Phase Diagram of Diblock Copolymer Melt in Dimension d=5

Abstract

Using the self-consistent field theory (SCFT) in spherical unit cells of various dimensionalities, D, a phase diagram of a diblock, A-b-B, is calculated in 5 dimensional space, d = 5. This is an extension of a previous work for d = 4. The phase diagram is parameterized by the chain composition, f, and incompatibility between A and B , quantified by the product \c{hi} N. We predict 5 stable nanophases: layers, cylinders, 3 D spherical cells, 4D spherical cells, and 5D spherical cells. In the strong segregation limit, that is for large \c{hi}N, the order-order transition compositions are determined by the strong segregation theory (SST) in its simplest form. While the predictions of the SST theory are close to the corresponding SCFT extrapolations for d=4, the extrapolations for d=5 significantly differ from them. We find that the S5 nanophase is stable in a narrow strip between the ordered S4 nanophase and the disordered phase. The calculated order-disorder transition lines depend weakly on d, as expected.