(708d) A Universal Scaling Law for Block Copolymer Feature Sizes

Cyclic block copolymers have been shown to form domains ~20-50% smaller than their linear analogs, making them intriguing alternatives for nanoscale patterning and templating applications. Because of the challenges involved in synthesis of these macromolecules, theory and simulation are critical to understanding their domain spacing behavior. To that end, we have used Dissipative Particle Dynamic (DPD) simulations to identify a universal scaling relationship describing the domain spacing (d) of symmetric linear and cyclic diblock copolymers as a function of χ (the Flory-Huggins interaction parameter between blocks) and N (the overall degree of polymerization). This relationship modifies Strong Segregation Theory (d~N^2/3χ^1/6), developed in the long polymer limit, to include the effects of macromolecular architecture and short chain lengths. We show that the newly proposed scaling relation quantitatively predicts DPD domain spacings of both cyclic and linear diblock copolymers over a wide range of chain lengths, segregation strengths, and compositions. These nanoscale feature sizes are critical to the macroscopic properties, and ultimately applications, of block copolymers.