Structure and thermodynamics of mixed polymeric micelles with crystalline cores: tuning properties via co-assembly.

We investigate micelles formed by mixtures of n-alkyl-poly(ethylene oxide) block copolymers, C-n-PEO, with different alkyl block lengths in aqueous solution. This model system has previously been used to shed light on the interplay between exchange kinetics and crystallinity in self-assembling systems [Konig et al., Phys. Rev. Lett., 2019, 122, 078001]. Now we report on the structure and thermodynamics of these micelles by combining results from small-angle X-ray scattering, differential scanning calorimetry and volumetric measurements. We show that mixed micelles are formed despite the fact that length-mismatched n-alkanes of similar weights in bulk tend to demix below the crystallization temperature. Instead, the system exhibits similar properties as single-component micelles but with a modulated melting region. Interestingly, the melting point depression due to self-confinement within the micellar core can be approximately described by a generalized Gibbs-Thomson equation, similar to single-component micelles [Zinn et al. Phys. Rev. Lett., 2014, 113, 238305]. Furthermore, we find a novel scaling law for these micelles where, at least for larger n, the aggregation number scales with the third power of the length of the hydrophobic block, N-agg proportional to n(3). Possibly, there might be a cross-over from the conventional N-agg proportional to n(2) behaviour around n approximate to 19. However, the reason for such a transition as well as the strong n dependence remains a challenge and requires more theoretical work.