Lamellar Diblock Copolymer Grain Boundary Morphology. 4. Tilt Boundaries

Graphoepitaxy of Symmetric Six-Arm Star-Shaped Poly(methyl methacrylate)-block-Polystyrene Copolymer Thin Film

The authors perform directed self-assembly based on graphoepitaxy of symmetric six-arm star-shaped poly(methyl methacrylate)-block-polystyrene copolymer [(PMMA-b-PS)₆ ] thin film. The affinity between each block and the trench wall is adjusted by using polymer brushes or selective gold (Au) deposition. When the surface of the trench is strongly selective for the PMMA block, (n+0.75)L₀ thick (n is the number of the lamellae, L₀ is lamellar domain spacing) lamellae parallel to the trench wall are formed at each side, while nanotubes are formed away from the trench wall. However, for a trench grafted with PS brushes, nanotubes are formed beside (n+0.25)L₀ thick lamellar layers. By adjusting the trench width (W) and the affinity between the block and the wall, various dual nanopatterns consisting of lines and nanotubes are fabricated. Moreover, when the trench wall is selectively deposited by Au, asymmetric dual nanopattern is formed, where different numbers of lines exist on each side wall, while nanotubes are formed in the middle of the trench. The observed morphologies depending on the commensurability condition between W and L₀ are consistent with predictions by self-consistent field theory.

Fluctuations can induce local nematic order and extensile stress in monolayers of motile cells

Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations. Our work shows that activity can drive either extensile or contractile stresses in tissue, depending on the relative strength of the contractility of the cortical cytoskeleton and tractions by cells on the extracellular matrix.

Bending Behavior and Directed Self-Assembly of Rod-Coil Block Copolymers

The formation of zigzags, chevrons, Y-junctions, and line segments is demonstrated in thin films formed from cylindrical morphology silicon-containing conformationally asymmetric rod-coil diblock copolymers and triblock terpolymers under solvent annealing. Directed self-assembly of the block copolymers within trenches yields well-ordered cylindrical microdomains oriented either parallel or transverse to the sidewalls depending on the chemical functionalization of the sidewalls, and the location and structure of concentric bends in the cylinders is determined by the shape of the trenches. The innate etching contrast, the spontaneous sharp bends and junctions, and the range of demonstrated periodicity and line/space ratios make these conformationally asymmetric rod-coil polymers attractive for nanoscale pattern generation.

Grain-Boundary-Induced Alignment of Block Copolymer Thin Films

We present and discuss the capability of grain boundaries to induce order in block copolymer thin films between horizontally and vertically assembled block copolymer grains. The system we use as a proof of principle is a thermally annealed 23.4 nm full-pitch lamellar Polystyrene-block-polymethylmetacrylate (PS-b-PMMA) di-block copolymer. In this paper, grain-boundary-induced alignment is achieved by the mechanical removal of the neutral brush layer via atomic force microscopy (AFM). The concept is also confirmed by a mask-less e-beam direct writing process. An elongated grain of vertically aligned lamellae is trapped between two grains of horizontally aligned lamellae. This configuration leads to the formation of 90° twist grain boundaries. The features maintain their orientation on a characteristic length scale, which is described by the material's correlation length ξ. As a result of an energy minimization process, the block copolymer domains in the vertically aligned grain orient perpendicularly to the grain boundary. The energy-minimizing feature is the grain boundary itself. The width of the manipulated area (e.g., the horizontally aligned grain) does not represent a critical process parameter.

Directed self-assembly of a two-state block copolymer system

In this work, ladder-shaped block copolymer structures consisting of parallel bars, bends, and T-junctions are formed inside square confinement. We define binary states by the two degenerate alignment orientations, and study properties of the two-state system. We control the binary states by creating openings around the confinement, changing the confinement geometry, or placing lithographic guiding patterns inside the confinement. Self-consistent field theory simulations show templating effect from the wall openings and reproduce the experimental results. We demonstrate scaling of a single binary state into a larger binary state array with individual binary state control.

