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

TL;DR

This paper demonstrates how substrate curvature can be used to control the orientation of nanostructures in thin films of smectic block copolymers, providing a predictive model for pattern alignment based on surface geometry.

Contribution

It introduces a two-dimensional model incorporating film thickness to predict stripe orientations on curved substrates, advancing control over nanostructure self-assembly.

Findings

Stripes tend to align along directions of maximal curvature.

The model predicts preferred orientations on various curved surfaces.

Substrate curvature can serve as an external ordering field.

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.