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

Abstract

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.

Complex-tensor theory of simple smectics

“…Furthermore, if the higher-order ∼ ∇ϕ Á ∇ϕ ð Þ 2 term is neglected then Eqs. ( 23)-( 24) reduces to the Brazovskii free energy, which is commonly employed to model for lamellar diblock copolymers [100][101][102][103][104][105][106][107] .…”

Arrangement and Decomposition of Grain Boundary Dislocations: Two-Mode Phase-Field Crystal Simulation

“…The evolution morphology of multi-scale material microstructure is vividly given (Zhang et al, 2018;Zhao et al, 2019). Combined with EBSD (Nielsen et al, 2020;Zhao et al, 2021) and HRTEM (Zhang et al, 2019;Shuai et al, 2021) technology, the research efficiency is greatly improved. It is worth mentioning that the phase-field crystal method is more suitable for studying the microstructure defects of crystals.…”

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

“…Defect and texture engineering of soft matter [1,2] are promising design approaches for tuning the properties of materials by controlling the presence and spatial distribution of defects. Modulated soft phases, such as block copolymers [3], smectic liquid crystals [4], active and living matter [5], are of particular interest in this context since their broken translational symmetry is associated with lamellar patterns of uniaxial symmetry, which allows for a variety of topological defects.…”