Dynamics of pattern coarsening in a two-dimensional smectic system

Active smectics on a sphere

The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e. the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles.

Complex-tensor theory of simple smectics

Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials - they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.

Priming self-assembly pathways by stacking block copolymers

Block copolymers spontaneously self-assemble into well-defined nanoscale morphologies. Yet equilibrium assembly gives rise to a limited set of structures. Non-equilibrium strategies can, in principle, expand diversity by exploiting self-assembly's responsive nature. In this vein, we developed a pathway priming strategy combining control of thin film initial configurations and ordering history. We sequentially coat distinct materials to form prescribed initial states, and use thermal annealing to evolve these manifestly non-equilibrium states through the assembly landscape, traversing normally inaccessible transient structures. We explore the enormous associated hyperspace, spanning processing (annealing temperature and time), material (composition and molecular weight), and layering (thickness and order) dimensions. We demonstrate a library of exotic non-native morphologies, including vertically-oriented perforated lamellae, aqueduct structures (vertical lamellar walls with substrate-pinned perforations), parapets (crenellated lamellae), and networks of crisscrossing lamellae. This enhanced structural control can be used to modify functional properties, including accessing regimes that surpass their equilibrium analogs.

Solvent-assisted self-assembly of block copolymer thin films

Solvent-assisted block copolymer self-assembly is a compelling method for processing and advancing practical applications of these materials due to the exceptional level of the control of BCP morphology and significant acceleration of ordering kinetics. Despite substantial experimental and theoretical efforts devoted to understanding of solvent-assisted BCP film ordering, the development of a universal BCP patterning protocol remains elusive; possibly due to a multitude of factors which dictate the self-assembly scenario. The aim of this review is to aggregate both seminal reports and the latest progress in solvent-assisted directed self-assembly and to provide the reader with theoretical background, including the outline of BCP ordering thermodynamics and kinetics phenomena. We also indicate significant BCP research areas and emerging high-tech applications where solvent-assisted processing might play a dominant role.

Equilibrium phases and domain growth kinetics of calamitic liquid crystals

The anisotropic shape of calamitic liquid crystal (LC) particles results in distinct values of energy when the nematogens are placed side by side or end to end. This anisotropy in energy which is governed by a parameter κ^{'} has deep consequences on equilibrium and nonequilibrium properties. Using the Gay-Berne (GB) model, which exhibits the nematic (Nm) as well as the low-temperature smectic (Sm) order, we undertake large-scale Monte Carlo and molecular dynamics simulations to probe the effect of κ^{'} on the equilibrium phase diagram and the nonequilibrium domain growth following a quench in the temperature T or coarsening. There are two transitions in the GB model: (i) isotropic to Nm at T_{c}^{1} and (ii) Nm to Sm at T_{c}^{2}<T_{c}^{1}. κ^{'} decreases T_{c}^{1} significantly but has relatively little effect on T_{c}^{2}. Domain growth in the Nm phase exhibits the well-known Lifshitz-Allen-Cahn (LAC) law, L(t)∼t^{1/2} and the evolution is via annihilation of string defects. The system exhibits dynamical scaling that is also robust with respect to κ^{'}. We find that the Sm phase at the quench temperatures T (T>T_{c}^{1}→T<T_{c}^{2}) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers (SmB-H phase). Coarsening in this phase exhibits a striking two-timescale scenario: First, the LC molecules align and develop orientational order (or nematicity), followed by the emergence of the characteristic layering (or smecticity) along with the hexatic bond-orientational-order within the layers. Consequently, the growth follows the LAC law L(t)∼t^{1/2} at early times and then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest that L(t)∼t^{1/4} in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes and the scaling function is universal. The dynamics is also robust with respect to changes in κ^{'}, but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to the Sm phase even with other kinds of local order within the Sm layers.

Pathway-Dependent Grain Coarsening of Block Copolymer Patterns under Controlled Solvent Evaporation

Solvent evaporation annealing (SEA) is a straightforward, single-step casting and annealing method of block copolymers (BCP) processing yielding large-grained morphologies in a very short time. Here, we present a quantitative analysis of BCP grain-coarsening in thin films under controlled evaporation of the solvent. Our study is aimed at understanding time and BCP concentration influence on the rate of the lateral growth of BCP grains. By systematically investigating the coarsening kinetics at various BCP concentrations, we observed a steeply decreasing exponential dependence of the kinetics power-law time exponent on polymer concentration. We used this dependence to formulate a mathematical model of BCP ordering under nonstationary conditions and a 2D, time- and concentration-dependent coarsening rate diagram, which can be used as an aid in engineering the BCP processing pathway in SEA and also in other directed self-assembly methods that utilize BCP-solvent interactions such as solvent vapor annealing.

