Elasticity and yielding of mesophases of block copolymers in water–oil mixtures†
Amphiphilic block copolymers self-assemble at the water/oil interface to form different mesomorphic structures, such as lamellar, micellar cubic, normal hexagonal, and reverse hexagonal structures. Usually, these structures are polycrystalline and the value of their elastic modulus depends on the average orientation of their constituent's single crystals. We provide a model to predict the elastic modulus and yielding of mesophases from their characteristic length and intermicellar interactions. Shear modulus of each structure is calculated as a function of deformation (strain). Zero-shear modulus, G0, depends on the inverse of the intermicellar distance with a power law model. The power law index for each structure is approximately n + 2 where n is the degree of confinement in the mesophase: 1 for lamellar, 2 for both normal and reverse hexagonal, and 3 for micellar cubic structures. Rheological properties of different mesophases of Pluronic P84 in the presence of water and p-xylene are used as a case study. The model is found to be in good agreement with experimental data in the linear viscoelastic region. When compared to experimental data, the yield strain value obtained from the model is one order of magnitude higher than the limit of the linear viscoelastic regime and close to the strain at the cross-over point of storage and loss moduli. Frequency sweep measurements are done to characterize the relaxation and cooperative model behaviors of each mesophase structure.