Mechanisms and Epitaxial Relationships between Close-Packed and BCC Lattices in Block Copolymer Solutions

Abstract

The epitaxial relationships between two close-packed lattices (face-centered cubic (fcc) and hexagonally close packed (hcp)) and the body-centered cubic (bcc) lattice of spherical micelles were investigated by small-angle X-ray scattering (SAXS) in two in situ shear cells. Two symmetric poly(styrene-b-isoprene) diblock copolymers with block molecular weights of 8.0 × 103 and 7.0 × 103 g/mol, and 1.5 × 104 and 1.5 × 104 g/mol, respectively, were employed. Thermoreversible fcc → bcc order−order transitions were identified in three styrene-selective solvents, dimethyl phthalate, diethyl phthalate and dibutyl phthalate, and in two isoprene-selective solvents, tetradecane and squalane. Upon shearing an fcc solution, a mixture of highly oriented fcc and hcp crystals was produced, due to the random stacking of the {111} planes along the shear gradient. A bcc phase was grown epitaxially from each hcp/fcc mixture by heating to a temperature within the bcc window without shear. By employing two shear cells, access to scattering along both the gradient axis and the vorticity axis was achieved. This proved crucial to elucidating both the fcc → bcc and hcp → bcc transformations. These mechanisms are related to the Bain distortion and the Burgers mechanism, respectively, which are well-established in simple metals. Interestingly, the close-packed planes in fcc/hcp ({111}fcc and {0002}hcp planes) and bcc ({110} planes) were preserved during these transformations, but bcc unit cells with nine distinct orientations were produced. These reflect particular orientation relationships (ORs) between the parent fcc/hcp and the newly formed bcc crystals, which correspond to the Kurdjumov-Sachs, Burgers, Nishiyama-Wassermann, and Pitsche-Schrader ORs that are prevalent in metals.