The nature of phase transitions of symmetric diblock copolymer melts under confinement

The effects of confinement, both the structure frustration and the surface field, on phase transitions of symmetric diblock copolymer melts are investigated within several theoretical methods on the mean-field level. Confinements are applied by restricting polymer chains in the finite spaces of slabs. The surface can be neutral or preferential depending on the strength of the surface field. Within the one-dimensional self-consistent mean-field theory, for the neutral surface case, an oscillative behavior is observed for the size dependence of the order-disorder transition (ODT) point (χN)t due to the structure frustration. The spinodal (χN)s for this corresponding confined system is also calculated using the Gaussian fluctuation theory and the Landau-Brazovskii theory, and (χN)s coincides exactly with (χN)t. On the other hand, the surface effect plays the role to decrease (χN)t due to the surface-induced spatial oscillation for the preferential surface case. In all confined systems considered, the ODT for symmetric diblock copolymer melts is a continuous second-order phase transition in the present mean-field calculation.