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.

Synthesis, molecular characterization and self-assembly of (PS-b-PDMS)n type linear (n = 1, 2) and star (n = 3, 4) block copolymers

Well-defined linear (n = 1, 2) and star (n = 3, 4) architecture (PS-b-PDMS)_n block copolymers were synthesized by anionic polymerization in combination with chlorosilane chemistry. The self-assembly is significantly influenced by entropy constraints for the star samples due to overcrowding.

Anhydrous Proton Conducting Polymer Electrolyte Membranes via Polymerization-Induced Microphase Separation

Solid-state polymer electrolyte membranes (PEMs) exhibiting high ionic conductivity coupled with mechanical robustness and high thermal stability are vital for the design of next-generation lithium-ion batteries and high-temperature fuel cells. We present the in situ preparation of nanostructured PEMs incorporating a protic ionic liquid (IL) into one of the domains of a microphase-separated block copolymer created via polymerization-induced microphase separation. This facile, one-pot synthetic strategy transforms a homogeneous liquid precursor consisting of a poly(ethylene oxide) (PEO) macro-chain-transfer agent, styrene and divinylbenzene monomers, and protic IL into a robust and transparent monolith. The resulting PEMs exhibit a bicontinuous morphology comprising PEO/protic IL conducting pathways and highly cross-linked polystyrene (PS) domains. The cross-linked PS mechanical scaffold imparts thermal and mechanical stability to the PEMs, with an elastic modulus approaching 10 MPa at 180 °C, without sacrificing the ionic conductivity of the system. Crucially, the long-range continuity of the PEO/protic IL conducting nanochannels results in an outstanding ionic conductivity of 14 mS/cm at 180 °C. We posit that proton conduction in the protic IL occurs via the vehicular mechanism and the PEMs exhibit an average proton transference number of 0.7. This approach is very promising for the development of high-temperature, robust PEMs with excellent proton conductivities.

Defects in the Self-Assembly of Block Copolymers and Their Relevance for Directed Self-Assembly

Block copolymer self-assembly provides a platform for fabricating dense, ordered nanostructures by encoding information in the chemical architecture of multicomponent macromolecules. Depending on the volume fraction of the components and chain topology, these macromolecules form a variety of spatially periodic microphases in thermodynamic equilibrium. The kinetics of self-assembly, however, often results in initial morphologies with defects, and the subsequent ordering is protracted. Different strategies have been devised to direct the self-assembly of copolymer materials by external fields to align and perfect the self-assembled nanostructures. Understanding and controlling the thermodynamics of defects, their response to external fields, and their dynamics is important because applications in microelectronics either require extremely low defect densities or aim at generating specific defects at predetermined locations to fabricate irregular device-oriented structures for integrated circuits. In this review, we discuss defect morphologies of block copolymers in the bulk and thin films, highlighting (a) analogies to and differences from defects in other crystalline materials, (b) the stability of defects and their dynamics, and (c) the influence of external fields.

Harnessing Anisotropic Nanoposts to Enhance Long-Range Orientation Order of Directed Self-Assembly Nanostructures via Large Cell Simulations

Self-assembly behaviors of cylinder-forming diblock copolymers directed by an array of anisotropic nanoposts with elliptical shape are explored by large cell simulations of self-consistent field theory. The strategy using elliptical nanoposts allows us to generate long-range order cylinders with single orientation by suppressing other selections of cylinder alignment. The anisotropy of nanoposts plays a significant role in improving the tolerance of commensurability conditions between the dimensions of nanopost lattices and the period of cylinders. Moreover, the local defect structures could be regulated through varying the spacing and orientation of elliptical nanoposts. This work may provide useful guidelines for designing the topographical templates and lay the groundwork for fabricating well-ordered nanostructures of block copolymer lithography.

