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, 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 is often approximated by using strong segregation theory (SST), but utilizing these values to estimate the interface width () 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 /, where is the block copolymer pitch, as a thermodynamic parameter. We experimentally measure and for a series of lamellar A--(B--C) copolymers via resonant soft X-ray reflectivity and extract values of χ based on previous data collected for A--B copolymers. The composition profiles measured via reflectivity match the extracted χ values, while those calculated with SST predict much more mixed composition profiles. The extracted χ 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, and the importance of for line edge roughness metrics.