Microphase separation in polyelectrolytic diblock copolymer melt : weak segregation limit

TL;DR

This paper develops a generalized theoretical framework for microphase separation in charged-neutral diblock copolymer melts, analyzing stability limits, ordered structure periods, and morphology transitions using RPA and SCFT methods.

Contribution

It introduces explicit analytical free energy expressions and compares RPA and SCFT results, advancing understanding of electrostatic effects on microphase separation in copolymers.

Findings

Higher chemical mismatch needed for separation in charged-neutral systems

Ordered microstructure periods are shorter than in neutral systems

RPA and SCFT results are in perfect agreement for stability limits

Abstract

We present a generalized theory of microphase separation for charged-neutral diblock copolymer melt. Stability limit of the disordered phase for salt-free melt has been calculated using Random Phase Approximation (RPA) and self-consistent field theory (SCFT). Explicit analytical free energy expressions for different classical ordered microstructures (lamellar, cylinder and sphere) are presented. We demonstrate that chemical mismatch required for the onset of microphase separation ($\chi^{\star} N$) in charged-neutral diblock melt is higher and the period of ordered microstructures is lower than those for the corresponding neutral-neutral diblock system. Theoretical predictions on the period of ordered structures in terms of Coulomb electrostatic interaction strength, chain length, block length, and the chemical mismatch between blocks are presented. SCFT has been used to go beyond the stability limit, where electrostatic potential and charge distribution are calculated self-consistently. Stability limits calculated using RPA are in perfect agreement with the corresponding SCFT calculations. Limiting laws for stability limit and the period of ordered structures are presented and comparisons are made with an earlier theory. Also, transition boundaries between different morphologies have been investigated.