Fluctuations, conformational asymmetry and block copolymer phase behaviour

Phase behaviour near the order-disorder transition (ODT) of 58 model hydrocarbon diblock copolymers, representing four different systems, is summarized. Six distinct ordered-state microstructures are reported, including hexagonally modulated lamellae (HML), hexagonally perforated layers (HPL) and a bicontinuous cubic morphology with Ia3d space group symmetry. Two non-classical parameters, ε and N̄, control the occurrence and distribution of these phases, in addition to the classical variables f and χ N, where f, χ and N are the composition, segment-segment interaction parameter and degree of polymerization, respectively. ε accounts for differences in the conformational and volume-filling characteristics of each block. Conformational asymmetry, ε ≠ 1, produces an asymmetric phase diagram around f = 1/2. The importance of fluctuation effects are inversely related to the magnitude of N̄, a type of Ginzburg parameter that is proportional to N. As N decreases, the bicontinuous Ia3d phase appears adjacent to the ODT. Development of this cubic phase can be rationalized based on chain-packing frustration near the lamellar hexagonal state. Apparently the Ia3d cubic state is stabilized by fluctuations since it disappears when N̄ becomes large. These findings provide new insights into the origins of phase complexity in condensed soft matter.