A15, σ, and a Quasicrystal: Access to Complex Particle Packings via Bidisperse Diblock Copolymer Blends

Symmetry breaking in particle-forming diblock polymer/homopolymer blends

Compositionally asymmetric diblock copolymers provide an attractive platform for understanding the emergence of tetragonally close-packed, Frank-Kasper phases in soft matter. Block-polymer phase behavior is governed by a straightforward competition between chain stretching and interfacial tension under the constraint of filling space at uniform density. Experiments have revealed that diblock copolymers with insufficient conformational asymmetry to form Frank-Kasper phases in the neat-melt state undergo an interconversion from body-centered cubic (bcc) close-packed micelles to a succession of Frank-Kasper phases (σ to C14 to C15) upon the addition of minority-block homopolymer in the dry-brush regime, accompanied by the expected transition from bcc to hexagonally packed cylinders in the wet-brush regime. Self-consistent field theory data presented here qualitatively reproduce the salient features of the experimental phase behavior. A particle-by-particle analysis of homopolymer partitioning furnishes a basis for understanding the symmetry breaking from the high-symmetry bcc phase to the lower-symmetry Frank-Kasper phases, wherein the reconfiguration of the system into polyhedra of increasing volume asymmetry delays the onset of macroscopic phase separation.

Stabilizing Phases of Block Copolymers with Gigantic Spheres via Designed Chain Architectures

It is generally believed that the spherical domains self-assembled from AB-type block copolymers are composed of the minority A blocks with a volume fraction of f_A < 1/2. Breaking this generic rule so that the spherical domains are formed by the majority A blocks (f_A > 1/2) requires mechanisms to drastically expand the stable region of spherical packing phases. Self-consistent field theory predicts that dendron-like AB-type block copolymers, composed of G - 1 generations of A blocks connected with the outermost generation of B blocks, exhibit a stable region of spherical packing phases extending to f_A ∼ 0.7. The extremely expanded spherical regions shed light on the mechanisms governing the self-assembly of amphiphilic macromolecules, as well as provide opportunities to engineer complex spherical packing phases.

Emergence of a C15 Laves Phase in Diblock Polymer/Homopolymer Blends

The observation of complex, Frank-Kasper (FK) particle packings in diblock polymer melts has until recently been limited to low molecular weight, conformationally asymmetric polymers. We report temperature-dependent small-angle X-ray scattering (SAXS) studies of blends of a sphere-forming poly(styrene-block-1,4-butadiene) (SB) diblock polymer (M_n = 33.3 kg/mol, Đ = M_w/M_n = 1.08, f_B = 0.18) with two different poly(1,4-butadiene) (B) homopolymer additives. When the B additive M_n is the same as that of the diblock core-forming B segment, these blends remarkably form tetrahedrally close-packed FK σ and Laves C14 and C15 phases with increasing B content. However, binary blends in which the B additive M_n is 60% of that of the diblock B segment form only the canonical body-centered cubic (BCC) particle packing and hexagonally-packed cylinders (HEXc). The observed phase behavior is rationalized in terms of "wet" and "dry" brush blending, whereby higher B M_n drives stronger localization of the homopolymer in the particle cores while preserving the interfacial area per SB diblock chain. The consequent packing constraints in these blends destabilize the BCC packing, and FK phases emerge as optimal minimal surface solutions to filling space at constant density while maximizing local particle sphericity.

Synthesis and Self-Assembly of ABn Miktoarm Star Polymers

The stability of tetrahedrally close-packed (TCP) phases in block copolymer melts is predicted by theory to depend on molecular architecture, yet no experimental studies to date have probed its effect. Motivated by this open question, here we report an efficient synthesis of asymmetric AB_n miktoarm star polymers using functionalized sugars as cores for orthogonal grafting-from block copolymerizations. A combination of ring-opening and atom transfer radical polymerization produced model low dispersity materials comprising a single A = poly(lactide) (L) and multiple B = poly(dodecyl acrylate) (D) arms that amplify "conformational asymmetry" through two concerted effects: the mikto architecture and disparate block statistical segment lengths. Analyzing the self-assembly of LD₂ and LD₃ samples resulted in the discovery of two TCP phases, σ and A15, that remained stable to significantly higher A-block volume fractions as the number of B arms increased. These results experimentally establish the importance of conformational asymmetry and molecular architecture as powerful design tools for the self-assembly of block copolymers into nonclassical phases.