Defectivity in Laterally Confined Lamella-Forming Diblock Copolymers: Thermodynamic and Kinetic Aspects

Droplet-like Defect Annihilation Mechanisms in Hexagonal Cylinder-Forming Block Copolymers

The annihilation of typical individual defects in hexagonal cylinder-forming block copolymers is investigated using the self-consistent field theory (SCFT) in conjunction with the string method. Usually, defect removal in two-dimensional hexagonal patterns involves reorganizing the cylindrical domains. Unlike atoms in solid crystals, the self-assembled cylindrical domains of block copolymers are "soft". Thus, the kinetic motions of the cylindrical domains resemble liquid droplets. Dislocations in hexagonal patterns are eliminated via creating and removing cylindrical domains. Our results show that new cylindrical domains are created via either a nucleation-like process or a fission-like process, whereas excessive domains are eliminated via a fusion-like or evaporation-like process. For weakly segregated block copolymers, the nucleation-like and evaporation-like processes are preferred.

Nonequilibrium Processes in Polymer Membrane Formation: Theory and Experiment

Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processes─evaporation, solvent-nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrest─that dictates the complex structure of the membrane on different scales.

Self-consistent field theory study of polymer-mediated colloidal interactions in solution: Depletion effects and induced forces

Polymer-mediated colloidal interactions control the stability and phase properties of colloid-polymer mixtures that are critical for a wide range of important applications. In this work, we develop a versatile self-consistent field theory (SCFT) approach to study this type of interaction based on a continuum confined polymer solution model with explicit solvent and confining walls. The model is formulated in the grand canonical ensemble, and the potential of mean force for the polymer-mediated interaction is computed from grand potentials. We focus on the case of non-adsorbing linear polymers and present a systematic investigation on depletion effects using SCFT. The properties of confined polymer solutions are probed, and mean-field profiles of induced interactions are shown across different physical regimes. We expose a detailed parametric dependence of the interaction, concerning both attractive and repulsive parts, on polymer concentration, chain length, and solvent quality and explore the effect of wall surface roughness, demonstrating the versatility of the proposed approach. Our findings show good agreement with previous numerical studies and experiments, yet extend prior work to new regimes. Moreover, the mechanisms of depletion attraction and repulsion, along with the influence of individual control factors, are further discussed. We anticipate that this study will provide useful insights into depletion forces and can be readily extended to examine more complex colloid-polymer mixtures.

Understanding Kinetics of Defect Annihilation in Chemoepitaxy-Directed Self-Assembly

Directed self-assembly (DSA) of block copolymers (BCP) has attracted considerable interest from the semiconductor industry because it can achieve semiconductor-relevant structures with a relatively simple process and low cost. However, the self-assembling structures can become kinetically trapped into defective states, which greatly impedes the implementation of DSA in high-volume manufacturing. Understanding the kinetics of defect annihilation is crucial to optimizing the process and eventually eliminating defects in DSA. Such kinetic experiments, however, are not commonly available in academic laboratories. To address this challenge, we perform a kinetic study of chemoepitaxy DSA in a 300 mm wafer fab, where the complete defectivity information at various annealing conditions can be readily captured. Through extensive statistical analysis, we reveal the statistical model of defect annihilation in DSA for the first time. The annihilation kinetics can be well described by a power law model, indicating that all dislocations can be removed by sufficiently long annealing time. We further develop image analysis algorithms to analyze the distribution of dislocation size and configurations and discover that the distribution stays relatively constant over time. The defect distribution is determined by the role of the guiding stripe, which is found to stabilize the defects. Although this study is based on polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA), we anticipate that these findings can be readily applied to other BCP platforms as well.

Lithographically Defined Cross-Linkable Top Coats for Nanomanufacturing with High-χ Block Copolymers

The directed self-assembly (DSA) of block copolymers (BCPs) is a powerful method for the manufacture of high-resolution features. Critical issues remain to be addressed for successful implementation of DSA, such as dewetting and controlled orientation of BCP domains through physicochemical manipulations at the BCP interfaces, and the spatial positioning and registration of the BCP features. Here, we introduce novel top-coat (TC) materials designed to undergo cross-linking reactions triggered by thermal or photoactivation processes. The cross-linked TC layer with adjusted composition induces a mechanical confinement of the BCP layer, suppressing its dewetting while promoting perpendicular orientation of BCP domains. The selection of areas of interest with perpendicular features is performed directly on the patternable TC layer via a lithography step and leverages attractive integration pathways for the generation of locally controlled BCP patterns and nanostructured BCP multilayers.

