticle distribution in the film depends on the grafting density and the length of the grafted chains. Furthermore, the effects of the solvent evaporation rate can be anticipated from the equilibrium nanoparticle distribution in the swollen and dry states.

Structure, Stability, and Reorganization of 0.5 L0 Topography in Block Copolymer Thin Films

The structure, stability, and reorganization of lamella-forming block copolymer thin film surface topography ("islands" and "holes") were studied under boundary conditions driving the formation of 0.5 L₀ thick structures at short thermal annealing times. Self-consistent field theory predicts that the presence of one perfectly neutral surface renders 0.5 L₀ topography thermodynamically stable relative to 1 L₀ thick features, in agreement with previous experimental observations. The calculated through-film structures match cross-sectional scanning electron micrographs, collectively demonstrating the pinning of edge dislocations at the neutral surface. Remarkably, near-neutral surface compositions exhibit 0.5 L₀ topography metastability upon extended thermal treatment, slowly transitioning to 1 L₀ islands or holes as evidenced by optical and atomic force microscopy. Surface restructuring is rationalized by invoking commensurability effects imposed by slightly preferential surfaces. The results described herein clarify the impact of interfacial interactions on block copolymer self-assembly and solidify an understanding of 0.5 L₀ topography, which is frequently used to determine neutral surface compositions of considerable importance to contemporary technological applications.

Rapid ordering of block copolymer thin films

Block-copolymers self-assemble into diverse morphologies, where nanoscale order can be finely tuned via block architecture and processing conditions. However, the ultimate usage of these materials in real-world applications may be hampered by the extremely long thermal annealing times-hours or days-required to achieve good order. Here, we provide an overview of the fundamentals of block-copolymer self-assembly kinetics, and review the techniques that have been demonstrated to influence, and enhance, these ordering kinetics. We discuss the inherent tradeoffs between oven annealing, solvent annealing, microwave annealing, zone annealing, and other directed self-assembly methods; including an assessment of spatial and temporal characteristics. We also review both real-space and reciprocal-space analysis techniques for quantifying order in these systems.

Confinement effects on the miscibility of block copolymer blends

Thin films of long and short symmetric AB diblock copolymers are examined using self-consistent field theory (SCFT). We focus on hard confining walls with a preference for the A component, such that the lamellar domains orient parallel to the film with an even number ν of monolayers. For neat melts, confinement causes the lamellar period, D, to deviate from its bulk value, Db, in order to be commensurate with the film thickness, i.e., L = νD/2. For blends, however, the melt also has the option of macrophase separating into ν(l) large and ν((s)) small monolayers so as to provide a better fit, where L = ν(l)D(l)/2 + ν(s)D((s))/2. In addition to performing full SCFT calculations of the entire film, we develop a semi-analytical calculation for the coexistence of thick and thin monolayers that helps explain the complicated interplay between miscibility and commensurability.

Swelling of block copolymer nanoparticles: a process combining deformation and phase separation

Swelling of block copolymers is a complex process in which deformation and microphase separation couple together. Here we demonstrated that nanoparticles of block copolymers and polymer composites which have a large variety of phase separation patterns and different shapes can be generated through swelling process. Particularly, we focused on the swelling process of lamellae-forming diblock copolymer nanoparticles and first observed the formation of terrace edges in diblock copolymer nanoparticles as a metastable microstructure in swelling. Moreover, the trace amount of swelling solvent shows a significant influence on the shape of polymer nanoparticles, leading to block copolymer nanodisks and snowman-like composite nanoparticles.