Theory for phase transitions in diblock copolymers: the lamellar case

A mean-field type theory is proposed to study order-disorder transitions (ODT's) in block copolymers. The theory applies to both the weak segregation and the strong segregation regimes. An energy functional is proposed without appealing to the random phase approximation (RPA). We find additional terms unaccounted for within the RPA. We work out in detail transitions to the lamellar state and compare the method to other existing theories of the ODT and numerical simulations. We find good agreement with recent experimental results and predict that the intermediate segregation regime may have more than one scaling behavior.