Linear response and stability of ordered phases of diblock copolymer melts

TL;DR

This paper introduces a more efficient numerical method for calculating the linear susceptibility of ordered phases in diblock copolymer melts, enabling better stability analysis of complex structures like the Gyroid phase.

Contribution

A new pseudo-spectral numerical method improves efficiency in calculating the linear susceptibility, allowing detailed stability analysis of diblock copolymer phases.

Findings

Re-examination of phase stability with higher spatial resolution.

Identification of an epitaxial instability of the Gyroid phase.

Close competition between different instability modes.

Abstract

An efficient pseudo-spectral numerical method is introduced for calculating a self-consistent field (SCF) approximation for the linear susceptibility of ordered phases in block copolymer melts (sometimes referred to as the random phase approximation). Our method is significantly more efficient than that used in the first calculations of this quantity by Shi, Laradji and coworkers, allowing for the study of more strongly segregated structures. We have re-examined the stability of several phases of diblock copolymer melts, and find that some conclusions of Laradji et al. regarding the stability of the Gyroid phase were the result of insufficient spatial resolution. We find that an epitaxial (k=0) instability of the Gyroid phase with respect to the hexagonal phase that was considered previously by Matsen competes extremely closely with an instability that occurs at a nonzero crystal wavevector k.