A Landau free energy for diblock copolymers with compressibility difference between blocks

Abstract

A new Landau free energy is derived for diblock copolymers of incompatible pairs based on the recently developed compressible random-phase approximation analysis. Finite compressibility of each block is generally allowed. The inhomogeneity of each block density and free volume is analyzed in the weak segregation regime. Free volume inhomogeneity fluctuates in two ways: One represents compressibility difference between blocks and the other stands for the screening of unfavorable cross-contacts. It is shown from the Landau energy that a continuous transition, observed in a symmetric block copolymer either incompressible or with no compressibility difference, disappears provided that one block is more compressible. Microphase transitions and their pressure response of commonly used diblock copolymers are calculated and compared with experimental results. A Flory-type interaction parameter χcRPA, which is suggested from the effective second-order vertex function in the free energy, is shown to be useful, owing to its compressible nature in understanding the phase behavior of various copolymers.