Phase Diagram of Diblock Copolymer Melt in Dimension d = 5

Abstract

Using 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 previuos work for d=4. The phase diagram is parameterized by the chain composition, f , and incompatibility between A and B, quantified by the product χN . We predict 5 stable nanophases: layers, cylinders, 3D spherical cells, 4D spherical cells, and 5D spherical cells. In the strong segregation limit, that is for large χN , 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 S 5 nanophase is stable in a narrow strip between ordered S 4 nanophase and the disordered phase. The calculated order-disorder transition lines depend weakly on d, as expected. *

Diblock Copolymer Melt in Spherical Unit Cells of Higher Dimensionalities

“…The phase boundaries can be calculated as f L/C = (8 + 4 √ 2)/48 ≈ 0.284517, (36) f C/S3 ≈ 0.117192,…”

Monte Carlo simulations and self-consistent field theory applied to calculations of density profiles in A1BA2 triblock copolymer melts

“…Self-consistent field theory was successfully applied to the block copolymer melts [8,14,15]. It enables a relatively fast and accurate calculation of phase diagrams corresponding to diagrams obtained experimentally.…”