Stability of Ordered Phases in Diblock Copolymer Melts

The stability of the diblock copolymer ordered phases is investigated by means of a novel theory of anisotropic composition fluctuations. The analogy between a polymer chain in a periodic structure and an electron in a crystalline solid is exploited in the development of the theory. This theory allows the calculation of the spinodal lines, the most unstable modes, and the scattering functions of the ordered phases. The one-phase regions of the lamellar, cylindrical, and spherical phases are found to be within their corresponding stability regions. On the other hand, the hexagonally-perforated lamellar phase is unstable along the lamellar−cylindrical phase boundary. The most unstable fluctuation modes are readily identified and are used to infer the kinetic pathways of the order−order phase transitions. We speculate that the experimentally observed modulated and/or perforated layered states along the lamellar−cylindrical phase boundary are a consequence of the infinitely degenerate fluctuation modes of the lamellar phase. The scattering functions of all ordered phases are calculated. The stability of the double gyroid phase is also investigated.