Various Low-Symmetry Phases in High-χ and Conformationally Asymmetric PDMS- b-PTFEA Copolymers

Since the discovery of the Frank-Kasper (FK) phase a decade ago, single-component block copolymer systems have offered unique opportunities to explore the structural and phase-transition properties of topologically close-packed FK phases composed of point-particle motifs. Here, we present the formation of complex low-symmetry phases and their thermodynamic stability using high-χ and high-ϵ linear diblock copolymers, where χ and ϵ are the Flory-Huggins interaction parameter and conformational asymmetry between the two blocks, respectively. A series of polydimethylsiloxane-b-poly(2,2,2-trifluoroethyl acrylate) (PDMS-b-PTFEA) copolymers are prepared by tuning the volume fraction (fPTFEA) of a minor PTFEA block. The packing structures of PDMS-b-PTFEAs are mapped in the space of temperature versus fPTFEA using X-ray scattering measurements. In addition to the packing structures reported earlier, we identify another A15 phase at higher fPTFEA close to a hexagonally packed cylinder (HEX) phase and establish the phase sequence of HEX-A15-σ-C14-BCC with decreasing fPTFEA. Theoretical calculation of relative free-energy densities confirms the experimental phase sequence of the composition-dependent sphere-packing structures. Interestingly, the domain sizes of three-dimensional (3D) sphere-packing structures are nearly temperature-invariant compared to that of a two-dimensional HEX structure, and we attribute this dimensional stability to the strong enthalpic effects in the formation of 3D packing structures and the geometrical characteristics of spherical domains. Our results demonstrate that the interaction parameter χ, together with the known role of conformational asymmetry ϵ, serves as the primary thermodynamic parameter for selecting and stabilizing various low-symmetry packing structures in sphere-forming linear diblock copolymer systems.