Derivation of coarse-grained force fields for buckling-induced topological defects of liquid crystals

Microscopic details of buckling-induced topological defects are required for molecular design of smectic liquid crystals to control buckling instability of the layers. In this study, we present a multiobjective optimization method to derive the coarse-grained (CG) force fields with sufficiently precise buckling characteristics including the molecular details for molecular dynamics (MD) simulations. We perform CGMD simulations of buckling deformation at sample points in the CG force field parameter space, from which the response surfaces of objective functions such as the scalar orientational order parameters, critical angles of layer collapse, and radial distribution functions are estimated. Since not all objective functions can be optimized simultaneously, we use a genetic algorithm to calculate the Pareto set of optimal solutions. We select the models with different molecular head-tail symmetries to study buckling deformation. The extracted CG model successfully reproduces the buckling deformation in terms of the collapse of smectic layers through the generation of dislocations with dipole disclinations. We also find that the molecular symmetry is a dominant factor to control the class of the buckling-induced dislocations.

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.

Self-assembly of block copolymers under non-isothermal annealing conditions as revealed by grazing-incidence small-angle X-ray scattering

An accurate knowledge of the parameters governing the kinetics of block copolymer self-assembly is crucial to model the time- and temperature-dependent evolution of pattern formation during annealing as well as to predict the most efficient conditions for the formation of defect-free patterns. Here, the self-assembly kinetics of a lamellar PS-b-PMMA block copolymer under both isothermal and non-isothermal annealing conditions are investigated by combining grazing-incidence small-angle X-ray scattering (GISAXS) experiments with a novel modelling methodology that accounts for the annealing history of the block copolymer film before it reaches the isothermal regime. Such a model allows conventional studies in isothermal annealing conditions to be extended to the more realistic case of non-isothermal annealing and prediction of the accuracy in the determination of the relevant parameters, namely the correlation length and the growth exponent, which define the kinetics of the self-assembly.

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.

Reorientation of Polymers in an Applied Electric Field for Electrochemical Sensors

This mini review investigates the relationship and interactions of polymers under an applied electric field (AEF) for sensor applications. Understanding how and why polymers are reoriented and manipulated by under an AEF is essential for future growth in polymer-based electrochemical sensors. Examples of polymers that can be manipulated in an AEF for sensor applications are provided. Current methods of monitoring polymer reorientation will be described, but new techniques are needed characterize polymer response to various AEF stimuli. The unique and reproducible stimuli response of polymers elicited by an AEF has significant potential for growth in the sensing community.

Strategies for Increasing the Rate of Defect Annihilation in the Directed Self-Assembly of High-χ Block Copolymers

Directed self-assembly (DSA) of high-χ block copolymer thin films is a promising approach for nanofabrication of features with length scale below 10 nm. Recent work has highlighted that kinetics are of crucial importance in determining whether a block copolymer film can self-assemble into a defect-free ordered state. In this work, different strategies for improving the rate of defect annihilation in the DSA of a silicon-containing, high-χ block copolymer film were explored. Chemo-epitaxial DSA of poly(4-methoxystyrene-block-4-trimethylsilylstyrene) with 5× density multiplication was implemented on 300 mm wafers by using production level nanofabrication tools, and the influence of different processes and material parameters on dislocation defect density was studied. It was observed that only at sufficiently low χN can the block copolymer assemble into well-aligned patterns within a practical time frame. In addition, there is a clear correlation between the rate of the lamellar grain coarsening in unguided self-assembly and the rate of dislocation annihilation in DSA. For a fixed chemical pattern, the density of kinetically trapped dislocation defects can be predicted by measuring the correlation length of the unguided self-assembly under the same process conditions. This learning enables more efficient screening of block copolymers and annealing conditions by rapid analysis of block copolymer films that were allowed to self-assemble into unguided (commonly termed fingerprint) patterns.

