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Thin-film confinement of self-assembling block polymers results in materials with myriad potential applications—including membranes and optical devices—and provides design parameters for altering phase behavior that are not available in the bulk, namely, film thickness and preferential wetting. However, most research has been limited to lamella- and cylinder-forming polymers; three-dimensional phases, such as double gyroid (DG), have been observed in thin films, but their phase behavior under confinement is not yet well understood. We use self-consistent field theory to predict the equilibrium morphology of bulk-gyroid-forming AB diblock polymers under thin-film confinement. Phase diagrams reveal that the (211) orientation of DG, often observed in experiments, is stable between nonpreferential boundaries at thicknesses as small as 1.2 times the bulk DG lattice parameter. The (001) orientation is stable between modestly B-preferential boundaries, where B is the majority block, while a different (211)-oriented termination plane is stabilized by strongly B-preferential boundaries, neither of which has been observed experimentally. We then describe two particularly important phenomena for explaining the phase behavior of DG thin films at low film thicknesses. The first is “constructive interference,” which arises when distortions due to the top and bottom boundaries overlap and is significant for certain DG orientations. The second is a symmetry-dependent, in-plane unit-cell distortion that arises because the distorted morphology near the boundary has a different preferred unit-cell size and shape than the bulk. These results provide a thermodynamic portrait of the phase behavior of DG thin films. 

The C14 and C15 Laves phases form as micelle packing structures in many types of soft matter, but the related C36 phase, which consists of alternating C14-type and C15-type layers, has not been observed in any such system. To understand this absence in the context of diblock polymers, we used self-consistent field theory to relate the morphology and energetics of C36 to other known mesophases. Two case studies were conducted: blends of AB diblock polymers with A homopolymers (where A forms the micelle core), in which C14 and C15 have stability windows, and neat AB diblock melts, in which Laves phases are metastable. Laves phases exhibit nearly identical micelle morphologies and nearly degenerate free energies, with the free energy of C36 being a near-perfect bisector of the C14 and C15 free energies in all cases, revealing an intrinsic symmetry in free energy that is attributed solely to the structural relationship between the phases in which the packing of C36 is intermediate between C14 and C15. Based on this connection between structure and free energy, C36 is thus not expected to form in flexible diblock polymers, since C14 and C15 can always form instead via facile mass transfer.