Kinetic Pathways of Block Copolymer Directed Self-Assembly: Insights from Efficient Continuum Modeling

We introduce a computationally efficient continuum technique to simulate the complex kinetic pathways of block copolymer self-assembly. Subdiffusive chain dynamics is taken into account via nonlocal Onsager coefficients. An application to directed self-assembly of thin films of diblock copolymers on patterned substrates reveals the conditions under which experimentally observed metastable structures intervene in the desired thin-film morphology. The approach generalizes easily to multiblock copolymers and more complex guiding patterns on the substrate, and its efficiency allows for the systematic optimization of guiding patterns and process conditions.

Thermodynamics and ordering kinetics in asymmetric PS-b-PMMA block copolymer thin films

The ordering kinetics of standing cylinder-forming polystyrene-block-poly(methyl methacrylate) block copolymers (molecular weight: 39 kg mol^-1) close to the order-disorder transition is experimentally investigated following the temporal evolution of the correlation length at different annealing temperatures. The growth exponent of the grain-coarsening process is determined to be 1/2, signature of a curvature-driven ordering mechanism. The measured activation enthalpy and the resulting Meyer-Neldel temperature for this specific copolymer along with the data already known for PS-b-PMMA block copolymers in strong segregation limit allow investigation of the interplay between the ordering kinetics and the thermodynamic driving force during the grain coarsening. These findings unveil various phenomena concomitantly occurring during the thermally activated ordering kinetics at segmental, single chain, and collective levels.

Lattice self-consistent field calculations of confined symmetric block copolymers of various chain architectures

The effects of chain architecture and confinement on the structure and orientation of lamellae formed by incompressible and symmetric AB-type block copolymer melts confined between two parallel and identical surfaces are investigated using self-consistent field calculations on a simple cubic lattice. Five systems of various chain architectures (linear, ring, and star) and lengths are studied, with their bulk lamellar period L₀ chosen such that they have comparable L₀/R_g, where R_g denotes the ideal-chain radius of gyration. For thin films of thickness D = L₀ confined between two neutral surfaces, we define the rescaled volume fraction profiles of A, B, chain end, and joint segments in the parallel and perpendicular lamellae such that these profiles can be directly compared among the five systems to quantitatively reveal the interplay between the chain-end enrichment near confining surfaces and the surface-induced A-B compatibilization, and how such interplay is affected by the chain architectures (for example, the chain-crowding effects in the star block copolymers). The effects of D and surface preference for one of the blocks are also investigated.

Role of Defects in Achieving Highly Asymmetric Lamellar Self-Assembly in Block Copolymer/Homopolymer Blends

Lamellar structure is a prominent state in soft condensed matter. Swelling lamellar layers to highly asymmetric structures by a second component is a facile, cost-effective strategy to impart materials with adaptive size and tunable properties. One key question that remains unsolved is how defects form and affect the asymmetric lamellar order. This study unravels the role of defects by swelling a miktoarm block copolymer with a homopolymer. Ordered lamellae first lose translational order by a significant increase in the number of dislocations and then lose orientational order by the generation of disclinations. The homopolymers are not uniformly distributed in defective lamellae and primarily segregate in the vicinity of disclination cores. The free energy of defects is mainly contributed by molecular splay and significantly alleviated by an increased radius of local curvature. This study provides direct evidence to reveal the role of defects and lamellar order in block copolymer/homopolymer blends and also sheds light on understanding analogous structural transitions in other soft systems, including lyotropic liquid crystals, phospholipid membranes, and polymer nanocomposites.

Strain-Dependent Nanowrinkle Confinement of Block Copolymers

This paper describes an all-soft, templated assembly of block copolymers (BCPs) with programmable alignment. Using polymeric nanowrinkles as a confining scaffold, poly(styrene)-block-poly(dimethylsiloxane) (PS-b-PDMS) BCPs were assembled to be parallel or perpendicular to the wrinkle orientation by manipulating the substrate strain. Self-consistent field theory modeling revealed that wrinkle curvature and surface affinity govern the BCP structural formation. Furthermore, control of BCP alignment was demonstrated for complex wrinkle geometries, various copolymer molecular weights, and functional wrinkle skin layers. This integration of BCP patterning with flexible 3D architectures offers a promising nanolithography approach for next-generation soft electronics.

