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

Phase behavior of symmetric diblock copolymers under 3D soft confinement

The phase behavior of symmetric diblock copolymers under three-dimensional (3D) soft confinement is investigated using self-consistent field theory. Soft confinement is realized in binary blends composed of AB diblock copolymers and C homopolymers, where the copolymers self-assemble to form a droplet embedded in a homopolymer matrix. The phase behavior of the confined block copolymers is regulated by the degree of confinement and the selectivity of the homopolymers, resulting in a rich variety of novel structures. When the C homopolymers are neutral to the A- and B-blocks, stacked lamellae (SL) are formed where the number of layers increases with the droplet volume, resulting in a morphological transition sequence from Janus particles to square SL. When the C homopolymers are strongly selective for the B-blocks, a series of non-lamellar morphologies, including onion-, hamburger-, cross-, ring-, and cookie-like structures, are observed. A detailed free energy analysis reveals a first-order reversible transformation between SL and onion-like (OL) structures when the selectivity of the homopolymers is changed. Our results provide a comprehensive understanding of how various factors, such as the copolymer concentration, homopolymer chain length, degree of confinement, and homopolymer selectivity, affect the self-assembled structures of diblock copolymers under soft 3D confinement.

Equilibrium phase behavior of gyroid-forming diblock polymer thin films

Thin-film confinement of self-assembling block polymers results in materials with myriad potential applications-including membranes and optical devices-and provides design parameters for altering phase behavior that are not available in the bulk, namely, film thickness and preferential wetting. However, most research has been limited to lamella- and cylinder-forming polymers; three-dimensional phases, such as double gyroid (DG), have been observed in thin films, but their phase behavior under confinement is not yet well understood. We use self-consistent field theory to predict the equilibrium morphology of bulk-gyroid-forming AB diblock polymers under thin-film confinement. Phase diagrams reveal that the (211) orientation of DG, often observed in experiments, is stable between nonpreferential boundaries at thicknesses as small as 1.2 times the bulk DG lattice parameter. The (001) orientation is stable between modestly B-preferential boundaries, where B is the majority block, while a different (211)-oriented termination plane is stabilized by strongly B-preferential boundaries, neither of which has been observed experimentally. We then describe two particularly important phenomena for explaining the phase behavior of DG thin films at low film thicknesses. The first is "constructive interference," which arises when distortions due to the top and bottom boundaries overlap and is significant for certain DG orientations. The second is a symmetry-dependent, in-plane unit-cell distortion that arises because the distorted morphology near the boundary has a different preferred unit-cell size and shape than the bulk. These results provide a thermodynamic portrait of the phase behavior of DG thin films.

Directed Self-Assembly by Sparsely Prepatterned Substrates with Self-Responsive Polymer Brushes

The guiding pattern in the chemoepitaxially directed self-assembly (DSA) of block copolymers is often fabricated by periodically functionalizing homogeneously random copolymer brushes tethered on a substrate. The prepatterned copolymer brushes constitute a soft penetrable surface, and their two components can in principle locally segregate in response to the overlying self-assembly process of block copolymers. To reveal how the self-responsive behavior of the copolymer brushes affects the directing effect, we develop a dissipative particle dynamics model to explicitly include the prepatterned polymer brushes and implement it to simulate the DSA of a cylinder-forming diblock copolymer melt on the sparse pattern of polymer brushes. Through large-scale dynamic simulations, we identify the windows of the content of the random copolymer, the film thickness, and the diameter of the patterned spot, for the formation of perfectly ordered hexagonal patterns composed of perpendicular cylinders. Our dynamic simulations reveal that the random copolymer brushes grafted on the unpatterned area exhibit a remarkable self-responsive ability with respect to the self-assembly of the diblock copolymers overlying them, which may widen the effective window of the content of the random copolymer. Within the processing windows of these key parameters, defect-free patterns are successfully achieved both in simulations and in experiments with sizes as large as a few micrometers for 4-fold density multiplications. This work demonstrates that highly efficient computer simulations based on an effective model can provide helpful guidance for experiments to optimize the critical parameters and even may promote the application of DSA.

