Unifying Weak- and Strong-Segregation Block Copolymer Theories

TLDR

Earlier approximation schemes for mean‑field behavior of block copolymers are reviewed and compared to a more accurate calculation. The authors compute a mean‑field phase diagram across weak‑ to strong‑segregation regimes without traditional approximations, mapping stability regions for disordered melts and various ordered structures such as lamellae, cylinders, spheres, and bicontinuous networks. The phase diagram shows that the CPS phase appears only near the order–disorder transition for χN ≥ 17.67, the QIa3̄d phase is unstable above χN ≈ 60, a hexagonally perforated lamellar phase is nearly stable along L/QIa3̄d boundaries, and the bicontinuous Pn3̄m (OBDD) phase is unstable in diblock melts.

Abstract

A mean-field phase diagram for conformationally symmetric diblock melts using the standard Gaussian polymer model is presented. Our calculation, which traverses the weak- to strong-segregation regimes, is free of traditional approximations. Regions of stability are determined for disordered (DIS) melts and for ordered structures including lamellae (L), hexagonally packed cylinders (H), body-centered cubic spheres (QIm3̄m), close-packed spheres (CPS), and the bicontinuous cubic network with Ia3̄d symmetry (QIa3̄d). The CPS phase exists in narrow regions along the order−disorder transition for χN ≥ 17.67. Results suggest that the QIa3̄d phase is not stable above χN ∼ 60. Along the L/QIa3̄d phase boundaries, a hexagonally perforated lamellar (HPL) phase is found to be nearly stable. Our results for the bicontinuous Pn3̄m cubic (QPn3̄m) phase, known as the OBDD, indicate that it is an unstable structure in diblock melts. Earlier approximation schemes used to examine mean-field behavior are reviewed, and comparisons are made with our more accurate calculation.