Correlations in a rigid–flexible diblock copolymer system

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Abstract
We study density–density, nematic–nematic, and density–nematic order‐parameter correlation functions in an incompressible system of rigid–flexible diblock copolymers. Rigid parts are modeled as rods of zero thickness, and flexible parts as chains with freely rotating bonds. The Hamiltonian contains interactions of the isotropic Flory–Huggins and anisotropic Maier–Saupe forms. Correlation functions are calculated in the Gaussian approximation, and are found to oscillate with a characteristic period equal to the length of the rigid part. They also show that lamellar domain boundaries of systems with longer rods are sharper than those with shorter ones, and that the linear density measured along any direction is anticorrelated with the order parameter measuring nematic order in that direction. This latter effect is due to the isotropy of the system, and is relatively independent of the Maier–Saupe and Flory–Huggins parameters. We also study the stability of the system against nematic and lamellar perturbations, and show how the general features of the phase diagram change with the Maier–Saupe parameter.