DENSITY-FUNCTIONAL THEORY OF PHASE-TRANSITIONS IN DIBLOCK COPOLYMER SYSTEMS

We present a general theoretical scheme which allows the characterization of microphase separation of A-B diblock copolymer systems at all degrees of segregation. Our method is based on the density functional theory of Melenkevitz and Muthukumar and uses the technique of density profile parameterization to greatly reduce the technical complexity of the solution. The microphase-separated systems are observed to pass through three stages of ordering as the system is quenched. These are the weak, intermediate, and strong segregation regimes. The phase diagram is calculated for three ordered morphologies: lamellae, hexagonally-packed cylinders, and body-centered-cubic spheres. We also characterize these microphases by the dependence of the lattice constant, D, and the interfacial width, sigma(o), on the quench parameter (chi)N. The theory correctly reproduces the behavior predicted by previous theories describing the weak and strong segregation regimes and establishes the experimental conditions for the validity of these regimes. In the intermediate regime, the effective exponent alpha describing the N dependence of D (D almost-equal-to N(alpha)) is larger than that in the strong segregation regime. Alpha depends strongly on both block length and morphology in the intermediate regime. We attribute this behavior to chain stretching arising from the localization of junctions.