Stability of Complex Phases in Diblock Copolymer Melts

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports computational and theoretical research and education on how polymers, long chain-like molecules, organize themselves into 3D structures more complex than packed spherical balls. AB diblock polymers are formed by chemically bonding together two distinct polymer chains end-to-end. At sufficiently low temperatures, a mixture of polymers A and B will separate into two distinct phases, much the same as the way oil and water separate into two layers when salad dressing sits in the refrigerator. Such macroscopic phase separation is not possible for a melt of diblock polymers; owing to the chemical bond between the two blocks, the furthest the two blocks can separate is the length of the polymer chain. As a result, diblock polymer melts undergo microphase separation into ordered structures with nanometer length scales set by the size of the blocks. The PIs will investigate the microphase separation that occurs for the case where the diblock polymer is compositionally asymmetric, that is when the volume fraction of A is small, and conformationally asymmetric, i.e. where the elasticity of the A block and the B block differ. The compositional asymmetry leads to a system where spheres of A form inside a continuous matrix of B. For decades, it was assumed that the stable ordered state of sphere-forming, microphase separated diblock polymers was a body-centered cubic structure, a type of close-packed structure analogous to that seen in stacks of cannon balls or oranges. Recently, experiments and theory have demonstrated that conformationally asymmetric diblock polymers can also form considerably more complicated packings known as Frank-Kasper and Laves phases. These phases were first seen in metallic alloys, where the atoms have different sizes, and the corresponding phases in diblock polymers involve the packing of spherical particles of different sizes formed by the spontaneous self-assembly of the polymers as they are cooled. This project will determine whether simplified theories based on the geometry of these packings can explain their origin in diblock polymers. Subsequent work will explore the role of the exchange of polymers between different particles, aiming to explain experimental results showing that thermal processing can produce different particle packings. The project aims to develop a connection between the formation of these complex phases in diblock polymers and their emergence in the different context of metallic alloys. Additional broader impacts will emerge from the development of computational tools required to study this problem and their release to the community at large. Graduate students and undergraduate students will receive advance training in polymer physics and, more broadly, materials science through their participation in the research activities of this project. The results will be communicated to the general public through a collated collection of images of complex phases on a dedicated website. These complex phases possess an aesthetic beauty, embodied by the well-known Penrose tiling. The image collection will not only include images of these complex phases generated by the project, but an explanation of their origins in the context of block polymers. TECHNICAL SUMMARY This award supports computational and theoretical research and education aiming to advance understanding of the stability of complex phase formation in sphere-forming diblock polymers. The research in this project consists of two parts. In the first part, the PIs will assess the ability of geometric theories such as sphericity and the diblock foam model to predict the relative stability of Frank-Kasper and Laves phases in diblock polymers. The results of these calculations will be compared to the predictions from field-theoretical models for diblock polymers. In the second part of the project, the PIs will use dissipative particle dynamics simulations to determine the effect of chain exchange on the transitions between different complex phases during thermal processing of block polymer melts. The field-theoretic results will be included as part of the "Broadly Accessible Self-Consistent Field Theory" website, which includes software for performing these calculations and solved examples emerging from research projects using the software. These computational results will be combined with data-processing tools to produce slices through various planes, which will provide the image collection for the public outreach component of the project. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.