Using Fluids Density-Functional Theory to Investigate the Structure of Linearly-Tapered Diblock Copolymers

An increasing number of applications require the use of materials with a very precise structure, sometimes down to the nanometer scale. The physical limitations of directly fabricating such materials are obvious; however, self-assembling materials provide a means to fabricate nanostructured materials with the potential for mass production. Diblock copolymers, composed of blocks of two chemically different monomers A and B bonded together in the same chain, are well known to self-assemble into various microscopically ordered structures. In this research, classical fluids density functional theory (fDFT) was used to study the morphology of 50% linearly-tapered diblock copolymers (containing a linear gradient in composition from A to B between the pure A and B blocks). In the applications of interest such as robust and nonflammable battery electrolytes, A would allow for ion diffusion and B would provide mechanical strength. Specifically, we investigated the effect of chain length N and unfavorable A-B interaction strength (quantified by the Flory parameter χ) on the equilibrium density profiles of lamellar (layered) systems, with a special focus on the lamellar spacing, L_z. The polymers studied had chain lengths from N = 24 to 120 beads and A-B repulsive strengths that map to χ = 0.25 to 1.5. We find that when the lamellar spacing is normalized by √N and plotted against the segregation strength χN, the results for all systems collapse onto a single curve. Besides enhancing present knowledge relevant to the design of novel materials, the fDFT results can be used to initialize more detailed and computationally intensive molecular dynamics simulations.