Fusion and clustering of spherical micelles by extruding through a cylindrical channel

Experiments have shown that worm-like cylindrical micelles can be obtained by extruding spherical micelles through a cylindrical channel. The uniaxial symmetry of the cylindrical confinement can help fuse the spherical micelles into the cylindrical phase. Here, a theoretical model is proposed to investigate this fusion transition driven by external pressure in the cylindrical channel. In this model, spherical micelles are formed by diblock copolymers dissolved in a homopolymer solvent. And the external pressure is controlled by the average center distance of the neighboring spherical micelles. In addition to the fusion transition, the addition of the homopolymers leads to a depletion effect induced by the attraction between adjacent spherical micelles. Thus, spherical micelles in the channel can correlate together and form a linear cluster. The free energy barrier of fusion and the free energy potential well of the clustering of spherical micelles are investigated by a numerical computation of the self-consistent mean field theory. We present a full phase diagram of these transitions depending on the radius of the channel and the external pressure.