Shell with Striped, Helical, and Bipolar Lamellae Structures from Soft Confinement-Induced Self-Assembly of AB Diblock Copolymers on a Nanocylinder

The soft confinement-induced self-assembly of AB diblock copolymers on a nanocylinder is studied via a simulated annealing method. The formation of multiple copolymer shells was predicted by varying the interfacial interaction, the size of confinement, and the height and diameter of the nanocylinder. The competition between solvent repulsion and nanocylinder attraction determined the degree of encapsulation of the copolymer shell. The formation of a helical copolymer shell was induced by the maximization of conformational entropy. The preferential distribution position of copolymers on anisotropic nanocylinder surfaces was induced by interfacial energy minimization. Our study contributes to the understanding of the formation mechanism of the helical structure in block copolymer aggregates and the fabrication of copolymer shells with predesigned morphologies.

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.

Finding the bulk periodicity of lamellar and cylindrical structures using the pressure tensor

It has been known for nearly thirty years that in all molecular simulations of periodic ordered morphologies (such as those formed by block copolymers), when the periodic boundary conditions of the simulation box do not match the bulk periodicity L₀ of the morphology, they change the structure and even the stability of the morphologies obtained in the simulations. Few studies, however, have focused on finding L₀ in simulations. Taking dissipative particle dynamics simulations of asymmetric diblock copolymer melts as an example, we found a simple way of using the pressure tensor, which can be readily calculated in molecular simulations in the continuum, to find L₀ of lamellae and (regular-hexagonally packed) cylinders regardless of their orientation in (cuboid) simulation boxes. Variation of the diagonal and off-diagonal elements of the pressure tensor with the orientation of lamellae and cylinders in the box is explained by coordinate system rotation and confirmed by our simulation results. We also showed that the pressure tensor cannot be used to find L₀ of 3D periodic ordered structures with a cubic symmetry such as the double gyroid.

Periodicity and global order parameter of hexagonally packed cylinders in a periodic box

In all molecular simulations of periodic ordered morphologies (such as those formed by block copolymers), the periodic boundary conditions (PBCs) of the simulation box usually do not match the bulk periodicity L₀ of the morphology, thus changing the structure and even the stability of the morphologies obtained in the simulations. To address this problem for hexagonally packed cylinders, we first proposed a general method of calculating the periodicity of such cylinders in a cuboid simulation box with the PBCs applied in all directions, which further allows one to enumerate all possible orientations and periodicities of such cylinders within an estimated range that can fit into a cuboid box of given lengths. We then showed how to choose the lengths of a cuboid box such that regular-hexagonally packed (RHP) cylinders with given intercylinder distance and orientation can fit into the box. Next, taking as an example the dissipative particle dynamics (DPD) simulations of a cylinder-forming diblock copolymer melt, we showed that L₀ of RHP cylinders oriented along the body diagonal of a cubic box is found when all the off-diagonal elements of the pressure tensor vanish. Finally, based on our general method of calculating the periodicity of hexagonally packed cylinders, we designed a global order parameter for such cylinders, which takes into account their ordering only for the orientations that can fit into the simulation box. Using again the DPD simulations, we showed that our global order parameter can be used to quantify the formation of hexagonally packed cylinders in each collected configuration and to monitor their orientation (thus periodicity) during the simulation run.

A simulation study of the self-assembly of ABC star terpolymers confined between two parallel surfaces

The phase behavior of ABC star terpolymers confined between two identical parallel surfaces is systematically studied using a simulated annealing method. Several phase diagrams are constructed for systems with different bulk phases or with different interfacial interaction strength ratios in the space of surface distance (D) and surface preference for different arms, or in the space of D and the arm-length ratio x. Phases, including tiling patterns [6.6.6], [8.8.4], [8.6.6; 8.6.4], [8.6.6; 8.6.4; 10.6.6; 10.6.4] and hierarchical lamellar structures of lamella + cylinders and lamella + rods, are identified both in the bulk and in the films. Our results suggest that the self-assembled structure of a phase is largely controlled by x, while an increase of the interfacial interaction strength ratio shifts the x-window for each phase to the smaller x side. The orientation of a confined phase depends on the "effective surface preference" which is a combined effect of the interfacial interaction strength ratio, the surface preference, and the entropic preference. In the case of neutral or weak "effective surface preference", phases with a perpendicular orientation are usually observed, while in the case of strong "effective surface preference" phases with a perpendicular orientation or also with outermost wetting-layers can be frequently observed under some circumstances.