The influence of curvature on domain distribution in binary mixture membranes

Curvature-induced domain sorting, a strategy exploited by cells to organize membrane components, is a promising mechanism to control self-assembly of materials. To understand this phenomenon, this work explores the effects of curvature on component rearrangement in thin polymer films and lipid bilayers supported on sinusoidal substrates. Specifically, self-consistent field theory (SCFT) was used to study the spatial distribution of polymers in blends containing conformationally asymmetric chains. In addition, coarse-grained molecular dynamics (MD) simulations were used to probe the arrangement of rigid lipid domains in a relatively soft lipid matrix. Besides the expected preference of rigid species localizing in regions with low mean curvature, both systems exhibit unexpected localization of rigid components in comparatively high curvature regions. The origins of this unexpected sorting are discussed in terms of entropic and enthalpic contributions. In summary, this study demonstrates that domain distribution strongly depends on local topography and further highlights the collective effects that thermodynamic forces have on the morphological behavior of membranes.

Shear-solvo defect annihilation of diblock copolymer thin films over a large area

Achieving defect-free block copolymer (BCP) nanopatterns with a long-ranged orientation over a large area remains a persistent challenge, impeding the successful and widespread application of BCP self-assembly. Here, we demonstrate a new experimental strategy for defect annihilation while conserving structural order and enhancing uniformity of nanopatterns. Sequential shear alignment and solvent vapor annealing generate perfectly aligned nanopatterns with a low defect density over centimeter-scale areas, outperforming previous single or sequential combinations of annealing. The enhanced order quality and pattern uniformity were characterized in unprecedented detail via scattering analysis and incorporating new mathematical indices using elaborate image processing algorithms. In addition, using an advanced sampling method combined with a coarse-grained molecular simulation, we found that domain swelling is the driving force for enhanced defect annihilation. The superior quality of large-scale nanopatterns was further confirmed with diffraction and optical properties after metallized patterns, suggesting strong potential for application in optoelectrical devices.

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.

Defect Annihilation Pathways in Directed Assembly of Lamellar Block Copolymer Thin Films

Defects in highly ordered self-assembled block copolymers represent an important roadblock toward the adoption of these materials in a wide range of applications. This work examines the pathways for annihilation of defects in symmetric diblock copolymers in the context of directed assembly using patterned substrates. Past theoretical and computational studies of such systems have predicted minimum free energy pathways that are characteristic of an activated process. However, they have been limited to adjacent dislocations with opposite Burgers vectors. By relying on a combination of advanced sampling techniques and particle-based simulations, this work considers the long-range interaction between dislocation pairs, both on homogeneous and nanopatterned substrates. As illustrated here, these interactions are central to understanding the defect structures that are most commonly found in applications and in experimental studies of directed self-assembly. More specifically, it is shown that, for dislocation dipoles separated by several lamellae, multiple consecutive free energy barriers lead to effective kinetic barriers that are an order of magnitude larger than those originally reported in the literature for tightly bound dislocation pairs. It is also shown that annihilation pathways depend strongly on both the separation between dislocations and their relative position with respect to the substrate guiding stripes used to direct the assembly.

Nano-confinement of block copolymers in high accuracy topographical guiding patterns: modelling the emergence of defectivity due to incommensurability

Extreme ultraviolet interference lithography (EUV-IL) is used to manufacture topographical guiding patterns to direct the self-assembly of block copolymers. High-accuracy silicon oxide-like patterns with trenches ranging from 68 nm to 117 nm width are fabricated by exposing a hydrogen silsesquioxane (HSQ) resist layer using EUV-IL. We investigate how the accuracy, the low line width roughness and the low line edge roughness of the resulting patterns allow achieving DSA line/space patterns of a PS-b-PMMA (polystyrene-block-poly methyl methacrylate) block copolymer of 11 nm half-pitch with low defectivity. We conduct an in-depth study of the dependence of the DSA pattern morphology on the trench width and on how the neutral brush covers the guiding pattern. We identify the relation between trench width and the emergence of defects with nanometer precision. Based on these studies, we develop a model that extends available free energy models, which allows us to predict the patterning process window.

