Fluctuation Effects in Semiflexible Diblock Copolymers

Computational Design of High-χ Block Oligomers for Accessing 1 nm Domains

Molecular dynamics simulations are used to design a series of high-χ block oligomers (HCBOs) that can self-assemble into a variety of mesophases with domain sizes as small as 1 nm. The exploration of these oligomers with various chain lengths, volume fractions, and chain architectures at multiple temperatures reveals the presence of ordered lamellae, perforated lamellae, and hexagonally packed cylinders. The achieved periods are as small as 3.0 and 2.1 nm for lamellae and cylinders, respectively, which correspond to polar domains of approximately 1 nm. Interestingly, the detailed phase behavior of these oligomers is distinct from that of either solvent-free surfactants or block polymers. The simulations reveal that the behavior of these HCBOs is a product of an interplay between both "surfactant factors" (headgroup interactions, chain flexibility, and interfacial curvature) and "block polymer factors" (χ, chain length N, and volume fraction f). This insight promotes the understanding of molecular features pivotal for mesophase formation at the sub-5 nm length scale, which facilitates the design of HCBOs tailored toward particular desired morphologies.

Polymer Semiflexibility Induces Nonuniversal Phase Transitions in Diblock Copolymers

The order-disorder phase transition and the associated phase diagrams of semiflexible diblock copolymers are investigated using the wormlike chain model, incorporating concentration fluctuations. The free energy up to quartic order in concentration fluctuations is developed with chain-rigidity-dependent coefficients, evaluated using our exact results for the wormlike chain model, and a one-loop renormalization treatment is used to account for fluctuation effects. The chain length N and the monomer aspect ratio α directly control the strength of immiscibility (defined by the Flory-Huggins parameter χ) at the order-disorder transition and the resulting microstructures at different chemical compositions f_{A}. When monomers are infinitely thin (i.e., large aspect ratio α), the finite chain length N lowers the χN at the phase transition. However, fluctuation effects become important when chains have a finite radius, and a decrease in the chain length N elevates the χN at the phase transition. Phase diagrams of diblock copolymers over a wide range of N and α are calculated based on our fluctuation theory. We find that both finite N and α enhance the stability of the lamellar phase above the order-disorder transition. Our results demonstrate that polymer semiflexibility plays a dramatic role in the phase behavior, even for large chain lengths (e.g., N≈100).