Structural Relaxation and Anisotropic Elasticity of Ordered Block Copolymer Melts

TL;DR

This paper uses self-consistent field theory to analyze the long-time elastic relaxation and anisotropic stiffness of ordered block copolymer melts, revealing how domain morphology influences rigidity.

Contribution

It introduces a method to compute the anisotropic elastic response and stiffness tensors of various ordered BCP phases at equilibrium, highlighting differences due to domain segregation.

Findings

Lamellar and columnar phases exhibit anisotropic stiffness modulated by domain spacing.

Cubic BCC and double gyroid phases have characterized full stiffness tensors.

Columnar phases are significantly stiffer and more resistant to bending than lamellae.

Abstract

Block copolymer (BCP) melts play a critical role in the design of thermoplastics, owing in large part to the creation of alternating nano-scale domains of soft and stiff components. Considerable attention has been given to the short-to-intermediate time response of BCP melts, when the storage modulus is expected to dominate the viscoelastic properties. However, less attention has been paid to the long-time relaxation and rigidity of microphase separated BCP melts or the role that domain morphology plays in modulating near-equilibrium response. We take advantage of the ability of self-consistent field theory (SCFT) to calculate equilibrium properties of BCP melts to explore the anisotropic elastic response of ordered ABA and AB copolymer melts as quasistatic deformation processes. This allows us to determine the anisotropic stiffness of the liquid crystal-like lamellar and columnar phases due to modulations in domain spacing, as well as the full stiffness tensor of the cubic BCC sphere and double gyroid phases. We explore elastic modulus landscapes for both single grain materials and random polycrystals over architectural parameters and segregation strengths, using AB diblock and ABA triblock melts as key examples. Comparing AB and ABA melts, we show slight differences in equilibrium rigidity, which are shown to be due to a difference in effective domain segregation. Finally, we consider the equilibrium bending stiffnesses of lamellae and columnar phases, showing that the columnar phase is significantly stiffer than lamellae, with a characteristic bending length scale that is an order of magnitude larger.