Engineering the Kinetics of Directed Self-Assembly of Block Copolymers toward Fast and Defect-Free Assembly

Directed self-assembly (DSA) of block copolymers (BCPs) can achieve perfectly aligned structures at thermodynamic equilibrium, but the self-assembling morphology can become kinetically trapped in defective states. Understanding and optimizing the kinetic pathway toward domain alignment is crucial for enhancing process throughput and lowering defectivity to levels required for semiconductor manufacturing, but there is a dearth of experimental, three-dimensional studies of the kinetic pathways in DSA. Here, we combined arrested annealing and TEM tomography to probe the kinetics and structural evolution in the chemoepitaxy DSA of PS- b-PMMA with density multiplication. During the initial stages of annealing, BCP domains developed independently at first, with aligned structures at the template interface and randomly oriented domains at the top surface. As the grains coarsened, the assembly became cooperative throughout the film thickness, and a metastable stitch morphology was formed, representing a kinetic barrier. The stitch morphology had a three-dimensional structure consisting of both perpendicular and parallel lamellae. On the basis of the mechanistic information, we studied the effect of key design parameters on the kinetics and evolution of structures in DSA. Three types of structural evolutions were observed at different film thicknesses: (1) immediate alignment and fast assembly when thickness < L₀ ( L₀ = BCP natural periodicity); (2) formation of stitch morphology for 1.25-1.45 L₀; (3) fingerprint formation when thickness >1.64 L₀. We found that the DSA kinetics can be significantly improved by avoiding the formation of the metastable stitch morphology. Increasing template topography also enhanced the kinetics by increasing the PMMA guiding surface area. A combination of 0.75 L₀ BCP thickness and 0.50 L₀ template topography achieved perfect alignment over 100 times faster than the baseline process. This research demonstrates that an improved understanding of the evolution of structures during DSA can significantly improve the DSA process.

Defect Patterns from Controlled Heterogeneous Nucleations by Polygonal Confinements

Defects are often observed in crystalline structures. To regulate the formation or annihilation of defects presents an interesting question. In this work, we propose a method to fabricate defect patterns composed of regularly distributed steady "programmed defects", which is proceeded via the heterogeneous nucleation of a hexagonal pattern from a homogeneous state. The nucleation process occurring in a model system of AB-diblock/C-homopolymer blends under polygonal confinement is modeled by the time-dependent Ginzburg-Landau theory and is simulated by the cell dynamics simulations. Specifically, we demonstrate the validity of this method by means of three polygonal confinements including square, pentagon, and octagon, which have mismatched angles with the hexagonal lattice. Each corner or side of the polygons induces a nucleation event separately. Two nucleated domain grains by two neighboring corners or sides exhibit incommensurate orientations, and thus their merging leads to a radial line of clustered defects in the form of five-seven pairs. As a result, these radial lines constitute a radial pattern of defects, and their number is equal to the side number of the polygon. The distance of five-seven defect pairs is dictated by the incommensurate angle between two neighboring grains, which is similar to that of defects in hard crystals. This method can be extended to fabricate diverse defect patterns by programming the nucleation agents beyond simple polygonal confinements.

Effect of Preferential Orientation of Lamellae in the Interfacial Region between a Block Copolymer-based Pressure-Sensitive Adhesive and a Solid Substrate on the Peel Strength

We have investigated the relationship between the peel strength of a block copolymer-based pressure-sensitive adhesive comprising of poly(methyl methacrylate) (PMMA) and poly(n-butyl acrylate) (PnBA) components from the substrate and the microdomain orientations in the interfacial region between the adhesive and the substrate. For the PMMA substrate, the PMMA component in the adhesive with a strong affinity for the substrate is attached to the surface of the substrate during an aging process of the sample at 140 °C. Next, the PMMA layer adjacent to the substrate surface is overlaid with a PnBA layer, which gets covalently connected, resulting in the horizontal alignment of the lamellae in the interfacial region. The peel strength of the adhesive substantially increases during aging at 140 °C, which takes the same time as the completion of the horizontally oriented lamellar structure. However, in the case of the polystyrene (PS) substrate, both the components in the adhesive repel the substrate, leading to the formation of the vertically oriented lamellar structure. As a result, the peel strength of the adhesive with respect to its PS substrate does not entirely increase on aging. It is suggested that the peel strength of the adhesive is highly correlated with the interfacial energy between the adhesive and substrate, which can be estimated from the microdomain orientation in the interfacial region.

Rapid Ordering in "Wet Brush" Block Copolymer/Homopolymer Ternary Blends

The ubiquitous presence of thermodynamically unfavored but kinetically trapped topological defects in nanopatterns formed via self-assembly of block copolymer thin films may prevent their use for many envisioned applications. Here, we demonstrate that lamellae patterns formed by symmetric polystyrene-block-poly(methyl methacrylate) diblock copolymers self-assemble and order extremely rapidly when the diblock copolymers are blended with low molecular weight homopolymers of the constituent blocks. Being in the "wet brush" regime, the homopolymers uniformly distribute within their respective self-assembled microdomains, preventing increases in domain widths. An order-of-magnitude increase in topological grain size in blends over the neat (unblended) diblock copolymer is achieved within minutes of thermal annealing as a result of the significantly higher power law exponent for ordering kinetics in the blends. Moreover, the blends are demonstrated to be capable of rapid and robust domain alignment within micrometer-scale trenches, in contrast to the corresponding neat diblock copolymer. These results can be attributed to the lowering of energy barriers associated with domain boundaries by bringing the system closer to an order-disorder transition through low molecular weight homopolymer blending.

