Determining Structure and Thermodynamics of A-b-(B-r-C) Copolymers

The self-assembly of block copolymers (BCPs) is dictated by their segregation strength, χN, and while there are well-developed methods for determining χ in the weak and strong segregation regimes, it is challenging to accurately measure χ of copolymers with intermediate segregation strengths, especially when copolymers have inaccessible order-disorder transition temperatures. χ_eff is often approximated by using strong segregation theory (SST), but utilizing these values to estimate the interface width (w_m) of BCPs in the intermediate segregation regime often results in predictions that deviate significantly from measured values. Therefore, we propose using the extent of mixing, quantified as the normalized interface width w_m/L₀, where L₀ is the block copolymer pitch, as a thermodynamic parameter. We experimentally measure w_m and L₀ for a series of lamellar A-b-(B-r-C) copolymers via resonant soft X-ray reflectivity and extract values of χ_effN based on previous data collected for A-b-B copolymers. The composition profiles measured via reflectivity match the extracted χ_effN values, while those calculated with SST predict much more mixed composition profiles. The extracted χ_eff values agreed quantitatively between copolymers of different molecular weights. We believe that this methodology will be well-suited for block copolymers used in lithographic applications due to their inaccessible order-disorder transition temperatures, intermediate values of χN, and the importance of w_m for line edge roughness metrics.