Ordering mechanisms in confined diblock copolymers

TL;DR

This paper investigates various ordering mechanisms in confined diblock copolymers, analyzing surface effects, morphological transitions, and phase diagrams in different regimes using theoretical models and Fourier analysis.

Contribution

It introduces a linear response theory for weak segregation and explores surface pattern decay, lamellar orientation transitions, and phase diagrams under electric fields in diblock copolymers.

Findings

Surface pattern decay analyzed via Fourier modes.

Lamellae tilt and orientation depend on surface periodicity.

Phase diagram includes parallel, perpendicular, and mixed states.

Abstract

We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of confining flat surfaces. The surfaces are chemically patterned where different regions attract different parts of the copolymer chain. The surface pattern or template is decomposed into its Fourier modes, and the decay of these modes is analyzed. The persistence of the surface pattern into the disordered bulk is given for several types of patterns (e.g. uniform and striped surface). It further is shown that complex morphology can be induced in a thin film even though the bulk is disordered. We next consider lamellar diblock copolymers (low temperature regime) in the presence of a striped surface. It is shown that lamellae will appear tilted with respect to the surface, if the surface periodicity is larger than the bulk one. The lamellae close to the surface are strongly distorted from their perfect shape. When the surface and lamellar periodicities are equal lamellae form perpendicular to the surface. Lastly, the transition from parallel to perpendicular lamellae to the surfaces in a thin film is presented. The transition between the two states depends on the surface separation and strength of surface interactions. We further calculate the phase diagram in the presence of perpendicular electric field favoring perpendicular ordering. In the strong segregation limit we introduce a simple model to calculate the phase diagram of the fully parallel, fully perpendicular and mixed (parallel and perpendicular) states.