End-Functionalized Ions Promote Stability of Highly Frustrated Phases in Diblock Copolymers

Abstract

Block copolymers self-assemble into ordered nanostructures whose geometry is governed by a competition between interfacial energy and chain conformational entropy. While this competition produces a rich sequence of morphologies, topologically complex ``frustrated'' phases, such as the primitive cubic network and single networks, incur severe packing penalties and are difficult to access in neutral systems. Here we show that ions functionalized at the termini of one block in an AB diblock copolymer melt introduce a qualitatively new stabilization mechanism. Strong ion correlations drive chain-end association and generate a curvature preference toward the charged domain; the resulting tendency of end-localized ion clusters to adopt compact, curved geometries selectively favors the highly frustrated single-primitive-cubic network ($Pm\bar{3}m$) and single-gyroid network ($I$4$_1$32) over the classical phases, in a region of parameter space with a segregation strength lying below the order-disorder transition of the neutral system. Free energy decomposition reveals that the electrostatic energy, arising almost entirely from beyond-mean-field ion correlations, becomes increasingly negative with increasing interfacial curvature. In the primitive cubic network, pronounced local segregation of ions into the cylindrical struts generates compact curved clusters whose correlation energy gain more than offsets the enhanced packing frustration, so the very geometry that is the source of packing frustration in neutral systems becomes the source of its stability here. Increasing ion size weakens correlations and suppresses the network phases, consistent with experimental observations. Our results establish curvature-selective end-group association as a general principle for accessing frustrated topologies in block copolymer systems.