Intrinsic Ion Transport Properties of Block Copolymer Electrolytes

Knowledge of intrinsic properties is of central importance for materials design and assessing suitability for specific applications. Self-assembling block copolymer electrolytes (BCEs) are of great interest for applications in solid-state energy storage devices. A fundamental understanding of ion transport properties, however, is hindered by the difficulty in deconvoluting extrinsic factors, such as defects, from intrinsic factors, such as the presence of interfaces between the domains. Here, we quantify the intrinsic ion transport properties of a model BCE system consisting of poly(styrene-block-ethylene oxide) (SEO) and lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt using a generalizable strategy of depositing thin films on interdigitated electrodes and self-assembling fully connected parallel lamellar structures throughout the films. Comparison between conductivity in homopolymer poly(ethylene oxide) (PEO)-LiTFSI electrolytes and the analogous conducting material in SEO over a range of salt concentrations (r, molar ratio of lithium ion to ethylene oxide repeat units) and temperatures reveals that between 20% and 50% of the PEO in SEO is inactive. Using mean-field theory calculations of the domain structure and monomer concentration profiles at domain interfaces-both of which vary substantially with salt concentration-the fraction of inactive PEO in the SEO, as derived from conductivity measurements, can be quantitatively reconciled with the fraction of PEO that is mixed with greater than a few volume percent of polystyrene. Despite the detrimental interfacial effects for ion transport in BCEs, the intrinsic conductivity of the SEO studied here (ca. 10^-3 S/cm at 90 °C, r = 0.085) is an order of magnitude higher than reported values from bulk samples of similar molecular weight SEO (ca. 10^-4 S/cm at 90 °C, r = 0.085). Overall, this work provides motivation and methods for pursuing improved BCE chemical design, interfacial engineering, and processing.

Photoinduced Modulation of Polymeric Interfacial Behavior Controlling Thin-Film Block Copolymer Wetting

The tunable surface-wetting properties of photosensitive random copolymer mats were used to spatially control the orientations of thin-film block copolymer (BCP) structures. A photosensitive mat was produced via thermal treatment on spin-coated random copolymers of poly(styrene-ran-2-nitrobenzyl methacrylate-ran-glycidyl methacrylate), synthesized via reversible-deactivation radical polymerization. The degree of UV-induced deprotection of the nitrobenzyl esters in the mat was precisely controlled through the amount of UV-irradiation energy imparted to the mat. The resulting polarity switching of the constituents collectively altered the interfacial wetting properties of the mat, and the tunability allowed lamellar or cylinder-forming poly(styrene-b-methyl methacrylate) BCP thin films, applied over the mat, to change the domain orientation from perpendicular to parallel at proper UV exposures. UV irradiation passing through a photomask was capable of generating defined regions of BCP domains with targeted orientations.

Surface-induced phase transitions in thin films of dendrimer block copolymers

The phase morphologies and phase transitions of dendrimer block copolymer thin films confined between two homogeneous, planar hard substrates had been investigated by a three-dimensional real space self-consistent field theory (SCFT). From the perspectives of property and strength of the preferential substrate, when the film system confined within neutral substrates, the thinner film was easier to take the undulated and perpendicular cylinder phases. For the attractive preference of the substrate on block segment A, the polymer films tended to take the surface-wetting structures that was composed by block segment A. On the contrary, for the repulsive preference of the substrate on block segment A, a phase transition of cylinder-lamellae could be observed increasing with the relative surface strength of the preferential substrate.

