Microphase separation in two-length-scale multiblock copolymer melts

The question we address in the thesis concerns the phase behavior of monodisperse multiblock copolymer melts of the general formula A_{fmN}-b-(B_{N/2}-b-A_{N/2})_{n}-b-B_{(1-f)mN}. Upon cooling mesophases of different crystal symmetries are formed. The aim of this thesis is to study the influence of the architectural parameters of the macromolecule on the symmetry of the mesophase. Depending on the temperature different theoretical approaches can be used to investigate the phase behavior. We start from the weak segregation regime near the order-disorder temperature where we apply a Landau free energy expansion and then apply a more elaborate self-consistent field theory at lower temperatures. In accordance whit this strategy, the underlying theoretical backgrounds are given in the corresponding chapters. The rest of the thesis is organized as follows. In chapter 2 we analyze the phase behavior of symmetric A_{mN/2}-b-(B_{N/2}-b-A_{N/2})_{n}-b-B_{mN/2} multiblock copolymer melts using the well known Landau free energy expansion, first applied to diblock copolymers by Leibler. The validity of such an approach rests on the presence of a very weakly segregated periodic structure, something that is guaranteed by the compositional symmetry of the macromolecules under consideration. In the subsequent chapter the influence on the phase behavior of the presence of asymmetric end blocks is addressed by studying multiblock copolymer melts A_{fmN}-b-(B_{N/2}-b-A_{N/2})_{n}-b-B_{(1-f)mN}. We identify the critical points of these systems in the (n, m)-plane as a function of f and study the phase behavior, using the weak segregation approach, relatively close to a critical point. In chapter 4 we go beyond the mean-field approach and discuss the influence of fluctuation corrections on the phase diagrams. Finally, in chapter 5 we go still one step further by applying a numerical self-consistent field approach that allows us to go beyond the weak segregation limit.