Self-assembling Behaviors of Symmetric Diblock Copolymers in C Homopolymers

The micelle formation of AB symmetric diblock copolymers in C homopolymers (or solvents) is studied by means of the calculations of the self-consistent field theory. Under the condition that C homopolymer has no preferential interaction for any of the two blocks, anisotropic ellipsoidal micelles, which are composed of segmented layers of A/B domains with a normal direction along the major axis of ellipsoid, are observed. The length ratio, the ratio of the major axis of an ellipsoidal micelle to its minor axis, is used to quantify the extent of anisotropy. We systematically study the formation of a single micelle in our calculations, through focusing on the length ratio as functions of the volume of micelles, the A/B interactions as well as the length of homopolymer, instead of considering a huge system consisting of a number of micelles with variable volumes. Our results are presented through three main conclusions. First, with fixed interactions, the length ratio of micelles decreases as increasing the micellar volume. When the micellar volume is raised to some critical extent, one more layer of A or B domains is added into the micelle, which leads to a sudden jump of the major axis, thereby inducing a corresponding increase of the length ratio. Second, for a given micellar stucture with fixed volume, the length ratio of micelle continuously rises up as adding the incompatibility of the two blocks. While the incompatibility rises up to high enough, the length ratio varies more mildly because the energy arising from the packing frustation has overwhelmed the interfacial energy between block copolymers and homopolymers. Third, for a micelle with fixed interaction and volume, the length ratio increases as reducing the length of homopolymer. In a limit case of small molecule solvent, the length ratio goes up to an extremely large value, thereby forming a worm-like micelle. Our results are of great interest for the understanding of the response of the micelles with segmented layers of A/B domains to enviromental conditions, including temperature (imcompatibility), homopolymer (or solvent), and shearing (volume).