Pathway-engineering for highly-aligned block copolymer arrays

While the ultimate driving force in self-assembly is energy minimization and the corresponding evolution towards equilibrium, kinetic effects can also play a very strong role. These kinetic effects, such as trapping in metastable states, slow coarsening kinetics, and pathway-dependent assembly, are often viewed as complications to be overcome. Here, we instead exploit these effects to engineer a desired final nano-structure in a block copolymer thin film, by selecting a particular ordering pathway through the self-assembly energy landscape. In particular, we combine photothermal shearing with high-temperature annealing to yield hexagonal arrays of block copolymer cylinders that are aligned in a single prescribed direction over macroscopic sample dimensions. Photothermal shearing is first used to generate a highly-aligned horizontal cylinder state, with subsequent thermal processing used to reorient the morphology to the vertical cylinder state in a templated manner. Finally, we demonstrate the successful transfer of engineered morphologies into inorganic replicas.

Flash Light Millisecond Self-Assembly of High χ Block Copolymers for Wafer-Scale Sub-10 nm Nanopatterning

One of the fundamental challenges encountered in successful incorporation of directed self-assembly in sub-10 nm scale practical nanolithography is the process compatibility of block copolymers with a high Flory-Huggins interaction parameter (χ). Herein, reliable, fab-compatible, and ultrafast directed self-assembly of high-χ block copolymers is achieved with intense flash light. The instantaneous heating/quenching process over an extremely high temperature (over 600 °C) by flash light irradiation enables large grain growth of sub-10 nm scale self-assembled nanopatterns without thermal degradation or dewetting in a millisecond time scale. A rapid self-assembly mechanism for a highly ordered morphology is identified based on the kinetics and thermodynamics of the block copolymers with strong segregation. Furthermore, this novel self-assembly mechanism is combined with graphoepitaxy to demonstrate the feasibility of ultrafast directed self-assembly of sub-10 nm nanopatterns over a large area. A chemically modified graphene film is used as a flexible and conformal light-absorbing layer. Subsequently, transparent and mechanically flexible nanolithography with a millisecond photothermal process is achieved leading the way for roll-to-roll processability.

Thickness-dependence of block copolymer coarsening kinetics

Despite active research, many fundamental aspects of block copolymer ordering remain unresolved. We studied the thickness-dependence of block copolymer grain coarsening kinetics, and find that thinner films order more rapidly than thicker films. Bilayer films, or monolayers with partial layers of islands, order more slowly than monolayers because of the greater amount of material that must rearrange in a coordinated fashion. Sub-monolayer films order much more rapidly than monolayers, exhibiting considerably smaller activation energies, as well as larger exponents for the time-growth power-law. Using molecular dynamics simulations, we directly study the motion of defects in these film regimes. We attribute the enhanced grain growth in sub-monolayers to the film boundaries, where defects can be spontaneously eliminated. The boundaries thus act as efficient sinks for morphological defects, pointing towards methods for engineering rapid ordering of self-assembling thin films.

Non-native three-dimensional block copolymer morphologies

Self-assembly is a powerful paradigm, wherein molecules spontaneously form ordered phases exhibiting well-defined nanoscale periodicity and shapes. However, the inherent energy-minimization aspect of self-assembly yields a very limited set of morphologies, such as lamellae or hexagonally packed cylinders. Here, we show how soft self-assembling materials-block copolymer thin films-can be manipulated to form a diverse library of previously unreported morphologies. In this iterative assembly process, each polymer layer acts as both a structural component of the final morphology and a template for directing the order of subsequent layers. Specifically, block copolymer films are immobilized on surfaces, and template successive layers through subtle surface topography. This strategy generates an enormous variety of three-dimensional morphologies that are absent in the native block copolymer phase diagram.

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.

