Interfaces and Fluctuations in Diblock Copolymer Melts and Ternary Mixtures with Homopolymers

Abstract

Self-consistent field theory (SCFT) is a powerful tool for study of equilibrium phase behavior of block copolymer melts and mixtures. However, it fails to take into account the effect of fluctuations. This leads to some incorrect predictions for the phase behavior including the nature and location of order-disorder tran- sitions, associated phenomemon and phases. SCFT solutions are also limited by finite amount of computer resources available for numerical calculations. This is especially true of highly swollen self-assembled structures with large characteris- tic length scales. Accurate thermodynamic description of the interfaces in these swollen structures is sufficient to describe the phase behavior in this limit. Here we present our studies of the phase behavior of and interfaces in block copolymer melts and mixtures where we incorporate fluctuation effects and study highly swollen phases. The different approaches we take are, in a large part, guided by the limitations of SCFT.We present the first theoretical study into the role of conformational asym- metry in ternary mixtures of AB diblock copolymers, A homopolymers and B homopolymers which are high molecular counterparts of oil-water-surfactant mixtures. We show that the sign of the spontaneous curvature of an asym- metric diblock copolymer monolayer in these ternary mixtures is controlled by competition between swelling and stretching of copolymer brushes. We explore the phase behavior in highly swollen limit using the analytical Helfrich theory of bending elasticity for diblock copolymer monolayers. Further, we present a generalized version of the Helfrich theory that eliminates arbritrary choices in controlling variables needed to stabilize interfaces and presents a simplified description of these monolayers as a pseudo-one component system. We demon- strate the utility of our generalized theory by presenting an accurate thermody- namic description of a metastable phase in the highly swollen limit. Fluctuation effects are considered in the latter part of this thesis. In neat melts of volumetrically symmetric diblock copolymers, we view the strongly correlated disordered phase, near the order-disorder transition to the ordered lamellar phase, as an ensemble of multiple network topologies. We claim that the entropy associated with this ensemble is a constant per junction of the network. We present a free energy model of the disordered phase as the free energy per junction of a surrogate ordered network phase stabilized by this constant junction entropy. We test this claim and the predictions from this model by comparing to results from molecular simulations. We then extend this model to the ternary mixtures. We incorporate the effect of interfacial fluctuations in these mixtures through their effect on the renormalization of rigidities in the disordered phase and an undulation pressure in the lamellar phase. Using these models we predict phase behavior that is consistent with reported behavior in experiments and simulations.