Weak Segregation Theory and Non-Conventional Morphologies in the Ternary ABC Triblock Copolymers

TL;DR

This paper extends weak segregation theory to ternary ABC triblock copolymers, revealing new non-conventional morphologies and phase behaviors, including cubic phases and complex segregation patterns.

Contribution

It generalizes Leibler's weak segregation theory to ternary copolymers, incorporating second shell harmonics and predicting novel morphologies and phase diagrams.

Findings

Symmetric linear copolymers undergo continuous order-disorder transition into cubic phases.

Asymmetric linear copolymers exhibit a weakly segregated double gyroid phase.

Miktoarm copolymers tend toward strong segregation with stable BCC and weakly segregated BCC3 phases.

Abstract

The Leibler weak segregation theory in molten diblock copolymers is generalized with due regard for the 2nd shell harmonics contributions defined in the paper and the phase diagrams are built for the linear and miktoarm ternary ABC triblock copolymers. The symmetric linear copolymers with the middle block non-selective with respect to the side ones are shown to undergo the continuous ODT not only into the lamellar phase but also into various non-conventional cubic phases (depending on the middle block composition it could be the simple cubic, face-centered cubic or non-centrosymmetric phase revealing the symmetry of space group No.214 first predicted to appear in molten block copolymers). For asymmetric linear ABC copolymers a region of compositions is found where the weakly segregated gyroid (double gyroid) phase exists between the planar hexagonal and lamellar or one of the non-conventional cubic phases up to the very critical point. In contrast, the miktoarm ABC block copolymers with one of its arm non-selective with respect to the two others are shown to reveal a pronounced tendency towards strong segregation, which is preceded by increase of stability of the conventional BCC phase and a peculiar weakly segregated BCC phase (BCC3), where the dominant harmonics belong to the 3rd co-ordination sphere of the reciprocal lattice. The validity region of the developed theory is discussed and outlined in the composition triangles both for linear and miktoarm copolymers.