Block Copolymers in Electric Fields: A Comparison of Single-Mode and Self-Consistent Field Approximations

TL;DR

This paper compares two theoretical models for dielectric diblock copolymer melts in electric fields, highlighting their agreement and differences in phase stability and deformation predictions, with implications for practical and computational applications.

Contribution

It introduces a simple analytic expansion approach and compares it with the more accurate self-consistent field theory for copolymer phase behavior under electric fields.

Findings

The phase diagram shows shrinking of the bcc phase with increasing electric field.

The simple model predicts larger elongation of spheres than SCF theory.

Both models agree on general deformation features, validating the simple approach for exploratory studies.

Abstract

We compare two theoretical approaches to dielectric diblock copolymer melts in an external electric field. The first is a relatively simple analytic expansion in the relative copolymer concentration, and includes the full electrostatic contribution consistent with that expansion. It is valid close to the order-disorder transition point, the weak segregation limit. The second employs self-consistent field (SCF) theory and includes the full electrostatic contribution to the free energy at any copolymer segregation. It is more accurate but computationally more intensive. Motivated by recent experiments, we explore a section of the phase diagram in the three-dimensional parameter space of the block architecture, the interaction parameter and the external electric field. The relative stability of the lamellar, hexagonal and distorted body-centered-cubic (bcc) phases is compared within the two models. As function of an increasing electric field, the distorted bcc region in the phase diagram shrinks and disappears above a triple point, at which the lamellar, hexagonal and distorted bcc phases coexist. We examine the deformation of the bcc phase under the influence of the external field. While the elongation of the spheres is larger in the one-mode expansion than that predicted by the full SCF theory, the general features of the schemes are in satisfactory agreement. This indicates the general utility of the simple theory for exploratory calculations.