Tunable helical structures formed by ABC triblock copolymers under cylindrical confinement

Block copolymers confined in nanopores provide unique achiral systems for the formation of helical structures. With AB diblock copolymers, stable single and double helical structures are observed. Aiming to obtain more different helical structures, we replace the AB diblock copolymer with linear ABC triblock copolymers. We speculate that a core-shell superstructure is formed within the nanopore, which is composed of a C-core cylinder wrapped by B-helices within the A-shell. Accordingly, the pore surface is set to be most attractive to the majority A-block and a typical set of interaction parameters is chosen as χACN ≪ χABN = χBCN = 80 to generate the frustrated interfaces. Furthermore, the volume fraction of B-block is fixed as fB = 0.1 to form helical cylinders. A number of helical structures with strands ranging from 1 to 5 are predicted by self-consistent field theory, and in general, the number of strands decreases as the volume fraction of C-block fC increases in a given nanopore. More surprisingly, the variation of helical strand in the confined system has an opposite trend to that in the bulk, which mainly results from the constraint of the cylindrical confinement on the change of the curvature between the outer A-layer and the inner B/C-superdomain. Our work demonstrates a facile way to fabricate different helical superstructures.

Hybrid patterns from directed self-assembly of diblock copolymers by chemical patterns

The surface affinity is a critical factor for controlling the formation of monolayer nanostructures in block copolymer thin films. In general, strong surface affinity tends to induce the formation of domains with low spontaneous curvature. Abiding by this principle, we propose a facile chemoepitaxial scheme for producing large-scale ordered hybrid patterns by the directed self-assembly of diblock copolymers. The guiding chemical pattern is designed as periodic stripes with alternately changing surface affinities. As a consequence, two different geometries of domains are formed on the stripes with different affinities. The self-assembly process of block copolymers guided by the stripe patterns is investigated using cell dynamics simulations based on time-dependent Ginzburg-Landau theory, and the kinetic stability diagram is estimated. Hybrid patterns are successfully achieved with both cylinder-forming and sphere-forming diblock copolymers. In the cylinder-forming system, the major hybrid pattern exhibiting a considerable stability window is composed of parallel cylinders and perforated lamellae, while it is composed of monolayer spheres and parallel cylinders in the other system. Encouragingly, the chemoepitaxial method is valid till the period of the guiding pattern is a large multiple of the domain spacing. The chemoepitaxial scheme demonstrated in this work serves as a nice supplement to the graphoepitaxial one proposed in our previous work.

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.

Shear-induced parallel and transverse alignments of cylinders in thin films of diblock copolymers

Coarse-grained Langevin dynamics simulations were performed to investigate the alignment behavior of monolayer films of cylinder-forming diblock copolymers under steady shear, a structure of significant importance for many technical applications such as nanopatterning. The influences of shear conditions, the interactions involved in the films, and the initial morphology of the cylinder-forming phase were examined. Our results showed that above a critical shear rate, the cylinders can align either along the shearing direction or transverse (log-rolling) to the shearing direction depending on the relative strength between the interchain attraction in the cylinders (εAA) and the surface attraction of the confining walls with the film (εBW). To understand the underlying mechanism, the microscopic properties of the films under shear were systematically investigated. It was found that at low εAA/εBW, the majority blocks of the diblock polymer that are adsorbed on the confining walls prefer to move synchronously with the walls, inducing the cylinder-forming blocks to align along the flow direction. When εAA/εBW is above a threshold value, a strong attraction between the cylinder-forming blocks restrains their movement during shear, leading to the log-rolling motions of the cylinders. To predict the threshold εAA/εBW, we developed an approach based on equilibrium thermodynamics data and found good agreement with our shear simulations.

