Smectic block copolymer thin films on corrugated substrates

Sublimation of isolated toric focal conic domains on micro-patterned surfaces

Toric focal conic domains (TFCDs) in smectic liquid crystals exhibit distinct topological characteristics, featuring torus-shaped molecular alignment patterns with rotational symmetry around a central core. TFCDs have attracted much interest due to their unique topological structures and properties, enabling not only fundamental studies but also potential applications in liquid crystal (LC)-based devices. Here, we investigated the precise spatial control of the arrangement of TFCDs using micropatterns and sublimation of TFCDs to estimate the energy states of the torus-like structures. Through simulations, we observed that the arrangement of TFCDs strongly depends on the shape of the topographies of underlying substrates. To accurately estimate the energetic effects of non-zero eccentricity and evaluate their thermodynamic stability, we propose a geometric model. Our findings provide valuable insights into the behavior of smectic LCs, offering opportunities for developing novel LC-based devices with precise control over their topological properties.

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.

Curvature-assisted self-assembly of Brownian squares on cylindrical surfaces

HYPOTHESIS

We hypothesize that curved surfaces, including cylindrical surfaces, which go beyond prior experiments using flat surfaces, can significantly influence and alter the phase behavior and self-assembly of dense two-dimensional systems of Brownian colloids.

EXPERIMENTS

Here, we report a first experimental study regarding the self-assembly of Brownian square platelets with an edge length L = 2.3 μm on cylindrical surfaces having different curvatures; these platelets are subjected to a depletion attraction in order to form a monolayer above the cylindrical surface, yet have nearly hard interactions within the monolayer. Simulations are also performed to confirm and explain the experimental observations.

FINDINGS

Phase diagrams as a function of curvature are determined experimentally. Interestingly, hexagonal rotator crystal structures are observed for tubes having radii > 10.9L, but a tetratic phase is seen instead for the 10.9L tube at the corresponding platelet area fractions. We show that this transition is caused by the curvature-induced orientation-dependence of the depletion attraction between the squares and the underlying cylindrical surface. Brownian dynamics simulation results confirm the experimental observations and also illustrate helical structures formed by squares packing on cylinders. Our results demonstrate a way towards control over the self-assembly of anisotropic particles through curvature and depletion-attraction-induced orientational confinement.

Phase-field model for a weakly compressible soft layered material: morphological transitions on smectic-isotropic interfaces

A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a conserved mass density in order to accommodate non-solenoidal flows near the smectic-isotropic boundary arising from density contrast between the two phases. The model aims to describe morphological transitions in smectic thin films under heat treatment, in which arrays of focal conic defects evolve into conical pyramids and concentric rings through curvature dependent evaporation of smectic layers. The model leads to an extended thermodynamic relation at a curved surface that includes its Gaussian curvature, non-classical stresses at the boundary and flows arising from density gradients. The temporal evolution given by the model conserves the overall mass of the liquid crystal while still allowing for the modulated smectic structure to grow or shrink. A numerical solution of the governing equations reveals that pyramidal domains are sculpted at the center of focal conics upon a temperature increase, which display tangential flows at their surface. Other cases investigated include the possible coalescence of two cylindrical stacks of smectic layers, formation of droplets, and the interactions between focal conic domains through flow.

Substrate curvature governs texture orientation in thin films of smectic block copolymers

Self-assembly of ordered nanometer-scale patterns is interesting in itself, but its practical value depends on the ability to predict and control pattern formation. In this paper we demonstrate theoretically and numerically that engineering of extrinsic as well as intrinsic substrate geometry may provide such a controllable ordering mechanism for block copolymers films. We develop an effective two-dimensional model of thin films of striped-phase diblock copolymers on general curved substrates. The model is obtained as an expansion in the film thickness and thus takes the third dimension into account, which crucially allows us to predict the preferred orientations even in the absence of intrinsic curvature. We determine the minimum-energy textures on several curved surfaces and arrive at a general principle for using substrate curvature as an ordering field, namely that the stripes will tend to align along directions of maximal curvature.

Long-Range Order Self-Assembly of Conjugated Block Copolymers at Inclined Air-Liquid Interfaces

Here, we report that long-range order, direction-controlled, ultrathin conjugated polymer films can be formed by the self-assembly of conjugated block copolymers (i.e., poly(3-hexylthiophene)-block-poly(ethylene glycol)) at inclined air-water interfaces. Structure analyses revealed well-aligned nanowire arrays of poly(3-hexylthiophene) with a dramatically increased ordered domain size compared to the polymer films formed on a flat water surface. The improved degree of order was attributed to the flow field created by the enhanced solvent evaporation at the top of the water contact line. Note that it is challenging to prepare such well-ordered and molecularly thin films of conjugated polymers by conventional fabrication methods. The long-range order polymer film showed hole mobility an order of magnitude higher than polymer films formed on a flat interface when implemented as an active layer of field-effect transistor devices. This study demonstrates that a simple interface modification can significantly impact the self-assembly process, structure, and function of polymer films formed at the air-liquid interface.

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.

Multilayer block copolymer meshes by orthogonal self-assembly

Continued scaling-down of lithographic-pattern feature sizes has brought templated self-assembly of block copolymers (BCPs) into the forefront of nanofabrication research. Technologies now exist that facilitate significant control over otherwise unorganized assembly of BCP microdomains to form both long-range and locally complex monolayer patterns. In contrast, the extension of this control into multilayers or 3D structures of BCP microdomains remains limited, despite the possible technological applications in next-generation devices. Here, we develop and analyse an orthogonal self-assembly method in which multiple layers of distinct-molecular-weight BCPs naturally produce nanomesh structures of cylindrical microdomains without requiring layer-by-layer alignment or high-resolution lithographic templating. The mechanisms for orthogonal self-assembly are investigated with both experiment and simulation, and we determine that the control over height and chemical preference of templates are critical process parameters. The method is employed to produce nanomeshes with the shapes of circles and Y-intersections, and is extended to produce three layers of orthogonally oriented cylinders.