Sphere-forming block copolymers are known to self-assemble into body-centered cubic crystals near the order-disorder transition temperature. Small-angle x-ray scattering and transmission electron microscopy experiments on diblock and tetrablock copolymer melts have revealed an equilibrium phase characterized by a large tetragonal unit cell containing 30 microphase-separated spheres. This structure, referred to as the sigma (σ) phase by Frank and Kasper more than 50 years ago, nucleates and grows from the body-centered cubic phase similar to its occurrence in metal alloys and is a crystal approximant to dodecagonal quasicrystals. Formation of the σ phase in undiluted linear block copolymers (and certain branched dendrimers) appears to be mediated by macromolecular packing frustration, an entropic contribution to the interparticle interactions that control the sphere-packing geometry.

A series of polylactide-polymenthide-polylactide triblock copolymers containing either amorphous poly(D,L-lactide) or semicrystalline, enantiopure poly(L-lactide) or poly(D-lactide) end segments were synthesized. Small-angle X-ray scattering and differential scanning calorimetry data were consistent with microphase separation of these materials. The Young's moduli and ultimate tensile strengths of the semicrystalline triblock copolymers were 2- and 3-fold greater, respectively, than their amorphous analogs. Symmetric (50:50) and asymmetric (95:5) blends of the triblock copolymers containing two different enantomeric forms of the polylactide segments formed stereocomplex crystallites, as revealed by wide-angle X-ray scattering and differential scanning calorimetry. Compared to the enantiopure analogs, these blends exhibited similar ultimate elongations and tensile strengths, but significantly increased Young's moduli. Collectively, these results demonstrate that the properties of these new biorenewable thermoplastic elastomers can be systematically modulated by changing the stereochemistry of the polylactide end blocks.

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Varying the length of poly(dimethylsiloxane) in poly-(cyclohexylethylene-b-ethylene-b-cyclohexylethylene-b-dimethylsiloxane) (CECD) block terpolymers between 0 and 20% produces the sequence of ordered phases: cylindrical-to-network-to-cylindrical. Small-angle X-ray scattering and transmission electron microscopy demonstrate Pnna space group symmetry and a unique network morphology stabilized by the asymmetric molecular architecture and block interactions. These results establish a new design principle for the generation of triply periodic and multiply continuous nanostructured soft materials.