Computational Design of High-χ Block Oligomers for Accessing 1 nm Domains

Molecular dynamics simulations are used to design a series of high-χ block oligomers (HCBOs) that can self-assemble into a variety of mesophases with domain sizes as small as 1 nm. The exploration of these oligomers with various chain lengths, volume fractions, and chain architectures at multiple temperatures reveals the presence of ordered lamellae, perforated lamellae, and hexagonally packed cylinders. The achieved periods are as small as 3.0 and 2.1 nm for lamellae and cylinders, respectively, which correspond to polar domains of approximately 1 nm. Interestingly, the detailed phase behavior of these oligomers is distinct from that of either solvent-free surfactants or block polymers. The simulations reveal that the behavior of these HCBOs is a product of an interplay between both "surfactant factors" (headgroup interactions, chain flexibility, and interfacial curvature) and "block polymer factors" (χ, chain length N, and volume fraction f). This insight promotes the understanding of molecular features pivotal for mesophase formation at the sub-5 nm length scale, which facilitates the design of HCBOs tailored toward particular desired morphologies.

Perpendicular Orientation of Diblock Copolymers Induced by Confinement between Graphene Oxide Sheets

We have studied an orientation structure of self-assembled block copolymers (dPS-b-PMMA) of deuterated polystyrene (dPS) and poly(methyl methacrylate) (PMMA) confined between graphene oxide (GO) surfaces. The results of combination techniques, such as neutron reflectivity, time-of-flight secondary-ion mass spectrometry, grazing-incidence small-angle X-ray scattering, and scanning electron microscopy, show that self-assembled domains of the block copolymers in thin films near the GO sheets are oriented perpendicular to the surface of the GO monolayers, in contrast to the horizontal lamellar structure of the copolymer thin film in the absence of the GO monolayers. This is due to the amphiphilic nature of the GO, which leads to a nonpreferential interaction of both dPS and PMMA blocks. Double-sided confinement with the GO monolayers further extends the ordering behavior of the dPS-b-PMMA thin films. Continuous vertical orientation of the block copolymer thin films is also obtained in the presence of alternating GO layers within thick copolymer films.

Designing an ordered template of cylindrical arrays based on a simple flat plate confinement of block copolymers: a coarse-grained molecular dynamics study

In this paper we study the morphology formed by asymmetric di-block copolymers (di-BCPs) under various confinements using a large-scale coarse-grained molecular dynamics (CGMD) framework. We start with a simple flat plate confinement with the bottom and the top substrate attractive to the minor phase. Studies at a lower confinement length of 17σ have shown that there exists a critical chain length above which a transition from a three-domain morphology to a two-domain morphology is observed. Increasing the confinement length to 42σ, where the chains experience considerably lower confinement effects, also revealed the existence of a critical chain length - a transition from a multi-domain morphology (>3) to a three-domain morphology. The results obtained from the flat plate study with two confinement dimensions were used to design a topography of silica pillars with and without a bottom substrate to form ordered cylindrical BCP arrays. The least and highest radial separation lengths between adjacent pillars are kept at 17σ and 42σ, respectively. A direct correlation was observed in the number of continuous micro-domains of the maximum and minimum confinement dimensions with the 17σ and 42σ flat plate trials. With the optimum chain length employed, the surfaces with affinity to the minor phase can direct the BCP self-assembly to form ordered arrays of minor phase cylinders. The current study thus elucidates a useful tool to predict the morphology formed in an intricate nano-lithographic template by using simple length scale arguments derived from a flat plate confinement study.

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.

Self-Assembled Morphologies of Linear and Miktoarm Star Triblock Copolymer Monolayers

Monolayers of linear and miktoarm star ABC triblock copolymers with equal A and C blocks were investigated using self-consistent field theory. Monolayers of ABC triblock copolymers were formed between two parallel surfaces that were attractive to the A and C blocks. The repulsive interaction parameter χ_ACN between the A and C blocks was chosen to be weaker than the A/B and B/C interactions, quantified by χ_ABN and χ_BCN, respectively, such that the B blocks were confined at the A/C interface, resulting in various B domains with different geometries and arrangements. It was observed that two variables, namely, the strength of the surface fields and the film thickness, were dominant factors controlling the self-assembly of the B blocks into various morphologies. For the linear triblock copolymers, the morphologies of the B domains included disks, stripes (parallel cylinders), and hexagonal networks (inverse disks). For the miktoarm star triblock copolymers, the competition between the tendency to align the junction points along a straight line and the constraint on their arrangement from the surface interactions led to richer ordered morphologies. As a result of the packing of the junction points of the ABC miktoarm star copolymers, a counterintuitive phase sequence from low-curvature phases to high-curvature phases with increasing length of B block was predicted. The study indicates that the self-assembly of monolayers of ABC triblock copolymers provides an interesting platform for engineering novel morphologies.

