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.