Abstract
We have investigated the formation of ordered bicontinuous nanostructures in a diblock copolymer composed of a stereoregular block, isotactic polypropylene-block- polystyrene (iPP-b-PS). The ordered bicontinuous double diamond (OBDD) and ordered bicontinuous double gyroid (OBDG) nanostructures in iPP-b-PS were revealed by temperature-dependent small angle x-ray scattering (SAXS) experiments. The OBDG structure developed at the temperature above the melting point of iPP block upon heating from the as-cast state. The OBDG structure transformed into disordered state as further heating to the order-disorder transition (ODT) temperature. The subsequent cooling from the disordered state resulted in the formation of OBDG phase which coexisted with the disordered phase. Further cooling induced the development of the OBDD structure. Eventually, OBDD became the dominant structure, indicating that there was an order-order transition (OOT) from OBDG to OBDD and the OBDD was more stable at the lower temperature. We further discussed the thermodynamic stabilities of OBDG and OBDD by comparing the interfacial free energy and packing frustration of iPP and PS blocks in these two phases. The OBDG constructed by the tripods of iPP prescribed lower packing frustration for the PS block, while the OBDD constructed by the tetrapod iPP domains offered smaller packing frustration for the iPP block chains. In the case of the interfacial free energy, OBDD was found to exhibit a slightly higher specific interface (S/V) than OBDG if the iPP domains exhibit hyperbolic surface. However, as the iPP domains approach cylinder in geometry, (i.e., the domain with constant mean curvature) OBDG displays a slightly higher (S/V). Therefore, we proposed that the stabilities of OBDG and OBDD were governed by the packing frustration of PS and iPP blocks constituting the matrix phase and microdomains, respectively. At high temperature, the release of packing frustration of PS block dominated, such that OBDG was more stable. On the other hand, the relief of iPP packing frustration became increasingly important with decreasing temperature, and when the temperature was sufficiently low, this thermodynamic driving force dominated, such that OBDD became the stable structure. The relief of the packing frustration of iPP block was probably relevant to its strong tendency to form helical segments at lower temperature.