Fluctuations, conformational asymmetry and block copolymer phase behaviour

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Abstract
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 Iatext-decoration:overline3d space group symmetry. Two non-classical parameters, ε and text-decoration:overlineN, control the occurrence and distribution of these phases, in addition to the classical variables ƒ and χN, where ƒ, 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 ƒ= 1/2. The importance of fluctuation effects are inversely related to the magnitude of text-decoration:overlineN, a type of Ginzburg parameter that is proportional to N. As text-decoration:overlineN decreases, the bicontinuous Iatext-decoration:overline3d 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 Iatext-decoration:overline3d cubic state is stabilized by fluctuations since it disappears when text-decoration:overlineN becomes large. These findings provide new insights into the origins of phase complexity in condensed soft matter.