Dynamic Ordering in High-χ Block Copolymer Lamellae Based on Cross-Sectional Orientational Alignment

Further development of next-generation block copolymer (BCP) lithography processes is contingent on comprehensive studies of the ordering dynamics of high-χ BCPs that can form sub-10 nm features on thin films. However, quantitative analyses of the degree of ordering on the surface and cross sections of thin films have been difficult to execute. To tackle this challenge, we employ a perpendicular lamella-forming high-χ BCP, poly(polyhedral oligomeric silsesquixone-block-2,2,2-trifluoroethyl methacrylate) (PMAPOSS-b-PTFEMA), and reveal that the high-χ PMAPOSS-b-PTFEMA requires three times the activation energy (E_a) compared to that of poly(styrene-block-methyl methacrylate) (PS-b-PMMA) for defect annihilation, at E_a = 2600 ± 420 kJ mol^-1, and a transition from a fast ordering regime with a growth exponent of Φ = 0.30 at lower orientational order parameters (ψ₂ < 0.36) to a slow ordering regime with Φ < 0.05 at ψ₂ > 0.36, where well-aligned lamellae restrict defect annihilations to enthalpically unfavorable glide mechanisms that require BCP intermixing.

Correlations between the leading Lyapunov vector and pattern defects for chaotic Rayleigh-Bénard convection

We probe the effectiveness of using topological defects to characterize the leading Lyapunov vector for a high-dimensional chaotic convective flow field. This is accomplished using large-scale parallel numerical simulations of Rayleigh-Bénard convection for experimentally accessible conditions. We quantify the statistical correlations between the spatiotemporal dynamics of the leading Lyapunov vector and different measures of the flow field pattern's topology and dynamics. We use a range of pattern diagnostics to describe the flow field structures which includes many of the traditional diagnostics used to describe convection as well as some diagnostics tailored to capture the dynamics of the patterns. We use the ideas of precision and recall to build a statistical description of each pattern diagnostic's ability to describe the spatial variation of the leading Lyapunov vector. The precision of a diagnostic indicates the probability that it will locate a region where the Lyapunov vector is larger than a threshold value. The recall of a diagnostic indicates its ability to locate all of the possible spatial regions where the Lyapunov vector is above threshold. By varying the threshold used for the Lyapunov vector magnitude, we generate precision-recall curves which we use to quantify the complex relationship between the pattern diagnostics and the spatiotemporally varying magnitude of the leading Lyapunov vector. We find that pattern diagnostics which include information regarding the flow history outperform pattern diagnostics that do not. In particular, an emerging target defect has the highest precision of all of the pattern diagnostics we have explored.

Coarsening dynamics in the Swift-Hohenberg equation with an external field

We study the Swift-Hohenberg equation (SHE) in the presence of an external field. The application of the field leads to a phase diagram with three phases, i.e., stripe, hexagon, and uniform. We focus on coarsening after a quench from the uniform to stripe or hexagon regions. For stripe patterns, we find that the length scale associated with the order-parameter structure factor has the same growth exponent (≃1/4) as for the SHE with zero field. The growth process is slower in the case of hexagonal patterns, with the effective growth exponent varying between 1/6 and 1/9, depending on the quench parameters. For deep quenches in the hexagonal phase, the growth process stops at late stages when defect boundaries become pinned.

Curvature as a Guiding Field for Patterns in Thin Block Copolymer Films

Experimental data on thin films of cylinder-forming block copolymers (BC)-free-standing BC membranes as well as supported BC films-strongly suggest that the local orientation of the BC patterns is coupled to the geometry in which the patterns are embedded. We analyze this phenomenon using general symmetry considerations and numerical self-consistent field studies of curved BC films in cylindrical geometry. The stability of the films against curvature-induced dewetting is also analyzed. In good agreement with experiments, we find that the BC cylinders tend to align along the direction of curvature at high curvatures. At low curvatures, we identify a transition from perpendicular to parallel alignment in supported films, which is absent in free-standing membranes. Hence both experiments and theory show that curvature can be used to manipulate and align BC patterns.

Scaling properties of ageing orientation fluctuations in stripe phases

We investigate the non-equilibrium dynamics of an ordered stripe-forming system free of topological defects. In particular, we study the ageing and the coarsening of orientation fluctuations parallel and perpendicular to the stripes via computer simulations based on a minimal phase-field model (model B with Coulomb interactions). Under the influence of noise, the stripe orientation field develops fluctuations parallel to the stripes, with the dominant modulation length λ*∥ increasing with time t as λ*∥ ∼ t1/4 and the correlation length perpendicular to the stripes ξ⊥θ increasing as ξ⊥θ ∼ t1/2. We explain these anisotropic coarsening dynamics with an analytic theory based on the linear elastic model for stripe displacements first introduced by Landau and Peierls. We thus obtain the scaling forms and the scaling exponents characterizing the correlation functions and the structure factor of the stripe orientation field. Our results reveal how the coarsening of orientation fluctuations prevents a periodically modulated phase free of topological defects from reaching equilibrium.

