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 Ia ($) over bar 3d space group symmetry. Two non-classical parameters, epsilon and ($) over bar N, control the occurrence and distribution of these phases, in addition to the classical variables f and N-chi, where f, chi and N are the composition, segment-segment interaction parameter and degree of polymerization, respectively. epsilon accounts for differences in the conformational and volume-filling characteristics of each block. Conformational asymmetry, epsilon not equal 1, produces an asymmetric phase diagram around f = 1/2. The importance of fluctuation effects are inversely related to the magnitude of ($) over bar N, a type of Ginzburg parameter that is proportional to N. As ($) over bar N decreases, the bicontinuous Ia ($) over bar 3d phase appears adjacent to the ODT. Development of this cubic phase can be rationalized based on chain-packing frustration near the lamellar hexagonal state. Apparently the Ia ($) over bar 3d cubic state is stabilized by fluctuations since it disappears when ($) over bar N becomes large. These findings provide new insights into the origins of phase complexity in condensed soft matter.