Structural and thermodynamic aspects of the cylinder-to-sphere transition in amphiphilic diblock copolymer micelles

The structure of diblock copolymers micelles depends on a delicate balance of thermodynamic forces driving the system towards equilibrium and kinetic factors which limit the systems' exploration of the phase space. The factors governing the morphological transition between cylindrical and spherical micelles are related to a fine balance between entropic forces from chains within the micellar core and corona. In order to understand and control these structures, it is important to gain insight into the fundamental thermodynamic driving forces governing the structure and answer fundamental questions concerning its equilibrium nature. In this work we aim to understand the relationship between thermodynamics and morphological transitions by investigating the detailed structure of a system undergoing a cylinder-to-sphere transition. We focus on the structural properties of micelles constituted of poly(ethylene-alt-propylene)-poly(ethylene oxide) (PEP1-PEO1, the numbers indicate the molar mass in kg/mole) diblock copolymers in dimethylformamide (DMF)/water solvent mixtures. This system is ideal for fundamental studies as it represents a classical well-segregated block copolymer micelle system where the interfacial tension can be controlled in detail without significantly changing other thermodynamic properties. Using small-angle neutron scattering (SANS) it is shown that the system undergoes a cylinder-to-sphere transition upon addition of DMF which lowers the interfacial tension. By applying a detailed thermodynamic model we show that both the dependence of the structural parameters with the interfacial tension as well as the morphological transition can be quantitatively understood. The transition itself is governed by the interfacial tension which dictates the stretching of chains within both corona and core. At high interfacial tensions (in water-rich solutions) discrepancies between structural data and predictions from the thermodynamic model are observed. A qualitative comparison with some preliminary results on the chain exchange kinetics in the system show that these deviations coincide with the region where this equilibration mechanism is not active, i.e. when the kinetics are frozen at high interfacial tensions.