The smectic order of wrinkles

A thin elastic sheet lying on a soft substrate develops wrinkled patterns when subject to an external forcing or as a result of geometric incompatibility. Thin sheet elasticity and substrate response equip such wrinkles with a global preferred wrinkle spacing length and with resistance to wrinkle curvature. These features are responsible for the liquid crystalline smectic-like behaviour of such systems at intermediate length scales. This insight allows better understanding of the wrinkling patterns seen in such systems, with which we explain pattern breaking into domains, the properties of domain walls and wrinkle undulation. We compare our predictions with numerical simulations and with experimental observations.

A thin elastic sheet can develop wrinkles which arrange into patterns similar to those characteristic of liquid crystals. Here the authors use this analogy to propose a mapping between the elastic sheet problem and the smectic liquid crystal problem which can enable a better understanding of wrinkling.

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.

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.

Selective directed self-assembly of coexisting morphologies using block copolymer blends

Directed self-assembly (DSA) of block copolymers is an emergent technique for nano-lithography, but is limited in the range of structures possible in a single fabrication step. Here we expand on traditional DSA chemical patterning. A blend of lamellar- and cylinder-forming block copolymers assembles on specially designed surface chemical line gratings, leading to the simultaneous formation of coexisting ordered morphologies in separate areas of the substrate. The competing energetics of polymer chain distortions and chemical mismatch with the substrate grating bias the system towards either line/space or dot array patterns, depending on the pitch and linewidth of the prepattern. This is in contrast to the typical DSA, wherein assembly of a single-component block copolymer on chemical templates generates patterns of either lines/spaces (lamellar) or hexagonal dot arrays (cylinders). In our approach, the chemical template encodes desired local spatial arrangements of coexisting design motifs, self-assembled from a single, sophisticated resist.

There is a limited range of structures available in nanolithography using directed self-assembled block copolymers. Here, Black and co-workers expand directed self-assembly chemical patterning by using a blend of lamellar and cylinder forming block copolymers on surface chemical line gratings.

Enhanced Lateral Ordering in Cylinder Forming PS-b-PMMA Block Copolymers Exploiting the Entrapped Solvent

The self-assembly of block copolymer (BCP) thin films produces dense and ordered nanostructures. Their exploitation as templates for nanolithography requires the capability to control the lateral order of the nanodomains. Among a multiplicity of polymers, the widely studied all-organic polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) BCP can easily form nanodomains perpendicularly oriented with respect to the substrate, since the weakly unbalanced surface interactions are effectively neutralized by grafting to the substrate an appropriate poly(styrene-random-methyl methacrylate) P(S-r-MMA) random copolymer (RCP). This benefit along with the selective etching of the PMMA component and the chemical similarity with the standard photoresist materials deserved for PS-b-PMMA the role of BCP of choice for the technological implementation in nanolithography. This work demonstrates that the synergic effect of thermal annealing with the initial solvent naturally trapped in the basic RCP + BCP system after the deposition process can be exploited to enhance the lateral order. The solvent content embedded in the total RCP + BCP system can be tuned by changing the molecular weight and thus the thickness of the grafted RCP brush layer, without introducing external reservoirs or dedicated setup and/or systems. The appropriate supply of solvent supports a grain coarsening kinetics following a power law with a 1/3 growth exponent for standing hexagonally ordered cylinders.

Reordering transitions during annealing of block copolymer cylinder phases

While equilibrium block-copolymer morphologies are dictated by energy-minimization effects, the semi-ordered states observed experimentally often depend on the details of ordering pathways and kinetics. Here, we explore reordering transitions in thin films of block-copolymer cylinder-forming polystyrene-block-poly(methyl methacrylate). We observe several transient states as films order towards horizontally-aligned cylinders. In particular, there is an early-stage reorganization from randomly-packed cylinders into hexagonally-packed vertically-aligned cylinders; followed by a reorientation transition from vertical to horizontal cylinder states. These transitions are thermally activated. The growth of horizontal grains within an otherwise vertical morphology proceeds anisotropically, resulting in anisotropic grains in the final horizontal state. The size, shape, and anisotropy of grains are influenced by ordering history; for instance, faster heating rates reduce grain anisotropy. These results help elucidate aspects of pathway-dependent ordering in block-copolymer thin films.

