Diblock Copolymer Melt in Spherical Unit Cells of Higher Dimensionalities

Using self-consistent field theory in spherical unit cells of various dimensionality, D = 1, 2, 3, and 4, we calculate phase diagram of a diblock, A-b-B, copolymer melt in 4-dimensional space, d = 4. The phase diagram is parameterized by the chain composition, f, and incompatibility between A and B, quantified by the product χ N. We predict 4 stable nanophases: layers, cylinders, 3D spherical cells, and 4D spherical cells. We also calculate order-disorder and order-order transition lines. In the strong segregation limit, that is for large χ N, the order-order transition compositions are determined by the strong segregation theory in its simplest form, for D = 1, 2, 3, and 4