Self-assembly of Block Polymers: Self-Consistent Field Theory and Monte-Carlo Simulations

Abstract

Block polymers are a class of soft materials that self-assemble at mesoscopic length scales to form a wide variety of ordered structures. The resulting nanostructures have been instrumental in the development of several advanced technologies such as separation membranes and photonic crystals. This thesis focuses on three diverse problems that use self-consistent field theory (SCFT) and Monte Carlo simulations to study the fundamental phase behavior of block polymers. In recent years, several experimental studies have witnessed the formation of complex low-symmetry structures, commonly referred to as Frank–Kasper phases, contain- ing particles of disparate sizes arranged in multiple coordination environments. The first problem of this thesis focuses on examining the stability of various Frank–Kasper phases in AB diblock copolymers. Using SCFT, we computed the free energies of a host of Frank–Kasper phases and observed that the associated free energies differ only marginally (10−3kBT), leading to a rugged free energy surface with many local minima that may be accessible via different nucleation pathways. We have highlighted the significance of these theoretical predictions in the context of two new Frank–Kasper phases discovered experimentally in poly(isoprene)-b-poly(lactide) diblock copolymers. During the course of this project, we have also made a few advancements in the numerical framework of SCFT. Specifically, we have developed a physically informed and robust approach that uses information from experiments to create guess structures of the ordered phases that are required to perform the SCFT calculations. Additionally, we have developed an improved version of the Anderson-mixing iteration algorithm that increases the computational efficiency by at least 5-10 times compared to the previous version. The second problem focuses on studying the phase behavior of three different multiblock polymers, ABC triblocks, ABCA tetrablocks, and ABAC tetrablocks. In each of the cases, we have performed extensive SCFT calculations and compared the resulting predictions with experimental results to further the understanding of experimentally observed morphologies. While investigating the phase behavior of multiblock polymers, we observed that an accurate temperature-dependence of all the involved Flory–Huggins χ parameters is crucial for making any reliable predictions using SCFT. In this context, we have studied the sensitivity of the phase behavior of a specific ABAC-type multiblock, poly(styrene)-b-poly(isoprene)-b-poly(styrene)-b-poly(ethylene oxide) tetrablock terpolymer, towards the set of required χ parameters (χIS,χSO,χIO). In the third problem, we have studied the order–disorder transition of short lamellae- forming diblock copolymers using Monte Carlo simulations. We have developed a systematic approach to accurately estimate the domain spacing of the lamellar structure, and thereby remove the incommensurability and finite-size effects in lattice simulations. This enabled us to precisely determine the order–disorder transition value for short symmetric diblock copolymers.