Hexagonal phase ordering in strongly segregated copolymer films

Strongly segregated copolymer mixtures with uneven composition ratio can form hexagonally ordered thin films. A simplified model describing the size and position of micellelike clusters is derived, allowing for investigation of much larger domain sizes than in previous studies. Simulations of this model are performed to study the generation of large scale order and evolution of pattern defects. We find three temporal regimes exhibiting different scaling laws for orientational correlation length and defect number. In the early stage, topological defects are rapidly eliminated by pairwise annihilation. A slower intermediate stage is characterized by the migration of grain boundaries and the elimination of small grains. In the final stage, grain boundaries become pinned and the evolution halts. A scaling law for defect interaction is proposed which is consistent with the crossover between the first and second stages.

Wrinkles and splay conspire to give positive disclinations negative curvature

Recently, there has been renewed interest in the coupling between geometry and topological defects in crystalline and striped systems. Standard lore dictates that positive disclinations are associated with positive Gaussian curvature, whereas negative disclinations give rise to negative curvature. Here, we present a diblock copolymer system exhibiting a striped columnar phase that preferentially forms wrinkles perpendicular to the underlying stripes. In free-standing films this wrinkling behavior induces negative Gaussian curvature to form in the vicinity of positive disclinations.

Latent Alignment in Pathway-Dependent Ordering of Block Copolymer Thin Films

Block copolymers spontaneously form well-defined nanoscale morphologies during thermal annealing. Yet, the structures one obtains can be influenced by nonequilibrium effects, including processing history or pathway-dependent assembly. Here, we explore various pathways for ordering of block copolymer thin films, using oven-annealing, as well as newly disclosed methods for rapid photothermal annealing and photothermal shearing. We report the discovery of an efficient pathway for ordering self-assembled films: ultrarapid shearing of as-cast films induces "latent alignment" in the disordered morphology. Subsequent thermal processing can then develop this directly into a uniaxially aligned morphology with low defect density. This deeper understanding of pathway-dependence may have broad implications in self-assembly.

Thermally-induced transition of lamellae orientation in block-copolymer films on 'neutral' nanoparticle-coated substrates

Block-copolymer orientation in thin films is controlled by the complex balance between interfacial free energies, including the inter-block segregation strength, the surface tensions of the blocks, and the relative substrate interactions. While block-copolymer lamellae orient horizontally when there is any preferential affinity of one block for the substrate, we recently described how nanoparticle-roughened substrates can be used to modify substrate interactions. We demonstrate how such 'neutral' substrates can be combined with control of annealing temperature to generate vertical lamellae orientations throughout a sample, at all thicknesses. We observe an orientational transition from vertical to horizontal lamellae upon heating, as confirmed using a combination of atomic force microscopy (AFM), neutron reflectometry (NR) and rotational small-angle neutron scattering (RSANS). Using molecular dynamics (MD) simulations, we identify substrate-localized distortions to the lamellar morphology as the physical basis of the novel behavior. In particular, under strong segregation conditions, bending of horizontal lamellae induce a large energetic cost. At higher temperatures, the energetic cost of conformal deformations of lamellae over the rough substrate is reduced, returning lamellae to the typical horizontal orientation. Thus, we find that both surface interactions and temperature play a crucial role in dictating block-copolymer lamellae orientation. Our combined experimental and simulation findings suggest that controlling substrate roughness should provide a useful and robust platform for controlling block-copolymer orientation in applications of these materials.

Smectic block copolymer thin films on corrugated substrates

In this work we study equilibrium and non-equilibrium structures of smectic block copolymer thin films deposited on a topographically patterned substrate. A Brazovskii free energy model is employed to analyze the coupling between the smectic texture and the local mean curvature of the substrate. The substrate's curvature produces out-of-plane deformations of the block copolymer such that equilibrium textures are modified and dictated by the underlying geometry. For weak curvatures it is shown that the free energy of the block copolymer film follows a Helfrich form, scaling with the square of the mean curvature, with a bending constant dependent on the local pattern orientation. On substrates of varying mean curvature simulations show that topological defects are rapidly expelled from regions with large curvature. These results compare well with available experimental data of poly(styrene)-co-poly(ethylene-alt-propylene) smectic thin films.