A surface interaction model for self-assembly of block copolymers under soft confinement

The surface interaction between substrates and block copolymers is one of the most important factors that control the alignment of self-assembled domains under thin film confinement. Most previous studies simply modeled substrates modified by grafting polymers as a hard wall with a specified surface energy, leading to an incomplete understanding of the role of grafted polymers. In this study, we propose a general model of surface interactions where the role of grafted polymers is decomposed into two independent contributions: the surface preference and the surface softness. Based on this model, we perform a numerical analysis of the stability competition between perpendicular and parallel lamellae of symmetric diblock copolymers on substrates modified by homopolymers using self-consistent field theory. The effects of the surface preference and the surface softness on the alignment of lamellar domains are carefully examined. A phase diagram of the alignment in the plane of the surface preference parameter and the surface softness parameter is constructed, which reveals a considerable parameter window for preparing stable perpendicular lamellae even on highly preferential substrates.

Fabrication of ultra-dense sub-10 nm in-plane Si nanowire arrays by using a novel block copolymer method: optical properties

The use of a low-χ, symmetric block copolymer as an alternative to the high-χ systems currently being translated towards industrial silicon chip manufacture has been demonstrated. Here, the methodology for generating on-chip, etch resistant masks and subsequent pattern transfer to the substrate using ultra-small dimension, lamellar, microphase separated polystyrene-b-poly(ethylene oxide) (PS-b-PEO) block copolymer (BCP) is described. Well-controlled films of a perpendicularly oriented lamellar pattern with a domain size of ∼8 nm were achieved through amplification of an effective interaction parameter (χeff) of the BCP system. The self-assembled films were used as 'templates' for the generation of inorganic oxides nanowire arrays through selective metal ion inclusion and subsequent processing. Inclusion is a significant challenge because the lamellar systems have less chemical and mechanical robustness than the cylinder forming materials. The oxide nanowires of uniform diameter (∼8 nm) were isolated and their structure mimics the original BCP nanopatterns. We demonstrate that these lamellar phase iron oxide nanowire arrays could be used as a resist mask to fabricate densely packed, identical ordered, good fidelity silicon nanowire arrays on the substrate. Possible applications of the materials prepared are discussed, in particular, in the area of photonics and photoluminescence where the properties are found to be similar to those of surface-oxidized silicon nanocrystals and porous silicon.

Reduction and control of domain spacing by additive inclusion: morphology and orientation effects of glycols on microphase separated PS-b-PEO

Cylindrical phase polystyrene-b-polyethylene oxide (PS-b-PEO) block copolymer (BCP) was combined with lower molecular weight poly/ethylene glycols at different concentrations and their effect on the microphase separation of BCP thin films were studied. Well-ordered microphase separated, periodic nanostructures were realized using a solvent annealing approach for solution cast thin films. By optimizing solvent exposure time, the nature and concentration of the additives etc. the morphology and orientation of the films can be controlled. The addition of the glycols to PS-b-PEO enables a simple method by which the microdomain spacing of the phase separated BCP can be controlled at dimensions below 50 nm. Most interestingly, the additives results in an expected increase in domain spacing (i.e. pitch size) but in some conditions an unexpected reduction in domain spacing. The pitch size achieved by modification is in the range of 16-31 nm compared to an unmodified BCP system which exhibits a pitch size of 25 nm. The pitch size modification achieved can be explained in terms of chemical structure, solubility parameters, crystallinity and glass transition temperature of the PEO because the additives act as PEO 'stress cracking agents' whereas the PS matrix remains chemically unaffected.