Measuring relative grain-boundary energies in block-copolymer microstructures

The (relative) energies of symmetric tilt grain boundaries in a strongly segregated lamellar block copolymer are determined by analysis of the dihedral angles at grain-boundary triple junctions. The analysis reveals two regimes: at low and intermediate misorientations (corresponding to a tilt-angle range 0≤θ≤85°) the grain-boundary energy is found to depend on the tilt angle as E(θ)∼θ(x), with 2.5>x≥0. At large misorientations the grain-boundary energy is found to be independent (within the experimental uncertainty) of the angle of tilt. The transition between the two scaling regimes is accompanied by the transition of the grain-boundary structure from the chevron to the omega morphology. Grain-boundary energy and frequency are found to be inversely related, thus suggesting boundary energy to be an important parameter during grain coarsening in block-copolymer microstructures, as it is in inorganic polycrystalline microstructures.

One-dimensional metal nanowire assembly via block copolymer soft graphoepitaxy

We accomplished a facile and scalable route to linearly stacked, one-dimensional metal nanowire assembly via soft graphoepitaxy of block copolymers. A one-dimensional nanoscale lamellar stack could be achieved by controlling the block copolymer film thickness self-assembled within the disposable topographic confinement and utilized as a template to generate linear metal nanowire assembly. The mechanism underlying this interesting morhpology evolution was investigated by self-consistent field theory. The optical properties of metal nanowire assembly involved with surface plasmon polariton were investigated by first principle calculations.

Self-assembly of symmetric diblock copolymers in planar slits with and without nanopatterns: insight from dissipative particle dynamics simulations

We present a dissipative particle dynamics simulation study on the formation of nanostructures of symmetric diblock copolymers confined between planar surfaces with and without nanopatterns. The nanopatterned surface is mimicked by alternating portions of the surface that interact differently with the diblock copolymers. The formation of the diblock-copolymer nanostructures confined between the planar surfaces is investigated and characterized by varying the separation width and the strength of the interaction between the surfaces and the diblock copolymers. For surfaces with nanopatterns, we also vary both the mutual area and location of the nanopatterns, where we consider nanopatterns on the opposing surfaces that are vertically (a) aligned, (b) staggered, and (c) partially staggered. In the case of planar slits without nanopatterns, we observe the formation of perpendicular and parallel lamellar phases with different numbers of lamellae. In addition, the symmetric diblock copolymers self-assemble into adsorbed layer and adsorbed layer-parallel lamellar phases and a mixed lamellar phase when the opposing surfaces of the planar slits are modeled by different types of wall beads. In the case of nanopatterned planar slits, we observe novel nanostructures and attempt to rationalize the diblock copolymer self-assembly on the basis of the behavior that we observed in the planar slits without nanopatterns. In particular, we investigate the applicability of predicting the structures formed in the nanopatterned slits by a superposition of the observed structures in slits without nanopatterns.

Random isotropic structures and possible glass transitions in diblock copolymer melts

We study the microstructural glass transition in diblock-copolymer melts using a thermodynamic replica approach. Our approach performs an expansion in terms of the natural smallness parameter--the inverse of the scaled degree of polymerization N--which allows us to systematically study the approach to mean-field behavior as the degree of polymerization increases. We find that in the limit of infinite chain length, both the onset of glassiness and the vitrification transition (Kauzmann temperature) collapse to the mean-field spinodal, suggesting that the spinodal can be regarded as the mean-field signature for glass transitions in this class of microphase-separating system. We also study the order-disorder transition (ODT) within the same theoretical framework; in particular, we include the leading-order fluctuation corrections due to the cubic interaction in the coarse-grained Hamiltonian, which has been ignored in previous studies of the ODT in block copolymers. We find that the cubic term stabilizes both the ordered (body-centered-cubic) phase and the glassy state relative to the disordered phase. In melts of symmetric copolymers the glass transition always occurs after the order-disorder transition (below the ODT temperature), but for asymmetric copolymers, it is possible for the glass transition to precede the ordering transition.