Empirical Scaling Relations for Block Copolymer Surface Micelles

Block copolymers (BCPs) form surface micelles at the air/water interface and change the structures with varying surface pressures. BCP surface micelles have the structure of core and corona similar to the conventional BCP micelles in solutions but their chain conformations are different because a micellization occurs two-dimensionally at the air/water interface. Thus, the structure of BCP surface micelles cannot be described with conventional scaling relations established for BCP micelles in solutions. Despite three decades of research progress since the first observation of BCP surface micelles, even the most fundamental principle of BCP surface micelles, such as scaling relations, is still in a veil. Here, we report empirical scaling relations of BCP surface micelles based on an extensive set of data collected from both scattering-based analysis and microscope-based analysis. We firstly found the intrinsic scaling relations in a surface pressure-free environment and then investigated the extrinsically changed scaling relations depending on the surface pressure, and finally unified the scaling relations regardless of the types of BCPs by introducing the concepts of excluded volume-dependent scaling exponent.