Recent Developments in Fully Fluctuating Field-Theoretic Simulations of Polymer Melts and Solutions

We review the latest developments in computational methods for direct simulation of fully fluctuating field theories of polymeric assemblies. In this context, we describe a newly developed theoretical and computational framework for accurately computing fluctuation-corrected phase diagrams of mesostructured polymer systems and report the first such complete phase diagram for a diblock copolymer melt. The method is based on complex Langevin sampling of a UV regularized field-theoretic model, with Helmholtz free energies computed using thermodynamic integration. UV regularization ensures that the free energies do not have an arbitrary reference; they can be compared between incommensurate phases, permitting for the first time the computation of order-order transitions with fluctuation corrections. We further demonstrate that computed free energies are accurate in the disordered phase by comparison to perturbation theory on the one-loop level. Importantly, we note that our method uses no uncontrolled approximations beyond the initial definition of a coarse-grained molecular model for the polymer melt or solution. The method can be applied straightforwardly to melts and solutions containing multiple species with diverse polymer architectures.

Order-disorder transition in thin films of horizontally-oriented cylinder-forming block copolymers: thermal fluctuations vs. preferential wetting

We present experimental and theoretical investigations of the order-disorder transition (ODT) in thin films of cylinder-forming diblock copolymers with asymmetric wetting conditions. Grazing incidence small-angle X-ray scattering (GISAXS) was implemented to determine the ODT temperatures (TODT) for poly(styrene-b-2-vinyl pyridine) (PS-P2VP) block copolymer thin films on a P2VP-preferential silicon substrate. Specifically, films consisting of multilayers of horizontally-oriented cylindrical structures (from 1- to 9-layers) were tested. We find that films with more than 2 cylindrical layers have a TODT comparable to the bulk case. However, TODT decreases as the film becomes thinner and the monolayer system has an ODT 30 °C below the bulk. Using self-consistent field theory (SCFT), we studied the ordering in corresponding thin films with asymmetric (top and bottom surface) wetting conditions. Surprisingly, SCFT is found to predict an opposite trend in TODT with film thickness than observed experimentally. Field-theoretic simulations with complex Langevin sampling were employed to resolve this discrepancy and demonstrate that thermal fluctuations in the PS-P2VP thin-film system dominate its ordering behavior in monolayer and bilayer films.

Sequential Nanopatterned Block Copolymer Self-Assembly on Surfaces

Bottom-up self-assembly of high-density block-copolymer nanopatterns is of significant interest for a range of technologies, including memory storage and low-cost lithography for on-chip applications. The intrinsic or native spacing of a given block copolymer is dependent upon its size (N, degree of polymerization), composition, and the conditions of self-assembly. Polystyrene-block-polydimethylsiloxane (PS-b-PDMS) block copolymers, which are well-established for the production of strongly segregated single-layer hexagonal nanopatterns of silica dots, can be layered sequentially to produce density-doubled and -tripled nanopatterns. The center-to-center spacing and diameter of the resulting silica dots are critical with respect to the resulting double- and triple-layer assemblies because dot overlap reduces the quality of the resulting pattern. The addition of polystyrene (PS) homopolymer to PS-b-PDMS reduces the size of the resulting silica dots but leads to increased disorder at higher concentrations. The quality of these density-multiplied patterns can be calculated and predicted using parameters easily derived from SEM micrographs of corresponding single and multilayer patterns; simple geometric considerations underlie the degree of overlap of dots and layer-to-layer registration, two important factors for regular ordered patterns, and clearly defined dot borders. Because the higher-molecular-weight block copolymers tend to yield more regular patterns than smaller block copolymers, as defined by order and dot circularity, this sequential patterning approach may provide a route toward harnessing these materials, thus surpassing their native feature density.

Tuning phase structures of a symmetrical diblock copolymer with a patterned electric field

Electric fields can induce the orientation of the phase interfaces of block copolymers and provide a potential method to tune polymer phase structures for nanomaterial manufacture. In this work, we applied self-consistent field theory to study the self-assembly of a diblock copolymer confined between two parallel neutral substrates on which a set of electrodes was imposed to form a patterned electric field. The results showed that an alternatively distributed electric field can induce the formation of a parallel lamellar phase structure, which exists stably only in the system with selective substrates. The phase structure was proved to be sensitive to the characteristics of the electric field distribution, such as the strength of the electric field, the size and position of the electrodes, and the corresponding phase diagram was calculated in detail. The transition pathway of the phase structure from the perpendicular layered phase to the parallel layered phase was further analysed using the minimum energy path method. It is shown that the path and the active energy barrier of the phase transition depend on the electric field strength. Compound electric field patterns that can be designed to control the formation of novel and complex microphase structures were also examined.