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

The self-assembly of block copolymers (BCPs) is dictated by their segregation strength, χ N , 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 / L 0 , where L 0 is the block copolymer pitch, as a thermodynamic parameter. We experimentally measure w m and L 0 for a series of lamellar A- b -(B- r -C) copolymers via resonant soft X-ray reflectivity and extract values of χ eff N based on previous data collected for A- b -B copolymers. The composition profiles measured via reflectivity match the extracted χ eff N 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 χ N , and the importance of w m for line edge roughness metrics.