Aging of orientation fluctuations in stripe phases

Stripe patterns, observed in a large variety of physical systems, often exhibit a slow nonequilibrium dynamics because ordering is impeded by the presence of topological defects. Using computer simulations based on a well-established model for stripe formation, we show that a slow dynamics and aging occur also in stripe patterns free of topological defects. For a wide range of noise strengths, the two-time orientation correlation function follows a scaling form that is typical for systems exhibiting a growing length scale. In our case, the underlying mechanism is the coarsening of orientation fluctuations, ultimately leading to power-law spatial correlations perpendicular to the stripes. Our results show that even for the smallest amount of noise, stripe phases without topological defects do not reach equilibrium. This constitutes an important aspect of the dynamics of modulated phases.

Self-assembled phases of block copolymer blend thin films

The patterns formed by self-assembled thin films of blended cylindrical and lamellar polystyrene-b-poly(methyl methacrylate) block copolymers can be either a spatially uniform, single type of nanostructure or separate, coexisting regions of cylinders and lamellae, depending on fractional composition and molecular weight ratio of the blend constituents. In blends of block copolymers with different molecular weights, the morphology of the smaller molecular weight component more strongly dictates the resulting pattern. Although molecular scale chain mixing distorts microdomain characteristic length scales from those of the pure components, even coexisting morphologies exhibit the same domain spacing. We quantitatively account for the phase behavior of thin-film blends of cylinders and lamellae using a physical, thermodynamic model balancing the energy of chain distortions with the entropy of mixing.

A generalized method for alignment of block copolymer films: solvent vapor annealing with soft shear

One of the key issues associated with the utilization of block copolymer (BCP) thin films in nanoscience and nanotechnology is control of their alignment and orientation over macroscopic dimensions. We have recently reported a method, solvent vapor annealing with soft shear (SVA-SS), for fabricating unidirectional alignment of cylindrical nanostructures. This method is a simple extension of the common SVA process by adhering a flat, crosslinked poly(dimethylsiloxane) (PDMS) pad to the BCP thin film. The impact of processing parameters, including annealing time, solvent removal rate and the physical properties of the PDMS pad, on the quality of alignment quantified by the Herman's orientational factor (S) is systematically examined for a model system of polystyrene-block-polyisoprene-block-polystyrene (SIS). As annealing time increases, the SIS morphology transitions from isotropic rods to highly aligned cylinders. Decreasing the rate of solvent removal, which impacts the shear rate imposed by the contraction of the PDMS, improves the orientation factor of the cylindrical domains; this suggests the nanostructure alignment is primarily induced by contraction of PDMS during solvent removal. Moreover, the physical properties of the PDMS controlled by the crosslink density impact the orientation factor by tuning its swelling extent during SVA-SS and elastic modulus. Decreasing the PDMS crosslink density increases S; this effect appears to be primarily driven by the changes in the solubility of the SVA-SS solvent in the PDMS. With this understanding of the critical processing parameters, SVA-SS has been successfully applied to align a wide variety of BCPs including polystyrene-block-polybutadiene-block-polystyrene (SBS), polystyrene-block-poly(N,N-dimethyl-n-octadecylammonium p-styrenesulfonate) (PS-b-PSS-DMODA), polystyrene-block-polydimethylsiloxane (PS-b-PDMS) and polystyrene-block-poly(2-vinlypyridine) (PS-b-P2VP). These results suggest that SVA-SS is a generalizable method for the alignment of BCP thin films.

Mixed-morphology and mixed-orientation block copolymer bilayers

Three-dimensional block copolymer structures with long-range order and mixed symmetries.

Kinetics of lamellar formation on sparsely stripped patterns

Chemical epitaxy based on the self-assembly of block copolymers is viewed as a promising technique to achieve ordered patterns on a large scale. Herein, we study the kinetics of lamellar formation of block copolymers under the direction of sparsely stripped patterns using cell dynamics simulations of the time-dependent Ginzburg-Landau theory. First, a scaling law is unveiled with the ordering time of lamellae, tp, with respect to the multiples between the periods of lamellae and stripe patterns, which is consistent with the power law evolution of the correlation length existing in the bulk phase of lamellae. Second, the tolerative windows of perfect order, with deviation from integer multiples, are also estimated from the aspect of kinetics. The results of the ordering time and tolerative windows are of great interest for relevant experiments or applications. Finally, a two-stage evolution is explored during the pattern formation of chemical epitaxy by probing into the evolution of defects, which is of fundamental interest for us to understand the coarsening kinetics of block copolymers under the direction of chemical patterns.