Defect structures and ordering behaviours of diblock copolymers self-assembling on spherical substrates

One of the main differences of ordered structures constrained on curved surfaces is the nature of topological defects. We here explore the defect structures and ordering behaviours of both lamellar and cylindrical phases of block copolymers confined on spherical substrates by the Landau-Brazovskii theory, which is numerically solved by a highly accurate spectral method with a spherical harmonic basis. For the cylindrical phase, isolated disclinations and scars are generated on the spherical substrates. The number of excess dislocations in a scar depends linearly on the sphere radius. The defect fraction characterizing the ordering dynamics decays exponentially. The scars are formed from the isolated disclinations via mini-scars. For the lamellar phase, three types of defect structures (hedgehog, spiral and quasi-baseball) are identified. The disclination annihilation is the primary ordering mechanism of the lamellar phase.

Simulations on a swollen gyroid nanostructure in thin films relevant to systems of ionic block copolymers

Self-assembly of symmetric A/S-B copolymer melt to gyroid nanostructure, partitioning space into interpenetrating nano-labyrinths (channels), in thin films, is investigated using a minimal lattice model with short-range interactions. This model is relevant to poly(styrenesulfonate)-b -polymethylbutylene melt consisting of three types of segments, A, B and S, corresponding to styrene, methylbutylene and styrenesulfonate, respectively. A single sequence of A, B, and S is used in simulations and the fraction of S segments is fixed at p = 0.647 which corresponds to experimental data. The film thickness, L(z), is restricted to nine values (L(z) = 17 , 22, 26, 30, 34, 42, 51, 60, and 68 in units of the underlying lattice constant). The gyroid nanostructure is found to be stable if the film thickness is equal to or greater than the bulk period of the nanophase. The observed gyroid is referred to as swollen since the volume fraction of two continuous networks made of the B segments is anomalous with respect to that of conventional diblock copolymers. In contrast to bulk state, we do not directly observe the order-disorder transition to the gyroid nanophase for thin films. In this case, however, simulations indicate a direct order-disorder transition to a lamellar phase and the order-disorder transition temperature is higher than that in the bulk state, varying strongly with the film thickness.

Exponential time differencing methods with Chebyshev collocation for polymers confined by interacting surfaces

We present a fast and accurate numerical method for the self-consistent field theory calculations of confined polymer systems. It introduces an exponential time differencing method (ETDRK4) based on Chebyshev collocation, which exhibits fourth-order accuracy in temporal domain and spectral accuracy in spatial domain, to solve the modified diffusion equations. Similar to the approach proposed by Hur et al. [Macromolecules 45, 2905 (2012)], non-periodic boundary conditions are adopted to model the confining walls with or without preferential interactions with polymer species, avoiding the use of surface field terms and the mask technique in a conventional approach. The performance of ETDRK4 is examined in comparison with the operator splitting methods with either Fourier collocation or Chebyshev collocation. Numerical experiments show that our exponential time differencing method is more efficient than the operator splitting methods in high accuracy calculations. This method has been applied to diblock copolymers confined by two parallel flat surfaces.

Fabrication of ordered, large scale, horizontally-aligned si nanowire arrays based on an in situ hard mask block copolymer approach

A simple technique is demonstrated to fabricate horizontal, uniform, and hexagonally arranged Sinanowire arrays with controlled orientation and density at spatially well defined locations on a substrate based on an in situ hard-mask pattern-formation approach by microphase-separated block-copolymer thin films. The technique may have significant application in the manufacture of transistor circuitry.

Shape variation of micelles in polymer thin films

The equilibrium properties of block copolymer micelles confined in polymer thin films are investigated using self-consistent field theory. The theory is based on a model system consisting of AB diblock copolymers and A homopolymers. Two different methods, based on the radius of gyration tensor and the spherical harmonics expansion, are used to characterize the micellar shape. The results reveal that the morphology of micelles in thin films depends on the thickness of the thin films and the selectivity of the confining surfaces. For spherical (cylindrical) micelles, the spherical (cylindrical) symmetry is broken by the presence of the one-dimensional confinement, whereas the top-down symmetry is broken by the selectivity of the confining surfaces. Morphological transitions from spherical or cylindrical micelles to cylinders or lamella are predicted when the film thickness approaches the micellar size.